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Aggregation kinetics and colloidal stability of functionalized nanoparticles
Aggregation kinetics and colloidal stability of functionalized nanoparticles Filippo Gambinossi, Steven E. Mylon, James K. Ferri PII: DOI: Reference:
S0001-8686(14)00242-5 doi: 10.1016/j.cis.2014.07.015 CIS 1469
To appear in:
Advances in Colloid and Interface Science
Received date: Revised date: Accepted date:
28 May 2014 30 July 2014 31 July 2014
Please cite this article as: Gambinossi Filippo, Mylon Steven E., Ferri James K., Aggregation kinetics and colloidal stability of functionalized nanoparticles, Advances in Colloid and Interface Science (2014), doi: 10.1016/j.cis.2014.07.015
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ACCEPTED MANUSCRIPT
Aggregation kinetics and colloidal stability of
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functionalized nanoparticles
Lafayette College, Department of Chemical and Biomolecular Engineering, Easton, Pennsylvania
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Filippo Gambinossia, Steven E. Mylonb, and James K. Ferria*
(USA) 18042. E-mail: [email protected]; [email protected] Lafayette College, Department of Chemistry, Easton, Pennsylvania (USA) 18042. E-mail:
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*To whom correspondence should be addressed: Prof. James K. Ferri James T. Marcus '50 Professor and Department Head Department of Chemical and Biomolecular Engineering Lafayette College Easton, Pennsylvania 18042 tel +1(610) 330-5820 fax +1(610) 330-5059 E-mail: [email protected]
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ACCEPTED MANUSCRIPT ABSTRACT
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The functionalization of nanoparticles has primarily been used as a means to impart stability in nanoparticle suspensions. In most cases even the most advanced nanomaterials lose their function should suspensions aggregate and settle, but with the capping agents designed for specific solution chemistries, functionalized nanomaterials generally remain monodisperse in order to maintain their function. The importance of this cannot be underestimated in light of the growing use of functionalized nanomaterials for wide range of applications. Advanced functionalization schemes seek to exert fine control over suspension stability with small adjustments to a single, controllable variable. This review is specific to functionalized nanoparticles and highlights the synthesis and attachment of novel functionalization schemes whose design is meant to affect controllable aggregation. Some examples of these materials include stimulus responsive polymers for functionalization which rely on a bulk solution physicochemical threshold (temperature or pH) to transition from a stable (monodisperse) to aggregated state. Also discussed herein are the primary methods for measuring the kinetics of particle aggregation and theoretical descriptions of conventional and novel models which have demonstrated the most promise for the appropriate reduction of experimental data. Also highlighted are the additional factors that control nanoparticle stability such as the core composition, surface chemistry and solution condition. For completeness, a case study of gold nanoparticles functionalized using homologous block copolymers is discussed to demonstrate fine control over the aggregation state of this type of material. KEYWORDS:
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Aggregation kinetics, core-shell nanoparticles, colloidal stability, dynamic light scattering, functional polymers, nanoparticle functionalization
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ACCEPTED MANUSCRIPT CONTENTS
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1. Introduction 2. Synthetic approaches to nanoparticle functionalization 2.1. Overview 2.2. Direct vs. step-wise functionalization 2.3. Macromolecular encapsulation 2.3.1 Macromolecular encapsulation: ‘grafting-from’ strategy 2.3.2 Macromolecular encapsulation: ‘grafting-to’ strategy 2.3.3 Macromolecular encapsulation: ‘in-situ’ strategy 3. Aggregation kinetics and colloidal stability: experimental methods 3.1. Overview 3.2. Spectral turbidimetry (and other optical methods) 3.3. Time resolved dynamic light scattering (TR-DLS) 3.4. Fluorescence correlation spectroscopy (FCS) 4. Theoretical models: a brief overview 4.1. Favorable (fast) and unfavorable (slow) aggregation rate 4.2. Theoretical instability ratio 4.3. DLVO interaction potentials: core-shell approach 5. Core-shell composition and solution conditions: implication for colloidal stability 5.1. Effect of nanoparticle core 5.2. Effect of surface chemistry 5.3. Effect of solution condition 6. Case study. Programmable aggregation kinetics of Au@MeO2MAx-co-OEGMAy NPs: effect of surface chemistry, ionic strength and temperature 6.1. Overview 6.2 Aggregation kinetics for Au@(MeO2MAx-co-OEGMAy) NPs 6.3 Colloidal stability ratio and interparticle potential for Au@(MeO2MAx-co-OEGMAy) NPs 6.4 Summary 7. Closure 8. Acknowledgements 9. References
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ACCEPTED MANUSCRIPT 1. INTRODUCTION Functionalized core-shell nanoparticles represent a growing class of materials which have a significant importance in diverse areas of science and technology, including water-oil separation, food
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processing, pharmaceutical formulation, biomedicine, energy storage, as well as for developing complex hierarchical systems [1-3]. The complexation between polymers and nanoparticles offers a good
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platform for engineering versatile hybrid structures with novel functionalities. One of the major
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challenges pertaining to all applications is the design of smart nanomaterials, whose colloidal stability
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can be easily controlled by an external trigger, such as pH, temperature or ionic strength. Depending on the particular application, dispersion stability or the kinetics of destabilization can be either a desired
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(material sensing, food processing) or an unwanted (waste-water treatment, water-oil separation, blood/brain barrier) effect.
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This introduction highlights the impact of surface chemistry on the colloidal stability of core-shell
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nanoparticles for specific applications including emulsion and foam stabilization, drug-delivery, sensing
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and actuation, and other technologies.
Emulsion and foam stabilizers. In general, amphiphilic polymers grafted on particle cores enhance fluid-fluid stability by increasing the interfacial energy and forming a mechanical barrier that prevents the coalescence of the dispersed phase. The potential to stabilize oil-water and air-water dispersions is of particular interest in applications such as oil recovery, cosmetics, pharmaceutical, agrochemicals and food processing [1, 4-8]. Polymer-coated nanoparticles can be used to control the release of encapsulated ingredients from an emulsified product or to manage the capture and release of water from crude oil. Recently, Calcagnile [1] and Nikje [9] presented flexible composite materials based on polyurethane foam functionalized with magnetic iron oxide nanoparticles, which can efficiently separate oil from water. These nanomaterials can recruit floating oil from polluted regions thereby purifying the aqueous phase.
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ACCEPTED MANUSCRIPT Smart delivery systems. Hybrid core-shell nanoparticles can be utilized as nanocarriers for drugs, catalysts, and enzymes, because the polymer scaffold can be used to immobilize smaller particles or macromolecules [10-12]. In this respect, the use of living radical polymerization techniques (either in
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the ‘grafting from’ technique and for the synthesis of functionalized polymers) can be beneficial by helping to design polymer systems that can change dispersion characteristics to facilitate the reversible
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transport and release of drug molecules from aqueous to hydrophobic environments in response to a
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stimulus. Partially hydrophobic nanomaterials are of particular interest as smart delivery systems for
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biological membranes, catalysis, tissue engineering, and agrochemicals [13]. For example Guo et al. [14] grafted iron oxide nanoparticles with pH-responsive Poly(methyl methacrylate), PMMA, shell to
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selectively load anticancer drugs and deliver it to targeted cells. The PMMA in the polymer shell was used to provide the appropriate environment for loading of the drug at neutral pH. At pH<5.5
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protonation of polycarboxylate anions in the PMMA chain was demonstrated to release the drug.
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Sensors and actuators. The possibility to exert active control over dispersion stability through the
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formation of core-shell nanoparticles can also be useful to develop chemical, biological or physical nanosensors [15-17]. Biomedical therapeutics and diagnostic device and combinations thereof, or socalled theranostics benefit from the NP/macromolecules complexation synergies. The need for real time monitoring of physicochemical functions has triggered the rapid expansion of information processing and biomedical fields. An interesting example of biomedical devices is that of Lai et al. [15]. The authors designed microfluidic channels, which can sort magnetic iron oxide nanoparticles coated with micelles containing the thermoresponsive polymer Poly(N-isopropylacrylamide), PNIPAM, depending on their aggregation state. Related to information processing Motornov et al. [16] were able to process logic operations based on the reversible aggregation of Poly(2-vinylpyridine), P2VP, coated silica nanoparticles. Coatings and lubricants. Another example of post-processing using nanoparticles and an important motivation for the fabrication of surface functionalized nanoparticles is the downstream incorporation in a matrix of other materials. Functionalized nanoparticles can be better dispersed in matrixes, this is 5
ACCEPTED MANUSCRIPT important for the realization of extrinsic self-healing materials [18, 19]. Self-healing anticorrosive coatings present an interesting active field for automotive and air transportation industries [20, 21]. 2. Synthetic approaches to nanoparticle functionalization
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2.1 Overview The ability to modify the surface chemisty of a nanoparticle is an important aspect in synthetic
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chemistry for a wide range of applications. This can be achieved by the addition of chemical
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functionality to the NP surface to tailor according to a specific application. The main functional groups
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utilized to anchor functional moieties to nanoparticle surfaces are thiols, disulfides, amines, nitriles, and carboxylic acids attached to small molecules or embedded in larger macromolecules [22-27]. There are
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numerous studies focusing on the functionalization of nanoparticles, and the topic has been already addressed in detail. [28-35]
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This review discusses the main synthetic approaches to the formation of core-shell nanoparticles and
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their colloidal stability against solution conditions, such as ionic strength, temperature, and pH. Benefits
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and drawbacks of the different functionalization protocols will be addressed including a summary of the potential applications.
2.2 Direct vs. step-wise functionalization There are two main strategies to introduce functional groups to the NPs surface. The first method is direct functionalization and consists in the addition of a bifunctional organic compound to a nanoparticle suspension. In this approach, one functional group reacts with the nanoparticle surface while the second group contains the required active functionality. The second method is a step-wise procedure or post-functionalization. This describes a bifunctional compound where a binding-chelating group is reacted first and the group of coupling site is converted in a second step to the final fuctional group. Direct functionalization requires a single conjugation step. However, the active functional group may react with the particle surface [36] and steric hindrance may limit binding strength and surface coverage. Step-wise modification is more versatile, because it can utilize a wide range of commercially available 6
ACCEPTED MANUSCRIPT coupling agents to functionalize almost all the nanoparticle systems. In addition the core-shell structure ensures a strong binding of the functional groups with a high surface coverage. The main problem with this approach is that the functional group must have a high affinity to the surfaces of the particles and
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cannot exist as isolated clusters. Both strategies have been successfully used to functionalize quantum dots, metal and metal oxide
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nanoparticles using small molecules containing silane agents, carboxylates groups [37] or polydentate
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ligands such as dithiols or oligomeric phospines [38]. However, the resulting core-shell nanoparticles
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offer limited processability to control both aggregation kinetics and colloidal stability. 2.3 Macromolecular encapsulation
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Nanoparticle encapsulation can be accomplished using a polymer that possesses both chelating and functional groups. These hybrid composites have encountered growing appreciation in the scale-up
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production of nanomaterials of various compositions and geometries [39-41]. Functional polymer
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nanocomposites combine the unique advantages of high surface area, quantum confinement exhibited
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by inorganic nanomaterials with the processability, functionality, and stability of polymers. [42, 43] Based on the mutual interactions between the organic macromolecules and the particles, a variety of synthetic approaches exist to create functional nanomaterials, which are schematically described in Scheme 1.
Ionic motifs via exchange or acid-base reactions or multidentate architectures using an array of weak physisorbed or hydrogen bond interactions [28, 44], all provide good stability control, especially when the dynamic character of the interface is considered a key contribution to the overall performance. Among these two strategies, the ionic bond is especially intriguing because it allows control of both structure and the dynamics through a simple and versatile materials platform suitable for a wide array of applications. Ionic bonded core-shell nanoparticles exhibit high dispersion stability due to electrostatic repulsion between the particles, both during synthesis and assembly, as well as in the final material. However, research studies mostly focus on covalently linking the polymer and the particle, which ensure strong binding and stability control, thus limiting depletion effects, which is one of the main 7
ACCEPTED MANUSCRIPT issue favoring the aggregation of nanoparticles [45]. Covalently bonded polymer brushes are less vulnerable to desorption, partial damage or environmental impacts, and can be classified into ‘graftingfrom’ strategy [13, 46-50], ‘grafting-to’ strategy [51], and direct or ‘in-situ’ synthesis method [52], as
2.3.1 Macromolecular encapsulation:
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schematically illustrated in Scheme 2. ‘Grafting-from’ strategy. In the ‘grafting-from’ method
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(Scheme 2A) the polymer chains are grown from the particle surface by using surface-initiated
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polymerization techniques, such as atom-transfer radical polymerization (ATRP) [53, 54], reversible
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addition fragmentation chain transfer (RAFT) [55], or ring-opening methatesis polymerization [56]. In all cases, an initiator is immobilized on the surface of previously formed nanoparticles and the polymer
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chains are subsequently grown from the attachment point. In particular ATRP has been reviewed by many authors with respect to polymerization from silica [57] and gold [58] surfaces. This method allows
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to create cross-linked core–shell nanostructures, such as gold nanoparticle (AuNP)/PNIPAM hybrid,
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which can be used as stimuli-responsive optical devices to trap and encapsulate other nanoparticles,
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biomolecules, dyes, or drugs [58].
Benefits. The grafting-from approach leads to polymer brushes with high grafting densities, since the steric hindrance is largely decreased with respect to other cases. Drawbacks. It is generally more difficult to achieve well-controlled polymer molecular weight during surface-initiated polymerization as opposed to when the polymers are synthesized in the bulk in the absence of particles. 2.3.2 Macromolecular encapsulation: ‘Grafting-to’ strategy. This method, schematically represented in Scheme 2B, involves the preparation of end-functionalized polymers and their subsequent covalent binding to the surface of pre-synthesized solid nanoparticles. The functionalization of the polymer brushes is usually achieved by modifying the end groups of the polymer of interest that are able to bind to surfaces such as gold [51], silica [59], or quantum dots [60]. The coating is then ensured by a ‘ligand exchange’ process, where the polymer chains replace the initial stabilizing agent. A more direct method, which does not require an initial stabilizing agent for the inorganic nanoparticles, employes a 8
ACCEPTED MANUSCRIPT combination of RAFT polymerization and coupling reactions to functionalize the particles surface with pre-synthesized polymer chains. In a recent work, Huang et al. [61] grafted silica nanoparticles with azido-functionalized poly(N-isopropylacrylamide) PNIPAM random copolymers in a two-step reaction
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mediated by trimethoxysilane agents to prepare ultrathin thermo-responsive microcapsules via click chemistry.
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Benefits. This method allows complete characterization of the macromolecular modifier prior to NP
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assembly enabling control of size and physico-chemical properties of the core-shell nanoparticles, since
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the synthesis occurs according to standard polymerization mechanisms without confinement effects. Drawbacks. Grafting requires the macromolecules to be functionalized beforehand with reactive
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groups that can bind to the chosen surface. The main limitation is that the achievable polymer surface density is relatively low compared to the other methods due to steric hindrance that prevents further
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polymers to approach the particle surface already coated with a relatively crowded layer. Moreover, the
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end groups of the polymer should have a higher binding affinity to the particle surface than the
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stabilizing ligand, to facilitate the ligand exchange process [62]. 2.3.3 Macromolecular encapsulation: ‘In-situ’ strategy. As shown schematically in Scheme 2C, NP precursors such as tetrachloroauric acid can be directly reduced by reducing agents (sodium borohydride) in the presence of pre-synthesized polymers, and directly form metal nanoparticles [52, 63, 64].
The most widely used polymer for coating inorganic nanoparticles is polyethylene glycol (PEG), because of the high colloidal stability of the resulting nanomaterials. For example Edwards et al. [64] synthesized stimuli-responsive nanoparticles using gold precursor and a disulfide functionalized copolymer made of random copolymers of oligo(ethylene glycol) methyl methacrylate (OEGMA) and 2-(2-methoxyethoxy) ethyl methacrylate (MEO2MA) in a one-step reduction in methanol. The resulting nanoparticles were 2-10nm in core diameter and exhibit long-term stability at room temperature in the presence of aqueous NaCl at concentrations as high as 0.15 M.
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ACCEPTED MANUSCRIPT Benefits. This technique offers high flexibility since the polymer chains can be precisely tailored and their properties can be tuned prior to the coating process. Moreover it is a ‘one-pot’ method that eliminates the customary washing steps necessary in other techniques.
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Drawbacks. The inability to reach particle size above 10 nm and the high polydispersity limit the applicability of this method to functionalize nanoparticles.
Aggregation kinetics and colloidal stability: experimental methods
3.1
Overview
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3.
kinetic process as shown in equation (1): [65]
for 1 i
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i1
dC z 1 k j ,i1C j Ci1 kizCi Cz dt 2 j1 z1
(eq. 1)
for i 1
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dCi k1,zCi Cz dt z1
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The rate of aggregation of monomeric nanoparticles into larger agglomerates can be represented as a
rate constant associated with aggregate formation, Ci and Cj are the concentration of aggregate or
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where Cz is the concentration of aggregates containing z-monomers, kij is the second-order aggregation
monomer where z > i, j, and kiz is the dissociation rate constant of aggregates of size z. For short times, the aggregation kinetics can be approximated by the rate of doublet formation, which dominated over other higher order aggregate formation: dC1 k11C12 k12C1C2 dt dC 2 1 k11C12 k12C1C2 dt 2
(eq. 2)
Here C1 and C2 are respectively the number concentrations of monomer and doublet particles and k11
and k12 are the forward and reverse rate constants. In case of irreversible association (i.e. no dissociation events), the increase in concentration of dimers is proportional to the product of the initial rate constant of aggregation, k11, and the square of the initial concentration of nanoparticle monomer, C0, simplifying equation (2):
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(eq. 3)
From equation (3) the instability ratio, W-1, under different solution conditions can be calculated by
the ratio of the rate constant for slow coagulation (unfavorable aggregation), (k11)slow to fast
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slow
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fast
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k k
(eq. 4)
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W 1
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(nonrepulsive) aggregation, (k11)fast:
The resulting values for the instability ratio (0≤W-1≤1) represents the probability of association resulting from the collision of two colloidal particles.
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The rate of aggregation, k11, of functionalized nanoparticles can be monitored using several experimental approaches. The most widely employed are optical methods such as turbidimetry, light
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scattering (DLS, SLS), and fluorescence correlation spectroscopy (FCS). Each technique has its own
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advantages and disadvantages – no single technique is appropriate for all samples, especially under the
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conditions of low concentration, high polydispersity, or sample complexity. Principles of operation as well as the benefits and drawbacks of the above mentioned techniques are discussed in the following sections. 3.2
Spectral turbidimetry
For diluted solutions (volume fraction < 10-4) spectral turbidimetry can be used to determine the particle size distribution (PSD) of suspensions composed of submicronic and micronic particles. [66] Turbidity has been used in the past to study the aggregation state of metal nanoparticles [67-69], and nanoemulsions [70]. In general the turbidity of a colloidal suspension can be defined as: [71, 72]
Cz t z z1
(eq. 5)
where Cz is the number of aggregates of z particles per unit volume, and z is their total light scattering
cross section, which is dependent on the wavelength and on the ratio of the particle refractive index to
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(eq. 6)
(5) and (6), the aggregation rate can be deduced:
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Here 1 and 2 are the optical cross sections of a single particle and a doublet. Combining equation (2),
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d 1 2 1k11C 20 dt t0 2
(eq. 7)
and fast aggregation regimes:
W 1
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Then the instability ratio, W-1, can be obtained from the initial slope of the curve vs. time under slow
d dt d dt
slow
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fast
(eq. 8)
than measurement of the intensity of light scattered at a particular angle. [73]
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Benefits. Turbidity measurements using the spectrophotometer are less sensitive to multiple scattering
Drawbacks. In order to interpret the experimental results, turbidity measurements require calculation of the optical properties (cross-section) of the aggregates involved in the process. Not suitable for very diluted suspensions. Both the aggregation process and aggregate-like interaction are dependent on the aggregates’ morphology. 3.3
Time resolved dynamic light scattering (TR-DLS)
Time resolved dynamic light scattering (TR-DLS) is the most common method to determine the aggregation kinetics of colloidal particles. [65] It has been used to study the aggregation behavior of a wide range of engineered nanomaterials including quantum dots [74], metal nanoparticles [75-79], carbon nanotubes [80, 81], and solid lipid nanoparticles [82]. In this technique, the temporal evolution of the intensity fluctuations due to the Brownian motion of colloidal particles is used to measure the translational diffusion coefficient of the particles in suspensions. The effective aggregate size is calculated from the diffusion coefficient, D, using the Stokes-Einstein equation.[83] The measured 12
ACCEPTED MANUSCRIPT hydrodynamic radius of a coagulation suspension is an average of the hydrodynamic radii of the individual aggregates, weighted by their scattered light intensities. According to the Rayleigh-GansDebey (RGD) approximation, which is valid for particles that are relatively small compared to the
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wavelength of the laser light,[65] the temporal evolution of the average hydrodynamic radius, (dRH/dt), of the system is given by:
1 R R
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H,2 H,1
(eq. 9)
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I q 1 dRH 2 k11C02 1 2I1 q RH,0 dt
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where I1(q) and I2(q) are the water vector q-dependent intensities of radiation scattered by monomers and dimers, respectively, RH,1 = f(RH,0) and RH,2 = 1.4f(RH,0) are the hydrodynamic radii of monomer and
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dimer, respectively, and RH,0 is the intitial monomeric nanoparticle radius. If dissociation events occur during the time of observation, however, k11 in equation (9) is replaced by
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16k113C02
R
2k21 4k11C0 k21 I 2 q I1 q
H,1
RH ,2
2
(eq. 10)
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K eff
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the effective association constant, Keff: [84]
which is usually lower than the rate for an irreversible aggregation. By taking k12=0 limit of no
dissociation equation (10) correctly recovers the well-known result for the irreversible aggregation kinetics, i.e. Keff=k11.
From equation (9) the instability ratio, W-1, at different solution conditions is then calculated by dividing the slope obtained under slow coagulation over the slope obtained under fast (nonrepulsive) aggregation:
W 1
dR dR
H H
dt
dt
slow
(eq. 11)
fast
Benefits. The determination of k11 by TR-DLS has been validated numerous times in the literature [65,
78, 80, 85-90]. Using conventional instrumentation, for moderate sized particles (RH > 30nm), this method is suitable for dilute suspensions; i.e. substantially less than that required for turbidity
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ACCEPTED MANUSCRIPT measurements. When the most sensitive detectors are employed, this method can be applied to extremely dilute suspensions of even smaller particles. Drawbacks. DLS measurements are greatly biased by the presence of large aggregates or polydisperse
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solutions that can only be partially corrected by the algorithms of the DLS software. Both the aggregation process and aggregate-like interaction are dependent on aggregate morphology. At high
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electrolyte concentrations (high rate – fast regime) multiple scattering may occur which leads to a
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diffuse halo around the primary laser beam inside the cell and a reduced intercept of the autocorrelation
3.4
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function. Fluorescence correlation spectroscopy (FCS)
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In this approach, the particle/aggregate diffusion coefficient, D, is determined for fluorescently labeled particles passing through a laser-illuminated confocal volume (~1m3). Similar to DLS
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technique, temporal fluctuations in the measured fluorescence intensity are used to derive an
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autocorrelation curve, which is related to the translational diffusion of the fluorophore through the
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confocal volume. [91, 92] FCS has been used to determine the diffusion coefficients and aggregation behavior of QDs, nTiO2, and nZnO. [93-96] Benefits. This is a single or near single particle detection technique that determines a weight-averaged D under the conditions of the experiment. This gives FCS an important advantage over several other techniques for determining particle size, because it is generally not necessary to increase particle concentration in order to improve the analytical signal.[97] Bias is much less important than in DLS and the technique is much better suited to small particles and very diluted suspensions. Drawbacks. Diffusion coefficients are determined by calibrating the size and shape of the confocal volume with a standard dye. Additionally, nanoparticles need to be fluorescently labeled. The single particle detection of colloidal particles is limited by their photophysical properties, such as fluorescence intermittency and blinking. Blinking is manifested as finite episodes of laser induced fluorescence followed abruptly by long periods where no light is emitted. The effect appears not only to slow diffusion but to increase the probability of the particle entering the probe volume. [98, 99] 14
ACCEPTED MANUSCRIPT 4. Theoretical models: a brief overview 4.1 Favorable (fast) and unfavorable (slow) aggregation rate Fast aggregation rate. Under the approximation of von Smoluchowski [100], i.e. steady-state
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diffusion of the colloidal particles in the absence of interparticle interaction, the rate constant for the dimer formation in the fast or ‘diffusion-limited’ aggregation is given by:
fast
8kBT 3
(eq. 12)
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11
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k
where kB is the Boltzman constant, T the absolute temperature, and is the viscosity of the medium. Reversible aggregration has been proposed by Zaccone [84] and others [87, 101-105] to account for
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experimental observations of fast aggregation rates, lower than Smoluchowski. Slow aggregation rate. Fuchs [106] provided a general expression for the slow or reaction-limited
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aggregation, considering (k11)slow as the flux of colloids in a force field around a central particle under
8kBT 3 f h
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kslow 2RH
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the influence of their mutual interactions:
h 2RH
T h
2
e
k BT
dh
h 2 h 6 13 2 RH RH f h h 2 h 6 4 RH RH
(eq. 13)
(eq. 14)
Here the interaction potential, (h), and the hydrodynamic retardation term [107], f(h), account for
the surface and viscous forces manifested between two spheres during mutual approach. Both terms are functions of the intersphere separation distance, h, and the particle size, RH.
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ACCEPTED MANUSCRIPT 4.2 Theoretical instability ratio In using equation (13) for the instability ratio, however, the theoretical curve for W-1 as a function of
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the interaction energy is always lower than unity at low potentials, since the rapid rate of coagulation assumes that no attraction forces are in operation until the particles are in contact.
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To account for the attractive contribution to the interaction potential in rapid coagulation, and to
expression for the distance-dependent instability ratio: k BT
e
h 2R f h e h 2R 2
0
dh
H
T h
k BT
2
0
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W 1
A h
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f h
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enable comparison between theory and experiments, McGown and Parfitt [108] derived the following
dh
D
H
(eq. 15)
particles. So defined, the instability ratio approaches to unity when the repulsion is entirely absent and is
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where (h) is the attraction potential energy, which depends on the geometry of the colloidal
expected to be more in accord with experimental reality. Details on the calculation of the contributions to the total interaction potential are shown in Section 4.3. Approximations for the calculation of the theoretical stability ratio. The theoretical instability ratio defined in equation (15) can be rewritten in the form:
1
W 1 2 0 e
T s
k BT
(eq. 16)
ds
s 2
2
where s is the non-dimensional surface-to-surface distance defined by s=[(h/RH)-2], and (s) is the total
interparticle interaction energy. This relationship can be used to understand the behavior of the stability ratio with respect to the barrier against coagulation and to evaluate the physico-chemical properties of the dispersion. Because of the complexity of the interparticle interaction energy, the above task requires
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ACCEPTED MANUSCRIPT numerical integration of equation (16). However, when the repulsion barrier is large, the expression for W-1 using asymptotic techniques can be expressed: 1 2k T 2 " B s T m
1
(eq. 17)
T s m
k BT e 2 s m 2 2
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W 1
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Here sm is the value of s corresponding to the maximum in and T" sm T s 2 evaluated at s=sm. Other models: Maxwell-Boltzmann approach.
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Recently, an approach based on the Maxwell-
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Boltzmann distribution coupled with DLVO theory has been developed to calculate the instability ratio of colloidal nanomaterials, including metal nanoparticles, polystyrene, carbon nanotubes, and graphite
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sheets.[109-111] Here we briefly summarize the main features of the model highlighting the main advantages with respect to the other approaches.
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This model considers the role of the binding energy, Eb=Emax-Emin, in aggregation kinetics and estimates the instability ratio W-1 as the ratio of the number of particles with kinetic energy exceeding
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Eb, N, to the total number of particles with kinetic energy ranging from zero to infinity, N: 3
W
1
NE b N0
v
m 2 mv 2 4 e 2kbT
2k b T
v dv
Eb
3
m 2 mv 2 4 0 2k T e b
v 2dv
2k b T
2
0
e E E1 2dE E
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e E dE
(eq. 18)
Here, m is the molecular mass, kb is the Boltzmann constant, T is the absolute temperature, v is the
velocity of random motion, and E is the random kinetic energy of nanoparticles. Since the denominator is constant, equation 19 symplifies to:
W 1
N E e E E1 2dE b N
(eq. 19)
where accounts for the drag effect on the kinetic energy distribution of nanoparticles and other
discrepancies of the DLVO prediction. To apply the Maxwell-Boltzmann distribution, the dispersed NPs are assumed to be Brownian particles with an average kinetic energy of 3kbT/2 in dilute systems.
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ACCEPTED MANUSCRIPT With respect to equation (15) the modified instability ratio calculated with this model better accounts for the nanoscale transport of nanoparticles, which is governed by both interaction energy and random Brownian diffusion.
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4.3 DLVO interaction potentials: core-shell systems The total potential energy of interaction, (h), is according to classic Derjaguin-Landau-Verwey-
Here we also include other contributions to the interaction
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electrostatic (electrostatic) interactions.
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Overbeek (DLVO) theory [112, 113] is the sum of the attractive Van der Waals (vdW) and repulsive
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potential, such as hydration (hydration) and osmotic (osmotic) forces:
h vdW h electrostatic h hydration h osmotic h
(eq. 20)
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A schematic of the DLVO interactions between two core-shell nanoparticles is shown in Scheme 3. Van der Waals potential. According to Vold and Vincent [114, 115] the van der Waals attraction
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potential for two identical nanoparticles of radius rcore coated with a homogenous polymer shell of thickness can be calculated as the sum of the contributions from the shell – shell interaction, shell –
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core interaction, and core – core interaction:
vdW h shellshell h corecore h coreshell h 2 2 h h 2 AW AS H ;1 AS AC H ;1 2r 2 2r 1 core core 12 h rcore h rcore AW AS AS AC H ; H ; 2r core rcore 2rcore 2 2rcore 2
(eq. 21)
where Ac, Aw, and As are the Hamaker constant for the particle core, water, and the particle shell and
H(x, y) is the unretarded geometrical function:
H x, y
x 2 xy x x y 2 2ln x 2 xy x x 2 xy x y x xy x y
(eq. 22)
In the case that the separation distance, h, is small compared to the particle radius, rcore, i.e. x<<1, the
unretarded geometrical function can be simplified to:
18
ACCEPTED MANUSCRIPT
lim H x , y x 0
y
(eq. 23)
x 1 y
vdW
2 2 r rcore AS AC AW AS core h h 2 1 h rcore rcore 12 AS AC 4 AW AS h 2r core
(eq. 24)
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and equation (22) becomes:
of the surrounding solution, the interparticle attraction potential also varies. The swelling/deswelling
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When the polymer shell on the surface of a particle swells or deswells as a function of ionic strength
capacity of the surface layer or swelling ratio, , is defined as the ratio of the volumes of the unswollen
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(V0) and isotropical swollen (V) shell around a rigid core sphere:[116, 117]
3
(eq. 25)
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3 V0 rcore d 0 rcore 3 3 V rcore rcore
where rcore is the core radius, is the polymer shell thickness, and d0 is the expected layer thickness at the pseudocritical coagulation concentration of salt (i.e. when W-1≈1). The relationship between the shell
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thickess and salt concentration, =f(CNaCl), can be derived by combining the Flory theory [118] with the Donnan model [119] and it is found to depend on the ionization of the outer layer. An exhaustive study on the salt effect on the swelling of ionized nanomaterials can be found here [116, 120]. In the case of non-ionic stimulus-responsive nanoparticles we found the shell thickness depends on CNaCl, through a linear relation:
0 kS CNaCl
(eq. 26)
where 0 is the polymer size in the absence of salt (reference state) and ks is the salt sensitivity to the
dehydration. Analogously, the Hamaker constant of the outer layer, AS, can be defined as a function of the swelling ratio, , of the polymer:[103, 116]
19
ACCEPTED MANUSCRIPT
AS AP 1
AW
2
(eq. 27)
where AP is the Hamaker constant of the completely dehydrated (deswelled) polymer, and
AW=4.35x10-20J is the Hamaker constant for water. [121]
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Electrostatic potential. The electrostatic potential is a repulsive contribution approximated as the
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double layer potential, electrostatic; the following two forms are typically used depending on the value of
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RH:[83]
electrostatic
k T e h h 4 R Y B ; RH 5 e h 2RH
2 H 0 r
2
(eq. 28a)
(eq. 28b)
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electrostatic h 2RH 0 r02 ln 1e h ; RH 5
Here 0 and r are the permittivity of the free space and of the medium, respectively, and 0 is the surface potential approximated with the measured value of the zeta potential of the coated core shell
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0 RkBT 1000e 2 NA ( 2CNaCl )
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1
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nanoparticle. The Debey lengthand Y are given by[83]:
8tanh 0r 0 4kBT
Y
1 1 2RH
R 1 tanh 2
H
(eq. 29a)
2
0 r
0
4kBT
(eq. 29b)
Hydration potential. The effect of hydration energy on the colloidal stabilization is a repulsive
potential that depends exponentially on the interlayer thickness. The empirical equation of repulsive hydration energy between two hydrophilic spheres with radius RH,0 can be written as:[121, 122]
hydration h RH,0 2 Phe
h
(eq. 30)
where is the characteristic decay length of this interaction, typically between 0.6 and 1.1 nm for 1:1
electrolytes,[121] and Ph is hydration pressure, which depends on the degree of hydration. Here, to account for differences in the hydration state of the core-shell nanoparticles, the hydration pressure is defined as:
20
ACCEPTED MANUSCRIPT Ph Ph,0 kB NATCNaCl
(eq. 31)
where Ph,0 is the hydration pressure in the absence of deswelling (no salt) and the second term represents the osmotic contribution to the hydration pressure. It can be seen from equation (31) that at
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high ionic strengths this contribution can be attractive. Calculation of the stability ratio, W-1. Once the attractive and the repulsive interaction potentials are
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known, equations (24), (28) and (30) can be substituted into equation (15). This allows the instability
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ratio to be expressed as a function of salt concentration, W-1=f(CNaCl).
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5. Core-shell composition and solution conditions: implication for colloidal stability 5.1 Effect of nanoparticle core
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Material properties such as particle size, morphology, and crystallinity are important parameters affecting nanoparticle stability. Quantitative relationships between NP composition and stability are
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imperative for understanding the potential risk of nanoparticles in the environment. The basis of the
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undesirable effects of NPs may stem from their chemical composition, size, surface charge, and shape. [123, 124]
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From a fundamental perspective, the particle composition most directly affects the interparticle potential via the Hamaker constant, AC, in equation (21). Figure 1 shows the impact of the variation of AC on the interparticle potential as a function of interparticle separation distance as calculated from equation (21) and the stability ratio as a function of ionic strength, i.e. concentration of aqueous sodium chloride as calculated using equations (15), (24), and (28a) for the stability ratio, interparticle van der Waals potential, and electrostatic potential respectively. Nanoparticle size, RH, also has a straightforward influence on stability. As a general rule smaller particles are more prone to aggregation than larger ones. Both van der Waals and electrostatic interparticle potentials fields have an explicit direct dependence on particle radius, hence a higher energy barrier is expected as particle size increases. This is shown in Figure 2.
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ACCEPTED MANUSCRIPT Several experimental studies on the colloidal stability of functionalized nanoparticles have confirmed the theoretical expectations [76, 89, 125, 126]. In particular, Zhou and He found a direct correlation between the critical coagulation concentration, CCC, and the particle hydrodynamic radius, RH, for
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spherical TiO2 (anatase) and hematite nanoparticles, respectively [89, 125]. However, while the aggregation of spherical particles is well understood, the impact of shape and
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crystal structure on colloidal stability is relatively unknown. In literature there are only few studies that
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systematically evaluate the role of shape on nanoparticle aggregation [89, 127-130]. Mulhivil et al.
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[128] investigated the aggregation kinetics of thiolate capped CdSe nanoparticles with different size and shape and they found CCC increases with specific surface area, SA. Nanoparticles with high aspect
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ratio exhibit increased stability with respect to added electrolyte. A strong correlation between CCC and SA was also found by Zhou et al. [89] for the colloidal stability of rod-like TiO2 (rutile) nanoparticles in
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aqueous suspensions.
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Recently Afrooz et al. [129] studied the influence of shape on nanomaterials aggregation using poly-
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acrylic acid (PAA) coated on gold nanospheres (AuNSs) and nanorods (AuNRs) having similar size and electrical surface potential. Here, it was shown that AuNSs have higher aggregation propensity, i.e. a lower CCC, than AuNRs nanoparticles (CCCNS=50mM < CCCNR=250mM in NaCl aqueous suspensions). It was hypothesized that electrosteric interactions and physical packing hindrance are the key mechanisms for the shape effects on nanoparticle aggregation. Spherical colloids possess higher curvature compared to rod-like particles resulting in a relatively compressed polyelectrolyte layer for AuNSs compared to an extended brush-like layer for AuNRs. 5.2 Effect of surface chemistry Nanoparticle functionalization promotes colloidal stabilization in high ionic strength media because of steric and hydration repulsions [121, 122]. In particular covalent grafting, moreso than physical adsorption, enables achievement of stable suspension, due to the minimization of potential desorption from the particle surface. As discussed in Section 2.1 the wide variety of synthetic approaches to the formation of functionalized nanoparticles provides access to a wide range of nanomaterials with defined 22
ACCEPTED MANUSCRIPT charge density and surface coverage, and therefore nanoparticle stability. For some applications, covalent grafting of short chains is preferred over longer polymers in order to increase the exposure of reactive molecules on the surface particularly in drug delivery and sensing applications. In these
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systems, stimulus-responsive nanoparticles are quite interesting since they allow control over colloidal stability through external stimuli such as ionic strength, pH or temperature. Interestingly, nanoparticles
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modified with thick, densely packed brushes (obtained via grafting-from technique [131]) tend to show
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collapse, rather than colloidal aggregation upon heating above their lower critical solution temperature
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(LCST). Those with less densely packed brushes (obtained by using the grafting-to technique [51]) tend to colloidal aggregate following dehydration transition. [132] In the case of high grafting densities, the
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interactions between the particle cores are completely shielded by the macromolecular shell, and the entropy of the grafted chains soley dictates the dispersion state. On the contrary, at low grafting
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densities when the grafted chains are well separated on the nanoparticle surface, the core-core
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interactions between the nanoparticles will only be prevented very close to the grafting points. In this
systems.
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latter case, the particles will interact with each other as “patchy” attractive particles, leading to unstable
Similarly to surface coverage, an increase in the shell thickness (or molecular weight of the macromolecule) may enhance the stability of nanoparticles due to an increase of the energy barrier to aggregation [133-136]. Barrera et al. [134] studied the effect of polyethylene glycol (PEG) thickness on magnetite nanoparticle aggregation. Here it was demonstrated that particles modified with low molecular weight PEG (<1kDa) aggregate in high ionic strength media, however steric repulsion of high molecular weight PEG (>1kDa) prevents nanoparticle colloidal aggregation under the same conditions. Moreover, Liu et al. [135] found colloidal stability of gold functionalized with thiol-ended PEG depends on molecular weight, with longer PEG and larger PEG/NPs ratio being more effective in stabilizing nanoparticles in suspension. These observations are in accordance with DLVO theory, which predicts greater stability for lower shell to core size ratios, G=rcore/RH, because the van der Waals attraction, which is primarily driven by core-core interactions, is attenuated. Flory-Kirbraun theory [112] also 23
ACCEPTED MANUSCRIPT indicates that longer surface-bound ligands and higher ligand coverage will favor stability because of increased steric repulsion. The effect of polymer shell thickness on the total interaction potential and instability ratio is shown in Figure 3 for a typical core-shell nanoparticle system; the core size ratio, G,
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is varied while maintaining the surface potential, 0, the hydrodynamic radius, RH, and the Hamaker constants, AC and AS=AP constant.
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As shown in Figure 3B, the instability ratio predicts a lower value for the CCC as G increases, i.e. the
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nanoparticles become less stable against salt.
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While the effect of size and surface coverage on nanoparticle aggregation is well documented in literature, the impact of the outer shell conformation on colloidal stability is lacking. Systematic studies
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on the effect of heterogeneity and macromolecular conformation on the aggregation mechanism are published only recently by Huang [137] and Gillich [104], respectively.
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Huang et al. [137] reported the effect of surface heterogeneity on the colloidal stability of thiol-coated
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nanoparticles (NPs). Here, the gold NPs were modified by different distributions of ligands with
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charged and nonpolar terminals. In one case a homogeneous distribution of the two ligands was grafted on the gold surface, and in the other case charged and nonpolar terminals decorated in stripe patterns. Although the functionalized NP were similar in size, ligand composition, and surface charge density, the different surface organization of the functional groups resulted in different stability behavior. The critical coagulation concentration of orderly patterned ligands on the NP surface was higher than the CCC for gold nanoparticles grafted with a homogeneous distribution of ligands. This difference was attributed to the differences in the relative adsorption and hydration of counterions within the Stern layer and was supported by molecular dynamics (MD) simulations. [138] In silico, a hydrogen bond network can be developed in the nanoscale nonpolar stripes and the hydration shell may increase the interaction energy barrier thus enhancing the stability of gold nanoparticle decorated with patterned ligands in contrast to homogeneous surface functionalization.
This underscores the role of shell
hydration, , on the stabilization effect.
24
ACCEPTED MANUSCRIPT Gillich et al. [104] synthesized superparamagnetic iron oxide nanoparticles (SPIONs) functionalized with poly(ethylene glycol) (PEG) and oligo(ethylene glycol) (OEG) polymers and compared the physicochemical properties of NPs stabilized with linear and dendritic macromolecules of similar
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molecular weight. They show polymeric interface architecture has significant impact on solubility, colloidal stability, and thermoresponsive behavior. Dendrite surface architechtures were found to confer
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superior colloidal stability as compared to linear PEG analogues. Moreover, for the same grafting
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density and molecular weight of the stabilizers, dendron-stabilized NPs show a reversible temperature-
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induced aggregation behavior, in contrast to irreversible aggregation observed for the linear PEG analogues. The significant difference in stability and colloidal phase behavior was attributed, in part, to
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differences in the hydration state of the shell.
The effect of polymer shell hydration on the total interaction potential and instability ratio is shown in
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Figure 4 for a typical core-shell nanoparticle system. The hydration state is parameterized by the
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swelling ratio of the shell, =V0/V, described in equation (25). In these calculations, the swelling ratio
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is varied while maintaining the surface potential, 0, the hydrodynamic radius, RH, and the Hamaker constants, AC and AP, constant.
In equation (25) and Figure 4B, it can be seen that as the shell becomes more hydrated, the swelling ratio decreases and the stability increases, as manifest by the increase in CCC. 5.3 Effect of solution condition
For the past decade or more researchers have often studied the effect various cations have on the stability of nanoparticle suspensions in an effort to predict the fate of nanoparticles in the environment.[139, 140] Electrolytes from the surrounding solution can have multiple effects on the stability of nanoparticle suspensions. Through adsorption onto particle surfaces or the shell polymers, anions of cations can directly influence the apparent surface potential. In many cases the adsorption of ions to nanoparticle surfaces results in the surface charge decrease. As the surface charge approaches the isoelectric point a transition from an unfavorable aggregation regime to a favorable one occurs.[141] Specific interactions through complexation of dissolved cations by adsorbed polymers will also result in 25
ACCEPTED MANUSCRIPT a transition of the surface charge to the IEP again resulting in transitions from unfavorable to favorable aggregation. [142] While alteration of surface potential can affect the stability of nanoparticle suspensions directly, an
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increase in ion concentrations in solution has an indirect effect on particle stability by increasing the
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screening of electrostatic interactions. Within the DLVO paradigm, the result is to decrease the barrier height to aggregation. As a first approximation it can be shown that the CCC for conventional systems
SC
is therefore proportional to z–6 where z is the charge of the background counter ion. This relationship is
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commonly referred to as the Shultze-Hardy rule and indicates that counterion valence is the primary driver of particle stability. [143] For suspensions of different functionalized nanoparticles many recent
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studies have shown the qualitative nature the relationship to be true.[144]
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Despite the Shultze-Hardy theory, experiments have nearly never shown scaling of the CCC by z-6.
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[77, 78, 145, 146] For unfunctionalized naturally occurring and engineered nanoparticles, this might be For
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a result of surface charge heterogeneities or differences in degree of ion hydration. [147]
functionalized nanoparticles, the result can be quite different owing to the direct interaction of counterions with the surface functionalities. Chen et al. showed apparent aggregation rates beyond the diffusion limitation when some divalent cations (Ca2+, Ba+2 and Sr+2) supported suspensions of alginate functionalized iron oxide nanoparticles but a similar effect was not observed with monovalent cations. [77, 78] In these cases, the alginate polymers formed strong complexes with divalent cations from solution resulting in an alginate network that captured the iron oxide nanoparticles as it was formed. In another system, naturally occurring bionanoparticles such as viruses were stable at concentrations of Na+ beyond 1M, but millimolar concentrations of Ca2+ resulted in virus aggregation. [148] This most likely resulted from Ca2+ complexation with the protein moieties that comprise the virus capsid that resulted in a loss of steric stabilization. For these extreme differences in CCC between mono and divalent cations, it has been important to look beyond the Shultze-Hardy rule to infer alternative mechanisms for aggregation.
26
ACCEPTED MANUSCRIPT An alternative model of colloid stability that takes into account ion type and can explain the aggregation of even uncharged species could include a series of cations and anions that have been studied for their ability to precipitate (salt-out) proteins from solutions. The series of ions is commonly
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referred to as the Hofmeister series. For a sample of anions, the order, from highest salting out ability to highest salting-in ability, has been shown to be F-, PO43-, SO42-, CH3COO-, Cl-, Br-, I-, and CNS-. For
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cations, this order includes (CH3)4N+, (CH3)2NH2+, NH4+, K+, Na+, Cs+, Li+, Sr2+, Mg2+, Ca2+, and Ba2+.
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[149]
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The ordering described above is empirical only. Those ions with highest salting-out effects are referred to as kosmotropes. They are generally small ions with a high charge density. In solution these
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ions often leads to higher surface tension and a lower solubility of macromolecules or polymers. Chaotropes are ions with a small charge density and a high polarizability. The presence of these ions in
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solution often leads to enhanced macromolecular solubility, i.e. salting-in effects. At certain concentrations, this category of salts actually improves the solubility of molecules in solution instead of
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causing aggregation of particles. [150] Kosmotropes, being small and having a high charge density and therefore exert a strong electric fields at a short distances. The result is a competition for water molecules in the vicinity of polymer chains.
For strong kosmotropes polymers might be easily
dehydrated. The effect of polymer-ion interactions, and the relationship between structure-making and structure-breaking properties with salting-in and salting-out effects can potentially be explained through hydration forces. An overlap between a hydration zone of an ion and a hydration zone of a polymer leads to a force with both repulsive and attractive elements. The overlap in hydration zones will partially dehydrate both the ion and the polymer; an unfavorable process for the ion, leading to a repulsive force, but a favorable process for the polymer, leading to an attractive force between the ion and the polymer. Significant control over nanoparticle stability in solutions of widely different chemistries has been achieved by employing a rational approach to surface functionalization. This involves using small
27
ACCEPTED MANUSCRIPT moleculs, hydrogels, proteins, and stimuli-responsive polymers such as Poly(N-isopropylacrylamide), PNIPAM as surface functionalities. [84, 151, 152] Control of nanoparticle stability has conventionally been a binary process. That is, nanoparticle
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suspensions are either stable (monodisperse) or in their aggregated state. A novel mode of stabilization
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now employ stimulus responsive functionalities, in-situ switching of the polymer-solvent interaction via
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external stimuli such as pH, ionic strength, and temperature offers an opportunity to control aggregation state on a fine scale. In the case of thermoresponsive polymers increasing temperature above LCST
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causes macromolecular conformational changes, which decrease steric effects, leading to aggregation. Additional sensitivity to environmental conditions can be achieved via the addition of electrolytes, or
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variation of pH, which tune the desolvation of macromolecules or change the surface charge density,
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respectively.
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New approaches to creating surface functionalities take a rational design approach to the polymer
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coatings for inorganic nanoparticles in order to tune them to different external stimuli such as temperature [101, 153-155] and pH [156-158]. Thermoresponsive polymers such as PNIPAM are, perhaps, the most highly used of this group. [84, 155, 159] Nabzar et al. [155] were the first to study this class of nanoparticles by studying the behavior of styrene/N-isoppropylacrylamide and styrene/Nisopropylamide-co-aminoethyl methacrylate core-shell latexe nanoparticles.
Critical coagulation
concentrations (CCC) of these were determined below and above LCST=32o C. Their results showed that these particles displayed similar stability behavior above LCST of PNIPAM chains. Below LCST, the CCC values were much higher (indicating a greater degree of stability) due to the swelling of the polymer layer which impared great steric stabilization for these nanoparticles. The authors claim that the driving forces of the ionic hydrogel shell swelling are the solvent-PNIPAM and the segment-segment interactions ruled out by the Flory [160] interaction parameter, , which increases with increasing salinity of the medium and temperature, and the osmotic pressure due to charged groups. A swelling increase leads to a decrease of the shell Hamaker constant - see equation (27), an increase of the number
28
ACCEPTED MANUSCRIPT of charged groups contributing to the diffuse layer potential and creates a non-DLVO additional stabilization term. When the temperature is increased above LCST, the PNIPAM surface layer shrinks as a consequence of an increase in the Flory parameter and hence provides a more favorable segment-
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segment contact.
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Lv et al. [159] prepared soft hydrogel nanoparticles with PNIPAM and characterize their temperature-
into larger aggregates.
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induced aggregation. Above LCST a fast association process was observed and the particles clustered Raising the temperature further caused their size to decrease due to the
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formation of hydrophobic shell layers accompanying the shrinkage of the PNIPAM chains with chain polar transformations, resulting in interparticle aggregation.
During the cooling process these
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contracted cores trapped in the aggregates gave rise to an early dissociation behavior.
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More recently Zaccone et al. [84] studied the reversible association of thermoresponsive silica
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nanoparticles coated with PNIPAM. By using a statistical mechanical analysis that account for dimer
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dissociation combined with light-scattering experiments, the authors developed a model to quantify the dissociation rate and the reversible association energy of core-shell nanoparticles as a function of temperature. They found the binding energy changes sharply near LCST of the PNIPAM chains, which they relate to the hydrophobic-hydrophilic transition of the thermoresponsive nanoparticles. While a novel initial approach to surface functionalization, PNIPAM is limited by only one critical solution temperature in water. For greater control of particle aggregation across a range of solution conditions, a more complex synthetic methodology is required.
Some approaches employ
copolymerization with, charged and/or uncharged monomers, pH-sensitive monomers or by the addition of hydrophilic/hydrophobic monomers such as acrylamide during polymerization.[161-163] Boyer et al. [164] exploited a combination of charged and neutral polymers to exert fine control of the surface charge imparted by the charged polymer component. In this study, a range of surface charges on gold NPs from-30 to +39 mV could be achieved. The surface-charges could also be modulated by
29
ACCEPTED MANUSCRIPT solution temperature. The resulted from the use of a thermosensitive neutral polymer coassembled with charged polymers. Boyer et Witaker[154] employed a series of thermosensitive copoly(oligoethylene oxide) acrylates by the copolymerization of oligo(ethylene oxide) acrylate and di(ethylene oxide) ethyl
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ether acrylate. These materials exhibited a tunable LCST over a range of 15-90oC. The monomer composition was the variable controlling the LCST temperature. The copolymer-stabilizing layer was
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shown to resist non specific interactions with proteins most likely due to steric interactions. As a result,
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these materials could later be assessed for their use in biotechnology and medicine.
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One goal of experimentalists in this field is to develop functionalization schemes that will respond to
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varying stimuli. pH responsive materials represent another advancement in this field. Strozyk et al. [165] developed a thermosensitive polymer that exhibits pH-dependent thermo-responsive behavior.
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These materials exhibited an LCST of 42oC in water and around 37oC under physiological conditions In this configuration a smart pH-dependent
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and could be grafted to protein coated gold NPs.
thermosensitive behavior was exhibited. Chen et al. [166] developed a dual temperature and pH
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responsive functionalization from based on hyperbranched polyethylenimine (PEI) by grafting lphenylalanine. These materials showed phase transitions resulting from both pH and temperature changes, and the LCST could be modulated by changes in the phenylalanine grafting density, amidation and pH of solution.
6. Case study. Programmable aggregation kinetics of Au@MeO2MAx-co-OEGMAy NPs: effect of surface chemistry, ionic strength and temperature 6.1 Overview As an example, a case study is presented of a novel functional polymer used to modify gold nanoparticles. This system demonstrates the capability to control the equilibrium interactions between nanoparticles and the underlying kinetic processes controlling the physical state of the dispersion while simultaneously furnishing an opportunity to elaborate the interrelationships between solution chemistry, temperature, and the intrinsic properties of the macromolecular layer.
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ACCEPTED MANUSCRIPT Recently, a novel stimulus-responsive system was reported based on gold (Au) NPs grafted with polymer brushes consisting of disulfide-functionalized random copolymers of oligo(ethylene glycol) methyl methacrylate (OEGMA) and 2-(2-methoxy-ethoxy)ethyl methacrylate (MeO2MA), or
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Au@(MeO2MAx-co-OEGMAy).[167] As a result of the presence of the ethylene glycol moieties (y), NPs capped by these co-polymers are responsive to temperature and ionic strength in aqueous
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dispersion media. [168, 169] Specifically, it was shown that different copolymer compositions (x:y)
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induce variable degrees of stabilization that are characterized by different phase transition temperatures
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and interaction energies. However, each displays similar sensitivity to ionic strength and temperature. Although the effect of salt concentration and temperature on the stability of these NPs was well
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established [170], systematic quantification of the relevant physical parameters, such as critical salt concentrations, critical particle concentrations, and aggregation kinetics was only recently addressed.
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[87, 90] This case study serves to inform understanding of the complex balance of interactions
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responsible for controlling NPs stability in aqueous suspension and at fluid-fluid interfaces.
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A homologous series of Au@(MeO2MAx-co-OEGMAy) NPs was prepared by Scheme 2B using ligand exchange for 95:5 < x:y < 80:20. A schematic of the core-shell nanoparticle and the disulfide (DS) functionalized copolymers, DS-Poly(MeO2MAx-co-OEGMAy), are shown in Scheme 4. In all cases, the Au NPs core radius rcore≈7.5 nm. For all (x:y), the co-polymer grafts have similar molecular weight (20
31
ACCEPTED MANUSCRIPT 6.2 Aggregation kinetics for Au@(MeO2MAx-co-OEGMAy) NPs The autoaggregation of thermoresponsive Au@(MeO2MAx-co-OEGMAy) NPs with 95:5<(x:y)<80:20 for 0.01 M
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(TR-DLS). Data shown in Figure 5 are at T=22oC. Experimental details are given in [90].
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To determine, k11, data in Figure 5A-C were analyzed using equation (9). Aggregation rate constants,
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k11, are reported in Figure 5D-F as a function of salt concentration. It can be seen that the aggregation rate increases with increasing salt concentration for all (x:y) homologues; the maximum rate constant in
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all cases 1.5x10-18 m3 s-1 < (k11)fast < 2.1x10-18 m3 s-1.
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6.3 Colloidal stability ratio and interparticle potential for Au@(MeO2MAx-co-OEGMAy) NPs By varying the solution conditions, such as the ionic strength, temperature, and the copolymer
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composition, the NPs stability (W-1) can be mapped. The inverse stability ratio, W-1, can be determined
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from the ratio of the experimental aggregation rate constant, k11, to the diffusion-limited aggregation
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rate constant, (k11)fast as defined by equation (4). In all cases the instability ratio increases with salt and the maximum achievable aggregation rate. However, changes in solution chemistry and temperature lead to differences in the stability curve. Unlike conventional mechanisms for aggregation which result from attractive van der Waals forces dominating over repulsive electrostatic forces as described by DLVO theory, the presence of salt in these NPs suspensions changes the affinity of the copolymer layer to water. This results in a partial dehydration of the swollen copolymer shell, leading to less hydrophilic systems, consequently decreasing the phase transition temperature, LCST.[171-175] As a consequence, hydrophobic interactions create attractive interactions between the NPs. When the temperature is increased above the LCST dehydration of the copolymer shell induces aggregation. The relationship between the external stimuli, i.e. temperature and salt concentration, for the transition point in the instability ratio, i.e. W-1 ~ 1, was parameterized previously [87] using:
32
ACCEPTED MANUSCRIPT
T T0 x : y kS CNaCl
where T and T0 are the critical solution temperature in the presence and in the absence of salt, respectively, and kS is a measure of the effectiveness of a particular salt in modifying the stability of the
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dispersion. For each of these homologues, these parameters are summarized in Table 1.
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It was shown that the solution temperature required for the phase transition increases nearly linearly
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with the OEGMA (y) fraction of the copolymer, corresponding to the expectation ideality for the dilute
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(y) monomer. This was consistent with the qualitative finding of Lutz et al. [171] for Poly(MEO2MAxco-OEGMAy) aqueous dispersions.
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The experimental trends observed in Figure 5 are consistent with a change in the hydration state of the nanoparticle shell caused by increasing salt concentration. This change gives rise to an osmotic pressure
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that counterbalance the repulsive interaction due to the accumulation of water around the copolymer surface. As described in the theoretical Section 4, the osmotic pressure term to accounts for this difference in the hydration state in equation (31).
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(eq. 32)
Using equation (30), the decay length, , and the hydration pressure, Ph,0, were calculated using the data in Figure 6 D-F and equations (15), (24), (28) and (30), i.e. DLVO theory modified to include hydration/osmotic contributions; and PH,0 are reported in Table 1 for (x:y)=95:5, 90:10, and 80:20. These parameters are consistent with constant reported by other authors for colloidal systems in 1:1 electrolytes (h =3-30 mJm-2). [122, 176] 6.4 Summary Here the application of a unified experimental and theoretical approach to the characterization of functionalized nanoparticles was demonstrated. The aggregation kinetics of a homologous series of copolymer-functionalized nanoparticles was measured using Time Resolved Dynamic Light Scattering (TR-DLS). Using the theoretical framework outlined in Section 4, the fundamental parameters underpinning the aggregation rate and colloidal stability were extracted. The parameters provide
33
ACCEPTED MANUSCRIPT insight into the mechanisms governing interparticle interaction and inform synthetic approaches to achieving specified performance, particularly with respect to dispersion stability and the kinetics of destabilization. This demonstrates the utility of a unified approach in developing guiding principles for
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the rational design of new functional systems. 7. Closure
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This review highlights the state-of-the-art synthetic approaches to nanoparticle functionalization,
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experimental methods for determining suspension stability and the kinetics of aggregation, and
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theoretical models for experimental data reduction which consider the composition and structure of nanoparticle core, the surface chemistry and solution condition. A case study describing a novel
stimulus responsive polymer is included.
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8. Acknowledgements
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approach to exerting fine control over the aggregation state of gold nanoparticles functionalized with a
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Financial support from National Aeronautics and Space Administration (NASA)/Glenn Research
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Center (Particle Stabilized Emulsions and Foams, Award NNX10AV26G) in cooperation with the European Space Administration (ESA) through opportunity AO-2009-0813 and the Camille and Henry Dreyfus Foundation is acknowledged.
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Table 1. Physical characteriztation of Au@(MeO2MAx-co-OEGMAy)
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ACCEPTED MANUSCRIPT Figure captions Scheme 1. Approaches for polymer brush attachment to create a core-shell nanoparticle: (A) physical (non-specific) adsorption, (B) ionic bonding, and (C) covalent grafting.
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Scheme 2. Polymer grafting approaches on nanoparticles: (A) ‘grafting from’ technique, (B) ‘grafting to’ technique, and (C) ‘in-situ’ technique.
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Scheme 3. Interactions between core-shell nanoparticles. Traditional forces for colloidal interactions
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(electrostatic, VdW) and other structural contributions (hydration and osmotic) that occur when particles are suspended in fluid media. Parameters used for DLVO calculations: two NPs with identical core
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radius rcore, and polymer shell thickness separated by a surface-to-surface distance h. The core-shell
Figure 1.
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radius is indicated as RH rcore .
Effect of the Hamaker constant of nanoparticle core, AC, on the colloidal stability of core-
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shell nanoparticles: 0=30mV, RH (=rcore)=20 nm, and AS=AP=7.5x10-20J: (—) Ac=5.0x10-20J; (– –)
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function of CNaCl. Figure 2.
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CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a
Effect of the particle size, RH (=rcore), on the colloidal stability of core-shell
nanoparticles:0=30mV, Ac=5.0x10-19J and AS=AP=7.5x10-20J: (—) RH=10nm; (– –) RH=20nm; (–·–) RH=30nm; (···) RH=40nm. (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl. Figure 3.
Effect of the particle core-shell geometry, G=(rcore/RH), on the colloidal stability of core-
shell nanoparticles: (—) G=0.60; (– –) G=0.70; (–·–) G=0.80; (···) G=0.85;RH=20nm,0=45mV, Ac=5.0x10-19J and AS=AP=7.5x10-20J (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl.
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Figure 4. nanoparticles:
Effect of the shell hydration, =(V0/V), on the colloidal stability of core-shell (—)
=0.50; (– –) =0.60; (–·–)=0.70; (···)=1.0;RH=20nm,0=30mV,
Ac=4.0x10-19J and AP=9.0x10-20J (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a
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function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl. Scheme 4. Thermoresponsive nanoparticles (NPs) obtained by grafting gold NPs with disulfide(DS)-Poly(MeO2MAx-co-OEGMAy):
Au@(MEO2MA95-co-OEGMA5);
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Au@(MEO2MA90-co-OEGMA10); Au@(MEO2MA80-co-OEGMA20).
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Figure 5. A-C. Aggregation kinetics of Au@(MeO2MAx-co-OEGMAy): hydrodynamic radius of Au@(MeO2MAx-co-OEGMAy) NPs as a function of time. The dashed lines represent the linear fit to
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the data for RH,1
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1.3M (); CNaCl = 1.4M (); CNaCl = 1.6M (); CNaCl = 1.85M (). (C) Au@(MeO2MA80-co-
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OEGMA20) NPs: CNaCl = 2.1M (); CNaCl = 2.2M (); CNaCl = 2.3M (); CNaCl = 2.4M (). D-F. Critical
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Aggregation rate, k11, as a function of CNaCl for Au@(MeO2MAx-co-OEGMAy) NPs.
coagulation concentration, CCC, was determined at the intersection between the reaction-limited and diffusion-limited regimes (dash-dotted lines). (D) Au@(MeO2MA95-co-OEGMA5) NPs; (E) Au@(MeO2MA90-co-OEGMA10) NPs; (F) Au@(MeO2MA80-co-OEGMA20) NPs. Figure 6. A-C. Total interaction potential, T, versus separation distance, h, for Au@(MeO2MAx-coOEGMAy) NPs at CNaCl=CCC. (A) Au@(MeO2MA95-co-OEGMA5) NPs; (B) Au@(MeO2MA90-coOEGMA10) NPs; (C) Au@(MeO2MA80-co-OEGMA20) NPs. D-F. Instability ratio, W-1, as a function of CNaCl for Au@(MeO2MAx-co-OEGMAy) (symbols). The solid lines are the best fit to equations (15), (24), (28) and (30); i.e. extended DLVO with hydration/osmotic contributions. (D) Au@(MeO2MA95co-OEGMA5) NPs; (E) Au@(MeO2MA90-co-OEGMA10) NPs; (F) Au@(MeO2MA80-co-OEGMA20) NPs.
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Graphical abstract
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We highlight synthetic approaches to nanoparticle functionalization, and experimental methods for determining suspension stability and the kinetics of aggregation. We discuss theoretical models to study interparticle potential and colloidal stability of core-shell nanoparticles, by varying the composition of nanoparticle core, the surface chemistry and solution conditions.
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HIGHLIGHTS Synthetic approaches to nanoparticle functionalization Experimental methods for aggregation kinetics characterization Theoretical frameworks for stability ratio calculation of core-shell particles Unified structure-property characterization using experimental platform and theoretical framework for rational nanoparticle design
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80:20 28100
'C, mV oP, nm“2 Rh,o
-5.9±0.4 0.61 23.40
-3.2±0.5 0.42 19.80
-5.2±0.3 0.34 20.00
G
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0.39
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1.9±0.2
2.4±0.2
CCC, mM
870±50
1850±90
2400±400
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51.2±1.0 -11.9±0.7 0.57±0.04
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o n 33.4±0.4 45.5±0.8 Salt effectiveness kT, °C M_1 -11.8±0.7 Hydration decay X, nm 0.68±0.02 length Hydration Ph,o, MPa 2.30±0.02 Pressure 2 Surface Hydration ithi0, mJ/m 1.56±0.06 Pressure Table 1. Physical characteriztation of Au@(MeO2MAx-co-OEGMAy)
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Copolymer molecular weight Zeta potential Grafting density Hydrodynamic radius (22 C) Shell aspect ratio rcore/RH,o Salt swelling sensitivity Critical coagualtion concentration Critical temperature o
(x:y) MW, gmol"1
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S0001-8686(14)00242-5 doi: 10.1016/j.cis.2014.07.015 CIS 1469
To appear in:
Advances in Colloid and Interface Science
Received date: Revised date: Accepted date:
28 May 2014 30 July 2014 31 July 2014
Please cite this article as: Gambinossi Filippo, Mylon Steven E., Ferri James K., Aggregation kinetics and colloidal stability of functionalized nanoparticles, Advances in Colloid and Interface Science (2014), doi: 10.1016/j.cis.2014.07.015
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Aggregation kinetics and colloidal stability of
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functionalized nanoparticles
Lafayette College, Department of Chemical and Biomolecular Engineering, Easton, Pennsylvania
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Filippo Gambinossia, Steven E. Mylonb, and James K. Ferria*
(USA) 18042. E-mail: [email protected]; [email protected] Lafayette College, Department of Chemistry, Easton, Pennsylvania (USA) 18042. E-mail:
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[email protected]
*To whom correspondence should be addressed: Prof. James K. Ferri James T. Marcus '50 Professor and Department Head Department of Chemical and Biomolecular Engineering Lafayette College Easton, Pennsylvania 18042 tel +1(610) 330-5820 fax +1(610) 330-5059 E-mail: [email protected]
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ACCEPTED MANUSCRIPT ABSTRACT
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The functionalization of nanoparticles has primarily been used as a means to impart stability in nanoparticle suspensions. In most cases even the most advanced nanomaterials lose their function should suspensions aggregate and settle, but with the capping agents designed for specific solution chemistries, functionalized nanomaterials generally remain monodisperse in order to maintain their function. The importance of this cannot be underestimated in light of the growing use of functionalized nanomaterials for wide range of applications. Advanced functionalization schemes seek to exert fine control over suspension stability with small adjustments to a single, controllable variable. This review is specific to functionalized nanoparticles and highlights the synthesis and attachment of novel functionalization schemes whose design is meant to affect controllable aggregation. Some examples of these materials include stimulus responsive polymers for functionalization which rely on a bulk solution physicochemical threshold (temperature or pH) to transition from a stable (monodisperse) to aggregated state. Also discussed herein are the primary methods for measuring the kinetics of particle aggregation and theoretical descriptions of conventional and novel models which have demonstrated the most promise for the appropriate reduction of experimental data. Also highlighted are the additional factors that control nanoparticle stability such as the core composition, surface chemistry and solution condition. For completeness, a case study of gold nanoparticles functionalized using homologous block copolymers is discussed to demonstrate fine control over the aggregation state of this type of material. KEYWORDS:
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Aggregation kinetics, core-shell nanoparticles, colloidal stability, dynamic light scattering, functional polymers, nanoparticle functionalization
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1. Introduction 2. Synthetic approaches to nanoparticle functionalization 2.1. Overview 2.2. Direct vs. step-wise functionalization 2.3. Macromolecular encapsulation 2.3.1 Macromolecular encapsulation: ‘grafting-from’ strategy 2.3.2 Macromolecular encapsulation: ‘grafting-to’ strategy 2.3.3 Macromolecular encapsulation: ‘in-situ’ strategy 3. Aggregation kinetics and colloidal stability: experimental methods 3.1. Overview 3.2. Spectral turbidimetry (and other optical methods) 3.3. Time resolved dynamic light scattering (TR-DLS) 3.4. Fluorescence correlation spectroscopy (FCS) 4. Theoretical models: a brief overview 4.1. Favorable (fast) and unfavorable (slow) aggregation rate 4.2. Theoretical instability ratio 4.3. DLVO interaction potentials: core-shell approach 5. Core-shell composition and solution conditions: implication for colloidal stability 5.1. Effect of nanoparticle core 5.2. Effect of surface chemistry 5.3. Effect of solution condition 6. Case study. Programmable aggregation kinetics of Au@MeO2MAx-co-OEGMAy NPs: effect of surface chemistry, ionic strength and temperature 6.1. Overview 6.2 Aggregation kinetics for Au@(MeO2MAx-co-OEGMAy) NPs 6.3 Colloidal stability ratio and interparticle potential for Au@(MeO2MAx-co-OEGMAy) NPs 6.4 Summary 7. Closure 8. Acknowledgements 9. References
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ACCEPTED MANUSCRIPT 1. INTRODUCTION Functionalized core-shell nanoparticles represent a growing class of materials which have a significant importance in diverse areas of science and technology, including water-oil separation, food
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processing, pharmaceutical formulation, biomedicine, energy storage, as well as for developing complex hierarchical systems [1-3]. The complexation between polymers and nanoparticles offers a good
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platform for engineering versatile hybrid structures with novel functionalities. One of the major
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challenges pertaining to all applications is the design of smart nanomaterials, whose colloidal stability
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can be easily controlled by an external trigger, such as pH, temperature or ionic strength. Depending on the particular application, dispersion stability or the kinetics of destabilization can be either a desired
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(material sensing, food processing) or an unwanted (waste-water treatment, water-oil separation, blood/brain barrier) effect.
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This introduction highlights the impact of surface chemistry on the colloidal stability of core-shell
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nanoparticles for specific applications including emulsion and foam stabilization, drug-delivery, sensing
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and actuation, and other technologies.
Emulsion and foam stabilizers. In general, amphiphilic polymers grafted on particle cores enhance fluid-fluid stability by increasing the interfacial energy and forming a mechanical barrier that prevents the coalescence of the dispersed phase. The potential to stabilize oil-water and air-water dispersions is of particular interest in applications such as oil recovery, cosmetics, pharmaceutical, agrochemicals and food processing [1, 4-8]. Polymer-coated nanoparticles can be used to control the release of encapsulated ingredients from an emulsified product or to manage the capture and release of water from crude oil. Recently, Calcagnile [1] and Nikje [9] presented flexible composite materials based on polyurethane foam functionalized with magnetic iron oxide nanoparticles, which can efficiently separate oil from water. These nanomaterials can recruit floating oil from polluted regions thereby purifying the aqueous phase.
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ACCEPTED MANUSCRIPT Smart delivery systems. Hybrid core-shell nanoparticles can be utilized as nanocarriers for drugs, catalysts, and enzymes, because the polymer scaffold can be used to immobilize smaller particles or macromolecules [10-12]. In this respect, the use of living radical polymerization techniques (either in
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the ‘grafting from’ technique and for the synthesis of functionalized polymers) can be beneficial by helping to design polymer systems that can change dispersion characteristics to facilitate the reversible
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transport and release of drug molecules from aqueous to hydrophobic environments in response to a
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stimulus. Partially hydrophobic nanomaterials are of particular interest as smart delivery systems for
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biological membranes, catalysis, tissue engineering, and agrochemicals [13]. For example Guo et al. [14] grafted iron oxide nanoparticles with pH-responsive Poly(methyl methacrylate), PMMA, shell to
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selectively load anticancer drugs and deliver it to targeted cells. The PMMA in the polymer shell was used to provide the appropriate environment for loading of the drug at neutral pH. At pH<5.5
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protonation of polycarboxylate anions in the PMMA chain was demonstrated to release the drug.
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Sensors and actuators. The possibility to exert active control over dispersion stability through the
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formation of core-shell nanoparticles can also be useful to develop chemical, biological or physical nanosensors [15-17]. Biomedical therapeutics and diagnostic device and combinations thereof, or socalled theranostics benefit from the NP/macromolecules complexation synergies. The need for real time monitoring of physicochemical functions has triggered the rapid expansion of information processing and biomedical fields. An interesting example of biomedical devices is that of Lai et al. [15]. The authors designed microfluidic channels, which can sort magnetic iron oxide nanoparticles coated with micelles containing the thermoresponsive polymer Poly(N-isopropylacrylamide), PNIPAM, depending on their aggregation state. Related to information processing Motornov et al. [16] were able to process logic operations based on the reversible aggregation of Poly(2-vinylpyridine), P2VP, coated silica nanoparticles. Coatings and lubricants. Another example of post-processing using nanoparticles and an important motivation for the fabrication of surface functionalized nanoparticles is the downstream incorporation in a matrix of other materials. Functionalized nanoparticles can be better dispersed in matrixes, this is 5
ACCEPTED MANUSCRIPT important for the realization of extrinsic self-healing materials [18, 19]. Self-healing anticorrosive coatings present an interesting active field for automotive and air transportation industries [20, 21]. 2. Synthetic approaches to nanoparticle functionalization
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2.1 Overview The ability to modify the surface chemisty of a nanoparticle is an important aspect in synthetic
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chemistry for a wide range of applications. This can be achieved by the addition of chemical
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functionality to the NP surface to tailor according to a specific application. The main functional groups
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utilized to anchor functional moieties to nanoparticle surfaces are thiols, disulfides, amines, nitriles, and carboxylic acids attached to small molecules or embedded in larger macromolecules [22-27]. There are
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numerous studies focusing on the functionalization of nanoparticles, and the topic has been already addressed in detail. [28-35]
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This review discusses the main synthetic approaches to the formation of core-shell nanoparticles and
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their colloidal stability against solution conditions, such as ionic strength, temperature, and pH. Benefits
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and drawbacks of the different functionalization protocols will be addressed including a summary of the potential applications.
2.2 Direct vs. step-wise functionalization There are two main strategies to introduce functional groups to the NPs surface. The first method is direct functionalization and consists in the addition of a bifunctional organic compound to a nanoparticle suspension. In this approach, one functional group reacts with the nanoparticle surface while the second group contains the required active functionality. The second method is a step-wise procedure or post-functionalization. This describes a bifunctional compound where a binding-chelating group is reacted first and the group of coupling site is converted in a second step to the final fuctional group. Direct functionalization requires a single conjugation step. However, the active functional group may react with the particle surface [36] and steric hindrance may limit binding strength and surface coverage. Step-wise modification is more versatile, because it can utilize a wide range of commercially available 6
ACCEPTED MANUSCRIPT coupling agents to functionalize almost all the nanoparticle systems. In addition the core-shell structure ensures a strong binding of the functional groups with a high surface coverage. The main problem with this approach is that the functional group must have a high affinity to the surfaces of the particles and
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cannot exist as isolated clusters. Both strategies have been successfully used to functionalize quantum dots, metal and metal oxide
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nanoparticles using small molecules containing silane agents, carboxylates groups [37] or polydentate
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ligands such as dithiols or oligomeric phospines [38]. However, the resulting core-shell nanoparticles
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offer limited processability to control both aggregation kinetics and colloidal stability. 2.3 Macromolecular encapsulation
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Nanoparticle encapsulation can be accomplished using a polymer that possesses both chelating and functional groups. These hybrid composites have encountered growing appreciation in the scale-up
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production of nanomaterials of various compositions and geometries [39-41]. Functional polymer
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nanocomposites combine the unique advantages of high surface area, quantum confinement exhibited
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by inorganic nanomaterials with the processability, functionality, and stability of polymers. [42, 43] Based on the mutual interactions between the organic macromolecules and the particles, a variety of synthetic approaches exist to create functional nanomaterials, which are schematically described in Scheme 1.
Ionic motifs via exchange or acid-base reactions or multidentate architectures using an array of weak physisorbed or hydrogen bond interactions [28, 44], all provide good stability control, especially when the dynamic character of the interface is considered a key contribution to the overall performance. Among these two strategies, the ionic bond is especially intriguing because it allows control of both structure and the dynamics through a simple and versatile materials platform suitable for a wide array of applications. Ionic bonded core-shell nanoparticles exhibit high dispersion stability due to electrostatic repulsion between the particles, both during synthesis and assembly, as well as in the final material. However, research studies mostly focus on covalently linking the polymer and the particle, which ensure strong binding and stability control, thus limiting depletion effects, which is one of the main 7
ACCEPTED MANUSCRIPT issue favoring the aggregation of nanoparticles [45]. Covalently bonded polymer brushes are less vulnerable to desorption, partial damage or environmental impacts, and can be classified into ‘graftingfrom’ strategy [13, 46-50], ‘grafting-to’ strategy [51], and direct or ‘in-situ’ synthesis method [52], as
2.3.1 Macromolecular encapsulation:
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schematically illustrated in Scheme 2. ‘Grafting-from’ strategy. In the ‘grafting-from’ method
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(Scheme 2A) the polymer chains are grown from the particle surface by using surface-initiated
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polymerization techniques, such as atom-transfer radical polymerization (ATRP) [53, 54], reversible
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addition fragmentation chain transfer (RAFT) [55], or ring-opening methatesis polymerization [56]. In all cases, an initiator is immobilized on the surface of previously formed nanoparticles and the polymer
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chains are subsequently grown from the attachment point. In particular ATRP has been reviewed by many authors with respect to polymerization from silica [57] and gold [58] surfaces. This method allows
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to create cross-linked core–shell nanostructures, such as gold nanoparticle (AuNP)/PNIPAM hybrid,
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which can be used as stimuli-responsive optical devices to trap and encapsulate other nanoparticles,
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biomolecules, dyes, or drugs [58].
Benefits. The grafting-from approach leads to polymer brushes with high grafting densities, since the steric hindrance is largely decreased with respect to other cases. Drawbacks. It is generally more difficult to achieve well-controlled polymer molecular weight during surface-initiated polymerization as opposed to when the polymers are synthesized in the bulk in the absence of particles. 2.3.2 Macromolecular encapsulation: ‘Grafting-to’ strategy. This method, schematically represented in Scheme 2B, involves the preparation of end-functionalized polymers and their subsequent covalent binding to the surface of pre-synthesized solid nanoparticles. The functionalization of the polymer brushes is usually achieved by modifying the end groups of the polymer of interest that are able to bind to surfaces such as gold [51], silica [59], or quantum dots [60]. The coating is then ensured by a ‘ligand exchange’ process, where the polymer chains replace the initial stabilizing agent. A more direct method, which does not require an initial stabilizing agent for the inorganic nanoparticles, employes a 8
ACCEPTED MANUSCRIPT combination of RAFT polymerization and coupling reactions to functionalize the particles surface with pre-synthesized polymer chains. In a recent work, Huang et al. [61] grafted silica nanoparticles with azido-functionalized poly(N-isopropylacrylamide) PNIPAM random copolymers in a two-step reaction
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mediated by trimethoxysilane agents to prepare ultrathin thermo-responsive microcapsules via click chemistry.
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Benefits. This method allows complete characterization of the macromolecular modifier prior to NP
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assembly enabling control of size and physico-chemical properties of the core-shell nanoparticles, since
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the synthesis occurs according to standard polymerization mechanisms without confinement effects. Drawbacks. Grafting requires the macromolecules to be functionalized beforehand with reactive
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groups that can bind to the chosen surface. The main limitation is that the achievable polymer surface density is relatively low compared to the other methods due to steric hindrance that prevents further
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polymers to approach the particle surface already coated with a relatively crowded layer. Moreover, the
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end groups of the polymer should have a higher binding affinity to the particle surface than the
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stabilizing ligand, to facilitate the ligand exchange process [62]. 2.3.3 Macromolecular encapsulation: ‘In-situ’ strategy. As shown schematically in Scheme 2C, NP precursors such as tetrachloroauric acid can be directly reduced by reducing agents (sodium borohydride) in the presence of pre-synthesized polymers, and directly form metal nanoparticles [52, 63, 64].
The most widely used polymer for coating inorganic nanoparticles is polyethylene glycol (PEG), because of the high colloidal stability of the resulting nanomaterials. For example Edwards et al. [64] synthesized stimuli-responsive nanoparticles using gold precursor and a disulfide functionalized copolymer made of random copolymers of oligo(ethylene glycol) methyl methacrylate (OEGMA) and 2-(2-methoxyethoxy) ethyl methacrylate (MEO2MA) in a one-step reduction in methanol. The resulting nanoparticles were 2-10nm in core diameter and exhibit long-term stability at room temperature in the presence of aqueous NaCl at concentrations as high as 0.15 M.
9
ACCEPTED MANUSCRIPT Benefits. This technique offers high flexibility since the polymer chains can be precisely tailored and their properties can be tuned prior to the coating process. Moreover it is a ‘one-pot’ method that eliminates the customary washing steps necessary in other techniques.
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Drawbacks. The inability to reach particle size above 10 nm and the high polydispersity limit the applicability of this method to functionalize nanoparticles.
Aggregation kinetics and colloidal stability: experimental methods
3.1
Overview
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3.
kinetic process as shown in equation (1): [65]
for 1 i
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i1
dC z 1 k j ,i1C j Ci1 kizCi Cz dt 2 j1 z1
(eq. 1)
for i 1
D
dCi k1,zCi Cz dt z1
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The rate of aggregation of monomeric nanoparticles into larger agglomerates can be represented as a
rate constant associated with aggregate formation, Ci and Cj are the concentration of aggregate or
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where Cz is the concentration of aggregates containing z-monomers, kij is the second-order aggregation
monomer where z > i, j, and kiz is the dissociation rate constant of aggregates of size z. For short times, the aggregation kinetics can be approximated by the rate of doublet formation, which dominated over other higher order aggregate formation: dC1 k11C12 k12C1C2 dt dC 2 1 k11C12 k12C1C2 dt 2
(eq. 2)
Here C1 and C2 are respectively the number concentrations of monomer and doublet particles and k11
and k12 are the forward and reverse rate constants. In case of irreversible association (i.e. no dissociation events), the increase in concentration of dimers is proportional to the product of the initial rate constant of aggregation, k11, and the square of the initial concentration of nanoparticle monomer, C0, simplifying equation (2):
10
ACCEPTED MANUSCRIPT dC2 1 dC1 1 k11C02 dt 2 dt 2
(eq. 3)
From equation (3) the instability ratio, W-1, under different solution conditions can be calculated by
the ratio of the rate constant for slow coagulation (unfavorable aggregation), (k11)slow to fast
11
slow
11
fast
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k k
(eq. 4)
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W 1
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(nonrepulsive) aggregation, (k11)fast:
The resulting values for the instability ratio (0≤W-1≤1) represents the probability of association resulting from the collision of two colloidal particles.
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The rate of aggregation, k11, of functionalized nanoparticles can be monitored using several experimental approaches. The most widely employed are optical methods such as turbidimetry, light
D
scattering (DLS, SLS), and fluorescence correlation spectroscopy (FCS). Each technique has its own
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advantages and disadvantages – no single technique is appropriate for all samples, especially under the
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conditions of low concentration, high polydispersity, or sample complexity. Principles of operation as well as the benefits and drawbacks of the above mentioned techniques are discussed in the following sections. 3.2
Spectral turbidimetry
For diluted solutions (volume fraction < 10-4) spectral turbidimetry can be used to determine the particle size distribution (PSD) of suspensions composed of submicronic and micronic particles. [66] Turbidity has been used in the past to study the aggregation state of metal nanoparticles [67-69], and nanoemulsions [70]. In general the turbidity of a colloidal suspension can be defined as: [71, 72]
Cz t z z1
(eq. 5)
where Cz is the number of aggregates of z particles per unit volume, and z is their total light scattering
cross section, which is dependent on the wavelength and on the ratio of the particle refractive index to
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ACCEPTED MANUSCRIPT the surrounding medium refractive index. In the small time limit (t0) the time evolution of a suspension due to aggregation can be achieved by differentiating equation (5): d dC dC 1 1 2 2 dt dt dt t0
(eq. 6)
(5) and (6), the aggregation rate can be deduced:
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Here 1 and 2 are the optical cross sections of a single particle and a doublet. Combining equation (2),
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d 1 2 1k11C 20 dt t0 2
(eq. 7)
and fast aggregation regimes:
W 1
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Then the instability ratio, W-1, can be obtained from the initial slope of the curve vs. time under slow
d dt d dt
slow
D
fast
(eq. 8)
than measurement of the intensity of light scattered at a particular angle. [73]
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Benefits. Turbidity measurements using the spectrophotometer are less sensitive to multiple scattering
Drawbacks. In order to interpret the experimental results, turbidity measurements require calculation of the optical properties (cross-section) of the aggregates involved in the process. Not suitable for very diluted suspensions. Both the aggregation process and aggregate-like interaction are dependent on the aggregates’ morphology. 3.3
Time resolved dynamic light scattering (TR-DLS)
Time resolved dynamic light scattering (TR-DLS) is the most common method to determine the aggregation kinetics of colloidal particles. [65] It has been used to study the aggregation behavior of a wide range of engineered nanomaterials including quantum dots [74], metal nanoparticles [75-79], carbon nanotubes [80, 81], and solid lipid nanoparticles [82]. In this technique, the temporal evolution of the intensity fluctuations due to the Brownian motion of colloidal particles is used to measure the translational diffusion coefficient of the particles in suspensions. The effective aggregate size is calculated from the diffusion coefficient, D, using the Stokes-Einstein equation.[83] The measured 12
ACCEPTED MANUSCRIPT hydrodynamic radius of a coagulation suspension is an average of the hydrodynamic radii of the individual aggregates, weighted by their scattered light intensities. According to the Rayleigh-GansDebey (RGD) approximation, which is valid for particles that are relatively small compared to the
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wavelength of the laser light,[65] the temporal evolution of the average hydrodynamic radius, (dRH/dt), of the system is given by:
1 R R
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H,2 H,1
(eq. 9)
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I q 1 dRH 2 k11C02 1 2I1 q RH,0 dt
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where I1(q) and I2(q) are the water vector q-dependent intensities of radiation scattered by monomers and dimers, respectively, RH,1 = f(RH,0) and RH,2 = 1.4f(RH,0) are the hydrodynamic radii of monomer and
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dimer, respectively, and RH,0 is the intitial monomeric nanoparticle radius. If dissociation events occur during the time of observation, however, k11 in equation (9) is replaced by
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16k113C02
R
2k21 4k11C0 k21 I 2 q I1 q
H,1
RH ,2
2
(eq. 10)
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K eff
D
the effective association constant, Keff: [84]
which is usually lower than the rate for an irreversible aggregation. By taking k12=0 limit of no
dissociation equation (10) correctly recovers the well-known result for the irreversible aggregation kinetics, i.e. Keff=k11.
From equation (9) the instability ratio, W-1, at different solution conditions is then calculated by dividing the slope obtained under slow coagulation over the slope obtained under fast (nonrepulsive) aggregation:
W 1
dR dR
H H
dt
dt
slow
(eq. 11)
fast
Benefits. The determination of k11 by TR-DLS has been validated numerous times in the literature [65,
78, 80, 85-90]. Using conventional instrumentation, for moderate sized particles (RH > 30nm), this method is suitable for dilute suspensions; i.e. substantially less than that required for turbidity
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ACCEPTED MANUSCRIPT measurements. When the most sensitive detectors are employed, this method can be applied to extremely dilute suspensions of even smaller particles. Drawbacks. DLS measurements are greatly biased by the presence of large aggregates or polydisperse
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solutions that can only be partially corrected by the algorithms of the DLS software. Both the aggregation process and aggregate-like interaction are dependent on aggregate morphology. At high
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electrolyte concentrations (high rate – fast regime) multiple scattering may occur which leads to a
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diffuse halo around the primary laser beam inside the cell and a reduced intercept of the autocorrelation
3.4
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function. Fluorescence correlation spectroscopy (FCS)
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In this approach, the particle/aggregate diffusion coefficient, D, is determined for fluorescently labeled particles passing through a laser-illuminated confocal volume (~1m3). Similar to DLS
D
technique, temporal fluctuations in the measured fluorescence intensity are used to derive an
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autocorrelation curve, which is related to the translational diffusion of the fluorophore through the
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confocal volume. [91, 92] FCS has been used to determine the diffusion coefficients and aggregation behavior of QDs, nTiO2, and nZnO. [93-96] Benefits. This is a single or near single particle detection technique that determines a weight-averaged D under the conditions of the experiment. This gives FCS an important advantage over several other techniques for determining particle size, because it is generally not necessary to increase particle concentration in order to improve the analytical signal.[97] Bias is much less important than in DLS and the technique is much better suited to small particles and very diluted suspensions. Drawbacks. Diffusion coefficients are determined by calibrating the size and shape of the confocal volume with a standard dye. Additionally, nanoparticles need to be fluorescently labeled. The single particle detection of colloidal particles is limited by their photophysical properties, such as fluorescence intermittency and blinking. Blinking is manifested as finite episodes of laser induced fluorescence followed abruptly by long periods where no light is emitted. The effect appears not only to slow diffusion but to increase the probability of the particle entering the probe volume. [98, 99] 14
ACCEPTED MANUSCRIPT 4. Theoretical models: a brief overview 4.1 Favorable (fast) and unfavorable (slow) aggregation rate Fast aggregation rate. Under the approximation of von Smoluchowski [100], i.e. steady-state
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diffusion of the colloidal particles in the absence of interparticle interaction, the rate constant for the dimer formation in the fast or ‘diffusion-limited’ aggregation is given by:
fast
8kBT 3
(eq. 12)
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11
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k
where kB is the Boltzman constant, T the absolute temperature, and is the viscosity of the medium. Reversible aggregration has been proposed by Zaccone [84] and others [87, 101-105] to account for
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experimental observations of fast aggregation rates, lower than Smoluchowski. Slow aggregation rate. Fuchs [106] provided a general expression for the slow or reaction-limited
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aggregation, considering (k11)slow as the flux of colloids in a force field around a central particle under
8kBT 3 f h
0
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kslow 2RH
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the influence of their mutual interactions:
h 2RH
T h
2
e
k BT
dh
h 2 h 6 13 2 RH RH f h h 2 h 6 4 RH RH
(eq. 13)
(eq. 14)
Here the interaction potential, (h), and the hydrodynamic retardation term [107], f(h), account for
the surface and viscous forces manifested between two spheres during mutual approach. Both terms are functions of the intersphere separation distance, h, and the particle size, RH.
15
ACCEPTED MANUSCRIPT 4.2 Theoretical instability ratio In using equation (13) for the instability ratio, however, the theoretical curve for W-1 as a function of
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the interaction energy is always lower than unity at low potentials, since the rapid rate of coagulation assumes that no attraction forces are in operation until the particles are in contact.
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To account for the attractive contribution to the interaction potential in rapid coagulation, and to
expression for the distance-dependent instability ratio: k BT
e
h 2R f h e h 2R 2
0
dh
H
T h
k BT
2
0
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W 1
A h
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f h
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enable comparison between theory and experiments, McGown and Parfitt [108] derived the following
dh
D
H
(eq. 15)
particles. So defined, the instability ratio approaches to unity when the repulsion is entirely absent and is
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where (h) is the attraction potential energy, which depends on the geometry of the colloidal
expected to be more in accord with experimental reality. Details on the calculation of the contributions to the total interaction potential are shown in Section 4.3. Approximations for the calculation of the theoretical stability ratio. The theoretical instability ratio defined in equation (15) can be rewritten in the form:
1
W 1 2 0 e
T s
k BT
(eq. 16)
ds
s 2
2
where s is the non-dimensional surface-to-surface distance defined by s=[(h/RH)-2], and (s) is the total
interparticle interaction energy. This relationship can be used to understand the behavior of the stability ratio with respect to the barrier against coagulation and to evaluate the physico-chemical properties of the dispersion. Because of the complexity of the interparticle interaction energy, the above task requires
16
ACCEPTED MANUSCRIPT numerical integration of equation (16). However, when the repulsion barrier is large, the expression for W-1 using asymptotic techniques can be expressed: 1 2k T 2 " B s T m
1
(eq. 17)
T s m
k BT e 2 s m 2 2
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W 1
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Here sm is the value of s corresponding to the maximum in and T" sm T s 2 evaluated at s=sm. Other models: Maxwell-Boltzmann approach.
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Recently, an approach based on the Maxwell-
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Boltzmann distribution coupled with DLVO theory has been developed to calculate the instability ratio of colloidal nanomaterials, including metal nanoparticles, polystyrene, carbon nanotubes, and graphite
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sheets.[109-111] Here we briefly summarize the main features of the model highlighting the main advantages with respect to the other approaches.
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This model considers the role of the binding energy, Eb=Emax-Emin, in aggregation kinetics and estimates the instability ratio W-1 as the ratio of the number of particles with kinetic energy exceeding
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Eb, N, to the total number of particles with kinetic energy ranging from zero to infinity, N: 3
W
1
NE b N0
v
m 2 mv 2 4 e 2kbT
2k b T
v dv
Eb
3
m 2 mv 2 4 0 2k T e b
v 2dv
2k b T
2
0
e E E1 2dE E
12
e E dE
(eq. 18)
Here, m is the molecular mass, kb is the Boltzmann constant, T is the absolute temperature, v is the
velocity of random motion, and E is the random kinetic energy of nanoparticles. Since the denominator is constant, equation 19 symplifies to:
W 1
N E e E E1 2dE b N
(eq. 19)
where accounts for the drag effect on the kinetic energy distribution of nanoparticles and other
discrepancies of the DLVO prediction. To apply the Maxwell-Boltzmann distribution, the dispersed NPs are assumed to be Brownian particles with an average kinetic energy of 3kbT/2 in dilute systems.
17
ACCEPTED MANUSCRIPT With respect to equation (15) the modified instability ratio calculated with this model better accounts for the nanoscale transport of nanoparticles, which is governed by both interaction energy and random Brownian diffusion.
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4.3 DLVO interaction potentials: core-shell systems The total potential energy of interaction, (h), is according to classic Derjaguin-Landau-Verwey-
Here we also include other contributions to the interaction
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electrostatic (electrostatic) interactions.
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Overbeek (DLVO) theory [112, 113] is the sum of the attractive Van der Waals (vdW) and repulsive
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potential, such as hydration (hydration) and osmotic (osmotic) forces:
h vdW h electrostatic h hydration h osmotic h
(eq. 20)
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A schematic of the DLVO interactions between two core-shell nanoparticles is shown in Scheme 3. Van der Waals potential. According to Vold and Vincent [114, 115] the van der Waals attraction
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potential for two identical nanoparticles of radius rcore coated with a homogenous polymer shell of thickness can be calculated as the sum of the contributions from the shell – shell interaction, shell –
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core interaction, and core – core interaction:
vdW h shellshell h corecore h coreshell h 2 2 h h 2 AW AS H ;1 AS AC H ;1 2r 2 2r 1 core core 12 h rcore h rcore AW AS AS AC H ; H ; 2r core rcore 2rcore 2 2rcore 2
(eq. 21)
where Ac, Aw, and As are the Hamaker constant for the particle core, water, and the particle shell and
H(x, y) is the unretarded geometrical function:
H x, y
x 2 xy x x y 2 2ln x 2 xy x x 2 xy x y x xy x y
(eq. 22)
In the case that the separation distance, h, is small compared to the particle radius, rcore, i.e. x<<1, the
unretarded geometrical function can be simplified to:
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ACCEPTED MANUSCRIPT
lim H x , y x 0
y
(eq. 23)
x 1 y
vdW
2 2 r rcore AS AC AW AS core h h 2 1 h rcore rcore 12 AS AC 4 AW AS h 2r core
(eq. 24)
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and equation (22) becomes:
of the surrounding solution, the interparticle attraction potential also varies. The swelling/deswelling
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When the polymer shell on the surface of a particle swells or deswells as a function of ionic strength
capacity of the surface layer or swelling ratio, , is defined as the ratio of the volumes of the unswollen
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(V0) and isotropical swollen (V) shell around a rigid core sphere:[116, 117]
3
(eq. 25)
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D
3 V0 rcore d 0 rcore 3 3 V rcore rcore
where rcore is the core radius, is the polymer shell thickness, and d0 is the expected layer thickness at the pseudocritical coagulation concentration of salt (i.e. when W-1≈1). The relationship between the shell
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thickess and salt concentration, =f(CNaCl), can be derived by combining the Flory theory [118] with the Donnan model [119] and it is found to depend on the ionization of the outer layer. An exhaustive study on the salt effect on the swelling of ionized nanomaterials can be found here [116, 120]. In the case of non-ionic stimulus-responsive nanoparticles we found the shell thickness depends on CNaCl, through a linear relation:
0 kS CNaCl
(eq. 26)
where 0 is the polymer size in the absence of salt (reference state) and ks is the salt sensitivity to the
dehydration. Analogously, the Hamaker constant of the outer layer, AS, can be defined as a function of the swelling ratio, , of the polymer:[103, 116]
19
ACCEPTED MANUSCRIPT
AS AP 1
AW
2
(eq. 27)
where AP is the Hamaker constant of the completely dehydrated (deswelled) polymer, and
AW=4.35x10-20J is the Hamaker constant for water. [121]
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Electrostatic potential. The electrostatic potential is a repulsive contribution approximated as the
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double layer potential, electrostatic; the following two forms are typically used depending on the value of
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RH:[83]
electrostatic
k T e h h 4 R Y B ; RH 5 e h 2RH
2 H 0 r
2
(eq. 28a)
(eq. 28b)
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electrostatic h 2RH 0 r02 ln 1e h ; RH 5
Here 0 and r are the permittivity of the free space and of the medium, respectively, and 0 is the surface potential approximated with the measured value of the zeta potential of the coated core shell
D
0 RkBT 1000e 2 NA ( 2CNaCl )
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1
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nanoparticle. The Debey lengthand Y are given by[83]:
8tanh 0r 0 4kBT
Y
1 1 2RH
R 1 tanh 2
H
(eq. 29a)
2
0 r
0
4kBT
(eq. 29b)
Hydration potential. The effect of hydration energy on the colloidal stabilization is a repulsive
potential that depends exponentially on the interlayer thickness. The empirical equation of repulsive hydration energy between two hydrophilic spheres with radius RH,0 can be written as:[121, 122]
hydration h RH,0 2 Phe
h
(eq. 30)
where is the characteristic decay length of this interaction, typically between 0.6 and 1.1 nm for 1:1
electrolytes,[121] and Ph is hydration pressure, which depends on the degree of hydration. Here, to account for differences in the hydration state of the core-shell nanoparticles, the hydration pressure is defined as:
20
ACCEPTED MANUSCRIPT Ph Ph,0 kB NATCNaCl
(eq. 31)
where Ph,0 is the hydration pressure in the absence of deswelling (no salt) and the second term represents the osmotic contribution to the hydration pressure. It can be seen from equation (31) that at
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high ionic strengths this contribution can be attractive. Calculation of the stability ratio, W-1. Once the attractive and the repulsive interaction potentials are
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known, equations (24), (28) and (30) can be substituted into equation (15). This allows the instability
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ratio to be expressed as a function of salt concentration, W-1=f(CNaCl).
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5. Core-shell composition and solution conditions: implication for colloidal stability 5.1 Effect of nanoparticle core
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Material properties such as particle size, morphology, and crystallinity are important parameters affecting nanoparticle stability. Quantitative relationships between NP composition and stability are
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imperative for understanding the potential risk of nanoparticles in the environment. The basis of the
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undesirable effects of NPs may stem from their chemical composition, size, surface charge, and shape. [123, 124]
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From a fundamental perspective, the particle composition most directly affects the interparticle potential via the Hamaker constant, AC, in equation (21). Figure 1 shows the impact of the variation of AC on the interparticle potential as a function of interparticle separation distance as calculated from equation (21) and the stability ratio as a function of ionic strength, i.e. concentration of aqueous sodium chloride as calculated using equations (15), (24), and (28a) for the stability ratio, interparticle van der Waals potential, and electrostatic potential respectively. Nanoparticle size, RH, also has a straightforward influence on stability. As a general rule smaller particles are more prone to aggregation than larger ones. Both van der Waals and electrostatic interparticle potentials fields have an explicit direct dependence on particle radius, hence a higher energy barrier is expected as particle size increases. This is shown in Figure 2.
21
ACCEPTED MANUSCRIPT Several experimental studies on the colloidal stability of functionalized nanoparticles have confirmed the theoretical expectations [76, 89, 125, 126]. In particular, Zhou and He found a direct correlation between the critical coagulation concentration, CCC, and the particle hydrodynamic radius, RH, for
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spherical TiO2 (anatase) and hematite nanoparticles, respectively [89, 125]. However, while the aggregation of spherical particles is well understood, the impact of shape and
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crystal structure on colloidal stability is relatively unknown. In literature there are only few studies that
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systematically evaluate the role of shape on nanoparticle aggregation [89, 127-130]. Mulhivil et al.
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[128] investigated the aggregation kinetics of thiolate capped CdSe nanoparticles with different size and shape and they found CCC increases with specific surface area, SA. Nanoparticles with high aspect
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ratio exhibit increased stability with respect to added electrolyte. A strong correlation between CCC and SA was also found by Zhou et al. [89] for the colloidal stability of rod-like TiO2 (rutile) nanoparticles in
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aqueous suspensions.
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Recently Afrooz et al. [129] studied the influence of shape on nanomaterials aggregation using poly-
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acrylic acid (PAA) coated on gold nanospheres (AuNSs) and nanorods (AuNRs) having similar size and electrical surface potential. Here, it was shown that AuNSs have higher aggregation propensity, i.e. a lower CCC, than AuNRs nanoparticles (CCCNS=50mM < CCCNR=250mM in NaCl aqueous suspensions). It was hypothesized that electrosteric interactions and physical packing hindrance are the key mechanisms for the shape effects on nanoparticle aggregation. Spherical colloids possess higher curvature compared to rod-like particles resulting in a relatively compressed polyelectrolyte layer for AuNSs compared to an extended brush-like layer for AuNRs. 5.2 Effect of surface chemistry Nanoparticle functionalization promotes colloidal stabilization in high ionic strength media because of steric and hydration repulsions [121, 122]. In particular covalent grafting, moreso than physical adsorption, enables achievement of stable suspension, due to the minimization of potential desorption from the particle surface. As discussed in Section 2.1 the wide variety of synthetic approaches to the formation of functionalized nanoparticles provides access to a wide range of nanomaterials with defined 22
ACCEPTED MANUSCRIPT charge density and surface coverage, and therefore nanoparticle stability. For some applications, covalent grafting of short chains is preferred over longer polymers in order to increase the exposure of reactive molecules on the surface particularly in drug delivery and sensing applications. In these
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systems, stimulus-responsive nanoparticles are quite interesting since they allow control over colloidal stability through external stimuli such as ionic strength, pH or temperature. Interestingly, nanoparticles
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modified with thick, densely packed brushes (obtained via grafting-from technique [131]) tend to show
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collapse, rather than colloidal aggregation upon heating above their lower critical solution temperature
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(LCST). Those with less densely packed brushes (obtained by using the grafting-to technique [51]) tend to colloidal aggregate following dehydration transition. [132] In the case of high grafting densities, the
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interactions between the particle cores are completely shielded by the macromolecular shell, and the entropy of the grafted chains soley dictates the dispersion state. On the contrary, at low grafting
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densities when the grafted chains are well separated on the nanoparticle surface, the core-core
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interactions between the nanoparticles will only be prevented very close to the grafting points. In this
systems.
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latter case, the particles will interact with each other as “patchy” attractive particles, leading to unstable
Similarly to surface coverage, an increase in the shell thickness (or molecular weight of the macromolecule) may enhance the stability of nanoparticles due to an increase of the energy barrier to aggregation [133-136]. Barrera et al. [134] studied the effect of polyethylene glycol (PEG) thickness on magnetite nanoparticle aggregation. Here it was demonstrated that particles modified with low molecular weight PEG (<1kDa) aggregate in high ionic strength media, however steric repulsion of high molecular weight PEG (>1kDa) prevents nanoparticle colloidal aggregation under the same conditions. Moreover, Liu et al. [135] found colloidal stability of gold functionalized with thiol-ended PEG depends on molecular weight, with longer PEG and larger PEG/NPs ratio being more effective in stabilizing nanoparticles in suspension. These observations are in accordance with DLVO theory, which predicts greater stability for lower shell to core size ratios, G=rcore/RH, because the van der Waals attraction, which is primarily driven by core-core interactions, is attenuated. Flory-Kirbraun theory [112] also 23
ACCEPTED MANUSCRIPT indicates that longer surface-bound ligands and higher ligand coverage will favor stability because of increased steric repulsion. The effect of polymer shell thickness on the total interaction potential and instability ratio is shown in Figure 3 for a typical core-shell nanoparticle system; the core size ratio, G,
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is varied while maintaining the surface potential, 0, the hydrodynamic radius, RH, and the Hamaker constants, AC and AS=AP constant.
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As shown in Figure 3B, the instability ratio predicts a lower value for the CCC as G increases, i.e. the
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nanoparticles become less stable against salt.
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While the effect of size and surface coverage on nanoparticle aggregation is well documented in literature, the impact of the outer shell conformation on colloidal stability is lacking. Systematic studies
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on the effect of heterogeneity and macromolecular conformation on the aggregation mechanism are published only recently by Huang [137] and Gillich [104], respectively.
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Huang et al. [137] reported the effect of surface heterogeneity on the colloidal stability of thiol-coated
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nanoparticles (NPs). Here, the gold NPs were modified by different distributions of ligands with
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charged and nonpolar terminals. In one case a homogeneous distribution of the two ligands was grafted on the gold surface, and in the other case charged and nonpolar terminals decorated in stripe patterns. Although the functionalized NP were similar in size, ligand composition, and surface charge density, the different surface organization of the functional groups resulted in different stability behavior. The critical coagulation concentration of orderly patterned ligands on the NP surface was higher than the CCC for gold nanoparticles grafted with a homogeneous distribution of ligands. This difference was attributed to the differences in the relative adsorption and hydration of counterions within the Stern layer and was supported by molecular dynamics (MD) simulations. [138] In silico, a hydrogen bond network can be developed in the nanoscale nonpolar stripes and the hydration shell may increase the interaction energy barrier thus enhancing the stability of gold nanoparticle decorated with patterned ligands in contrast to homogeneous surface functionalization.
This underscores the role of shell
hydration, , on the stabilization effect.
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ACCEPTED MANUSCRIPT Gillich et al. [104] synthesized superparamagnetic iron oxide nanoparticles (SPIONs) functionalized with poly(ethylene glycol) (PEG) and oligo(ethylene glycol) (OEG) polymers and compared the physicochemical properties of NPs stabilized with linear and dendritic macromolecules of similar
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molecular weight. They show polymeric interface architecture has significant impact on solubility, colloidal stability, and thermoresponsive behavior. Dendrite surface architechtures were found to confer
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superior colloidal stability as compared to linear PEG analogues. Moreover, for the same grafting
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density and molecular weight of the stabilizers, dendron-stabilized NPs show a reversible temperature-
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induced aggregation behavior, in contrast to irreversible aggregation observed for the linear PEG analogues. The significant difference in stability and colloidal phase behavior was attributed, in part, to
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differences in the hydration state of the shell.
The effect of polymer shell hydration on the total interaction potential and instability ratio is shown in
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Figure 4 for a typical core-shell nanoparticle system. The hydration state is parameterized by the
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swelling ratio of the shell, =V0/V, described in equation (25). In these calculations, the swelling ratio
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is varied while maintaining the surface potential, 0, the hydrodynamic radius, RH, and the Hamaker constants, AC and AP, constant.
In equation (25) and Figure 4B, it can be seen that as the shell becomes more hydrated, the swelling ratio decreases and the stability increases, as manifest by the increase in CCC. 5.3 Effect of solution condition
For the past decade or more researchers have often studied the effect various cations have on the stability of nanoparticle suspensions in an effort to predict the fate of nanoparticles in the environment.[139, 140] Electrolytes from the surrounding solution can have multiple effects on the stability of nanoparticle suspensions. Through adsorption onto particle surfaces or the shell polymers, anions of cations can directly influence the apparent surface potential. In many cases the adsorption of ions to nanoparticle surfaces results in the surface charge decrease. As the surface charge approaches the isoelectric point a transition from an unfavorable aggregation regime to a favorable one occurs.[141] Specific interactions through complexation of dissolved cations by adsorbed polymers will also result in 25
ACCEPTED MANUSCRIPT a transition of the surface charge to the IEP again resulting in transitions from unfavorable to favorable aggregation. [142] While alteration of surface potential can affect the stability of nanoparticle suspensions directly, an
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increase in ion concentrations in solution has an indirect effect on particle stability by increasing the
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screening of electrostatic interactions. Within the DLVO paradigm, the result is to decrease the barrier height to aggregation. As a first approximation it can be shown that the CCC for conventional systems
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is therefore proportional to z–6 where z is the charge of the background counter ion. This relationship is
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commonly referred to as the Shultze-Hardy rule and indicates that counterion valence is the primary driver of particle stability. [143] For suspensions of different functionalized nanoparticles many recent
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studies have shown the qualitative nature the relationship to be true.[144]
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Despite the Shultze-Hardy theory, experiments have nearly never shown scaling of the CCC by z-6.
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[77, 78, 145, 146] For unfunctionalized naturally occurring and engineered nanoparticles, this might be For
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a result of surface charge heterogeneities or differences in degree of ion hydration. [147]
functionalized nanoparticles, the result can be quite different owing to the direct interaction of counterions with the surface functionalities. Chen et al. showed apparent aggregation rates beyond the diffusion limitation when some divalent cations (Ca2+, Ba+2 and Sr+2) supported suspensions of alginate functionalized iron oxide nanoparticles but a similar effect was not observed with monovalent cations. [77, 78] In these cases, the alginate polymers formed strong complexes with divalent cations from solution resulting in an alginate network that captured the iron oxide nanoparticles as it was formed. In another system, naturally occurring bionanoparticles such as viruses were stable at concentrations of Na+ beyond 1M, but millimolar concentrations of Ca2+ resulted in virus aggregation. [148] This most likely resulted from Ca2+ complexation with the protein moieties that comprise the virus capsid that resulted in a loss of steric stabilization. For these extreme differences in CCC between mono and divalent cations, it has been important to look beyond the Shultze-Hardy rule to infer alternative mechanisms for aggregation.
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ACCEPTED MANUSCRIPT An alternative model of colloid stability that takes into account ion type and can explain the aggregation of even uncharged species could include a series of cations and anions that have been studied for their ability to precipitate (salt-out) proteins from solutions. The series of ions is commonly
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referred to as the Hofmeister series. For a sample of anions, the order, from highest salting out ability to highest salting-in ability, has been shown to be F-, PO43-, SO42-, CH3COO-, Cl-, Br-, I-, and CNS-. For
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cations, this order includes (CH3)4N+, (CH3)2NH2+, NH4+, K+, Na+, Cs+, Li+, Sr2+, Mg2+, Ca2+, and Ba2+.
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[149]
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The ordering described above is empirical only. Those ions with highest salting-out effects are referred to as kosmotropes. They are generally small ions with a high charge density. In solution these
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ions often leads to higher surface tension and a lower solubility of macromolecules or polymers. Chaotropes are ions with a small charge density and a high polarizability. The presence of these ions in
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solution often leads to enhanced macromolecular solubility, i.e. salting-in effects. At certain concentrations, this category of salts actually improves the solubility of molecules in solution instead of
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causing aggregation of particles. [150] Kosmotropes, being small and having a high charge density and therefore exert a strong electric fields at a short distances. The result is a competition for water molecules in the vicinity of polymer chains.
For strong kosmotropes polymers might be easily
dehydrated. The effect of polymer-ion interactions, and the relationship between structure-making and structure-breaking properties with salting-in and salting-out effects can potentially be explained through hydration forces. An overlap between a hydration zone of an ion and a hydration zone of a polymer leads to a force with both repulsive and attractive elements. The overlap in hydration zones will partially dehydrate both the ion and the polymer; an unfavorable process for the ion, leading to a repulsive force, but a favorable process for the polymer, leading to an attractive force between the ion and the polymer. Significant control over nanoparticle stability in solutions of widely different chemistries has been achieved by employing a rational approach to surface functionalization. This involves using small
27
ACCEPTED MANUSCRIPT moleculs, hydrogels, proteins, and stimuli-responsive polymers such as Poly(N-isopropylacrylamide), PNIPAM as surface functionalities. [84, 151, 152] Control of nanoparticle stability has conventionally been a binary process. That is, nanoparticle
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suspensions are either stable (monodisperse) or in their aggregated state. A novel mode of stabilization
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now employ stimulus responsive functionalities, in-situ switching of the polymer-solvent interaction via
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external stimuli such as pH, ionic strength, and temperature offers an opportunity to control aggregation state on a fine scale. In the case of thermoresponsive polymers increasing temperature above LCST
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causes macromolecular conformational changes, which decrease steric effects, leading to aggregation. Additional sensitivity to environmental conditions can be achieved via the addition of electrolytes, or
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variation of pH, which tune the desolvation of macromolecules or change the surface charge density,
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respectively.
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New approaches to creating surface functionalities take a rational design approach to the polymer
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coatings for inorganic nanoparticles in order to tune them to different external stimuli such as temperature [101, 153-155] and pH [156-158]. Thermoresponsive polymers such as PNIPAM are, perhaps, the most highly used of this group. [84, 155, 159] Nabzar et al. [155] were the first to study this class of nanoparticles by studying the behavior of styrene/N-isoppropylacrylamide and styrene/Nisopropylamide-co-aminoethyl methacrylate core-shell latexe nanoparticles.
Critical coagulation
concentrations (CCC) of these were determined below and above LCST=32o C. Their results showed that these particles displayed similar stability behavior above LCST of PNIPAM chains. Below LCST, the CCC values were much higher (indicating a greater degree of stability) due to the swelling of the polymer layer which impared great steric stabilization for these nanoparticles. The authors claim that the driving forces of the ionic hydrogel shell swelling are the solvent-PNIPAM and the segment-segment interactions ruled out by the Flory [160] interaction parameter, , which increases with increasing salinity of the medium and temperature, and the osmotic pressure due to charged groups. A swelling increase leads to a decrease of the shell Hamaker constant - see equation (27), an increase of the number
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ACCEPTED MANUSCRIPT of charged groups contributing to the diffuse layer potential and creates a non-DLVO additional stabilization term. When the temperature is increased above LCST, the PNIPAM surface layer shrinks as a consequence of an increase in the Flory parameter and hence provides a more favorable segment-
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segment contact.
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Lv et al. [159] prepared soft hydrogel nanoparticles with PNIPAM and characterize their temperature-
into larger aggregates.
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induced aggregation. Above LCST a fast association process was observed and the particles clustered Raising the temperature further caused their size to decrease due to the
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formation of hydrophobic shell layers accompanying the shrinkage of the PNIPAM chains with chain polar transformations, resulting in interparticle aggregation.
During the cooling process these
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contracted cores trapped in the aggregates gave rise to an early dissociation behavior.
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More recently Zaccone et al. [84] studied the reversible association of thermoresponsive silica
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nanoparticles coated with PNIPAM. By using a statistical mechanical analysis that account for dimer
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dissociation combined with light-scattering experiments, the authors developed a model to quantify the dissociation rate and the reversible association energy of core-shell nanoparticles as a function of temperature. They found the binding energy changes sharply near LCST of the PNIPAM chains, which they relate to the hydrophobic-hydrophilic transition of the thermoresponsive nanoparticles. While a novel initial approach to surface functionalization, PNIPAM is limited by only one critical solution temperature in water. For greater control of particle aggregation across a range of solution conditions, a more complex synthetic methodology is required.
Some approaches employ
copolymerization with, charged and/or uncharged monomers, pH-sensitive monomers or by the addition of hydrophilic/hydrophobic monomers such as acrylamide during polymerization.[161-163] Boyer et al. [164] exploited a combination of charged and neutral polymers to exert fine control of the surface charge imparted by the charged polymer component. In this study, a range of surface charges on gold NPs from-30 to +39 mV could be achieved. The surface-charges could also be modulated by
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ACCEPTED MANUSCRIPT solution temperature. The resulted from the use of a thermosensitive neutral polymer coassembled with charged polymers. Boyer et Witaker[154] employed a series of thermosensitive copoly(oligoethylene oxide) acrylates by the copolymerization of oligo(ethylene oxide) acrylate and di(ethylene oxide) ethyl
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ether acrylate. These materials exhibited a tunable LCST over a range of 15-90oC. The monomer composition was the variable controlling the LCST temperature. The copolymer-stabilizing layer was
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shown to resist non specific interactions with proteins most likely due to steric interactions. As a result,
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these materials could later be assessed for their use in biotechnology and medicine.
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One goal of experimentalists in this field is to develop functionalization schemes that will respond to
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varying stimuli. pH responsive materials represent another advancement in this field. Strozyk et al. [165] developed a thermosensitive polymer that exhibits pH-dependent thermo-responsive behavior.
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These materials exhibited an LCST of 42oC in water and around 37oC under physiological conditions In this configuration a smart pH-dependent
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and could be grafted to protein coated gold NPs.
thermosensitive behavior was exhibited. Chen et al. [166] developed a dual temperature and pH
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responsive functionalization from based on hyperbranched polyethylenimine (PEI) by grafting lphenylalanine. These materials showed phase transitions resulting from both pH and temperature changes, and the LCST could be modulated by changes in the phenylalanine grafting density, amidation and pH of solution.
6. Case study. Programmable aggregation kinetics of Au@MeO2MAx-co-OEGMAy NPs: effect of surface chemistry, ionic strength and temperature 6.1 Overview As an example, a case study is presented of a novel functional polymer used to modify gold nanoparticles. This system demonstrates the capability to control the equilibrium interactions between nanoparticles and the underlying kinetic processes controlling the physical state of the dispersion while simultaneously furnishing an opportunity to elaborate the interrelationships between solution chemistry, temperature, and the intrinsic properties of the macromolecular layer.
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ACCEPTED MANUSCRIPT Recently, a novel stimulus-responsive system was reported based on gold (Au) NPs grafted with polymer brushes consisting of disulfide-functionalized random copolymers of oligo(ethylene glycol) methyl methacrylate (OEGMA) and 2-(2-methoxy-ethoxy)ethyl methacrylate (MeO2MA), or
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Au@(MeO2MAx-co-OEGMAy).[167] As a result of the presence of the ethylene glycol moieties (y), NPs capped by these co-polymers are responsive to temperature and ionic strength in aqueous
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dispersion media. [168, 169] Specifically, it was shown that different copolymer compositions (x:y)
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induce variable degrees of stabilization that are characterized by different phase transition temperatures
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and interaction energies. However, each displays similar sensitivity to ionic strength and temperature. Although the effect of salt concentration and temperature on the stability of these NPs was well
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established [170], systematic quantification of the relevant physical parameters, such as critical salt concentrations, critical particle concentrations, and aggregation kinetics was only recently addressed.
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[87, 90] This case study serves to inform understanding of the complex balance of interactions
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responsible for controlling NPs stability in aqueous suspension and at fluid-fluid interfaces.
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A homologous series of Au@(MeO2MAx-co-OEGMAy) NPs was prepared by Scheme 2B using ligand exchange for 95:5 < x:y < 80:20. A schematic of the core-shell nanoparticle and the disulfide (DS) functionalized copolymers, DS-Poly(MeO2MAx-co-OEGMAy), are shown in Scheme 4. In all cases, the Au NPs core radius rcore≈7.5 nm. For all (x:y), the co-polymer grafts have similar molecular weight (20
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ACCEPTED MANUSCRIPT 6.2 Aggregation kinetics for Au@(MeO2MAx-co-OEGMAy) NPs The autoaggregation of thermoresponsive Au@(MeO2MAx-co-OEGMAy) NPs with 95:5<(x:y)<80:20 for 0.01 M
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(TR-DLS). Data shown in Figure 5 are at T=22oC. Experimental details are given in [90].
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To determine, k11, data in Figure 5A-C were analyzed using equation (9). Aggregation rate constants,
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k11, are reported in Figure 5D-F as a function of salt concentration. It can be seen that the aggregation rate increases with increasing salt concentration for all (x:y) homologues; the maximum rate constant in
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all cases 1.5x10-18 m3 s-1 < (k11)fast < 2.1x10-18 m3 s-1.
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6.3 Colloidal stability ratio and interparticle potential for Au@(MeO2MAx-co-OEGMAy) NPs By varying the solution conditions, such as the ionic strength, temperature, and the copolymer
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composition, the NPs stability (W-1) can be mapped. The inverse stability ratio, W-1, can be determined
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from the ratio of the experimental aggregation rate constant, k11, to the diffusion-limited aggregation
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rate constant, (k11)fast as defined by equation (4). In all cases the instability ratio increases with salt and the maximum achievable aggregation rate. However, changes in solution chemistry and temperature lead to differences in the stability curve. Unlike conventional mechanisms for aggregation which result from attractive van der Waals forces dominating over repulsive electrostatic forces as described by DLVO theory, the presence of salt in these NPs suspensions changes the affinity of the copolymer layer to water. This results in a partial dehydration of the swollen copolymer shell, leading to less hydrophilic systems, consequently decreasing the phase transition temperature, LCST.[171-175] As a consequence, hydrophobic interactions create attractive interactions between the NPs. When the temperature is increased above the LCST dehydration of the copolymer shell induces aggregation. The relationship between the external stimuli, i.e. temperature and salt concentration, for the transition point in the instability ratio, i.e. W-1 ~ 1, was parameterized previously [87] using:
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ACCEPTED MANUSCRIPT
T T0 x : y kS CNaCl
where T and T0 are the critical solution temperature in the presence and in the absence of salt, respectively, and kS is a measure of the effectiveness of a particular salt in modifying the stability of the
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dispersion. For each of these homologues, these parameters are summarized in Table 1.
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It was shown that the solution temperature required for the phase transition increases nearly linearly
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with the OEGMA (y) fraction of the copolymer, corresponding to the expectation ideality for the dilute
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(y) monomer. This was consistent with the qualitative finding of Lutz et al. [171] for Poly(MEO2MAxco-OEGMAy) aqueous dispersions.
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The experimental trends observed in Figure 5 are consistent with a change in the hydration state of the nanoparticle shell caused by increasing salt concentration. This change gives rise to an osmotic pressure
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that counterbalance the repulsive interaction due to the accumulation of water around the copolymer surface. As described in the theoretical Section 4, the osmotic pressure term to accounts for this difference in the hydration state in equation (31).
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(eq. 32)
Using equation (30), the decay length, , and the hydration pressure, Ph,0, were calculated using the data in Figure 6 D-F and equations (15), (24), (28) and (30), i.e. DLVO theory modified to include hydration/osmotic contributions; and PH,0 are reported in Table 1 for (x:y)=95:5, 90:10, and 80:20. These parameters are consistent with constant reported by other authors for colloidal systems in 1:1 electrolytes (h =3-30 mJm-2). [122, 176] 6.4 Summary Here the application of a unified experimental and theoretical approach to the characterization of functionalized nanoparticles was demonstrated. The aggregation kinetics of a homologous series of copolymer-functionalized nanoparticles was measured using Time Resolved Dynamic Light Scattering (TR-DLS). Using the theoretical framework outlined in Section 4, the fundamental parameters underpinning the aggregation rate and colloidal stability were extracted. The parameters provide
33
ACCEPTED MANUSCRIPT insight into the mechanisms governing interparticle interaction and inform synthetic approaches to achieving specified performance, particularly with respect to dispersion stability and the kinetics of destabilization. This demonstrates the utility of a unified approach in developing guiding principles for
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the rational design of new functional systems. 7. Closure
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This review highlights the state-of-the-art synthetic approaches to nanoparticle functionalization,
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experimental methods for determining suspension stability and the kinetics of aggregation, and
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theoretical models for experimental data reduction which consider the composition and structure of nanoparticle core, the surface chemistry and solution condition. A case study describing a novel
stimulus responsive polymer is included.
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8. Acknowledgements
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approach to exerting fine control over the aggregation state of gold nanoparticles functionalized with a
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Financial support from National Aeronautics and Space Administration (NASA)/Glenn Research
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Center (Particle Stabilized Emulsions and Foams, Award NNX10AV26G) in cooperation with the European Space Administration (ESA) through opportunity AO-2009-0813 and the Camille and Henry Dreyfus Foundation is acknowledged.
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ACCEPTED MANUSCRIPT Tables
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Table 1. Physical characteriztation of Au@(MeO2MAx-co-OEGMAy)
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ACCEPTED MANUSCRIPT Figure captions Scheme 1. Approaches for polymer brush attachment to create a core-shell nanoparticle: (A) physical (non-specific) adsorption, (B) ionic bonding, and (C) covalent grafting.
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Scheme 2. Polymer grafting approaches on nanoparticles: (A) ‘grafting from’ technique, (B) ‘grafting to’ technique, and (C) ‘in-situ’ technique.
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Scheme 3. Interactions between core-shell nanoparticles. Traditional forces for colloidal interactions
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(electrostatic, VdW) and other structural contributions (hydration and osmotic) that occur when particles are suspended in fluid media. Parameters used for DLVO calculations: two NPs with identical core
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radius rcore, and polymer shell thickness separated by a surface-to-surface distance h. The core-shell
Figure 1.
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radius is indicated as RH rcore .
Effect of the Hamaker constant of nanoparticle core, AC, on the colloidal stability of core-
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shell nanoparticles: 0=30mV, RH (=rcore)=20 nm, and AS=AP=7.5x10-20J: (—) Ac=5.0x10-20J; (– –)
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Ac=15.0x10-20J; (–·–) Ac=25.0x10-20J; (···) Ac=45.0x10-20J. (A) Total interaction potential T (W-1=0.5 or
function of CNaCl. Figure 2.
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CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a
Effect of the particle size, RH (=rcore), on the colloidal stability of core-shell
nanoparticles:0=30mV, Ac=5.0x10-19J and AS=AP=7.5x10-20J: (—) RH=10nm; (– –) RH=20nm; (–·–) RH=30nm; (···) RH=40nm. (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl. Figure 3.
Effect of the particle core-shell geometry, G=(rcore/RH), on the colloidal stability of core-
shell nanoparticles: (—) G=0.60; (– –) G=0.70; (–·–) G=0.80; (···) G=0.85;RH=20nm,0=45mV, Ac=5.0x10-19J and AS=AP=7.5x10-20J (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl.
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Figure 4. nanoparticles:
Effect of the shell hydration, =(V0/V), on the colloidal stability of core-shell (—)
=0.50; (– –) =0.60; (–·–)=0.70; (···)=1.0;RH=20nm,0=30mV,
Ac=4.0x10-19J and AP=9.0x10-20J (A) Total interaction potential T (W-1=0.5 or CNaCl=CCC) as a
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function of the dimensionless interparticle distance, h. (B) Instability ratio, W-1, as a function of CNaCl. Scheme 4. Thermoresponsive nanoparticles (NPs) obtained by grafting gold NPs with disulfide(DS)-Poly(MeO2MAx-co-OEGMAy):
Au@(MEO2MA95-co-OEGMA5);
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Figure 5. A-C. Aggregation kinetics of Au@(MeO2MAx-co-OEGMAy): hydrodynamic radius of Au@(MeO2MAx-co-OEGMAy) NPs as a function of time. The dashed lines represent the linear fit to
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1.3M (); CNaCl = 1.4M (); CNaCl = 1.6M (); CNaCl = 1.85M (). (C) Au@(MeO2MA80-co-
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Aggregation rate, k11, as a function of CNaCl for Au@(MeO2MAx-co-OEGMAy) NPs.
coagulation concentration, CCC, was determined at the intersection between the reaction-limited and diffusion-limited regimes (dash-dotted lines). (D) Au@(MeO2MA95-co-OEGMA5) NPs; (E) Au@(MeO2MA90-co-OEGMA10) NPs; (F) Au@(MeO2MA80-co-OEGMA20) NPs. Figure 6. A-C. Total interaction potential, T, versus separation distance, h, for Au@(MeO2MAx-coOEGMAy) NPs at CNaCl=CCC. (A) Au@(MeO2MA95-co-OEGMA5) NPs; (B) Au@(MeO2MA90-coOEGMA10) NPs; (C) Au@(MeO2MA80-co-OEGMA20) NPs. D-F. Instability ratio, W-1, as a function of CNaCl for Au@(MeO2MAx-co-OEGMAy) (symbols). The solid lines are the best fit to equations (15), (24), (28) and (30); i.e. extended DLVO with hydration/osmotic contributions. (D) Au@(MeO2MA95co-OEGMA5) NPs; (E) Au@(MeO2MA90-co-OEGMA10) NPs; (F) Au@(MeO2MA80-co-OEGMA20) NPs.
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We highlight synthetic approaches to nanoparticle functionalization, and experimental methods for determining suspension stability and the kinetics of aggregation. We discuss theoretical models to study interparticle potential and colloidal stability of core-shell nanoparticles, by varying the composition of nanoparticle core, the surface chemistry and solution conditions.
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HIGHLIGHTS Synthetic approaches to nanoparticle functionalization Experimental methods for aggregation kinetics characterization Theoretical frameworks for stability ratio calculation of core-shell particles Unified structure-property characterization using experimental platform and theoretical framework for rational nanoparticle design
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80:20 28100
'C, mV oP, nm“2 Rh,o
-5.9±0.4 0.61 23.40
-3.2±0.5 0.42 19.80
-5.2±0.3 0.34 20.00
G
0.33
0.39
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ks, M"
2.9±0.5
1.9±0.2
2.4±0.2
CCC, mM
870±50
1850±90
2400±400
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51.2±1.0 -11.9±0.7 0.57±0.04
-12.2±0.7 0.8±0.1
5.57±0.07
7.1±0.2
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o n 33.4±0.4 45.5±0.8 Salt effectiveness kT, °C M_1 -11.8±0.7 Hydration decay X, nm 0.68±0.02 length Hydration Ph,o, MPa 2.30±0.02 Pressure 2 Surface Hydration ithi0, mJ/m 1.56±0.06 Pressure Table 1. Physical characteriztation of Au@(MeO2MAx-co-OEGMAy)
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Copolymer molecular weight Zeta potential Grafting density Hydrodynamic radius (22 C) Shell aspect ratio rcore/RH,o Salt swelling sensitivity Critical coagualtion concentration Critical temperature o
(x:y) MW, gmol"1
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