Controlling the self-assembly of magnetic nanoparticles by competing dipolar and isotropic particle interactions

Accepted Manuscript Controlling the Self-Assembly of Magnetic Nanoparticles by Competing Dipolar and Isotropic Particle Interactions Manuela Hod, Celin Dobbrow, Mukanth Vaidyanathan, Debanjan Guin, Lhoussaine Belkoura, Reinhard Strey, Moshe Gottlieb, Annette M. Schmidt PII: DOI: Reference:

S0021-9797(14)00581-5 http://dx.doi.org/10.1016/j.jcis.2014.08.024 YJCIS 19759

To appear in:

Journal of Colloid and Interface Science

Received Date: Accepted Date:

30 April 2014 9 August 2014

Please cite this article as: M. Hod, C. Dobbrow, M. Vaidyanathan, D. Guin, L. Belkoura, R. Strey, M. Gottlieb, A.M. Schmidt, Controlling the Self-Assembly of Magnetic Nanoparticles by Competing Dipolar and Isotropic Particle Interactions, Journal of Colloid and Interface Science (2014), doi: http://dx.doi.org/10.1016/j.jcis. 2014.08.024

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Controlling the Self-Assembly of Magnetic Nanoparticles by Competing Dipolar and Isotropic Particle Interactions Manuela Hodb, Celin Dobbrowa,†, Mukanth Vaidyanathana,††, Debanjan Guina, Lhoussaine Belkouraa, Reinhard Streya, Moshe Gottliebb, Annette M. Schmidta,* a b

Department of Chemistry, Universität zu Köln, Luxemburger Str 116, D-50939 Köln, Germany Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

* tel. +49 221 470 5410, fax +49 221 470 5482, email [email protected] Control over the self-assembly of magnetic nanoparticles (MNP) into superstructures due to different types of coupling is of interest in the development of “bottom-up” fabrication schemes. Here we realize a simple strategy for the systematic variation of particle interaction potential in magnetic nanoparticles. This is achieved by varying the effective surface potential by means of a co-surfactant introduced in the course of the synthesis process. As a consequence, the ability to form chain-like assemblies is affected by the resulting balance of attractive and repulsive forces. We use electron microscopy, electron diffraction, and light scattering methods to study a series of cobalt nanoparticles as a characteristic example of ferromagnetic MNP. We demonstrate experimentally and substantiate theoretically that the observed behavior results from a balance between magnetic dipole-dipole, steric, and electrostatic interactions.

Introduction

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The “bottom-up” fabrication of complex structures by the selfassembly of simpler micro- or nano-scaled objects is an emerging pathway towards hierarchically organized, nano- or microstructured materials with unique anisotropic physical properties.1 The assembly occurs through non-covalent association due to specific interaction forces, and its control requires a detailed understanding of the different forces involved. While the formation of “colloidal molecules”, and the formation of two- and three-dimensional assemblies of microsized colloids is well-developed,2,3 it remains difficult to readily control the assembly of nanoparticles due to the strong van der Waals attraction and the impact of thermal fluctuations and collisions.4 Well-defined electrostatic interactions can lead to significant improvement towards achieving this goal.5 Predicted by de Gennes and Pincus,6 one-dimensional structures are accessible in the presence of dipolar (e. g. magnetic) interparticle forces. A large number of experimental and theoretical studies on ferromagnetic micro- and nanoparticles dispersions confirmed their predictions and improved the understanding of these systems.7–14 The resulting chain-like associations can readily be manipulated by means of external magnetic fields, and are of interest for the preparation of hybrid materials with uniaxial optical, magnetic or mechanical properties.15,16 Specifically, polymer coated single-domain ferromagnetic cobaltbased nanoparticles were shown to assemble into well-defined nanoscopic chains8,9 or rings17,18 under certain conditions, depending on the particle concentration, the strength of their dipolar interaction, the chain stiffness, and the thermal fluctuations of the particles. On the other hand, depending on the size of the particles, hexagonal superstructures are obtained when the dipolar forces are less dominating.19 A detailed understanding of the different forces involved is required if one desires to actively control nanostructure formation. Although dipolar interactions are dominant in the selfassembly process of magnetically blocked (ferromagnetic)

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nanoparticles, additional forces need to be considered. These might be attractive, such as van der Waals forces, or repulsive, such as steric or electrostatic interactions stemming from surfactants or polymers attached to the particle surface. The judicious selection of combinations of surfactants and/or polymers suitable for the specific particle composition, size, and shape, offers a pathway to the control of magnetic particles selfassembly. In the present study, we demonstrate how the combination of directed, dipolar interaction and isotropic, e.g. electrostatic repulsion of particles allows a gradual crossover from dynamic chain structures to individual particles via the occurrence of hexagonal patterns. While in previous experimental studies the resulting superstructures in diluted particle suspensions were addressed mainly by indirect methods such as electron microscopy or AFM on solidified (e.g. drop-casted) samples, information on the respective dynamic structures in fluid dispersions is scarce. The concern of this study is therefore the investigation of the respective equilibrium structures of dipolar particles in dispersion, and the systematic examination of the propertystructure relationship. In a recent communication,20 we reported on the preparation of ferromagnetic cobalt nanoparticles with gradually varying tendency for superstructure formation, depending on the ratio between two ligands present during the particle synthesis: carboxylic acid-terminal polystyrene (PS-COOH), and trioctylphosphine oxide (TOPO). The observations were mainly based on Transmission Electron Microscopy (TEM) of dropcasted samples, while preliminary experiments on liquid dispersions employing Dynamic Light Scattering (DLS) and Alternating Current (AC) susceptometry verified the selfassembly in the toluene-based particle dispersions as well. The systems are now systematically investigated by a combination of methods, including cryo-TEM, electron diffraction, Static Light Scattering (SLS), and DLS. The influence of the TOPO fraction on particle size and the core selfassembly is studied by TEM and dispersion-based methods. By careful correlation of the core size, hydrodynamic radius, and

magnetic properties to the evolving chain morphology and degree of order, we demonstrate the versatility of tailoring the structures by adjusting the synthetic conditions.

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Experimental Part 5

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Synthesis: While detailed procedures are given elsewhere,20 here we provide a succinct summary for the sake of completeness. All synthetic steps were performed under inert argon atmosphere. Carboxylic-acid terminated polystyrene (Mn = 6100 g·mol-1, Mw = 8200 g·mol-1 by SEC) was prepared by Atom Transfer Radical Polymerization (ATRP), using 1.0 g (6.1 mmol) αbromoisobutyric acid as the initiator, 0.9 g (6.3 mmol) Cu(I)Br / 1.8 g (11.6 mmol) 2,2-bipyridyl as the catalyst, and 60.0 ml (614 mmol) of styrene in 5 ml of DMF at 110 °C for 48 hours. The preparation of cobalt particles stabilized with carboxylic acid-telechelic PS-COOH and TOPO was performed by thermolysis of Co2(CO)8 in the presence of the stabilizers. Therefore, 0.80 g (2.30 mmol) of Co2(CO)8 is dissolved in 8.0 ml of dichlorobenzene (DCB) at ambient temperature, and the resulting solution is rapidly injected into a solution of 0.40 g (6.67 x 10−2 mmol) of carboxylic acid-telechelic polystyrene in 12 ml of DCB pre-heated to T = 180 °C in the presence of various amounts of TOPO (see Table 1). After 30 min of heating, the reaction mixture is cooled down to ambient temperature. The particles are washed several times with hexane and redispersed in toluene. The resulting black particle dispersions are highly stable against precipitation for several months. The sample denotation (Co-xTOPO) indicates the TOPO concentration during synthesis (x) expressed in mmol·L-1 (s. Table 1).

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Results and Discussion

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Table 1 Synthetic conditions and resulting grafting density of the (co)surfactants for Co@PS/TOPO nanoparticles employed in this study. sample

φTOPO

cTOPO

[mmol·L-1] [μmol·m-2] Co-0TOPO Co-6.3TOPO Co-12.7TOPO Co-25.4TOPO

0 6.3 12.7 25.4

0 0.80 2.20 4.77

[molec. ·nm-2] 0 0.48 1.32 2.87

φPS [μmol·m-2] 0.83 1.00 1.16 1.08

[molec. ·nm-2] 0.50 0.60 0.70 0.65

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cTOPO: concentration of TOPO during synthesis, φTOPO, φPS: grafting density of TOPO and PS-COOH, respectively

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Methods: Transmission Electron Microscopy (TEM) images and Selected Area Electron Diffraction (SAED) patterns were obtained with a Zeiss LEO 912 Omega electron microscope (Oberkochen, Germany), from samples prepared by drop-casting on a carbon-coated copper grid. The “measure IT” image analysis software (Olympus) was utilized to determine the core size and the chain length of the particles. At least 200 particles are measured for the size determination. Cryo-TEM images were obtained with a FEI T12 G2 dedicated cryogenic temperature transmission electron microscope. Toluene vitrification was achieved by immersing the toluene-based dispersion in liquid ethane at liquid nitrogen temperature using a perforated carbon grid. The vitrified specimen was subsequently loaded into either a Gatan 626 or an Oxford CT-3500 cryo-holder. Images were

recorded with a Gatan UltraScan 1000 bottom-mounted highresolution CCD camera, using the Gatan DigitalMicrograph software package. The electrophoretic mobility and zeta-potential experiments were performed by Laser-Doppler Anemometry on a Zetasizer Nano ZS (Malvern, UK) in toluene at 25 °C using a universal dip-cell for organic solvents. Dynamic Light Scattering was measured on the CGS-3 equipped with a LSE-5004 crosscorrelator (ALV, Germany) using clear glass vials (Aldrich). The scattering angle was varied from 30° to 90° by steps of 10° (scattering vector q from 0.00769 to 0.02101 nm-1). Reported values are the average of at least three measurements, each measurement consisting of 20 runs of 20 seconds each. Static Light Scattering (SLS) data were obtained with a CGS-3 with an automated goniometer, the scattering angle was varied from 20° to 150° by steps of 5° (scattering vector q from 0.00516 to 0.02357 nm-1). All scattering experiments were carried out in toluene at 25 °C at a wavelength of 632.8 nm. Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES) analyses on phosphorous in order to quantify the amount of incorporated TOPO were performed on an Agilent 700 series instrument. TGA experiments were carried out with a PerkinElmer STA 6000 between 25 °C and 600 °C, with a scan rate of 10 Kmin-1.

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The cobalt nanoparticles with gradually varied interaction potential are synthesized by thermal decomposition of Co2(CO)8 in the presence of carboxylic acid-telechelic polystyrene (PSCOOH) and TOPO, acting as co-surfactant. The concentration of the predominant steric stabilizer, PS-COOH with Mn = 6100 g·mol-1 and narrow molecular weight distribution, is kept constant in all preparations, while the concentration of TOPO is varied between batches, in order to investigate the self-assembly behaviour of the respective dispersions. As expected, the TOPO content as analyzed by ICP-OES increases significantly from 0 to 110 μmol·g-1 of cobalt, showing a linear increase of the surface concentration of the cosurfactant with its concentration during synthesis. The total organic fraction as analysed by TGA was constant at about 20 wt.-% for all samples, and the surface grafting density of the PS-COOH is about 0.6 ± 0.1 chains per nm2 for all samples (Table 1). Confirming our previous results,20 TEM images indicate an increase in the geometrical size of the highly contrasting particle cores from 17 nm to 30 nm with increasing TOPO content (Table 2). In addition, at low TOPO concentrations we predominantly find spherically shaped Co particles, whereas higher TOPO concentrations result in the formation of cubic particles (Figure 1 a-d or e-h). Puntes et al.21 reported a similar observation – increase in the size of Co nanorods with increase in TOPO concentration for a fixed concentration of an oleic acid cosurfactant. In addition to the effect of TOPO concentration on particle size and shape, TEM images also reveal a trend in the self-organization of the particles – a sharp decline in the tendency to form chains with increased TOPO concentration.

T Tablee 2 P Properties of C Co@P PS/TOPO O partticless andd theiir asssembblies synthhesizzed at diffferennt TO OPO cconccentraationns.

ζ

sam mple

dc [nm m]

mm [100-18 A A·m2]

[m mV]

q/m m [10-6 C C·g-1]

Dt [10-122 m2·ss-1]

Rh (Lh) [nnm]

Rg ((Lg) [nm m]

C Co-0T TOPO O Coo-6.33TOP PO Coo-12.77TOP PO Coo-25.44TOP PO

177.5 ± 0.9 222.4 ± 1.9 288.0 ± 1.3 299.4 ± 1.6

1.922 1.688 1.766 1.600

- 331.4 - 44.1 + 6.7 + 332.9

- 4.3 - 0.77 + 155 + 1335

66.31 ± 0.005 66.44 ± 0.005 77.13 ± 0.002 99.55 ± 0.005

62 ± 4 (4446 ± 29)) 61 ± 3 (3388 ± 20)) 55 ± 2 41 ± 2

86 ± 4 (2299 ± 15) 79 ± 3 (2272 ± 18) 61 ± 3 40 ± 1

cTOPO: conncentrration of TOP PO duuringg synnthesiis, dc: num mberr-averrage coree diam meterr as oobtained ffrom m TEM M im magess,20 mm: m magneetic m mom ment oobtainned ffrom m V VSM,20 ζ: peakk valuue off the zeta--poteentiall disttributtion, q/m:: chaarge-tto-maass raatio, Dt: ttransllationnal ddiffussion ccoeffficiennt (D DLS),, Rh oor Lh: hyddrodyynam mic raadiuss or cchainn lenggth reespecctiveely (oobtainned bby DL LS), Rg oor Lg: radiius off gyrrationn or cchainn lenggth reespecctiveely (oobtainned bby SL LS).

F Fig. 1 TEM M im magess (a – h, ddrop casteed onn am morphhous carboon; i – m, cryo-TE EM, vvitriffied ddispeersionns in toluuene) and electron diffrractioon paatternns (n - q) of C Co@P PS/T TOPO O parrticles from diiffereent prreparrationns (coloums). See Tab ble 1 for samplle deetails. 30

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A An iincreease in partticlee sizze iss geeneraally acccomppanieed bby aan inncreeasedd maagnetic m mom ment . Thhereffore an inncreeasedd conntribbutioon oof thhe atttracttive partticlee-parrticlee intteracctionns is exppecteed foor thhe laargeer paarticlles. Y Yet, we obseervee in tthe T TEM M im magess of the droppccasteed saamplles (F Figu ure 1 a-h h) loong cchainn forrmattion in thhe saample w with the smaallesst coore ssize (Co-0TO OPO O), aand nno cchainns foor thhe laargeest particcles (Co-25.44TO OPO)), whhichh exhhibitt an hexxagonnal oor

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sstatissticaal orgganizatioon of inddividdual partticles.20 IIn orrder to rulee outt thee poossibbilityy thaat thhese selff-orgganizzatioon ppatteerns are tthe rresullt off the sam mple prepparaationn metthodd forr TEM M imagging,, in particulaar thhe suurfacce ddepossitioon annd thhe inncrease in cconccentrrationn exxperiiencced ddurinng ddropp casstingg annd drrying, w we imagged bby ccryo--TEM M thhe diisperrsedd sam mplees inn vitrrifiedd toluenne. T The resuults ffrom m thee lattter techhniquue (F Figu ure 1 i––m) reprroducce

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q 3ε =ζ 2 m Rh ρ

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(1)

Here, Rh is the hydrodynamic radius of the translating object, ε is the permittivity of the medium, and ρ is the particle core mass density. Strictly speaking, equation 1 is only valid for spherical particles obeying Stokes’ law, and for the case of the chainforming systems Stokes law should be replaced by an appropriate relation for the drag on elongated objects. Yet qualitative trends will suffice for our purposes here thus, we replace the characteristic dimension of the elongated objects by L/2, half the chain length, recognizing the crudeness of the approximation. The following values have been used to obtain the results presented in Table 2: ε for toluene (2.11x10-11 F·m-1), ρfor cobalt (9.2 g·cm-3) and Rh (or L) from DLS measurements (s. discussion below). As shown in Figure 2, ζ changes sign from negative to positive with increasing TOPO concentration. The charge-per-mass ratio is of small negative value for Co-0TOPO, and increases to significant positive values with increasing TOPO concentration during synthesis. The observations are in accordance with the decreasing tendency for chain formation for samples with increasing q/m values (Table 2).

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Laser Doppler Anemometry using a dip-cell setup. For the noTOPO sample (Co-0TOPO) an unusually shallow and wide curve for the distribution of zeta-potential values was obtained, while the distribution becomes increasingly sharper and narrower with an increase in TOPO concentration (see ESI) for full zetapotential curves). The zeta-potential values (Table 2) that are extracted at the peak of the zeta potential distribution curve show a clear correlation with the increasing amount of TOPO and the decreasing tendency to form chains. By definition, the zetapotential value is associated with the effective potential at the “slipping plane” within the diffuse component of the electric double layer of the moving colloidal entity. The latter may correspond either to the individual diffusing particles (e.g. Co25.4TOPO), or to the bigger aggregates in the case of the chainforming samples (e.g. Co-0TOPO). As the zeta-potential is not independent of the object size, we calculate by means of equation 1 the charge-per-mass ratio q/m for all four samples in order to obtain a value for the relative surface charge of a single cobalt particle irrespective of its aggregation state .29

q/m / 10 C·g

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zeta-potential ζ / mV

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the observations from the drop-casted samples. The results confirm that the observed self-organization structures are the manifestation of the intrinsic particle properties, indicating they are of dynamic nature caused by an equilibrium between the inter-particle forces. Thus, it follows that in the case of Co-0TOPO, the dominant dipole-dipole forces lead to strong attractive interactions which in turn, result in the formation of long chains. These attractive forces are counteracted by a repulsive force emanating from the charge injection by addition of TOPO. At low TOPO content the equilibrium is slightly shifted resulting in the observed short chains whereas at high TOPO concentrations (Co-25.4TOPO) the repulsive forces overcome the attractive dipolar interactions. In search of a more detailed analysis of the observed behaviour, we present an estimate for the attractive and repulsive interaction forces between the particles. The attractive interactions result predominantly from the permanent magnetic dipole moment of the ferromagnetic particles, which is of axial nature. These are balanced by the stabilizing repulsive interactions that originate from i) the steric stabilization layer consisting of the PS-COOH surfactant on each particle, and ii) the TOPO coordinating stabilizer. Since the molar mass and the grafting density of the sterically dominating PS-COOH surfactant are similar for all samples, it is reasonable to conclude that the steric repulsion by the polymer is not responsible for the observed differences in self-assembled structures. While the contour length of a TOPO layer is about 1 nm,22 the thickness of a grafted PS-COOH layer can be estimated according to the blob-based model of Biver23 for polymer brushes on curved surfaces as approximately 8 – 10 nm. In the present study, shorter intrachain inter-particles distances are observed for Co-0TOPO and Co-6.4TOPO, indicating a deformation of the polymer layer under influence of the dipolar attraction. The obvious increase in repulsive interactions is thus related to the influence of TOPO. The goal of the present study is to investigate the role of TOPO in the self-assembly behaviour in more detail. It has been reported that TOPO is a reversibly coordinating ligand with donor properties, and can affect the particle size.24–26 Furthermore, the presence of TOPO is presumed to lead to the evolution of positive charge density on the particle surface by partial charge transfer to the particle bulk, resulting in the development of electrostatic repulsion.27,28 Considering the rather low ionic strength and the long range of the electrostatic repulsion in the organic medium with a low dielectric constant, in the present case the effect can be expected to be significant. Thus, a non-directional repulsive potential resulting from such partial charge separation may add to the steric repulsion stemming from the polymer, and can be associated with the decreased tendency for chain formation with increasing TOPO concentration. In order to support this hypothesis, the particles are investigated with respect to their zeta-potential, and its relation to the selfassembled structure formation that is further investigated by means of static and dynamic light scattering techniques. The electrophoretic mobility and the related zeta-potential ζ,29 provide an indication of the magnitude of the surface charges on the cobalt particles. Respective experiments were performed on diluted toluene-based particle dispersions (1.8x10-3 wt.-%) by

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15 20 -1 cTOPO / mmol·L

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Fig. 2 Experimental peak values of the zeta-potential ζ(filled squares) and charge-per-mass ratio q/m (open spheres) as function of TOPO concentration for Co@PS/TOPO particles. Best fit lines are drawn to emphasize the trends.

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Rg =

While the geometric core size is found to increase with the amount of TOPO (dc values in Table 2), magnetometry experiments20 show minor changes in the magnetic moment (mm values in Table 2). This raises the possibility that the addition of TOPO induces variations in the crystallinity of the particles. For this reason, information on the crystalline nature of the particles was obtained by means of Selected Area Electron Diffraction (SAED) (Figure 1 n-q). Comparison between the experimental d-spacing ratios (Table 3) and literature data,30 clearly proves that fcc crystalline cobalt is the dominant phase in all four particle samples. However, significant decrease in the sharpness and brightness of the reflection rings with the increase in content of the co-surfactant is observed. The decrease in the amount of crystallinity with increasing amount of TOPO serves to explain the minor change in magnetic moment despite the increase in particle size discussed above and the reported decrease in the saturation magnetization with increased particle size. No indication is found for the presence of a crystalline CoO phase neither in X-ray diffraction nor in electron diffraction experiments.

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CoCoCoCo0TOPO 6.3TOPO 12.7TOPO 25.4TOPO 1.16 1.14 1.16 1.19 1.17 1.19 1.17 1.40 1.41 1.40 1.40 1.63 1.61 1.62 1.95 1.90 1.92 -

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−

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lit.30 1.15 1.17 1.41 1.63 1.91

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( qR g ) 2 3

for qRg<1

(3)

For the chain-like structures (Co-0TOPO, Co-6.3TOPO) the chain length may be estimated from equation 3 by approximating the chain to a rod with diameter dc , the core diameter obtained by TEM (Table 2). The cylinder diameter may also be obtained from the Guinier plot at medium q range.31–33 A different procedure which, in principle, is not limited by q values may be used for the estimation of the chain length: the measured form factor S(q), is fitted to an expression for the scattering from a rod of length L31–33

( )⎤⎥

In order to get a better insight into the dynamic nature of the chain formation and the structures present in dispersion, we perform static (SLS) and dynamic light scattering (DLS) experiments on particle dispersions in toluene. Light scattering experiments for magnetic nanoparticles are scarce due to their high absorption, and in order to reduce this effect measurements are carried out at very low sample concentrations (~ 3 x 10-3 wt.%). The radius of gyration Rg of the dispersed nanostructures is obtained by analysis of SLS results. The particle concentration in toluene (2.8 x 10-3 wt.-%) and temperature (25 °C) are kept constant for all samples. The radius of gyration Rg , is determined from the Guinier approximation: 31–33

I ( q ) = I ( 0) ⋅ e

L2 d 2 + 12 8

x ⎡ sin x 2 sin u 2 S (q ) = ∫ du − ⎢ x0 u ⎢ x 2 ⎣

Table 3 Experimental d-spacing ratios from SAED patterns for Co@PS/TOPO particles in comparison with literature values. ratio of lattice planes [111]:[200] [220]:[311] [200]:[220] [111]:[220] [111]:[311]

aggregation number in line with the structures imaged by the different microscopy techniques. For rod-like objects, Rg is related to the rod length L and its diameter d by

(2)

where I(q) is the measured scattered intensity at scattering angle θ or scattering vector q = (4πn/λ)sin(θ/2) , n is the refractive index of toluene (1.496), and λ the wave length of the light source (632.8 nm). The resulting values (Table 2) show that with increasing concentration of TOPO, the radius of gyration Rg decreases, indicating that the scattering structures decrease in size and in

(4)

with x = qL. For Co-6.3TOPO there is a good agreement between the values obtained by the Guinier and by the form factor analyses (10% difference), a good fit of the form factor to the data, and the value for the cylinder diameter obtained by the midq Guinier plot (30 ± 6 nm) is close to the value estimated from TEM images (22.4 nm). This is taken as an indication of the validity of the approximation of these short chains (< 12 particles) by a short cylinder. In contrast, the best fit function for the form factor deviates considerably from the scattering data for Co-0TOPO samples at q values only marginally above Rg, the length obtained by the Guinier analysis is 30 % higher than that obtained from the form factor, and the cylinder diameter obtained by the mid-range Guinier plot (76 ± 4 nm) is very different from the value estimated from TEM images (17.5 nm). Thus, a cylindrical rod is too crude an approximation for the long flexible chains encountered in Co-0TOPO to properly represent its scattering behaviour. The DLS experiments were carried out at identical concentration in toluene for all samples. The translational diffusion coefficients Dt (or Deff the effective diffusion coefficient in case of elongated objects) are extracted from Γ(=Dq2), the reciprocal characteristic decay time of the autocorrelation function by an appropriate fitting method: the Schulz equation is applied to the data of Co-0TOPO, and a stretched single exponential fit to all the other samples. The translational diffusion coefficient increases with increasing positive surface charge (Table 2), indicating that the diffusing objects are smaller, in agreement with SLS results and cryo-TEM observations. For the case of non-interacting spherical particles in a dilute solution, the hydrodynamic radius Rh is obtained from the Stokes-Einstein relation

Rh = 95

⎥ ⎦

2

kBT 6πηDt

(5)

where kB is the Boltzmann constant, T is the absolute temperature (298 K), and ηis the viscosity of the medium (toluene, η= 0.556

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mPa·s). The hydrodynamic radii thus obtained (55 ± 2 nm and 41 ± 2 nm for Co-12.7TOPO and Co-25.4TOPO respectively) are in line with the Rg values from SLS. The dimensions of the chainlike structures (samples Co-6.3TOPO and Co-0TOPO) are extracted from the measured effective diffusion coefficient Deff by means of the Maeda-Fujime model (equation 6).34 The linear aggregates are approximated by a thin rod for which the different translational (D= parallel and D┴ normal to the rod axis) and rotational (Dr) diffusive motions are coupled.

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(6)

qL ⎤ L2 qL ⎡1 Deff = D − ΔD ⎢ − f 2 ⎛⎜ ⎞⎟⎥ + Dr f1 ⎛⎜ ⎞⎟ 3 2 12 ⎝ ⎠⎦ ⎝ 2⎠ ⎣ D=

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1 2 D = + D⊥ 3 3

ΔD = D= − D⊥

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The expressions for f1(qL/2) and f2(qL/2) are given in ref. 34, and the values for D=, D┴, and Dr are calculated as described by Tirado et al.35,36 A summary of the particle dimensions obtained by SLS and DLS is presented in Figure 3. The theoretical values for Rg/Rh are 0.78 for a sphere and 1.8 for a rod. The values measured here for Rg/Rh increase monotonically from 1.0 for Co25.4TOPO to 1.4 for Co-0TOPO, in agreement with the observed images: decreasing amount of TOPO results in formation of not well-defined chains of increasing size and complexity. Summarizing the observations from the different analytical approaches, the results indicate that the contribution of TOPO to the observed structure formation is threefold: while the fcc Co cores grow larger in the presence of TOPO during synthesis, this does not necessarily result in a higher magnetic moment of the core – but rather, it seems to result in the formation of a defect cobalt phase with reduced crystallinity. In addition, the presence of coordinating TOPO on the particle surface leads to a net surface charge as indicated by the zeta potential. The resulting electrostatic repulsion is hardly screened by ions in the medium, as the ionic strength in the organic, toluene based dispersion is expected to be quite low.

Rh; Rg; Lh; Lg / nm

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Fig. 3 Particle size from static and dynamic light scattering results of Co@PS/TOPO. DLS - Rh and Lh (open circles and open triangles, respectively) are plotted; SLS- Rg and Lg; (filled circles and filled triangles, respectively).

For the present particle systems, the interaction potential resulting from the different attractive and repulsive contributions is approximated by an addition ansatz in analogy to the DLVO theory.37 The model is based on an ensemble of monodisperse, core-shell magnetic nanoparticles for which the attractive forces are dominated by the magnetic dipole-dipole attraction. The repulsive forces stem from a combination of electrostatic interaction from the surface charge, and a steric repulsion from the polymer shell. We assume van-der-Waals attraction and all hydrodynamic effects may be safely neglected in view of the dominant magnetic dipole interaction, For the calculation of the magnetic dipolar interaction potential, the volume-average magnetic moment mm as obtained by Vibrating Sample Magnetometry (Table 2) is expected to be the most relevant observable, and thus, is used for the calculation of the potential.20 Furthermore, we assume that the particles behave as permanent dipoles, and that thermal remagnetization by spin reversal does not play a significant role. Due to the dipolar character of the interaction, the potential is orientation dependent. Here we use the expression valid for point dipoles in their most effective relative orientation, i. e. when they are in a head-to-tail configuration, as this configuration results most effectively in the formation of chains, and thus is relevant at short particle distances.38 μ mm2 (7) ⋅ Vmag (r ) = 2π r 3 -6 Here, r is the center-to-center distance, and μ= 1.2566 x 10 N·A2 is the magnetic permeability of the medium toluene. In agreement with the experimental results, the repulsive contribution can be assumed to be composed of a combination of a) the inorganic core, described by a hard sphere potential, b) an organic/polymeric layer (soft sphere contribution), and c) a contribution of the electrostatic surface potential. We account for the steric contribution (a and b) with a potential of the form39

500

Vster (r ) = ∞

400

Vster (r ) =

300 75

100 50 0

0

5

10 15 20 -1 cTOPO / mmol·L

80

25

6

for r < dc

(8)

λ

(r d )n −1

for r ≥ dc

The most relevant observable in this potential is the diameter dc of the inorganic core (Table 2). The parameters λ and n are the interaction strength and the repulsive index, respectively, and are taken as λ = 10 kBT and n = 12 in accordance with a soft steric repulsion in the range of a few nanometers.40

0

2 0 -2

20

40 60 distance r / nm

-25 0

80

25

2 c

35

40 60 distance r / nm

80

the chain formation observed for Co-0TOPO and Co-6.3TOPO.

Conclusion

(9) 45

with ε: permittivity of toluene (2.11x10-11 F·m-1), z: ion charge, e: electron charge, κ: Debye length. The effective zeta-potential ζp of a single particle is not accessible experimentally, and is instead estimated from equation 1.29 The latter depends on the dielectric constant of the medium and the ionic strength, and can thus be assumed to be low in the present system. In correspondence with other weakly charged particulate systems in organic media under virtually salt-free conditions, we assume a value for κR = 0.2, (R = dc/2) thus corresponding to a long-ranged electrostatic repulsion potential as a result of the low ionic strength in organic media (dashed lines in Figure 4).41,42 The resulting potential profiles obtained by the addition of these main contributions (solid lines in Figure 4) are in qualitative agreement with the experimental results and can be used as a reasonable explanation for the observed trends in chain formation. Vtot (r ) = Vmag (r ) + Vster (r ) + Vel (r )

30

40

2

⎛ k T ⎞ d ⎛ zeζ p ⎞ −κ ( r − d c ) ⎟⎟ e Vel (r ) = 4πε ⎜ B ⎟ ⋅ ⎜⎜ ⎝ ze ⎠ r ⎝ k BT ⎠ 2

20

20

Fig. 4 Approximation of the nanoparticle interaction potential for Co@PS/TOPO samples. a) Exemplary presentation of electrostatic (Vel(r), dashed line), steric (Vster(r), dotted), and magnetic (Vmag(r), dash-dotted) contributions, and resulting total interaction potential Vtot(r) (solid line) for Co-12.7TOPO; b) Vel(r) (dashed lines) and Vtot(r) (solid lines) for Co-0TOPO (blue), Co-6.3TOPO (green); Co-12.7TOPO (red), and Co-25.4TOPO (dark cyan). All potentials are given in units of kBT.

The electrostatic repulsion is accounted for by applying the Poisson-Boltzmann equation to spherical colloids of diameter dc, and using the Debye-Hückel approximation for weakly charged particles:

15

-10

-20 0

10

-5

-15

-4

5

ď

5

Vel; Vtot

Vmag; Vster; Vel; Vtot

10

Ă

4

50

55

60

In this work we investigated the interplay between attractive and repulsive forces in relation to the self-assembly and superstructure formation of ferromagnetic particles. The synthesis of Co particles is performed by thermolysis of Co2(CO)8 in the presence of micellar carboxylic acid-telechelic polystyrene and TOPO. The self-assembly of PS decorated Co-based magnetic nanoparticles is strongly influenced by the presence of TOPO as co-stabilizer with respect to their interaction potential in dispersion. By TEM and cryo-TEM imaging we observe that the synthesis of particles in the absence of TOPO leads to small, spherical particles, with a clear preference for chain formation. With increasing TOPO amount, hexagonal or even random organization is observed. The effect is attributed to the presence of strong attractive dipole-dipole forces leading to the chain formation, while the incorporation of TOPO leads to a net surface charge resulting in an electrostatic repulsive interaction between neighbouring particles. These charges are analyzed by means of zeta-potential measurements. While cryo-TEM and SLS confirm the presence of these structures in toluene-based particle dispersions, the dynamic properties of the chain forming particles are investigated with dynamic light scattering DLS, and they are in good correspondence with expectations for diffusing chains.

(10)

While the potential of Co-0TOPO shows a distinct minimum of several kBT, the minimum is less pronounced for Co-6.3TOPO. Both minima are located at a center-to center distance that is close to the core diameter dc, meaning that the surface-to-surface distance for the energetic minimum is just a few nanometers. Here, the magnetic interactions are dominating, and the strong orientational forces result in the formation of chains. In contrast, no pronounced attractive energy sink is observed for the systems with the highest surface charge, Co-12.7TOPO and Co-25.4TOPO. At a center-to-center distance of about 40 nm, the magnetic interaction does not play a significant role, and a random particle arrangement is found in cryo-TEM, rather than

Acknowledgements 65

We thank Prof. Y. Talmon and Ms. J. Schmidt for the cryo-TEM images. For financing, DFG (Emmy Noether-Programm, A. S.), NanoSciE+ (A. S., M. G.), and DAAD (WISE program, M. V.) are acknowledged.

Notes and References 70

7

a Institut für Physikalische Chemie, Department Chemie, Universität zu Köln, Luxemburger Str. 116, D-50939 Köln, Germany. Fax: +49 221 4705482; Tel: +49 221 470 5410; E-mail:[email protected] b Chemical Engineering Department, Ben Gurion University, Beer Sheva 84105 Israel.

22.

† present address: Daimler AG, Rather Str. 51, D-40476 Düsseldorf, Germany. ††present address: Department of Nanoengineering, University of California at San Diego, 9500, Gilman Drive, La Jolla, CA-92093, USA.

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*3: Graphical Abstract (for review)

Controlling the Self-Assembly of Magnetic Nanoparticles by Competing Dipolar and Isotropic Particle Interactions Manuela Hodb, Celin Dobbrowa,†, Mukanth Vaidyanathana,††, Debanjan Guina, Lhoussaine Belkouraa, Reinhard Streya, Moshe Gottliebb, Annette M. Schmidta,* a b

Department of Chemistry, Universität zu Köln, Luxemburger Str 116, D-50939 Köln, Germany Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

* tel. +49 221 470 5410, fax +49 221 470 5482, email [email protected]

Graphical Abstract

*Highlights (for review)

Controlling the Self-Assembly of Magnetic Nanoparticles by Competing Dipolar and Isotropic Particle Interactions Manuela Hodb, Celin Dobbrowa,†, Mukanth Vaidyanathana,††, Debanjan Guina, Lhoussaine Belkouraa, Reinhard Streya, Moshe Gottliebb, Annette M. Schmidta,* a b

Department of Chemistry, Universität zu Köln, Luxemburger Str 116, D-50939 Köln, Germany Chemical Engineering Department, Ben Gurion University of the Negev, Beer Sheva 84105, Israel

* tel. +49 221 470 5410, fax +49 221 470 5482, email [email protected]

Highlights (mandatory) x x

We investigate the superstructure formation of ferromagnetic cobalt nanoparticles. An interplay of attractive/repulsive forces is observed by combined analytical methods.

x

Dominant dipolar forces are counteracted by a repulsive force in the presence of TOPO.

x

Potential profiles are in agreement with the experimental trends in chain formation.