Reduced colloidal repulsion imparted by adsorbed polymer of particle dimensions

Journal of Colloid and Interface Science 349 (2010) 134–141

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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis

Reduced colloidal repulsion imparted by adsorbed polymer of particle dimensions Yu Ho Wen, Po-Chang Lin, Chun Yi Lee, Chi Chung Hua *, Tai-Chou Lee ** Department of Chemical Engineering, National Chung Cheng University, Chia Yi 62102, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 8 March 2010 Accepted 20 May 2010 Available online 26 May 2010 Keywords: Colloidal interactions Structure factor Polymer bridging Coated colloid Small-angle X-ray scattering

a b s t r a c t This work investigated the detailed interparticle interactions in a concentrated polymer-coated colloidal system in which the bare colloidal particles and the adsorbed polymers are of comparable size and, hence, the polymer adsorption cannot be foreseen to induce repulsive or attractive interactions. Specifically, poly(ethylene oxide) (PEO) chains (Rg  10 nm) adsorbed onto fine silica colloidal particles (SAXS-determined radius 7.4 nm; width of log-normal size distribution 0.28) were considered as a model system, for which the impact of a small amount of polymer adsorption (6 0:18 mg=m2 ) in controlling the interactions of the PEO-coated silica particles was systematically explored by analyzing the small-angle X-ray scattering (SAXS) data against three interaction potentials—the equivalent hard-sphere (EHS) potential, the Hayter–Penfold–Yukawa (HPY) potential, and the square-well (SW) potential. Moreover, the SAXS analysis was enforced by dynamic light scattering (DLS) for predetermining the adsorption behavior, as well as for evaluating the possibility of polymer bridging. Under a dilute condition, the DLS analysis showed no sign of forming colloidal multiplets. In concentrated dispersions, both the HPY and SW potentials clearly revealed a systematic decrease of colloidal repulsions with increased PEO coverage, ascribed to a partially ‘‘screened” electrostatic interaction and/or the formation of PEO-bridged silica doublets. The present findings have interesting implications for controlling the colloidal interactions and microstructures of fine polymer-coated particles in dense or condensed phases. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction Colloidal dispersions consisting of bare or polymer-coated colloidal particles are widely used in technological applications including coating, medication, biotechnology, and photography [1–3]. Understanding the fundamental particle interactions is crucial for the purpose of stabilizing a colloidal dispersion, controlling the rheological properties [4], or regulating the microstructures in their dense or condensed phases [5,6]. It has been well known that a large amount of adsorbed or grafted polymers on colloidal surfaces may act as a steric barrier to prevent colloidal flocculation [1–3,7], or they may serve as a medium to fine-tune colloidal attractions via changes in the system temperature or the so-called solvent quality for the adsorbed polymer [8,9]. Thus, depending on the objectives of a particular application, adsorbed polymers may be utilized to control colloidal interactions in a concentrated dispersion and its later condensed phases. In the literature, there have been plenty amounts of work investigating the modified colloidal interactions due to a small amount of polymer adsorbed onto nanometric colloidal particles in dilute or semidilute dispersions. For such fine colloidal particles, a large * Corresponding author. Fax: +886 5 2721206. ** Corresponding author. Fax: +886 5 2721206. E-mail addresses: [email protected] (C.C. Hua), [email protected] (T.-C. Lee). 0021-9797/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2010.05.071

amount of polymer adsorption is hampered by insufficient surface area to firmly grasp the dangling chains. Thus, the thin (and possibly loose) polymer layer atop the core particle typically did not play the roles as often noted for large colloidal particles, as introduced above. For instance, if the unsaturated polymer layers effectively extend beyond the range of electrostatic forces, each polymer chain may collect several particles at one time. This long-range bridging creates apparent interparticle attractions and causes particle flocculation. Bridging of fine particles by adsorbed polymers has been investigated extensively by optical or rheological experiments [10–17]. Theoretical analyses have also been carried out using scaling theories [18–21], especially for colloidal systems in which the polymer coil size is substantially greater than the bare particle dimensions so as to facilitate polymer bridging. To date, however, there has been little work devoted to the cases with unsaturated, concentrated polymer-coated dispersions consisting of nanometric particles whose dimensions are only comparable to the free solution radius of the polymer. For the major case considered in this study, i.e., silica volume fraction / = 0.165, the average intercenter distance is about 3 times the particle radius. In such a concentrated system, the unsaturated colloidal surfaces may be forced to interact via polymer bridging (attractive) while the adsorbed polymers may as well repel each other through the usual steric repulsions (repulsive). Since neither of the two competing mechanisms can be ensued to play the dom-

Y.H. Wen et al. / Journal of Colloid and Interface Science 349 (2010) 134–141

inant role for the system investigated, the net colloidal interaction cannot be easily foreseen. Given that there has recently been a substantial increase of applications taking advantage of the selfassembly behavior of fine colloidal particles in producing colloidal thin films for the fabrication of optoelectronic or biomedical devices [22–29], it is imperative to gain essential insights into this rarely explored colloidal regime. This paper reports a systematic study of the adsorption behavior and, in particular, colloidal interactions for poly(ethylene oxide) (PEO) chains adsorbed onto fine silica colloidal particles. Whereas the first perspective was investigated by dynamic light scattering (DLS) analysis on dilute samples, the small-angle X-ray scattering (SAXS) structure factors extracted from concentrated samples were scrutinized against the predictions of three interaction potentials to discriminate the effects of polymer adsorption. Below, we briefly introduce early studies utilizing similar optical schemes to characterize the colloidal interactions in polymer-coated colloidal dispersions. Afterward, we outline the experimental protocols and major findings of this study. In SAXS/SANS experiments, the absolute scattering intensity of a colloidal system can be factorized into the contributions from the form and structure factors, respectively [30–32]. For noninteracting particles in the dilute limit, there is no spatial correlation between different particles. The particle size and shape can, in principle, be unraveled by comparing the scattering data with analytic theories on form factor [33]. For concentrated samples, colloidal interactions introduce spatial correlations over distances considerably greater than the particle diameter and thus contribute additionally to the total scattering intensity. The spatial particle correlation can be described by the pair distribution function, whose Fourier transform yields the experimentally measurable structure factor. Since a concentrated dispersion is virtually a many-body interacting system, however, any potential models that describe the pair colloidal interaction can be linked with the experimental structure factor only with a certain closure relation or auxiliary approximations, as briefly summarized below. In principle, an interaction potential may be related to the scattering structure factor by solving the Ornstein–Zernike (OZ) integral equation [34] with a closure relation. For instance, the equivalent hard-sphere (EHS) potential describes the effective excluded volume of a colloidal particle [35] and can be solved analytically using the Percus–Yevick closure [36]. The Hayter–Penfold–Yukawa (HPY) potential was originally proposed for investigating macroion solutions and has embodied the effects of both hard-sphere and electrostatic repulsions. An analytical HPY structure factor had been deduced by Hayter and Penfold [37] using the mean spherical approximation (MSA), later refined by Hansen and Hayter for arbitrarily low volume fractions using a physical rescaling argument (rescaled MSA) [38]. Using the EHS or HPY potential, particle interactions of bare or polymer-coated colloids have been systematically explored for a variety of colloidal dispersions [5,32,39–44]. Another semi-empirical potential often employed for analyzing the structure factor of adhesive colloidal particles is the square-well (SW) potential [8,45,46] or the stickyhard-sphere (SHS) potential [47–49], which has stemmed from the Baxter’s sticky potential [50] describing the van der Waals (vdW) attractions between spherical particles. The structure factor for the SW potential has also been derived using the Percus–Yevick closure [51]. For polymer-adsorbed colloids, the polymer adsorption isotherm needs to be established before one may proceed with the investigation of experimental form factor or structure factor. For this purpose, centrifugal depletion methods were often employed to separate non-adsorbed polymer chains and the polymer-coated particles, and the amount of polymer adsorption was later determined by a mass balance [3] or UV spectroscopy [52]. Alterna-

135

tively, a combination of various optical-scattering experiments (typically, DLS and SAXS or SANS) has been employed for a similar purpose [33,44,53]. In this study, DLS analysis was first utilized to determine the adsorption isotherm for PEO-coated particles. In addition, DLS is sensitive to the formation of colloidal multiplets by polymer bridging. On the other hand, SAXS can help resolve the colloidal size (and size distribution) and provide the total surface area of polydisperse colloidal particles. Accordingly, four series of unsaturated PEO-coated silica dispersions were prepared, and the corresponding SAXS data were collected and analyzed against the interaction potentials described above. There have been two conventional ways to characterize the effects of adsorbed or grafted polymers on colloidal interactions. One is to gradually increase colloidal volume fraction while keeping the polymer coverage identical. Thus, the combined electrostatic and steric repulsive forces between the coated particles can be systematically explored [5,42,44,54]. The other approach, usually aimed at resolving the steric repulsion imparted by polymer, was to fix the colloidal volume fraction while gradually increasing the extent of polymer adsorption [44]. The present work adopted the latter strategy for fine PEO-coated silica particles with, however, a much smaller amount of PEO coverage. In this case, analysis of the SAXS structure factors against the EHS potential might provide a basic idea about how a slim amount of absorbed PEO chains would, in general, modify the bare, hard-core interactions. Further examination against the HPY potential, in particular, has clearly disclosed a systematic decrease of colloidal repulsions with increased PEO coverage. This trend was later confirmed by the analysis based on the SW potential. The underlying mechanisms of this phenomenon and the central implications for controlling the colloidal interactions and microstructures of fine polymer-coated particles in dense or condensed phases are discussed. This paper is organized as follows: we first describe the preparation of PEO-coated silica dispersions and the analyzing schemes for DLS and SAXS data. Afterward, the dynamic features and adsorption behavior inferred by DLS for a series of dilute samples are discussed, followed by a detailed analysis of the structure factors and colloidal interactions for three sets of unsaturated, concentrated samples. Finally, we conclude the major observations and implications of this study. 2. Experimental section 2.1. Materials A silica colloidal dispersion (Bindzil 830) was kindly supplied by Eka Chemicals in Taiwan and was used as received. Bindzil 830 has a solid content of 30.1 wt.%, a Na2O content of 0.48–0.62 wt.%, a density of 1.21 g/cm3, and a pH of 10.4. PEO standard with a weight-average molecular weight of 1.03  105 Da (with a mean radius of gyration Rg  10 nm) and a low polydispersity index of 1.04 was purchased from Polymer Laboratories in US. 2.2. Sample preparation In preparing each sample dispersion, deionized water was further purified by syringe membrane filter with a pore size of 220 nm (Millipore Millex-GN) to remove dust particles. The PEO solutions were prepared under mild shaking for 48 h and were later mixed with diluted silica dispersions. The hybrid dispersions were then mildly stirred for another 24 h. For the determination of PEO adsorption onto bare silica, a series of sample dispersions made of various PEO concentrations (0.5, 1, 2, and 4 mg/ml) in dilute silica dispersions (/ = 0.005) were first prepared for DLS characterization, and the properties of particle

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sizing and polymer adsorption were analyzed using the methods described later. The maximum PEO adsorption was thus determined to be 0.56 mg/m2, which corresponds to a PEO concentration 1 mg/ml for the sample dispersions described above. To investigate the structure factors of concentrated PEO-coated silica dispersions, we have prepared four series of sample dispersions with silica volume fractions / = 0.005, 0.041, 0.083, and 0.165 for SAXS measurements; see Table 1. The sample dispersions in the same column of Table 1 have an identical PEO coverage but different silica volume fractions. And the sample dispersions in the same row have an identical silica volume fraction yet different PEO coverages (from left to right: 0.03, 0.10, and 0.18 mg/m2), whose values are substantially below the saturated one noted above (i.e., 0.56 mg/m2) so as to ensure the absence of free PEO chains in the sample dispersions.

information about the mean hydrodynamic radius, hRhiz, and its dispersity. The double-exponential formula is easy to implement and was enforced by simplex optimizations to extract information on particle sizing as well as to help determine the PEO adsorption isotherm.

2.3. Measurements

IðqÞ ¼ NjFðqÞj2 ;

DLS measurements were performed on a Zetasizer 3000 Has (Malvern) equipped with a 10 mW He–Ne laser. The wavelength of the incident light is 633 nm, and the scattered light is detected at an angle of 90°. SAXS data for scattering vectors q ranging from 0.01 to 0.2 Å1 were collected at the National Synchrotron Radiation Research Center (NSRRC) in Taiwan. All measurements were conducted at 25 °C. For SAXS experiments, the absolute scattering intensities were obtained by subtracting the intensity of each sample dispersion with that of deionized water.

where N is the number of the particles per unit volume, and F(q) is the scattering amplitude from a single particle, defined as

3. Data evaluation

3.2. Small-angle X-ray scattering 3.2.1. Form factor SAXS measurements have been a very useful tool for studying fine structural features in a polymer or colloid system. In a dispersion system, the structural features of the probed macromolecule are resolved through their electron-density contrast with the dispersing medium. We first consider the case with a structure factor S(q) = 1, namely, dilute solutions. The total scattering intensity of a monodisperse system I(q) is given by [30–32,49]

FðqÞ ¼

Z

½qðrÞ  qm  expðiq  rÞdr;

ð4Þ

with qm the scattering length density of the dispersion medium (¼ 0:93  1011 cm2 ) for water [58]. For spherical colloidal particles, a hard-sphere core with radius R and uniform scattering length density qp (¼ 1:86  1011 cm2 for silica) is surrounded by the dispersion medium, and the scattering length density profile can be expressed as

qðrÞ  qm ¼

3.1. Dynamic light scattering

ð3Þ



qp  qm ; r 6 R 0;

r>R

ð5Þ

:

DLS measurements involve the analysis of the normalized intensity correlation function g(2)(s, q), which is related to the normalized field correlation function |g(1)(s, q)| by the Siegert relation [55]

Solving Eq. (4) for the above profile, one obtains the scattering amplitude of a spherical particle F(q), which can be written as

g ð2Þ ðs; qÞ ¼ 1 þ bjg ð1Þ ðs; qÞj2 ;

where Vp = 4pR3/3 is the volume of the sphere. As will be presented later, due to a generally low surface coverage as well as low contrast between PEO (which has a scattering length density 1.13  1011 cm2) and water, the scattering curves for dilute dispersions with different PEO adsorption are hardly distinguishable. Therefore, the spherical form factor introduced above seems sufficient for the present purpose. For a similar reason, effects due to the collapse of adsorbed polymers [59] or the layer fluctuation [60] were also neglected. Since the silica particles investigated are fairly polydisperse, as often encountered for fine colloidal particles, I(q) is evaluated using a log-normal distribution D(R) for the radius R. In this case, it seems common to assume a constant particle density N while treating the volume fraction of colloidal particles / as a floating parameter [43]. Noticing that the latter is more readily available in experiment, the following formulas assuming a constant / instead have been adopted in this work:

ð1Þ

where q ¼ ð4pn=kÞ sinðh=2Þ is the scattering vector (n; k; and h being the refractive index of the solvent, the wavelength of the incident light in vacuum, and the scattering angle, respectively), and b is an instrumental factor (0 6 b 6 1) depending on the number of coherence areas that generate the signal. In this study, the double-exponential formula is used by assuming a bimodal distribution in particle size [56]:

jg ð1Þ ðs; qÞj ¼ A1 expðC1 sÞ þ A2 expðC2 sÞ;

ð2Þ

where A1 + A2 = 1; Ai is the amplitude corresponding to the decay rate Ci, and Ci can be related to the hydrodynamic radius Rh,i through the Stokes–Einstein relation (Ci = kBTq2/6pgRh,i with kB, T, and g being the Boltzmann constant, absolute temperature, and solvent viscosity, respectively) [57]. The computed Ai and Ci can be used to obtain the average line width hCi and variance h(C - hCi)2i/hCi2 through the relations hCi = A1C1 + A2C2 and hðC  hCiÞ2 i=hCi2 ¼ ðA1 C21 þ A2 C22 Þ=ðA1 C1 þ A2 C2 Þ2  1, thus yielding

FðqÞ ¼ V p ðqp  qm Þ

IðqÞ ¼ /

Z 0

Table 1 Four series of unsaturated PEO-coated silica dispersions investigated in this study; from left to right, the amounts of PEO adsorption are 0.03, 0.10, and 0.18 mg/m2. Sample series

/

CPEO (mg/ml)

I II III IV

0.005 0.041 0.083 0.165

0.0625 0.5 1 2

0.1875 1.5 3 6

0.3125 2.5 5 10

1

3ðsin qR  qR cos qRÞ ðqRÞ3

jFðqÞj2 V 1 p DðRÞdR;

;

ð6Þ

ð7Þ

and

" #  2 1 ðln R  ln RÞ ; DðRÞ ¼ pffiffiffiffiffiffiffi exp  2r2 2prR

ð8Þ

 is the mean radius and r is the width of the distribution. where R Accordingly, the number density of particles Np—which is now a floating parameter—in a polydisperse system may be calculated at a given / according to the following relation:

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Np ¼ R 1 0

/

pR3 DðRÞdR

4 3

ð9Þ

:

In the above formulas, there are two adjustable parameters: the  and the width of the radius distribution r. Note that mean radius R the same size distribution D(R) determined from the form factor for a dilute sample is later used to self-consistently determine Np for all concentrated samples (with varying /) via the relation given by Eq. (9). Moreover, compared to the conventional strategy, Eq. (7) was noticed to yield a particle density Np that better captures the structure factor of the data under investigation. 3.2.2. Structure factor Eq. (3) may be extended to a concentrated sample as [31,49,61]

IðqÞ ¼ NhjFðqÞj2 if1 þ aðqÞ½SðqÞ  1g;

ð10Þ

where a(q) = h|F(q)|i2/h|F(q)|2i reflects the effect of polydispersity on the form factor, and S(q) is the structure factor which accounts for the additional scattering intensity arising from the interparticle interference in a concentrated system. To extract the experimental structure factor S(q)exp for Sample series IV in Table 1, for example, we assume that Sample series I represents the corresponding dilute, noninteracting cases. Thus, S(q)exp can be obtained experimentally through the following relation:

IðqÞconc /dilute ¼ 1 þ aðqÞ½SðqÞ  1: IðqÞdilute /conc

SðqÞexp ¼

ð11Þ

It is worth noting that S(q)exp is an approximation for a slightly polydisperse system, and S(q)exp and S(q) become identical for a monodisperse system in which a(q) = 1 [49]; possible disparities between these two were ignored in this work. 3.2.3. Three potential models for analyzing structure factor Below, we detail three interaction potentials employed in this study for analyzing SAXS structure factor, along with a generalization to account for the effect of polydispersity in the particle radius. First, the EHS potential can be expressed as

( UðrÞ ¼

1; r < DEHS 0;

r > DEHS

ð12Þ

:

pe0 eD2HPY w20 exp ½jðr  DHPY Þ r

for r > DHPY ;

ð13Þ

where e0 is the permittivity of free space, e is the dielectric constant of the dispersion medium, w0 is the surface potential, and j is the Debye–Hückel inverse screening length so that j1 essentially represents the decay constant of the potential. This form is basically equivalent to that for the Yukawa potential:

DHPY U 0 exp ½jðr  DHPY Þ UðrÞ ¼ ; r

ð14Þ

where U0 is the strength of the potential. The thickness of electrical double layer can be estimated if the functional form of U(r) is known or determined experimentally [62]:

dHPY

1 ¼ 2

Z

1

DHPY

8 r < DSW > < 1; UðrÞ ¼ u; DSW 6 r 6 kDSW ; > : 0; r > kDSW

½1  expðUðrÞ=kB TÞdr:

ð15Þ

ð16Þ

where DSW, u, and k denote the SW diameter, the depth and (dimensionless) width of the potential well, respectively. In the literature, there have been a few works investigating the structure factors of polydisperse systems for hard spheres [41–43], Yukawa spheres [63,64], and adhesive spheres [47,65]. Thus, an^ other log-normal distribution DðRÞ is assumed in calculating the theoretical structure factor using the local monodisperse approximation (LMA) [66], in which the structure factor can be calculated as the weighted sum of the structure factor of the monodisperse subsystems:

SðqÞ ¼

Z

1

^ Sðq; RÞDðRÞdR;

ð17Þ

0

where in the monodisperse EHS [35] and SW [51] models

1 ; 1  4pRU3 =3 cðq; RÞ

Sðq; RÞ ¼

ð18Þ

and in the monodisperse HPY model (rescaled MSA) [37,38]

1 : 1  24Ucðq; RÞ

Sðq; RÞ ¼

ð19Þ

The expressions for c(q, R)—the Fourier transform of the direct correlation function—can be found in the original papers cited above. It should be reminded that for a self-consistent analysis of form factor and structure factor, the model-dependent hard-sphere volume fraction U in Eq. (18) or (19) has been calculated from the predetermined number density Np in Eq. (9) as follows:

U ¼ Np

Z 0

where r is the intercenter distance between two particles. Note that the effective particle radius REHS (=DEHS/2) and the corresponding volume fraction UEHS are fitted instead of the actual particle radius and volume fraction. The HPY potential assumes that particle interactions are entirely repulsive and electrostatic by nature. The repulsive potential between two identical spherical particles of diameter DHPY is given by

UðrÞ ¼

In contrast, the square-well (SW) potential describes colloidal particles with a short-range attraction, and the potential function U(r) is given by

1

4 3^ pR DðRÞdR: 3

ð20Þ

All the parameters used to fit the experimental S(q) were determined by simplex optimizations. In the EHS potential, the floating  EHS and rEHS (Table 3); in the HPY potential, the parameters are R  HPY , rHPY, w0, and j1 (Table 4); in the SW potenparameters are R Table 2 DLS analyses based on double-exponential distribution for dilute PEO-coated silica dispersions (/ = 0.005). Sample

CPEO (mg/ml)

Rh,1 (nm)

Rh,2 (nm)

hRhiz (nm)

h(C  hCi)2i/ hCi2

A1

1 2 3 4 5

0 0.5 1 2 4

9.3 9.6 14.1 15.1 18.8

65.4 61.0 61.8 102.6 92.9

10.8 11.2 15.9 17.7 23.5

0.13 0.14 0.10 0.14 0.19

0.84 0.83 0.85 0.83 0.75

Table 3 Fitted parameter values for the equivalent hard-sphere (EHS) potential for Sample series IV in Fig. 4. CPEO (mg/ml)

 EHS (nm) R

rEHS UEHS

v2

2

6

10

9.9 0.05 0.29 2.2  103

9.9 0.10 0.30 1.6  103

9.9 0.14 0.31 3.2  103

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Table 4 Fitted parameter values for the Hayter–Penfold–Yukawa (HPY) potential for Sample series IV in Fig. 5. CPEO (mg/ml)

 HPY (nm) R

rHPY UHPY

w0 (mV) j1 (nm)  dHPY (nm)

v2

2

6

10

7.8 ± 0.1 0.03 ± 0.01 0.15 54 ± 4 1.3 ± 0.1 2.3 ± 0.1 2.1  103

7.9 ± 0.1 0.03 ± 0.01 0.15 44 ± 7 1.2 ± 0.1 1.9 ± 0.1 6.6  104

7.9 ± 0.2 0.04 ± 0.01 0.15 30 ± 4 1.5 ± 0.2 1.8 ± 0.2 1.2  103

 SW , rSW, u, and k (Table 5). For the latter tial, the parameters are R two cases, since various sets of slightly different parameters could lead to a nearly identical matching of the objective function in simplex optimizations, the error bars—if not negligibly small—are provided to reflect the uncertainty in the parameter fitting. Besides, the quality of the overall fit of the S(q) curve is assessed from the reduced v2 value defined by

v2 ¼

N exp h i2 1 X SðqÞexp;i  SðqÞcalc;i ; Nexp i¼1

ð21Þ

where Nexp is the number of datum points. 4. Results and discussion 4.1. DLS analyses and adsorption isotherm for dilute PEO-coated silica dispersions DLS results on four dilute PEO-coated silica dispersions are shown in Fig. 1. The predictions based on the double-exponential distribution (Eq. (2)) are included for comparison; see the detailed Table 5 Fitted parameter values for the square-well (SW) potential for Sample series IV in Fig. 7. CPEO (mg/ml)

 SW (nm) R

rSW USW u/kBT k

v2

2

6

10

9.9 0.07 0.27 6.8 ± 0.1 1.01 6.8  104

9.7 0.06 0.26 6.9 ± 1.0 1.01 9.9  104

9.5 0.08 0.24 7.8 ± 1.0 1.01 2.3  104

1.0

0.6

|g

(1)

(τ,q)|

0.8

0.4 φ = 0.005 φ = 0.005 with 0.5 mg/ml PEO φ = 0.005 with 1 mg/ml PEO φ = 0.005 with 2 mg/ml PEO φ = 0.005 with 4 mg/ml PEO

0.2

0.0 10

0

10

1

10

2

10

3

τ ( μ s) Fig. 1. DLS results and analytical fitting using double-exponential distribution for dilute PEO-coated silica dispersions with / = 0.005 and various amounts of PEO adsorption.

information in Table 2. As can be seen from Table 2, for PEO concentrations above 1 mg/ml, there is an abrupt increase in the hydrodynamic radius of the slow mode, Rh,2, suggestive of the formation of large aggregate species. These aggregate species likely were formed by non-adsorbed PEO chains, as PEO aggregates of similar size have been detected for pure PEO solutions in early studies [67,68] as well as in the present experiment (not shown). On the other hand, the values of Rh,2 for sample dispersions with PEO concentrations equal to or below 1 mg/ml are almost identical, suggesting that it basically reflects the polydispersity of the core (silica) particle itself. Thus, the maximum PEO adsorption may be inferred to occur at a PEO concentration around 1 mg/ml. Note that the aforementioned PEO concentration, 1 mg/ml, is equivalent to an adsorption amount of 0.56 mg/m2 or about 2 PEO chains per silica, as estimated by the total colloidal surface area deduced from a later SAXS analysis. The adsorption amount seems to be close to what has been reported for silica particles of comparable or larger sizes [10,17,54,69]. Moreover, at a PEO concentration of 1 mg/ml, the size of the equivalent ‘‘core–shell” particles (hRhiz = 15.9 nm) is only slightly smaller than that of the bare silica particles (hRhiz = 10.8 nm) plus the known radius of gyration for single PEO chains (10 nm), suggesting that PEO chains did not collapse on silica surface at a high pH value 10 [69,70]. As a possible polymer bridging between unsaturated PEO-coated particles (i.e., PEO concentration smaller than 1 mg/ml) is concerned, the DLS results noted above essentially show no sign of the formation of colloidal doublets or other multiplets. 4.2. SAXS analyses and colloidal interactions in concentrated PEOcoated silica dispersions According to the maximum PEO adsorption determined above, we have prepared four series of unsaturated PEO-coated silica dispersions; see Table 1. In particular, we were interested in understanding the effects of a relatively small amount of adsorbed PEO chains on the resultant particle interactions. Thus, we considered only the cases in which the average PEO adsorption amount is no greater than 0.18 mg/m2 or, equivalently, 0.6 PEO chains per silica or about 30% surface coverage. The SAXS scattering profiles of Sample series I (/ = 0.005) and IV (/ = 0.165) are shown in Fig. 2a and b, respectively. For Sample series I, given that the contribution of the thin PEO layer to I(q) is hard to discern in this dilute limit [40,44], only insignificant difference exists between the scattering curves at various PEO concentrations. Thus, the form factor for spherical particles, Eq. (7), may be used to fit the scattering curves, yielding  ¼ 7:4 nm and r = 0.28. At large q, I(q) exhibits the characteristic R scaling law q4 as expected for spherical colloidal particles [71]. In contrast, for Sample series IV, the total intensity is considerably modified by the interactions between the particles as the amount of PEO adsorption is increased, especially at low and intermediate q values (i.e., 0.01 Å1 6 q 6 0.04 Å1); see Fig. 2b. At still larger q beyond the aforementioned range, the curves in Fig. 2b can, as expected, be superimposed onto those shown in Fig. 2a through a vertical shift according to the respective volume fractions, indicating that the interference effect between different particles becomes negligibly small [31]. The structure factor S(q) for Sample series II–IV can be extracted using Eq. (11) along with the data for dilute Sample series I. Considering Sample series IV (/ = 0.165) for example, the results for S(q) are shown in Fig. 3. One sees that the peak height decreases notably with increased PEO coverage, suggestive of a less structured state. This trend is somewhat surprising, for it is indicative of a reduced colloidal repulsion due to PEO adsorption. For Sample series II and III, because the mean interparticle spacing is much greater than the effective interaction range, the overall trend cannot be clearly resolved (not shown).

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tial to take into account the effect of polydispersity using Eq. (17). We noticed that in the EHS and HPY potentials, Np (and thus /) needs to be slightly increased by 5% so as to capture the peak position of the experimental S(q). In the SW model, Np can be set to be that determined from Eq. (9) to obtain a good fit without any further adjustments. Fig. 4 examines the predictions of the EHS potential. In using Eqs. (17) and (18) to compute S(q), we have assumed a log-normal ^ EHS Þ for the equivalent hard-sphere radius. Still, we distribution DðR later found that it is not possible to capture the much smeared S(q)exp at high q without considerably deteriorating the overall fit for the q range (i.e., 0.01 Å1 6 q 6 0.04 Å1) where the effect of PEO adsorption is the most pronounced (Recall that the I(q) curves shown in Fig. 2 with various PEO adsorptions are superposed at higher q values). Hence, simplex optimizations have been applied only to a restricted q range, i.e., 0.01 Å1 6 q 6 0.06 Å1 for all the results shown in Figs. 4, 5, and 7. The EHS parameters are com EHS remains essentially invaripiled in Table 3. It can be seen that R ant with increased PEO adsorption, although the width of the size distribution rEHS (and thus UEHS; see Eq. (20)) increases somewhat systematically, possibly owing to the effect of adsorbed PEO chains and the resultant polydispersity in particle size. Note, in particular,

4

S(q)

3

2

1

Fig. 2. SAXS data for: (a) Sample series I and (b) Sample series IV at various PEO concentrations (or in terms of PEO coverage, s: 0.03 mg/m2; 4: 0.10 mg/m2; h: 0.18 mg/m2); line is fit to Eq. (7). The inset in (a) shows the size distribution of silica particles determined from the form factor.

φ = 0.165 with 2 mg/ml PEO φ = 0.165 with 6 mg/ml PEO φ = 0.165 with 10 mg/ml PEO

0 0.02

0.06

0.08

q (Å ) Fig. 4. Experimental structure factors for Sample series IV at various PEO concentrations; lines are fits to the EHS potential. For the sake of clarity, the curves have been shifted vertically by various amounts.

1.5

S(q)

0.04 -1

2.0

4

1.0

3

φ = 0.165 with 2 mg/ml PEO φ = 0.165 with 6 mg/ml PEO φ = 0.165 with 10 mg/ml PEO 0.0 0.02

0.04

0.06

0.08

S(q)

0.5

2

q (Å-1) 1 Fig. 3. Experimental structure factors for Sample series IV at various PEO concentrations (or in terms of PEO coverage, s: 0.03 mg/m2; 4: 0.10 mg/m2; h: 0.18 mg/m2).

φ = 0.165 with 2 mg/ml PEO φ = 0.165 with 6 mg/ml PEO φ = 0.165 with 10 mg/ml PEO

0

0.02

To gain deeper insights, the S(q) of Sample series IV have been examined against the predictions of three interaction potentials introduced in the prior section. Given that the size distribution of the PEO-coated silica particles is fairly broad (r = 0.28), it is essen-

0.04

0.06

0.08

-1

q (Å ) Fig. 5. Experimental structure factors for Sample series IV at various PEO concentrations; lines are fits to the HPY potential (using rescaled MSA).

Y.H. Wen et al. / Journal of Colloid and Interface Science 349 (2010) 134–141

Fig. 6. A schematic representation of the formation of a colloidal doublet by polymer bridging.

that the mean EHS radius is considerably greater than that deter ¼ 7:4 nm). This is bemined earlier from the SAXS form factor (R  EHS reflects the effects of hard-core potential as well as cause R electrostatic potential, and the disparity between these two is consistent with a later estimated thickness of electrical double layer (ca. 2 nm). Aside from this expected trend, it appears that the analysis based on the EHS potential virtually yields no information about the impact of adsorbed PEO chains on the detailed colloidal interactions. Thus, we have further examined the experimental S(q) against the prediction of the HPY potential, for it accounts for the geometric effect (or excluded volume) as well as the electrostatic interaction in an explicit manner. Because of the tiny shell formed by the adsorbed polymer, we assume that the excluded volume effects of the core and the shell could be lumped together. For the HPY potential, a comparison is given in Fig. 5, and the fitting parameters are compiled in Table 4, where two essential features can be noted  HPY (which is in close immediately. Firstly, the mean HPY radius R  ¼ 7:4 nm estimated from the form factor), the agreement with R width of size distribution rHPY, and the effective volume fraction UHPY remain essentially invariant with increased PEO coverage, suggesting there is little change in the equivalent excluded volume due to polymer adsorption. On the other hand, the magnitude of the mean surface potential w0 decreases systematically with increased PEO coverage, indicative of a less charged colloidal surface. To further resolve the overall interparticle repulsion in light of the effective range, we have utilized the size distribution, surface potential, and decay constant provided in Table 4 to estimate the mean electrical double layer thickness  dHPY via the following R1 R1 ^ HPY Þ½1  expðUðrÞ=kB TÞdrdRHPY . expression:  dHPY ¼ 12 0 DHPY DðR HPY also decreases systematically with inAs shown in Table 4, d creased PEO adsorption. In general, an increased steric repulsion may be expected with increased polymer adsorption, unless there is an evident tendency toward polymer bridging. Recall, however, that for the dilute samples investigated earlier, there was no clear sign of forming colloidal multiplets. Evidently, due to a generally low PEO coverage (6 0:18 mg=m2 ) for the fine silica particles investigated, the adsorbed PEO has not yet formed an effective repulsive shell that is dominant over the electrical double layer, which has been estimated to be  dHPY  2 nm for Sample series IV. According to the estimated mean values of  dHPY , radius of silica colloidal particles (7.4 nm), face-toface particle separation (7 nm), and equilibrium coil size of PEO (10 nm), Fig. 6 depicts how a colloidal doublet might, in principle, be formed under the given conditions. The formation of even larger colloidal multiplets is prohibited, however, since it would require a considerable stretching of the PEO chain. Although there seem to be plausible reasons for such polymer bridging to account for an

apparent reduction in colloidal repulsions, the earlier observation for dilute samples suggested that polymer bridging should not be thermodynamically favorable, probably because the adsorbed polymer assumes a coil size only comparable to the particle dimension and, moreover, the hydrogen bonds linking the two species are impeded by a relatively high pH value of the sample dispersions investigated. There is, in fact, another possibility that might as well account for the reduced colloidal repulsion due to polymer adsorption. The postulation is that the tiny PEO shell could play the role of ‘‘screening” the electrostatic repulsion between different coated silica particles. In principle, a direct measurement of the zeta potential could provide evidence to the postulated screening mechanism. The difficulty is, however, that even a small amount of adsorbed PEO could considerably modify the drifting velocity of the coated particles, and hence any changes in pure zeta potential cannot be easily discriminated in usual electrophoresis measurements. Nevertheless, we mention that a reduced zeta potential due to adsorbed polymers has been reported earlier [44]. Moreover, Table 4 also shows that the mean surface potential, w0, changes from 54 to 30 mV with increased PEO adsorption, indicative of a transition from high-charged to low-charged surfaces. Apparently, the present data were insufficient to further discriminate between the two possibilities noted above. To affirm the central implication reached by using the HPY potential, the SW potential was employed to attest whether a similar trend can be revealed, namely, a decreased interparticle repulsion with increased PEO coverage. The predictions are shown in Fig. 7, and the SW potential parameters are compiled in Table 5. From the results shown in Table 5, the extracted SW potential appears  SW  0.19 nm), largely indepento be rather short-ranged (ðk  1ÞD dent of the amount of PEO adsorption. The insensitivity to the PEO adsorption might have to do with the fact that the SW potential basically describes the range and strength of an attractive potential rather than the repulsive one as encountered here. Nevertheless, the following features seem to evidence a similar trend as has been  SW (or USW) disclosed for the HPY potential: the mean SW radius R was noted to decrease slightly with increased PEO coverage, and the depth of attractive potential well u/kBT increases accordingly. A consistent explanation of these features is that increasing PEO coverage results in a less repulsive (or more attractive) state for  EHS , R  SW might rethe coated silica particles. Note that, similar to R flect the effects of both excluded-volume and electrostatic potentials, and the overall trend is consistent with a slight decrease in  dHPY with increased PEO coverage as has been noted in Table 4.

4

3

S(q)

140

2

1

φ = 0.165 with 2 mg/ml PEO φ = 0.165 with 6 mg/ml PEO φ = 0.165 with 10 mg/ml PEO

0 0.02

0.04

0.06

0.08

q (Å-1) Fig. 7. Experimental structure factors for Sample series IV at various PEO concentrations; lines are fits to the SW potential.

Y.H. Wen et al. / Journal of Colloid and Interface Science 349 (2010) 134–141

In summary, the analyses of the SAXS structure factors against the predictions of the HPY and SW potentials, respectively, have consistently revealed an anomalous decrease in the interparticle repulsion by adsorbing a small amount of PEO onto fine silica particles. This central finding has interesting implications in stabilizing a dispersion consisting of coated colloidal particles at low polymer coverage, as well as in fine-tuning the colloidal interactions so as to regulate the self-assembly behavior in dense or condensed phases. For instance, an initially reduced colloidal repulsion due to a partial screening of the electrostatic interaction and/or polymer bridging would bring the coated particles to closer separation in dense solution. With a gradual evacuation of the solvent molecules, polymer bridging might eventually dominate the colloidal phase, forming a network comprised mostly of doublets. In a similar fashion, colloidal networking formed by specific multiplets may be produced by controlling the polymer-colloid size ratio. 5. Conclusion The present study utilizing DLS and SAXS analyses on hybrid PEO-silica dispersions has clearly revealed that for unsaturated, concentrated polymer-coated colloidal dispersions, reduced colloidal repulsions may be imparted by the adsorbed polymer of sizes comparable to particle dimensions. Specifically, whereas the EHS potential was unable to resolve a definite trend, the HPY potential clearly indicated a systematic reduction in both the strength and range of the effective electrostatic interaction with increased PEO coverage. The analysis based on the SW potential, which probes the effective colloidal attraction, also confirmed the aforementioned trend. Two possible molecular mechanisms underlying this phenomenon were considered. The first invoked the formation of colloidal doublets by polymer bridging, whereas the second ascribed the reduced colloidal repulsion to a partial screening of the electrostatic interaction. Although polymer bridging has commonly been noted for dispersions consisting of fine colloidal particles, the present DLS analysis on dilute samples showed no sign of forming colloidal multiplets, suggesting that polymer bridging is not thermodynamically favorable for the sample dispersions investigated. Nevertheless, in increasingly dense or condensed phases, polymer bridging might eventually play the dominant role of controlling the colloidal phase, by creating a network comprised mainly of colloidal doublets as the elementary packing unit. The overall findings are suggestive of yet open possibilities of fine-tuning the interactions of nanometric colloidal particles in dense or condensed phases for a wide range of upcoming applications. Acknowledgments We thank the reviewers’ comments for a general improvement of this article. The support from the National Science Council of ROC is acknowledged. We also thank NSRRC for providing X-ray beamtime and are grateful for the technical support from Drs. U.S. Jeng, Y.-H. Lai, and Y.-S. Sun at the BL23A SWAXS end station. References [1] D.H. Napper, Polymeric Stabilization of Colloidal Dispersions, Academic Press, London, 1983. [2] W.B. Russel, D.A. Saville, W.R. Schowalter, Colloidal Dispersions, Cambridge University Press, New York, 1989. [3] G.J. Fleer, M.A. Cohen Stuart, J.M.H.M. Scheutjens, T. Cosgrove, B. Vincent, Polymers at Interfaces, Chapman & Hall, London, 1993. [4] N.J. Wagner, J.F. Brady, Phys. Today 62 (2009) 27. [5] R.H. Ottewill, Langmuir 5 (1989) 4. [6] A. van Blaaderen, P. Wiltzius, Science 270 (1995) 1177. [7] B. Vincent, Adv. Colloid Interface Sci. 4 (1974) 193. [8] T. Narayanan, M. Sztucki, G. Belina, F. Pignon, Phys. Rev. Lett. 96 (2006) 258301.

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