Effect of particle polydispersity on the structure and dynamics of complex formation between small particles and large polymer

Abstract

The effect of particle polydispersity on the structure and dynamics of small silica particle–large polymer chain mixtures at low polymer concentration has been investigated. Two types of silica particles were used as model systems, having similar mean size, specific surface area and surface properties but differing substantially in size polydispersity. Mixtures of PEO with the polydisperse silica particles showed strong shear-thickening upon shaking, while mixtures of the same composition with the monodisperse silica did not. Fluorescence correlation spectroscopy revealed that larger flocs were formed in the polydisperse particle–PEO systems. Particle polydispersity was identified as the major factor accounting for these differences and a plausible mechanism was proposed based on the spatial distribution of the silica particles within the complexes. This work suggests that the rheological behavior of colloid–polymer mixtures can be dramatically modified by a simple change in particle polydispersity, rather than more involved surface modifications or the use of additives.

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Introduction

It is well known that colloidal particles can interact with polymers. Different particle–polymer complexes may form depending on the relative dimensions and concentrations of particle and polymer. With small polymer coils and relatively large particles, polymer adsorption on colloidal surface may take place.^1–4 In this case, if the particles are in excess and the surface not saturated, bridging of particles by the polymer may occur and bridging flocculation could be observed.^5,6 Instead, when polymer coils are quite large compared to the particles, particles are expected to adsorb onto the polymer coils in a so-called nano-necklace structure,^7–9 which may display a variety of rheological behaviors. Depending on the polymer–particle ratio, Newtonian, shear-thinning and shear-thickening behavior have all been observed.^9–15

It is generally accepted that shear-thinning occurs because of structural destruction or orientation, while shear-thickening is accompanied by larger scale structure formation.¹⁴ Shear-thickening usually occurs when the particle surface is not saturated by polymer; in that case, shearing results in the stretching of the chains and bridging of neighboring particles. Instead, when the particles surface is saturated, shear-thinning is normally expected.^9,10,16 The microstructural changes in particle–polymer systems should be related to particle–polymer interactions, thus the adsorption strength has been proposed as a key factor dictating the rheological behavior. In most studies, particles with uniform size distribution, such as silica nanoparticles or laponite nanoparticles, have been used as models to study the flow behavior of colloid–polymer mixtures.^9–19 However, colloidal particles are usually polydisperse in practical applications, such as those found in food, paint, coating, cement, or drilling fluids, as they are mixtures of particles of different sizes.

In this study, we investigated the effect of particle polydispersity on the structure and dynamics of colloid–polymer mixtures at low polymer concentration (below the overlapping concentration).

Experimental

Materials

All colloidal silica dispersions were extensively dialyzed against pure water for 2 weeks (pH = 10) before use. LUDOX-TM40 was purchased from Sigma-Aldrich and Eka-BINDZIL2040 was kindly donated by AkzoNobel Ltd. Taiwan. KLEBOSOL 30R12, 30R50 were kindly donated by AZ Electronic Materials France SAS. Specific information on each type of silica particles used is summarised in Table 1.

Table 1 Information of silica particles

	Rh^a (nm)	BET specific area^b (m^2 g^−1)
a Measured by DLS.b Measured by BET.
BINDZIL2040	15.7	126
TM40	15.5	120
30R12	9.2	164
30R50	40.3	48

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Poly(ethylene oxide) (PEO) with molecular weights M_n = 95 000 g mol⁻¹ (Polymer Source Inc. M_w/M_n = 1.08) and M_v = 1 000 000 g mol⁻¹ (Sigma-Aldrich, polydisperse) were used as received. Pure water (generated by an ELGA Purelab® system) with a resistivity of 18.2 MΩ cm were used for all samples. Tetraethoxysilane (TEOS, purchased from Xilong Chemical) was distilled under vacuum before use. 3-Aminopropyltriethoxysilane (APS, purchased from Alfa-Aesar), rhodamineisothiocyanate (RBI, purchased from Sigma-Aldrich), absolute ethanol (Beijing Chemistry), ammonia solution (Beijing Chemistry) and heavy water (ARMAR Chemicals) were used as received.

Sample preparation

Samples were prepared by mixing silica dispersions with PEO aqueous solution, followed by shaking gently on a rolling device for 3 days before measurements. The pH of the samples was adjusted to 9–10 by adding HCl or NaOH. PEO of M_v = 1 000 000 g mol⁻¹ was used as model large polymer and the final PEO concentration in all samples was fixed at 0.2 wt%. Samples for ¹H-NMR solvent relaxation studies were prepared by the same procedure but with a lower molecular weight PEO (M_n = 95 000 g mol⁻¹), in order to reduce the viscosity to a level suitable for manipulation in small NMR tubes. Artificial polydisperse samples were made up by varying the weight ratio of the different-sized monodisperse particles at a given total particle concentration of 17 wt%, where the ratio of 30R12 to 30R50 was adjusted to keep the z-average diameter of the particles in the range 26–28 nm (Table 2).

Table 2 Sample composition

	Weight fraction
	TM40	30R12	30R50
TM40–R12–R50–PEO-1	0.9	0.066	0.034
TM40–R12–R50–PEO-2	0.8	0.132	0.068
TM40–R12–R50–PEO-3	0.7	0.198	0.102
TM40–R12–R50–PEO-4	0.6	0.264	0.136
TM40–R12–PEO-1	0.95	0.05	0
TM40–R12–PEO-2	0.9	0.1	0
TM40–R12–PEO-3	0.8	0.2	0
TM40–R50–PEO-1	0.95	0	0.05
TM40–R50–PEO-2	0.9	0	0.1
TM40–R50–PEO-3	0.8	0	0.2

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Fluorescent nanoparticle synthesis

The fluorescent silica nanoparticles with a hydrodynamic radius of 15.7 nm were synthesized using a sol–gel method.²⁰ Briefly, the RBI dye molecules were first covalently conjugated to APS then condensed to form a dye-rich core. TEOS were subsequently added to form a silica shell around the dye-rich core.

Characterization

Visual observation of flow behaviour

The samples were shaken vigorously by hand for 30 s. If the samples became viscous (gelled) or had bubbles suspended in the samples, they were considered to be shear thickening.¹⁰

Viscosity-shear measurements

Viscosity-shear measurements were performed on a stress-controlled rheometer (Thermo Scientific HAAKE MARS III) at 25 °C. Both cone-and-plate (60 mm diameter, 1 degree cone) and parallel plate (35 mm diameter, 0.8 mm gap) geometries were used to ensure reproducibility. Each sample was measured at least 5 times to check reproducibility.

DLS measurements

Dynamic light scattering (DLS) measurements were performed on a commercial LS spectrometer (ALV/DLS/SLS-5022F) at 25 °C, which was equipped with a multi-τ digital time correlator (ALV5000) and a cylindrical 22 mW UNIPHASE He–Ne laser (λ = 632.8 nm). The scattering angle was fixed at 90°. Samples for DLS measurements were filtered through a 0.22 μm pore-sized membrane directly into cylindrical optical glass cuvettes, which had been extensively cleaned over an acetone steamer before use.

¹H solvent relaxation NMR

Solvent relaxation NMR has been successfully used to measure the interaction between polymers and nanoparticles.^{2,3,21–25 1}H solvent relaxation NMR measurements rely on the fact that mobile and immobile protons have very different spin relaxation times.²⁶ Free or bulk solvent molecules are highly mobile and have a relatively smaller relaxation rate constant R₂ = 1/T₂, where R₂ and T₂ are relaxation rate constant and relaxation time constant, respectively. When the solvent molecules are bound at a surface, for instance onto colloidal particles, their motions are restricted, which leads to a higher R₂. The adsorption of polymers to particles can bind the water at the surface more tightly, leading to a further enhancement in R₂. The enhancement of water R₂ can therefore be used to give information on the polymer interaction with a surface.

¹H solvent spin–spin relaxation measurements were performed on a 300 MHz NMR spectrometer (Bruker DMX300) using the CPMG pulse sequence.²⁷ T₂ was extracted from the measured magnetization (M) relaxation decay curves by fitting the data to a single-exponential decay and the specific relaxation rate constants (R_2sp) were calculated from T₂ (ref. 2, 3 and 21–25)

where T₂⁰ is the relaxation time constant of a reference species (H₂O for example).

FCS measurement

The details of the fluorescence correlation spectroscopy (FCS) setup used in this study can be found in previous reports.^28–30 Briefly, the setup was constructed on an inverted microscope (Olympus IX-71) equipped with a water-immersion objective lens (Plan Apochromat 60× , numerical aperture = 1.2). The excited light source is the 532 nm output of a solid-state laser, and the fluorescence excitation and collection were conducted at the confocal geometry. The background noise was greatly suppressed by a combination of a dichroic mirror and optical filters (Chroma Tech). The fluorescence was split into two parts of identical intensity, which were detected separately by two single photon counting modules (Hamamatsu, Japan). The fluorescence photon count signal was coupled into a multichannel FCS data acquisition board, and the data analysis was conducted by its software (ISS, USA).

The FCS measures the diffusion of fluorescent molecules by monitoring fluorescence fluctuation within the excitation-detection volume and by the analysis of the autocorrelation function of the fluctuation:

G(τ) = 〈δF(t)·δF(t + τ)〉/〈F(t)〉²

where F(t) denotes the fluorescence intensity at time t. The numerical fitting of the function adopting the Gaussian profile and three dimensional diffusion model can be used to determine the translational diffusion coefficient (D) and the average concentration 〈c〉 of the fluorescence probe. The expression of the autocorrelation function by the three-dimensional Gaussian model is

G(τ) = (π^3/2w₀²z₀〈c〉)⁻¹(1 + 4Dτ/w₀²)⁻¹(1 + 4Dτ/z₀²)^−1/2

where w₀ and z₀ are the lateral radius and the half length of the excitation-detection volume, respectively. R_h of the probe is therefore determined through the Stokes–Einstein equation:

R_h = k_BT/6πηD

where k_B, T, and η are the Boltzmann constant, the absolute temperature, and solvent viscosity, respectively.

Rhodamine 6G molecules were used as the standard for calibration, which showed a diffusion coefficient of 420 ± 6 μm² s⁻¹ in pure water at 25 °C, corresponding to a hydrodynamic radius of 0.55 nm, as expected.

SAXS measurements

The SAXS measurements were carried out on BL16B1 at Shanghai Synchrotron Radiation Facility (SSRF). The wavelength of X-rays was 1.24 Å. The sample detector distance was 5 m, covering a momentum transfer (q) range of 0.007–0.07 Å⁻¹. The samples were placed in a sealed quartz capillary of 1 mm path length. All measurements were carried out at room temperature.

SANS measurements

The SANS measurements were carried out on D11 at the ILL, Grenoble, France. Cold neutrons of 8 Å were used. The volume fraction of H₂O in the solvent was fixed to 0.83, which gives a scattering length density of 0.64 × 10⁻⁶ Å⁻². At this contrast, the PEO is invisible to neutrons.^21,31 Rectangular quartz cells with 2 mm path length were used for the samples. A typical measurement took around 10 min to give good statistics. All measurements were carried out at room temperature.

Results

Characteristics of model silica colloids

BIDNIZL2040 and TM40 silica colloidal particles obtained from different suppliers both have similar hydrodynamic radii, but different size distributions, as shown below. The first step was to characterize both particle systems in detail. The viscosity-shear profile of the two colloidal silica dispersions are shown in Fig. 1. At a similar solid content (17%), these two dispersions have a very similar viscosity and shear rate dependence. Neither silica dispersion shows obvious non-Newtonian behavior at this concentration over the whole range of shear rates explored.

Fig. 1 Shear rate dependence of viscosity for TM40 and BINDZIL2040 dispersions at silica particle concentration of 17 wt%: ■ BINDIZL2040, □ TM40.

The silica particle size and polydispersity were further investigated by DLS and SAXS. The DLS measurements showed a R_h of 15.7 nm for BINDZIL2040, thus very similar to that of TM40 silica particles (15.5 nm). The size distribution function revealed that the half peak width for BINDZIL2040 was significantly larger (Fig. S1†). SAXS measurements were also used to characterize the two types of silica particles (Fig. 2). The scattering data could be suitably fitted to a sphere model with polydispersity (Gaussian distribution). Parameters obtained from the fits showed comparable radii for the two types of silica particles: 13.4 and 10.1 nm for TM40 and BINDZIL2040, respectively. As expected, the radii obtained from SAXS are smaller than those from DLS because of the hydrodynamic layers around the silica particles. However, they differed markedly in uniformity of size distribution: the polydispersity returned by the fits was 0.13 and 0.39 for TM40 and BINDZIL2040, respectively.

Fig. 2 SAXS spectra from TM40 and BIDNZIL2040 silica dispersions at a silica particle concentration 0.2 wt%: □ BINDZIL2040, ○ TM40. The solid lines are fits to a sphere model with polydispersity.

We then characterized the surface properties of BINDZIL2040 and TM40 silica particles by ¹H solvent spin–spin relaxation NMR. In principle, the specific relaxation rate constant (R_2sp) of water reflects the restriction of water by colloidal particle surface, thus representing the affinity of water to the surface at similar surface areas.^2,3,21–25 The results for bare silica dispersions are shown in Fig. 3. As expected, the data showed a linear relationship between available surface area and relaxation rate constant. Both data sets overlap almost perfectly, indicating that the affinity of water to the two colloidal silica particles were very similar, in other words, they had a similar hydrophilicity.

Fig. 3 R_2sp of silica dispersions as a function of silica concentration (w/w) where pure water was used as reference: ■ BIDNZIL2040, ○ TM40.

As both silica dispersions have similar hydrodynamic sizes and surface properties, it is reasonable to assume that they would have a similar interaction with PEO, which would thus result in a similar amount of PEO segments in ‘train’ conformation, i.e. directly in contact with the particle surface.³² The interaction strength between PEO and the particles was also assessed by ¹H spin–spin solvent relaxation NMR, monitoring the enhancement of R_2sp with increasing polymer concentration (Fig. 4). For both systems, with an increase in PEO : silica ratio, R_2sp increased up to a maximum of 0.50 mg m⁻² and 0.52 mg m⁻² for BINDZIL2040–PEO and TM40–PEO, respectively, after which a plateau was observed, indeed suggesting very similar PEO–silica interactions for both types of silica.

Fig. 4 R_2sp of PEO–silica dispersions as a function of nominal PEO surface coverage at a fixed particle concentration of 3 wt% (3 wt% bare silica dispersions were used as the reference): ● TM40–PEO, □ BINDZIL2040–PEO.

Flow behavior of silica particle–PEO complexes

It has been reported that some types of colloidal particle–polymer mixtures can show gelation¹⁰ or thickening¹¹ under vigorous shaking. In this work, we compare mixtures of PEO with either BINDZIL2040 or TM40, both having very similar size, surface properties but differing widely in their polydispersity. Prepared samples of BINDZIL2040–PEO and TM40–PEO (silica 17 wt%, PEO 0.2 wt%) were shaken vigorously by hand, and a strikingly different behaviour was observed (Fig. 5): while initially the samples have viscosities that were not significantly different from pure water, after vigorous shaking the BINDIZL2040–PEO mixture turned into a very viscoelastic sample, i.e. shear-gelled, with visible suspended bubbles (Fig. 5d and also ESI, Movie 1†). Instead, the TM40–PEO remained fairly liquid-like.

Fig. 5 Optical pictures of BINDIZL2040–PEO and TM40–PEO mixtures (silica 17 wt%, PEO 0.2 wt%): (a) TM40–PEO in a quiescent state, (b) TM40–PEO after shaking, (c) BIDNZIL2040–PEO in a quiescent state, (d) BINDZIL2040–PEO after shaking.

Given the similarity in properties of both silica suspensions, except their size distribution, this would suggest that the differences observed in silica–PEO mixture behavior may be attributed to particle polydispersity. The viscosity-shear rate profiles of PEO solution (0.2 wt%), BINDZIL2040–PEO mixture and TM40–PEO mixture (silica 17 wt%, PEO 0.2 wt%) were also investigated (Fig. 6a). PEO solution is a low viscosity Newtonian fluid, indicating that the concentration is lower than overlapping concentration. The TM40–PEO mixture is also Newtonian over the entire shear range. Instead, at the same composition, BINDZIL2040–PEO displays a higher viscosity and shows a slight shear thinning behavior. While the behavior of BINDZIL2040–PEO and TM40–PEO under vigorous shaking differs markedly (Fig. 5), the rheological measurements could not be used to demonstrate this because of the limitation in the dynamic shear range of the rheometer.

Fig. 6 Shear rate dependence of viscosity for samples: (a) ○ PEO solution (0.2 wt%), ● BINDZIL2040–PEO and ■ TM40–PEO mixture (silica 17 wt%, PEO 0.2 wt%). (b) □ TM40–PEO; ● TM40–R12–R50–PEO-1; △ TM40–R12–R50–PEO-2; ▼ TM40–R12–R50–PEO-3; ○ TM40–R12–R50–PEO-4.

In order to investigate further this hypothesis of a polydispersity effect, three types of silica of varying sizes were mixed together to make up a polydisperse silica dispersion: TM40, 30R12 and 30R50 (Table 2). The DLS measurements showed that the TM40, 30R12 and 30R50 were all fairly monodisperse particles (see ESI†). Fig. 6b shows the shear rate dependence of viscosity for the silica particle–PEO mixtures with different particle compositions. TM40–R12–R50–PEO series have higher viscosity than TM40–PEO and show a slight shear thinning behavior, very like BINDZIL2040–PEO (Fig. 6a). The TM40–R12–R50–PEO mixtures were also shaken vigorously. For TM40 weight fractions below 0.7, shear-thickening was observed (Fig. 7), very similar to the BINDZIL2040–PEO mixture.

Fig. 7 Pictures of TM40–R12–R50–PEO-4: (a) TM40–R12–R50–PEO-4 in a quiescent state. (b) TM40–R12–R50–PEO-4 after shaking.

Microstructure of silica particle–PEO mixtures

The rheological behavior of silica particle–PEO mixtures are directly related to the microstructures formed in the system. SAXS and SANS were used to investigate the interparticle correlations in both the bare particle dispersion and in the silica particle–PEO mixtures, which can be extracted from the static structure factors. In SANS measurements, the ratio of D₂O–H₂O was adjusted to 83% v/v H₂O, thereby contrast-matching the PEO (scattering length density of 0.64 × 10⁻⁶ Å⁻²); thus at this contrast, only silica particles are visible to neutrons.^21,31 The system therefore can be regarded as an effective dispersion of colloidal particles, and a simple spherical form factor is applicable. As can be seen from Fig. 8a and b, for both systems, at the same particle concentration, the scattering spectra from the bare silica dispersion and the silica particle–PEO mixture overlay at high q, indicating that the shape of the individual scattering units do not change with the addition of PEO. The structure factors of bare silica particle dispersions and silica particle–PEO mixtures derived from the fits are shown in Fig. 8c and d. The structure peak in both systems is shifted to higher q in the presence of PEO, indicating that the average interparticle separation has been reduced. Thus, one can conclude that PEO chains pulls silica particles closer due to their adsorption on their surface and thus that more than one particle are adsorbed onto one polymer chain.

Fig. 8 (a) SANS (□) spectra from BINDZIL2040–PEO mixture (silica 17 wt%, PEO 0.2 wt%) with PEO contrast-matched and SAXS (●) spectra from BINDZIL2040 dispersion (17 wt%); (b) SANS (□) spectra from TM40–PEO mixture (silica 17 wt%, PEO 0.2 wt%) with PEO contrast-matched and SAXS (●) spectras from TM40 dispersion (17 wt%); (c) structure factors of BINDZIL2040 particle dispersion (17 wt%, ●) and BINDIZL2040–PEO mixture (silica 17 wt%, PEO 0.2 wt%, □); (d) structure factors of TM40 particle dispersion (17 wt%, ●) and TM40–PEO mixture (silica 17 wt%, PEO 0.2 wt%, □). Note: SAXS data have been multiplied by a fudge factor to overlay with SANS data at high-q.

FCS was then used to shed more light on the microstructure of the systems. Fluorescent silica nanoparticles were used as probes. From the autocorrelation of time-domain signal, the diffusion coefficient of emitters can be determined, giving the particle size through the Stokes–Einstein equation.³³ Fig. 9a shows the correlation function of fluorescent particle diffusing in water. The FCS data was fitted to a three-dimensional diffusion model and a hydrodynamic radius (R_h) of 15.7 nm was obtained, consistent with TEM (Fig. 9b). Therefore, these fluorescent particles are very similar in size to the model silica particles and are ideal probes for these systems.

Fig. 9 (a) Autocorrelation function of fluorescent silica particles in water. The solid line is the fitting line obtained by using a three-dimensional diffusion model. (b) TEM (JEM-2200FS) image of fluorescent silica particles.

In order to investigate the microstructures formed, we added the fluorescent silica particles as probes (concentration: ∼10⁻⁹ M) into the BINDZIL2040–PEO, TM40–PEO and TM40–R12–R50–PEO-4 mixtures. The correlation functions of these samples are shown in Fig. 10, and the corresponding results are summarized in Table 3. The correlation functions were adequately fitted using a two-component three-dimensional diffusion model. One diffusion coefficient around 14.5 μm² s⁻¹ corresponds to a R_h of 15.7 nm, which can be assigned to the free silica particles, while the other took lower values, ranging from 49 to 75 nm, which can be assigned to silica particles adsorbed onto the polymer coils. In this study, the polymer coils are larger than the silica particles (DLS showed the R_h of PEO M_v = 1 000 000 was 39 nm). Since there are more particles than polymer coils (with a silica particle–polymer number ratio of ca. 8), particles may not all be adsorbed onto the polymer coils, so this binary distribution is reasonable. For TM40–PEO mixtures, the sum of volumes of a PEO chain (R_(PEO) = 39 nm) and eight TM40 particles (R_(particle) = 13 nm) is ∼3.2 × 10⁵ nm³, which is lower than volume of PEO–particle complex (R_(complex) = 49 nm) ∼4.9 × 10⁵ nm³, suggesting that the polymer coil is expanded, probably due to the electrostatic repulsions between the adsorbed silica particles. From Table 3, it is clear that the complexes formed in BINDZIL2040–PEO and TM40–R12–R50–PEO-4 are larger than in TM40–PEO, suggesting that particle polydispersity may lead to a different microstructure, thus underlying their flow behaviour.

Fig. 10 Autocorrelation function curves of silica particles–PEO mixtures. The solid lines are the results of the numerical fitting using a three-dimensional diffusion model. (a) TM40–R12–R50–PEO-4, (b) TM40–PEO, (c) BINDZIL2040–PEO.

Table 3 Parameters obtained from fits to the FCS data

	Component 1		Component 2
	D/μm^2 s^−1	Rh/nm	D/μm^2 s^−1	Rh/nm
TM40–PEO	14.5	15.7	4.7	49.1
TM40–R12–R50–PEO-4	14.5	15.7	3.7	62.4
BINDZIL2040–PEO	14.5	15.7	3.1	74.5

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Discussion

Shear-thinning or shear-thickening is related to structural orientation/destruction or formation, respectively. Numerous studies have reported shear-thinning behavior in colloid–polymer mixtures, however, shear-thickening is less documented and understood. Previous studies^9,10,16 have shown that particle surface coverage by the polymer is one of the key factors determining the type of flow behavior of nanoparticle–PEO mixtures. Shear-thickening is usually observed at a PEO concentration below the threshold for complete saturation of particle surface by the polymer.¹⁰ In the quiescent state, the small particles are adsorbed onto large polymer chains, forming small flocs composed of several particles. When a sufficiently strong shear is applied, the polymer chain segments attached to the particles may desorb to expose additional surfaces, thus making it possible for polymer chains from other coils to adsorb onto the particles, forming larger flocs and enhancing viscosity.^9–12,14 When the shear ceases, thermal fluctuation may strip some polymer segments off the particles and the sample can relax to a low viscosity fluid.^9–12,16

As shown earlier, these two model silica particles (TM40 and BINDZIL2040) have similar average hydrodynamic sizes, specific surface areas and direct interaction with PEO, but very different particle polydispersity. They show a strikingly different response to vigorous shaking: BINDZIL2040–PEO mixture shows shear-thickening upon shaking while TM40–PEO remains liquid-like. Since there are more particles than the number of polymer coils (silica particle–polymer coils ∼ 8), there would be several particles adsorbed onto one polymer coil to form a floc (see SANS and FCS results). Due to the electrostatic repulsion between silica particles, the polymer coils may expand, thus leading to a higher viscosity than solutions of PEO alone. In this study, the PEO concentration was below the overlapping concentration, therefore, the flocs may still remain isolated and the silica–PEO mixtures are largely Newtonian and of low viscosity at low shear rates (Fig. 6).

When polydisperse particles are used (BINDZIL2040), which have both smaller and larger particles, different microstructures are observed: the R_h of the flocs changes from 49 nm to 75 nm (Table 3). The distribution of particles in the polymer coils may give us a handle to understand the differences in flow behavior. Small particles can become entrapped in polymer coils, as suggested by Otsubo et al.,¹¹ and the polymer coils may expand due to the electrostatic repulsion between particles, leading to a larger floc size and higher viscosity. However, larger particles with size comparable to the polymer coils cannot enter the polymer coils but stay adsorbed at the edges of the coils.¹² When shear is applied, some polymer segments from the particles may be pulled off and these large particles could provide more available surface to accommodate polymer segments from other flocs, resulting in the formation of larger flocs and then shear-thickening (Fig. 11). These larger particles work as effective binders.

Fig. 11 Structural models of silica particles–PEO complex in a quiescent state (left) and under shear (right).

Based on the above arguments, we can speculate that smaller particles mainly contribute to viscosity and large particles to shear-thickening. In order to test this hypothesis, we have investigated the flow behavior of TM40–R12–PEO series (with smaller particles) and TM40–R50–PEO series (with larger particles). It can be seen from Fig. 12a and 13 that with smaller particles added, TM40–R12–PEO series show a higher viscosity at fixed shear rate but no shear thickening. Instead, with larger particles added, TM40–R50–PEO-3 shows shear thickening but little change in low-shear viscosity (Fig. 12b and 13). These two control experiments strongly support the proposed mechanism (Fig. 11).

Fig. 12 Shear rate dependence of viscosity for samples at concentration of 0.2 wt% PEO and 17 wt% silica particle: (a) ○ TM40–PEO; □ TM40–R12–PEO-1; ● TM40–R12–PEO-2; ■ TM40–R12–PEO-3. (b) □ TM40–PEO; ● TM40–R50–PEO-1; ■ TM40–R50–PEO-2; ○ TM40–R50–PEO-3.

Fig. 13 Pictures of TM40–R12–PEO-3 and TM40–R50-3: (a) TM40–R12–PEO-3 in a quiescent state. (b) TM40–R12–PEO-3 after shaking. (c) TM40–R50–PEO-3 in a quiescent state. (d) TM40–R50–PEO-3 after shaking.

Conclusions

The effect of particle polydispersity on the structure and dynamics of small particle–large polymer chain mixtures at low polymer concentration has been investigated. Two types of silica particles (TM40 and BINDZIL2040) were used as models. Mixtures of PEO with the polydisperse silica particles showed shear-thickening upon shaking, while mixtures with the monodisperse silica did not. FCS revealed that larger flocs were formed in the polydisperse silica particles–PEO systems. The particle polydispersity was identified as the major factor accounting for these differences and a possible mechanism was proposed, where the larger particles behave as effective binders to crosslink different polymer coils under shaking, while smaller particles penetrate and expand the polymer coils, serving as “good solvent”. This work suggests that the flow behavior of colloid–polymer mixture can be controlled simply through changing particle polydispersity, instead of more involved surface modifications or additives.

Acknowledgements

This work was supported by National Natural Science Foundation of China (Project no. 91027032), National Key Technology R&D Program of China (Project no. 2011BAI02B05) and State Key Development Program of Basic Research of China (Project no. 2012CB933200). SSRF and ILL were thanked for providing beam times. CSNS was appreciated for funding SANS measurements overseas. We also thank Akzo Nobel Ltd. and AZ Electronic Materials France SAS for kindly donating silica colloids.

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Footnote

† Electronic supplementary information (ESI) available: The DLS measurements of TM40, BINDZIL2040, 30R12 and 30R50 silica particles, and the movie of BINDZIL2040–PEO mixture (silica 17 wt%, PEO 0.2 wt%) during vigorously shaking. See DOI: 10.1039/c4ra00929k

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