Molecular Weight Effects on Particle and Polymer Microstructure in

Aug 8, 2013 - *E-mail: (C.F.Z.) [email protected]. ... Our results reveal that polymer mobility varies from the particle surface to the bulk with ...
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Molecular Weight Effects on Particle and Polymer Microstructure in Concentrated Polymer Solutions So Youn Kim† and Charles F. Zukoski* Department of Chemical and Biomolecular Engineering, University of Illinois at UrbanaChampaign, Urbana, Illinois 61801 S Supporting Information *

ABSTRACT: Microstructure of particles and polymers in concentrated polymer solutions are examined. Silica nanoparticles with diameters of 44 nm are suspended in concentrated poly(ethylene glycol) (PEG) solutions working with PEG molecular weights from 300 to 20 000. Using timedomain NMR, we explore the effects of PEG adsorption on the silica particles on the mobility of polymer segments. Our results reveal that polymer mobility varies from the particle surface to the bulk with different relaxation times; polymers are glassy near the particle surface and mobile in the bulk. While polymer segments adsorb to the particle surfaces to form a glassy layer in a molecular weight independent manner, the number of polymer segments with intermediate mobility between that of the glassy state and the bulk increases with molecular weight. Systematic variations in the nanoparticle and polymer microstructure in concentrated polymer solutions are explored using contrast-matching small angle neutron scattering techniques demonstrating that the thickness of adsorption layer of polymer segments increases with increasing PEG molecular weights supporting NMR observations. However, the particle microstructure evolves in a manner suggesting attractive interactions increase with molecular weight. We compare experimental observations and predictions by the polymer reference interaction site model (PRISM) revealing the limits of the theory when applied to the silica-concentrated PEG solution system. While PRISM predicts experimental observations in polymer and particle microstructure quantitatively at low molecular weight, it fails as molecular weight increases, suggesting that polymer configurations are not able to sample equilibrium configurations.

I. INTRODUCTION When the size of particles blended with polymers shrinks, properties emerge that cannot be predicted by standard mixing rules.1,2 Polymer nanocomposites, produced by adding nanoparticles to polymer melts, for example, have exhibited significantly reinforced mechanical properties.3−5 Attempts to understand these properties have focused attention on the role of the particle interface in altering polymer configurations, degrees of entanglement and segment mobility.6−8 With increasing interest in polymer nanocomposites, progress has been also made on the computational works and theories.9−12 One of the most successful approaches for describing equilibrium composite properties is the polymer reference site interaction model (PRISM)13−15 of Schweizer and coworkers who have developed an integral equation based approach for calculating correlation functions for particles, polymers and their interfaces. This theory predicts that the state of particle dispersion is very sensitive to the strength of polymer segment−particle surface cohesion.14 In the absence of sufficiently strong attractions between polymer segments and the particle surface, the particles aggregate due to depletion forces, whereas the strength of cohesion between polymer segments and the particle surface is too strong, the polymer segments bridge particles, resulting in aggregation. Only intermediate strengths of attraction between segments and the particle surface result in thermodynamic stability of particles in polymer nanocomposites or concentrated polymer solutions. © XXXX American Chemical Society

This theory has been tested in detail for low molecular weight polymers showing the capacity to predict particle and polymer density fluctuations over a wide range of length scales.16−18 Key experimental results show that the strength of cohesion is independent of particle volume fraction; however, it is sensitive to polymer type and can be varied by diluting the polymer with different solvents and by altering temperature.17,19 In this study, we explore the effects of polymer molecular weight on the microstructure of polymer segment and particle in concentrated polymer solutions. Particles in concentrated polymer solutions are often in an intermediate state to formulate polymer nanocomposites; nanocomposites can be made by mixing relatively dilute suspensions with polymer solutions and then evaporating of the low molecular weight solvent. Furthermore, thermodynamic properties of concentrated systems resemble that of polymer nanocomposites since the monomer collective density fluctuation correlation length is of the order of the segment size when the concentration of polymer solution is dense enough.14 In nanocomposites, when the polymer segments adsorb strongly enough to the particle surface to stabilize the system, particles induce the polymers to entangle at a sufficiently high particle volume fraction where the average of particle surfaceReceived: March 3, 2013 Revised: June 9, 2013

A

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Table 1. Sample Descriptions Used in This Study particle volume fractions (ϕc) techniques

Rpa

PEG molecular weight

SAXS

0.45

300 400 3000 8000 12 000 20 000 300 1000 3000 12 000 400 1000 3000 8000

NMR (FID)

SANS

a

0.5

0.45

0.087 0.084 0.073

0.120 0.122 0.130 0.1

0.0 0.0 0.0 0.0 0.05b

0.100 0.100 0.100b 0.100

0.181 0.176 0.160 0.17 0.17 0.17

0.238 0.237 0.242 0.2

0.294 0.299 0.3

0.349 0.349 0.330 0.350

0.300 0.300 0.300 0.300 0.300b 0.300

0.200 0.200 0.200b 0.200 0.250 0.250

Rp = vol. of PEG/vol. of (PEG + solvent). bData are obtained from ref 18.

to-surface separation is ∼6Rg or smaller where Rg is the polymer radius of gyration in the bulk, altering nonlinear nanocomposite rheology.3,20 Interpreting these observations includes the dispersion morphologies of the system and estimation of bound polymer layers; 3,8,21 however, these are often complicated by the increasing relaxation times with increasing polymer molecular weight raising questions about how close the nanocomposite lies to equilibrium since large molecular weight polymers might not achieve equilibrium configurations yet.22 In this study, we connect the thermodynamic information from the state of particle/polymer segments dispersions to the dynamic information from polymer mobility to fully understand the microstructure of concentrated particle/polymer systems. We characterize the state of polymer dispersions in concentrated polymer solutions as a function of particle volume fraction with increasing polymer molecular weight. Silica nanoparticles with a diameter of 44 nm are suspended in concentrated poly(ethylene glycol) (PEG) solutions. The PEG molecular weight (Mw) is varied from 300 to 20 000. PEG adsorbs onto the silica particles creating a gradient in polymer segment mobility as one moves from the bulk to near particle surface.7,23 Here, we examine the changes in polymer dynamics and the microstructure of nanoparticles and polymers as a function of polymer molecular weight and particle volume fraction. Polymer concentration, described by the ratio of the volume of PEG to that of PEG plus solvent (Rp), is fixed at a value of 0.45. This ensures physical behavior of concentrated polymer solution is representative of polymer melts since the correlation length of monomer collective density fluctuation is of order the statistical segment size, a nanometer. A segment of the freely jointed chain model is a sphere of diameter d, which represent a few PEG monomers. First, small-angle X-ray scattering technique is used to characterize systematic variations of osmotic compressibility and the ordering of particle dispersions as polymer molecular weight is altered. Second, we explore the changes in polymer mobility using free induction decay (FID) NMR relaxation technique. These experiments demonstrate that particle surface produces polymers in a glassy state with longer relaxation time; however, the fraction of spins in a glassy state is independent of polymer molecular weight, suggesting that the polymer adsorbs

to the particle surface in a largely molecular weight independent manner. Third, we further explore the adsorption property of the polymer near the particle surface using contrast-matching small angle neutron scattering experiment, yielding the thickness of adsorbed polymer layer extracted from polymer and particle partial scattering structure factors. This provides evidence for changes in polymer layer thickness with varying polymer molecular weight. Lastly, we contrast these results with the predictions of PRISM, which predicts a weak sensitivity of particle order to the polymer’s degree of polymerization, polymer molecular weight. We conclude that changes in polymer packing at the particle surface and the resulting particle microstructure do not result from variations in the strength of segment−surface cohesion, but from strong adhesion of the PEG segments to the particle surface and the resulting nonequilibrium polymer configurations.

II. EXPERIMENT AND THEORY Sample Preparation. Silica nanoparticles were synthesized based on the method of Stöber et al.24 using the base-catalyzed hydrolysis and condensation of tetraethylorthosilicate (TEOS). The reaction temperature was 55 °C. Then, 3610 mL of pure ethanol was mixed with 96 mL of deionized water, and 156 mL of ammonium hydroxide was then added as a catalyst. The mixing was allowed to run for 4 h. After mixing, 156 mL of TEOS was added and the reaction was allowed to run for 7 h. This procedure produces nanoparticles of diameter D = 44 ± 4 nm suspended in ethyl alcohol. Particle diameters were determined based on SEM performed on 100 particles yielding a diameter of 43 ± 5 nm; alternatively, fitting of the single particle form factor determined by the angle dependence of X-ray scattering from a dilute suspension of particles yielded a diameter of 43 ± 1 nm. PEG was purchased from Sigma-Aldrich, and ethyl alcohol was supplied from Decon Lab. Inc. The effective diameter of a PEG monomer is d ∼ 0.6 nm. The nanoparticle size was chosen to minimize the size asymmetry ratio, D/d, but have a large enough particle such that small-angle X-ray scattering can be used to probe both long wavelength and cage scale collective concentration fluctuations. After particle synthesis, the alcosol was concentrated approximately 10 times by heating in a ventilation hood. During this process, the excess ammonium hydroxide was removed. For the preparation of polymer suspensions, the exact mass of each component (silica, PEG, H2O/D2O) was determined in order to create the desired particle and polymer concentrations. In this process, the initial volume fraction of particles is required. Particle volume fractions were calculated using B

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the masses of each component and their densities. The silica particle density is 1.6 g/cm.3,25 The defined mass of alcosol is then mixed with the defined mass of PEG. Samples were heated in a vacuum oven to drive off ethanol. The vacuum oven was purged several times with nitrogen followed by evacuation of the chamber to remove oxygen which degrades PEG at high temperature. Once the ethanol was evaporated, the necessary amount of water was added to the sample and fully mixed on the vortex mixer to produce the desired concentrations of particles and PEG. In the absence of PEG, the alcosol appears transparent blue. As the silica and PEG have nearly identical refractive indices (nsilica =1.4555, nPEG = 1.4539), the polymer/particle mixture becomes increasingly transparent as polymer concentration is increased. In the absence of water, the polymer nanocomposite melt is fully transparent and this index matching greatly reduces (nearly eliminates) van der Waals attractions between silica particles thereby rendering them model hard spheres.25 Polymer concentration will be described in terms of the parameter Rp, defined as the ratio of the polymer volume to that of polymer plus solvent. For Rp > 0.45, the suspensions are observed to be stable and well dispersed. In all experiments Rp is fixed at 0.45 or 0.5 depending on the experiment shown in Table 1 to only observe the effect of the molecular weights. Deionized water (H2O) was used for solvent for SAXS experiments and D2O was used for NMR experiments. Small Angle X-ray Scattering. Small-angle X-ray scattering (SAXS) experiments were conducted at the Sector 5 of the Advanced Photon Source (Argonne National Laboratory) to explore the microstructure of silica nanoparticles in polymer solutions, employing a sample-to-detector distance of 4.04 m and radiation wavelength λ = 1.378 Å. Scattered X-rays were recorded on a Mar CCD area detector. The 2-D SAXS patterns were then azimuthally averaged, and relative one-dimensional scattering intensity was plotted as a function of scattering vector q (q = 4π sin(θ/2)/λ), where θ is the scattering angle. The measured scattering, after subtraction of the scattering of the corresponding polymer solution in absence of the particles, was considered to arise only from the silica nanoparticles thereby enabling use of the effective one-component model. The X-ray scattering intensity from a single component material was written as

I(q , ϕc ) = ϕc Vc Δρe 2 P(q)Scc(q , ϕc ) + B

implicitly by reducing the bulk polymer packing fraction and adjusting the polymer adsorption strength, roughly in the spirit of an effective mean field chi-parameter and effective (but compressible) 2component mixture model. The mixture model and PRISM theory employed here are identical to prior studies and well-documented.13,14,16,17 The homopolymer is a freely jointed chain composed of N spherical sites (diameter d) with a bond length of l/d = 4/3, and nanoparticles are spheres of diameter D. All species interact via pair decomposable hard core repulsions. The chemical nature of the polymer−particle mixtures enters via a twoparameter Yukawa interfacial attraction with contact attractive energy of εpc and decay length of the segment-colloid interaction of αd. ⎛ − (r − (D + d)/2) ⎞ ⎟ Upc(r ) = − εpc exp⎜ ⎝ ⎠ αd

In the context used here, PRISM theory consists of three coupled nonlinear integral equations for the site−site intermolecular pair correlation functions, gij(r), where i and j refer to the polymer monomer (p) or nanoparticle (c). The dimensionless partial structure factors, Sij(q), describe collective concentration fluctuations on a length scale 2π/q. The theory uses the site−site Percus−Yevick closure for p−p and p−c correlations and the hypernetted chain approximation for c−c correlations.14 Unless otherwise noted, N = 100, D/d = 10, α = 0.5, and εpc = 0.45 kT which are typical values for the current experimental studies. Details of the theory are summarized in references.13,16,17 The final input to the theory is the monomer and particle packing (volume) fractions: ϕp ≡ πρpd3/6 and ϕc ≡ πρcD3/6, respectively, where ρj are the corresponding number densities. For simplicity, we treat the polymer solution as having a volume fraction of ϕp0 set by Rp.17 In the melt ϕp0,m = 0.4 as this yields a realistic dimensionless isothermal compressibility Spp(ϕc = 0, q = 0) ∼ 0.2. In the presence of particles, total particle volume fraction (ϕt), (colloid plus polymer segments) is adjusted to account for the ability of polymer segments to pack in the interstices between particle segments.16 Calculations based on this approach for particle−polymer mixtures agree well with experimental scattering profiles over a wide range of particle volume fractions and under both weak and intermediate strengths of interfacial cohesion.16,17,19 MSE-FID. The shape of the H NMR time domain signal is mainly influenced by strong dipolar 1H−1H couplings and thus provides information about the polymer’s molecular structure and dynamics. The higher mobility in the mobile phase results in a stronger motional averaging of the dipolar couplings and a longer transverse relaxation time (T2m) while stronger dipolar couplings in the rigid phase induce a fast transverse relaxation of the signal and a shorter relaxation time (T2r). As a consequence, changes in relaxation time scales depend on the 1H environment. Measurement of the free induction decay (FID) NMR time domain signal thus allows quantification of the proton relaxation rates and fractions of protons in mobile and rigid environments. Although 1H-FID analysis has become popular since it is readily available with low-field NMR spectrometers, the inherent noise in the initial part of the FID often caused by rf-pulse breakthrough leads a time delay in the start of the acquisition time and obscures the initial rapid decay associated with protons in glassy environments. To avoid this “dead-time” issue, we use dipolar timereversed mixed magic sandwich echo (MSE). The MSE refocuses the dipolar couplings and gives a time-reverse of the signal decay. This method results in much greater sensitivity to short time relaxation processes, thus, enabling that we obtain the complete FID signal. FID or MSE-FID is a consequence of different spin−spin proton relaxations, which allows quantifying the polymer mobility with different relaxation times. A detailed discussion of the technique used in this study can be found in the literature.23,26,27 In this process, we use elective filters to emphasize different time domains. For example, a dipolar “magic-angle-polarization” (MP) is used for the mobile phase in order to remove unwanted contributions from the fast relaxation processes. Briefly, by increasing the overall cycle time of the central spin-lock portion of the MSE sequence with increasing interpulse

(1)

where ϕc is the nanoparticle volume fraction, Δρeis the excess electron scattering length density of the particles relative to the PEG solution phase, Vc is the particle volume, P(q) is the single particle form factor, Scc(q,ϕc) is the collective nanoparticle structure factor (normalized to unity at large q), and B is the background scattering amplitude. Moderate nanoparticle polydispersity is taken into account using a Gaussian diameter distribution to calculate an average form factor.17,25 Fitting the experimental form factor to the experimental data yields a standard deviation in size of 0.13D̅ , where D̅ is the average diameter. Collective nanoparticle structure factors were obtained by dividing the scattering intensity from the concentrated particle suspension by its dilute limit analogue (ds) at the same polymer concentration. In the dilute particle limit, Scc(q) = 1. Structure factors are extracted under high polymer concentration conditions where the nanoparticles are stable (miscible homogeneous phase).

Scc(q , ϕc ) =

I(q , ϕc ) ϕc , ds Ids(q , ϕc ) ϕc

(3)

(2)

PRISM Theory. PRISM theory has been extensively applied to polymer nanocomposite melts and concentrated polymer solutions.14,17−19 Recently PRISM was extended to account for the expected increase in total system packing fraction with the addition of hard nanoparticles to a polymer melt composed of monomers which can fill the interstitial space between the nanoparticles.16 The model accounts for an excluded volume around each particle corresponding to a polymer segment radius while at larger segment-surface separations the polymer takes on its pure melt density.16 Following our recent studies, we here use the extended model to a three phase system published in ref 17. In the model, the solvent is treated C

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spacing time (τϕ), the echo becomes inefficient for strong dipolarcoupled spins and their signal is suppressed while the magnetization of mobile segments remains due to weak dipolar coupling and a resulting smaller dephasing of the spins. On the other hand, selective magnetization of the rigid phase is realized with 1H-double quantum (DQ) filter. The detailed information is also provided in the literature.26,28,29 The selective polarization of the rigid phase by a DQ-filter is based on the excitation of double quantum coherences in the rigid region. The excitation and reconversion of DQ-coherences depends on the DQ-excitation time (τDQ) determined in advance to be that time where the excitation intensity is the largest. A challenge in interpreting the 1H signals comes from hydroxyl group of silica particles. Note that less than 3% of total polymer segments are rigid or glassy in our system and therefore, to determine the contribution of hydroxyl groups of silica to the 1H signals is critical because glassy polymer fractions can be overestimated. The pH of the current system could not be measured in the concentrated PEG solutions whereas a similar system was reported to have pH of 7, approximately30 in the absence of PEG. The content of −OH groups in silica has been estimated by various methods.31−33 For example, Kim et al.33 reported that the −OH group contents in silica were approximated as ∼1 wt % of silica which corresponds to hydroxyls that can contribute to the rigid part signals or less in other references.33 In the present study, for instance, a system at Rp = 0.5 and ϕc = 0.3 has roughly 50% of PEG, 50% of solvent and 30% of silica. Since it has approximately 4% of glassy PEG (see Figure 5), the mass of glassy components in the total sample mass is determined to be 2 wt % (=0.5 × 0.04). On the other hand, the OH mass fraction in silica is 0.3 wt % (=0.3 × 0.01) which may contribute to the rigid like polymer signals. Thus, we estimate that less than 15% of the rigid signal may come from proton spins associated with the particle, irrespective of the presence of PEG. This represents a safe margin, considering that water may be present in addition. Small Angle Neutron Scattering (SANS). SANS experiment was performed on the NG7 30 m SANS instrument at the NIST Center for Neutron Research, National Institute of Standards and Technology. Samples were loaded into 1 mm path length demountable titanium cells. The cell temperature was maintained to 25 ± 0.1 °C using the 10CB sample holder with a NESLAB circulating bath. A large range in scattering wave vector, q (0.001−0.1 Å−1), was covered by combining the sector-averaged scattering intensity from two different instrument configurations at 4 and 13.5 m detector distance. SANS data reduction and analysis of the scattering intensity, I versus q was performed using the SANS reduction and analysis program with IGOR Pro available from NIST.34 The intensity, I(q), of scattered neutrons at wave vector q, has three contributions:

increasing particle volume fraction (ϕc). Figure 1 shows structure factors for PEG 300 at Rp = 0.45 with varying ϕc. With increasing ϕc, trends are shown in Figure 1: (i) long wavelength density fluctuations are suppressed (Scc (0) decreases), (ii) the coherency of the cage scale order increases (Scc(q*) increases), and (iii) the position of the cage peak moves to the higher value of qD. Figure 2 shows the structure factors at a fixed ϕc = 0.17, but with increasing polymer molecular weight. From PEG 300 to PEG 400, no quantitative difference is found. However, when molecular weight increases from 300 to 3000, 8000, and 12000, features are distinctively changed. First, the zero angle limit structure factor (Scc(0)) continuously increases as molecular weight increases. This suggests long wavelength density fluctuations increase indicating that the particle subsystem becomes more compressible with higher molecular weight. Second, the height of the first peak decreases significantly indicating the particles are less ordered as molecular weight increases. When PEG molecular weight is 12000, there is only weak structure with Scc(q), approaching unity at all length scales. Lastly, position of the first peak moves to the higher wave vectors, suggesting the distance between particle centers of mass is smaller at higher molecular weights in a qualitatively similar manner, seen when particle volume fractions are increased (Figure 1). With increasing molecular weight, the observed trends consistently indicate the silica particle subsystem becomes less stable, suggesting a change from repulsive to attractive pair potentials of mean force. To clarify the variations in the structures more quantitatively, we plot the inverse osmotic compressibility from the inverse of the zero-limit structure factors (Scc(0)) as a function of particle volume fractions. Figure 3 shows the inverse osmotic compressibility as a function of particle volume fraction with different polymer molecular weights; 300, 400, 3000, and 8000. As indicated in Figure 2 the particle subsystem is least compressible when particles are suspended in the concentrated PEG 300 solution and become more compressible at higher molecular weights for a wide range of particle volume fractions. Increasing compressibility with molecular weight shown in Figure 3 is analogous to the previous study where system compressibility was reported in nanocomposite melts.20 Previously, in studying the effects of dilution of a nanocomposite melt with a low molecular weight solvent and with changes of the chemical composition of the low molecular

I(q) = nc Δρc 2 Pc(q)Scc(q , ϕc ) + 2Δρc Δρp nc npPc(q) Spc(q) + npΔρp 2 Spp(q)

(4)

ρ*jVj2,

and ρ*j, and Vj are number density and unit volume where nj = of the jth component, respectively. Δρj is the difference of scattering length density of component j and the medium, Pc(q) is the particle form factor, and Sij(q) are the structure factors associated with two components (pp, pc, cc) where the subscript p (c) indicates polymer segments (particles). The details of how to extract partial structure factors are beyond the context of the current study. Thus, one can find the experimental details from the Supporting Information.

III. RESULTS Small Angle X-ray Scattering. The state of particle dispersion and the particle contribution to the osmotic compressibility of particle and polymer solution are analyzed with small-angle X-ray scatterings. Collective particle structure factors are calculated with eqs 1 and 2 so that we can observe the change in particle microstructure with varying molecular weight. We first look at the change of structure factor with

Figure 1. Particle structure factors for Rp = 0.45 PEG 300 for varying ϕc ratios. D

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accounting of all spin contributions. Thus, by obtaining a complete FID polarization spin relaxation time spectrum, we are able to estimate the fraction of spins in these different states. Characterization of polymer dynamics using MSE-FID has been well-established and employed in many studies.23,26,28,29,35 The FID time spectrum is written IFID(t ) = I0(fg exp( −t(τg )bg + fi exp( −t(τi)bi + fm exp( −t(τm)bm )

(5)

I0 is the intensity at t = 0, f k is the fraction of the component k, τα are relaxation times for the α process with α = g, i, and m corresponding to glassy, intermediate and mobile parts, respectively. Figure 4a shows MSE-FID for PEG 300 at Rp = 0.5 with ϕc is fixed at 0.0 and 0.3. With no particles in the polymer solution, the intensity decays exponentially with a single relaxation time. As particles are added, the relaxation time spectra changes dramatically suggesting at least two different polymer relaxation processes exist. While it is clear that many of the spins retain their bulk relaxation times, the growth of fast relaxation processes suggests that there is strong coupling of spins associated with physically adsorbed polymer segments. For the molecular weights studied, the MSE-FID spectra are fitted with eq 5 to quantify the polymer dynamics more precisely. Figure 4b shows FID relaxations at a fixed particle volume fraction of ϕc = 0.3 with various polymer molecular weights. Interestingly, all four signals decay in a similar manner despite the large changes seen in structure factors shown in Figure 2

Figure 2. Particle structure factors at a fixed ϕc = 0.17, Rp = 0.45 with varying polymer molecular weights as shown in the legend.

Figure 3. Experimental results for the inverse osmotic compressibility as a function of particle volume fraction (ϕc) with varying polymer molecular weight as shown in the legend.

weight polymers, increasing density fluctuations have been interpreted as indicating a decreasing strength of attraction between polymer segment and particles (εpc).19 Below, we question if this interpretation is correct when polymer molecular weight is increased with all other parameters held constant. Polymer Mobility. If polymer is interacting differently with particle surface as molecular weight is increased, we expect segment mobility near the surface to vary with molecular weight. The FID of polarized proton spins is used here to probe the impact of silica nanoparticles on the dynamics of polymer segments. Specifically, we focus on how the polymer molecular weight alters the polymer segment mobility. Using FID techniques introduced in refs 28 and 35, we assume a multiple exponential spin−spin relaxation response (T2) is associated with three different types of polymer segmental mobility: (i) mobile and melt-like polymer segments as would be observed in the bulk, far from the particle surfaces or in the absence of particles, (ii) intermediately perturbed polymer segments such as loops and tails near the particle surface, but not directly in contact with the particle surface, and (iii) rigid and glassy polymer segments in direct contact with the particle surface. In the bulk, there is weak coupling and the spin polarization decays slowly while in the glassy state, the spins are strongly coupled and polarization decays rapidly. To estimate the fraction of proton spins in each environment, we have a full

Figure 4. MSE-FID signals as a function of the acquisition time (a) for ϕc = 0.0 and ϕc = 0.3 for Rp = 0.5 PEG 300 and its fit to eq 5 (b) at a fixed ϕc = 0.3 for various PEG molecular weights at Rp = 0.5 as shown in the legend. E

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is written as Asδ where As = 6ϕc/D is the specific surface area of silica in the composite, D is the particle diameter. Since the volume fraction of polymer is Rp(1 − ϕc) and thus, the fraction of glassy polymers in a total volume is fg × Rp(1 − ϕc), one can find fg = 6δϕc/DRp(1 − ϕc). The fits to the data in Figure 5b yield nearly constant layer thicknesses of 0.82 ± 0.1 and 0.78 ± 0.1 nm for PEG 3000 and 12000 respectively. Noting that a statistical segment length of PEG is ∼0.6 nm, these results suggest a layer with a thickness of 1−2 polymer segments are held in a glassy state next to each particle surface. The glassy fraction as defined by the most rapidly decaying segment of the FID signal does not account for a gradient of polymer segment mobility that arises from having a few polymer segments per chain strongly adsorbed and the rest of the molecule dangling into the polymer melt as loops and tails. This state of polymer segments contributes to the relaxation times intermediate between the glassy segments in close proximity of the surface and the bulk. A detailed discussion of how to interpret intermediate relaxation times can be found in work of Mauri et al.28 We do not explore these effects here except to note that the fraction of spins associated with intermediate relaxation times increases with molecular weight. The consistency of the glassy fraction suggests that the probability of finding a polymer segment at the particle surface does not vary with polymer molecular weight. However, the increasing fraction of the intermediate spin relaxation times with molecular weight indicates the corona of dangling loops and tails grows with polymer molecular weight. These results indicate that polymer segments remain strongly associated with the particle surface independent of polymer molecular weight. Polymer−Polymer Density Fluctuations. In previous work, we reported measurements of all partial structure factors at Rp = 0.45 for PEG 400 with different particle volume fractions.18 Here, fixing particle volume fractions at 0.2 or 0.25, we observe trends of collective particle and polymer structure factors with increasing molecular weight. As shown in Figures 2 and 3, X-ray scattering studies demonstrate that as polymer molecular weight increases the particle subsystem is more compressible while there is less ordering on the length scale of nearest neighbor cages. The neutron scattering results confirm this trend for a wider range of polymer molecular weights. Using eq 4, we extract partial polymer and interface structure factors as described in the Supporting Information. In Figure 6a, we show the “polymer” partial structure factor, Spp(q). In agreement with the particle partial structure factors, the data again reflects a loss of correlations between polymer segments in moving from PEG 400 to PEG 8000 with the largest drop occurring between PEG 400 and PEG 1000, as the “microphase” peak at nonzero wave vector continuously decreases. As polymer molecular weight increases, there is a suppression of the dimensionless polymer osmotic compressibility, Spp(0). Generally, as molecular weight increases, correlations on the length scale of particle diameter quickly disappear. In Figure 6b, we show the “particle−polymer” structure factor which has a negative value at q = 0 and with increasing qD, Spc(q) decreases and goes through a well-defined minimum at qD ∼ 4−6 for all polymer molecular weights. These negative values and peak locations indicate anticorrelation of particle and polymer segment concentration fluctuations over a range of length scales. At the particle/polymer interface, polymer segments cannot penetrate particle core, but, remain on the surface. As molecular weight increases, the minimum in Spc(q)

and 3. The overlapped data sets for different molecular weights shown in Figure 4b indicates that the fraction of spins in the glassy polymer at a fixed ϕc = 0.3 with various polymer molecular weights are almost independent of polymer molecular weight (Figure 5a). The detailed information on fitting and extraction of f k is found in the Supporting Information and in prior studies.23,26,28,29,35 This suggests that there is little variation in the number of polymer segments in contact with the surface as we increase molecular weight. On the other hand, the result may not be surprising, noting the fraction of glassy polymers was estimated based on the segment per surface. If the density of adsorbed polymer layer does not change with polymer molecular weight, the total number of contacts contributing to the fraction of glassy polymers remains same. The fraction of proton spins in a glassy state increases in an approximately linear manner with particle volume fractions for PEG 3000 and 12000. If we assume that the adsorbed polymers are uniformly distributed on the silica particle surfaces, we can estimate a thickness of the glassy polymer layer by assuming the glassy response arises from an adsorbed polymer layer of a uniform density and thickness δ. The volume of this thin layer

Figure 5. (a) Polymer glassy fractions at a fixed ϕc = 0.3 for various PEG molecular weights determined from Figure 4b and fitted to Eq. 5. (b) Polymer glassy fractions as a function of ϕc for two PEG molecular weights, 3000 and 12000. Curves are fits to fg = 6δϕc/DRp(1 − ϕc). F

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Ps*(q) =

C′ Vshell

2 ⎡ 3Vc(ρ − ρ )j (qrc) 3Vshell(ρshell − ρs )j1 (qrshell) ⎤ c shell 1 ⎢ ⎥ + qrc qrshell ⎣ ⎦

(6)

where C′ is a constant, j1(x) = (sin x − x cos x)/x , rshell = rc + t, t is the layer thickness, rc is the radius of particle, Vi = (4π/3)ri3, and ρshell is average value of the scattering length density within the adsorbed polymer layer. Particle polydispersity is taken into account, while the ratio rc/rshell is held constant also using the NCNR curve fitting program.34 The detailed procedures are found in ref 18 and the Supporting Information. At Rp = 0.45, for particles suspended in PEG 1000, the resulting Ps*(q) overlap well at all particle volume fractions indicating relatively constant layer thickness shown in Figure 7a. Using the scattering length density parameters at a match condition explained in the Supporting Information and a core− shell model form factor in eq 6, the thickness of polymer shells is extracted to be ∼2.0−2.4 nm. This shell thickness indicates that PEG 1000 adsorbs to silica surface to produce a layer of 3− 4 polymer segments in thickness in a particle volume fraction independent manner. Figure 7b presents experimentally deduced Ps*(q) along with the bare particle form factor at all polymer molecular weights. With increasing PEG molecular weight we observe that Ps*(q) 2

Figure 6. (a) Polymer collective structure factor, Spp as a function of reduced wave vector at different polymer molecular weights as shown in the legends. (b) Interfacial collective structure factor, Spc.

reduces in magnitude, tracking the increased local interparticle correlations and growth of the polymer collective structure factor peak. The positions of the minima in Spc(q) and maxima in Spp(q) at a value of qD ∼ 2π confirm again the presence of the strong correlations of polymer segment density fluctuations on particle surfaces. We further characterize the particle−polymer segment density correlations by considering the scattering in a system where Δρc = 0.18 Under these conditions, the scattered neutron intensity is due to non-bulk-like polymer concentration fluctuations associated with shells of adsorbed polymer surrounding each particle. We approximate this scattered intensity in eq 4 as Spp(q) ∼ Spp*(q)Ps(q), where Ps(q) is the polymer shell form factor that would be measured as ϕc → 0 and Spp*(q) is the structure factor associated with correlations between the shell centers-of-mass (CM). We argue that the adsorbed polymer shell CM will, to a good approximation, have the same correlations as experienced by the CM of the nanoparticles (Spp*(q) ∼ Scc(q)) such that when Δρc = 0, I(q) ∼ Spp(q) ∼ CScc(q)Ps*(q), where C is a ϕc-dependent normalization constant. We are thus able to extract the polymer shell form factor by having independent measures of Scc(q) determined where Δρp = 0 as: Ps*(q) =Spp/Scc. This form factor can be fit with a core− shell model form factor using NCNR scattering fitting program34

Figure 7. Polymer layer shell form factor as a function of reduced wave vector. The bare spherical-particle form factor, Pc(q) based on eq 1 is shown as the solid curve for comparison to Ps*(q), experimentally obtained from dilute particle suspensions and fitted to the standard homogeneous sphere model. (a) PEG 1000 with varying ϕc and (b) PEG 400, 1000, 3000, and 8000 at ϕc = 0.20 or 0.25 as indicated in the legend. G

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decays faster than the bare silica form factor with peaks occurring at lower qD than seen in Pc(q). Using the same scattering length density independent of molecular weights and a core−shell model form factor in eq 6, an approximate polymer shell thickness extracted to be ∼0.8 ± 0.5, 2.4 ± 0.5, 4.4 ± 1.0, and 6.4 ± 1.0 nm for PEG 400, 1000, 3000, and 8000, respectively. These values may slightly increase or decrease within the standard deviation, depending on the number of data points used for fitting; however, their relative differences do not vary. The actual fits can be found in the Supporting Information. The radii of gyration for these molecular weights are expected to be 0.7, 1.3, 2.0, and 3.8 nm, respectively. We conclude that the adsorbed layer thickness grows with increasing polymer molecular weight on the order of the radius of gyration of the adsorbed polymer, which is also in agreement with the FID measurements. Polymer Reference Interaction Site Model (PRISM). The experimental results discussed above demonstrate that PEG adsorbs in a manner that produces glassy-like polymer segments independent of molecular weight, and creates a layer surrounding each particle with a thickness that increases with polymer molecular weight. These features would suggest that the particles have an effectively larger volume fraction at a given particle number density, as polymer molecular weight is increased, providing more repulsive interparticle interactions. At a fixed particle volume fraction, therefore, this would be manifested in reduced long wavelength density fluctuations and increased order on cage length scales as polymer molecular weight increases. This expectation is not met. Indeed, we see substantially suppressed order and enhanced long wavelength density fluctuations for both particles and polymer segments, as molecular weight is increased. (Figure 2 and 3) Previously, we have demonstrated that for low molecular weight polymers, near quantitative comparisons can be made between scattering measures of polymer and particle microstructures and PRISM predictions.18,19 In these comparisons α, N, and D/d were held constant and variations in microstructure were associated with variations in εpc. Here we explore the ability of PRISM to capture the observed changes to particle microstructures by varying the input parameters that are associated with the polymer−particle interactions. For the present comparisons, we hold N = 100, D/d = 10, and α = 0.5d, as our base case since these are typical values motivated from previous studies.16−18 These parameters are chosen because of an observed weak dependency of predictions on N, and that as D/d gets large, predictions of microstructure saturate in the large particle limit (experimentally we have a system where D/d = 44/0.6),16 and physically realistic extent of interaction between polymer segments and particle surfaces under the action of van der Waals forces.25 When polymer molecular weight is increased, the first assumption one can make in PRISM theory is N will increase with molecular weight. Figure 8a shows the PRISM predictions when is N increased from 100 to 400, 2000, and 10000. The lack of change in microstructure with variations in N was reported by Hall et al.13,16 who associate the weak dependence on a high total volume fraction. Furthermore, a weak dependency is to be expected in equilibrium when the density correlation length in a polymer melt is of the order of a monomer diameter. Indeed, while varying N will fine-tune the potential of mean force (PMF) by enhancing or suppressing

Figure 8. Experimental results and PRISM predictions for the inverse osmotic compressibility as a function of particle volume fraction (ϕc) with varying polymer molecular weight. Dots are experimental result shown in Figure 3 and predictions are shown with curves as indicated in the legends. PRISM predictions are made at a fixed α = 0.5d, εpc = 0.45, D/d = 10 with varying number of monomers, N. Black solid line is a prediction for hard-sphere.

local minimum features, PRISM is unable to predict the experimental trends observed with increasing molecular weight. As an alternative, we attempt to capture the observed experimental trends by allowing εpc, α, and D/d to have molecular weight dependence (see Supporting Information). When εpc (or α) is allowed to decrease (or increase) in a favor of increasing interparticle attractions with increasing molecular weight, we are able to partially capture the experimental trends. In the same manner, the data can be qualitatively captured if all parameters are held constant except that D/d changes as molecular weight increases. While this exercise can force qualitative fits to the data, there are no physical reasons to justify that the enthalpy of segment-surface attraction (εpc), the range of the segment particle surface interaction (α) or the effective segment size (d) should show such dramatic changes with the polymer molecular weight. Generally, the suppression of 1/Scc(0) with increasing polymer molecular weight is an indication of decreased particle stability, reducing repulsive forces between particles. As discussed in the Supporting Information, PRISM associates this with a reduced density of polymer segments at the particle surface. However, this prediction is not supported by experimental observations that the fraction of polymer segments in a glassy state is independent of molecular weight and the adsorbed layer thickness increases with molecular weight. As a result, we are unable to reconcile PRISM predictions of microstructure with experimental microstructures complimented by FID and neutron scattering studies that providing ample evidence of polymer strongly adsorbing to the particle surfaces when the polymer has a molecular weight greater than ∼1000. On the other hand we note that PRISM predictions are nearly quantitative when compared with measures of polymer and particle microstructure at low molecular weight (PEG 400).17,18 We hypothesize that the discrepancies are associated with nonequilibrium configurations of polymer. Nonequilibrium effects in adsorbed polymer layers have been reported experimentally and theoretically.12 In high molecular weight polymer solutions, polymer relaxation kinetics within the layer can be severely retarded, leading to nonequilibrium layers and the structure and dynamics in nonequilibrium polymer layers depend on adsorption kinetics and layer aging.12 de Gennes H

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molecular weight grows. FID measurements with time-domain NMR experiments show that these changes occur when polymer segments are anchored to the particle surface while contrast-matching neutron scattering indicates that the thickness of a bound polymer layer grows with molecular weight. At higher polymer molecular weights than 1000, PRISM cannot capture these observations while holding εpc, α, and D/d constant and only increasing N. Taken together, this study suggests that polymers adsorb strongly to silica surfaces in dilute solution and except for low molecular weights where the number of attachments to per particle is small, the polymer chains cannot equilibrate with polymers in the bulk even in concentrated polymer solutions. As a result, for the higher molecular weights, PRISM can only be applied if we accept that an enthalpy of exchange of a polymer segment from the bulk to the particle surface is weightdependent. Rheological20 and multiple quantum dipolar coupling relaxation experiments23 indicate that for higher molecular weights as the average distance between particle surfaces is reduced below ∼6Rg, the polymer experiences greater entanglements than observed in the bulk.23 On the basis of observations made here, we suggest these effects are correlated with the nonequilibrium nature of polymer configurations and the approach of a phase separation boundary as molecular weight of the adsorbing polymer increases.

assumed simple reptation model for equilibrium relaxation time36 when the exchange of chains between the bulk and the layer becomes slow due to the fact that incoming and outgoing chains have to pass through unfavored configurations having a small fraction of bound monomers. The longest relaxation time of the layer is scaled as τeq ∼ τsN3 where τs is the relaxation time of an adsorbed monomer, which may be much larger than that of the bulk, τa for entangled layers37 while Semenov and Joanny38 assumed τeq ∼ τaN2 where τs ∼ τa for unentangled layers. In our experimental system, this scaling law implies the layer dynamics of PEG 8000 can be much slower than that of PEG 400 by a factor of 106. In the same picture, the mean lifetime of an adsorbed chain before its desorption can be also estimated to be τex ∼ τaN3.7/f p and τex ∼ τaN2.42/f p for entangled36 and unentangled38 layers, respectively, where f p is the volume fraction of polymer in the bulk, implying the mean lifetime of PEG 8000 is much longer than that of PEG 400 by a factor of 108. On the other hand, Mubarekyan and Santore39 explored the kinetics of poly(ethylene oxide) (PEO) adsorption on silica using total internal reflectance fluorescence in the dilute systems. Their results showed the bulk-layer exchange kinetics are dependent on the chain length and aging; with increasing chain length, the exchange kinetics started to slow down and could not be described by a single exponential exchange law, which can be a signature of equilibrium kinetics.12,39 For long chains, a fraction of the layer appeared unexchangeable during the experiment’s duration, of hours.39 To prepare our samples, we mix dilute particles with a modestly concentrated polymer solution under conditions where the polymer adsorbs strongly to the particle surface. This will encourage rapid polymer adsorption in configurations that will change slowly due to the multiple contacts between a single polymer chain and the particle surface. We anticipate that the number of contacts will grow with polymer molecular weight with the result being very slow equilibration of segments on the surface with those in the bulk. We suggest that this results in adsorbed polymer being effectively bound to the particle surface yet not in equilibrium. Therefore, the system we are studying is PEG-coated particles suspended in concentrated PEG solutions where the completeness of the coating increases with polymer molecular weight. Under these conditions, to a first approximation, PRISM would predict εpc would decrease with polymer molecular weight. We emphasize that this interpretation is only applicable if the polymer segments bound to the particle surface cannot exchange with segments in the bulk and thus on a time scale of our experiments do not relax to equilibrium configurations. Thus, in determining the potential of mean force between particles within a PRISM framework, we would estimate εpc as the enthalpy change in moving a segment from the bulk up to a surface that increasingly looks like it is formed from PEG as polymer molecular weight grows. This would result in a decrease in the effective value of εpc thus, despite strong polymer adsorption to the particle surface and push the particles toward a phase separation boundary.

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ASSOCIATED CONTENT

S Supporting Information *

Scattering length density, MSE-FID fitting, and PRISM prediction. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: (C.F.Z.) [email protected]. Present Address †

Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Small angle X-ray scattering was performed at the DuPontNorthwestern-Dow Collaborative Access Team (DND-CAT) located at Sector 5 of the Advanced Photon Source (APS). DND-CAT is supported by E.I. DuPont de Nemours & Co., The Dow Chemical Company and Northwestern University. Use of the APS, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Argonne National Laboratory, was supported by the U.S. DOE under Contract No. DE-AC02-06CH11357. We also acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work. This work was supported by the Nanoscale Science and Engineering Initiative of the National Science Foundation under NSF Award DMR0642573. We appreciate helpful discussions with Dr. Kenneth Schweizer and Dr. Lisa Hall, who also kindly provided codes for the theoretical comparisons in this research. We also appreciate Dr. Kay Saalwächter and Henriette W. Meyer for help with NMR experiments.

IV. SUMMARY In this work, changes of particle microstructures in a concentrated polymer solution composed of particles and polymer that adsorbs to the particle surface are studied as polymer molecular weight increases. The particle subsystem becomes more compressible and are less ordered suggesting that the particles feel increasing attractions as polymer I

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REFERENCES

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