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Rheology and Microstructure of Polymer Nanocomposite Melts: Variation of Polymer Segment-Surface Interaction Benjamin J. Anderson† and Charles F. Zukoski* Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801. †Present address: Sandia National Laboratories, Albuquerque, New Mexico 87185-1245 Received November 25, 2009. Revised Manuscript Received January 19, 2010 We have studied the effects of particle packing fraction, polymer molecular weight (MW), and polymer-segment-particle-surface affinity on the phase behavior of 44 nm silica dispersions in unentangled, low MW polyethylene oxide (PEO), polyethylene oxide dimethyl ether (PEODME), and polytetrahydrofuran (PTHF) through rheological measurement and small-angle X-ray scattering. Particles are shown to be stable in PEO nanocomposites up to high volume fractions due to an adsorbed layer of polymer segments that stabilizes particles in the melt. Comparison of the PEO nanocomposite to PEODME and PTHF nanocomposites reveals little evidence of an adsorbed layer in the spirit of the PEO nanocomposite. Measurement of the PTHF nanocomposite viscosity reveals evidence of segment slip at the particle surface by the particle intrinsic viscosity being less than Einstein’s value. At higher particle volume fractions, the viscosity diverges, yielding an elastic response. The elastic response of the PEO nanocomposite has the signatures of a colloidal glass, while the PEODME and PTHF nanocomposites resemble a gel. Measurement of the particle structure factor reveals a change from overall repulsive particles in PEO to attractive particles in PTHF as the segment-surface interaction is changed.
I. Introduction Polymer nanocomposites are an important class of materials where nanosized particles are dispersed in a polymer matrix to enhance the mechanical, electrical, rheological, optical, and/or thermal properties of the neat polymer.1 They have considerable commercial importance in the manufacture of rubber, building materials, biomaterials, insulating and conductive polymers, and in coatings. Changes in the material properties of the nanocomposite are strongly linked to the interaction of polymer segments and the particle surface and how this interaction influences the state of particle dispersion.1,2 Optimization of nanocomposite properties requires deeper understanding of how variation of polymer segment-surface interaction affects the state of the particle dispersion. Recent studies demonstrate that when equilibrium is achieved, particles in polymer melts display the same states as do particles suspended in low molecular weight fluids: the particles can disperse in a single phase, separate into two distinct liquidlike phases (one dense and one dilute in particles), or crystallize. In addition, the particles are expected to form nonequilibrium gel and glassy phases. Unique to the polymer nanocomposite, these models predict equilibrium bridging states where particles are held together by polymer chains that bridge the interparticle gap.3,4 The state of a nanocomposite depends sensitively on the polymer-segment-particle-surface interaction potential. Here, we report a detailed study of the mechanics and microstructures of a single particle type suspended in melts of three polymers and *To whom correspondence should be addressed. E-mail: czukoski@ illinois.edu. (1) Koo, J. H. Polymer Nanocomposites. In Nanoscience and Technology; Manasreh, O., Ed.; McGraw-Hill: New York, 2006. (2) Wang, M.-J. Effect of polymer-filler and filler-filler interactions on dynamic properties of filled vulcanizates. Rubber Chem. Technol. 1998, 71(3), 520. (3) Hooper, J. B.; Schweizer, K. S. Contact aggregation, bridging, and steric stabilization in dense polymer-particle mixtures. Macromolecules 2005, 38(21), 8858-8869. (4) Hooper, J. B.; Schweizer, K. S. Theory of Phase Separation in Polymer Nanocomposites. Macromolecules 2006, 39(15), 5133-5142.
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provide evidence that changes in the resulting phase behavior are related to segment-surface interaction. Theories of Hooper and Schweizer3,4 predict particle stability based on hard sphere colloid interactions and threadlike models of polymer configuration in the melt. The phase behavior of the composite is predicted from calculation of the polymer induced particle pair potential which is modeled as depending on the ratio of the particle to polymer segment size, the degree of polymerization, and the strength and range of segment-surface interaction. The combined contribution of these variables drives particle organization in the polymer matrix. Previous studies have focused on polymer nanocomposites composed of 44 nm silica particles suspended in hydroxyl terminated polyethylene oxide (PEO).5-8 The effects of varying particle volume fraction and polymer molecular weight uncovered a variety of behavior. Through rheological and microstructural studies, we find that the adsorption of PEO segments on the particle surface creates a bound polymer layer that increases the effective hydrodynamic size of the particles.6 The thickness of the bound layer scales on the polymer radius of gyration, Rg. This observation is in agreement with past surface forces measurements of confined polymer melts.9-12 Below the critical entanglement molecular weight, Mc, of 4000 g/mol from a rheological point of (5) Anderson, B. J.; Zukoski, C. F. Nanoparticle stability in polymer melts as determined by particle second virial measurement. Macromolecules 2007, 40(14), 5133-5140. (6) Anderson, B. J.; Zukoski, C. F. Rheology and Microstructure of an Unentangled Polymer Nanocomposite Melt. Macromolecules 2008, 41(23), 9326-9334. (7) Anderson, B. J.; Zukoski, C. F. Colloidal glass transition in unentangled polymer nanocomposite melts. J. Phys.: Condens. Matter 2009, 21(28), 285102. (8) Anderson, B. J.; Zukoski, C. F. Rheology and Microstructure of Entangled Polymer Nanocomposite Melts. Macromolecules 2009, 42(21), 8370-8384. (9) Granick, S.; Hu, H.-W. Nanorheology of Confined Polymer Melts. 1. Linear Shear Response at Strongly Adsorbing Surfaces. Langmuir 1994, 10(10), 3857-3866. (10) Horn, R. G.; Hirz, S. J.; Hadziioannou, G.; Frank, C. W.; Catala, J. M. A Reevaluation of Forces Measured across Thin Polymer-Films - Nonequilibrium and Pinning Effects. J. Chem. Phys. 1989, 90(11), 6767-6774.
Published on Web 02/17/2010
DOI: 10.1021/la9044573
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view, particle interactions are well described by hard sphere models when the particle size is rescaled to account for the adsorbed polymer layer. At high volume fractions, colloidal glasses are observed in molecular weights of 1000 g/mol and below.7 For nanocomposites with a polymer of molecular weights above Mc, particle interactions are longer range and softer than those of hard spheres.8 The origin of the longer range interaction is linked to entanglements of surface polymer and bulk polymer. For these systems, as the volume fraction is increased, adsorbed polymers are forced to overlap and entangle at volume fractions below that required for the particles to undergo a glass transition. At high volume fractions where the polymer is significantly confined between particles, the high molecular weight PEO nanocomposites undergo a ductile to brittle mechanical transition. This transition is linked to the onset of attractions and of a phase transition in the nanocomposite. These observations are supported by the linear and nonlinear stress response of the nanocomposites and scattering measurement of the particle structure factor as volume fraction is increased. In this Article, three nanocomposites are studied where the polymer segment-surface interaction and polymer molecular weight are varied. The rheology and microstructures of the same silica particles dispersed in hydroxyl terminated low molecular weight polyethylene oxide are compared with the same properties measured on nanocomposites composed of silica particles dispersed in melts of polyethylene oxide dimethyl ether (PEODME) and polytetrahydrofuran (PTHF). The surface activities of PEODME and PTHF are distinct from those of PEO in two separate ways. PEODME is a change of the hydroxyl end groups of PEO to methoxy end groups, and PTHF is a change of half of the backbone oxygen atoms to methyl groups. These two modifications of PEO have been shown to lower polymer surface activity.13-16 Nevertheless, all three polymers wet a silica surface. This is seen experimentally by the spreading of the polymer on a glass slide with a contact angle that is less than 90. Here, we report the impact of a change in segment-surface interaction and polymer molecular weight on nanocomposite mechanics and particle microstructure. As found with PEO, there is evidence of surface adsorbed polymer segments in PEODME but little to no evidence of surface adsorbed polymer segments in PTHF. Instead, we identify slip of PTHF segments on the particle surface from the reduction of the particle intrinsic viscosity below Einstein’s value. The change in the segment-surface interaction is also found through measurement of the second order term of the relative viscosity which quantifies particle interactions in the pair limit. The influence of the segment-surface interaction on particle-particle interactions is clearly seen by comparing the particle structure factors where particle density fluctuations are more prevalent in PTHF than PEO and PEODME. At higher volume fraction, nanocomposites of silica in PEODME and (11) Montfort, J. P.; Hadziioannou, G. “Equilibrium” and dynamic behavior of thin films of a perfluorinated polyether. J. Chem. Phys. 1988, 88(11), 7187-7196. (12) Van Alsten, J.; Granick, S. Shear rheology in a confined geometry: polysiloxane melts. Macromolecules 1990, 23(22), 4856-4862. (13) Van der Beek, G. P.; Cohen Stuart, M. A.; Fleer, G. J.; Hofman, J. E. Segmental Adsorption Energies for Polymers on Silica and Alumina. Macromolecules 1991, 24(25), 6600-6611. (14) Huang, Y. D.; Santore, M. M. Dynamics in adsorbed layers of associative polymers in the limit of strong backbone-surface attractions. Langmuir 2002, 18(6), 2158-2165. (15) Kelly, M. S.; Santore, M. M. The Role of a Single End Group in Poly(Ethylene Oxide) Adsorption on Colloidal and Film Polystyrene - Complimentary Sedimentation and Total Internal Reflectance Fluorescence Studies. Colloids Surf., A 1995, 96(1-2), 199-215. (16) Ouali, L.; Francois, J.; Pefferkorn, E. Adsorption of telechelic poly(ethylene oxide) on colloids: Influence on colloid stability. J. Colloid Interface Sci. 1999, 215(1), 36-42.
8710 DOI: 10.1021/la9044573
Anderson and Zukoski Table 1. Polymer Properties MW
Na
Rg [nm]
Tm [C]
PEO1000 23 1.3 40 PEO2000 45 1.9 55 PEODME1000 23 1.3 42 PEODME2000 45 1.9 53 PTHF1000 14 1.4 29 PTHF2000 28 1.9 34 a Number of monomers. b Temperature of 75 C.
ηp[P]b 0.35 0.90 0.20 0.73 0.90 3.8
PTHF undergo liquid to solid transitions whereas particles remain stable in PEO. These results are interpreted as demonstrating how diminishing the surface activity of the polymer changes particle interaction potentials from repulsive in PEO to attractive in PTHF.
II. Experimental Methods A. Sample Preparation. Silica particles were synthesized by the base catalyzed hydrolysis and condensation of tetraethylorthosilicate according to the method of St€ ober et al.17 The synthesis produces an alcosol solution of silica particles. Particles were synthesized with a number average diameter of 43 ( 4 nm as determined from transmission electron microscopy measurements and a volume average diameter of 44 ( 4 nm determined from static scattering measurements. Particles were dispersed in PEODME and PTHF of two molecular weights purchased from Sigma-Aldrich. Polymer properties are listed in Table 1. The radius of gyration of the polymers was calculated from reported measurement of the polymer characteristic ratios.18,19 We assume that PEODME has a similar value to PEO. The polymers are all unentangled. Particle dispersions were made by mixing the alcosol and polymer at a temperature above the melting temperature of the polymer. The ethanol is evaporated in a vacuum oven purged with nitrogen to avoid oxidative polymer degradation. Previously, we have developed a mixing method that avoids premature particle flocculation as the alcosol and polymer are mixed.8 This mixing method is employed here yielding well dispersed particles in all the polymers under dilute conditions. We have found that premature particle flocculation occurs if the polymer is diluted too extensively by the addition of alcosol. The time of particle flocculation in the presence of solvent varies from days to near instantaneous depending on the molecular weight of the polymer. Higher molecular weight polymers flocculate the particles more rapidly. We have found that the particle flocculation can be overcome by concentrating the alcosol so that the polymer is diluted less. We believe the polymer initiates depletion flocculation of the particles under dilute polymer conditions. Under concentrated conditions, the particles restabilize in the polymer solution. The filled polymer melts are transparent, since silica and the polyethers have similar refractive indices. The density of the particle filled melt, FT, was measured using a Mettler/KEM DA-100 density/specific gravity meter. The particle volume fraction, φc, was calculated from the mass of silica, mc, added to a mass of polymer, mp, using the measured density of the filled melt and a particle density, Fc, of 1.6 g/cm3.5 φc ¼
FT mc Fc mc þ mp
! ð1Þ
(17) St€ober, W.; Fink, A.; Bohn, E. Controlled growth of monodisperse silica spheres in the micron size range. J. Colloid Interface Sci. 1968, 26(1), 62-69. (18) Higgins, J. S.; Nicholson, L. K.; Hayter, J. B. Observation of single chain motion in a polymer melt. Polymer 1981, 22(2), 163-167. (19) Kugler, J.; Fischer, E. W.; Peuscher, M.; Eisenbach, C. D. Small angle neutron scattering studies of poly(ethylene oxide) in the melt. Makromol. Chem. 1983, 184(11), 2325-2334.
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The use of a densitometer is important because we have found that filled melts typically have negative volumes of mixing. B. Rheology. Rheological measurements were performed using a constant stress C-VOR Bohlin rheometer with cone and plate geometry. The cone diameter was 40 mm, and the angle was 4. Measurements were made at a sample temperature of 75 C to be consistent with previous measurements on filled PEO melts. Viscous samples were presheared followed by an equilibration period prior to viscosity measurements. Viscoelastic samples were subjected to a high strain oscillatory stress followed by a waiting time which allowed the structure to build back into the sample. The waiting time for each polymer nanocomposite was determined as the time for the elastic modulus measured at a low strain of 10-3 to reach an upper plateau value. The waiting time for solidlike PEO nanocomposites was approximately 5 min, whereas the waiting time for PEODME was 12 h and PTHF was 24 h. C. SAXS. Small angle X-ray scattering (SAXS) was performed at the 8ID-E XOR beamline located at the Advance Photon Source, Argonne National Laboratory. The instrument has effective pinhole collimation, removing the need for slit desmearing. Samples were loaded in custom-made aluminum cells sealed with two kapton polyimide slides. The beam path length was approximately 1 mm. The cells were secured to a heating block set to a temperature of 75 C and maintained by a peltier controller. Scattered photons were collected using an area detector. We have found that, as the sample viscosity increases due to an increase in the molecular weight of the polymer or at higher particle volume fractions, extended exposure to X-rays results in radiation damage and particle aggregation. This aggregation is believed to be due to the slowing down of energy dissipation in the illuminated region of the sample as the viscosity of the sample increases. Aggregation occurs only in the illuminated region of the sample. This was verified by successive illumination of different regions of the sample. We have found that the influence of aggregation on the scattering was minimized if the total exposure time to X-rays was limited to less than 60 s. The rapid shutter speed of the detector allowed well over 1000 frames to be collected in that time. We found that 50 frames were sufficient to obtain well averaged static scattering data. Three different regions of the sample were illuminated, and the scattering pattern was averaged over the three regions. The scattering intensity of X-rays for a single component dispersion is given by Iðq, φc Þ ¼ φc Vc ΔFe 2 PðqÞ Sðq, φc Þ
ð2Þ
The first term refers to scattering from the particles where φc is the particle volume fraction, Vc is the volume of a single particle, and ΔFe is the difference of electron scattering length density of the particles above that of the polymer. The variable q is the scattering vector, q = (4π/λ)sin(θ/2) where λ is the wavelength of incident X-rays and θ is the scattering angle. P(q) is the form factor accounting for intraparticle scattering interference, and S(q,φc) is the structure factor accounting for interparticle scattering interference. Scattering from the silica particles dominates. This enables us to neglect cross scattering terms between the polymer and particle, and the dispersion is viewed as an effective one component system.20-23 (20) George, A.; Wilson, W. W. Predicting Protein Crystallization from a Dilute-Solution Property. Acta Crystallogr., Sect. D: Biol. Crystallogr. 1994, 50, 361-365. (21) Kulkarni, A. M.; Chatterjee, A. P.; Schweizer, K. S.; Zukoski, C. F. Depletion Interactions in the Protein Limit: Effects of Polymer Density Fluctuations. Phys. Rev. Lett. 1999, 83(22), 4554-4557. (22) Rosenbaum, D.; Zamora, P. C.; Zukoski, C. F. Phase behavior of small attractive colloidal particles. Phys. Rev. Lett. 1996, 76(1), 150-153. (23) Rosenbaum, D. F.; Zukoski, C. F. Protein interactions and crystallization. J. Cryst. Growth 1996, 169(4), 752-758.
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In the dilute particle limit, the structure factor goes to unity and the scattering equation reduces to I(q,φc) = φcVcΔFe2P(q). The form factor for spherical particles is given by !2 sinðqDc =2Þ -ðqDc =2ÞcosðqDc =2Þ PðqÞ ¼ 3 ð3Þ ðqDc =2Þ3 We account for modest polydispersity in particle size by calculating P(q) for a size distribution. This is done by employing a Gaussian diameter distribution to calculate an average form factor for a population of particles with volume average diameter, Dc, and standard deviation, ν. The integration variable Dc is the variable diameter of a particle. ! ðDc -Dc Þ2 R 1 2ν2 pffiffiffiffiffiffiffiffiffiffi e Dc 6 PðqÞ dDc 2 2πν ! PðqÞ ¼ ð4Þ ðDc -Dc Þ2 R 1 2ν2 pffiffiffiffiffiffiffiffiffiffi e Dc 6 dDc 2πν2 Experimental scattering of dilute suspensions are fit to the scattering equation for q > 0.007 A˚-1 utilizing eq 4 for the form factor to determine a scattering size and standard deviation in the polymer melt (Figure 1). The depression in the scattering at low q for dilute PEODME and PTHF nanocomposites in Figure 1 is due to the influence of S(q,φc) which is not truly unity at all q, but less than unity at low q. The fitting procedure has three adjustable parameters: particle diameter, standard deviation, and electron contrast density. The electron contrast is not a true contrast, since the intensity units are arbitrary. As the volume fraction of filler is raised, the structure factor measures the spatial distribution of filler particles in inverse space. Formally, the structure factor for a single component dispersion is defined as the Fourier transform of the total correlation function, hcc (r), eq 5. Z ¥ φ sinðqrÞ dr ð5Þ Sðq, φc Þ ¼ 1 þ c 4πr2 hcc ðrÞ ðqrÞ Vc 0 The total correlation function is the nonrandom part of the pair correlation function, gcc (r), hcc (r) = gcc (r) - 1. Experimental structure factors for concentrated suspensions are calculated by dividing the intensity of a concentrated suspension by the intensity of a dilute suspension (ds), eq 6. In the dilute limit, the structure factor goes to unity since particle positions are uncorrelated. The result leaves S(q,φc) for the concentrated suspension, Iðq, φc Þ φc, ds Sðq, φc Þ ¼ ð6Þ Ids ðq, φc Þ φc
III. Results A. Rheology. Due to the Newtonian behavior of unentangled polymer and the large particle to polymer size ratio, we assume that the low molecular weight polymer-particle composites may be viewed as a particle suspension in a high viscosity continuum. This assumption proved to be valid for the case of nanoparticles dispersed in low molecular weight PEO. Under this premise, the low shear relative viscosity, ηr,o, of the filled polymer melts at low volume fractions is characterized by ηr, o ¼ 1 þ ½ηφc þ Pφc 2
ð7Þ
where [η] is the particle intrinsic viscosity and P is the pair interaction coefficient that defines the contribution of two particle DOI: 10.1021/la9044573
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Anderson and Zukoski Table 2. Nanocomposite Viscosity Parameters MW
k
P
P/k2
PEO1000 PEO2000 PEODME1000 PEODME2000 PTHF1000 PTHF2000
1.34 ( 0.05 1.48 ( 0.03 1.26 ( 0.07 1.25 ( 0.02 0.81 ( 0.03 0.8 ( 0.1
10.1 ( 1.3 13.4 ( 1.1 38 ( 4 37 ( 1 42 ( 3 383 ( 42
5.6 ( 0.7 6.1 ( 0.5 24 ( 3 24 ( 1 64 ( 3 245 ( 27
_ c3/ neat polymer. We define the Peclet number, Pe = 3πηpγD 4kBT, where γ_ is the shear rate and kBT is the product of Boltzmann’s constant and absolute temperature. An equivalent _ c2/4Do, where Do = kBT/3πηpDc is the alternative definition is γD dilute particle diffusion coefficient. The particle intrinsic viscosity is defined here as [2.5k], where 2.5 is Einstein’s coefficient and k is a parameter that defines how polymer adsorption influences the particle intrinsic viscosity. Equation 7 is linearized in terms of the volume fraction to the reduced viscosity, ηred. ηred ¼
Figure 1. Experimental scattered intensity and model fit [solid line] of a dilute suspension (φc = 0.01) of particles in (A) PEO1000, (B) PEODME1000, and (C) PTHF1000 utilizing an average form factor, P(q). Fitting parameters are Dc = 44 nm and ν = 4 nm.
interactions to the viscosity. The low shear relative viscosity is measured in the zero shear limit, ηr,o = limPef0η/ηp, where η is the viscosity of the nanocomposite and ηp is the viscosity of the 8712 DOI: 10.1021/la9044573
ηr, o -1 ¼ ½η þ Pφc φc
ð8Þ
We anticipate that the adsorption of polymer segments on the particle surface will affect the particle intrinsic viscosity to varying degrees depending of the strength of the segment-surface attraction. When particles are dispersed in weakly adsorbing polymer, slip of segments on the surface will reduce the intrinsic viscosity and k will be less than unity. In contrast, when particles are dispersed in strongly adsorbing polymer, the sticking of segments will increase the intrinsic viscosity due to the enhanced energy dissipation associated with each particle dragging adsorbed polymer through the melt under shear. This will cause k to be greater than unity. In this sense, k quantifies a larger excluded volume of the particle due to polymer adsorption. Taking this view, k can be defined as k = φη/φc, where φη is an effective particle volume fraction that is higher than the core silica volume fraction. The particle is viewed as having a larger effective volume with an intrinsic viscosity of 2.5. Previously, we showed that k = 1.34 ( 0.05 and P = 10.1 ( 1.3 for particles in PEO1000.6 Values for k and P are listed in Table 2 for PEO1000 and the other polymers in this study. The value of k being greater than unity resulted from PEO adsorption to the particle surface causing the particles to have a larger effective hydrodynamic size. The larger effective size was taken into account in the pair interaction coefficient by dividing P by k2. P/k2 = 5.6 ( 0.7, which compares well with the theoretical value of 5.9 for particle interactions governed by hard core excluded volume repulsions.24 Further, at high particle volume fractions, the low shear viscosity mimicked other experimental hard sphere suspensions ultimately leading to a colloidal glass transition at an effective volume fraction, φη = kφc, of 0.58.7 For the case of a weakly adsorbing polymer, we expect k will be less than unity and will quantify the degree of slip. Slip is measured from the intercept of a plot of the reduced viscosity versus φc. In addition, the pair interaction coefficient will be affected by slip. The influence of slip has been derived for hard spheres but has yet to be incorporated into other potentials thereby limiting our ability to directly characterize the influence of slip on pair particle interactions.24 Therefore, pair interactions will be compared at the more general level of the pair interaction coefficient with minor corrections for slip. (24) Cichocki, B.; Felderhof, B. U. Long-time self-diffusion coefficient and zerofrequency viscosity of dilute suspensions of spherical Brownian particles. J. Chem. Phys. 1988, 89(6), 3705-3709.
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Figure 2. (A) Measurement of the low shear reduced viscosity of PEO1000 [9], PEODME1000 [b], and PTHF1000 [[]. (B) Measurement of the low shear reduced viscosity of PEO1000 [9] and PEO2000 [solid vertical bowtie]. (C) Measurement of the low shear reduced viscosity of PEODME1000 [b] and PEODME2000 [2]. (D) Measurement of the low shear reduced viscosity of PTHF1000 [[] and PTHF2000 [1]. Solid lines show linear fits to eq 8.
In Figure 2A, the dilute low shear viscosity of PEO1000 is compared to results for the silica particles dispersed in PTHF1000 and PEODME1000. The reduced viscosity is plotted as a function of silica volume fraction over the range φc e 0.10 and the data are fit to eq 8 over a region where the reduced viscosity appears linear and higher order terms are negligible. In PTHF1000, k = 0.81 ( 0.03, which is convincingly less than unity. This result suggests that PTHF1000 segments slip at the particle surface, a result expected for polymer segments that bind weakly to the particle surface. The degree of slip is quantified by expressing k in terms of the slip parameter, ξ:25 1 -ξ k¼ , ke1 ð9Þ 1 þ 2ξ The slip parameter is zero for a pure stick boundary condition and 1/3 for a pure slip boundary condition. We calculate the slip parameter to be 0.07 ( 0.01, meaning partial slip of segments at the surface. P/k2 = 64 ( 3, a value significantly greater than expected for hard spheres. The larger value can imply either added (25) Cichocki, B.; Felderhof, B. U. Short-time diffusion coefficients and high frequency viscosity of dilute suspensions of spherical Brownian particles. J. Chem. Phys. 1988, 89(2), 1049-1054. (26) Russel, W. B.; Saville, D. A.; Schowalter, W. R. Colloidal Dispersions; Cambridge University Press: Cambridge, UK, 1992.
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attractions or repulsions.26 The particles are not charged in PTHF due to the low dielectric constant of the polymer, and there is no detectable presence of an adsorbed layer. The particles are also index matched, making van der Waals interactions negligible. Based on the model of Hooper and Schweizer for weak polymer segment-surface interactions,3,4 we infer that the large pair interaction coefficient results from depletion attractions. In PEODME, k equals 1.26 ( 0.07, implying that the PEODME adsorbs to the particle surface and enhances the effective hydrodynamic size of the particles. The value is less than that in PEO which may indicate that the adsorbed layer is not as thick as that in PEO. Another explanation for a lower k value in PEODME may be the influence of segment slip in addition to a bound layer. In PEODME, the pair interaction coefficient is 38 ( 2. When dividing out the contribution of polymer drag on the intrinsic viscosity, P/k2 is 24 ( 2 which is greater than in that PEO where pair interactions mimic hard spheres and is less than the attractive contribution in PTHF, supporting the conclusion that PEODME has a moderate segment-surface attraction. The pair interaction coefficient being larger than the PEO nanocomposite shows that there are additional attractive and/or repulsive contributions to the particle pair potential. The simple view of a steric bound polymer layer that explained the PEO nanocomposite is not sufficient for the PEODME nanocomposite. DOI: 10.1021/la9044573
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In Figure 2B-D, the effect of a change in molecular weight on the dilute low shear viscosity in PEO, PEODME, and PTHF is shown. In PEO nanocomposites, the intercept, which defines the value of k, increases with molecular weight. The origin of the molecular weight dependence of k is the formation of an adsorbed polymer layer that increases the particle excluded volume such that k = φη/φc, where φη defines an effective particle volume fraction.6,8 The thickness of the adsorbed layer scales on the polymer radius of gyration, Rg, such that k = (Dη/Dc)3 = [1 þ (2.82Rg/Dc)]3. This result is in agreement with studies of polymer melts confined between two surfaces9,11,12,27-29 and suggests that attractions between polymer segments and the surface result in an increase in the particle’s hydrodynamic size due to the formation of an adsorbed polymer layer. When the larger effective particle size is taken into account, the pair interaction coefficient is similar to the hard sphere value showing that particle interactions mediated by the adsorbed polymer layer appear hard-sphere-like. In PEODME, k and P are insensitive to polymer molecular weight, suggesting that for this system the degree of polymerization of the polymer does not affect particle pair interactions. In PEODME2000, k and P/k2 are 1.25 ( 0.02 and 24 ( 1, respectively. This lack of molecular weight dependence of k suggests that in PEODME the magnitude of k results from a fundamentally different mechanism than in PEO such that the definition of k as expressing an enhanced particle excluded volume does not apply to PEODME nanocomposites. The pair interaction coefficients are also equivalent in PEODME regardless of molecular weight, while pair interactions in PEO are only similar after accounting for the larger particle excluded volume due to an adsorbed polymer molecular layer. As shown in Figure 2D, we find that k = 0.8 for both PTHF1000 and PTHF2000, again showing a complete lack of sensitivity to polymer molecular weight. The similar value also suggests that slip of segments on the surface is weakly dependent on molecular weight. P/k2 is 245 ( 27 which is much larger than that in PTHF1000, indicating that attractions increase with polymer molecular weight in PTHF. These attractions are sufficient to produce nonlinearity in the reduced viscosity in PTHF2000 at volume fractions as low as 0.04. At higher volume fractions, shear thinning is observed in all polymers studied, and low and high shear rate plateau viscosities are defined. (Figure 3) The low shear relative viscosities of PEODME1000 and PTHF1000 appear to diverge at lower volume fractions than those of PEO1000. (Figure 4) A divergence in the viscosity points to the onset of solidlike behavior. At higher volume fractions, elasticity grows into the sample shown by a measurable growth in the elastic modulus. In Figure 5, the linear elastic and viscous moduli are plotted as a function of frequency for PEO, PEODME, and PTHF for volume fractions where the low shear rate plateau viscosity shifts to shear rates that are beyond ability to measure. The PEO1000 nanocomposites display the mechanical response expected of a colloidal suspension undergoing a glass transition. The suspensions develop a plateau elastic modulus at high frequency indicating a solidlike response and display terminal behavior at low frequency indicating flow. In between the transition from solidlike to liquidlike behavior, the viscous modulus develops a (27) Horn, R. G.; Israelachvili, J. N. Molecular organization and viscosity of a thin film of molten polymer between two surfaces as probed by force measurements. Macromolecules 1988, 21(9), 2836-2841. (28) Israelachvili, J. N.; Kott, S. J. Liquid structuring at solid interfaces as probed by direct force measurements: The transition from simple to complex liquids and polymer fluids. J. Chem. Phys. 1988, 88(11), 7162-7166. (29) Luengo, G.; Schmitt, F.-J.; Hill, R.; Israelachvili, J. Thin Film Rheology and Tribology of Confined Polymer Melts: Contrasts with Bulk Properties. Macromolecules 1997, 30(8), 2482-2494.
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Figure 3. Measurement of the relative viscosity versus Pe of (A) PEO1000 for φc of 0.000 [O], 0.091 [0], 0.177 [4], 0.270 [#], 0.373 [/], and 0.445 [þ]; (B) PEODME1000 for φc of 0.000 [O], 0.093 [0], 0.136 [4], and 0.174 [:]; and (C) PTHF1000 for φc of 0.000 [O], 0.091 [0], 0.135 [4], 0.177 [:], 0.218 []], and 0.260 [þ].
maximum and minimum that are associated with R and β relaxations, respectively.30-32 (30) Conrad, J. C.; Dhillon, P. P.; Weeks, E. R.; Reichman, D. R.; Weitz, D. A. Contribution of Slow Clusters to the Bulk Elasticity Near the Colloidal Glass Transition. Phys. Rev. Lett. 2006, 97(26), 265701.
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Figure 4. Measurement of the low shear relative viscosity of PEO1000 [b], PEODME1000 [9], and PTHF1000 [[].
The solidlike responses of the PEODME1000 and PTHF1000 nanocomposites in Figure 5 are different from those of the PEO1000 nanocomposites. At a volume fraction of 0.193 in PEODME1000 and 0.280 in PTHF1000, the nanocomposites are in a region where a low shear rate viscosity plateau cannot be measured. At these volume fractions, the linear elastic modulus exceeds the viscous modulus at high frequency and crosses over to terminal liquidlike behavior at low frequency. At higher volume fractions, the elastic modulus is much greater than the viscous modulus. A plateau elastic modulus develops, indicating a long time solidlike response. Over the frequency range of the elastic plateau, the viscous modulus lacks the minimum and maximum frequency that identified the emergence of a colloidal glass in the PEO nanocomposite. The differences lead to the conclusion that the PEODME and PTHF nanocomposites do not form glasses, but instead form gels. B. Microstructure. In this section, we compare particle packing in the nanocomposite when the polymer segment-particle surface interaction is altered. Based on the mechanical characterization above, we expect microstructures to change from those characterizing stable, hard-sphere-like packing in PEO to those showing evidence of attractions in PEODME and PTHF. The flow properties also suggest that a change in molecular weight will have a more noticeable effect on particle structure in PEO and PTHF than in PEODME based on the change of k and P in PEO and the change of P/k2 in PTHF. Changes in the potential of mean force between particles in PEO, PEODME, and PTHF nanocomposites are reflected in the second virial coefficient which is measured from zero angle scattering of the structure factor through eq 10, lim
qf0
1 Vc DΠ ¼ ¼ 1 þ 8B2 φc þ Oðφc 2 Þ Sðq, φc Þ kB T Dφc
ð10Þ
∂Π/∂φc is the inverse particle compressibility, and Π is the osmotic pressure. B2 is the particle second virial coefficient, B2, normalized by the particle excluded volume, 4Vc. In Figure 6, 1/S(0,φc) under dilute conditions is shown as a function of volume fraction for the three polymer nanocomposites with a polymer molecular weight (31) Debenedetti, P. G. Metastable Liquids; Princeton University Press: Princeton, NJ, 1996. (32) Mason, T. G.; Weitz, D. A. Linear viscoelasticity of colloidal hard sphere suspensions near the glass transition. Phys. Rev. Lett. 1995, 75(14), 2770.
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Figure 5. Linear G0 [solid symbols] and G00 [open symbols] as a
function of low strain frequency for (A) PEO1000 at φc = 0.442 [b, O], 0.446 [9,0], 0.450 [2,4], 0.454 [solid vertical bowtie, :], 0.458 [[,]], and 0.463 [1,3]; (B) PEODME1000 at φc = 0.173 [b,O], 0.193 [9,0], 0.214 [2,4], and 0.234 [solid vertical bowtie, :]; and (C) PTHF1000 at φc = 0.260 [b,O], 0.280 [9,0], 0.300 [2,4], and 0.320 [solid vertical bowtie, :].
of 1000 g/mol. 1/S(0,φc) in PEO1000 is linear at low φc, and a second virial coefficient of B2 = 1.4 ( 0.3 is extracted by a linear fit to eq 10. B2 is greater than unity and implies that particles are more repulsive than a simple hard core repulsion. Dilute viscosity measurements reveal that the particles have hard-sphere-like DOI: 10.1021/la9044573
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Figure 6. 1/S(0,φc) versus φc for silica dispersed in PEO1000 [9], PEODME1000 [b], and PTHF1000 [[].
Figure 7. Particle structure factors versus the dimensionless scattering vector in PEO1000 (red) at φc of 0.042 []], 0.091 [O], 0.177 [0], 0.270 [4], and 0.373 [:] and in PEO2000 (black) at φc of 0.091 [þ], 0.177 [#], 0.250 [/], and 0.317 [].
interaction when an adsorbed molecular layer is viewed as enhancing the particle excluded volume. As a result, we expect values of k and B2 to be similar and indeed find agreement. Thus, under dilute conditions, scattering measurement and intrinsic viscosity measurement find particle interactions in PEO nanocomposites to be well described as effective hard particles with sizes slightly larger than the core silica particle size. At higher volume fractions, there is a jump rise in 1/S(0,φc) at φc = 0.091. This increase is greater than expected based on the effective hard sphere interpretation of the viscosity and the second virial measurements. One interpretation would be that the particle interactions change with volume fraction. The low shear viscosities of the suspensions, however, are well described by the effective hard sphere analogy suggesting that the rise in 1/S(0,φc) for φc > 0.091 must have a limited impact on the low shear rate viscosities beyond those predicted by the effective hard sphere model. In PEODME and PTHF, 1/S(0,φc) at low φc is a much stronger function of volume fraction, showing that long wavelength density fluctuations in these other polymers are suppressed more than in PEO. We are unable to reach a linear scattering regime as a function of particle volume fraction in PEODME and PTHF because higher order volume fraction terms become important at φc > 0.01. The stronger rise in 1/S(0,φc) implies that particles are initially more repulsive in PEODME and PTHF than in PEO. Particle attractions cause B2 to fall below unity with strong attractions, causing B2 to be less than zero. Since 1/S(0,φc) increases faster than hard spheres (shown by the dashed line in Figure 6), B2 must be positive and greater than unity. As the volume fraction is increased, 1/S(0,φc) continues to rise in PEODME, indicating that long wavelength density fluctuations continue to be suppressed as volume fraction is increased. In PTHF, 1/S(0,φc) passes through a maximum at a volume fraction of 0.032 and decreases, indicating an increase in particle density fluctuations. An increase in density fluctuations suggests that the potential of mean force transitions from repulsive to attractive as the volume fraction is increased. In Figure 7, the structure factors in PEO1000 and PEO2000 are compared. Based on the larger effective particle size in PEO2000 than in PEO1000 measured from the dilute viscosity, particles in PEO2000 nanocomposites are expected to appear more dense at a
similar core volume fraction. Instead, nanocomposites made with PEO1000 appear more dense in particles than those made with PEO2000. The structure factors show greater structuring of particles in PEO1000 due to a more intense first structure peak, which measures the coherence of first nearest neighbor particle shells, and a greater suppression of S(0,φc), indicating greater suppression of large wavelength density fluctuations. These two features are quantified in Figure 8 where 1/S(0,φc) and S(q*,φc), the magnitude of the first structure peak located at q*Dc, are plotted in the various nanocomposites studied as a function of φc. At φc = 0.091, the microstructures of PEO1000 and PEO2000 are similar. As the volume fraction is raised, greater structure is observed in the PEO1000 nanocomposites, implying greater stability in the lower molecular weight polymer. At higher volume fractions, 1/S(0,φc) continues to rise in PEO1000 and the magnitude of the first structure peak also rises up to φc = 0.52. As discussed in more detail in a previous publication,6 the microstructure in PEO1000 cannot be fit with hard sphere structure factors with a volume fraction independent size. Our conclusion in this previous work was that structuring of polymer around the particle must contribute to the static structure, but the structuring of polymer has a minor influence on nanocomposite viscosity beyond that predicted by the effective hard sphere model. At low volume fractions, there is little difference in the particle microstructure between the PEO1000 and PEO2000 nanocomposites despite the difference in the effective particle size from viscosity measurements. As the volume fraction is raised, values of 1/S(0,φc) and S(q*,φc) for the PEO2000 fall below PEO1000 at volume fractions exceeding 0.09, showing that particles are less structured in PEO2000 at higher volume fractions. At φc = 0.317 in PEO2000, we observe an upturn in scattering at low qDc suggesting the formation of clusters. We attribute this upturn to the volume fraction dependent turning on of particle attractions. This phenomenon is clearly seen in Figure 8 where a maximum in 1/S(0,φc) is reached at φc ∼ 0.25. In the same volume fraction region, S(q*,φc) continues to increase, showing that the rise in large wavelength density fluctuations causes greater coherence of the first nearest neighbor particle shell. The location of the scattering peak demonstrates that, on average, particles are not in direct contact, suggesting that the clusters are formed by a network of particles that are still separated by
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Figure 9. Particle structure factors versus the dimensionless scattering vector in PTHF1000 (gold) at φc of 0.040 []], 0.091 [O], 0.177 [0], 0.260 [4], and 0.300 [∞] and in PTHF2000 (purple) at φc of 0.040 [þ] and 0.091 [#].
Figure 8. (A) 1/S(0,φc) and (B) S(q*,φc) versus φc for silica dispersed in PEO1000 [0], PEO2000 [:], PEODME1000 [O], PEODME2000 [4], PTHF1000 []], and PTHF2000 [3].
polymer. In addition to the evidence of cluster formation from small angle scattering, the PEO2000 nanocomposites were previously shown to transform rheologically from a fluidlike material to one that displays brittle behavior as the volume fraction is increased from 0.250 to 0.317.8 In Figure 9, the structure factors of PTHF1000 nanocomposites show dramatically different microstructures from those seen in PEO1000 nanocomposites. At higher volume fractions, there are clearly larger wavelength density fluctuations and less structuring of particles in PTHF1000 than in PEO1000. 1/S(0,φc) and S(q*,φc) are significantly suppressed and fall below hard spheres shown by the dashed line in Figure 8 for φc g 0.091. The rise in the structure factor up to a value of unity with increasing q is shifted to low qDc, suggesting that particle density fluctuations are being suppressed by particles being held at large separation distances. The suppression of density fluctuations does not correlate with a first peak in S(q) (i.e., S(q*,φc) ∼ 1), indicating that there is no average distance that can be equated to particle separations. At φc = 0.091, S(0,φc) is slightly higher than that at 0.04. There is a damped first peak in the structure factor at qDc ∼ 7. The intensity of this peak grows as φc is increased. A peak in S(q) at qDc ∼ 7 supports particles being in direct contact. Despite these indications of particle attractions, the suspensions still flow and a low shear Langmuir 2010, 26(11), 8709–8720
viscosity is measured. There is also no upturn in the scattering at low qDc except at φc = 0.300 where only a small upturn is observed. At this volume fraction, the nanocomposite behaves as an elastic solid. These results suggest that particles are initially stable at volume fractions of φc < 0.04. Attractions become significant at φc > 0.04 as indicated by the appearance of a structure peak at qDc of 7. These attractions are relatively weak such that a fluid is still maintained up to φc = 0.260. At φc = 0.300, the attractions are of sufficient magnitude that particles percolate and the particle structure can store an applied stress. The φc = 0.300 PTHF1000 gel has a microstructure that is substantially different from that of depletion or thermal gels, both of which display strong first peaks in the structure factor at qDc of 7.33,34 The depletion gels show strong upturns at low qDc, while density fluctuations in the thermal gels are believed to occur at larger length scales than are probed at qDc ∼ 0.5. However, in both systems, there is a pronounced region of liquid like compressibility (i.e., small values of S(qDc) between the upturn at low qDc and the first peak at S(q*Dc)). The nanocomposite gel formed by silica in PTHF1000 has a liquidlike compressibility region and the appearance of a small upturn, but the first structure peak lacks in intensity in comparison to depletion and thermal gels, suggesting little correlation in first nearest neighbor particle positions causing destructive scattering interference. As the PTHF molecular weight is raised, the dispersion becomes unstable at much lower volume fractions. A strong scattering upturn appears at low qDc indicative of particle clusters. A weak structure peak similar in magnitude to PTHF1000 is located at qDc ∼ 7, suggesting that particles are either in or near direct contact. The weak adsorbance of PTHF segments indicated by slip at the surface suggests that clusters are formed from direct contact of particle surfaces rather than bridged by polymer. The presence of clusters in PTHF2000 and the lack of them in PTHF1000 at a similar volume fraction imply (33) Ramakrishnan, S.; Gopalakrishnan, V.; Zukoski, C. F. Clustering and Mechanics in Dense Depletion and Thermal Gels. Langmuir 2005, 21(22), 9917-9925. (34) Shah, S. A.; Chen, Y. L.; Ramakrishnan, S.; Schweizer, K. S.; Zukoski, C. F. Microstructure of dense colloid-polymer suspensions and gels. J. Phys.: Condens. Matter 2003, 15(27), 4751-4778.
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Figure 10. Particle structure factors versus the dimensionless scattering vector in PEO1000 (red) at φc of 0.043 []], 0.091 [O], 0.177 [0], and 0.270 [4] and in PEODME1000 (blue) at φc of 0.033 [], 0.091 [þ], 0.177 [#], and 0.270 [/].
stronger attractions in PTHF2000, and this agrees with the measured value of P/k2 which increases as the molecular weight is raised and identifies the large P/k2 with strong attractions. Particle structure factors in PEODME1000 are liquidlike and resemble the character of the structure factors in PEO1000 where particles are repulsive and stable. The structure factors in PEODME1000 and in PEO1000 are directly compared in Figure 10. At low volume fractions, as indicated by a more intense first structure peak and a greater suppression of S(0,φc), the particles are more structured in PEODME1000 than in PEO1000. We also notice that the position of the peak in PEODME1000 is shifted to lower qDc, indicating that particles are structuring at larger separation distances in PEODME1000 than in PEO1000. The greater amount of particle structure in PEODME agrees with B2 being larger in PEODME than in PEO and supports a longer range particle repulsion in PEODME. At φc = 0.177, this trend is reversed. S(0,φc) is suppressed more, and the structure peak is more intense in PEO1000. The position of the peak is similar in the two polymers at φc = 0.177. The loss of structure in PEODME1000 relative to PEO1000 implies either a decline in particle repulsions or an increase in attractions. At φc = 0.275, where in the previous section the PEODME1000 nanocomposite behaved rheologically as a gel, the first structure peak is wiped out and there is an increase in the scattering at a qDc ∼ 7, meaning particles are near or in direct contact. There is not a large upturn in the scattering at low qDc suggesting that either particle clusters are larger than the length scales probed or the gel is structurally not composed of clusters. In contrast, the particle structure factors in PEO continue to have a liquidlike structure with increasing volume fraction. We conclude that the greater amount of structuring at low φc can be correlated with the higher relative viscosity of PEODME1000 over that seen in PEO1000. While repulsive interactions are suggested by the liquidlike structure factors in this low φc region, the gelation of the PEODME1000 nanocomposites indicated by a peak growing at q*Dc ∼ 7 suggest the turning on of attractions at higher volume fractions. A change in molecular weight does not have a noticeable impact on the structure in the miscible liquid state based on the similarity of the structure factors in PEODME1000 and 8718 DOI: 10.1021/la9044573
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Figure 11. Particle structure factors versus the dimensionless scat-
tering vector in PEODME1000 (blue) at φc of 0.091 [O] and 0.177 [0], and in PEODME2000 (green)at φc of 0.091 [þ] and 0.177 [/].
PEODME2000 shown in Figure 11 where we compare nanocomposites with different molecular weights of PEODME and find identical structure factors at φc of 0.091 and 0.177. The similarity of the structure factors correlates well with dilute nanocomposite viscosities which are insensitive to polymer molecular weight.
IV. Discussion Our measurements in the PEO nanocomposites support the strong adsorption of PEO segments to a silica particle surface. The strong adsorption of segments increases the intrinsic viscosity of a particle by producing a bound layer of polymer on the surface that increases the effective hydrodynamic particle size. The segment-surface interaction is sufficiently strong such that the segments do not desorb as the particle density is increased. The strongly adsorbed segments resist the entropic consequence of confining polymer between two particles. This is confirmed by the pair interactions being equivalent to hard spheres in PEO. As a result, the particles have liquidlike structure factors up to high volume fractions. As the molecular weight is increased, the viscosity is still well described by particles with a larger excluded volume due to adsorbed polymer and particle interactions are hard-sphere-like. The particle structure factors show a different characterization of the PEO nanocomposites and support a phase transition in the higher molecular weight PEO at a volume fraction of 0.317. At the transition, the location of the scattering peak shows that particles are not in direct contact, suggesting that a change in the state of the nanocomposite results from a network of particles that are still separated by polymer. These observations may support a phase transition through some type of polymer bridging phase transition. Another explanation may be adsorption induced polymer vitrification that may result in the suspension falling out of equilibrium. In PTHF, the segment-surface attraction is weak. The weaker attraction is caused by reduction of the number of backbone oxygen atoms compared to PEO. The weaker attraction results in slip of segments on the particle surface and a reduction in the particle intrinsic viscosity. P/k2 is much larger than that in PEO and is attributed to particle attractions. Particle attractions are significantly increased as the molecular weight is raised. The particle microstructure in PTHF1000 is different from that in PEO1000 nanocomposites at the same particle volume fraction. Langmuir 2010, 26(11), 8709–8720
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Attractions disrupt the particle microstructure shown by greater large wavelength particle density fluctuations and a first peak in the structure factor occurring at qDc ∼ 7 impying that particles are in direct contact. At a volume fraction of ∼0.29, the suspension undergoes a gel transition shown rheologically by the disappearance of a measurable low shear viscosity plateau and the emergence of an elastic modulus that increases with particle volume fraction. The particle structure factor shows a rise in large wavelength particle density fluctuations at this volume fraction. The gel does not appear to be characterized by dense particle clusters, since there was no strong scattering at low scattering vector. An increase in PTHF molecular weight significantly lowers the gel volume fraction, and particle clusters are identified by an upturn in the scattering at low scattering vector. The lack of clusters in PTHF1000 and the appearance of clusters in PTHF2000 are further evidence that attractions are significantly increased by an increase in molecular weight. In PEODME, the adsorption of segments to the surface increases the particle intrinsic viscosity and this increase is independent of molecular weight. In PEO, the increase was attributed to a bound layer of polymer around the particles that increases the particle hydrodynamic size. Direct application of this interpretation to PEODME is problematic because the intrinsic viscosity is independent of molecular weight. P/k2 also suggests attractions or repulsions in PEODME that were not present in PEO. The formation of a gel above φc = 0.20 confirms that attractions are present. On the other hand, the structure factor in PEODME is liquidlike at volume fractions preceding the formation of a gel, suggesting that particles are not purely attractive. Particles in PEODME1000 are more structured than those in PEO1000 at φc = 0.091, suggesting that particles feel long range repulsions in addition to the hard core repulsion in PEODME1000 and therefore structure more at large interparticle distances. A comparison of the structure factor between PEODME1000 and 2000 also shows the molecular weight independence of the particle microstructure in agreement with the molecular weight independence of the particle intrinsic viscosity. The insensitivity of the PEODME nanocomposite to molecular weight as compared to the other nanocomposites is not clear, nor is a longer range repulsion at lower volume fractions prior to gel formation as compared to the PEO nanocomposites that causes particles to structure more at a larger interparticle separation distance. The sudden loss of particle stability and the formation of a gel in PEODME suggest a complicated balance of enthalpic and entropic forces. At low volume fractions, the adsorption of segments stabilizes particles. As the polymer is confined between two particles at higher volume fractions, the segments desorb and the polymer migrates from the interparticle space. This leaves a polymer depleted region resulting in a classical depletion attraction. Our results are consistent with PEO adsorbing more strongly than PEODME. The stronger segment adsorption of PEO combats the entropically unfavorable polymer confinement between two particles leading to stable particles up to high particle concentrations. Studies of polymer nanocomposites using the PRISM theory predict the pair particle potential in a polymer melt to depend on the strength and range of the segment surface attraction and additional parameters such as the segment to particle size ratio and the polymer molecular weight. 3,35 The potential varies from (35) Hooper, J. B.; Schweizer, K. S.; Desai, T. G.; Koshy, R.; Keblinski, P. Structure, surface excess and effective interactions in polymer nanocomposite melts and concentrated solutions. J. Chem. Phys. 2004, 121(14), 6986-6997.
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overall attractive to repulsive depending on the strength of the segment-surface attraction and is oscillatory with a period of the segment length. The oscillations protrude ∼3 segment lengths from the surface, and an increase in molecular weight deepens the potential wells of the oscillations. For weak segment-surface attraction, the potential is a strong depletion attraction. For moderate segment-surface attraction, the oscillations become repulsive similar to a DLVO potential with an attractive well near the surface. For a strong segment-surface attraction, the potential is purely repulsive. A particle phase diagram is constructed which predicts a miscible particle regime at moderate to strong segment-surface attraction that is bordered by direct contact aggregation at weak segment-surface attraction and bridging flocculation at strong segment-surface attraction.4 PTHF segments experience weak attractions with the particle surface. For this condition, PRISM theory predicts phase separation at low volume fractions due to depletion. Particles in PTHF1000 are attractive, but attractions appear weak such that a fluid is maintained up to high volume fractions even though particles appear to be in near contact. Our results also show that the particles feel a stronger effective attraction as molecular weight is increased, leading to phase separation at extremely low volume fractions. This suggests an increase in depletion attraction as the molecular weight is raised. The theory predicts that the phase boundaries are more sensitive to a change in the segment surface attraction with minor sensitivity to molecular weight. Assuming the theory is correct, the greater attraction in PTHF2000 would be attributed to a change in the segment-surface attraction rather than molecular weight PTHF. A change in the segment-surface interaction may be explained by a rise in polymer hydrophobicity with an increase in molecular weight. PTHF is hydroxyl terminated, and it is known that the hydrophobicity of polar capped polymers increases with molecular weight.36 An increase in hydrophobicity is expected to weaken the segment-surface interaction, since silica is a hydrophilic surface. PEODME appears to have a segment-surface attraction intermediate between that of PEO and PTHF. Results point to the presence of repulsions which stabilize particles and give liquidlike structure factors at lower volume fractions and attractions that lead to phase separation at modest volume fractions. The polymer appears to wet the surface due to an increase in the particle intrinsic viscosity, suggesting that adsorption of polymer segments stabilizes particles. The relative viscosity and the particle microstructure are also insensitive to a change in molecular weight, a feature predicted by the theory. The weaker segment-surface interaction of PEODME compared to PEO suggests that the phase transition is controlled by depletion of polymer segments as the polymer becomes confined at elevated volume fraction. At low volume fractions, the positive enthalpic contributions from adsorption of segments stabilize particles, but at higher volume fractions the entropic consequences of confining segments causes depletion of segments, leading to phase separation. In light of our attempt to explain the results with the theory of Hooper and Schweizer,3,4 we mention that the rheological characterization of PEO nanocomposites reveals an adsorbed molecular layer that scales on Rg. The concept of a bound layer with a thickness dependent on the polymer molecular weight is not predicted by the theory. On the other hand, this feature of the PEO nanocomposites agrees with confined polymer melt experiments. Our observations and those that directly measure surface (36) Chakraborty, A. K.; Tirrell, M. Polymer adsorption. MRS Bull. 1996, 21(1), 28-32.
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forces of confined polymer melts may suggest nonequilibrium adsorption of PEO on silica and possibly be explained by DeGennes’ “pinned” segment concept.9,11,12,29,37,38 Yet, PEO does not appear to be irreversibly adsorbed to the surface, since cooling of the nanocomposites below the melting temperature of PEO causes the formation of particle clusters when φc g 0.09. This means that polymer molecules can change their configuration on the surface upon cooling. Upon further evaluation of cooling in other nanocomposites, particles in PEO2000 had little sensitivity to freezing, particles in PEODME2000 aggregated at volume fractions of as little as 0.01, particles in PEODME1000 had little sensitivity to freezing, and particles in PTHF1000 developed some aggregation or phase separation when freezing concentrated nanocomposites. These features are additional complexities of these nanocomposites that will require further study. In summary, a comparison of the physical properties of PEO, PTHF, and PEODME nanocomposites shows that the ability of the polymer to adsorb to a particle surface affects particle stability, microstructure, and rheological properties. In PEO and PEODME, the adsorption of segments increases the particle intrinsic viscosity and yields repulsive liquidlike structure factors (37) DeGennes, P. G. Interactions between Plates in a Polymer Melt. C. R. Acad. Sci., Ser. II 1987, 305(14), 1181-1184. (38) Mansfield, K. F.; Theodorou, D. N. Interfacial structure and dynamics of macromolecular liquids: a Monte Carlo simulation approach. Macromolecules 1989, 22(7), 3143-3152.
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at low volume fractions. Weak segment-surface attraction in PTHF leads to slip of segments on the surface and particle attractions. Particle attractions are minor in lower molecular weight PTHF and are substantial at higher molecular weight, leading to phase separation at extremely low volume fractions. The moderate segment-surface interaction in PEODME 1000 and 2000 stabilizes particles at low volume fractions, but particles phase separate and gel as the volume fraction is increased. This is contrasted by a strong segment-surface interaction in PEO which results in greater particle stability. In PEO1000 particles, are stable up to high volume fractions leading to the formation of a particle glass. However, particles in PEO2000 seem to cross a phase transition boundary at moderately high volume fractions, yet particles remain separated by polymer and are not in direct contact. Acknowledgment. SAXS data were collected at the X-ray Operations and Research beamline 8ID-E at the Advanced Photon Source (APS), Argonne National Laboratory. The APS is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357. We appreciate our collaborative relationship and helpful discussions with Ken Schweizer and Lisa Hall. This work was supported by the Nanoscale Science and Engineering Initiative of the National Science Foundation under NSF Award Number DMR-0642573.
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