Langmuir 2002, 18, 10435-10442
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Poly(ethylene oxide)/Silica Nanocomposites: Structure and Rheology Qiang Zhang and Lynden A. Archer* School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853 Received August 1, 2002. In Final Form: September 27, 2002 The effects of polymer-particle and particle-particle interactions on viscoelastic properties of nanocomposite materials are investigated using narrow molecular weight distribution poly(ethylene oxide) (PEO) containing isotropic silica nanospheres. Nanocomposites are prepared using a “freeze-drying” method to guarantee homogeneous dispersion of silica. The dispersion state of silica nanospheres is characterized by atomic force microscopy phase contrast imaging, and mechanical rheometry is used to study relaxation dynamics and viscoelastic properties of these materials in the melt state. Linear viscoelastic data indicate a transition to a solidlike response at low oscillation frequencies for particle volume fractions φ as low as 2%, dramatically lower than the theoretical percolation threshold (φ ∼ 30%). Nanoparticle volume fraction, surface chemistry, and PEO molecular weight are all found to strongly influence nanocomposite structure and dynamics. A filler networking mechanism, wherein nanosized silica particles surrounded by an immobilized shell of PEO are bridged by much larger polymer molecules, is proposed to explain our observations.
Introduction Many polymer materials are composites containing isotropic particles such as carbon black and silica. In these systems, polymer volume fraction is typically large, so that the composite structure can be described as particle aggregates dispersed in a polymer matrix.1 Interactions between individual particles within aggregates, as well as between aggregates, hinder relative motion between material planes, enhancing mechanical properties of the host polymer. In a filled polymer containing particles with micron or submicron dimensions, two filler particles can only interact when their separation distance is small compared with the particle size. High particle volume fractions are therefore required to significantly change mechanical properties of the host material. For example, in highly filled polymers, filler interactions are so strong that solidlike yield phenomenon can be observed even at temperatures above the quiescent melting temperature or glass transition temperature of the polymer.2 This behavior is often attributed to the existence of a filler network that spans large sections of the polymer matrix.1,3 When filler particles become so small that their size (at least in one dimension) approaches the mean radius of gyration of host polymer chains, several new noncontinuum effects become important. For highly interactive polymer-particle systems in which we are interested, the physisorption is strong enough to be considered irreversible. Individual polymer molecules can adopt stretched configurations that allow them to simultaneously adsorb to the surfaces of many particles. Nanosized filler particles are therefore connected by polymer molecules even when they are quite far apart in comparison with their size. Thus, even at relatively small particle volume fractions significant changes in continuum properties can be observed in nanocomposite materials. Relative motion between polymer chains is retarded by immobilization at (1) Wang, M. J. Rubber Chem. Technol. 1998, 71, 520. (2) Vinogradov, G. V.; Malkin, A. Y.; Plotnikova, E. P.; Sabsai, O. T.; Nikolayeva, N. E. Int. J. Polym. Mater. 1972, 2, 1. (3) Yurekli, K.; Krishnamoorti, R.; Tse, M. F.; Mcelrath, K. O.; Tsou, A. H.; Wang, H. C. J. Polym. Sci., Part B: Polym. Phys. 2001, 39, 256.
and polymer confinement between nanoparticle surfaces. As the affinity between polymer molecules and particles increases, the degree of immobilization increases. The kinetics of polymer surface exchange (adsorption/desorption) naturally sets the time scale on which solidlike behavior is observed in these systems.4 Assuming the diameter of filler particles D ) 10 nm and that these particles are homogeneously distributed on a cubic lattice in a polymer host with random coil diameter, 2Rg ) 20 nm, the spacing between particle surfaces is approximately 13 nm for particle volume fraction φ as low as 4%, implying that significant levels of confinement can exist even in this moderately filled material. Finally, adsorbed polymer molecules enhance the effective filler volume fraction in nanocomposites. The equilibrium thickness of the immobilized polymer layer on flat, neutral substrates has been shown by theory5 and experiment6 to be of the order of Rg ∼ N0.5. Filler particles can therefore be regarded as a hard core surrounded by an immobilized polymer shell of comparable size.7 Physical properties of the polymer shell are much different from those of the bulk material, so adsorbed polymer effectively enhances the volume fraction of filler particles in the nanocomposite. The unique continuum level properties that result from nanoscale interactions between polymer hosts and nanosized particles have attracted considerable recent interest.8,9 Many studies have also focused on synthesis and characterization of polymer nanocomposites containing surface-modified particles.10,11 To design nanocomposite materials with controlled mechanical properties, it is essential that the fundamental determinants of macro(4) Horigome, M.; Otsubo, Y. Langmuir 2002, 18, 1968. (5) Silberberg, A. J. Colloid Interface Sci. 1988, 125, 14. (6) Cohen-Addad, J. P. Polymer 1989, 30, 1820. (7) Kaufman, S.; Slichter, W. P.; Davis, D. D. J. Polym. Sci., Part A-2 1971, 9, 829. (8) Brus, L. E.; Brown, W. L.; Andres, R. P.; Averback, R. S.; Goddard, W. A.; Kaldor, A.; Louie, S. G.; Moskovits, M.; Peercy, P. S.; Riley, S. J.; Siegel, R. W.; Spacpen, F. A.; Wang, Y. J. Mater. Res. 1989, 4, 704. (9) Herron, N.; Thorn, D. L. Adv. Mater. 1998, 10, 1173. (10) Park, S. J.; Seo, D. I.; Lee, J. R. J. Colloid Interface Sci. 2002, 251, 160. (11) Wolff, S. Rubber Chem. Technol. 1982, 55, 976.
10.1021/la026338j CCC: $22.00 © 2002 American Chemical Society Published on Web 11/21/2002
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scopic properties be understood. However, due to the complicated nature of molecular interactions, there is a lack of general agreement on this aspect of nanocomposite science. The most successful models introduce various simplifying assumptions that are difficult to validate. Leonov et al.,12 for example, proposed a rheological model for highly filled polymers with weak polymer-particle interactions. In this system, polymer-polymer (“polymer mode”) and viscoelastic particle-particle (“particle mode”) interactions are taken to be the most important determinants of macroscopic rheological properties. Polymerparticle interactions are not considered in the constitutive equations. This model can predict the transient, yield, and thixotropic behavior of hybrids. Doremus et al.13 proposed to describe highly interactive polymer-particle hybrids with a double network model, neglecting particleparticle interactions. The system consists of two independent networks: a polymer network and a polymerparticle network formed by polymer-particle junctions. This model successfully describes the yield behavior but cannot describe stress overshoots in start-up flows. Both models have limitations as neither polymer-polymer interactions nor polymer-particle interactions can be simply neglected in many polymer composites. The overall objective of this study is to determine how nanoscale polymer-particle interactions influence macroscopic properties of nanocomposites. For simplicity, we will use model nanocomposite materials, created by blending nanosized particles with well-defined sizes and surface properties with narrow molecular weight distribution linear polymers, to study the effect of particle volume fraction, particle surface chemistry, and polymer molecular weight on nanocomposite properties. This article focuses on preparation, characterization, and rheological properties of nanocomposites of poly(ethylene oxide) (PEO) and silica. PEO is known to have high affinity for silica particles;14 therefore, strong polymer-particle interactions are expected in this system. PEO is also a widely used material in biomedical15 and electrochemical16 applications. Therefore, our work should also shed light on specific approaches for creating PEO nanocomposites with improved mechanical properties. Experimental Section Nanocomposite Preparation. PEO/silica nanocomposites used in the study were prepared using a new procedure. This procedure is advantageous because it produces a homogeneous dispersion of silica particles in the polymer matrix. Silica particles (Ludox AS30 colloidal silica, with a specific surface area of 220 m2/g and an average diameter of 12 nm) were purchased from Aldrich as a 30 wt % colloidal suspension in aqueous NH4OH (pH 9.1). Various high-molecular-weight narrow molecular weight distribution PEOs were purchased from Polymer Source, Inc. Molecular weight information for the PEO materials used in the study is provided in Table 1. A three-step procedure was followed to disperse silica nanoparticles in the PEO matrix. In the first step, Ludox AS30 colloidal silica was diluted with deionized water to produce a 1 wt % colloidal dispersion. The dilute suspension is mixed with an aqueous PEO solution. Sterically stabilized silica nanoparticles are homogeneously dispersed by continuously stirring for 24 h. In the second step, the suspension is frozen rapidly with liquid nitrogen and freeze-dried for 72 h at -46 °C to remove water and NH4OH. The freeze-drying procedure yields (12) Leonov, A. I. J. Rheol. 1990, 34, 1039. (13) Doremus, P.; Piau, J. M. J. Non-Newtonian Fluid Mech. 1991, 39, 335. (14) Wind, B.; Killmann, E. Colloid Polym. Sci. 1998, 276, 903. (15) Alcantar, N. A.; Aydil, E. S.; Israelachvili, J. N. J. Biomed. Mater. Res. 2000, 51, 343. (16) Capuano, F.; Croce, F.; Scrosati, B. J. Electrochem. Soc. 1991, 138, 1918.
Zhang and Archer Table 1. PEO/Silica Nanocomposites Used in This Study sample name
M h n (g/mol)
M h w/M hn
P45-S4 P96-S4 P189 P189-S0.5 P189-S1 P189-S2 P189-S3 P189-S4 P189-SPEO2 P189-SIB2 P292-S4
45 000 96 000 189 000 189 000 189 000 189 000 189 000 189 000 189 000 189 000 292 000
1.04 1.04 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.06
a
particle typea S S none S S S S S SPEO SIB S
φ (%) 4 4 none 0.5 1 2 3 4 2 2 4
Additional information is provided in Table 2.
a porous hybrid that is finally compressed in a vacuum at 75 °C to form 2 mm thick nanocomposite films. The compressive force used in the final step is deliberately kept small to avoid creation of voids in the film. Silica particles tend to aggregate into clusters during evaporative drying of aqueous suspensions at room temperature.17 The major advantage of freeze-drying was to prevent particle aggregation as the solvent was removed. It guaranteed more homogeneous dispersion of silica nanospheres in the PEO matrix. Particle concentrations and PEO molecular weights of the PEO/ silica nanocomposites studied are summarized in Table 1. The table also explains the nomenclature used to identify nanocomposite samples. To investigate the effect of particle-particle and polymerparticle interactions on nanocomposite properties, PEO/silica nanocomposites containing surface-modified silica particles were also created. Surface modification was realized by grafting organosilanes purchased from Gelest, Inc. The nomenclature of silica particles with different surface properties is given in Table 2. The organosilane grafted on SPEO is an oligomeric PEO terminated with a trimethoxy silanyl group. The organosilane grafted on SIB is an organophilic isobutylene terminated in the same way. Silica particles were modified by direct reaction of organosilane molecules with bare silica particles in a 1 wt % particle suspension. For full surface coverage, excess organosilane was used so that its total wetting surface area was larger the total surface area of silica particles. The mixture was shaken for 6 h to guarantee complete surface reaction. Hydrolysis of the three labile methoxyl groups yielded hydrogen bridges to the surface and cross-linking of organosilane molecules. The surfacefunctionalized silica particles were homogeneously dispersed in an aqueous PEO solution by continuously stirring for 24 h. The following procedures for surface-treated silica particles were the same as for untreated silica particles. As water was removed by freeze-drying, covalent Si-O-Si bonds formed between organosilane molecules and the silica surface. Nanocomposite Characterization. Nanocomposite films prepared in the previous part of the study were characterized by atomic force microscopy (AFM) in Tapping Mode and by mechanical rheometry. The dispersion state of silica nanoparticles in the PEO matrix was studied in detail using a Dimension 3100 AFM (Digital Instruments). Prior to AFM scans, the sample was microtomed to reduce surface roughness. Scans were performed at room temperature, with the scan area varying from 1 × 1 to 10 × 10 µm2. Both surface height images and phase contrast images of the sample were obtained. In the phase contrast image, the measured phase angle is a function of surface stiffness. Therefore, the large difference in stiffness of silica and PEO will result in a large phase contrast. Although surface topography of the sample will induce some contrast in the phase image, the contrast between silica and PEO is sufficiently large to facilitate easy differentiation. Viscoelastic properties of PEO/silica nanocomposites were studied using a Paar Physica Modular Compact Rheometer 300 (MCR300) equipped with 10 mm diameter stainless steel parallel disks (0.4 mm gap separation). Measurements were performed in oscillatory shear and step shear configurations at a fixed temperature of 75 °C, that is, well above the melting temperature (17) Haw, M. D.; Gillie, M.; Poon, W. C. K. Langmuir 2002, 18, 1626.
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Table 2. Characteristics of Bare and Surface-Modified Silica Particles particle name
grafted organosilane
specific wetting surface of silanea (m2/g)
suspending liquid
S SPEO SIB
none CH3(CH2CH2O)6-9(CH2)3Si(OCH3)3 (CH3)2CHCH2Si(OCH3)3
∼150 ∼400
water water water + methanol
a
The specific wetting surface of a silane is determined from the minimum amount of silane required to provide a uniform surface.
of PEO (Tm ∼ 65 °C). All measurements were performed in a dry nitrogen atmosphere to avoid oxidative degradation. An additional benefit of this protocol is that degradation of PEO by microorganisms carried in humid air is eliminated during the measurements. Nanocomposite samples were subjected to a thermal annealing for several days at 75 °C in a dry nitrogen atmosphere to allow for complete microstructural equilibration prior to rheological testing. In oscillatory shear experiments, a sinusoidal shear strain γ(t) ) γ0 sin(ωt + φ) was imposed. In the frequency sweep measurements, γ0 was a small constant and frequency-dependent elastic modulus G′(ω) and loss modulus G′′(ω) were determined. In step shear experiments, a small strain γ ) γ0H(t) was imposed on the sample and time-dependent stress σxy(t) was measured. Relaxation modulus G(t) ≡ σxy(t)/γ0 deduced from the measured stress provides direct insight into the dynamics of the nanocomposites. These moduli can also be Fourier transformed in the linear regime to yield frequency-dependent elastic moduli G′(ω) ≡ ω ∫∞0 sin(ωt) G(t) dt and loss moduli G′′(ω) ≡ ω ∫∞0 cos(ωt) G(t) dt over an often wider frequency range than that possible with oscillatory shear measurements.
Results and Discussion Viscoelastic properties of PEO/silica nanocomposites are presented in Figure 1 at fixed PEO molecular weight but multiple particle volume fractions and in Figure 2 at fixed particle volume fraction but variable PEO molecular weights. It is immediately apparent from Figure 1 that silica nanospheres have a dramatic effect on nanocomposite properties, even at particle volume fractions as low as 0.5%. As the particle loading increases, elastic modulus G′(ω) increases, especially at low frequencies, while loss modulus G′′(ω) slightly decreases at high frequencies and dramatically increases at low frequencies. Pure P189 has a typical terminal regime with the following scaling properties: G′ ∼ ω2, G′′ ∼ ω.1 However, at a particle volume fraction above 2%, this terminal behavior totally disappears in the experimental frequency range (10-3 s-1 < ω < 600 s-1), and the dependence of G′ and G′′ on ω at low frequencies is very weak. It suggests stress relaxation of these hybrids is effectively arrested by the presence of silica nanoparticles. That G′ is almost independent of ω at low frequencies when the particle volume fraction is higher than 2% is indicative of a transition from liquidlike to solidlike viscoelastic behavior. At high oscillation frequencies, the effect of particle loading is relatively weak. These results suggest that the influence of silica nanoparticles on stress relaxation dynamics is much stronger than their influence on plateau elastic modulus. Figure 2 shows that viscoelastic behaviors of the nanocomposites are strongly dependent on PEO molecular weight. As PEO molecular weight increases, the elastic modulus increases. These results indicate that PEO chain length is also important for molecular interactions in these materials. However, all the hybrids exhibit small lowfrequency power law slopes of G′(ω). This is indicative of solidlike behaviors at high particle volume fractions (4%) despite the PEO molecular weight difference. In the same plot, all the hybrids are compared with their pure polymer counterparts, illustrating strong reinforcement with introduction of 4% nanoparticles. Similar solidlike behaviors at low frequencies have been reported in other isotropic particle filled polymer composites, except at much higher particle loadings.3 In these
Figure 1. Frequency response of PEO/silica nanocomposites with fixed PEO molecular weight and different particle volume fractions. Measurements were carried out at 75 °C; strain amplitudes ranging from 1% to 3% were used for the filled materials, while strain amplitudes up to 10% were used for unfilled PEO. (a) Elastic modulus G′; (b) loss modulus G′′.
systems, this behavior has been credited to the formation of a filler network in the polymer host. Specifically, as the particle loading increases, larger and larger particle clusters form until these clusters span the whole system. The critical particle loading can be calculated with the help of percolation theory.18 For randomly dispersed spherical particles, the theoretical percolation threshold is around 30 vol %. If the interparticle distance is close to the effective length of the particle attraction zone or the polymer-particle interaction is dominant, this percolation threshold can be much lower, but it is typically higher than 10 vol %.19,20 This should be contrasted with (18) Kirkpatrick, S. Rev. Mod. Phys. 1973, 45, 574. (19) Janzen, J. J. Appl. Phys. 1975, 46, 966. (20) Vinogradov, G. V. Rheol. Acta Suppl. 1988, 27, 218.
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Figure 2. Frequency-dependent storage modulus of PEO/silica nanocomposites with fixed particle volume fraction and different PEO molecular weights. Measurements were performed at 75 °C; strain amplitudes ranging from 1% to 3% were used for the filled materials, while strain amplitudes up to 10% were used for unfilled PEO.
Figure 3. AFM phase contrast image of P96-S4: (a) before annealing; (b) after annealing.
the 2 vol % threshold seen in this study, which is dramatically lower than the value expected from theory. Determining the dispersion state of silica nanoparticles may help to find the source of the unusual enhancement of viscoelastic properties in PEO/silica melts. AFM measurements were performed on several systems before and after thermal annealing. Figure 3a provides a typical AFM phase contrast micrograph of PEO/silica hybrids before annealing, while Figure 3b is the micrograph of the same material after annealing. The bright phase represents the stiffer silica particles, while the dark background represents the softer PEO matrix. The first micrograph clearly shows that before annealing, particle
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Figure 4. Time evolution of the elastic modulus G′ of PEO/ silica nanocomposites. Measurements were performed at 75 °C, with ω ) 0.1 s-1 and γ ) 0.02.
aggregates are small and homogeneously distributed, confirming that the “freeze-drying” method produces very good particle dispersion. In the second micrograph, the average size of particle aggregates increases. Obviously, particle flocculation occurs during annealing, as the mobility of silica particles becomes much higher. At the same time, particles are still homogeneously distributed throughout the matrix. Together, these observations appear to provide support for the idea that formation of particle aggregates is responsible for the enhanced properties observed from oscillatory shear rheological experiments. Additional evidence in support of this idea can be obtained from rheological results themselves. Specifically, rheological properties of the nanocomposites are found to change dramatically with time during thermal annealing. Figure 4, for example, shows the time-dependent evolution of the elastic modulus G′(ω ) 1 s-1) at the annealing temperature of 75 °C for two nanocomposites (P189-S2 and P96-S4) that have not been annealed. For comparison, the time-dependent G′ is provided for the same two materials that have been annealed. It is evident that whereas the elasticity of preannealed samples experiences little change over a long period, unannealed samples manifest a huge increase in elasticity. That the elastic modulus for the unannealed samples eventually attains values similar to those of the preannealed counterparts confirms that a thermodynamic equilibrium microstructure of the nanocomposites is approached. Flocculation of silica nanoparticles can influence nanocomposite viscoelasticity in several ways. First, shortrange particle-particle interactions,12 such as van der Waals forces and electrostatic forces, are enhanced by close approach of particles in a flocculated composite. Second, bridging of nanoparticles with adsorbed polymer molecules is expected to be substantially stronger for flocculated systems than for materials containing wellisolated nanoparticles. Two closely spaced silica nanoparticles can be easily bridged by adsorbed PEO molecules, simultaneously enhancing particle connectivity and reducing mobility of polymer chains. The affinity between PEO molecules and silica particles is high. It is believed that the adsorption mechanism between PEO molecules and silica particles is through hydrogen bonding between the ether oxygen of PEO molecules and isolated silanol groups on the silica surface (the silanol group density on
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silica particles is ∼4-5 SiOH/nm2).21 The strength of hydrogen bonds is usually several times higher than the van der Waals force and the electrostatic force, and therefore, the adsorption of PEO on silica can be considered to be irreversible.21,22 The average diameter,
D h PEO ) 2Rg )
x2N3 b
of random coils of PEO molecules in the melt state can be derived from their degree of polymerization N ) M h /m0 and their statistical segment length b. In P189-series nanocomposites, D h PEO is estimated to be around 20 nm, even larger than the average diameter of silica particles (D h ) 12 nm). This situation should result in formation of strong polymer bridges between particles, where a single polymer chain can bridge two silica particles by anchoring to multiple sites on each particle or bridge more particles by anchoring to fewer sites on each particle.23 Therefore, it is reasonable to assume that polymer-particle interactions are much more important than direct particleparticle interactions.24 This point was tested experimentally with surface modification of particles and will be discussed in the next section. Similar increases in material elasticity have also been reported to accompany particle flocculation in other polymer composites.25 For example, in carbon black filled rubbers both the tensile elastic modulus E′(ω) and loss tangent tan δ ) E′′(ω)/E′(ω) have been observed to increase after annealing at elevated temperatures. Compared with those systems, a significant difference for the PEO/silica nanocomposites studied here is that while the elastic modulus G′(ω) is indeed observed to be enhanced during thermal annealing, the loss tangent tan δ decreases. This difference, we believe, highlights an important difference in filler structure in the nanocomposites. Specifically, in the case of carbon black filled rubbers, particles are already well aggregated before annealing. Further flocculation provides more energy dissipation mechanisms such as particle friction than increased elasticity, producing a larger tan δ. In the case of PEO/silica hybrids, the filler structure is not developed without annealing. Energy dissipation is mainly through the polymer matrix. As flocculation occurs, the formed filler structure results in more energy storage than dissipation. It is possible that conformational changes of adsorbed polymer molecules also contribute to the observed increase in elasticity during thermal annealing. Durning et al.26 reported an increase of adsorption layer thickness of poly(methyl methacrylate) (PMMA) melt on a flat silica surface during thermal annealing. In his study, a PMMA layer was formed on quartz by spin casting. Initially, adsorbed polymer chains are almost flat on the surface with an adsorption layer of around 10 Å. During annealing, the adsorbed polymer molecules slowly approach an equilibrium conformation. The equilibrium surface layer thickness was found to scale as Rg ∼ N0.5, consistent with other studies.5-6 The same process may occur during thermal annealing of PEO/silica nanocomposites in this study. It is already known that adsorbed PEO molecules on silica particles in colloidal suspensions have rather flat con(21) Rubio, J.; Kitchener, J. A. J. Colloid Interface Sci. 1976, 57, 132. (22) Howard, G. J.; McConnell, P. J. Phys. Chem. 1967, 71, 2974. (23) Otsubo, Y. Langmuir 1992, 8, 2336. (24) Cai, J. J.; Salovey, R. J. Polym. Sci., Part B: Polym. Phys. 1999, 37, 815. (25) Bohm, G. G. A.; Nguyen, M. N. J. Appl. Polym. Sci. 1995, 55, 1041. (26) Durning, C. J.; O’Shaughnessy, B.; Sawhney, U.; Nguyen, D.; Majewski, J.; Smith, G. S. Macromolecules 1999, 32, 6772.
Figure 5. Effective filler volume fraction of P189-series nanocomposites as a function of real particle volume fraction. Square symbols, calculated from Guth-Smallwood equation; diamond symbols, estimated with equilibrium adsorption layer thickness assumption.
formations.22 The adsorbed PEO layer on silica nanoparticles before annealing may have a nonequilibrium structure. At the annealing temperature, the conformations of adsorbed PEO molecules evolve with time, approaching a final equilibrium structure corresponding to an immobilized layer thickness of the order of Rg ∼ N0.5. As discussed in the Introduction, filler particles in polymer composites can be usually described as a hard core surrounded with an immobilized polymer shell. The increase of immobilized layer thickness results in a higher effective particle volume fraction and hence higher material elasticity. A filler networking mechanism is proposed based on the analysis above. First, the effective particle volume fraction is much larger than the real particle volume fraction in PEO/silica nanocomposites. The effective particle volume fraction can be estimated with two different methods. The first method is to calculate the volume of immobilized polymer shells around silica particles. The equilibrium immobilized layer thickness of PEO on a flat surface is assumed to be Rg. The confined polymer shell thickness δ around silica nanospheres (radius r ) 6 nm) is deduced from the following relationship: 3
Rg )
4π (r + δ) - r 3 4πr2
3
For P189-series nanocomposites, Rg ∼ 10 nm, and δ ∼ 5 nm. The effective filler volume fraction is around 6 times as large as the real particle volume fraction (Figure 5). The second method is to estimate the effective particle volume fraction from the plateau elastic modulus GN. GN can be obtained from Figure 1 as the elastic modulus G′ at the angular frequency corresponding to a local minimum of the loss modulus G′′. For isotropic particle filled systems, the dependence of the plateau elastic modulus GN(φe) on the effective particle volume fraction φe can be related with the Guth-Smallwood equation.27
GN(φe) ) GN(0)(1 + 2.5φe + 14.1φe2) With GN(φe) and GN(0) already known, the effective particle (27) Smallwood, H. M. J. Appl. Phys. 1944, 15, 758.
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volume fraction φe can be easily calculated at different particle loadings (Figure 5). Although results of the two approaches do not agree very well, they both show a large difference between the effective particle volume fraction and the real particle volume fraction. Oscillatory shear results suggest the existence of a filler network when the particle loading is above 2 vol % in P189-series nanocomposites. At this particle loading, the estimated effective particle volume fraction is around 10 vol % (Figure 5), still much lower than the theoretical percolation threshold for spherical particles. The unusually low filler networking threshold is attributed to physical cross-linking of PEO molecules with silica nanoparticles serving as cross-link sites. Small particle size plus strong polymer-particle interactions will result in a polymer-particle network even at very low particle loadings. In this filler networking mechanism, both the polymer-particle network and the immobilized polymer layer are taken into account. Highly filled PEO/silica nanocomposite melts (φ g 2%) are not true solids, although a solidlike behavior is observed at low frequencies in oscillatory shear experiments. The lowest frequency in oscillatory shear experiments is 10-3 s-1. In other words, the solidlike behavior is only observed within a time scale of 103 s. It is important to determine whether this behavior still exists at lower frequencies (or on larger time scales). One approach is to study the time response of the nanocomposites upon a step shear strain in the linear regime. Step shear experiments often reveal characteristic relaxation dynamics of a material under flow and also characteristic relaxation time. Theoretically, the time range of step shear experiments can be infinitely long. The long-time response upon a step shear strain contains information that oscillatory shear experiments cannot measure because of limitation in the frequency range. Step shear experiments are performed for the nanocomposites with different PEO molecular weights and different particle volume fractions. The time-dependent relaxation modulus G(t) is plotted against time in Figure 6. The results are qualitatively consistent with the oscillatory shear results in Figures 1 and 2, if a rough approximation, t ∼ 1/ω, is used. However, a noteworthy finding is that all the materials clearly show two distinct relaxation dynamics. One is fast, while the other is slow. The fast mode corresponds to relaxation of bulk polymer molecules. The slow one is related to relaxation of the filler structure with much longer time scales, below which the elastic energy is stored through elastic deformation of the filler network. Above these time scales, the nanocomposites still show quite liquidlike properties. In the linear regime, the low-frequency response can be extracted from the long-time response upon a step shear strain. The elastic modulus G′(ω) and the loss modulus G′′(ω) at frequencies lower than 10-3 s-1 can be obtained via Fourier transformation of the relaxation modulus G(t) in the time domain. Fourier transformed G′(ω) and G′′(ω) of P292-S4 agree very well with directly measured G′(ω) and G′′(ω) from oscillatory shear experiments (Figure 7). A solidlike behavior is observed at frequencies above 10-4 s-1. At lower frequencies, a typical terminal behavior is observed. This result is consistent with our filler networking mechanism. As silica particles are physically connected with adsorbed polymer molecules, the formed polymer-particle network is a temporary network. On a long time scale, relaxation of this network occurs when originally immobilized PEO molecules connecting silica particles become free. Immobilized PEO molecules may
Zhang and Archer
Figure 6. Relaxation modulus G(t) of P189-series nanocomposites at 75 °C after step shear, γ ) 0.1. (a) Fixed PEO molecular weight but various particle volume fractions; (b) fixed particle volume fraction but various PEO molecular weights.
Figure 7. Fourier transformed (FT) frequency response of P292-S4 with an extended frequency range compared with directly measured data. The elastic modulus G′ and loss modulus G′′ are plotted against the angular frequency ω. Measurements were carried out at 75 °C.
relax via dissociation from silica particles, disentanglement from other immobilized PEO molecules, or other mechanisms.
Poly(ethylene oxide)/Silica Nanocomposites
For most polymer composites, linear viscoelasticity is not preserved above a critical strain amplitude γc. This phenomenon is called the Payne effect.28 In typical polymer composites having a percolated filler network, the critical strain amplitude is of the order of 1% with the oscillatory frequency at 1 Hz. However, for the PEO/silica nanocomposites in this study, the linear range of strain amplitude is always higher than 10% at ω ) 1 s-1 (e.g., for P189-S2, 75 °C, and ω ) 1 s-1, γc ∼ 0.3, while for P189-S4, γc ∼ 0.25 at the same frequency and temperature). Effects of Particle Surface Modification. The microscopy and rheology of PEO/silica nanocomposites discussed previously suggest that adsorption of PEO molecules on silica particles strongly influences melt state rheological properties. The phase structure of polymer nanocomposites also depends on the surface energy difference between polymer and particles. Specifically, if the surface energy difference is high, there is a strong tendency for filler particles to aggregate. Therefore, nanocomposite properties depend critically on surface properties of nanoparticles. A common method to modify surface properties of filler particles is to graft small molecules on the surface. The surface can be made hydrophobic by grafting hydrophobic species and hydrophilic by grafting hydrophilic species. Surface properties of silica particles were modified by grafting organosilanes to the surface. Two types of modified silica particles were obtained using the procedures described in the Experimental Section. When silica particles are grafted with a layer of organosilanes, polymer-particle interactions are largely weakened and there should be no polymer-particle network, as the adsorption sites for PEO molecules are now occupied by grafted organosilanes. At the same time, a confined polymer shell around the silica hard core does not exist. Therefore, in a hybrid containing modified silica particles, the effective particle volume fraction should not be much different from the real particle volume fraction. Nanocomposite structure is sensitive to surface properties of filler particles.1 If the surface is chemically similar with the bulk polymer, the surface energy difference is low, and vice versa. The grafted species of SPEO is chemically similar to PEO molecules in the bulk, while the bare silica surface and the SIB surface are quite different from PEO molecules. Compared with SIB and bare silica, SPEO is more compatible with the PEO matrix and has much less tendency to aggregate. In hybrids containing SPEO particles, the average size of particle aggregates should be smaller. The AFM phase contrast image in Figure 8 shows the dispersion state of SPEO particles in P189-SPEO2. Large particle aggregates are barely observed, and SPEO particles are homogeneously dispersed as isolated primary particles or very small aggregates. The frequency response of P189-SPEO2 without thermal annealing is studied immediately after it is loaded (Figure 9). It is found that the frequency response of P189-SPEO2 is almost identical to that of pure P189. It is because melted P189-SPEO2 behaves as a simple suspension of SPEO particles in a polymeric fluid. With no filler structure existing and weak polymer-particle interactions, this material exhibits almost no enhancement of viscoelastic properties. Linear viscoelastic behaviors of hybrids containing bare and modified silica nanoparticles are compared. Oscillatory shear experiments were performed for annealed samples, and the frequency-dependent elastic modulus (28) Payne, A. R. J. Polym. Sci. 1962, 6, 57.
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Figure 8. AFM phase contrast image of P189-SPEO2 before thermal annealing.
Figure 9. Frequency response of P189 and P189-SPEO2 (before annealing) at 75 °C. The elastic modulus G′ and loss modulus G′′ are plotted against the angular frequency ω.
Figure 10. Frequency response of PEO/silica nanocomposites filled with bare and surface-modified silica nanoparticles. The elastic modulus G′ is plotted as a function of the angular frequency ω. Measurements were performed at 75 °C.
G′ is plotted in Figure 10. Frequency responses of the three hybrids are quite different. P189-SPEO2 is quite liquidlike with an apparent terminal regime in the experimental frequency range. SPEO particles have little contribution to the flow behaviors. G′ of P189-S2 is high throughout the experimental frequency range, and a solidlike behavior is observed at low frequencies. For P189-SIB2, the effect of filler particles on nanocomposite dynamics is weaker than the case of P189-S2 but stronger
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than the case of P189-SPEO2. As shown from Figure 10, its G′(ω) curve is well between the other two. The difference of the three hybrids can be explained as follows. In the case of P189-SPEO2, polymer-particle interactions are weak, and no filler structure exists. This system, therefore, has very weak reinforcement. For P189-SIB2, although polymer-particle interactions are weak, particle-particle interactions play an important role in particle flocculation. Some reinforcement is induced due to formation of particle aggregates. In the case of P189-S2, strong polymer-particle interactions result in much higher effective particle volume fraction and a physical polymer-particle network. This system has the highest reinforcement. It again suggests that polymerparticle interactions are much stronger than particleparticle interactions for PEO/silica nanocomposites. Conclusions A freeze-drying procedure is used to prepare PEO/silica nanocomposites. With this technique, silica particles can be very well dispersed in PEO. Without preannealing, the nanocomposite structure is not thermodynamically stable in the melt state. During thermal annealing, structural evolution occurs, and material elasticity increases until the nanocomposite structure is under thermodynamic equilibrium. AFM studies confirm that partial flocculation occurs during thermal annealing. Another possible mechanism is that the immobilized PEO layer thickness on silica particles increases during thermal annealing. Linear viscoelastic properties of the nanocomposites with fixed polymer molecular weight and various particle volume fractions show that filler particles have a stronger effect on the low-frequency response than on the highfrequency response. This result suggests that silica nanoparticles influence the relaxation dynamics more than the plateau elastic modulus. For P189-series nanocomposites, a solidlike behavior at low frequencies is observed if the particle loading is above 2 vol %, dramatically lower than the theoretical percolation threshold for spherical particles, 30 vol %. This low filler networking threshold is due to strong polymer-particle interactions and small particle sizes. It is found the molecular weight of the PEO matrix also has a strong influence on viscoelastic behaviors of the nanocomposites. The following filler networking mechanism is proposed. First, confined polymer shells surrounding silica nanoparticles make the effective par-
Zhang and Archer
ticle volume fraction much higher than the real particle volume fraction. Second, silica particles are strongly bridged with adsorbed PEO molecules, forming a temporary polymer-particle network. The long-time response of PEO/silica nanocomposite melts following imposition of small-amplitude step shear strains reveals two distinct relaxation modes: a fast mode believed to arise from relaxation of “free” PEO molecules in the matrix and a slow mode believed to arise from relaxation of the filler structure. Relaxation of the filler structure is through reorganization of the polymerparticle network. For highly filled hybrids, solidlike behavior is dominant below the characteristic time scale for immobilized PEO molecules to become free. The lowfrequency response of the elastic modulus G′ and the loss modulus G′′ can be obtained from Fourier transformation of the relaxation modulus G(t). It clearly shows a terminal regime at very low frequencies. Therefore, the nanocomposites still have quite liquidlike properties. Nanocomposites containing surface-modified silica particles are also studied. Experiments show that surface properties of silica particles greatly influence nanocomposite structure and viscoelastic properties. In nanocomposites filled with surface-modified silica, adsorption of PEO molecules on silica particles is prohibited and therefore polymer-particle interactions are very weak. In hybrids containing SPEO particles, filler particles are not aggregated, and little reinforcement is induced. In hybrids containing SIB, particle aggregates exist due to the higher surface energy difference. Although polymerparticle interactions are weak, some reinforcement is observed. In bare silica filled nanocomposites, strong polymer-particle interactions result in a physical polymer-particle network, accompanied with the strongest reinforcement. Acknowledgment. This work was supported by the National Science Foundation, Surface Engineering Program (Grant No. CMS0004525). The research was performed in part at the Cornell Nanofabrication Facility (a member of the National Nanofabrication Users Network), which is supported by the National Science Foundation under Grant ECS-9731293, Cornell University, and industrial affiliates. The authors also thank Cornell Center for Materials Research (CCMR) for use of their facilities. LA026338J
