Ind. Eng. Chem. Res. 2010, 49, 11985–11990
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Linear Viscoelasticity of Spherical SiO2 Nanoparticle-Tethered Poly(butyl acrylate) Hybrids Vivek Goel,† Joanna Pietrasik,‡,§ Krzysztof Matyjaszewski,§ and Ramanan Krishnamoorti*,† Department of Chemical and Biomolecular Engineering, UniVersity of Houston, Houston, Texas 77204, Department of Chemistry, Technical UniVersity of Lodz, Institute of Polymer and Dye Technology, 90 924 Lodz, Poland, and Department of Chemistry, Carnegie Mellon UniVersity, Pittsburgh, PennsylVania 15213
The melt state linear viscoelastic properties of spherical silica nanoparticles with grafted poly(n-butyl acrylate) chains of varying molecular weight were probed using linear small amplitude dynamic oscillatory measurements and complementary linear stress relaxation measurements. While the pure silica-tethered-polymer hybrids with no added homopolymer exhibit solid-like response, addition of matched molecular weight free matrix homopolymer chains to this hybrid, at low concentrations of added homopolymer, maintains the solid-like response with a lowered modulus that can be factored into a silica concentration dependence and a molecular weight dependence. While the silica concentration dependence of the modulus is strong, the dependence on molecular weight is weak. On the other hand, increasing the amount of added homopolymer changes the viscoelastic response to that of a liquid with a relaxation time that scales exponentially with hybrid concentration. Introduction Understanding the relation between the structure and properties and the influence of processing on such structure-property correlations remains an outstanding scientific and technological issue for nanocomposites where nanoparticles are dispersed in a polymer matrix.1 While there has been significant understanding of colloidal-sized particle dispersions in a Newtonian fluid,2,3 the issues manifested in nanoparticle dispersions in nonNewtonian polymer matrices are only now being addressed.4 Yurekli and Krishnamoorti5 reviewed the rheological properties of layered silicate-based polymer nanocomposites, while recent efforts of Hobbie et al.6 and Chatterjee et al.7 have begun to address the rheological issues associated with nanotubes dispersed in polymer matrices. In both classes of nanocomposites with anisotropic nanoparticles, the linear viscoelastic properties, especially those at times much longer than the longest relaxation times of the polymer, are primarily dictated by the dispersion state of the nanoparticles and the network structures that such dispersed nanoparticles or clusters of nanoparticles might form under quiescent conditions. These observations are analogous to the linear viscoelastic properties for roughly spherical colloidal dispersions in both Newtonian and non-Newtonian fluids, with only the volume fraction at which such behavior is observed to be much lower for the case of the anisotropic nanoparticles.3,8 Novel polymer nanoparticle hybrids are those where the polymers are tethered onto the nanoparticle by either “grafting-from” or “grafting-to” techniques, where dispersion is promoted by mechanisms similar to steric-stabilized colloidal particles. Such nanoparticle dispersions of model, relatively monodisperse, polymer-grafted nanoparticles, either as undiluted hybrid materials or as mixtures with homopolymers that are chemically similar to the grafted chains, provide a good framework for developing a better understanding of the structureprocessing-property correlations for nanoparticle-dispersed polymer hybrids.9-11 * To whom correspondence should be addressed. E-mail: ramanan@ uh.edu. † University of Houston. ‡ Technical University of Lodz. § Carnegie Mellon University.
Such grafted hybrids based on spherical nanoparticles combine the behavior of soft linear polymer chains and hard nanoparticles and are capable of bridging much of our understanding of colloidal dispersions and that of star polymers.12 When the grafting density of the polymer chains is high enough that the crowding caused by the grafting results in significantly altered conformations of the polymer, significant new issues arise and are captured by the developments in “polymer brushes”. In this work, we studied such hybrid materials where linear polymers are attached to spherical silica nanoparticles and the polymers are grafted such that they are in the “strong brush” regime. Specifically, in this work we report on the linear rheological properties of such hybrid materials under conditions where the ungrafted polymers would be considered as liquids with relaxation times significantly smaller than 1 s.11 Previously, linear rheological measurements of other polymer hybrids (with no free polymer chains), including ones where the polymers have been attached to layered silicates, have indicated that with increased nanoparticle loading, at roughly the same grafting density, there is a transition from liquid-like to solid-like behavior.9,11,13 This behavior has been attributed to the formation of a sample spanning percolative network that gets created with increased nanoparticle loading.14 On the other hand, highfunctionality star polymers have shown extremely interesting behavior either as pure melts or as dispersions in linear chains. For instance, upon addition of linear chains in the stars a re-entrant gelation transition is observed in those dispersions.15 Interestingly, the hybrids studied here show some structural similarity with highly functional star polymers, most notably the formation of facecentered cubic ordered crystalline order16 that has been hinted previously in some studies of star polymers. Experimental Section Materials. The syntheses of the homopolymers and the hybrids have been described previously and are only briefly summarized here.17 The monomer n-butyl acrylate (BA, Acros, 99%) was purified by filtration through a basic alumina column to remove inhibitors before the synthesis. The synthesis of 1-(chlorodimethylsilyl)propyl 2-bromoisobutyrate and functionalization of the silica (30% wt silica in methyl isobutyl ketone,
10.1021/ie1007129 2010 American Chemical Society Published on Web 09/24/2010
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Table 1. ATRP of n-Butyl Acrylate (BA) from Functionalized Silica Particles or Small Molecular Weight Initiatora entry 1 2 3 4 5 6
media
initiation
miniemulsion miniemulsion miniemulsion solution, 10% vol solvent solution, 50% vol solvent solution, 50% vol solvent
AGET AGET AGET normal normal normal
[BA]:[initiating site] 200:1 600:1 600:1 150:1 300:1 400:1
Mn, SEC, g/mol b
24 700 53 500b 79 400b 21 100 55 000 79 600
Mw/Mn
no. of tethered chains/particle
1.27 1.25 1.29 1.07 1.23 1.09
∼600 ∼600 ∼600
a Entries 1-3, AGET ATRP in miniemulsion; [SiO2-Br]:[CuBr2]:[BPMODA]:[AA] ) 1:0.5:0.5:0.2, 80 °C, hexadecane 5 wt % based on monomer; Brij 98, 14 wt % solid content. Entries 4-6, normal ATRP; [SiO2-Br]:[CuBr]:[PMDETA] ) 1:1:1, 70 °C, anisole. b Polymers were analyzed after etching silica with HF.
diameter d ) 16.5 nm, MIBK-ST, Nissan) was described previously.10 Bis(2-pyridylmethyl)octadecylamine (BPMODA) was synthesized according to methods described previously.18 CuBr (Aldrich, 99%) was purified via several slurries in acetic acid followed by filtration and washing with methanol and ethyl ether and stored under nitrogen before use. CuBr2 (Aldrich, 99.999%), polyoxyethylene (20) oleyl ether (Brij 98, Aldrich), hexadecane (Aldrich), L-ascorbic acid (AA, Aldrich, 99%), dimethyl-2,6-dibromoheptanedioate (DMDBrHD, Aldrich, 97%), N,N,N′,N′,N′′-pentamethyldiethylenetriamine (PMDETA, Aldrich, 99%), anisole (Aldrich), and hydrofluoric acid (50 vol % HF, Acros) were used as received. Poly(n-butyl acrylate) brushes were synthesized by activators generated by electron transfer (AGET) ATRP of BA from 2bromoisobutyrate-functionalized silica particles in miniemulsion under conditions similar to those reported previously and summarized in Table 1.19 Characterization of Polymers. The characteristics of the polymers are provided in Table 1. Number-average molecular weight (Mn) and molecular weight distribution (Mw/Mn) were determined by GPC (Waters, 717 plus), with THF as the eluent at 1 mL/min (Waters, 515) and four columns (guard, 105 Å, 103 Å, 100 Å; Polymer Standards Services) in series. Toluene was used as the internal standard. Calculations of molar mass were determined using PSS software and a calibration based on linear polystyrene standards. Polymers were analyzed after etching silica with HF. Rheological Characterization. Rheological measurements were conducted using a TA Instruments ARES rheometer with a torque transducer with an operating torque range of 0.2-2000 g cm and normal force range of 2-2000 g. Dynamic oscillatory shear measurements in the linear range were performed using a set of 25 mm diameter parallel plates. Frequency sweeps were performed using small amplitude oscillatory shear to study the linear dynamic viscoelastic properties, characterized by the storage and loss moduli (G′ and G′′, respectively). A sinusoidal strain of the form γ(t) ) γ0 sin(ωt) was applied, and the resultant shear stress σ(t) () γ0 {G′ sin(ωt) + G′′ cos(ωt)}) was monitored. The complex viscosity (η*) () (G′′(ω)2 + G′(ω)2)1/2/ ω ) G*/ω) is also reported, where G* is the complex modulus. The operating temperatures were 30 and 80 °C, with the data reduced forming a master curve, via the principle of timetemperature superposition, at the reference temperature of 30 °C. Stress relaxation measurements were conducted at 30 °C using a cone and plate geometry with a cone angle of 0.0998 rad and a diameter of 25 mm. Specifically, this geometrical setup of the cone and plate type was employed in order to produce a uniform shearing rate across the sample space as •
γ ) ν/tan R
(1)
where γ• is the shear rate (s-1), ν is the cone angular velocity, and R is the cone angle. A step strain γo was applied at time t
Figure 1. Linear dynamic oscillatory shear response of the 80K PBA-based SiO2 hybrid sample. The data collected at temperatures between 30 and 80 °C were reduced to a single master curve using the principle of time-temperature superpositioning. The horizontal frequency shift factors (aT) were similar to that for the pure PBA homopolymer.
) 0 and the shear stress monitored as a function of time, with the modulus G(t) obtained as G(t) ) σ(t)/γo. Results and Discussions The linear dynamic viscoelastic behavior of the SiO2-PBA hybrids was examined for each of the three hybrid samples described in Table 1 and for the blends of the hybrid materials with their corresponding matched molecular weight free polymer using small strain amplitude oscillatory measurements. Typical linear dynamic viscoelastic data for the undiluted hybrid materials, with no free polymer chains, is shown in Figure 1. The presence of a frequency-independent plateau in G′ at low frequencies, with the value of the storage modulus, G′, exceeding that of the loss modulus, G′′, is observed in the time-temperature superposed linear dynamic viscoelasticity mastercurves. We note that excellent time-temperature superpositioning is observed and that the temperature-dependent frequency shift factors for the nanocomposites are virtually identical to that of the homopolymers of PBA. Such solid-like rheological behavior is reminiscent of cross-linked elastomers, percolated and fillerdominated nano- and macrocomposites, and perhaps most relevantly of ordered block copolymers that form either bodycentered or face-centered cubic structures. In fact, structural studies using small-angle X-ray and neutron scattering along with electron microscopy of these undiluted hybrid materials indicate that the silica nanoparticles organize themselves in a face-centered cubic lattice, and this arrangement might in fact be responsible for the observed solid-like character.
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Figure 3. Cross plot of the complex modulus (G*) and the complex viscosity (η*) from linear dynamic oscillatory measurements for the blends of the PBA80K homopolymer with the SiO2-PBA80K hybrid material. The samples with liquid-like behavior (pure homopolymer and low hybrid concentrations) demonstrate Newtonian behavior with the viscosity being well behaved down to the lowest value of the complex modulus. On the other hand, for the blends with higher levels of hybrid material, the viscosity diverges at significant values of the complex modulus, a feature characteristic of materials with a yield stress.
Figure 2. (a) Storage modulus (bTG′) as a function of reduced frequency (aTω) from small amplitude oscillatory shear for the SiO2-PBA80k hybrid and its matched blends. While the SiO2-PBA80k hybrid shows solid-like character, addition of homopolymer chains increases the mobility of hybrids. Also shown is the scaling of storage modulus G′ with frequency ω for a homopolymer, which is expected to scale as G′ ≈ ω2. (b) Frequency dependence of the linear complex modulus (η*) for the blends of SiO2-PBA80K with a 80K PBA homopolymer are shown. Data collected over a temperature range of 30-80 °C were superposed using the principle of time-temperature superpositioning to obtain the master curves shown here.
The value of the elastic modulus corresponding to the longlived plateau (at low frequencies) for the three different chain length hybrids are 3.5 × 105 dyn/cm2 for SiO2-PBA25K, 5.3 × 104 dyn/cm2 for SiO2-PBA53K, and 8.0 × 104 dyn/cm2 for the SiO2-PBA80K material. On the basis of the silica content for these three hybrids (8.5, 3.9, and 2.7 vol %, respectively), it is clear that the modulus reported here is not just a function of the silica content, i.e., it does not scale with the number of silica particles per unit volume. Further, the modulus also does not scale with the molecular weight of the tethered chains independent of the silica content. We discuss the origins of this modulus behavior later in this paper. The polymer-tethered silica hybrids were blended with a homopolymer with matched molecular weight to the one tethered to the silica nanoparticles (Table 1). These mixtures of the grafted nanoparticles and their matched homopolymers were found to be homogeneous using both electron microscopy and small-angle X-ray scattering measurements. The linear viscoelastic properties of these blends were examined using linear dynamic oscillatory melt rheological measurements, and typical data for a series of such blends is reported in Figure 2. We focus on the frequency dependence of the storage modulus (G′) (Figure 2a) and the complex viscosity (η*) (Figure 2b) for the set of matched homopolymer-grafted nanoparticle blends that covers the range from pure hybrid to pure homopolymer. The blends, like the pure hybrids, exhibit thermorheological simplicity, and further, the shift factors are virtually identical in all cases. Blending of free homopolymer molecules to the polymertethered silica hybrid systematically alters the viscoelastic response and is most clearly observed in the low-frequency response of G′ and η*.9 The low frequency plateau value of G′
decreases with increasing homopolymer content. Similarly, the value of the complex viscosity at low frequencies monotonically decreases with increasing homopolymer concentration. For the samples with homopolymer concentration in excess of 55%, liquid-like behavior is observed in the modulus and viscosity data. For these blends, the elastic modulus at the lowest frequencies shows classic liquid-like behavior and scales as ω-2. This is also manifested as a low-frequency turnover to near “Newtonian” behavior in the complex viscosity, η*, which becomes independent of frequency for the 45% silica hybrid blend. On the other hand, the viscosity for the blends with higher hybrid concentration demonstrated a strong power-law behavior at low frequencies, consistent with the solid-like modulus behavior described in Figure 2a. Addition of small amounts of homopolymer to the hybrid results in the overall preservation of the cubic lattice structure (corresponding to the FCC arrangement) and therefore the solidlike behavior.20 The decrease in the modulus and viscosity for such blends with dilution is consistent with the swelling of the lattice and dilution of the lattice centers per unit volume. However, for the blends with ∼50% homopolymer (and up to 75% homopolymer), even though the scattering and electron microscopy data indicate that the lattice structure is preserved, clearly the dynamic nature of the polymer chains (both tethered and free) results in the dynamic nature of the lattice centers and therefore the long time relaxation of the stress supported by the lattice structure. A convenient way to ascertain the transition from solid-like to liquid-like behavior is through a cross plot of the complex modulus G* versus the complex viscosity η*, as shown in Figure 3. Again, for the blends with 55% or more of the homopolymer, the blends demonstrate Newtonian behavior: the viscosity is well behaved at the lowest complex modulus values. On the other hand, the pure hybrid and the blends with a high concentration of the silica hybrid exhibit a diverging viscosity at finite values of the complex modulus, typical of materials with a finite yield stress, with the value of the complex modulus at which η* diverges being a measure of the yield stress. While this yield stress is clearly detected for the high hybrid concentration hybrids, the behavior of complex modulus for the blends with 55% or less of the hybrid material is not well defined to identify a yield stress.
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Figure 4. Linear stress relaxation data after instantaneous step shear for the matched blends of SiO2-PBA80K with a homompolymer PBA80K. The lines are the predictions based on the application of eq 2 and using the data obtained from linear dynamic viscoelastic measurements on the same samples and shown in Figure 2. The agreement between the experimentally measured and calculated data indicates the applicability of the two-point collocation method to understand the rheology of such hybrids and their blends.
Corroboration of the long-time (low-frequency) viscoelastic response observed in the linear dynamic oscillatory results for the blends is obtained from the stress-relaxation behavior of the blends of homopolymer and hybrid shown in Figure 4. We note that while the longest relaxation time for a free homopolymer chain of length corresponding to that of a single grafted chain is
