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Strain Hardening in Model Polymer Brushes under Shear Ramanan Krishnamoorti*,† and Emmanuel P. Giannelis‡ Department of Chemical Engineering, University of Houston, Houston, Texas 77204, and Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853 Received January 13, 2000. In Final Form: December 21, 2000 The nonlinear dynamic response of polymer melt brushes to large amplitude oscillatory shear is studied using melt state rheology of end-tethered polymer layered-silicate nanocomposites. These model melt brushes exhibit reversible strain hardening at moderate strain amplitudes, characterized by the presence of a critical strain amplitude for the transition that is only a function of the interlayer distance (i.e., silicate fraction). These results differ qualitatively from those observed for solvent-filled polymer brushes. A phenomenological explanation based on stretching of already distorted chains in response to the applied shear and predicated on the space filing requirements of a melt brush is provided to explain these unique results.
Introduction Understanding experimentally the dynamic behavior of polymers tethered to a surface has far reaching relevance in the areas of biophysics, polymer-stabilized colloids, and polymer blends and interfaces. Extensive theoretical and experimental investigations of the dynamic response of tethered polymers, both in the dilute and concentrated surface coverage regimes (“mushroom” and “brush” regimes), have been performed.1-7 However, most of the experimental emphasis has been on solvent-filled brush systems, and the absence of melt-based experiments is primarily due to experimental difficulties. While many interesting phenomena have been elucidated and at least partially understood in the case of solvent-filled brushes,1-3,7,8 these are unlikely to hold for the case of melt brushes due to the unique space-filling constraints of the latter. Using mica-type layered silicates as host surfaces from which tethered polymer chains are grown, we have been able to develop model polymer melt brush systems for study using conventional experimental techniques such as melt-state rheometry and small angle neutron scat* To whom correspondence to be addressed. E-mail: ramanan@ bayou.uh.edu. † University of Houston. ‡ Cornell University. (1) Doyle, P. S.; Shaqfeh, E. S. G.; Gast, A. P. Phys. Rev. Lett. 1997, 78, 1182. (2) Fytas, G.; Anastasiadis, S. H.; Seghrouchni, R.; Vlassopoulos, D.; Li, J. B.; Factor, B. J.; Theobald, W.; Toprakcioglu, C. Science 1996, 274, 2041. (3) Klein, J. Annu. Rev. Mater. Sci. 1996, 26, 581. (4) Szleifer, I.; Carignano, M. A. Adv. Chem. Phys. 1996, 94, 165. (5) Rabin, Y.; Alexander, S. Europhys. Lett. 1990, 13, 49. de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. Joanny, J.-F. Langmuir 1992, 8, 989. Subramanian, G.; Williams, D. R. M.; Pincus, P. A. Macromolecules 1996, 29, 4045. Milner, S. T. Science 1991, 251, 905. Semenov, A. N. Langmuir 1995, 11, 3560. Brochard-Wyart, F. Europhys. Lett. 1993, 23, 105. BrochardWyart, F.; Hervet, H.; Pincus, P. Europhys. Lett. 1994, 26, 511. (6) Israelachvili, J. N.; Tabor, D. Proc. R. Soc. London, Ser. A 1972, 331, 19. Klein, J. J. Chem. Soc., Faraday Trans 1 1983, 79, 99. Overney, R. M. Trends Polym. Sci. 1995, 3, 359. Israelachvili, J. N. Surf. Sci. Rep. 1992, 14, 109. (7) Reiter, G.; Demirel, A. L.; Granick, S. Science 1994, 263, 1741. Klein, J.; Perahia, D.; Warburg, S. Nature 1991, 352, 143. Granick, S. MRS Bull. 1996, 21, 33. Cai, L. L.; Peanasky, J.; Granick, S. Trends Polym. Sci. 1996, 4, 47. Granick, S.; Demirel, A. L.; Cai, L. L.; Peanasky, J. Isr. J. Chem. 1995, 35, 75. (8) Baker, S. M.; Smith, G. S.; Anastassopoulos, D. L.; Toprakcioglu, C.; Vradis, A. A.; Bucknall D. G. Macromolecules 2000, 33, 1120.
tering (SANS). Specifically, we have synthesized and studied polymer brushes based on poly(-caprolactone) chains end-tethered to montmorillonite (a naturally occurring 2:1 phyllosilicate). Individual silicate layers are highly anisotropic ∼1 nm thick with an aspect ratio of ∼100-1000. The charge-carrying capacity of the silicate layer dictates the surface area accessible per chain, and for the cases examined here the montmorillonite layers have a charge exchange capacity of ∼100 mequiv/100 g. On this basis the area per chain tethered is thus estimated to be ∼0.7 nm2. It is well-known that naturally occurring layered silicates, such as montmorillonite, are inhomogeneous across layers and hence such a surface area calculation serves only as an approximate guide. On the basis of the unperturbed size of the polymers (Rg ∼ 50 Å) and the surface area per chain (a ∼ 0.7 nm2), we estimate that the systems examined in this study are in the strong brush regime. Such a high average grafting density leads to the product of the areal density of grafting and Rg to be much greater than 1, the appropriate criterion to assign these systems to be in the strong brush regime. This results in a crowding of the chains at the surface and hence causes the chains to stretch away from the surface. These systems are hence excellent model systems to understand the static conformations and dynamics of polymer brushes. We have previously used these systems along with bulk rheological and SANS techniques to study the linear viscoelastic response and influence of shear in the alignment of these systems.9 In this paper we extend the work to the melt-state nonlinear dynamic properties. In particular, we report on the first observed strain-hardening effects of model polymer melt brushes under shear. We contrast these unusual results to those observed in solution-based polymer brushes where shear thinning is observed. Experimental Section The model polymer brushes consist of poly(-caprolactone) (PCL) chains ionically bound to nanometer thick negatively charged silicate layers. The synthesis involves tethering first the initiating group to the surface of the highly anisotropic silicate layers followed by in situ polymerization in the presence of the (9) Krishnamoorti, R.; Giannelis, E. P. Macromolecules 1997, 30, 4097. Giannelis, E. P.; Krishnamoorti, R.; Manias, E. D. Adv. Polym. Sci. 1998, 138, 107.
10.1021/la0000365 CCC: $20.00 © 2001 American Chemical Society Published on Web 02/10/2001
Response of Polymer Brushes under Shear exfoliated layers to form a nanocomposite.10 Samples were extensively dried prior to any characterization or rheological measurements. Detailed synthesis and characterization information, including molecular weights and molecular weight distributions, have been reported earlier.10 In addition to the 3, 5, and 10 wt % silicate nanocomposites used in the previous study,9 a 7 wt % nanocomposite with a higher molecular weight polymer (Mw ) 47 000 and Mw/Mn ) 1.75, a result of reduction in chain transfer events) was also used in this study. We note briefly that the molecular weight and polydispersity for the chains attached to the layered silicate in the case of the 3, 5, and 10 wt % poly(-caprolactone) nanocomposites are roughly equal (Mn ∼ 10 000 and Mw/Mn ∼ 1.6). Samples for melt rheology were prepared by pressing the nanocomposites between two Teflon-covered aluminum sheets sandwiching a 2 mm thick aluminum spacer in a Carver press at 60 °C, with minimal compressive forces to form a bubble-free 25-mm disk. Rheological measurements were carried out on a Rheometrics RDA II with 25-mm parallel plates in oscillatory shear mode (γ ) γo sin(ωt)). Some measurements were also performed on a Rheometrics ARES melt rheometer with 25-mm parallel plates and a transducer with a range of 0.2-200 gf cm. To verify the linearity and the magnitude of the higher harmonics of the viscoelastic response, we attached an electronic recorder via the BNC connections provided and applied Fourier transforms to the measured torque signals. Three types of rheological measurements were performed: (a) low amplitude oscillatory shear over a range of frequency and temperature to probe the linear viscoelasticity; (b) large amplitude oscillatory shear at a given frequency and temperature in order to align the nanocomposite; (c) oscillatory shear at a given temperature and frequency over an extended range of strain amplitudes to probe the nonlinear viscoelasticity as well as the transition from linear to nonlinear behavior.
Results and Discussion The linear viscoelastic behavior as characterized by the storage and loss moduli (G′ and G′′, respectively) using small amplitude oscillatory shear have been reported earlier.9 The linear viscoelastic response of a 10 wt % silicate end-tethered PCL hybrid (unaligned) is shown in Figure 1. Time-temperature superposition (55 °C e T e 160 °C) was employed in order to generate the rheological master curves, with frequency shift factors similar to those for pure PCL and independent of silicate fraction in the nanocomposite.9 At high frequencies both the storage (G′) and loss (G′′) moduli show nonterminal behavior with a frequency dependence of ∼ω0.5. This behavior is attributed to the tethering of the soft PCL chains to the hard silicate layers and the formation of domains of parallel layers (or at least geometrically correlated layers) with the presence of defects at the domain edges. At low frequencies both G′ and G′′ show a frequency-independent plateau with G′ exceeding G′′, indicative of a pseudo-solid-like response possibly due to the incomplete relaxation of the polymers tethered to the silicate layers 9 or the formation of a percolated filler network structure.11 Application of prolonged large-amplitude oscillatory shear (γo ) 150%; ω ) 1 rad/s; T ) 95 °C; time ) 3 h for PCLC10) results in an initial decrease in both G′ and G′′12 followed by a saturation of both G′ and G′′ to values (10) Messersmith, P. B.; Giannelis, E. P. J. Polym. Sci., Part A: Polym. Chem. 1995, 33, 1047. Messersmith, P. B.; Giannelis, E. P. Chem. Mater. 1993, 5, 1064. Messersmith, P. B.; Giannelis, E. P. Chem. Mater. 1994, 6, 1719. (11) Ren, J.; Silva, A. S.; Krishnamoorti, R. Macromolecules 2000, 33, 3739. Krishnamoorti, R.; Ren, J.; Silva, A. S. J. Chem. Phys., in press. (12) During the early stages of the large amplitude oscillatory shear (i.e., first 5 to 10 cycles of shear), the third harmonic of the torque was in the range of 1-7% of the primary harmonic. However, at later times the torque signal was dominated by the primary harmonic and the higher order harmonics were negligibly small.
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Figure 1. Storage (G′) and loss (G′′) moduli for unaligned (filled symbols) and aligned (open symbols) 10 wt % layered silicatepoly(-caprolactone) nanocomposite (PCLC10). Data were obtained with the lowest strain amplitude possible over a temperature range of 55-160 °C and shifted using timetemperature superposition. Alignment was carried out at T ) 95 °C; ω ) 1 rad/s; γo ) 150%, and for a time of 3 h. The lowfrequency responses of G′ for the aligned sample (for frequencies below 4 rad/s) are possibly a result of the measured torque being close to the instrumental limits or being caused by the disorientation of the layered silicates at long times from their aligned state.
considerably lower than those at the start of the experiment. Typically, alignment experiments were stopped after all viscoelastic functions had acquired timeindependent values. The time to obtain time-independent viscoelastic functions, i.e., time for alignment, depended on the silicate loading, temperature, frequency of oscillatory shear, strain amplitude imposed, and prior processing history and ranged from a few tens of minutes to over 10 h in some cases. While SANS experiments (not shown here) suggest an orientation of the silicate layers with layer normals perpendicular to the flow direction, the orientation cannot be quantified by SANS measurements because of the large lateral dimensions of the silicate layers, the irregularity of the natural occurring layered silicates, and large polydispersity of the silicate layers. Small amplitude oscillatory shear response of such an aligned sample is shown in Figure 1 and found to be independent of the frequency, temperature, and strain amplitude imposed to obtain an aligned sample. Both G′ and G′′ are considerably lower than those observed in the unaligned state. Furthermore the frequency dependence of both G′ and G′′ is considerably enhanced from those in the unaligned state and resemble those of a homopolymer. The curvature observed in G′ for frequencies below 4 rad/s might result from the fact that the torque values were close to the lower limits of the transducer or possibly a manifestation of the disorientation of the layers from the aligned state. However, we did ensure that no bubbles were present in the samples, as microvoids or bubbles could also be responsible for such a response in G′. Similar alignment results were also obtained for 3, 5, and 7 wt % silicate PCL nanocomposites and are similar to those observed for intercalated polymer nanocomposites.11 Strain sweeps at fixed frequencies (ω) and temperature were carried out on aligned samples, i.e., samples where all the viscoelastic functions under large amplitude strain were independent of time. We note that the following results were independent of the alignment conditions imposed as long as time-independent viscoelastic functions were obtained at the end of the alignment experiments
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Figure 2. (a) Complex viscosity (η*) and (b) phase angle (tan δ) ()G′′/G′) as a function of strain amplitude (γo) for 10 wt % poly(-caprolactone) nanocomposite (PCLC10) at T ) 55 °C and ω ) 1 and 3 rad/s. Open symbols were obtained with increasing strain amplitude and filled symbols with decreasing strain amplitude.
Figure 3. Complex viscosity (η*) as a function of strain amplitude for a 5 wt % poly(-caprolactone) nanocomposite (PCLC5) over a wide range of frequencies (part a, 0.3 rad/s e ω e 10 rad/s; and part b, 10 rad/s e _ω e 100 rad/s) at T ) 70 °C. Data shown were obtained with increasing strain amplitude.
and the frequency scans exhibited a liquidlike behavior. Complex viscosity (η*) and phase angle (tan δ) as a function of strain amplitude for PCLC10 at ω ) 1 and 3 rad/s (T ) 55 °C) during both increasing and decreasing strain amplitude cycles are shown in Figure 2. At all strain amplitudes the force signal was confirmed to be sinusoidal,13 thereby allowing for interpretation in terms of standard viscoelastic functions. The complex viscosity at low strain amplitudes is independent of strain amplitude and is dominated by the viscous response. However, progression to higher strain amplitudes leads to an increase in η* with the elastic component becoming more prominent as seen by the decrease in the tan δ. At the highest strain amplitudes η* appears to saturate, with a value much higher than that observed at low strain amplitudes. A slight hysteresis in the transition from high to low viscosity is also observed when the strain amplitude
is decreased from a large value to a small value (as compared to the case where the strain amplitude is increased from low to high values). Further, the magnitude of the viscosity increase is considerably greater at low frequencies, primarily because of the low value of the viscosity at low frequencies. However, it is emphasized that all the frequencies examined here correspond to relaxation times much longer than the longest relaxation time of the polymer. Similar results were obtained on all four samples over a range of frequencies and temperatures. The data for η* as a function of strain amplitude for PCLC5 at T ) 70 °C over more than 2 decades in frequency are shown in Figure 3. While the data shown are limited to η* with increasing strain amplitude, the hysteresis and the sharp decline in tan δ are also present in each case. The upturn in the viscosity (and the downturn in tan δ) occur at a critical strain amplitude over a wide range of temperatures and frequencies (for a given silicate loading). Three important features are observed in the rheological response of all three samples: (a) the process is reversible (Figure 2a); (b) there is a critical strain amplitude for the transition that decreases with increasing silicate content (Figure 4);
(13) The torque signal, as recorded electronically by connecting via the BNC connections provided in the rheometer, was sinusoidal with the higher order harmonics being negligibly small. Further, experiments repeated with gap widths ranging from 0.8 to 2.0 mm revealed viscoelastic functions independent of the thickness of the polymer sample.
Response of Polymer Brushes under Shear
Figure 4. Silicate content dependence of the critical strain amplitude for the onset of strain hardening in the melt-brush nanocomposites described in Figures 2 and 3.
(c) the elastic component to the rheological response becomes more important with increasing strain amplitude (Figure 2b). Typically homopolymers in a shear flow exhibit decreasing viscosity with increasing shear rate. Previous experiments on intercalated and non-end-tethered layered silicate-based nanocomposites exhibit shear thinning behavior both in dynamic oscillatory shear and in steady shear flows.9,11 Also, confined polymer solutions, such as those present in a surface force apparatus, shear thin at a critical velocity presumably due to the slip of the confining mica layers.3,6,7 These systems have also shown a dramatic increase in normal force beyond a critical Weissenberg number, and this has been attributed to either hydrodynamic instabilities or flow-induced brush thickening, as well as shear-induced diffusion.1,4 However, recent neutron reflectivity measurements of tethered chains in good solvents have suggested that the chain configurations remain unaffected to very high shear rates,8 raising some questions regarding the mechanisms responsible for the unusual viscoelasticity in solution brushes. Regardless, for a solution brush created by adding 50 wt % toluene, a good solvent, to a 7 wt % silicate nanocomposite, the shear thinning behavior is recovered as shown in Figure 5. The strain amplitude (γ0) at which the brush starts to shear thin decreases roughly linearly with increasing frequency (ω), consistent with the earlier observations.3,6,7 This would suggest that the product of γ0 and ω is roughly constant, indicating that there exists a critical velocity for the observation of shear thinning, consistent with previous studies.3,6,7 Further, little or no hysteresis is observed in the viscoelastic response for this solution brushes. We also note that the magnitude of the viscosity decrease is considerably smaller in the case of the solution brushes as compared to the large increases observed for the melt brushes. In contrast, in the aligned end-tethered melt nanocomposites we observe an increase in viscosity with increasing shear strain amplitude, with the transition occurring at modest strain amplitudes (in the same range where shear thinning occurs in the solution). We suggest that the brush-like nature of the tethered polymer is
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Figure 5. Complex viscosity (η*) as a function of strain amplitude for a solution brush: 7 wt % poly(-caprolactone) nanocomposite diluted with toluene (50 wt %), over a wide range of frequencies at T ) 60 °C. Data shown were obtained with increasing strain amplitude. The solution brush clearly exhibits shear thinning while the melt brush exhibits strain hardening. Note that the abscissa is on a linear scale in this figure, while in the melt brush figures (Figures 2 and 3) it is on a logarithmic scale.
responsible for the observed viscoelastic response. On the basis of the density of grafting and the unperturbed Rg of the polymer, the systems examined are expected to be in the “strong” brush regime, wherein the chains are strongly stretched away from the tethering surface, even in the absence of any external force. Upon application of shear strain (beyond the critical strain amplitude identified in Figure 4), the tethered polymers are expected to completely unwind in response to the applied shear.2,3 On the basis of the limitations of a “melt-brush” system, wherein the tethered polymer has to fill all space, the chains stretch. This stretching occurs at a critical displacement that only depends on the geometrical restrictions of the system, i.e., the distance between tethering surfaces. This firstorder-like sharp transition from low viscosity to high viscosity results, in our opinion, from the stretching of the chains perpendicular to the surface leading to an increased viscosity. The sharp transition suggests that although the silicate layers are exfoliated by the polymer matrix, in the aligned state there is a well-defined spacing between the layers, and given the fixed grafting density, the chains undergo a stretch transition at a critical displacement. Interestingly, the critical displacement required is independent of the molecular weight of the polymer employed. First, the molecular weight for the 3, 5, and 10 wt % chains are roughly similar. Second, the critical displacement decreases with increasing silicate content, and the 7% nanocomposite with a significantly higher molecular weight (roughly three times higher) follows the trend established by the three lower molecular weight nanocomposites. A simple estimation of the interlayer distance, based on the assumption of uniform distribution, suggests an inverse dependence of the interlayer distance with the weight fraction of silicate in the composite, consistent with the results presented in Figure 4. Further, it is expected that as the spacing between layers is decreased, the equilibrium chain structure is further distorted, and therefore the critical shear displacement required for chain stretching is decreased. Joanny5 has examined the response of Rouse and entangled polymer melt brush to steady shear flows. He predicted a shear thinning viscosity beyond a critical
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velocity for the melt brushes, similar to the response of solution brushes. On the other hand, Joanny5 has examined only the linear viscoelastic response of the melt brushes to oscillatory shear, thereby precluding detailed comparisons to the results of this paper. Further, the linear viscoelastic oscillatory viscosity predicted by the theory of Joanny cannot be compared to the experimental results described here and in previous publications,9,11 as the linear viscoelastic response of the nanocomposites is dominated by the mesoscopic structure and the defect density and distribution. Alternate explanations for the observed stain hardening observed here include a physical jamming (or network formation) of the layers as a result of the applied shear. This appears unlikely as the layers are oriented parallel to the platens of the rheometer and would be forced to jam in a lateral manner. In addition, the complete reversibility of the strain hardening is further suggestion that the jamming of layers is not responsible for this effect. Further, recent experiments in our laboratories on other exfoliated and intercalated nanocomposites based on a similar layered silicate and where the chains are not end-tethered display the classical shear thinning behavior that would be expected for these materials.11 Nevertheless, we briefly note that two of the puzzling observationssthe sinusoidal nature of the torque signal in the strain-hardening region and the molecular weight independence of the critical strain amplitudesremain issues that warrant further investigation. The reversible strain hardening observed in the melt brushes is an unexpected result in light of solution-based experiments, where the systems exhibit a decrease in viscosity beyond a critical velocity and have been theoretically attributed to the disentangling of chains from adjacent tethering surfaces and consequent slip of the layers. Further, mechanisms such as shear-induced diffusion or brush thickening would require a frequency and temperature dependence to the observed phenomena and
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are also predicated on the presence of space-filling solvent. We clearly show in this work that the mechanism of flow in a melt brush is dramatically different than that in solution brushes and these effects manifest as opposite rheological responses with the controlling parameter for the transition being a critical displacement for the melt brushes as opposed to a critical velocity for the solution brushes. Concluding Remarks The results reported here are the first systematic study on the strain-hardening behavior of model nanocomposites and provide vital insight regarding the dynamics of molten polymer brushes. The observed strain hardening is thought to result from the high-grafting density and is due to chain stretching beyond a critical strain amplitude in response to the applied shear. This supposition is supported by the reversibility of the process, by the increasing importance of the elastic component with increasing strain amplitude, and most importantly by the presence of a critical strain amplitude independent of frequency and temperature. Further, solution brushes created by dispersing these nanocomposites in a good solvent display the conventional shear thinning behavior associated with solution brushes. These observations are expected to have profound influence on design of rheology modifiers in lubricants and polymer processing as well as provide guidelines for improved rheological properties of polymer-stabilized colloids. Acknowledgment. This work was supported in part by ONR and AFOSR. We benefited from the use of CCMR central facilities supported by NSF. R.K. acknowledges funding support from the ACS-PRF(G) and Texas Coordinating Board. We also thank Professor E. J. Kramer, Professor I. Szleifer, and Professor E. D. Manias for helpful discussions. LA0000365
