Physics of Amorphous Polymers - CiteSeerX

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PHYSICS OF AMORPHOUS POLYMERS Gregory B. McKenna, Texas Tech University, Lubbock, TX and l’Ecole Supérieure de Physique et de Chimie Industrielles, Paris, FR Abstract Amorphous polymers are of continuing great fundamental and practical interest. From the melt state through the glass transition these materials exhibit highly nonlinear properties that are readily interrogated using methods of both linear and nonlinear rheology and mechanics. Here we examine several novel methods developed by the author to investigate swelling in rubber, nonlinear behavior of polymer glasses and the behavior of materials at the nanoscale .

Introduction Amorphous materials have a wide variety of applications from the glassy solid state and into the rubbery state. Furthermore, there is increasing interest in amorphous polymers in applications that require nanoscale dimensions and, therefore, a possible change of properties due to finite size constraints on the materials. Here we briefly examine some of the contributions by the author to these diverse fields. We will first look at rubber swelling and how a continuum mechanicsthermodynamics approach was used to elucidate the validity of the Flory-Rehner (1) hypothesis. We will then examine new work in which normal force measurements in glassy polymers show surprisingly strong differences when molecular structure is changed. Finally, we will briefly examine a novel method to measure the viscoelastic properties of polymer films at the nanoscale.

The Continuum Assumptions in the FloryRehner Model The Flory-Rehner (1) “theory” is widely used to describe the swelling of rubber. This model has often been misunderstood because it contains multiple layers of complexity and assumptions. The present author worked with multiple colleagues (2-7) to develop a means of testing the broadest of the Flory-Rehner assumptions: The free energy of mixing and the elastic free energy of the swollen network are equal and balance in swelling equilibrium without recourse to a specific model for the elastic or the mixing free energies. The work went on to show that the elastic free energy in the swollen state is the same as that in the “dry” state simply corrected for the degree of swelling deformation. At the same time, evidence was provided that suggested that the polymer-

solvent interaction parameter χ is cross-link density dependent (see Figure 1). While there are subtle issues still surrounding the swelling of rubber, such as the explanation of the peak in the plot of swelling activity parameter S vs. the degree of swelling, (8,9) this picture is now widely viewed as a good approximation of the swelling of cross-linked polymers.

Normal Forces in Polymer Glasses: Molecular Structure Effects It is commonly accepted that there is a reasonable underlying molecular understanding of the nonlinear deformation behavior of rubber and of polymer melts. Finite elasticity theories based on rubber network concepts have been highly successful and lead to important insights concerning the deformation of these materials. (10-12) Similarly, the reptation ideas of de Gennes (13) and Doi and Edwards (14-17) have provided a strong basis for the understanding of the molecular rheology of linear chain polymers. In the case of glassy polymers such microscopic or molecular models simply do not exist. Hence, we undertook to provide experimental evidence that molecular structure is important in determining the nonlinear deformation behavior of amorphous polymers in the glassy state. Importantly, the deformations were into the nonlinear regime, but well below the yield point. We performed torsional experiments (18) on polymers of different molecular structure in which both the torque and normal force were measured.(19,20) The polymers were poly(methyl methacrylate) (PMMA), poly(ethyl methacrylate) (PEMA), polycarbonate (PC) and polysulfone (PSF). The interesting findings were that the normal force responses for the materials with the large β or sub-glass transition intensity exhibited large normal force responses. Hence, both the PMMA and the PEMA had large normal force responses while the PC and PSF showed very weak normal forces. Analysis of the results in terms of the derivative of the strain energy functions lead to the finding that that the PC and PSF are nearly “neo-Hookean” materials meaning that the nonlinear modulus is independent of the deformation while the PMMA and PEMA exhibit strongly non-neo-Hookean behaviors. (See Figure 2). The results demonstrate definitively that molecular structure significantly impacts the nonlinear response in the glassy state, even well below the yield point.

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A Novel Nanomechanical Measurement

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There is an increasing interest in the behavior of materials at the nanoscale, not only because materials are being increasingly used in devices at this size level, but also because the nanoscale behavior of materials offers the opportunity to tailor properties in previously unforeseen ways. In the case of ultrathin films of polymers, it is difficult to make direct mechanical measurements and we have developed a novel biaxial deformation method to directly measure the creep compliance of the ultrathin polymer films. (22-24) The method is based on the reduction in size of the macroscopic bubble inflation or bulge test and uses the atomic force microscope to measure the bubble shape or deformation. (See Figure 3). Two important findings have come from the work. First, the nanoscale rheology of poly(vinyl acetate) (PVAc) has been shown to be the same as that of the bulk material for the segmental relaxations. Hence, there is no significant reduction in the glass transition temperature for films as thin as 27 nm and the glassy compliance behavior is the same as that of the bulk. Second, we have discovered a dramatic stiffening of the material in the rubbery plateau regime for both polystyrene (PS) and the PVAc that cannot be fully attributed to, e.g., surface tension effects. (See Figure 4). Further experimentation in this area is underway.

2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

Summary

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Amorphous polymers have a rich range of behaviors from the rubbery state to the glassy state. Furthermore, their behavior at the nanoscale is also replete with interesting phenomena. The present author has been fortunate enough to be able to collaborate with many colleagues while pursuing the active interrogation of the physics of these materials.

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Acknowledgements The author is thankful to the National Institute of Standards and Technology (originally the National Bureau of Standards) for having supported much of this work. He is also thankful to the National Science Foundation, the American Chemical Society Petroleum Research Fund and the U.S. Army Research Office for their support of the work. The John R. Bradford Endowment at Texas Tech University also made much of this work possible. Finally, the author would like to thank all those with whom he has collaborated as it is they who made these studies possible.

References

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17. 18. 19. 20. 21. 22. 23.

P.J. Flory and J.J. Rehner, Jr., J. Chem. Phys., 11, 521 (1943). G.B. McKenna and J.A. Hinkley, Polymer, 27, 1368 (1986). G.B. McKenna, K.M. Flynn and Y. Chen, Polym. Comm., 29, 272 (1988). G.B. McKenna, K.M. Flynn and Y. Chen, Polymer, 31, 1937 (1990). G.B. McKenna, K.M. Flynn and Y. Chen, Macromolecules, 22, 4507 (1989). G.B. McKenna, J.F. Douglas, K.M. Flynn and Y. Chen, Polymer, 32, 2128 (1991). N.A. Neuberger and B.E. Eichinger, Macromolecules, 21, 3060 (1988). G.B. McKenna and J.M. Crissman, J. Polym. Sci. B: Polym. Phys., 35, 817 (1997). P.J. Flory and B. Erman, Macromolecules, 15, 800 (1982). B. Erman and L. Monnerie, Macromolecules, 22, 3342 (1989). W.H. Han, F. Horkay and G.B. McKenna, Math. Mech. of Solids, 4, 139 (1999). P.-G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY (1979). M. Doi and S.F. Edwards, J. Chem. Soc., Faraday Trans. II, 74, 1789 (1978). M. Doi and S.F. Edwards, J. Chem. Soc., Faraday Trans. II, 74, 1802 (1978). M. Doi and S.F. Edwards, J. Chem. Soc., Faraday Trans. II, 74, 1818 (1978). M. Doi and S.F. Edwards, J. Chem. Soc., Faraday Trans. II, 75, 38 (1979) G.B. McKenna and L.J. Zapas, J. Rheol., 23, 23 (151). A.L. Flory and G.B. McKenna, Polymer, 46, 5211 (2005). A. Flory and G.B. McKenna, Macromolecules, 38, 1760 (2005). M. Altcoutlabi and G.B. McKenna, J. Phys. Cond. Matter, 17, R461 (2005). P.A. O’Connell and G.B. McKenna, Science, 307, 1760 (2005). P.A. O’Connell and G.B. McKenna, Eur. Phys. J. E., 20, 143 (2006). P.A. O’Connell and G.B. McKenna, Rev. Sci. Instr., (in press).

Key Words: amorphous polymers, rubber, swelling, glass, nanomechanics, glass transition

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Figure 1. The polymer-solvent interaction parameter χ in reduced form as a function of cross-link density for poly(isoprene) rubber cross-linked with dicumyl peroxide and showing the effect of cross-link density on χ. (After reference 4).

Figure 2. Normal force vs. angle of twist times torque for four polymers showing that PMMA (squares) and PEMA (circles) are far from neo-Hookean in behavior while PSF (upright triangles) and PC (inverted triangles) are close to neo-Hookean. Tests performed at approximately T=Tβ (After reference 19).

A)

Figure 4. Rubber compliance for ultrathin films of polystyrene and poly(vinyl acetate) as a function of film thickness in a double logarithmic representation. Upper data set (open symbols) includes surface tension effects. Lower data set (filled symbols) does not include surface tension effects. After reference 23).

B) Figure 3. AFM images of inflated membranes (nanobubbles) of A) poly(vinyl acetate) at 40 oC and a pressure of 48 kPa. Film thickness=150 nm. B) polystyrene at 100 oC and a pressure of 27 kPa. Film thickness=65 nm. (After reference 23).

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