Polymer Networks and Gels

• Biopolymer Networks are found all over nature. The cytoskeleton is supported by a network of actin, which is a semi-flexible polymer with globular proteins as a monomer unit. They are proving to be ideal model systems for understanding the physics of semi-flexible polymer, both in solution and cross-linked network states.

• Liquid Crystalline Elastomers combine the various broken symmetries of liquid crystalline phases the the elasticity of polymer networks. One obvious effect is that the single crystal elastomers can undergo spontaneous shape changes when they undergo a liquid crystalline transition. There are many more subtle effects in the interplay between the fluctuations of the familiar liquid crystalline and elastic degrees of freedom (for example, and perfect single crystal nematic elastomer can, in theory, exhibit elastic moduli of zero when deformed in certain directions. These dramatic effects are, of course, drastically influenced by the disorder, which makes them perfect for sudying quenched disorder.

Papers:

We describe a high-resolution, high-bandwidth technique for determining the local viscoelasticity of soft materials such as polymer gels. Loss and storage shear moduli are determined from the power spectrum of thermal fluctuations of embedded micron-sized probe particles, observed with an interferometric microscope. This provides a passive, small-amplitude measurement of rheological properties over a much broader frequency range than previously accessible to microrheology. We study both F-actin biopolymer solutions and polyacrylamide (PAAm) gels, as model semiflexible and flexible systems, respectively. We observe high-frequency \omega^{3/4} scaling of the shear modulus in F-actin solutions, in contrast to Rouse-like scaling for PAAm.

Local viscoelasticity of biopolymer solutions , B. Schnurr, F. Gittes, P, D. Olmsted, C. F. Schmidt, and F. C. MacKintosh, to be published in Proceedings of 1996 MRS Fall Meeting (Boston, MA).

Mean Field Nematic-Smectic-A Transition in a Random Polymer Network P. D. Olmsted and E. M. Terentjev, Physical Review E 53 (1996) 2444-2453. (abstract or preprint)

Liquid crystal elastomers present a rich combination of effects associated with orientational symmetry breaking and the underlying rubber elasticity. In this work we focus on the effect of the network on the nematic--smectic-A transition, exploring the additional translational symmetry breaking in these elastomers. We incorporate the crosslinks as a random field in a microscopic picture, thus expressing the degree to which the smectic order is locally frozen with respect to the network. We predict a modification of the NA transition, notably that it can be treated at the mean-field level (type-I system), due to the coupling with elastic degrees of freedom. There is a shift in the transition temperature T_NA, a suppression of the Halperin-Lubensky-Ma (HLM) effect (thus recovering the mean-field continuous transition to the smectic state), and a new tri-critical point, depending on the conditions of network formation. When the nematic phase possesses `soft elasticity', the NA transition becomes of first order due to the coupling with soft phonons in the network. We also discuss the microscopic origin of phenomenological long-wavelength coupling between smectic phase and elastic strain.

Rotational Invariance and Goldstone Modes in Nematic Elastomers and Gels P. D. Olmsted, Journal de Physique II (France) 4 (1994) 2215-2230.

We investigate the symmetries of elastomers and gels cross-linked in a nematic state. The coupling between the local nematic order parameter and an applied deformation leads to a class of uniform deformations which cost no elastic energy, when accompanied by a given rotation of the nematic director; this is a specific realization of a class of soft modes originally proposed, on symmetry arguments, by Golubovi\'c and Lubensky [PRL 63 (1989) 1082]. The corresponding elastic theory has a set of Goldstone modes which possesses singular fluctuations. We describe several experimental signatures of these ideas, and elucidate the physical picture of these soft modes.

Strain-Induced Nematic Phase Separation in Polymer Gels and Blends. P. D. Olmsted and S. T. Milner, Macromolecules 27 (1994) 6648-6660.

Recent experiments strongly suggest the existence of nematic-like short-range orientational interactions in polymer melts and networks. In this paper we study a mean-field model which includes a Maier-Saupe interaction between monomers of polymer chains in a melt or a polymer network, and find that external strain can induce phase separation in a mixture of chemically identical species which differ only in molecular weight. This mechanism for phase separation results from an exchange of mixing entropy, lost upon separating the small chains from the longer chains, for nematic free energy, gained by orienting the the longer chains. The essential point is that the external strain field acts directly only on the longer chains. A detailed analysis of the spinodal condition, which incorporates elastic strain and orientational degrees of freedom, reveals that the interplay between strain and orientational fluctuations induces anisotropic spinodal decomposition in a blend under uniaxial strain: the peak in the accompanying structure factor lies either along or perpendicular to the axis of strain, depending on material parameters.