Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session Y5: Fluctuating Random Solids and their universal properties |
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Sponsoring Units: GSNP DCMP Chair: Horacio Castillo, Ohio University Room: Colorado Convention Center Korbel 1A-1B |
Friday, March 9, 2007 11:15AM - 11:51AM |
Y5.00001: Nonaffine deformations in random solid media Invited Speaker: The elastic properties of materials which are inhomogeneous on mesoscopic length scales is a subject of broad interest in soft matter physics. Example systems include stiff polymer or biopolymer gels, foams, emulsions, grain packs, and microstructured solids. These diverse systems share the common feature that their linear elastic response is highly non-uniform, or ``non-affine'' at intermediate length-scales. I will present a general theoretical framework for interpreting the non-affine component of the linear elastic response of inhomogeneous materials. I will outline the connection between measured correlation functions and internal quantities such as correlation lengths, internal stress fields, and the degree of local elastic heterogeneity. I will show that the simplest 2-point correlation function gives misleading results in 2 dimensions, and I will propose better functions to measure. [Preview Abstract] |
Friday, March 9, 2007 11:51AM - 12:27PM |
Y5.00002: Incompressibility, fluctuations, and elasticity in random solids Invited Speaker: Rubbers and elastomers are usually characterized by two common properties: entropic elasticity and incompressibility. At short length-scales, these systems behave as incompressible liquids. Nevertheless, macroscopic shear deformations reduce the entropy of the polymer network, and therefore cost an elastic free energy that is proportional to temperature. In this talk I shall discuss the role of incompressibility in the elasticity of rubbery materials, and its interplay with the long wave-length fluctuations. Rubbers gain shear rigidity through the vulcanization transition, a second-order phase transition driven by cross-link density and closely related to percolation. The scaling of shear modulus as a critical phenomenon sensitively depends on the incompressibility. We have recently discovered that the vulcanization theory naturally exhibits two universality classes: phantom systems and incompressible systems. Each class exhibits distinct scaling exponent for the shear modulus near the transition. Incompressibility also crucially affects the nonlinear elasticity of rubbery materials. As we have shown recently, a subtle interplay between incompressibility and long wave-length fluctuations leads to a qualitative modification of the stress-strain relation predicted by the classical theory. To leading order, this mechanism provides a simple and generic explanation for the peak structure of Mooney-Rivlin stress-strain relation, and shows good agreement with experiments. It also leads to the prediction of a phonon correlation function that depends on the strain deformation. If time permits, I will also address incompressibility and fluctuations in liquid crystalline elastomers. [Preview Abstract] |
Friday, March 9, 2007 12:27PM - 1:03PM |
Y5.00003: Floppy modes and non-affine deformations in biopolymer networks Invited Speaker: Fibrous materials are ubiquitous in nature. They form the cytoskeleton of cells and are essential components of the extracellular matrix. Its building blocks are stiff protein filaments and a myriad of associated crosslinking proteins. The interplay between the elasticity of the biopolymers and the binding and elastic properties of the crosslinkers lead to a variety of network architectures [1]. We review recent advances in understanding the elastic properties of these networks in terms of ``floppy modes'' [2], which are the relevant low-energy excitations characterizing non-affine deformations. This approach might very well serve as a novel paradigm to understand the elasticity of microstructured materials. The theoretical concepts are applied to recent experimental studies of F-actin networks crosslinked with fascin. [1] C. Heussinger and E. Frey, Stiff Polymers, Foams and Fiber Networks, Phys. Rev. Lett. 96, 017802 (2006). [2] C. Heussinger and E. Frey, Floppy Modes and Non-Affine Deformations in Random Fiber Networks, Phys. Rev. Lett. 97, 105501 (2006) [Preview Abstract] |
Friday, March 9, 2007 1:03PM - 1:39PM |
Y5.00004: Molecular dynamics studies of rigidity in solids Invited Speaker: We have used molecular dynamics (MD) to study the elastic properties of systems of particles randomly and permanently crosslinked to each other as function of crosslink density $p$. At zero temperature, such systems generically lose the ability to withstand shear at a rigidity percolation point, $p_r$, that is (at least for particles interacting through central forces) different from the geometric percolation point $p_c$. At finite temperatures there is an entropy-generated component of the shear modulus $G(p,T)$ that remains finite for all $p > p_c$ and which vanishes with a characteristic power law $G(p,T)\sim (p-p_c)^t$. Our simulations in both two and three dimensions seem to indicate that $t$ is model-independent and, within our error bars, the same as the exponent that describes the behavior of a disordered network of conductors near its percolation point. [Preview Abstract] |
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