Linear elasticity of polymer gels in terms of negative energy elasticity

Abstract

We recently found that the energy contribution to the linear elasticity of polymer gels in the as-prepared state can be a significant negative value; the shear modulus is not proportional to the absolute temperature [1]. Our finding challenges the conventional notion that the polymer-gel elasticity is mainly determined by the entropy contribution. Existing molecular models of classical rubber elasticity theories, including the affine, phantom, and junction affine network models, cannot be used to estimate the structural parameters of polymer gels. In this focus review, we summarize the experimental studies on the linear elasticity of polymer gels in the as-prepared state using tetra-arm poly(ethylene glycol) (PEG) hydrogels with a homogenous polymer network. We also provide a unified formula for the linear elasticity of polymer gels with various network topologies and densities. Using the unified formula, we reconcile the past experimental results that seemed to be inconsistent with each other. Finally, we mention that there are still fundamental unresolved problems involving the linear elasticity of polymer gels.

Tardigrade CAHS Proteins Act as Molecular Swiss Army Knives to Mediate Desiccation Tolerance Through Multiple Mechanisms

“…Thus, the length of the linker may tune the gel point by determining the monomeric molecular volume, setting the overlap concentration, which is a key determinant of the gel point. 39, 40…”

Negative Energetic Elasticity of Lattice Polymer Chain in Solvent

“…The energetic contributions of such materials have been conventionally considered to originate from the conformational change of polymer chains and have been theoretically modeled (e.g., the rotational isometric state model [9]) in accordance with that notion. However, the significant negative energetic contributions G U that originates from attractive polymer-solvent interaction was recently observed in a rubberlike polymer gel, which is a chemically crosslinked polymer network containing a large amount of solvent [10][11][12]. In this case, G U is much larger than that of the energetic elasticity originating from the conformational changes, and the absolute value of G U reaches the same order of magnitude as that of the entropic elasticity G S , as shown in Fig.…”

“…We decompose the elasticity into its energetic and entropic contributions as k = k U + k S in the same way as in Refs. [10,11]. According to thermodynamics, A = U − T S, where U is the internal energy, and S is the entropy.…”

“…1(b), T * U ≡ TU ( T * ) denotes the Tintercept of the tangent of k = k( T ) at the reference temperature T = T * . For polymer gels [10,11], T * U [Fig. 1(a)] is a key factor in the analysis of negative energetic elasticity.…”

Structural Stability Analysis of Proteins Using End-to-End Distance: A 3D-RISM Approach

“…It is considered that the softness of polymers, in general, can be explained through entropic elasticity [40][41][42]. Polymer gels containing a large amount of water solvent are significantly softer than rubber without water and show a negative energy elasticity [43][44][45]. The microscopic origin of negative energy elasticity is the solvent-polymer interaction with the deformation of a polymer.…”