The inhomogeneous distribution of crosslinks in polymer networks results in nonuniform swelling. Concomitant with this behavior is local variability in the elastic properties of synthetic and biopolymer gels. Articular cartilage exemplifies the compositional and structural complexities found in soft tissues. At the most basic level, cartilage extracellular matrix (ECM) is a relatively stiff network of collagen type II fibers with entangled hyaluronic acid chains and enmeshed aggrecan molecules. Despite significant differences in composition, synthetic and biological gels exhibit qualitatively similar responses (e.g., viscoelasticity and nonlinear stress-strain behavior at large deformation). Scaling theory [1] and experiments [2–3] have verified that the shear modulus (Ge) of chemically identical, fully swollen gels differing only in the degree of crosslinking is proportional to the polymer concentration (ce):
where A and n are constants. In a good solvent, n = 2.25 [1]. Recent studies have shown that the power law applies to collagen gels, with n ≈ 2.68 [4]. In the general case,
where G and c are the general shear modulus and polymer concentration, respectively, and m = 1/3 [5].
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