Cartilage polymers: From viscoelastic solutions to weak gels*

Abstract

The dynamic properties of the polymeric components of cartilage are important for understanding the many biological functions of this biological tissue. Knowledge of the rheology of these materials is also crucial for the development of therapeutic treatments for diseases, such as arthritis, in which cartilage loses its functional physiological properties. In the present work complementary noninvasive techniques, rheology and dynamic light scattering (DLS) are used to probe the structural and dynamic properties of solutions of the principal proteoglycan components of cartilage extracellular matrix at different levels of structural hierarchy (chondroitin sulfate, aggrecan, aggrecan‐hyaluronic acid complex). It is shown that the bottlebrush shaped aggrecan molecules form large, loosely organized polyelectrolyte domains comprised of molecules organized into diffuse branched polymer network structures permeated by a diffuse cloud of counter‐ions. The rheological behaviors of these polymer solutions vary from viscoelastic solutions, consistent with the formation of dynamic polymer clusters in solution, to “weak gel” materials exhibiting approximate power law shear stress relaxation or creep over a wide range of timescales.

Thermodynamic–Dynamic Interrelations in Glass-Forming Polymer Fluids

“…Notably, this divergence exists even though G(t) decays to zero at long times and at the same time the zero-frequency shear modulus is zero. A power-law decay of G(t) means that the material stress is proportional to the fractional derivative of the strain, [101][102][103] where the power of the fractional order differential operator determines the "degree of intermediacy" between the ordinary fluid and solid states. New transport properties are required for materials in this type of critical state at the transition from liquid-like to solid-like behavior.…”

“…New transport properties are required for materials in this type of critical state at the transition from liquid-like to solid-like behavior. 103 It is not generally appreciated that this type of material is actually rather common, encompassing many gels and everyday materials, such as foods and other biological materials. From a measurement standpoint, this type of material can be problematic because the apparent viscosity or modulus can vary over a large range with the frequency.…”

Parallel Emergence of Rigidity and Collective Motion in a Family of Simulated Glass-Forming Polymer Fluids

“…A power-law decay of G ( t ) means that the material stress is proportional to the fractional derivative of the strain, − where the power of the fractional order differential operator determines the “degree of intermediacy” between the ordinary fluid and solid states. New transport properties are required for materials in this type of critical state at the transition from liquid-like to solid-like behavior . It is not generally appreciated that this type of material is actually rather common, encompassing many gels and everyday materials, such as foods and other biological materials.…”

“…Notably, this divergence exists even though G ( t ) decays to zero at long times and at the same time the zero-frequency shear modulus is zero. A power-law decay of G ( t ) means that the material stress is proportional to the fractional derivative of the strain, − where the power of the fractional order differential operator determines the “degree of intermediacy” between the ordinary fluid and solid states. New transport properties are required for materials in this type of critical state at the transition from liquid-like to solid-like behavior .…”

Editorial: In honor of Gregory B. McKenna's contributions to the field of polymer science

“…Other articles in this volume, although not being explicitly fundamental studies, include very fundamental and general concepts as the mathematically elegant description of weak gels formed by cartilage components by fractional calculus in the article by Ferenc Horkay and Jack Douglas [ 5 ] or the application of the Ozawa‐Avrami model for the crystallization kinetics of materials for additive manufacturing by Alexis Thézé et al [ 6 ] Finally, Bernard Lotz [ 7 ] makes a strong point for the fundamental relevance of crystalline polymers, a sometimes‐neglected topic in polymer physics.…”