Polymer Osmotic Pressure in Hydrogel Contact Mechanics

Highlights

• Hydrogels behave in accordance with Hertz's contact theory.

• There is no evidence of volumetric compression of polymer under persistent load.

• Diffusive restructuring of hydrogels appear to be driving long-time relaxations in hydrogels.

• Hydrogels cannot be compressed unless their osmotic pressure is exceeded.

Abstract

Simple, semi-dilute hydrogels made from flexible polymers are often used as material surrogates for biological tissues, despite the dramatic differences between gels and tissues in their micro- and nano-structure, osmotic properties, and fluid permeability. Moreover, these simple hydrogels are often treated as poroelastic, even when applied pressures are below the hydrogel's osmotic pressure. Here we investigate the role of polymer osmotic pressure in hydrogel contact mechanics with a series of local indentation tests and bulk compression tests. Performing hydrogel indentation atop an inverted confocal microscope and applying surface pressures less than the hydrogel osmotic pressure, we find that hydrogel deformation behavior agrees with the Hertz model, observing no evidence of fluid flow or volumetric gel compression. A long-time creep of the hydrogel is also found, which can be predicted from a model of diffusive relaxations within the gel. In bulk compression tests, the gel is found to be incompressible, and therefore water cannot be driven out of the gel, unless the applied pressure exceeds the hydrogel osmotic pressure.

Introduction

Hydrogels have been broadly employed for many decades as material surrogates for biological tissues, largely because the elastic modulus and fluid permeability of hydrogels can be tuned to approximate the material and transport properties of various tissues [1], [2]. This level of control allows the design of tribological and mechanical experiments that test fundamental questions about tissue properties while mitigating the variability within tissue samples that arise from factors such as age, sex, health of the donor, and sample preparation [2], [3], [4], [5]. Popular hydrogel systems used as experimental tissue surrogates include polyacrylamide and polyethylene glycol, which, in their simplest formulations, are semi-dilute networks made from flexible polymers, having material and transport properties that are determined by the thermal fluctuations of their constituent polymer chains at the nano-scale [6], [7]. By contrast, living tissues are complex assemblies of cells, extracellular matrix, and numerous other biopolymers and biomaterials, having material and transport properties that depend strongly on micro-scale architecture and interstitial pore space between cells [8], [9]. This dominantly entropic difference between simple hydrogels and tissues may manifest in how they compress; both the elastic modulus and osmotic pressure of simple hydrogels arise from polymer thermal fluctuations and are approximately equal, while tissues behave more like bi-phasic poroelastic solids [10]. Often, the long-time dissipative response of hydrogels to compressive loads is interpreted as poroelastic without considering the role of the polymer osmotic pressure [11], [12], [13]. However, osmotic pressure of a hydrogel is a qualitatively different physical parameter from the effective compression modulus of a poroelastic solid. Thus, if the osmotic pressure dominates the hydrogel response to compressive loads, caution must be taken in interpreting the response as poroelastic and assuming pressure-driven fluid flow occurs.

Here we investigate the role of osmotic pressure in the response of a simple hydrogel system to applied, direct-contact pressure. Using a hemispherical indenter, we integrate classic contact-mechanics indentation tests with confocal microscopy, enabling the measurement of contact area, indentation depth, and applied normal load without assuming any specific elastic, viscoelastic, or poroelastic model to generate loading curves. The loading-rate dependence of hydrogel response to applied loads and evidence of fluid flow are both investigated. Applying surface pressures below the hydrogel osmotic pressure, we find that polyacrylamide gel slabs behave as described by Hertz, observing no evidence of pressure driven fluid flow. A time-dependent gel response is observed, in which the system creeps slowly under persistently applied load over very long timescales, which are hypothesized to be diffusive micro-structural relaxations within the hydrogel rather than water flow. These results are corroborated in bulk compression tests in which a thin slab is squeezed between two parallel plates; the gel does not compress until the applied pressure exceeds the gel osmotic pressure.