Contents lists available at ScienceDirect Biotribology journal homepage: www.elsevier.com/locate/biotri Hydrogel compression and polymer osmotic pressure Abir Bhattacharyya a , Chris O'Bryan b , Yongliang Ni c , Cameron D. Morley c , Curtis R. Taylor c , Thomas E. Angelini c, ⁎ a Department of Metallurgical and Materials Engineering, Indian Institute of Technology, Jodhpur, Karwar, Rajasthan 342037, India b Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia 19104, USA c Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville 32611, USA ARTICLE INFO Keywords: Soft matter Osmotic pressure Indentation Contact mechanics Hydrogel ABSTRACT Controlling the elastic modulus of simple synthetic hydrogels like polyacrylamide is essential to their use in many areas of biotechnology, including tissue engineering, medical device development, and drug delivery applications. Indentation-based methods for measuring hydrogel elastic moduli are preferred over measurements in shear rheometers or tensile testing instruments when the freedom to choose sample volume and shape are restricted; contact lenses represent such an example. It is often believed that the local application of indentation loads will volumetrically compress hydrogels, increasing the sample's polymer concentration even when the applied pressure is less than the hydrogel's osmotic pressure. Here, we test this idea by volumetrically com- pressing polyacrylamide hydrogels of different compositions while measuring the degree of compression with increasing applied pressure. Our results reveal that at applied pressures below the hydrogel osmotic pressure, the gels exhibit only marginal compression, while above the osmotic pressure the gels compress as predicted by classical polymer physics theory. Combining measurements of osmotic pressure and polymer mesh size, we determine the scaling relationships between hydrogel composition, mesh size, and osmotic pressure. By de- monstrating agreement between experiment and theory, we use our measurements to determine the Kuhn length of the individual polymer chains constituting the hydrogels. 1. Introduction The ease with which hydrogels can be synthesized to have elastic moduli comparable to that of living tissue makes them useful in nu- merous biologically related applications such as scaffolds for tissue engineering and medical devices like contact lenses [1–5]. While a di- versity of different kinds of hydrogel exist, varying in nanostructure, microstructure, polymer solvation strength, elastic modulus, and fluid permeability [6–9], the most basic and fundamental starting point for understanding hydrogel properties is the fully swollen network of permanently crosslinked flexible polymers in a good solvent [10]. Our ability to leverage simple polymer physics to understand the behaviors of such “ideal” hydrogels like polyacrylamide (pAAm) has made them useful in biotribological studies [3,11], as all their material and trans- port properties are governed by the correlation length of their thermally fluctuating polymer chains [12,13]. This correlation length, known as the mesh size, ξ, is typically on the order of nanometers. While these ideal hydrogels represent a powerful experimental platform for funda- mental study, in addition to their usefulness in applications, their ability to mimic tissue is limited; biological tissues contain microscale pores, by contrast, and can be potentially described as water permeated cellular solids [14]. These differences between ideal hydrogels and tissues in terms of their micro- and nano-structure and the corre- spondingly different role of entropy in determining their material properties may lead to contrasting mechanical response to compressive loading. It was recently demonstrated that pAAm hydrogels do not compress under local pressure applied by indentation loading, and globally compress only when the applied pressure exceeds the osmotic pressure, Π, of the hydrogel network [15]. However, only one compo- sition of the hydrogel was tested in this study. To firmly establish that the change in compressibility is associated with osmotic pressure, a systematic investigation needs to be performed for various hydrogel compositions and the scaling relationships between Π, ξ, and polymer concentration, c, must be tested. A direct comparison between em- pirical measurements of these scaling relations and basic polymer physics predictions is necessary to provide new interpretations of the responses of flexible semi-dilute hydrogels to applied loads, most no- tably those measured under local contact pressures generated in micro- https://doi.org/10.1016/j.biotri.2020.100125 Received 29 August 2019; Received in revised form 3 March 2020; Accepted 9 March 2020 ⁎ Corresponding author. E-mail address: t.e.angelini@ufl.edu (T.E. Angelini). Biotribology 22 (2020) 100125 Available online 11 March 2020 2352-5738/ © 2020 Published by Elsevier Ltd. T