Session: 13-15-01: Mechanics of Soft Materials I

Paper Number: 164519

How Entanglements Affect Gel Swelling 

The swelling behavior of polymer networks plays a crucial role in applications such as oil packers, drug delivery systems, diapers, and smart actuators. The swelling behavior is governed by a competition between the polymer–solvent enthalpy of mixing, which promotes swelling, and the network elasticity, which limits it. Network elasticity depends on both crosslinks and entanglements. Although their coupled effects have been extensively studied in rubbers under incompressible deformation, it remains poorly understood in swelling due to the experimental challenge to separate the crosslink effect and the entanglement effect. Consequently, most constitutive models neglect entanglements, and experimental characterizations indicate that such models offer only order-of-magnitude predictability, forcing current designs to rely largely on inefficient trial and error.

In this work, we use the novel fully constrained swelling test to directly separate the volumetric contributions of crosslinks and entanglements during swelling. This test prevents deviatoric deformation while allowing free solvent exchange, enabling direct measurement of osmotic pressure as a function of swelling ratio without interference from nonlinear deformation. By comparing the osmotic pressure produced by networks of different numbers of crosslinks and entanglements, the contributions from crosslinks and entanglements can be separated. Specifically, we use polyacrylamide hydrogel as our model material. We use the amount of crosslinker added during synthesis to control the crosslink density and the polymer volume fracture during synthesis to control the entanglement density. We then swell or deswell the as-synthesized polymer networks to characterize the effects of crosslinks and entanglements during swelling: if a change in the amount of crosslinkers does not affect osmotic pressure between two networks, the osmotic pressure is dominated by entanglements; conversely, if varying the polymer volume fraction has no effect, the osmotic pressure is dominated by crosslinks. These limiting behaviors reflect the individual contributions from crosslinks and entanglements, which can be directly compared with existing models without additional assumptions.

Our measurements show that both crosslinks and entanglements tend to limit swelling, but their effects evolve differently: the influence of crosslinks weakens while entanglement constraints strengthen as the polymer network swells. These observations qualitatively align with existing models based on the nonaffine tube theory. However, quantitative discrepancies remain. We discuss the implications of these deviations and their impact on future constitutive modeling through three perspectives: (1) the power law governing the deformation of the entanglement tubes; (2) the existence of a term for the translational entropy of the entanglements and crosslinks; (3) the proper reference state for the evolution of entanglements with swelling.

Presenting Author: Qihan Liu University of Pittsburgh

Presenting Author Biography: Dr. Liu is an assistant professor at the University of Pittsburgh. His research engages in multiple aspects of the mechanics and manufacturing of soft materials, with particular focuses on stimuli-responsive adhesion between soft materials and fiber-reinforced soft composites.

Authors:

Zefan Shao University of Pittsburgh
Qihan Liu University of Pittsburgh