Modeling solvent dynamics in polymers with solvent-filled cavities

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ORIGINAL PAPER

Modeling solvent dynamics in polymers with solvent-filled cavities Michele Curatolo1 · Paola Nardinocchi1

· Luciano Teresi2

Received: 6 August 2020 / Accepted: 26 August 2020 © The Author(s) 2020

Abstract Dynamics of solvent release from polymer gels with small solvent-filled cavities is investigated starting from a thermodynamically consistent and enriched multiphysics stress-diffusion model. Indeed, the modeling also accounts for a new global volumetric constraint which makes the volume of the solvent in the cavity and the cavity volume equal at all times. This induces a characteristic suction effect into the model through a negative pressure acting on the cavity walls. The problem is solved for gel-based spherical microcapsules and microtubules. The implementation of the mathematical model into a finite element code allows to quantitatively describe and compare the dynamics of solvent release from full spheres, hollow spheres, and tubules in terms of a few key quantities such as stress states and amount of released solvent under the same external conditions. Keywords Polymer gels · Microcapslules dynamics · Solvent release · Suction pressure

1 Introduction In the last years, solvent release from polymer gels has been intensively studied, as it is able to drive quite large deformations in polymer-based structures. Solvent release in response to specific stimuli is used in multi-responsive materials to meet clearly defined functional demands such as the onset of specific deformation patterns and the delivery of fixed amounts of solvent to the external environment. Multifunctional devices based on these multi-responsive materials are common in both nature and industries [1–8]. Solvent release drives a wide variety of deformations in multi-responsive bulk materials, depending on material architecture, boundary conditions, and external stimuli, only to cite a few key factors [4, 9–14]. On the other hand, the dynamics of the release process depends on the deformations which can significantly affect the rate of release; then, its control is as important as the control of the shape changes induced by the release in polymer-based structures. Solvent release processes have been largely studied within the frame of the so-called stress-diffusion models which view the solvent-polymer mixture as a single homogenized continuum body allowing for a mass flux of the solvent [13, 15–18]. Typically, stress-diffusion models are based on the Flory-Rehner constitutive theory which describes the thermodynamics of the solvent-polymer mixture. Mostly, they deal with the analysis of the steady response of polymer gels under constraint and applied forces [11, 19–24]; however, the transient dynamics occurring during swelling or drying processes have been studied, too [13, 15, 17, 18, 25–27]. A different story has been going on when small solvent-filled cavities are present in the bulk polymer: solvent release comes from bulk as well as from cavities and the release changes the size of cavities which, on its turn, depends