# Entropy-Regulated Swelling as the Mechanistic Driver of Drug Diffusion in a Mechanically Robust Hydroxyapatite/PVA Hybrid Hydrogel

## TL;DR

This paper explains how drug diffusion in a hydroxyapatite and PVA hydrogel is driven by entropy changes during swelling.

## Contribution

The study introduces a novel understanding of drug release as an entropy-regulated process in a mechanically robust hybrid hydrogel.

## Key findings

- Hydrogel swelling and drug diffusion are governed by entropy changes despite unfavorable enthalpic contributions.
- The hybrid hydrogel maintains mechanical robustness and spontaneous drug release at physiological temperatures.
- Water migration into the hydrogel network hinders drug release due to high-entropy environments.

## Abstract

Hydrogels exhibit excellent permeability for solute transport,
with their degree of swelling directly modulating drug diffusion through
their polymer network. This dynamic hinders the quantitative prediction
of the swelling mechanisms of these materials, owing to a decrease
in configurational entropy resulting from the extension of polymer
chains during water absorption. This study provides important insights
into transport phenomena in a hydroxyapatite (HAp)–poly­(vinyl
alcohol) (PVA) hydrogel by considering the thermodynamic principles
governing molecular diffusion up to equilibrium and elucidating mechanisms
relevant to drug delivery. HAp shows a hexagonal phase, and its unit
cell volume increases by ∼2% after vinyl functionalization
(HAp–π). PVA was converted to a chemically cross-linkable
polymer and subsequently reacted with HAp–π to form a
hybrid hydrogel network. The resulting system exhibits mechanical
robustness resulting not only from chemical cross-links but also from
noncovalent network constraints, which cooperatively give rise to
a high density of effective cross-linking points. The hydrogel absorbs
water and releases the drug slowly due to strong constraints imposed
by the polymer structure. Despite these restrictions, molecular diffusion
remains thermodynamically spontaneous (ΔG <
0), driven by a low, positive entropy change (ΔS), while enthalpic contributions (ΔH) are
unfavorable. During swelling, water penetrates the hydrogel, driven
by its higher chemical potential in the initially pure surrounding
liquid, migrating into the polymer matrix and inducing network expansion,
in a direction opposite to that of drug diffusion out of the hydrogel
which further hinders the release dynamics because the solute is already
in a high-entropy environment. Mass transport through a water-swellable
release system constitutes an entropically driven process, dominated
by diffusion within a constrained network. This work provides insight
into entropy-regulated drug release, demonstrating that spontaneity
is achieved at physiological temperature (∼37 °C) without
altering the thermal energy so as to compromise long-term practical
applications.