  Citation: Laktionov, M.; Nová, L.; Rud, O.V. Water Desalination Using Polyelectrolyte Hydrogel: Gibbs Ensemble Modeling. Gels 2022, 8, 656. https://doi.org/10.3390/gels8100656 Academic Editor: Gary E. Wnek Received: 9 August 2022 Accepted: 10 October 2022 Published: 15 October 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). gels Article Water Desalination Using Polyelectrolyte Hydrogel: Gibbs Ensemble Modeling Mikhail Laktionov 1,2 , Lucie Nová 1 and Oleg V. Rud 1,3 * 1 Department of Physical and Macromolecular Chemistry, Faculty of Science, Charles University in Prague, 12800 Prague, Czech Republic 2 Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics, 197101 Saint-Petersburg, Russia 3 Institute of Macromolecular Compounds of Russian Academy of Sciences, 199004 Saint-Petersburg, Russia * Correspondence: oleg.rud@natur.cuni.cz Abstract: Polyelectrolyte hydrogels can absorb a large amount of water across an osmotic membrane as a result of their swelling pressure. On the other hand, the insoluble cross-linked hydrogel network enables dewatering under the influence of external (thermal and/or mechanical) stimuli. Moreover, from a thermodynamic perspective, a polyelectrolyte hydrogel is already an osmotic membrane. These properties designate hydrogels as excellent candidates for use in desalination, at the same time avoiding the use of expensive membranes. In this article, we present our recent theoretical study of polyelectrolyte hydrogel usage for water desalination. Employing a coarse-grained model and the Gibbs ensemble, we modeled the thermodynamic equilibrium between the coexisting gel phase and the supernate aqueous salt solution phase. We performed a sequence of step-by-step hydrogel swellings and compressions in open and closed systems, i.e., in equilibrium with a large and with a comparably small reservoir of aqueous solution. The swelling in an open system removes ions from the large reservoir, whereas the compression in a closed system decreases the salt concentration in the small reservoir. We modeled this stepwise process of continuous decrease of water salinity from seawater up to freshwater concentrations and estimated the energy cost of the process to be comparable to that of reverse osmosis. Keywords: polyelectrolye hydrogel; simulation; desalination 1. Introduction Wastewater treatment and technology are one of the greatest concerns of modern soci- ety and must dispose of both biological [1] and chemical [2,3] pollutants. Most importantly, water treatment technologies are needed for the ever-increasing demand for the production of potable water from brine, i.e., for desalination. 1.1. Water Desalination Technologies Two basic approaches for separating water from salt are present in modern desalination technology [4,5]. The first approach is distillation, which uses heat to cause a phase change of the water to vapor. The vapor phase is separated from the brine and condenses to liquid fresh water. The released condensation energy is directed back to heat the feed solution. Distillation was the first desalination technique conducted on a large commercial scale and still accounts for a large portion of the modern world’s desalination capacity. The second approach is to physically separate the brine components using an osmotic membrane through which only water molecules can pass; the water molecules move in response to the difference in water chemical potential. In the context of our study, we mention reverse osmosis (RO) as the major process of all modern desalination industries, and the newly emerging membrane technology is described as forward osmosis (FO) [6]. Gels 2022, 8, 656. https://doi.org/10.3390/gels8100656 https://www.mdpi.com/journal/gels