Chen Gang
Department of Mechanical Engineering, Massachusetts Institute of Technology, USA.
Phys Chem Chem Phys. 2022 May 25;24(20):12329-12345. doi: 10.1039/d2cp00356b.
Most thermodynamic modeling of hydrogels is built on Flory's theories for the entropy of mixing and rubber elasticity, and Donnan's equilibrium conditions if polyelectrolyte polymer and mobile ions are involved. The entropy of mixing depends on the number of solvent and polymer molecules while the configurational entropy depends on the volume the polymer occupied. Flory's theory treated these two entropy terms in the Gibbs free energy on an equal basis: using the molecular numbers as the variable. I argue that the molecular number and volume are two independent thermodynamic variables and reformulate Flory's classical hydrogel thermodynamic model by minimizing the Helmholtz free energy of a combined system consisting of the hydrogel and its environment. This treatment enables us to unequivocally state that the osmotic pressure is the thermodynamic pressure of the solvent inside the hydrogel and to unambiguously write down the chemical potential of each species. The balance of the chemical potentials of the mobile species, including both the solvent and the mobile ions gives a set of equations that can be simultaneously used to solve for the equilibrium volume of the hydrogel, the osmotic pressure, and the Donnan potential, including their coupling. The model is used to study the thermodynamic properties of both pure and salty water in non-electrolyte and electrolyte hydrogels such as (1) the latent heat of evaporation, (2) the ability of hydrogels to retain water and to absorb water from the atmosphere, (3) the use of hydrogels for desalination solar or forward osmosis, (4) the antifouling characteristics of hydrogels, and (5) melting point suppression and boiling point elevation, and solubility of salts in hydrogels. These properties are of interest in solar-driven interfacial water evaporation for desalination and wastewater treatment, atmospheric water harvesting, and forward osmosis. The reformulated thermodynamic framework will also be useful for understanding polymer electrolytes and ion transport in electrochemical and biological systems.
大多数水凝胶的热力学模型是基于弗洛里的混合熵和橡胶弹性理论构建的，如果涉及聚电解质聚合物和移动离子，则基于唐南平衡条件。混合熵取决于溶剂和聚合物分子的数量，而构象熵取决于聚合物占据的体积。弗洛里理论在吉布斯自由能中对这两个熵项进行了同等对待：将分子数作为变量。我认为分子数和体积是两个独立的热力学变量，并通过最小化由水凝胶及其环境组成的组合系统的亥姆霍兹自由能，重新构建了弗洛里经典的水凝胶热力学模型。这种处理使我们能够明确指出渗透压是水凝胶内部溶剂的热力学压力，并明确写出每种物质的化学势。包括溶剂和移动离子在内的移动物种的化学势平衡给出了一组方程，这些方程可同时用于求解水凝胶的平衡体积、渗透压和唐南电位，包括它们之间的耦合。该模型用于研究非电解质和电解质水凝胶中纯水和盐水的热力学性质，例如：（1）蒸发潜热；（2）水凝胶保持水分和从大气中吸收水分的能力；（3）水凝胶用于太阳能或正渗透脱盐的应用；（4）水凝胶的抗污特性；（5）熔点降低和沸点升高，以及盐在水凝胶中的溶解度。这些性质在用于脱盐和废水处理的太阳能驱动界面水蒸发、大气水收集和正渗透方面具有重要意义。重新构建的热力学框架对于理解电化学和生物系统中的聚合物电解质和离子传输也将是有用的。
