Department of Chemical and Biological Engineering, SUNY at Buffalo, Buffalo, New York 14260, USA.
J Chem Phys. 2013 Nov 14;139(18):184709. doi: 10.1063/1.4828459.
The thermodynamics of hydration is expected to change gradually from entropic for small solutes to enthalpic for large ones. The small-to-large crossover lengthscale of hydrophobic hydration depends on the thermodynamic conditions of the solvent such as temperature, pressure, presence of additives, etc. We attempt to shed some light on the temperature dependence of the crossover lengthscale by using a probabilistic approach to water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a solute and solute radius. Incorporating that approach into the density functional theory, one can examine the solute size effects on its hydration over the entire small-to-large lengthscale range at a series of different temperatures. Knowing the dependence of the hydration free energy on the temperature and solute size, one can also obtain its enthalpic and entropic contributions as functions of both temperature and solute size. These functions can provide some interesting insight into the temperature dependence of the crossover lengthscale of hydrophobic hydration. The model was applied to the hydration of spherical particles of various radii in water in the temperature range from T = 293.15 K to T = 333.15 K. The model predictions for the temperature dependence of the hydration free energy of small hydrophobes are consistent with the experimental and simulational data on the hydration of simple molecular solutes. Three alternative definitions for the small-to-large crossover length-scale of hydrophobic hydration are proposed, and their temperature dependence is obtained. Depending on the definition and temperature, the small-to-large crossover in the hydration mechanism is predicted to occur for hydrophobes of radii from one to several nanometers. Independent of its definition, the crossover length-scale is predicted to decrease with increasing temperature.
水合的热力学预计将逐渐从小分子的熵变变为大分子的焓变。疏水水合的小到大转变长度尺度取决于溶剂的热力学条件，如温度、压力、添加剂的存在等。我们试图通过使用一种概率方法来研究温度对转变长度尺度的影响，该方法允许获得水分子与其距离和溶质半径的氢键数量的解析表达式。将该方法纳入密度泛函理论中，可以在一系列不同的温度下，在整个小到大长度尺度范围内检查溶质尺寸对其水合的影响。了解水合自由能对温度和溶质尺寸的依赖关系，还可以获得其焓和熵贡献作为温度和溶质尺寸的函数。这些函数可以为疏水水合的转变长度尺度的温度依赖性提供一些有趣的见解。该模型应用于各种半径的球形颗粒在水中的水合，温度范围从 T = 293.15 K 到 T = 333.15 K。该模型对小疏水分子水合自由能的温度依赖性的预测与简单分子溶质水合的实验和模拟数据一致。提出了三种替代定义来定义疏水水合的小到大转变长度尺度，并获得了它们的温度依赖性。根据定义和温度的不同，预计半径从一到几个纳米的疏水分子的水合机制会发生从小到到大的转变。无论其定义如何，转变长度尺度都预计会随着温度的升高而降低。
