Scaled-particle theory analysis of cylindrical cavities in solution

Abstract

The solvation of hard spherocylindrical solutes is analyzed within the context of scaled-particle theory, which takes the view that the free energy of solvating an empty cavitylike solute is equal to the pressure-volume work required to inflate a solute from nothing to the desired size and shape within the solvent. Based on our analysis, an end cap approximation is proposed to predict the solvation free energy as a function of the spherocylinder length from knowledge regarding only the solvent density in contact with a spherical solute. The framework developed is applied to extend Reiss's classic implementation of scaled-particle theory and a previously developed revised scaled-particle theory to spherocylindrical solutes. To test the theoretical descriptions developed, molecular simulations of the solvation of infinitely long cylindrical solutes are performed. In hard-sphere solvents classic scaled-particle theory is shown to provide a reasonably accurate description of the solvent contact correlation and resulting solvation free energy per unit length of cylinders, while the revised scaled-particle theory fitted to measured values of the contact correlation provides a quantitative free energy. Applied to the Lennard-Jones solvent at a state-point along the liquid-vapor coexistence curve, however, classic scaled-particle theory fails to correctly capture the dependence of the contact correlation. Revised scaled-particle theory, on the other hand, provides a quantitative description of cylinder solvation in the Lennard-Jones solvent with a fitted interfacial free energy in good agreement with that determined for purely spherical solutes. The breakdown of classical scaled-particle theory does not result from the failure of the end cap approximation, however, but is indicative of neglected higher-order curvature dependences on the solvation free energy.

On the Role of Nonspherical Cavities in Short Length-Scale Density Fluctuations in Water

“…22,23 The solvation thermodynamics of non-spherical shapes has also been explored with morphometric thermodynamics 24 and scaled-particle theory. 25 However, these shapes are still idealized as they do not capture the actual shapes that emerge from microscopic inhomogeneities and molecular roughness that characterizes regions of free space in the HB network. Sulimov and co-workers examined the cavitation free energies of organic molecules consisting of di↵erent sizes and shapes with molecular dynamic simulations and found that for systems with an e↵ective radii less than 7Å the computed free energies appeared to exhibit a linear dependence in the volume.…”

“…22,23 The solvation thermodynamics of nonspherical shapes has also been explored with morphometric thermodynamics 24 and scaled-particle theory. 25 In another recent study, classical scaled particle theory was used to show that free energy for cavity formation depends on the geometry by an analysis comparing thermodynamics of sphere and spherocylindrical cavity formation in water. 26 However, these shapes are still idealized as they do not capture the actual shapes that emerge from microscopic inhomogeneities and molecular roughness that characterizes regions of free space in the HB network.…”

“…In this context, quantities such as the excess chemical potential for inserting a cavity in water, as used in the information theory for hydrophobic effects, examine the number density fluctuations that occur within spherical regions. There have been recent studies examining the nature of density fluctuations (i.e., the geometrical and thermodynamical properties of regions of empty space forming within the water network) for nonspherical geometries such as cubes, cuboids, and cylinders. , The solvation thermodynamics of nonspherical shapes has also been explored with morphometric thermodynamics and scaled-particle theory . In another recent study, classical scaled particle theory was used to show that free energy for cavity formation depends on the geometry by an analysis comparing thermodynamics of sphere and spherocylindrical cavity formation in water .…”

Cavity-based free energy analysis of osmolyte effects on protein denaturation

“…5,6 It is also true that the spherocylinder result is equal to what is found from the more rigorous derivation that ''grows'' the cavity in two steps, though that, too, requires an additional assumption. 8 There is not likewise validation for the spheroidal result used in this work. Since both geometries are ultimately models onto which the WASA is mapped, the slight increase in reality of the prolate spheroid does not likely justify its use without a more rigorous derivation to support the equation used in this work.…”

“…SPT results are derived on the basis of a hard particle fluid, but it has been noted that the application to water, when taking into account its vapor pressure, provides qualitatively correct values for the local water density in contact in the cavity, and for the free energy change corresponding to the expansion or contraction of that cavity. 5,6 More accurate SPT-based equations can be derived in which water's properties are better represented, [6][7][8] but those formulations cannot be written in simple algebraic forms. Another important aspect of this approach is an SPT-based derivation for the free energy required to create a non-spherical cavity.…”