Thermodynamics of Rigid Self-Assembled Crystals: Molecular Simulation of Two-Phase Systems under External Fields

Abstract

A general methodology for determining the thermodynamic characteristics of orientationally ordered rigid crystals is presented. The basic problem here is associated with a very small flux of primary molecules that are released from a narrow interface and carry main information on thermodynamic properties of the crystal. The proposed approach is based on the kinetic Monte Carlo simulation of the gas−crystal system with an external "damping field" that reduces the intermolecular potential at the crystal edges and switches it off in the gas phase. Such a technique increases the primary molecular flux by several orders of magnitude, which is crucial for accurate determination of thermodynamic functions. In this study, we applied the approach to the thermodynamic analysis of the trimesic acid monolayer, explicitly accounting for hydrogen bonds, the dispersion, and electrostatic potentials. We considered equations of state, heat capacities, Helmholtz free energies, and entropies of three polymorphous structures: honeycomb, flower-like, and hexagonally close-packed structures in a wide range of temperatures and pressures. The calculated free energy and entropy excellently obey the Gibbs−Duhem equation, which confirms the thermodynamic consistency of our approach. The role of hydrogen bonds in the stability of different phases, as well as the condition of phase transitions, was also considered.

Thermodynamics of self-assembled molecular layers of trimesic acid from fields-supported kinetic Monte Carlo simulation

“…In this study we used the same model for the TMA molecule as that published previously 18 with a small change in the dispersion potential of molecules i and j :The distinction is that the parameter σ (the distance where the dispersion potential passes through zero) now depends on mutual orientation of interacting molecules as follows: σ / σ 0 = b − (1 − b )cos[3( α i − α j )]where α is the smallest angle of a carboxylic group of the molecule relative to x -axis. Eqn (15) accounts for the fact that molecules can be closer to each other if a carboxylic group of one molecule is between two carboxylic groups of the other when, for example, α i = α j = 0.…”

“…After substitution f to eqn (17) and accounting for μ = f + p / ρ , we have:The parameters n 1 and n 2 in the expansions (18)–(21) are taken as 4 and 3, respectively, which ensures sufficient accuracy of the data fitting. In our previous study 18 a set of p and u values was first generated with the standard Metropolis Monte Carlo method in a uniform simulation cell, followed by regression analysis using eqn (19) and (20). As a result, we have determined the coefficient c and all coefficients b jk except b 10 .…”

“…A correct analysis of equilibrium structures and polymorphism in organic adsorption layers requires the development of an approach for determination of the chemical potential, free energy, and other thermodynamic functions of the crystalline layer with chemical accuracy. [15][16][17][18] The main problem is the rigidity of such structures. Nowadays, the thermodynamic functions of crystals are commonly evaluated by the thermodynamic integration 19,20 and enhanced sampling techniques such as the overlapping distribution method by Bennett, 21 the umbrella sampling, 22 the continuous fractional component Monte Carlo method 23,24 and others.…”

“…To demonstrate the possibilities of the proposed approach, we have performed the thermodynamic analysis of surface confined TMA polymorphs and phase transitions between them. In this study we accurately adjusted parameters of a simplified model 17,18,43 of the TMA molecule to reproduce potential energy of several structures obtained with DFT-based approaches. We have studied thermodynamic properties of TMA polymorphs and the disordered phase at high temperatures relying on a recently proposed 17,18,43 and refined here approach.…”

Modeling of Different Ordering Schemes for Halogen-Functionalized Molecules with Triazine and Benzene Core

“…Density functional theory (DFT) methods are often used to determine the possible geometries and energies of interactions in supramolecular networks. − Molecular dynamics and Monte Carlo (MC) modeling has been performed to find the most stable phases of triangular, ,− linear, cross-shaped, V-shaped, and other , molecules with various functional groups.…”