Mayer-sampling Methods for Calculation of Statistical - Mechanical Cluster Integrals: Nanotechnology and Other Applications

Kofke, David A. / SUNY Buffalo "Mayer-Sampling Methods For Calculation Of Statistical-Mechanical Cluster Integrals: Nanotechnology And Other Applications." Intellectual merit. This project aims to develop and apply methods for calculating cluster integrals that appear in statistical mechanical theories of fluids. In the general approach, Monte Carlo sampling is performed on a number of molecules equal to the order of the integral, and configurations are weighted according to the absolute value of the integrand. Ensemble averages yield the value of the cluster integral in reference to a known integral. Preliminary studies have shown the technique to be very effective for cluster-integral calculations. This general approach is called Mayer sampling, and in its basic form it has similarities to the umbrella-sampling method for free-energy calculation of condensed phases. Some of the objectives of this work are to build upon this basic idea, and examine the efficiency and effectiveness of this and other free-energy based methods for the calculation of cluster integrals in general, and virial coefficients in particular. One consideration includes formulation of strategies for conducting the calculations on parallel computing architectures, while another is concerned with developing facilities for generating the many clusters needed in some of the calculations. In addition to these development activities, the work also has objectives to apply the methods to understand and predict fluid properties. The methods are used to calculate virial coefficients for a range of model potentials and their mixtures, allowing for the first time examination of high-order coefficients for realistic model systems. One aim of this activity is to understand how well these few-molecule simulations can be used, via the virial equation, to estimate critical properties. Another aim is to uncover features that can improve understanding complex phenomena, such as hydrophobicity other behaviors important to nanotechnology and environmental applications. Broader impact. Several special forms of dissemination are performed to ensure that others readily adopt this work. First, molecular simulation modules are developed for use in instructional settings, such as undergraduate courses. Each includes a simple interactive, graphically-oriented simulation that performs a particular calculation of the type developed here, supplemented with supporting material describing its use, all presented via a web-based interface. Second, a graphically-oriented software application is developed and made available via the web. This software is designed to permit the user to calculate cluster integrals using the methods being developed in the project, and is extensible so that the user can apply it to any model system of interest. Finally, a web site devoted to the description and generation of clusters is developed. A visitor to the site can specify features of a cluster set, and will have returned a listing of all clusters (numbering just a few, or perhaps thousands, depending on the specification) meeting the given criteria, in a form suitable for use by his or her own computer codes; alternatively the clusters can be presented pictorially for instruction or contemplation. Development of methods for routine calculation of high-order cluster integrals would have a very large impact on chemical physics and applied thermodynamics. This in turn can impact a broad range of applications, such as the development of environmentally benign materials and processes. Elegant and powerful theories developed over many decades have been hindered by an inability to calculate some of the key quantities appearing in them, and consequently they are being supplanted by brute-force molecular simulation. The infusion of molecular simulation methods into these treatments will imbue them a new practicality, and renew their application and development. Such efforts could inspire many advances, including new ways for handling multiscale systems and modeling for nanotechnological applications.