Molecular structures statistical mechanical approach

Computer simulation methods for studying liquid-liquid interfaces are exactly the same as those applied to investigate bulk solutions. In molecular-level, statistical-mechanical approaches, molecular dynamics and Monte Carlo methods are used. Classical molecular dynamics simulations require solving the equations of motion of the system as a function of time. The thermal and structural properties of the system are calculated as time averages along the generated sequence of... 

The statistical mechanics approach can be generalized to different molecular architectures. Chemistry provides an extraordinary wealth of structures including inter alia linear chains composed of different components (e.g., diblock copolymer or... 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

Many other approaches for finding a correct structural model are possible. A short description of ab-initio, density functional, and semiempirical methods are included here. This information has been summarized from the paperback book Chemistry with Computation An Introduction to Spartan. The Spartan program is described in the Computer Software section below.65 Another description of computational chemistry including more mathematical treatments of quantum mechanical, molecular mechanical, and statistical mechanical methods is found in the Oxford Chemistry Primers volume Computational Chemistry,52... 

The need to reliably describe liquid systems for practical purposes as condensed matter with high mobility at a given finite temperature initiated attempts, therefore, to make use of statistical mechanical procedures in combination with molecular models taking into account structure and reactivity of all species present in a liquid and a solution, respectively. The two approaches to such a description, namely Monte Carlo (MC) simulations and molecular dynamics (MD), are still the basis for all common theoretical methods to deal with liquid systems. While MC simulations can provide mainly structural and thermodynamical data, MD simulations give also access to time-dependent processes, such as reaction dynamics and vibrational spectra, thus supplying — connected with a higher computational effort — much more insight into the properties of liquids and solutions. 

Exploiting the principles of statistical mechanics, atomistic simulations allow for the calculation of macroscopically measurable properties from microscopic interactions. Structural quantities (such as intra- and intermolecular distances) as well as thermodynamic quantities (such as heat capacities) can be obtained. If the statistical sampling is carried out using the technique of molecular dynamics, then dynamic quantities (such as transport coefficients) can be calculated. Since electronic properties are beyond the scope of the method, the atomistic simulation approach is primarily applicable to the thermodynamics half of the standard physical chemistry curriculum. 

During the last two decades, studies on ion solvation and electrolyte solutions have made remarkable progress by the interplay of experiments and theories. Experimentally, X-ray and neutron diffraction methods and sophisticated EXAFS, IR, Raman, NMR and dielectric relaxation spectroscopies have been used successfully to obtain structural and/or dynamic information about ion-solvent and ion-ion interactions. Theoretically, microscopic or molecular approaches to the study of ion solvation and electrolyte solutions were made by Monte Carlo and molecular dynamics calculations/simulations, as well as by improved statistical mechanics treatments. Some topics that are essential to this book, are included in this chapter. For more details of recent progress, see Ref. [1]. 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

In this review, we introduce another approach to study the multiscale structures of polymer materials based on a lattice model. We first show the development of a Helmholtz energy model of mixing for polymers based on close-packed lattice model by combining molecular simulation with statistical mechanics. Then, holes are introduced to account for the effect of pressure. Combined with WDA, this model of Helmholtz energy is further applied to develop a new lattice DFT to calculate the adsorption of polymers at solid-liquid interface. Finally, we develop a framework based on the strong segregation limit (SSL) theory to predict the morphologies of micro-phase separation of diblock copolymers confined in curved surfaces. 

Finally, one word about the lattice theories of microemulsions [30 36]. In these models the space is divided into cells in which either water or oil can be found. This reduces the problepi to a kind of lattice gas, for which there is a rich literature in statistical mechanics that could be extended to microemulsions. A predictive treatment of both droplet and bicontinuous microemulsions was developed recently by Nagarajan and Ruckenstein [37], which, in contrast to the previous theoretical approaches, takes into account the molecular structures of the surfactant, cosurfactant, and hydrocarbon molecules. The treatment is similar to that employed by Nagarajan and Ruckenstein for solubilization [38]. 

An alternative simulation procedure is to replace the explicit solvent molecules with a continuous medium having the bulk dielectric constant. - " Once the solvent has been simplified, it is much easier to employ quantum mechanical techniques for the ENP relaxation of electronic and molecular structure in solution thus this approach is complementary to simulation insofar as it typically focuses on the response of the solute to the solvent. Since the properties of the continuum solvent must represent an average over solvent configurations, such approaches are most accurately described as quantum statistical models. 

Our knowledge of the structure of matter and of its electric, magnetic, and optical properties is based on the theory of the electron, " quantum theories, quantum and dassical electrodynanucs, statistical mechanics, " and the theory of molecular interactions. " The fundamentals of electron theory were first stated in the classical work of Lorentz and then developed in a modem approach by Rosenfeld. The quantum-mechanical theory of the electromagnetic properties of matter is presented semi-dassically in the work of Born and Jordan, and to Heitler is due the complete quantum theory of interaction between matter and the electromagnetic field. The above-named methods have permitted the determination of the atomic and molecular structure of matter, in... 

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