Structure formation statistical thermodynamics

It is not the purpose of chemistry, but rather of statistical thermodynamics, to formulate a theory of the structure of water. Such a theory should be able to calculate the properties of water, especially with regard to their dependence on temperature. So far, no theory has been formulated whose equations do not contain adjustable parameters (up to eight in some theories). These include continuum and mixture theories. The continuum theory is based on the concept of a continuous change of the parameters of the water molecule with temperature. Recently, however, theories based on a model of a mixture have become more popular. It is assumed that liquid water is a mixture of structurally different species with various densities. With increasing temperature, there is a decrease in the number of low-density species, compensated by the usual thermal expansion of liquids, leading to the formation of the well-known maximum on the temperature dependence of the density of water (0.999973 g cm-3 at 3.98°C). 

The thermodynamic approach considers micropores as elements of the structure of the system possessing excess (free) energy, hence, micropore formation processes are described in general terms of nonequilibrium thermodynamics, if no kinetic limitations appear. The applicability of the thermodynamic approach to description of micropore formation is very large, because this one is, in most cases, the result of fast chemical reactions and related heat/mass transfer processes. The thermodynamic description does not contradict to the fractal one because of reasons which are analyzed below in Sec. II. C but the nonequilibrium thermodynamic models are, in most cases, more strict and complete than the fractal ones, and the application of the fractal approach furnishes no additional information. If no polymerization takes place (that is right for most of processes of preparation of active carbons at high temperatures by pyrolysis or oxidation of primary organic materials), traditional methods of nonequilibrium thermodynamics (especially nonequilibrium statistical thermodynamics) are applicable. 

Both the structures and the dynamics of macromolecules are studied in terms of statistical thermodynamics. In the following section, we introduce the helix-coil transition theory that accounts for formation of the ubiquitous a-helical structure of peptide chains in aqueous solution. To a large extent, current research on protein... 

D. Nicholson, N.G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press (1982). (Contains, besides simulation work, much information on the thermodynamics and structure formation in interfaces.)... 

The characteristic feature of block copolymers in the solid state is their microphase separated structure, with domains of the minor component dispersed in a matrix of the major component Domain symmetry is chiefly determined by copolymer composition, however, the route to the solid state (i.e. melt prepared or solvent cast) may influence this factor. The major aim of recent small angle scattering experiments on block copolymers has been the investigation of current statistical thermodynamic theories of domain formation. In this respect, it should also be noted that small angle X-ray scattering has been used to investigate block copolymers, the work of Hashimoto et al. being particularly noteworthy. 

It is interesting to note that although apparently unaware of the development of molecular imprinting, Pande et al. [28] proposed the use of thermodynamic control for the preparation of synthetic polymer systems with a memory for a template structure. Monte Carlo computer simulations were performed to validate their hypothesis. From these calculations they identified the formation of non-random polymer sequences arising from an evolution-like preferred selection of various monomer components by similar species. These studies have since been expanded upon using statistical mechanics to examine the consequences for protein folding [29]. 

Thermodynamic properties calculated for the current study are presented in Table 7.5. Enthalpy of formation and entropy values are reported at 298 K, as most experimental data are referenced or available at 298 K. This facilitates the use of these thermodynamic properties and the use of isodesmic reaction set. Entropies and heat capacities are calculated by statistical mechanics using the harmonic-oscillator approximation for vibrations, based on frequencies and moments of inertia of the optimized B3LYP/6-311G(d,p) structures. Torsional frequencies are not included in the contributions to entropy and heat capacities instead, they are replaced with values from a separate analysis on each internal rotor analysis (IR). 

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