Mesoscopic continuum modeling

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

Another important class of materials which can be successfully described by mesoscopic and continuum models are amphiphilic systems. Amphiphilic molecules consist of two distinct entities that like different environments. Lipid molecules, for instance, comprise a polar head that likes an aqueous environment and one or two hydrocarbon tails that are strongly hydrophobic. Since the two entities are chemically joined together they cannot separate into macroscopically large phases. If these amphiphiles are added to a binary mixture (say, water and oil) they greatly promote the dispersion of one component into the other. At low amphiphile... 

Though this entry has focused on equilibrium properties, mesoscopic and continuum models in chemical physics can also describe non-equilibrium phenomena, and we shall mention some techniques briefly. 

First, the statistical theory - a theory in which only the global swelling is of interest - is reviewed. By refining the scale, two different mesoscopic models are presented first, the chemo-electro-mechanical transport model and second, a continuum model based on porous media. These models are capable of describing the changes of the local variables concentrations, electric field, and displacement. So, e. g., by the application of an electric field, a bending movement of the polymer gel can be realized which is in excellent correlation with experimental investigations. 

As noted by Warshel and coworkers,continuum models for the calculation of electrostatic effects in proteins and, in particular pK s of ionizable groups, have undergone significant modifications since the classical work of Tanford and Kirkwood and at present should rather be named discretized continuum (DC) models. Another possibility is to name them mesoscopic models because many elements of the microscopic structure of proteins enter the continuum models. First, the atomic structure is used to define the dielectric boundary between the protein and the solvent, with fixed charges at positions of the protein atoms. Second, since hydrogen atoms are not resolved in X-ray structures, they are added later by the modeler and their positions minimized by... 

The problem of linking atomic scale descriptions to continuum descriptions is also a nontrivial one. We will emphasize here that the problem cannot be solved by heroic extensions of the size of molecular dynamics simulations to millions of particles and that this is actually unnecessary. Here we will describe the use of atomic scale calculations for fixing boundary conditions for continuum descriptions in the context of the modeling of static structure (capacitance) and outer shell electron transfer. Though we believe that more can be done with these approaches, several kinds of electrochemical problems—for example, those associated with corrosion phenomena and both inorganic and biological polymers—will require approaches that take into account further intermediate mesoscopic scales. There is less progress to report here, and our discussion will be brief. 

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