ABSTRACT
Many systems of interest to the food and health industries are mesoscopic: that is, their components give rise to interacting phenomena encompassing a wide range of spatial scales and timescales which are, respectively, much larger and much longer than the characteristic spatial scales and timescales of the components themselves. Some examples are hydrogels with embedded proteins or other macromolecules, polymer mixtures, and liposomes and vesicles as delivery systems. In order to understand observations made on such systems, it is important to have mathematical models which can be used to make predictions. The operator which describes the total energy of a system, the Hamiltonian operator, can be written down, but a number of problems immediately arise. The first is whether we make use of classical or semiclassical models of atomic phenomena or whether we try to include quantum effects. At present, it is unrealistic to attempt to address quantum effects in mesoscopic systems and here we restrict ourselves to the first approach. Again, two decisions must be made. What are the ranges of length scales and timescales that the model must describe? To require a description of molecular phenomena on the smalles length scale of, say, 102 nm or less requires atomic models in which details of the atomic electron densities, jwj2 are utilized. This generally takes the form of representing atomic constituents of molecules by shapes reflecting their van derWaals radii. These interact among themselves via various potential of which the 6-12 van der Waals potential is the simplest. If, however, one is satisfied with a larger scale, then some form of
MD: DUTCHER, JOB: 03309, PAGE:
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‘‘minimal model’’ might be used. In this case, the structures employed to represent molecular shapes do not necessarily reflect the details of electron densities.
