Interaction free energy matrix

Each diagonal electrostatic free energy interaction matrix element is the difference between the free energy change of ionization for group i in the otherwise un-ionized protein, and in a model compound in water of p modei,/ ... 

In some cases, an alternative explanation is possible. It may be assumed that any very complex organic counterion can also interact with the CP matrix with the formation of weak non-ionic bonds, e.g., dipole-dipole bonds or other types of weak interactions. If the energy of these weak additional interactions is on the level of the energy of the thermal motion, a set of microstates appears for counterions and the surrounding CP matrix, which leads to an increase in the entropy of the system. The changes in Gibbs free energy of this interaction may be evaluated in a semiquantitative way [15]. 

The difference between GB0 and Gsc resides in their second terms, which comprise the interaction free energy between the solute charge distribution and the solvent electronic polarization. In particular, the matrix elements of V are the cavity surface integrals... 

Surface free energy (surface tension) of the fillers determines both matrix/filler and particle/particle interaction. The former has a pronounced effect... 

As an example we consider a system composed of two spin-free states, [S] and [T], which are mixed by the spin interaction Q. It is assumed that the zero-order, spin-free energies °[5] and E°[T] are functions of a system parameter Q, e.g., an internal nuclear coordinate, such that t the spin-free levels cross as shown in Figure 2. The matrix element... 

Here asx is the activity of the bound species and ax and as are the activities of the species in the sample and of the binding site in the sensor, respectively. For the purpose of this discussion, the binding site can be thought of as a defined but separate component of the selective layer, such as in heterogeneous selective layers, or it may be a specific part of the uniform matrix, as in homogeneous selective layers. (More on the origins of selectivity are discussed later.) The free energy of interaction for reaction depicted in (1.1) is... 

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