Thermodynamic perturbation theory averages

This takes the conventional form of standard thermodynamic perturbation theory, but with the decisive feature that interactions with only one molecule need be manipulated. Here (.., )r indicates averaging for the case that the solution contains a distinguished molecule which interacts with the rest of the system on the basis of the function AUa, i.e., the subscript r identifies an average for the reference system. Notice that a normalization factor for the intramolecular distribution cancels between the numerator and denominator of (9.22). 

Tautomerization, 82 tertiary structure 101 thermal average 3-5 thermal fluctuation 4, 31 thermal motion 3, 34 thermodynamic perturbation theory 47,120,183 TIPS 31,245... 

All discussions of transport processes currently available in the literature are based on perturbation theory methods applied to kinetic pictures of micro-scattering processes within the macrosystem of interest. These methods do involve time-dependent hamiltonians in the sense that the interaction operates only during collisions, while the wave functions are known only before and after the collision. However these interactions are purely internal, and their time-dependence is essentially implicit the over-all hamiltonian of the entire system, such as the interaction term in Eq. (8-159) is not time-dependent, and such micro-scattering processes cannot lead to irreversible changes of thermodynamic (ensemble average) properties. 

We will later consider the approximation that affects the transition from Eq. (4.4) to Eq. (4.6) in detail. But this result would often be referred to as first-order perturbation theory for the effects of - see Section 5.3, p. 105 - and we will sometimes refer to this result as the van der Waals approximation. The additivity of the two contributions of Eq. (4.1) is consistent with this form, in view of the thermodynamic relation pdpi = dp (constant T). It may be worthwhile to reconsider Exercise 3.5, p. 39. The nominal temperature independence of the last term of Eq. (4.6), is also suggestive. Notice, however, that the last term of Eq. (4.6), as an approximate correction to will depend on temperature in the general case. This temperature dependence arises generally because the averaging ((... ))i. will imply some temperature dependence. Note also that the density of the solution medium is the actual physical density associated with full interactions between all particles with the exception of the sole distinguished molecule. That solution density will typically depend on temperature at fixed pressure and composition. 

For the last fifteen years perturbation theory has been the most widely used tool for quantitative work on the structure and thermodynamic properties of homogeneous liquids. It is founded on the fact that the structure of a dense fluid of simple, reasonably spherical, molecules is determined primarily by the repulsive forces between the molecular cores. The attractive forces bind the system together and are responsible for the existence of states of high density at low external pressure, but they are not the primary determinants of the structure, as expressed in terms of the distribution functions of low order, p (i ). The thermodynamic effects of the attractive forces can be found by averaging the attractive energy, Ui(r), over the structure determined by the repulsive forces. 

If the Flory theory is indisputably a reference for the thermodynamics of polymer solutions, it suffers from a lack of accuracy in its description of dilute polymer solutions as previously mentioned. Well suited to the case of concentrated solutions, this theory depicts the behavior of dilute solutions and describes the forces due to excluded volume as the result of a perturbation to random walk statistics for example, it does not account for the significant variations experienced by the density of segments in dilute media. Indeed, the replacement of the radial variation of this function (which describes the density of interaction in the medium) by an average value is not satisfactory. 

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