Self-Consistent Theories

Berne B. J. A self-consistent theory of rotational diffusion, J. Chem. Phys. 62, 1154-60 (1975). 

The most important new concept to come from thermodynamics is entropy. Like volume, internal energy and mole number it is an extensive property of a system and together with these, and other variables it defines an elegant self-consistent theory. However, there is one important difference entropy is the only one of the extensive thermodynamic functions that has no obvious physical interpretation. It is only through statistical integration of the mechanical behaviour of microsystems that a property of the average macrosystem, that resembles the entropy function, emerges. 

Rubinstein has constructed on a reptation-fluctuation approach a detailed self-consistent theory of constraint release, allowing each loss of entanglement in one chain to permit a random jump in the tube of another [37]. When this is done the form of predicted relaxation functions are in good accord with experiments. However, in monodisperse linear melts it appears that the fluctuation contribution is more important than constraint release. 

The mode coupling theory of molecular liquids could be a rich area of research because there are a large number of experimental results that are still unexplained. For example, there is still no fully self-consistent theory of orientational relaxation in dense dipolar liquids. Preliminary work in this area indicated that the long-time dynamics of the orientational time correlation functions can show highly non-exponential dynamics as a result of strong in-termolecular correlations [189, 190]. The formulation of this problem, however, poses formidable difficulties. First, we need to derive an expression for the wavevector-dependent orientational correlation functions C >m(k, t), which are defined as... 

The Self-Consistent Theory Involves Three Stages. 104... 

The fine distinction between traveling times and the shift in interference fringes may not be clear from the point of view of Newtonian mechanics, which predicts both to be changing. Finally, classical physics and the geometric optics are refuted or restricted by experience, notwithstanding the fact that these are self-consistent theories in their own right. 

Another kind of self-consistent theory used a continuum diffusion representation to describe the distribution of segments.21 23 The segments were assumed to be subjected to an external potential of a mean field. An analytical approximation of the latter self-consistent theory was suggested by Milner et al. (the MWC model)24 on the basis of the observation that at high stretching the partition function of the brush is dominated by the classical path as the most probable distribution. Under this assumption, it was found that the self-consistent field is parabolic and leads to a parabolic distribution of the monomer density. Similar theories for polyelectrolyte brushes25 27 also adopted the parabolic distribution approximation. 

E.G. Emberly, G. Kirczenow, Multiterminal molecular wire systems A self-consistent theory and computer simulations of charging and transport, Phys. Rev. B 62 (2000) 10451. 

In this section, we consider the intramolecular liquid-crystalline ordering of the relatively small macromolecules, we will see that the properties of the globules in this case (small globules) are not universal. As already noted in the introduction, the analysis of the structure of small globules requires the use of the formalism of the self-consistent theory of polymer globules proposed by Lifshitz in Ref,23). 

Odijk, T. (1992). Self-consistent theory of a charged multimembrane system. Langmuir 8, 1690-1691. 

The most influential Greek philosopher was 0RISTOTLE (384 - 323 B.CJ, who is also well known as the tutor of Alexander the world conqueror. Aristotle built up a great body of self-consistent theories (i.e. theories that do not contradict each other] attempting to explain all nature in a more detailed fashion than any of his predecessors. 

Hayter, J. B. A self-consistent theory of dressed micelles. Langmuir 1992 8 2873-2876. 

As will be seen from this account, Pople s simplification of Roothaan s self-consistent theory was aimed at clarifying the description of the ground state, particularly of alternant hydrocarbons.65 It was not concerned, in the first instance, with the characteristic problems which arise when one is discussing excited electronic states. However, Pople and Hush63 developed from it a theory of the ionization potentials and electron affinities of aromatic hydrocarbons, based on a consideration of the Hartree-Fock eigenvalues Ef. According to Koopmann s theorem, the ionization potential of a closed shell should approximate to the... 

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