Mean-field theory structure

Weeks J D, Katsov K and Vollmayr K 1998 Roles of repulsive and attractive forces in determining the structure of non uniform liquids generalized mean field theory Phys. Rev. Lett. 81 4400... 

Dodd, L. R. and Theodorou, D. N. Atomistic Monte Carlo Simulation and Continuum Mean Field Theory of the Structure and Equation of State Properties of Alkane and Polymer Melts. Vol 116,pp, 249-282,... 

The previous result is an important one. It indicates that there can be yet another fruitful route to describe lipid bilayers. The idea is to consider the conformational properties of a probe molecule, and then replace all the other molecules by an external potential field (see Figure 11). This external potential may be called the mean-field or self-consistent potential, as it represents the mean behaviour of all molecules self-consistently. There are mean-field theories in many branches of science, for example (quantum) physics, physical chemistry, etc. Very often mean-field theories simplify the system to such an extent that structural as well as thermodynamic properties can be found analytically. This means that there is no need to use a computer. However, the lipid membrane problem is so complicated that the help of the computer is still needed. The method has been refined over the years to a detailed and complex framework, whose results correspond closely with those of MD simulations. The computer time needed for these calculations is however an order of 105 times less (this estimate is certainly too small when SCF calculations are compared with massive MD simulations in which up to 1000 lipids are considered). Indeed, the calculations can be done on a desktop PC with typical... 

The single-configuration mean-field theories of electronic structure neglect correlations among the electrons. That is, in expressing the interaction of an electron at r... 

The structure factor diverges at a spinodal point defined by 1 (xN)s = F(x, f) where x is given by eqn 2.10 with q = q. The spinodal for block copolymers is close to, but not identical to, the ODT (except for symmetric block copolymers in mean field theory) and defines the stability limit of the disordered phase. 

The effect of harmonics in the composition profile has been considered in Landau Brazovskii theory, as well as mean field theory. Olvera de la Cruz (1991) found a hexagonal perforated layer (HPL) structure to be stable for symmetric or nearly symmetric diblocks in addition to the classical phases. Recent work has... 

The dynamic structure factor of block copolymer liquids (melts and solutions) has been accounted for using dynamical mean-field theory by Benmouna et al. (1987a,6). For a block copolymer melt, the dynamic structure factor can be written (Stepanek and Lodge 1996)... 

In mean field theory, two parameters control the phase behavior of diblock copolymers the volume fraction of the A block /A, and the combined interaction parameter xTak- V. where Xab is the Flory-Huggins parameter that quantifies the interaction between the A and B monomers and N is the polymerization index [30], The block copolymer composition determines the microphase morphology to a great extent. For example, comparable volume fractions of block copolymer components result in lamella structure. Increasing the degree of compositional asymmetry leads to the gyroid, cylindrical, and finally, spherical phases [31]. 

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