Field Treatment

The integral under the heat capacity curve is an energy (or enthalpy as the case may be) and is more or less independent of the details of the model. The quasi-chemical treatment improved the heat capacity curve, making it sharper and narrower than the mean-field result, but it still remained finite at the critical point. Further improvements were made by Bethe with a second approximation, and by Kirkwood (1938). Figure A2.5.21 compares the various theoretical calculations [6]. These modifications lead to somewhat lower values of the critical temperature, which could be related to a flattening of the coexistence curve. Moreover, and perhaps more important, they show that a short-range order persists to higher temperatures, as it must because of the preference for unlike pairs the excess heat capacity shows a discontinuity, but it does not drop to zero as mean-field theories predict. Unfortunately these improvements are still analytic and in the vicinity of the critical point still yield a parabolic coexistence curve and a finite heat capacity just as the mean-field treatments do. 

Syimnetrical tricritical points are predicted for fluid mixtures of sulfur or living polymers m certain solvents. Scott (1965) in a mean-field treatment [38] of sulfiir solutions found that a second-order transition Ime (the critical... 

Humphries R L, James P G and Luckhurst G R 1972 Molecular field treatment of nematic liquid crystals J. Chem. Soc. Faraday Trans. II 68 1031-44... 

The concentration of salt in physiological systems is on the order of 150 mM, which corresponds to approximately 350 water molecules for each cation-anion pair. Eor this reason, investigations of salt effects in biological systems using detailed atomic models and molecular dynamic simulations become rapidly prohibitive, and mean-field treatments based on continuum electrostatics are advantageous. Such approximations, which were pioneered by Debye and Huckel [11], are valid at moderately low ionic concentration when core-core interactions between the mobile ions can be neglected. Briefly, the spatial density throughout the solvent is assumed to depend only on the local electrostatic poten-... 

Obviously, the mean-field treatment of the attraetive van der Waals inter-aetion results in negleet of the influenee of the interpartiele eorrelations on as well as the influenee of attraetive forees on assoeiation effeets (ef. the definition of Eq. (78)). To obtain a more adequate approximation, Johnson and Gubbins (see, e.g., [114]), have developed an aeeurate equation of state for assoeiating Lennard-Jones fluids, or more preeisely for the following nonassoeiative potential... 

The mean field treatment of such a model has been presented by Forgacs et al. [172]. They have considered the particular problem of the effects of surface heterogeneity on the order of wetting transition. Using the replica trick and assuming a Gaussian distribution of 8 Vq with the variance A (A/kT < 1), they found that the prewetting transition critical point is a function of A and... 

It is well known that lattiee gas modeling of surfaee reaetions, in eontrast to traditional mean-field treatments, provides a realistie deseription of the fluetuations and eorrelations resulting from the adsorption and reaetion... 

Young, A. B., Proper field treatment checks corrosion, Drilling Contractor, December 1986/January 1987. 

In the previous section we assumed that disorder results in random fluctuations of the order parameter around some average value A<). Such an approach is, essentially, a mean field treatment of the lattice. It requires sufficiently strong interchain interactions, whose role is to establish a coherence between the phases of the order parameter in different chains. 

SCF, see Self-consistent field treatment (SCF) Schroedinger equation, 2,4,74 Secular equations, 6,10, 52 solution by matrix diagonalization, 11 computer program for, 31-33 Self-consistent field treatment (SCF), of molecular orbitals, 28 Serine, structure of, 110 Serine proteases, 170-188. See also Subtilisin Trypsin enzyme family comparison of mechanisms for, 182-184, 183... 

Chalermchat, Y, Fincan, M., and Dejmek, P, Pulsed electric field treatment for solid-hquid extraction of red beetroot pigment mathematical modelling of mass transfer, J. Food Eng., 64, 229, 2004. 

Findlay M, S Fogel, L Conway, A Taddeo (1995) Field treatment of coal tar-contaminated soil based on results of laboratory treatment studies. In Microbial transformation and degradation of toxic organic chemicals (Eds LY Young, CE Cerniglia), pp. 487-513. Wiley-Liss, New York. 

The analysis of the pes data for Cr(Cp)2 and Cr(MeCp)2 is however rather more difficult. In the first place, although the ligand field treatment does lead to the prediction of a 3A(a5 3) ground state forDt/B > 3.20, the 32 (a2 82) level is calculated to lie lower for a small region of Dt(B values (see Sections 2 and 3), and the first order separation,... 

Cortes C, Esteve MJ, Rodrigo D, Torregrosa F and Frrgola A. 2006. Changes of colour and carotenoid contents during high intensity pulsed electric field treatment in orange juices. Food Chem Toxicol 44 1932-1939. 

Fincan M, DeVito F and Dejmek P 2004. Pulsed electric field treatment for solid—liquid extraction of red beetroot pigment. J Food Eng 64(3) 381—388. 

---