Order parameter domain, temperature

We review Monte Carlo calculations of phase transitions and ordering behavior in lattice gas models of adsorbed layers on surfaces. The technical aspects of Monte Carlo methods are briefly summarized and results for a wide variety of models are described. Included are calculations of internal energies and order parameters for these models as a function of temperature and coverage along with adsorption isotherms and dynamic quantities such as self-diffusion constants. We also show results which are applicable to the interpretation of experimental data on physical systems such as H on Pd(lOO) and H on Fe(110). Other studies which are presented address fundamental theoretical questions about the nature of phase transitions in a two-dimensional geometry such as the existence of Kosterlitz-Thouless transitions or the nature of dynamic critical exponents. Lastly, we briefly mention multilayer adsorption and wetting phenomena and touch on the kinetics of domain growth at surfaces. 

In a set of experiments, x is temperature expressed in degrees Celsius and is varied between 0°C and 100 C. Fitting a full second-order polynomial in one factor to the experimental data gives the fitted model y, = 10.3 + 1.4xi, + 0.0927xf, + r,. The second-order parameter estimate is much smaller than the first-order parameter estimate h,. How important is the second-order term compared to the first-order term when the temperature changes from 0°C to 1°C How important is the second-order term compared to the first-order term when temperature changes from 99°C to 100°C Should the second-order term be dropped from the model if it is necessary to predict response near the high end of the temperature domain ... 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

Fig. 46. Schematic order parameter (magnetization) profiles m(z) near a free surface, according to mean field theory. Various cases arc shown (a) Extrapolation length X positive. The transition of the surface from the disordered state to the ordered state is driven by the transition in the bulk ( ordinary transition ). The shaded area indicates the definition of the surface magnetization ms. (b) Extrapolation length X = oo. The transition of the surface is called "special transition ( surfacc-bulk-multicritical point ), (c), (d) Extrapolation length X < 0, temperature above the bulk critical temperature (c) or below it (d). The transition between states (c) and (d) is called the extraordinary transition , (c) Surface magnetic field Hi competes with bulk order (mi, > 0, 0 < H such that mi < -mb). In this case a domain of oppositely oriented magnetization with macroscopic thickness ( welting layer ) separated by an interface from the bulk would form at the surface, ir the system is at the coexistence curve (T < Tv, H = 0). From Binder (1983).

To analyse the phenomenon of domain size growth in a quantitative way, let us consider a simpler physical system, a metallic alloy. There are two kinds of atoms, A and B, with volume fractions (j)A and 4>b, respectively. For the sake of simplicity, assume that the averaged volume fractions (pA) and 4>b) are equal. There exists a temperature Tc such that for T > Tc the fractions are mixed, i.e. the order parameter (p = (pA — thermodynamically stable phases, one with (p > 0 ( A-rich phase") and the other with (p < 0 ( B-rich phase"). A mathematical model of this phenomenon has been suggested by Cahn and Hilliard [25]. From the point of view of thermodynamics, phase separation can be described by means of the Ginzburg-Landau free energy functional... 

Structural changes in the lipid bilayer upon insertion of the transmembrane domain of the membrane-bound protein phospholamban (PLB) were studied using P and solid state NMR. Phospholamban is a 52-amino acid integral membrane protein that regulates the flow of Ca " ions in cardiac muscle cells. Solid state NMR experiments were carried out to study the behavior of lipid bilayers in the presence of the hydrophobic PLB at different temperatures. P NMR was used to study the different phases formed by phospholipid membranes. Simulations of the P NMR spectra were carried out to reveal the formation of different vesicle sizes upon PLB insertion. Molecular order parameters were calculated by performing solid state NMR studies on deuterated phospholipid bilayers. 

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