Transitions fluctuations

The SmAj-SmA transition is found to be weakly first order with unusually large pre-transitional fluctuations [99]. 

On compression, a gaseous phase may condense to a liquid-expanded, L phase via a first-order transition. This transition is difficult to study experimentally because of the small film pressures involved and the need to avoid any impurities [76,193]. There is ample evidence that the transition is clearly first-order there are discontinuities in v-a plots, a latent heat of vaporization associated with the transition and two coexisting phases can be seen. Also, fluctuations in the surface potential [194] in the two phase region indicate two-phase coexistence. The general situation is reminiscent of three-dimensional vapor-liquid condensation and can be treated by the two-dimensional van der Waals equation (Eq. Ill-104) [195] or statistical mechanical models [191]. 

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

For a one-component fluid, the vapour-liquid transition is characterized by density fluctuations here the order parameter, mass density p, is also conserved. The equilibrium structure factor S(k) of a one component fluid is... 

Levine R D 1987 Fluctuations in spectral intensities and transition rates Adv. Chem. Phys. 70 53-95... 

Zhang Z, Zuckermann M J and Mouritsen O G 1993 Phase transition and director fluctuations in the 3-dimensional Lebwohl-Lasher model of liquid crystals/Mo/. Phys. 80 1195-221... 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

The reason that non-adiabatic transitions must be included for protons is that fluctuations in the potential for the quantum degrees of freedom due to the environment (e.g. solvent) contain frequencies comparable to the transition frequencies between protonic quantum states. In such cases pure quantum states do not persist. 

The influence of solvent can be incorporated in an implicit fashion to yield so-called langevin modes. Although NMA has been applied to allosteric proteins previously, the predictive power of normal mode analysis is intrinsically limited to the regime of fast structural fluctuations. Slow conformational transitions are dominantly found in the regime of anharmonic protein motion. 

Polytetrafluoroethylene transitions occur at specific combinations of temperature and mechanical or electrical vibrations. Transitions, sometimes called dielectric relaxations, can cause wide fluctuations in the dissipation factor. 

Explosion-bonded metals are produced by several manufacturers in the United States, Europe, and Japan. The chemical industry is the principal consumer of explosion-bonded metals which are used in the constmction of clad reaction vessels and heat-exchanger tube sheets for corrosion-resistant service. The primary market segments for explosion-bonded metals are for corrosion-resistant pressure vessels, tube sheets for heat exchangers, electrical transition joints, and stmctural transition joints. Total world markets for explosion-clad metals are estimated to fluctuate between 30 x 10 to 60 x 10 annually. 

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