Cooperative critical process

Another type of kinetics pattern currently under discussion is related to the so-called Mode-Coupling Theory (MCT) developed by Gotze and Sjogren [74], In the MCT the cooperative relaxation process in supercooled liquids and amorphous solids is considered to be a critical phenomenon. The model predicts a dependence of relaxation time on temperature for such substances in the form... 

The overshoot-hump in the n-A curve of DNP DPPE monolayer was foimd with constant-speed compression. From the absorption spectra of the lipid thin film, the hump reflected the formation of condensed layers at the critical surface pressure. A computer simulation was carried out on the basis of a cooperative aggregation process between the DNP-DPPE molecules at the air/water interface, the characteristic feature in the n-A curve was able to be reproduced. 

The presence of a critical St content in ASt-x can also be seen in fluorescence spectra [29], This copolymer in aqueous solution shows an excimer emission peaking at 325 nra. As shown in Fig. 8, the intensity of the excimer emission increases, while the monomer emission decreases, with increasing St content. Eventually the excimer dominates the monomer emission at an St content of 72 mol%. The excimer emission becomes apparent at an St content of about 50 mol%, which agrees with the critical St content estimated by viscometry and NMR spectroscopy. The existence of the critical St content suggests the hydro-phobic self-aggregation to be a cooperative process. 

The value of EM for a cooperative self-assembled structure provides a measure of the monomer concentration at which trivial polymeric structures start to compete, and therefore EM represents the upper limit of the concentration range within which the cooperative structure is stable (Scheme 2). The lower limit of this range is called the critical self-assembly concentration (csac) and is determined by the stoichiometry of the assembly and the strength of the non-covalent binding interactions weaker interactions and larger numbers of components raise the csac and narrow the stability window of the assembly (8). Theoretical treatments of the thermodynamics of the self-assembly process have been reported by Hunter (8), Sanders (9), and Mandolini (10). The value of EM is lowered by enthalpic contributions associated with... 

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

This book is the first attempt to summarize, probably from our subjective point of view, the state of the art in a very rapidly developing theory of many-particle effects in bimolecular reactions in condensed matter, which up to now was a subject of several review papers only [1—10]. We have focused mainly on several basic bimolecular reactions trying not to cover all possible cases (e.g., more complicated reactions, cooperative processes in alloys under irradiation [11] or initial macroscopic separation of reactants, etc.) but to compare critically results and advantages/limitations of numerous approaches developed in the last years. We focused on processes induced by point particles (defects) only the effects of dislocation self-organization are discussed in [12-16] whereas diffusion-limited particle aggregation with a special attention to fractal cluster formation has extensive literature [17-21],... 

At low temperatures, rj will be unity because all of the Cu atoms will be localized on A sites. 1 But the degree of disorder increases as the temperature increases until the Cu and Zn atoms are mixed randomly on the two sublattices and 77 = 0. This process, called a positional (order + disorder) transition, is often described as a cooperative phenomenon because it becomes easier to produce additional disorder once some disorder is generated. In the vicinity of a critical temperature, the order parameter rj behaves like the density difference (pi — pg) near the gas-liquid critical point. Thus,... 

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