Phase transitions complexes

Bina C. R. (2002) Phase transition complexity and multiple seismic reflectors in subduction zones. Eos, Trans., AGU 83(47), Fall Meet. Suppl., Abstract S52C-05. 

Ohashi, H. Hiraoka, Y Yamaguchi, T. An autonomous phase transition-complexation/decomplexation polymer system with a molecular recognition property. Macromolecules 2006, 39, 2614-2620. 

Wight C A and Armentrout P B 1993 Laser photoionization probes of ligand-binding effects in multiphoton dissociation of gas-phase transition-metal complexes ACS Symposium Series 530 61-74... 

Frenkel D 1995 Numerical techniques to study complex liquids Observation, Prediction and Simuiation of Phase Transitions in Oompiex Fiuids vol 460 NATO ASi Series C ed M Baus, L F Rull and J-P Ryckaert (Dordrecht Kluwer) pp 357-419... 

Phase transitions in adsorbed layers often take place at low temperatures where quantum effects are important. A method suitable for the study of phase transitions in such systems is PIMC (see Sec. IV D). Next we study the gas-liquid transition of a model fluid with internal quantum states. The model [193,293-300] is intended to mimic an adsorbate in the limit of strong binding and small corrugation. No attempt is made to model any real adsorbate realistically. Despite the crudeness of the model, it has been shown by various previous investigations [193,297-300] that it captures the essential features also observed in real adsorbates. For example, the quite complex phase diagram of the model is in qualitative agreement with that of real substances. The Hamiltonian is given by... 

The theory of quenched-annealed fluids is a rapidly developing area. In this chapter we have attempted to present some of the issues already solved and to discuss only some of the problems that need further study. Undoubtedly there remains much room for theoretical developments. On the other hand, accumulation of the theoretical and simulation results is required for further progress. Of particular importance are the data for thermodynamics and phase transitions in partly quenched, even quite simple systems. The studies of the models with more sophisticated interactions and model complex fluids, closer to the systems of experimental focus and of practical interest, are of much interest and seem likely to be developed in future. 

F. Schmid, M. Schick. Phase transitions of a confined complex fluid. Phys Rev 45 1882-1888, 1993. 

In a fundamental sense, the miscibility, adhesion, interfacial energies, and morphology developed are all thermodynamically interrelated in a complex way to the interaction forces between the polymers. Miscibility of a polymer blend containing two polymers depends on the mutual solubility of the polymeric components. The blend is termed compatible when the solubility parameter of the two components are close to each other and show a single-phase transition temperature. However, most polymer pairs tend to be immiscible due to differences in their viscoelastic properties, surface-tensions, and intermolecular interactions. According to the terminology, the polymer pairs are incompatible and show separate glass transitions. For many purposes, miscibility in polymer blends is neither required nor de-... 

It has been shown that ab initio total energy DFT approach is a suitable tool for studies of phase equilibria at low temperatures and high pressures even when small energy differences of the order of 0.01 eV/mol are involved. The constant pressure optimization algorithm that has been developed here allows for the calculation of the equation of state for complex structures and for the study of precursor effects related to phase transitions. 

It would appear that the tradeoffs between these two requirements are optimized at the phase transition. Langton also cites a very similar relationship found by Crutchfield [crutch90] between a measure of machine complexity and the (per-symbol) entropy for the logistic map. The fact that the complexity/entropy relationship is so similar between two different classes of dynamical systems in turn suggests that what we are observing may be of fundamental importance complexity generically increases with randomness up until a phase transition is reached, beyond which further increases in randomness decrease complexity. We will have many occasions to return to this basic idea. 

However intuitive the edge-of-chaos idea appears to be, one shoidd be aware that it has received a fair amount of criticism in recent years. It is not clear, for example, how to even define complexity in more complicated systems like coevolutionary systems, much less imagine a phase transition between diffen ent complexity regimes. Even Langton s sugge.stion that effective computation within the limited domain of cellular automata can take place only in the transition region has been challenged. ... 

Jourjine [jour85] generalizes Euclidean lattice field theory on a d-dimensional lattice to a cell complex. He uses homology theory to replace points by cells of various dimensions and fields by functions on cells, the cochains, in hopes of developing a formalism that treats space-time as a dynamical variable and describes the change in the dimension of space-time as a phase transition (see figure 12.19). 

The dependence on the temperature of the specific resistance (Q/cm) of the pure MEPBr and MEMBr complexes, and a 1 1 mixture there of, as obtained in Ref. [73], is listed in Table 4. It is remarkable that within the complex phases consisting of Br2 and either pure MEP or MEM the change of specific resistance at the liquid —> solid phase transition amounts to about one order of magnitude, where as the value is only doubled in the 1 1 mixture. The table also indicates that MEMBr complexes possess higher melting temperatures. 

The delay, t0, preceding the onset of the main reaction may include contributions from (i) the time required for the sample to attain reaction temperature, h, (ii) additions to fh resulting from changes within the reaction sample, e.g. water removal (endothermic) from a hydrate, td, phase transitions, etc. and (iii) slow processes preceeding establishment of the main reaction, which are to be regarded as the true induction period, The effective values of th, td and may show different temperature coefficients so that the magnitude of t0(=th + ta + i) may vary with temperature in a complex manner, perhaps differently from that of the subsequent rate process. 

As with other crystalline substances, on heating coordination compounds may melt, sublime, decompose, or undergo a solid phase transition. The greater complexity of the constituents present increases the number of types of bond redistribution processes which are, in principle, possible within and between the coordination spheres. The following solid-state transitions may be distinguished (i) changes in relative dispositions... 

Allen MP (1995) In Bans M, Rull LF, Ryckaert J-P (eds) Observation, prediction and simulation of phase transitions in complex fluids. Kluwer, Dordrecht Palke WE, Emsley JW, Tildesley DJ (1994) Mol Phys 82 177... 

M. P. Allen, Introduction to Monte Carlo simulations. In Observation, Prediction and Simulation of Phase Transitions in Complex Fluids, M. Bans, L. F. Rull, and J.- P Ryckaert, Eds., Kluwer Academic Publishers, Boston, 1995, 339-356. 

Applying MD to systems of biochemical interest, such as proteins or DNA in solution, one has to deal with several thousands of atoms. Models for systems with long spatial correlations, such as liquid crystals, micelles, or any system near a phase transition or critical point, also must involve a large number of atoms. Some of these systems, including synthetic polymers, obey certain scaling laws that allow the estimation of the behaviour of a large system by extrapolation. Unfortunately, proteins are very precise structures that evade such simplifications. So let us take 10,000 atoms as a reasonable size for a realistic complex system. 

In a subsequent study, the effect of reducing the ELP molecular weight on the expression and purification of a fusion protein was investigated. Two ELPs, ELP [V-20] and ELP[VsA2G3-90], both with a transition temperature at 40°C in phosphate-buffered saline (PBS) containing 1 M NaCl, were applied for the purification of thioredoxin. Similar yields were observed for both fusion proteins, resulting in a higher thioredoxin yield for the ELP[V-20] fusion, since the ELP fraction was smaller. However, a more complex phase transition behavior was observed for this ELP and therefore a selection of an appropriate combination of salt concentration and solution temperature was required [39]. 

The previous ELP fusions all are examples of protein purification in which the ELP is covalently connected to the protein of choice. This approach is suitable for the purification of recombinant proteins that are expressed to high levels, but at very low concentrations of ELP the recovery becomes limited. Therefore this approach is not applicable for proteins expressed at micrograms per liter of bacterial culture, such as toxic proteins and complex multidomain proteins. An adjusted variant of ITC was designed to solve this problem. This variant makes use of coaggregation of free ELPs with ELP fusion proteins. In this coaggregation process, an excess of free ELP is added to a cell lysate to induce the phase transition at low concentrations of... 

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