Freezing transitions

The insertion probability falls below 10 , well before the freezing transition at q 0.49. Similar estimates can be made for the Leimard-Jones fluid. The lower this factor becomes, the poorer the statistics, and the more... 

Palberg T, Mdnch W, Bitzer F, Piazza R and Bellini T 1995 Freezing transition for colloids with ad]ustable charge a test of charge renormalization Phys. Rev. Lett. 74 4555-8... 

Freezing transitions have been examined in recent years by density functional methods [306-313]. Here we review the results [298] of a modification of the Ramakrishnan-Yussouff theory to the model fluid with Hamiltonian (Eq. (25)) a related study of phase transitions in a system of hard discs in two dimensions with Ising internal states which couple anti-ferromagnetically to their neighbors is shown in Ref. 304. First, a combined... 

For systems where the bulk freezing transition is well understood, one may want to go one step further and investigate the modifications of the phase transition and the sohd phases in the event of external influence on the system. Flow does freezing happen in a confined situation where external boundaries are present What is freezing in porous media like A related question is What does the interface between sohd and liquid look like This is an intrinsic inhomogeneity that the system builds up by itself (if, as usual, the transition is first order). Let us describe some papers dealing with freezing under external influence. 

Figure 6.7 Plot of the stress-dependent packing fraction

Relaxors where there is no macroscopic symmetry breaking and where, in view of site and charge disorder, there is an extremely broad distribution of correlation times. The longest correlation time diverges at the freezing transition whereas other correlation times are still finite [e.g., Pb (Mgi/3Nb2/3) O3]. 

A variational theory which includes all these different contributions was recently proposed and applied for completely stretched polyelectrolyte stars (so-called porcupines ) [203, 204]. As a result, the effective interaction V(r) was very soft, mainly dominated by the entropy of the counterions inside the coronae of the stars supporting on old idea of Pincus [205]. If this pair potential is used as an input in a calculation of a solution of many stars, a freezing transition was found with a variety of different stable crystal lattices including exotic open lattices [206]. The method of effective interactions has the advantage to be generalizable to more complicated complexes which are discussed in this contribution-such as oppositely charged polyelectrolytes and polyelectrolyte-surfactant complexes-but this has still to be worked out in detail. 

The 6-6 X-ray diffractometer used was ideal for our investigation, as we could see both the transition from the gel phase to the crystalline phase of the clay (at high salt and sol concentrations) and the formation of ice. The clay volume fraction was held constant at r = 0.1 for two reasons first, to obtain a d- value in the gel phase that would be observable within the 0-range of the instrument and, second, because the sample container of the X-ray instrument was too small to conveniently study low volume fractions of clay. We already know from the LOQ experiments that the freezing transition behavior is not strongly affected by r in the range between 0.01 to 0.3, or between 1 and 30% clay, so it is natural to choose somewhere in the middle of this range, and r = 0.1 results could be compared directly with the LAD data. 

I should note that the limit of sensitivity of these experiments restricts us to saying that the phase transitions are simultaneous only in the sense that they both occur between -1 and 0°C (in either direction). More subtle variations, of the order of 0.1°C, would not have been detectable. According to Debye-Huckel theory [3], the depression of the freezing point of pure water is 0.18°C in a 0.1 M uni-univalent electrolyte solution. We would expect the clay to cause a further small depression in the freezing point, as discussed below. Within these limits, the temperature where both the freezing transition and the gel-crystalline phase transition occur is the same in our model clay colloid system, and it can be concluded to be the ordinary freezing point of the soaking solution. 

Equation (5) is the familiar Ornstein-Zernike relation and hereafter we denote the direct correlation function C2(r) as c(r). Based on (1) and (4) with (2), one can discuss freezing transition of one-component liquids. " For an S-component mixture, which is specified by S density fields, nj(r) j = l,- -,5), we have, instead of (4),... 

The study of phase transitions has played a central role in the study of condensed matter. Since the first applications of molecular simulations, which provided some of the first evidence in support of a freezing transition in hard-sphere systems, to contemporary research on complex systems, including polymers, proteins, or liquid crystals, to name a few, molecular simulations are increasingly providing a standard against which to measure the validity of theoretical predictions or phenomenological explanations of experimentally observed phenomena. 

In some cases the transition looks like a continuous glass transition, but at temperatures and pressures that are far from the glass region in the bulk phase diagram. In fact, the molecules may not readily form glasses in the bulk. In other cases the transition from liquid to solid behavior of the film appears to occur discontinuously, as if the film underwent a first-order freezing transition [200,205]. Simulations suggest that this is most likely to happen when the crystalline phase of the film is commensurate with the solid walls and when the molecules have a relatively simple stmcture that facilitates order [178 180,191,209]. Unfortunately, no direct experimental determination of the stmcture of confined films has been made to determine whether they are crystalline or amorphous, and different behavior has been reported for the same... 

Carraro, C. (2002). Existence and nature of a freezing transition inside three-dimensional arrays of narrow channels. Phys. Rev. Lett., 89, 115702. 

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