Phase transition ordering

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

A type of the adsorption is connected with a type of the phase transition in which adspecies could be involved. The adspecies condensation (the first type of the phase transition) as usually occurs at the physical adsorption, while the adspecies ordering (the second type of the phase transition) occurs at the chemical adsorption. However, more complex phase transitions (ordering with condensation) are quite often realized at the chemical adsorption. 

There are two major types of structural phase transitions order-disorder and displacive. An order-disorder phase transition is characterized by disorder of the atoms or molecules in the structure of one of the phases. Sometimes both phases are disordered in different degrees. The disordered (or more disordered) phase is more symmetric, because disorder makes the average distribution of atoms more even. Most of the phase transitions in clathrate crystals are of this type. 

In a displacive phase transition, the positions of atoms are ordered in both phases, but the position changes from a less symmetric site to a more symmetric one as the crystal undergoes the phase transition. Order-disorder transitions are distinguished from displacive transitions by, among other properties, a large entropy of phase transition, dielectric dispersion at low frequencies, and directly, by crystal structure revealing two or more sites fractionally occupied by the same atom. 

One of the reasons for the extensive use of scanning calorimeters is the possibility of selecting different working temperatures. But the main advantage lies in the fact that many reactions (e.g., phase transitions, order processes, chemical reactions) are thermally activated and that kinetic data of the reactions can also be obtained. 

One reason may be that liquid crystals have first-order phase transitions that are so weakly discontinuous, their first-order nature escapes detection by traditional methods such as adiabatic calorimetry [3]. Recently, a macroscopic qualitative test of phase transition order [4] revealed that even immeasurably small discontinuities at first-order phase transitions [5] using static tests, have a distinct dynamic signature in interface (front) propagation compared to second-order or continuous phase transitions [4], It is important to know the order of a phase transition because for universality to apply at all levels of its hierarchy [2], must approach infinity continuously there can be no discontinuities at T. If there are, all bets are off [6],... 

Many of the compounds in the large list of Garland and Nounesis have N-SmA phase transitions determined to be continuous by calorimetry and X-ray diffraction and discontinuous using the more powerful dynamic test of phase transition order [4]. In particular, the compounds known as 8CB and 9CB, with second order N-SmA phase transitions by the standard tests [25], were... 

The latent heat of this transition is usually small and may even vanish if the width of the nematic temperature range is sufficiently large [23]. Thus, the transition can be either of first or second order. For the second-order transition the discontinuity in the orientational order parameter S and, hence, the dielectric (or diamagnetic) susceptibility, disappears and the field influence on both phases is the same. Thus we do not anticipate any field-induced shift in the N-A transition temperature. For the weak first-order transition there is a small discontinuity in both S and dielectric (and magnetic) susceptibilities, and the shift depends on the competition between two small quantities the difference in susceptibilities for the nematic and smectic A phases on the one hand and transition enthalpy on the other. In particular, the field may induce a change in the phase transition order, from first to the second order, as shown in Fig. 4 [24]. 

A mechanism of local ordering has in fact been described by previous authors. Allen and Cahn [32] have made an extensive analysis of phase transition/ordering phenomena in... 

The concentration of dissolved solute in NMR studies is typically 1 mole % or larger. Such concentrations can have an effect on more subtle effects such as phase transition order in weakly first-order phase transitions. However, it is an excellent probe of mean-field effects, especially when the effects are probed for different solutes and the results found solute independent. Orientational order in some smectic-A phases changes less rapidly as a function of temperature than in the nematic phase with no break at the phase transition [31-34]. 

Much recent work has addressed the vexing question of phase transition order, reviewed in the following section. While clearly the measurements of critical exponents is predicated on the non-existence of a discontinuity, the discontinuities being argued over are small enough so as not to suppress the pre-transitional... 

One suggested way [55, 56] to compare different experimental probes of phase transition order is to express the phase transition discontinuity in terms of the dimensionless quantity t = - T )/T, where T na is the equilibrium NA... 

The nematic-smectic-A (NA) transition is one that has been studied theoretically with fluctuations being accounted for within different levels of approximation. It has also been studied experimentally by a diverse array of high-resolution techniques in laboratories around the world. While much has been understood about the transition, almost every probe of the NA transition, whether mean-field behaviour of solutes, nature of divergences and values of critical exponents or phase transition order, has met with conflicting experimental results. It appears that another generation of resolution and precision enhancement is required before the complete story is told. As remarked several years ago by deGennes and Frost [3] It seems that we almost understand, but not quite . 

Phase Transitions, Order Parameter and Heterophase Behaviour... 

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