Chemicals phase transitions

The momentous notion of inflation is likened to a chemical phase transition, which is a prime example of an emergent event, induced by the thermodynamic environment. There is no such an environment for an expanding embryonic universe and nothing to initiate a phase transition or define a supercooled state. Inflation is no more than idle speculation. 

The underlying issue (as to whether ozone and oxygen are or are not allotropes or polymorphs) seems to be the question how to situate various physico-chemical (phase) transitions relative to chemical transformations on the one hand and physical transitions on the other. 

In addition to chemical transformation and (physico-chemical) phase transition, there are other physical transitions, e.g. a magnetic transformation (of, say, a-ferrite to / -ferrite). The latter can be dist.inguished from phase (or polymorphic) transitions because they don t take place at a definite temperature. 

As one would expect, developments in the theory of such phenomena have employed chemical models chosen more for analytical simplicity than for any connection to actual chemical reactions. Due to the mechanistic complexity of even the simplest laboratory systems of interest in this study, moreover, application of even approximate methods to more realistic situations is a formidable task. At the same time a detailed microscopic approach to any of the simple chemical models, in terms of nonequilibrium statistical mechanics, for example, is also not feasible. As is well known, the method of molecular dynamics discussed in detail already had its origin in a similar situation in the study of classical fluids. Quite recently, the basic MD computer model has been modified to include inelastic or reactive scattering as well as the elastic processes of interest at equilibrium phase transitions (18), and several applications of this "reactive" molecular dynamicriRMD) method to simple chemical models involving chemical instabilities have been reported (L8j , 22J. A variation of the RMD method will be discussed here in an application to a first-order chemical phase transition with many features analogous to those of the vapor-liquid transition treated earlier. 

First Order Chemical Phase Transition in a Cooperative Isomerization Reaction. S convenient model of a first order transition is provided by a reversible isomerization reaction in a macroscopically homogeneous system... 

Consider how the change of a system from a thennodynamic state a to a thennodynamic state (3 could decrease the temperature. (The change in state a —> f3 could be a chemical reaction, a phase transition, or just a change of volume, pressure, magnetic field, etc). Initially assume that a and (3 are always in complete internal equilibrium, i.e. neither has been cooled so rapidly that any disorder is frozen in. Then the Nemst heat... 

Fundamentais of thermodynamics. Appiications to phase transitions. Primariiy directed at physicists rather than chemists. Reid C E 1990 Chemical Thermodynamics (New York McGraw-Fliii)... 

For both first-order and continuous phase transitions, finite size shifts the transition and rounds it in some way. The shift for first-order transitions arises, crudely, because the chemical potential, like most other properties, has a finite-size correction p(A)-p(oo) C (l/A). An approximate expression for this was derived by Siepmann et al [134]. Therefore, the line of intersection of two chemical potential surfaces Pj(T,P) and pjj T,P) will shift, in general, by an amount 0 IN). The rounding is expected because the partition fiinction only has singularities (and hence produces discontinuous or divergent properties) in tlie limit i—>oo otherwise, it is analytic, so for finite Vthe discontinuities must be smoothed out in some way. The shift for continuous transitions arises because the transition happens when L for the finite system, but when i oo m the infinite system. The rounding happens for the same reason as it does for first-order phase transitions whatever the nature of the divergence in thennodynamic properties (described, typically, by critical exponents) it will be limited by the finite size of the system. 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

T B J and T E Wainwright 1957. Phase Transition for a Hard-sphere System. Journal of Chemical Physics 27 1208-1209. 

Since an analyte and interferent are usually in the same phase, a separation often can be effected by inducing a change in one of their physical or chemical states. Changes in physical state that have been exploited for the purpose of a separation include liquid-to-gas and solid-to-gas phase transitions. Changes in chemical state involve one or more chemical reactions. 

Besides the chemical composition, porosity is another property of stone which has great influence on its preservation. An increased porosity increases the exposed surface and pores allow movement of materials such as water and its solutes through the stones. If the pores are blocked or reduced in diameter such substances may be trapped within resulting in increased local interior damage. Exposure to the climatic elements is one important source of decay. Freeze-thaw cycles, in particular, result in pressures on the pore walls of the stone s interior from changes in volume during the phase transition... 

The entropy change AS/ - and the volume change AV/ - are the changes which occur when a unit amount of a pure chemical species is transferred from phase I to phase v at constant temperature and pressure. Integration of Eq. (4-18) for this change yields the latent heat of phase transition ... 

However, we also need to discuss how the attractive interactions between species can be included in the theory of partly quenched systems. These interactions comprise an intrinsic feature of realistic models for partially quenched fluid systems. In particular, the model for adsorption of methane in xerosilica gel of Kaminsky and Monson [41] is characterized by very strong attraction between matrix obstacles and fluid species. Besides, the fluid particles attract each other via the Lennard-Lones potential. Both types of attraction (the fluid-matrix and fluid-fluid) must be included to gain profound insight into the phase transitions in partly quenched media. The approach of Ford and Glandt to obtain the chemical potential utilizing... 

Beyond the CMC, surfactants which are added to the solution thus form micelles which are in equilibrium with the free surfactants. This explains why Xi and level off at that concentration. Note that even though it is called critical, the CMC is not related to a phase transition. Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114] others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs the total surfactant concentration [115], or plotting the surfactant chemical potential vs ln( ) [119]. 

Phase transition irreversible, 225 order - disorder, 224-228 reversible, 225, 229, Physicochemical properties of ammonium hydrofluoride, 39 deviations from ideal, 149 ideal system, 148 NbF5 and TaFs, 25 niobium containing melts, 150 tantalum containing melts, 151 M5Nb3OFlg, 234-235 Piezoelectric properties, 245-247 Plasma chemical decomposition equipment, 311... 

An example of the determination of activation enthalpies is shown in Figs. 11 and 12. A valuable indication for associating the correct minimum with the ionic conductivity is the migration effect of the minimum with the temperature (Fig. 11) and the linear dependence in the cr(T versus 1/T plot (Fig. 12). However, the linearity may be disturbed by phase transitions, crystallization processes, chemical reactions with the electrodes, or the influence of the electronic leads. 

In the studies that attribute the boundary friction to confined liquid, on the other hand, the interests are mostly in understanding the role of the spatial arrangement of lubricant molecules, e.g., the molecular ordering and transitions among solid, liquid, and amorphous states. It has been proposed in the models of confined liquid, for example, that a periodic phase transition of lubricant between frozen and melting states, which can be detected in the process of sliding, is responsible for the occurrence of the stick-slip motions, but this model is unable to explain how the chemical natures of lubricant molecules would change the performance of boundary lubrication. 

The present chapter will focus on the practical, nuts and bolts aspects of this particular CA approach to modeling. In later chapters we will describe a variety of applications of these CA models to chemical systems, emphasizing applications involving solution phenomena, phase transitions, and chemical kinetics. In order to prepare readers for the use of CA models in teaching and research, we have attempted to present a user-friendly description. This description is accompanied by examples and hands-on calculations, available on the compact disk that comes with this book. The reader is encouraged to use this means to assimilate the basic aspects of the CA approach described in this chapter. More details on the operation of the CA programs, when needed, can be found in Chapter 10 of this book. 

Thallous halides offer a unique possibility of studying the stereochemistry of the (chemically) inert electron pair, since their structures and their pressure and temperature-dependent phase transitions have been well established. Thallium (1) fluoride under ambient conditions, adopts an orthorhombic structure in the space group Pbcm which can be regarded as a distorted rocksalt structure (Fig. 2.4). In contrast to TIF, the thallium halides with heavier halogens, TlCl, TlBr and Til, adopt the highly symmetric cubic CsCl structure type under ambient conditions [46]. Both TlCl and TlBr, at lower temperatures, undergo phase transitions to the NaCl type of structure [47]. 

Tanaka, T, Phase Transitions of Gels. In Polyelectrolyte Gels, Properties, Preparation, and Applications, ACS Symposium Series Harland, RS Prud homme, RK, eds. American Chemical Society Washington, DC, 1992 Vol. 480, p 1. 

For the reduction of NO with propene, the catalyst potential dependence of the apparent activation energies does not show a step change and is much less pronounced than it is for the CO+O2 and NO+CO systems. There is persuasive evidence [20] that the step change is associated with a surface phase transition - the formation or disruption of islands of CO. It is reasonable to assume that this phenomenon cannot occur in the NO+propene case, since there is no reason to expect that large amounts of chemisorbed CO can be present under any conditions. That there should be a difference in this respect between CO+O2/CO+NO on the one hand, and NO+propene on the other hand, is therefore understandable however, the chemical complexity of the adsorbed layer in the NO+-propene precludes any detailed analysis of the Ea(VwR> effect. 

Similar considerations apply to chemical or physicochemical equilibria such as encountered in phase transitions. A chilled salt solution may be stable (at or below saturation), metastable (supercooled to an extent not allowing nucle-ation), or unstable (cooled sufficiently to nucleate spontaneously). In the case of a solid, S, dispersed in a binary liquid, Li + L2, instability at the instant of formation gives way to a neutral or metastable condition wherein three types of contacts are established ... 

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