Phase transition nucleation

At higher temperatures, other degrees of freedom than the radius R must also be considered in the fluctuation. However, this becomes critical only near the critical point where the system goes through a phase transition of second order. The nucleation arrangement described here is for heterogeneous or two-dimensional nucleation on a flat surface. In the bulk, there is also the formation of a three-dimensional nucleation, but its rate is smaller ... 

Assume that a sudden change in the system parameters initiates a phase transition. After a set of clusters of different size has been generated by a nucleation process, the smaller clusters will shrink again and disappear,... 

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 ... 

The most developed and widely used approach to electroporation and membrane rupture views pore formation as a result of large nonlinear fluctuations, rather than loss of stability for small (linear) fluctuations. This theory of electroporation has been intensively reviewed [68-70], and we will discuss it only briefly. The approach is similar to the theory of crystal defect formation or to the phenomenology of nucleation in first-order phase transitions. The idea of applying this approach to pore formation in bimolecular free films can be traced back to the work of Deryagin and Gutop [71]. 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

Phase transitions of the PS-fo-PI system have been extensively studied. The morphological transition from the I phase to the G phase proceeds through nucleation and growth. The difference in the geometrical characteristics of these two phases induces considerable local distortion of both morphologies... 

Structural changes on surfaces can often be treated as first-order phase transitions rather than as adsorption process. Nucleation and growth of the new phase are reflected in current transients as well as dynamic STM studies. Nucleation-and-growth leads to so-called rising transients whereas mere adsorption usually results in a monotonously falling transient. In Fig. 10 are shown the current responses to potential steps across all four current peaks in the cyclic voltammogram of Fig. 8a [44], With the exception of peak A, all structural transitions yield rising current transients sug-... 

These results stimulated a number of studies, both in industry (Conoco, Esso, Shell Pipeline) and in academia (University of Maryland, M.I.T.). The objective was, primarily, to delineate the mechanism that led to these explosive events. The results of many small-scale experiments, primarily conducted by Shell Pipeline Corporation and M.I.T., led to the hypothesis that the apparent explosion was, in fact, a very rapid vaporization of superheated LNG. Contact of LNG, of an appropriate composition, with water led to the heating of a thin film of the LNG well above its expected boiling temperature. If the temperature reached a value where homogeneous nucleation was possible, then prompt, essentially explosive vaporization resulted. This sequence of events has been termed a rapid phase transition (RPT), although in the earlier literature it was often described by the less appropriate title of vapor explosion. 

A subcritical aggregate having fewer subunit components than a nucleus. When this term is applied in the kinetics of precipitation, n refers to the number of subunits in a particle and n defines the number of subunits in a particle of critical size. This definition avoids confusion by distinguishing between subcritical (n < n subunits), critical (n = n subunits), and supercritical (n > n subunits) particle sizes. If a nucleus is defined as containing n n subunits, then an embryo contains n n subunits. Note that in this treatment, we are not using a phase-transition description to describe nucleation, and we are focusing on the smallest step in the process that leads to further aggregation. 

When a phase transition occurs from a pure single state and in the absence of wettable surfaces the embryogenesis of the new phase is referred to as homogeneous nucleation. What is commonly referred to as classical nucleation theory is based on the following physical picture. Density fluctuations in the pre-transitional state result in local domains with characteristics of the new phases. If these fluctuations produce an embryo which exceeds a critical size then this embryo will not be dissipated but will grow to macroscopic size in an open system. The concept is applied to very diverse phenomena ... 

Keywords Order-disorder transitions Soft mode Phase segregation Nucleation Takagi defects... 

The NMR results presented in Sect. 2 allow for D-RADP-x (with x = 0.20,0.25, 0.30), in fact for no other interpretation than a multitude of local first order phase transitions with a probabihty distribution of transition temperatures. We beheve therefore that we deal with a nucleation mechanism. To illustrate this possibihty we have to make some assumptions ... 

The second type is simple phase transitions in which one phase transforms into another of identical composition, e.g., diamond graphite, quartz coe-site, and water ice. This type sounds simple, but it involves most steps of heterogeneous reactions, including nucleation, interface reaction, and coarsening. 

A second-order phase transition is one in which the enthalpy and first derivatives are continuous, but the second derivatives are discontinuous. The Cp versus T curve is often shaped like the Greek letter X. Hence, these transitions are also called -transitions (Figure 2-15b Thompson and Perkins, 1981). The structure change is minor in second-order phase transitions, such as the rotation of bonds and order-disorder of some ions. Examples include melt to glass transition, X-transition in fayalite, and magnetic transitions. Second-order phase transitions often do not require nucleation and are rapid. On some characteristics, these transitions may be viewed as a homogeneous reaction or many simultaneous homogeneous reactions. 

Ideally, MD or MC gives a complete description of the equilibrium states of liquids and crystals, and a molecular-level picture of any chemical process occurring within the system, including phase transitions. The limitations are obvious. The calculation is heavy, with some 5,000 molecules at most, and times or time-equivalents of the order of at most milliseconds. Force fields are by necessity restricted to atom-atom empirical ones. One gets at best a blurred and very short glimpse of the simulated process. And yet, appropriately designed molecular simulation is, for example, the only access to molecular aspects of chemical evolution involved in crystal nucleation and growth. 

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