Heterophase Fluctuations

The value of the pre-exponential factor is very important in Frenkel s theory of pre-transition states and heterophase fluctuations [10]. However, simple qualitative arguments appear to show that the effects considered by... 

It has been established experimentally that all thermodynamic properties of supersaturated phases (a supersaturated vapor, a liquid heated beyond the boiling point, or a liquid cooled down below the melting point) are in no way remarkable and fail to show any substantial deviations that would point to strong heterophase fluctuations. All the more, d, fortiori, it may hence be concluded that before the transition point and at the point itself the quantity J is negligibly small. 

Thus, melting of a crystalline substance without superheating is a superficial effect. Pre-melting phenomena are apparently also related to the formation of liquid films on the surfaces of crystals, if not to other incidental causes (for example, impurities), and are not pertinent to Frenkel s theory. Heterophase fluctuations are quite large where the difference between two phases and the surface tension between them tend to zero—near the critical point and near the Curie point. The first case is commonly known, the second was earlier investigated quantitatively in Landau s fine work [13, 14]. 

To generate sharp transitions the interaction term T in Eq. (10.2) must be large. An alternative approach has been used by Sorai and Seki34) following the theory of heterophase fluctuations. They assume cooperative domains of LS and HS molecules, resp., with a strong interaction within the domains, so that the complexes change spin simultaneously. For n atomes per domain the partition function becomes... 

Protein mobility and aggregation are inherent problems in the in situ STM and AFM characterization. This can, however, also be turned to the better and brought to open other new perspectives for mapping of molecular and collective protein dynamics such as phase transitions, heterophase fluctuations etc. 

The ordering may also occur in liquid states especially in those which are able to form liquid crystals. The lower the heat of the phase transition, the higher will be the probability of appearance of heterophasal fluctuations, whose existence has been proved directly for the acids studied (23). 

This section presents the theory of liquid solidification, in which both crystalline and noncrystalline heterophase fluctuations in supercooled liquids are taken into account [6.76]. A general discussion of this problem is presented in Sect. 6.2... 

Frenkel, J. (1939). A general theory of heterophase fluctuations and pretransition phenomena. Jf. Chem. Phys. 7, 538-47. [87]... 

There is another corollary of Z) — 0 near the spinodal an infinitely low rate of dispersal of the fluctuations arisen spontaneously. According to Onsager s criterion (see subsection 2.3.3), these fluctuations turn out to be long-living regions of heterophase fluctuations which can be regarded as colloidal particles, and the system itself as a quasicolloidal one (inicroheterogeneous) (J. Frenkel, 1938 Skripov, 1960). 

Processes of the first type include formation of the new phase nuclei in the contact zone as a result of heterophase fluctuations under chemical potential and concentration gradient. The description of solid-state reactions of the second and third types, namely those at the moving boundaries between phases that already exist in the diffusion zone, is reduced to the following consecutive stages ... 

In this section we will investigate fluctuations that result in the formation of small spatial regions of the low temperature, liquid-crystal phase in the isotropic phase, as the temperature T approaches Tc from above. These so-called heterophase fluctuations produce a... 

Since the phenomenon of supercooling depends critically on the absence of embryos with radius p > p, it is of interest to estimate the relative probability A of thermally generating an embryo with radius p by heterophase fluctuations. We have, for T near... 

Figure 2. First order phase transition a) homophase fluctuation, b) heterophase fluctuation [2].

The transition from a power dependence with p 1 to a dependence with P 4.2 takes place for concentrations of 0.2-0.7%. This transition is usually correlated [20,21] with the formation of a fluctuation network of contacts. The value of P in this region is slightly lower than for solutions of flexible-chain polymers (5-6) this was previously indicated in [18, 23] and theoretically predicted in [25, 52]. A stronger dependence of t (c) with an exponent of 6.0 is observed for c > 6.5%. Similar figures were found in the literature 6.8 [17] and 5-8 [87], but for the entire range of c between c and c. Near c, heterophase fluctuations with random orientation of the macromolecules apparently have the determining effect on the rate of the increase in the viscosity with an increase in the concentration [69]. Traces of mesophase woe also found for c 0.5-1.0% lower than c, and an increase in the order parameter is mentioned in [25] beginning with c > 8/9 c. ... 

A thermal mobility in liquid results in continuous formation and disappearance of heterophase fluctuations, which are potential centres of future crystalline formations [43]. At a temperature decrease to below the melting temperature the chemical potential of molecules in a crystal is smaller than in a liquid and therefore the crystallisation nucleus in heterophase fluctuation can be stable and begins to grow spontaneously [43]. 

It is supposed that geometry, morphology and crystalline phase nucleation and growth mechanism will be defined to a considerable degree by the nature of heterophase fluctuations in the amorphous state. So, the supposition of heterophase fluctuation from folded chains (Yech model [44]) results in the formation of crystallites with folded chains (CFC). In paper [43], an alternative model of heterophase fluctuation supposes the availability of parallel parts of different chains of macromolecules in it. The use of these models supposes the possibility of formation in the crystallisation process of CFC, crystallites with stretched chains (CSC) or some intermediate morphology... 

By its physical essence the heterophase fluctuation type, proposed in paper [43], is similar to local order domain (cluster) in the cluster model of the amorphous state structure of polymers [7, 8]. The last model application allows a quantitative description of such heterophase fluctuations and, as a consequence, analysis of the change in crystallisation morphology and nucleation mechanism [46]. In papers [47, 48] such analysis was carried out on the example of PCP and LDPE orientational crystallisation. 

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