Results first-order phase transitions

Although Eqs. (33), (34), and especially (35), are useful they have a problem. They all predict that the hard sphere system is a fluid until = 1. This is beyond close packing and quite impossible. In fact, hard spheres undergo a first order phase transition to a solid phase at around pd 0.9. This has been estabhshed by simulations [3-5]. To a point, the BGY approximation has the advantage here. As is seen in Fig. 1, the BGY equation does predict that dp dp)j = 0 at high densities. However, the location of the transition is quite wrong. Another problem with the PY theory is that it can lead to negative values of g(r). This is a result of the linearization of y(r) - 1 that... 

Before trying to solve the master equation for growth processes by direct stochastic simulation it is usually advisable to first try some analytical approximation. The mean-field approximation often gives very good results for questions of first-order phase transitions, and at least it provides a qualitative understanding for the interplay of the various model parameters. 

The boundary layers, or interphases as they are also called, form the mesophase with properties different from those of the bulk matrix and result from the long-range effects of the solid phase on the ambient matrix regions. Even for low-molecular liquids the effects of this kind spread to liquid layers as thick as tens or hundreds or Angstrom [57, 58], As a result the liquid layers at interphases acquire properties different from properties in the bulk, e.g., higher shear strength, modified thermophysical characteristics, etc. [58, 59], The transition from the properties prevalent in the boundary layers to those in the bulk may be sharp enough and very similar in a way to the first-order phase transition [59]. 

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]. 

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-... 

Nonspecific hydration, or hydration of the lattice without first-order phase transitions, also must be considered. Cox et al. [40] reported the moisture uptake profile of cromolyn sodium, and the related effects on the physical properties of this substance. Although up to nine molecules of water per molecule of cromolyn sodium are sorbed into the crystalline lattice at 90% relative humidity, the sorption profile does not show any sharp plateaus corresponding to fixed hydrates. Rather, the uptake profile exhibits a gradual increase in moisture content as relative humidity increases, which results in... 

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 ... 

Another interesting limit is the quasistatic limit r 0. Based on the numerical solution of the saddle point equations (160)-(162), it was suggested in Ref. 117 that T q) converged to a constant value over a finite range of work values. Figure 15a shows the results obtained for the heat distributions, whereas the path temperature is shown in Fig. 15b. A more detailed analysis [134] has shown that a plateau is never fully reached for a finite interval of heat values when r 0. The presence of a plateau has been interpreted as the occurrence of a first-order phase transition in the path entropy s q) [134]. 

With sufficient compression the isotherm of the LE state shows a sharp break to enter a situation variously known as the intermediate or transition state, indicated by I in Figure 7.6. Recent results suggest that the region I does represent a first-order phase transition (Knobler 1990a). 

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

Figure 16 illustrates the dependences of the parameter 4>N/4>o on the composition of water - ethanol mixtures for three samples differing in the content of polycations. From the data shown in Fig. 16, it follows that the network acquires the ability to exhibit the first order phase transition as a result of... 

Abstract. Two forms of CoO have been prepared from spec, pure Co metal and CoC03 and the magnetic susceptibility of CoO(I) and CoO(II) examined over a temperature range300-700 deg. K. The magnetic data of CoO(II) have shown an anomalous temperature dependence of that in this temperature range CoO(II) passes into CoO(I). This result is in conformity with Mossbauer spectra. Furthermore, D.T.A and temperature dependence of magnetic susceptibility of CoO(II) arises from a first order phase transition. 

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