Ising regime

In concluding this section, we draw attention to the amplitudes 0 derived from the scattering experiments. As shown later, 0 enters into theoretical expressions for the crossover temperature. Large 0 favor a small Ising regime. In simple nonelectrolyte mixtures, 0 is of the order of the molecular... 

Linear and non-linear effects of thermal composition fluctuations become visible in a scattering experiment. Within the mean field and Ising regimes the susceptibility S(0) and the correlation length are described by simple scaling laws as functions of the reduced temperature r according to Cr ) with the critical amplitudes C( o) and the critical exponents y(v). The critical exponents y(v) are known to be equal to y = 1 and 1.239 0.003 and V = 0.5 and 0.634 0.001 in the mean field and Ising cases, respectively [66]. The mean field case has already been discussed in the context with Eq. 11. 

Figure 19 depicts the critical amplitudes of the susceptibility and correlation length in the mean field and Ising approximations versus the polymer concentration. While the amplitudes C+show a slight linear decrease by about 20%, the mean field Cmf show an increase more quantitatively, in double logarithmic representation one evaluates exponents from the slope which are (1.1 0.1) and - (1 0.25) for PB(1,4)/PS, while (0.35 0.5) and - (2.4 0.5) for PB(1,2 1,4)/PS within the mean field and Ising regimes, respectively. 

Although the asymptotic critical regime with the Ising-like scaling exponents has been neglected in this description, the fit curves in Fig. 8 are a reasonable parameterization for all three coefficients in the one-phase regime. This parameterization then serves as input for the numerical model. A more detailed discussion of the whole procedure can be found in [100],... 

One may however look at the data in Table 1 from a different point of view (see also ref 22). It is seen that a transition from Ising to mean-field behavior is observed, if the dielectric constant decreases, the transition regime occuring somewhere near D = 4.5. Could the dielectric constant be the major parameter controlling criticality In the latter case specific interactions play an indirect role They shift and thus enabling phase separations to occur... 

Crossover. Generally, crossover from an Ising-like asymptotic behavior to mean-field behavior further away from the critical point [86, 87] may be expected. Such a behavior is also expected for nonionic fluids, but occurs so far away, that conditions close to mean-field behavior are never reached. Reports about crossover [88] and the finding of mean field criticality [14—16] suggest that in ionic systems the temperature distance of the crossover regime from the... 

Fig. 31. Log-log plot of mN,/2 at T = Tc vs L/N, for the bond fluctuation model at <)>, = 0.5. Different symbols show various chain lengths N, as indicated. The dashed line illustrates the power law expected in the mean-field regime of finite size scaling M >ocL-3, for L/N 1) and the dash-dotted line in the non-mean-field regime K M >ocL-p/v, with p/v 0.515 for Ising exponents [274]. From Binder and Deutsch [275].

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