Mixtures correlation length

Measurements of static light or neutron scattering and of the turbidity of liquid mixtures provide information on the osmotic compressibility x and the correlation length of the critical fluctuations and, thus, on the exponents y and v. Owing to the exponent equality y = v(2 — ti) a 2v, data about y and v are essentially equivalent. In the classical case, y = 2v holds exactly. Dynamic light scattering yields the time correlation function of the concentration fluctuations which decays as exp(—Dk t), where k is the wave vector and D is the diffusion coefficient. Kawasaki s theory [103] then allows us to extract the correlation length, and hence the exponent v. 

Conflicting results have been found for the explicit time evolution of the correlation length during isothermal phase separation. A 1/3-power law in the growth of patterns, which is characteristic for the hydrodynamically controlled Lifshitz Slyozov process, was confirmed in Ref. [99] while an exponential increase over a certain period of time was established in Ref. [21]. Nevertheless, it is evidenced that in blends comprising liquid-crystalline polymers spinodal decomposition and subsequent coarsening processes take a course similarly to isotropic liquid mixtures. 

Fig. 21. Log-log plot of Tc(oo)-Tc(D) versus D, for the bond-fluctuation model of a symmetric polymer mixture with NA=NB=N=32. For small D, the straight line corresponds to a shift Tc(°o)-Tc(D)oc1/d, while the second straight line for larger D shows the result Tc(°o)-Tc(D)ocD"1/v, with v=0.63 being the critical exponent of the three-dimensional Ising model correlation length [229,230]. From Rouault et al. [55]...

Nishikawa, K., Hayashi, H., lijima, T. (1989). Temperature dependence of the concentration fluctuation, the Kirkwood-Buff parameters, and the correlation length of tert-butyl alcohol and water mixtures studied by small-angle X-ray scattering. Journal of Physical Chemistry, 93, 6559-6565. 

Y0 0.2 dyn/cm, compared to the values obtained in the case of critical points for pure fluids or binary mixtures ( y0 a few tens of dyn/cm). This small value remains to be understood. The values of the prefactors of the correlation lengths are of the order of magnitude of a molecular size. Experiments are currently under way to study thoroughly those systems. 

Comparing Eqs (4.92) and (4,93) reveals the correlation length for the mean-field theory of binary mixtures ... 

Here z(( )00) is the distance from the surface (at depth z=0) to the plateau in composition. The surface enriched/depleted in blend component A is characterized by positive/negative z (see Fig. 15). Relatively large correlation lengths for polymer mixtures (see Sects. 2.1 and 2.2.2) lead to the surface profiles ( )(z) of sufficient spatial extent that may be easily traced by current depth profiling techniques [29]. Surface enrichment has been observed at a free surface [164,165] and at a substrate [92] as well as at an interface between binary blend and a homopolymer [166]. 

Analysis of correlation length and density fluctuations in pure and solvent-modified SCFs, in particular around the mixture critical curve (P - PJ. Also measurement of the mean nuclei size and microscale mixing segregation (8). 

Figure 3 (a) Mean-square density fluctuation and (b) correlation length as functions of pressure at constant temperature 313.1 K for pure carbon dioxide and a mixture containing 1.6 mol % of ethanol. 

A porous medium affects a liquid mixture not only by mere confinement to volumes of nanoscopic dimensions [91] but also by the energetic preference of the solid substrate for molecules of one of the components of the mixture [92, 93]. This selectivity causes an enrichment of the component in the proximity of the pore walls. For sufficiently wide pores, the decay length of the resulting concentration profile corresponds to the correlation length of concentration fluctuations [94]. In narrow pores, on the other hand, when the mean pore width D is less than concentration profiles near the pore walls overlap, thereby causing enhanced adsorption. 

At high temperatures (i.e., in the one-phase region of the liquid mixture) the scattering of the pore liquid is described by an Omstein-Zernike term, I q) oc (1 + a correlation length characterizing the compo-... 

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