Coexistence diameters

R. L. C. Vink, J. Horbach, and K. Binder (2005) Critical phenomena in coUoid-polymer mixtures Interfacial tension, order parameter, susceptibility, and coexistence diameter. Phys. Rev. E 71, 011401... 

Figure A2.5.10. Phase diagram for the van der Waals fluid, shown as reduced temperature versus reduced density p. . The region under the smooth coexistence curve is a two-phase liquid-gas region as indicated by the horizontal tie-lines. The critical point at the top of the curve has the coordinates (1,1). The dashed line is the diameter, and the dotted curve is the spinodal curve.

If the small temis in p- and higher are ignored, equation (A2.5.4) is the Taw of the rectilinear diameter as evidenced by the straight line that extends to the critical point in figure A2.5.10 this prediction is in good qualitative agreement with most experiments. However, equation (A2.5.5). which predicts a parabolic shape for the top of the coexistence curve, is unsatisfactory as we shall see in subsequent sections. 

As in tire one-fluid case, the experimental sums are in good agreement with the law of the rectilinear diameter, but the experimental differences fail to give a parabolic shape to tlie coexistence curve. 

An unexpected conclusion from this fonuulation, shown in various degrees of generality in 1970-71, is that for systems that lack tlie synunetry of simple lattice models the slope of the diameter of the coexistence curve... 

Figure A2.5.25. Coexistence-curve diameters as functions of reduced temperature for Ne, N2, C2H4, and SFg. Dashed lines indicate linear fits to the data far from the critical point. Reproduced from [19] Pestak M W, Goldstein R E, Chan M H W, de Bniyn J R, Balzarini D A and Ashcroft N W 1987 Phys. Rev. B 36 599, figure 3. Copyright (1987) by the American Physical Society.

Jungst S, Knuth B and Hensel F 1985 Observation of singular diameters in the coexistence curves of metals Phys. Rev. Lett. 55 2160-3... 

Fig. 4. Coexisting vapour-grown carbon fiber, with thicker diameter and hollow core, and carbon nanolubes, with thinner hollow core, (as-grown samples).

Bimodal pore size distribution in MCM-4I has been observed by several groups in the last few years [22-24], However, the relation between two types of mesopores were never fully understood. In a recent TEM study of an MCM-41-type silicate with a bimodal mesopore system, a paint-brush like morphology of the particles was observed (Figure 7) [25], It was then proposed that the two types of pores with the pore diameters of 2.5 nm and 3.5 nm respectively coexist and are parallel to each other in the particles. Due to different rates of crystal growth, the lengths of these two groups of mesopores are different, resulting in such a novel structure only on the (001) surface. 

Because the growth of ice crystals killed the affected cells 5.70 Liquid water and water vapor will coexist 5.72 Because it has a diameter in the nanometer range 5.74 (c) water... 

CoO-coated Co cluster and oxide-coated Fe cluster assemblies were prepared by a plasma-gas-aggregation cluster-beam-deposition technique [37-39]. For preparation of CoO-coated Co cluster assembly, oxygen gas was introduced through a nozzle near the skimmer into the deposition chamber. The Co clusters with CoO shells were formed before deposition onto the substrate [37], Figure 8 shows a TEM image of the clusters produced at oxygen gas flow rate R(02) = 1 seem. Clusters are almost monodispersed, with the mean diameter of about 13 nm. Electron diffraction pattern indicated the coexistence of Co and CoO phases. The cluster assemblies were formed on a polyimide film with a thickness of about 100 nm. 

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