Reentrant solid phase

Figure 47. Phase diagram of N2 on boron nitride based on adsorption isotherms coverage is repotted in units of the complete Vs mono-layer obtained from the top of the fluid to commensurate solid isotherm substep at low temperatures less than 51 K. Commensurate solid phase (C), fluid phase (F), reentrant fluid phase (RF). The solid lines correspond to phase boundaries based on measured features, the dotted line is an expected phase boundary, and the triangle marks the tricritical point. Second-layer growth instead of a transition to an incommensurate solid phase is expected beyond the reentrant fluid phase in the temperature range studied. (Adapted from Fig. 4 of Ref. 1.)...

Figure 48. Semilogarithmic plot of the isothermal compressibility of N2 on boron nitride at 60.8 K as a function of the coverage in units of the complete /3 monolayer. The peak sequence starting at low coverages is attributed to the fluid to commensurate solid F-C and commensurate solid to reentrant fluid C-RF transitions and finally to second-layer growth RF-B (instead of a transition from the reentrant fluid to an incommensurate solid phase). (Adapted from Fig. 5 of Ref. 1.)...

Figure 49. Phase diagram of CO physisorbed on graphite with the following phases commensurate orientationally disordered (>/3 x -s/3)/J30° solid phase (CD), commensurate orientationally ordered herringbone phase (HB), head-tail (dipolar) ordered commensurate herringbone phase (DHB), fluid (F), reentrant fluid (RF), incommensurate orientationally disordered solid (ID), incommensurate orientationally ordered pinwheel phase (PW), second-layer orientationally disordered solid (2SD), second-layer liquid (2L), second-layer vapor (2V), second-layer fluid (2F), bilayer orientationally ordered solid (BO) the parentheses are included for clarity only. The solid lines are based on experimental results, whereas the dashed lines are speculative. Note that the phase boundary (ID + CD) RF and the orientational disordering temperamre of the BO phase are unknown. Coverage unity corresponds to a coverage of CO forming a complete ( /3 x Vs) commensurate monolayer. (The phase diagram is based on Fig. 1 of Ref. 112, Fig. 2 of Ref. 113, and Refs. 380 and 381.

Liquid polymorphism in one-component fluids is an example of so-called anomalous phase behavior. This term is used to emphasized the difference with respect to the normal behavior characterizing prototypical (i.e., argon like) simple liquids. Anomalous behavior includes, in addition to polymorphism in the liquid and solid phases, reentrant melting, that is, melting by compression at constant temperature, and a number of other thermodynamic, dynamic, and structural anomalies, as, for example, the density anomaly (a decrease in density upon cooling), the diffusion anomaly (an increase of diffusivity upon pressurizing), and the structural anomaly (a decrease of structural order for increasing pressure). 

An incommensurate solid to a reentrant fluid transition and a reentrant fluid to commensurate transition, both being of second order. In particular, the existence of a novel reentrant fluid phase separating the commensurate and incommensurate phases constitutes clearly one of the most spectacular and interesting phenomena observed in the study of rare gases adsorbed on graphite. Another important result is that there is no multicritical (commensurate-incommensurate fluid) point at high temperatures. 

A clear disadvantage of the earliest lattice models [181] (and of density functional approaches) is that only commensurate solid phases (in addition to the fluid phases, obviously) are considered. A more complex lattice model including incommensurate phases has been developed by Caflisch et al. [144] for the particular case of Kr on graphite. The experimentally observed phase diagram, including the presence of the reentrant fluid is reproduced, as is shown in Fig. 5, where the lines indicate the Caflisch et al. [144] theoretical results. Although the application of this model to other systems seems possible, it could be very laborious. 

With respect to the computer simulations of helium on graphite, we would only note that they reproduce the presence of fluid, commensurate and incommensurate solids, and a reentrant fluid phase [238,325]. The phase diagram obtained is similar to that proposed by Ecke and Dash [237], which differs from the more recent proposal of Greywall [106] (Fig. 7) and does not include a liquid-vapor transition. 

Sushko YV, Ito H, Ishiguro T, Horiuchi S, Saito G (1993) Reentrant superconductivity in k-(BEDT-TTF)2Cu[N(CN)2]C1 and its pressure phase diagram. Solid State Commun 87 997-1000... 

Some gels were synthesized which underwent the phase transition twice as the solvent composition was monotonically varied from 0% to 100%. Figure 30 shows the swelling behaviors of NIPA (open circles) and acrylamide (solid circles) gels in a mixture of dimethylsulfoxide (DMSO) and water [24]. When the DMSO concentration was lower than 33%, the NIPA gel was slightly swollen. Above 33% DMSO, a discrete transition to a collapsed state occurred. However, the gel showed a discontinuous re-swelling at 90%. Such reentrant behavior has also been observed when temperature or pH were used as variables. 

Although these simplified models of hydrogen-bonded systems give a far from complete picture of the solid-fluid phase behavior of water, this kind of approach to identifying the key features required in the molecular model is an instructive one. Indeed, the inability of the PMW to generate reentrant melting of the low-density solid at thermodynamically stable states is an important result. It shows us that more than just short-range directional forces are required for this to occur. 

The freezing transition from the reentrant fluid to the commensurate solid monolayer seems to be of first order at low temperatures and changes to a continuous transition at a tricritical point near 85 K. This interpretation of the heat capacity and compressibility data [112], however, needs further experimental confirmation, and the corresponding tricritical point shown in the phase diagram Fig. 51 as an open triangle is only tentative. There are also conflicting theoretical predictions concerning the order of the RF - CD transition [77, 78, 151, 260], and the present resolution of the calorimetric data [112] does not allow us to draw a firm conclusion in this respect. 

Fig. 4. Reentrant fluid of Kr/graphite. High T region of the Kr/graphite phase diagram (from Ref. 30). The reentrant fluid (RF) phase is a domain wall fluid bounded by commensurate (C) and incommensurate (IC) regimes. S(23D) and L(3D) are the bulk solid and hquid phases. Sohd lines denote first-order transitions and dashed lines denote continuous transitions.

Typical example of the phase diagrams for the associating diblock copolymer blends of relatively short chains (jia = b = 20). MST (broken line) and SP (solid lines) are shown on the temperature-concentration plane. Points indicated by (LP) are I. ifshit points, while those shown by (e) and (e ) are eutectic points. Existence of a reentrant microphase (M ) is one of the remarkable features of the associating systems. y = A /fc5 = 3. (a)A.Q=l -20, (b) Xp = 1.26,... 

For a long time, there were major imcertainties about the commensurate-incommensurate phase transition, mainly because the experimental studies indicated a different order of that transition at high and low temperatures [113]. These uncertainties have been resolved by the proven existence of a reentrant fluid between the two solid regions [15,143]. The final proposed form for the phase diagram is shown in Fig. 5 [144], where the points are experimental data obtained from thermodynamic methods. 

FIG. 6 Pressure-teniperature phase diagram for krypton on graphite near the monolayer completion, proposed hy Specht et al. [143] fiom x-ray diffraction data. Dashed lines indicate the scans that were made in experiments. Triangles are from Ref. 137. (F = fluid, C = commensurate fluid, IC = incommensurate solid, RF = reentrant fluid, L = bulk liquid, S = bulk solid.)... 

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