Inverse temperature transitions phase diagram

Phase Diagram for Inverse Temperature Transitions and Related Analyses... 

Figure 5.3. Phase diagram for several elastic-contractile model proteins, showing an inverted curvature to the binodal or coexistence line (when compared with petroleum-based polymers) that is equivalent to the T,-divide, with the value of T, determined as noted in Figure 5.IB. Solubility is also inverted with insolubility above and solubility below the binodal line, that is, solubility is lost on raising the temperature whereas solubility is achieved by raising the temperature of most petroleum-based polymers in their solvents. Note that addition of a CHj group lowers the T,-divide and removal of the CH2 group raises the T,-divide. For these and the additional reason of increased ordering on increasing the temperature, the phase transitions of elastic-contractile model proteins are called inverse temperature transitions. (The curve for poly[GVGVP] is adapted with permission from Manno et al. and Sciortino et al. ).

Inverted Phase Diagrams of Hemoglobins A and S A Further Diagnostic of Inverse Temperature Transition Using the Spinodal Line... 

Enthalpy can be measured by liquid chromatography where enthalpy is a slope of the relationship between In k and the inverse value of the absolute temperature. A schematic diagram is shown in Figure 6.7. The slope depends upon the solutes being retained by the same liquid chromatographic mechanism. An example is given in Table 6.4. The results, measured on an octadecyl-bonded vinyl alcohol copolymer gel, did not show a simple linear relationship. This is due to a conformation change of the octadecyl-bonded vinyl alcohol copolymer gel stationary phase material, which has a phase transition point at about 33 °C. 

A phase diagram of the EuTiOs 1-nm nanowire (R 2.5 lattice constants) in coordinates temperature T — radial stress Opp = —p,// is illustrated in Fig. 4.43a for the temperature range of 0-300 K. Figure 4.43b is a magnified in view of Fig. 4.43a for temperatures lower than 30 K, which shows the multiferroic phase boundaries at lower temperatures. The FE + PM, FE + FM and FE + AFM phases appear in the nanowires subjected to the intrinsic surface stress Opp = — i R, in contrast to the bulk material with ct = 0, which can attain PM + PE and AFM + PE phases only. The FE and FM phase transition temperatures increase with the increase in the surface stress, which in turn is inversely proportional to the wire radius in the continuous theory. 

Figure 24.9 Phase diagram for K-carrageenan in K- and Na-salt forms. Inverse of the transition temperature (T ) as a function of the total ionic concentration (Cp). (+,0) when Cp < Cp and Tp (-I-) and Tq (O) when Cp > Cp with the...

The scheme, being displayed in Fig. 23.13, delineates the stabihty ranges and transition lines for these phases. The variables in this phase diagram are the temperature and the crystal size, whereby the inverse crystal thickness serves as size parameter. The thickness is given by the number n of structure units in a stem, i.e., n = dcjAz with Az denoting the stem length increment per structure unit. The transition lines are denoted Tnic , 7ac , Imcs, Tacs, Tam, all to be understood as functions of n. ... 

Figure 7.45 is the phase diagram for sodium carbonate and water. Three different hydrates are involved, and there are phase transitions at 32°C and 35.4°C. The solid forms of most interest are the decahydrate (washing soda) and the monohydrate. The diagram shows that the solubility of the monohydrate is nearly thermoneutral. The solubility as Na2CC>3 is about 33% at 36°C and 31% at 80°C. The inverse solubility prevents crystallization from a solution as it cools during transfer, and soda ash storage in the slurry form is usually as the monohydrate. The temperature in the tank should remain above 43-46°C to prevent transition to the hepta- or decahydrate. 

Figure 4.26 Sequence of phases observed on increasing solvent content, in a binary amphiphile-solvent system, representing a hypothetical phase diagram where phase transitions are controlled by solvent content only. Here a, b, c and d indicate intermediate phases (for example the bicontinuous cubic structure shown in Fig. 4.25d), L2 denotes the inverse micellar solution, Hn is the inverse hexagonal phase, L is the lamellar phase. Hi is the normal hexagonal phase and Li is the normal micellar phase. In practice, the full sequence of phases is rarely observed, and in reality the phase transitions depend on temperature as well as concentration...

Figure 13.18 Jamming diagram proposed by Liu and Nagel (1998), revised by O Hern et al. (2003), and experimentally determined by Trappe et al. (2001). The diagram illustrates that many disordered materials are in a jammed state for low temperature T, low load E, and large density ( ), but can become unjammed when these parameters are varied. For frictionless soft spheres, there is a well-defined jamming transition indicated by point 7 on the inverse density axis, which exhibits similarities to a critical phase transition.

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