Phase transition pressure

The ability to control pressure in the laboratory environment is a powerful tool for investigating phase changes in materials. At high pressure, many solids will transfonn to denser crystal stmctures. The study of nanocrystals under high pressure, then, allows one to investigate the size dependence of the solid-solid phase transition pressures. Results from studies of both CdSe [219, 220, 221 and 222] and silicon nanocrystals [223] indicate that solid-solid phase transition pressures are elevated in smaller nanocrystals. 

Jones, O.E. and Graham, R.A., Shear Strength Effects on Phase Transition Pressures Determined from Shock Compression Experiments, in Accurate Characterization of the High Pressure Environment (edited by Lloyd, E.C., National Bureau of Standards Special Publication 326, US Government Printing Office, Washington, DC, 1971, pp. 229-242. 

Generally, the following rules apply for pressure-induced phase transitions Pressure-coordination rule by A. Neuhaus with increasing pressure an increase of the coordination number takes place. 

Fig. 11 Defay-Crisp diagram for a binary monolayer A, ideal mixing B, non-ideal mixing C, complete immiscibility. and n2 are the phase transition pressures of components 1 and 2.

Also spin-lattice relaxation times T and spin-spin relaxation times T2 were measured as a function of pressure on different selectively deuterated DPPC (at C2, Cg and Ci3, respectively) by Jonas and co-workers (Fig. 14). The spin-latticed relaxation time T is sensitive to motions with correlation times tc near Uo i e., motions with correlation times in the range from 10 to 10 " s. In comparison with Ti, the spin-spin relaxation time T 2 is more sensitive to motions with correlation times near (e qQlh), i.e., in the intermediate to slow range (10 " to 10 s). The Ti and T2 values obtained showed characteristic changes at various phase transition pressures, thus indicating abrupt changes... 

Figure 19 shows the pressure effeets on the lateral self diffusion eoeffieient of sonicated DPPC and POPC vesicles. The lateral diffusion coefficient of DPPC in the LC phase decreases with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient 1 x 10 cm /s) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the... 

The phase behavior of monolayers is determined by the molecular structure of the am-phiphile and the conditions of the subphase. Phospholipids, for example, attract each other because of van der Waals interactions between the alkyl chains. The longer the alkyl chains, the more strongly the phospholipids attract each other. Thus, the LE-LC transition pressure will decrease with increasing chain length (at constant temperature). Double bonds in the alkyl chains increase this phase transition pressure. Charges and oriented dipole moments (see Chapter 6) in the headgroups, lead to a repulsion between the phopholipids and increase the pressure at which the transition occurs. Salts in the subphase, screen this repulsion and decrease the transition pressure. 

The olivine spinel phase transition Experimental phase equilibrium studies have confirmed deductions from seismic velocity data that below 400 km, olivine and pyroxene, the major constituents of Upper Mantle rocks, are transformed to denser polymorphs with the garnet, y-phase (spinel) and P-phase (wadsleyite) structures (fig. 9.2). In transformations involving olivine to the P- or y-phases, transition pressures... 

The rock-salt phase is a stable phase of nitrides at elevated pressures. The phase transition pressures are 370 - 520 kbar for GaN [6,15], 120 kbar for InN [6] and 230 kbar for AIN [5],... 

Very little is known about the motions of lipid bilayers at elevated pressures. Of particular interest would be the effect of pressure on lateral diffusion, which is related to biological functions such as electron transport and some hormone-receptor interactions. Pressure effects on lateral diffusion of pme lipid molecules and of other membrane components have yet to be carefully studied, however. Figure 9 shows the pressure effects on the lateral self diffusion coefficient of sonicated DPPC and POPC vesicles [86]. The lateral diffusion coefficient of DPPC in the liquid-crystalline (LC) phase decreases, almost exponentially, with increasing pressure from 1 to 300 bar at 50 °C. A sharp decrease in the D-value occurs at the LC to GI phase transition pressure. From 500 bar to 800 bar in the GI phase, the values of the lateral diffusion coefficient ( IT0 cm s ) are approximately constant. There is another sharp decrease in the value of the lateral diffusion coefficient at the GI-Gi phase transition pressure. In the Gi phase, the values of the lateral diffusion coefficient ( 1-10"" cm s ) are again approximately constant. 

A clear correlation has been observed between limiting surface tension ycmc and surfactant performance in water-in-C02 microemulsions, as measured by the phase transition pressure Ptnms- These results have important implications for the rational design of C02-philic surfactants. Studies of aqueous solutions are relatively easy to carry out, and surface tension measurements can be used to screen target compounds expected to exhibit enhanced activity in CO2. Therefore, potential surfactant candidates can be identified before making time-consuming phase stability measurements in high-pressure CO2. 

Phase Transition Pressure We shall take a closer look at a further example of the transition of a substance under pressure. Diamond is a high-pressure modification of carbon which should never appear at normal pressure. The most stable modification of carbon, the one with the lowest chemical potential, is graphite which we know from pencils. A characteristic of graphite is that its chemical potential increases more strongly with pressure than the potential of diamond so that, at one point, //(C graphite) should exceed /<(C diamond) making it possible for diamond to form (Fig. 5.8). 

As occurs with other observables, the range of the calculated phase transition pressure (Pt) and volumes (Table 16) also depends on the choice of the Hamiltonian to some extent. However, the overall agreement with experimental measmements is fairly good. 

Table 16 Phase Transition Pressure, Pt (GPa), and Volumes, Vbi and Vb2 (A ) Calculated with Different Hamiltonians...

This threshold pressure = (bPJ is called the phase transition pressure. The physical implication of this phase transition pressure is as follows. When the gaseous phase pressure is less than this phase transition pressure (y < y, the fractional loading will be in the range (0, 0 )- What we have here is the low density adsorption. At y = y , the fractional loading is... 

When the gaseous pressure is greater than the phase transition pressure (y > yj, the fractional loading is in the range (0, 1). This is what we call the high density adsorption. A computer code Fowler.m is provided with this book, and it calculates the fractional loading for a given value of pressure. 

When the value of c is greater than the critical value of 4, we see the two dimensional condensation when the pressure reaches the phase transition pressure. Take the case of c = 7, there is a two dimensional condensation, and this occurs at the fractional loading of one half and the nondimensional phase transition pressure of... 

An increase in the interaction (increase in c) will shift the phase transition pressure to the left, that is the phase condensation occurs at a lower pressure, which is attributed to the stronger attraction among adsorbed molecules. 

Here we see the two dimensional condensation when c > 27/4 = 6.75. For this case, the phase transition pressure is calculated from ... 

SCF processing is no different. In fact, a phase behaviour analysis is vital as it provides an estimation of the operating pressitfes required and also indicates whether separation fi om other components will be possible. This section will focus on the phase behavioiu of palmitic acid, methyl palmitate, ethyl pahnitate and tripalmitin in SC CO2, ethane and propane and concentrate on the data available and trends observed therein. In addition, the three solvents will be eompared and the effect of co-solvents, often used to decrease the operating pressiu e, will be eonsidered. In particular this section will focus on the phase transition pressures of the systems studied. The phase transition pressure indieates the pressitfe required for total solubility at the said temperature and composition. For the type of systems studied here, a higher phase transition pressure leads to a lower solubility, therefore lower phase transition pressures indieate improved solubility. 

Schwarz and Knoetze [24] found that for their VLE data an approximately linear relationship exists between temperature and the phase transition pressure at constant composition. This relationship has a positive gradient and indicates a higher solubility at lower temperatures, converse to that of the solid-vapour equilibrium (SVE) phase behaviour. This positive gradient was also found through the entire mass fraction range studied and the authors did not find any indications of temperature inversions in this system. 

Figme 5 shows the phase equilibrium data of the system C02/methyl palmitate of both Inomata et al. [48] and Lockemarm [49]. Figure 5 hints towards significant differences between the data sets, yet insufficient information is available to determine which data set us superior. However, the data clearly shows that an increase in temperature results in an increase in phase transition pressure. Due to the scatter in the data and slight inconsistencies between the two sources the exact nature of the relationship between temperature and the phase transition pressure can not be determined. Additional measurements would be required therefore. Both sets of data do, however, indicate that total solubility can be achieved at moderate pressures (less than 25 MPa at temperatures below 343 K). 

The data also indicates, as pointed out by Crampon et al., that an increase in temperature leads to an increase in phase transition pressure and suggests that a linear relationship between temperature and pressure exists. Gaschi et al. observed three phase behaviour at... 

Despite a number of studies considering the VLE of the C02/tripalmitin, significant discrepancies exist between the data sets and no conclusion can be made on which set of data is superior. However, the data of Munuklu et al. [53] do indicate that once again in the VLE region an increase in temperature leads to an increase in phase transition pressure. Additionally, irrespective of which source represents the phase behaviour most accurately, all four sources show that high pressures in excess of 30 MPa are required for total solubility. 

All four systems behave in a generally similar manner. For VLE an increase in temperature leads to an increase in phase transition pressure, resulting in a decrease in solubility. For the VSE the C02/pahnitic acid system showed the opposite temperature effect while insufficient data are available to comment on the temperature dependence of solid tripalmitin in SC CO2. However, both the C02/palmitic acid and C02/tripalmitin systems showed that the solid solubility is approximately an order of magnitude less than that of the liquid. 

The data shows that at both temperatures the esters have the highest solubility followed by palmitic acid and that tripalmitin has the lowest solubility. It is also noted that the systems C02/methyl pahnitate and C02/ethyl palmitate have very similar phase behaviour and similar phase transition pressures. This is expected due to the similarity of the moleeules. However, despite the fact that Bharath et al. [55] foimd that for Ci8 and higher esters the methyl ester has a higher phase transition pressure than the ethyl ester, Figure 9 indicates that the phase transition pressmes are indeed very similar and from the data available in the present analysis no outcome can be given in this regard. 

Details pertaining to the ethane/pahnitic acid system measurements are provided in Table 7 and the phase transition pressure, as a function of composition at various temperatures, can be seen in Figure 11. 

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