Pressure-density isotherms

The pressure-density isotherms of various water models in supercooled region, obtained in simulations, can be directly compared with the available experimental isotherms, showing transformations between amorphous ices upon compression." Experimental measured isotherms are unavoidably affected by the transformation kinetics and by the strong hysteresis. These two effects may be reduced by using slow compression rates and higher temperatures, respectively. Therefore, the equilibrium isotherms obtained in simulations we compare with the experimental pressurization curves," which were obtained under the slowest compression rate and at highest temperature. 

The equation of state for the model fluid whose constituent molecules interact with the prescribed potential is unknown. Instead, the pressure-density isotherms from NVT MC simulation provide a way to calculate the chemical potential as a function of pressure for each temperature. The chemical potential of the imperfect gas (fluid) for a spherical molecule is calculated as follows. At a given temperature, NVT MC simulations of pure guest are performed with various volumes (number densities, p). It is again important to take account of the long-range interaction in the calculation of the pressure. Thus, an isotherm of the pressure is obtained. The free energy per molecule, Sg, at Tand p is given by sum of the ideal and the nonideal parts as... 

The three general states of monolayers are illustrated in the pressure-area isotherm in Fig. IV-16. A low-pressure gas phase, G, condenses to a liquid phase termed the /i uid-expanded (LE or L ) phase by Adam [183] and Harkins [9]. One or more of several more dense, liquid-condensed phase (LC) exist at higher pressures and lower temperatures. A solid phase (S) exists at high pressures and densities. We briefly describe these phases and their characteristic features and transitions several useful articles provide a more detailed description [184-187]. 

Fig. 2. Reduced density, p, versus reduced pressure, P, isotherms for pure carbon dioxide, where the numbers on the curves represent = TjT values.

Surface pressure/area isotherms of mixtures of the cationic lipid (20, n = 12) with distearoylphosphatidylcholine (DSPC) are shown in Fig. 30. For all mixtures only one collapse point is observed. The collapse pressure increases continuously with increasing amount of DSPC, indicating miscibility of the two components. Plotting A versus molar ratio (Fie. 3D results in considerable deviation from linearity, which also suggests miscibility of the two compounds in monolayers. This is also confirmed by the fact that the polymerization rate, as measured by the increase of optical density at 540 nm, is reduced by a factor of 100 when the DSPC molar ratio is increased from 0 to 0.52,... 

Example 13.4. The result of a typical X-ray measurement is shown in Fig. 13.10 for a galactocerebroside [605], The plot on the left side shows the normalized reflected X-ray beam intensity versus the incident angle a for two different film pressures. The pressure-area isotherm is shown in the inset, together with the points of measurement a and b. On the right side are the extracted electron density profiles normal to the film surface taken at the same film pressures. At 0 A we find the monolayer surface (top of the alkyl chains), a depth of -40 A corresponds to pure water. In between is the film. The measurement is so sensitive that we even find two different electron densities within the monolayer. This is illustrated by the dashed boxes denoted by film 1 and film 2 (shown for curve b only) which represents the simplified electron density distribution in the so-called two-box model. A box is defined as a part in the film of a certain thickness where the electron density is constant. In the two-box model the film is divided into two layers. Film 1 represents the hydrocarbon tails, film 2 corresponds to the mean electron density of the head groups. 

Some properties are directly connected with mass and packing density (or its reciprocal specific volume), thermal expansibility and isothermal compressibility. Especially the mechanical properties, such as moduli, Poisson ratio, etc., depend on mass and packing. In this chapter we shall discuss the densimetric and volumetric properties of polymers, especially density and its variations as a function of temperature and pressure. Density is defined as a ratio ... 

In Figure 2 the experimental solubilities are represented as concentration (pressure) and concentration (density) isotherms for C02 at four different temperatures. The dependence of solubility versus temperature or density is quite usual, as it increases when one of these parameters is raising. C02 is a better solvent for the apolar P-carotene than CC1F,. The lower solvent power of CC1F3 can be explained from its dipole moment (1.7-10 30 C m) [21]. The non-polar C02 enables interactions between the solvent molecule and the solute whereas in the case of CC1F3 these effects are restrained. The thermodynamic background to this particular behavior can e.g. be derived from considerations by Prausnitz et al. [22],... 

Nitrogen isotherms were measured using an ASAP 2010 (Micromeritics) at 77 K. Before the experiment the samples were heated at 473K and then outgassed at this temperature under a vacuum of 10 torr to constant pressure. The isotherms were used to calculate the specific surface area, 8, 2. micropore volume, V , and total pore volume, V,. All of the above parameters were calculated using Density Functional Theory (DFT) [12, 13]. 

In summary with this system it has been possible to observe the transition from the osmotic to a salted and then to a collapsed brush. One might suspect that these transitions are also reflected in the pressure/area isotherms. However, we have not yet been able to relate the breaks in the isotherm slopes with parameters deduced from X-ray reflectivity. This would require an even higher precision of data analysis, and precision in density determination better than 1% is difficult to achieve. We realize that the transition at nc is accompanied by a change in relaxation times as expected for a... 

Shah et al. carried out a Monte-Carlo simulation in the isothermal-isobaric (NPT) ensemble of [C4mim][PF6] [12]. The authors calculated the molar volume, cohesive energy density, isothermal compressibility, cubic expansion coefficient, and liquid structure as a function of temperature and pressure. A united atom force field was developed using a combination of ab initio calculations and literature parameter values were also developed. Calculated molar volumes were within 5% of experimental values, and a reasonable agreement was obtained between calculated and experimental values of the isothermal compressibility and cubic expansion coefficient. [PF6] anions were found to cluster preferentially in two favorable regions near the cation, namely around the C2 carbon atom, both below and above the plane of the imidazole ring [12],... 

Fig. 2.24 Density isotherms as function of pressure (reduced values)...

The flow of compressible fluids (e.g., gases and vapors) through pipelines and other restrictions is often affected by changing conditions of pressure, temperature, and physical properties. The densities of gases and vapors vary with temperature and pressure. During isothermal flow, i.e., constant temperature (PV = constant) density varies with pressure. Conversely, in adiabatic flow, i.e., no heat loss (PV " = constant), a decrease in temperature occurs when pressure decreases, resulting in a density increase. At high pressures and temperatures, the compressibility factor can be less than unity, which results in an increase in the fluid density. 

Figure 9. Pbt of Kimelberg and Papahadjopoulos (6) results according to our representation. Surface pressure increases of pure human serum albumin mono-layer (HSA), AIIj, vs. phosphatidylserine surface density, S2. Phosphatidylserine surface densities are deduced from the surface pressure-area isotherm of...

Values of the density, isothermal compressibility, and coefficient of thermal expansion for some common fluids are listed in App. A. 10. Notice that for most fluids the effect of a change in temperaturej is more significant than the effect of a change in pressure. Normally a temperature decrease of 1°F will have the same effect as a pressure increase of 100 psi. 

This method, originally used by Andrews in his famous experiments on carbon dioxide in 1872, has been used recently, but very precise and elaborate apparatus is needed to obtain accurate results. Inspection of pressure-density graphs shows that it is very difficult to determine exactly which of the isotherms corresponds to the critical isotherm even if very precise p, V,T measurements are available. Hence critical data are usually obtained from such studies as a spinoff, the major aim being the determination of the p,F,T behaviour of the substances. 

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