Applied hydrostatic pressures

The technique of mercury porosimetry consists essentially in measuring the extent of mercury penetration into an evacuated solid as a function of the applied hydrostatic pressure. The full scope of the method first became apparent in 1945 when Ritter and Drake developed a technique for ... 

Like normal filtration, with ultrafiltration (UF), a feed emulsion is introduced into and pumped through a membrane unit water and some dissolved low molecular weight materials pass through the membrane under an applied hydrostatic pressure. In contrast to ordinary filtration however, there is no build-up of retained materials on the membrane filter. 

This form assumes that the effect of pressure on the molar volume of the solvent, which accelerates reactions of order > 1 by increasing the concentrations when they are expressed on the molar scale, has been allowed for. This effect is usually small, ignored but in the most precise work. Equation (7-41) shows that In k will vary linearly with pressure. We shall refer to this graph as the pressure profile. The value of A V is easily calculated from its slope. The values of A V may be nearly zero, positive, or negative. In the first case, the reaction rate shows little if any pressure dependence in the second and third, the applied hydrostatic pressure will cause k to decrease or increase, respectively. A positive value of the volume of activation means that the molar volume of the transition state is larger than the combined molar volume of the reactant(s), and vice versa. 

Fig. 8.9 ST curves 7hs( obtained from Mossbauer measurements on [Fe(2-pic)3]Cl2-C2H50H at ambient and applied hydrostatic pressures of 600 and 1,300 bar (from [19])...

The figure also shows the effect of an externally applied hydrostatic pressure (using the method of Figure 9.2C) the two outermost lines are seen to be shifted in opposite direction (Hagen 1982a). 

While the surface modification is not effective to suppress cavitation, Yee and coworkers performed an experiment to suppress the cavitation mechanically in a rubber-modified epoxy network. They applied hydrostatic pressure during mechanical testing of rubber toughened epoxies [160]. At pressures above BOSS MPa the rubber particles are unable to cavitate and consequently no massive shear yielding is observed, resulting in poor mechanical properties just like with the unmodified matrix. These experiments proved that cavitation is a necessary condition for effective toughening. 

According to the relationship between the lattice volume and Tc as described, cubic CssCgo would be an ultimate candidate for a higher Tc superconductor, but the conventional vapor-solid reaction affords only the thermodynamically stable CsCso and CS4C60 phases. In 1995, noncubic CssCgo was obtained by a solution process in liquid ammonia, and the superconductivity was observed below 40 K under an applied hydrostatic pressure of 1.4 GPa [311]. 

In 2008, the A15 or body-centered cubic (bcc) CssCgo phase, which shows bulk superconductivity under applied hydrostatic pressure, was obtained, together with a small amount of by-products of body-centered orthorhombic (bco) and fee phases, by a solution process in liquid methylamine (Prassides, Rosseinsky, et al.) [312]. Interestingly, the lattice contraction with respect to pressure results in an increase in Tc up to around 0.8 GPa, above which Tc gradually decreases. The highest Tc is... 

Achievement of the constant volume condition requires applying hydrostatic pressure and there is only one reliable set of experiments 22,23) which will be discussed later. Usually the thermomechanical experiments are carried out at the constant pressure condition. The expression for W, Q, AU, r and oj under P, T = const, are... 

Lyklema and Vliet8 determined the equilibrium thickness to of free liquid films stabilized by poly(vinyl alcohol) (PVA) adsorbed at the air-water interface. They estimated to at different applied hydrostatic pressures by measuring the intensities of light reflected from the surface of the film to that of the silvery film. The to values obtained increased with rising hydrostatic pressure and were extrapolated to zero pressure to obtain to for a free film. The extrapolated to should correspond to twice the thickness of the adsorbed PVA layer, but it far exceeded twice the latter determined by ellipsometry. The great difference was interpreted in terms of the presence of long dangling tails which are probably not to be seen by ellipsometry. 

In a similar way, the yield stress increases under applied hydrostatic pressure, P, leading to a modified Eyring equation ... 

Equation (2.37) is simplified by assuming that the membrane selectivity is high, that is, DiK jl DjKj/ . This is a good assumption for most of the reverse osmosis membranes used to separate salts from water. Consider the water flux first. At the point at which the applied hydrostatic pressure balances the water activity gradient, that is, the point of osmotic equilibrium in Figure 2.6(b), the flux of water across the membrane is zero. Equation (2.37) becomes... 

The effect of increasing the concentration of salt in the feed solution on membrane performance is illustrated in Figure 5.2(b). Increasing the salt concentration effectively increases the osmotic pressure term in Equation (5.1) consequently, at a constant feed pressure, the water flux falls with increasing salt concentration at a feed pressure of 1000 psi. The water flux approaches zero when the salt concentration is about 10 wt%, at which point the osmotic pressure equals the applied hydrostatic pressure. The salt rejection also extrapolates to zero rejection at this point but increases rapidly with decreasing salt concentration. Salt rejections of more than 99 % are reached at salt concentrations below 6 %, corresponding to a net applied pressure of about 400 psi. 

Figure 61 shows the ZFC and FC M(T) curves for the FMM phase II, which show a first-order transition at 7c where the bond-length fluctuations become frozen out to restore the phonon contribution to the thermal conductivity, fig. 62. In the I + II two-phase samples t = 0.973 and t = 0.974, phase II is suppressed and phase fluctuations inhibit phonon formation below Tco or 7c. Tokura et al. (1996) applied hydrostatic pressure to the FM phase II of (Ndo.i25Smo.875)o.5Sro.5Mn03 having / /c they reported the appearance of a CE AFI second phase having a volume fraction that increased with pressure below Too = 7n- Since pressure... 

Generally, the pure-water flux through a membrane layer, uw is directly proportional to the applied hydrostatic pressure difference (transmembrane pressure, AP) according to Darcy s law as follows ... 

The electronic configuration of free atoms is an important factor in the interpretation of atomic spectra, but less so for the understanding of chemical behaviour. Chemistry happens in crowded environments, which means that atomic electron densities fades to zero far from infinity. SCF wave functions are therefore not appropriate for atoms in a chemical environment. More suitable wave functions are obtained by terminating the SCF calculations at some fixed distance p from the nucleus, rather than infinity. The effect of such a new boundary condition is like applying hydrostatic pressure to the atom. 

On the other hand a brittle solid may be made ductile by applying hydrostatic pressure. Let us consider a brittle solid, which fails at a tensile stress cr. If a hydrostatic pressure p is applied, the tensile stress necessary for failure is p + a. Associated with this tensile stress is a shear stress equal to Vz(p + cr). If the critical shear stress is less than this, the material will flow in a ductile manner before the tensile stress is large enough to produce brittle failure. 

Crazes usually form under tensile stress when a critical strain is surpassed they do not occur under compressive stress applying hydrostatic pressure during tensile deformation can even inhibit their development. Crazes always nucleate preferentially at points of triaxial stress concentration. It is the dilatational strain which initiates crazes and cracks. 

In 1808, Rous, a colloid chemist, observed that imposing an electric potential difference across a porous wet clay led not only to the expected flow of electricity, but also to a flow of water. He later applied hydrostatic pressure to the clay and observed a flow of electricity. This experiment displayed the electrokinetic effect and demonstrated the existence of coupled phenomena where a flow may be induced by forces other than its own driving force. Therefore, the electric current is evidently caused by the electromotive force, but it may also be induced by the hydrostatic pressure. When two... 

If we represent the magnitude of this applied hydrostatic pressure by n, then the chemical potential of water on the right-hand side of the semipenneable membrane in Figure 2-8 is +RT In aw +Fwn. This solution is in equilibrium with pure water on the left-hand side of the membrane, where = /i,. Hence, + RT In aw + Vwn =, or RT In aw +VWII = 0,... 

Figure 4.24 shows the influence of pressure on the photoinduced anisotropy in PMMA-DRI observed by the Kerr gate experiment for several applied hydrostatic pressures up to 150 MPa, as indicated. The moments when the irradiating light was turned on and off are indicated. After the thermal isomerization is completed after the end of the irradiation, circularly polarized irradiation randomized the in-plane orientation, and photo-orientation at the next higher pressure value followed. Figure 4.24 clearly shows the time... 

FIG. 4.24 Influence of pressure on photo-orientation of DR I observed by the Kerr te setup for applied hydrostatic pressures up to ISO MPa.The numbers I to 6 refer to the api ied prssure,and the moments when the irradiating light is turned on and off are indicated.After the themriai isomerization is completed, circularly polarized irradiation, indicated by Erasure." randomized the in-plane orientation to erase the anisotropy, and photo-orientation at the next-higher pressure followed. Note that the level of the observed anisotrof decreases with the increased pressure, a fea.txire that indicates decreasing capability of photo-orientation with increasing pressure. After reference 48, redrawn by permission of OSA. 

Importance of solvent viscosity or free volume in the TICT phenomenon was discussed in the previous section. There are a number of ways to control viscosity of the medium. The easiest way is to change solvent, however, this brings about the complicated problem of influencing miscellaneous solvent effects. Use of mixed solvents also causes the ambiguity of selective solvation. The best method presumably is the study of pressure effects [20], By applying hydrostatic pressure to a solution, the solvent reduces its free volume without much affecting other solvent properties. 

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