Effect of hydrostatic pressure

2 Effect of hydrostatic pressure 12.2.1 Overall crystallization kinetics 

In order to establish the basis for analyzing the experimental results for both types of measurements, it is necessary to ascertain what modifications have to be made in Eq. (9.209), and related expressions, as a consequence of the applied pressure. There is the question with respect to the nucleation term in Eq. (9.209) whether the two interfacial free energies, (Ten and cTu , as well as AH, or A5u, depend on pressure. There is also concern as to whether the parameters U and C in the transport term vary. Pertinent experimental results can be examined, keeping in mind these concerns. 

Eigure 12.1 gives a set of isotherms, obtained dilatometrically, for the crystallization of poly(cis-isoprene) at different pressures and two crystallization temperatures.(2) The isotherms have similar shapes, irrespective of the temperature and pressure of crystallization. This leads to a set of superposable isotherms, for both temperatures and pressures, as is illustrated in Fig. 12.2. The experimental points 

The crystallization rate of poly(cis-isoprene) displays a maximum with crystallization temperature under atmospheric pressure (Fig. 9.6). As is illustrated in Fig. 12.3 this maximum is still maintained for crystallization under applied pres-sure.(2) Here the rate constant, from the derived Avrami expression, is plotted 

The overall crystallizahon rate of linear polyethylene, as a function of temperature and pressure has been extensively studied.(3-13) The polymorphism of linear polyethylene at elevated temperatures and pressures makes the analysis of its crystallization kinetics more complex. Depending on conditions, either a hexagonal 

Because the rates of reaction are much less sensitive to the effect of pressure than of temperature, studies of the effects of external pressure for reactions in solution are more difficult to carry out, and need pressures of several thousand atmospheres (kilobars). However, they do yield important information on the transition state, which helps understanding mechanisms. The theory of pressure effects was initially formulated by van t Hoff in terms of the effect of pressure on equilibrium constants 

The simplest way of separating this into the effects on the forward and back reactions is 

In interpreting volumes of activation, we need to consider both structural variations in reactants and activated complexes and also contributions due to the solvent. For a reaction in the gas phase, such as 

Volumes and entropies of activation for water exchange reactions of metal cations 

Knowing that the molar volume of water is 10 cm mol and assuming that the molar volumes of the hydrated ions and complexes are approximately equal, a value of = -10 cm mol can be estimated for a purely associative mechanism of water exchange. Similarly, for the dissociative case we have 

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Bridgman, P.W. (1952) Studies in Large Plastic Flow and Fracture, with Special Empha.sis on the Effects of Hydrostatic Pressure (McGraw-Hill, New York). 

Figure 11. Effect of hydrostatic pressure on elongation <5 and area reduction t/) of the Ti-6Al-2.5Mo-2Cr-a H alloys at room temperature tension, a = 0 (dashed line) and 0.15 (solid line).

It should be pointed out that hydrostatic pressure does not produce an effective compression and, therefore, is not considered. If the casing string is suspended at the top of the hole that is filled with fluid, then the only effect of hydrostatic pressure is reduction of casing weight per foot and the string is effectively under tension. 

Kobashigawa Y, Sakurai M, Nitta K. Effect of hydrostatic pressure on unfolding of alpha-lactalbumin volumetric equivalence of the molten globule and unfolded state. Protein Sci. 1999 8 2765-2772. 

Robert W. Keyes, The Effects of Hydrostatic Pressure on the Properties of III-V Semiconductors... 

Eto et al. (2001) studied the effect of hydrostatic pressure on the magnetostriction and the magnetisation of a polycrystalline Euo.sgSro.42Mn03 sample. At 6 K and ambient pressure, the estimated magnetostriction of about 400 ppm falls down in increasing fields... 

Toluene is to be chlorinated in a batch-operated bubble column such that, for any particular gas rate chosen, the height of the dispersion in the column is 2.2 m. The reactor will operate at a temperature of 20eC and a pressure of 1 bar (any effect of hydrostatic pressure differences in the column may be neglected). The catalyst will be stannic chloride at a concentration of 5 x 10 4 kmol/m3. 

To address this question, an interesting study has been carried out on the effect of hydrostatic pressure on the proton NMR fine width of BPA-PC [44]. Actually, the transverse relaxation time, XH T2, inversely proportional to the line width, is a more convenient parameter. 

The yielding of networks will be described first, beginning with the analysis of deformation mechanisms and the influence of physical aging. The effect of hydrostatic pressure will be treated with yielding criteria. The influence of physical (T, e) and structural parameters on yielding will then be described for ideal and nonideal networks. 

Emeietli, I.V. (1996). Separate effect of hydrostatic pressure and hypoxia on the activity of tissue lactate dehydrogenase in fishes with different mobility (In Russian). Gydrobiologii Zhumal 32,68-72. 

Most of the experimental and theoretical work on the aggregation of ionic surfactants in water has been devoted to understanding how this phenomenon is affected by such factors as concentration, temperature or chemical nature of the surfactants. Much less is known as to how surfactant aggregation is affected by an increase in hydrostatic pressure. Advances in the technique of high pressure vibrational spectroscopy (FT-IR and Raman) of aqueous systems have allowed us now to examine the effect of hydrostatic pressure on the structural and dynamic properties of a large number of surfactants in solution. 

Fig. 55. Effects of hydrostatic pressure on the temperature dependence of the thermoelectric power a(T) for Pro.5(Cao.9Sro.i)o.5Mn03, after Rivadulla et al. (2002).

Robertson, W.W., and Reynolds, R.E. 1958. Effects of hydrostatic pressure on the intensity of the singlet-triplet transition of 1-chloronaph-thalene in ethyl iodide. J. Chem. Phys. 29 138-141. 

The effect of hydrostatic pressure p on Te can be simply determined with the aid of the Clausius-Clapeyron equation. Kittel derives... 

Studies of the effect of hydrostatic pressure on the properties of organic metals have proved to be particularly fruitful. The major success was the discovery of the first organic superconductor, (TMTSF)2PF6 in 1980 [64],... 

We determined further thermodynamic parameters for the reversible phase transition between the crystalline (high temperature) and gel (low temperature) phases by studying the effect of hydrostatic pressure on the phase transition at c = 0.1 M. A swollen gel was loaded into a quartz cell as described above, and on this occasion the quartz cell was contained in a Zircal pressure cell designed for pressures up to 2 kbar [25],... 

FIGURE 1.19 Effect of hydrostatic pressure on the low-angle diffraction pattern of n-butylammonium vermiculite at T = 20°C, c = 0.1 M. 

The effect of hydrostatic pressure on vessel walls with respect to foam expansion ratio was also studied. It was established that the pressure increases linearly with increase in foam density and the angle of the slope of the p(l/n) dependence increases with the reduction of air pressure at which the foam is produced. 

The ejffect of centrifugal force is said to cause such a large increase in the vapour pressure of solid iodine that small aggregates of molecules seem to be thrown off the surface. i The effects of hydrostatic pressure, surface tension, and electrification are considered in 15-18.VIII L. 

However, Eq. (14.20) fails when it tries to describe the yield behavior of polymers over a wide range of temperatures. This has led to a modification of the model (20,21) that assumes that the deformation process involves two different flow processes that have different values of AE and V. Finally, another simple modification of Eyring s equation [Eq. (14.20)] (22) is to include the effect of hydrostatic pressure. This modification reflects the different yield behavior of polymers observed in tension and those in compression. 

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