Tait expression

The Tait expression may be employed in this context for the calculation of the isothermal compressibility, recast in the form ... 

Helmholz energy, molar Helmholz energy (in J mol ) thermodynamic activity of species X Tait expression temperature-dependent parameter activation energy for process x (tj, k, A, or D) cohesive energy (in kJ mol ) cohesive energy density (in MPa)... 

The radius and velocity of the bubble waU are given by R and U respectively. The values for H, the enthalpy at the bubble waU, and C, the local sound speed, maybe expressed as foUows, using the Tait equation of state for the Hquid. 

The Tait equation for the pressure—volume behavior of Hquids (1) correlates data accurately, and is expressed mathematically as... 

The expression in Eq. (29) can be evaluated numerically for all values of t, and the results for three different waiting times are shown in Fig. 11 for c = 0.1. The value of Tmin = 2.0 ps at E/To = 5.7 x lO", derived from the present theory (also consistent with Goubau and Tait [101]) was used. The results for t = 10 ps demonstrate that, due to a lack of fast relaxing systems at low energies, short-time specific heat measurements can exhibit an apparent gap in the TLS spectrum. Otherwise, it is evident that the power-law asymptotics from Eq. (30) describes well Eq. (29) at the temperatures of a typical experiment. 

Santner SJ, Pauley RJ, Tait L (1997) Aromatase activity and expression in breast cancer and benign breast tissue stromal cells. J Clin Endocrinol Metab 82 200-208... 

The need for solvation in anionic polymerization manifests itself in some instances by other deviations from the normal reaction rate expressions. Thus the butyllithium polymerization of methyl methacrylate in toluene at — 60°C shows a second-order dependence of Rp on monomer concentration [L Abbe and Smets, 1967]. In the nonpolar toulene, monomer is involved in solvating the propagating species [Busson and Van Beylen, 1978]. When polymerization is carried out in the mixed solvent dioxane-toluene (a more polar solvent than toluene), the normal first-order dependence of Rp on [M] is observed. The lithium diethylamide, LiN(C2H5)2, polymerization of styrene at 25°C in THF-benzene similarly shows an increased order of dependence of Rp on [M] as the amount of tetrahydrofuran is decreased [Hurley and Tait, 1976]. 

Adsorption phenomena are important in most Ziegler-Natta polymerizations, and this requires treatment by heterogeneous kinetics [Bohm, 1978 Boor, 1979 Chien and Ang, 1987 Chien and Hu, 1987 Cooper, 1976 Keii, 1972 Tait and Watkins, 1989]. The exact form of the resulting kinetic expressions differs depending on the specific adsorption... 

Water with ammonium sulphate in soln. has a smaller sp. vol. than water. From P. G. Tait s measurements of the press, necessary to produce a corresponding contraction in the sp. vol. of water, G. Tammann calculated that the increase in the internal press. P atm. of water produced by the dissolution of the salt expressed in grams of salt per 100 grms. of water, is as follows ... 

A rather accurate expression for the compressibility of most liquids is the Tait equation14 ... 

Tait 2 gives the following expression whereby the eompressibihties of water between 6° and 15° C. can be calculated for pressures ranging from 150 to 500 atmospheres ... 

On of the most useful expressions to represent the P(P,T)-behaviour of liquids, including polymeric liquids, is the Tait-relation (Tait 1888,1898 and Dorsey 1940) ... 

This method is to be used to calculate the specific volume of a pure polymer liquid at a given temperature and pressure. This procedure uses the empirical Tait equation along with a polynomial expression for the zero pressure isobar. The method requires only the equation constants for the polymer. 

This method uses the form of the Tait equation which gives the best representation of P-V-T data for most of the polymers. Other forms of the Tait equation which use a different expression for V(0,T) or a different value for the parameter C are available. For a few specific polymers, they might provide a better representation of the P-V-T behavior. 

Brain vascular endothelial cells are linked by tight junction proteins creating high-resistance junctions between cells that effectively prevent the movement of hydrophilic substances, including electrolytes, such as Na and K+. Water moves across the lipid bilayer of endothelial cells through simple diffusion and vesicular transport (Tait et al., 2008). However, specialized water channels are formed by molecules called aquaporins (AQPs), which are highly expressed in blood-brain interfaces to facilitate the transport of water across cell membranes. 

Subsequently Tait (Tl) introduced the metabolic clearance rate (MCR) as a combination of Pearlman s approach with Homer Smith s well-known concept of renal clearance. In this treatment the clearance rate of a hormone from the blood is expressed as the (conceptual) volume of blood which would contain the amount of steroid cleared from the (actual) blood per unit time. 

Blankenberg, F.G., Katsikis, P.D., Tait, J.F., Davis, R. E., Naumovski, L., Ohtsuki, K., Kopi-woda, S., Abrams, M.J., Darkes, M., Robbins, R.C., Maecker, H.T., and Strauss, H.W. In vivo detection and imaging of phosphatidylse-rine expression during programmed cell death. Proc. Natl. Acad. Sci. USA, 95 6349-6354, 1998. 

Proceeding directly from Eqn 4-53, isothermal compressibility can be written as gP). Since the Tait equation is a functional representation for most pressure-volume isotherms within the experimental accuracy of the data, compressibilities can be expressed functionally by... 

Lord Kelvin, On the Secular Cooling of the Earth, (W. Thomson and P. G. Tait s Treatise on Natural Philosophy, 1,711,1867), has compared the observed values of the underground temperature increments, d6jdxy with those deduced by assigning the most probable values to the terms in the above expressions. The close agreement—Calculated 1° increment per A ft. descent. Observed 1° increment descent—led him to the beliefthat the data are nearly... 

Numerous theoretical equations of state forpolymer liquids have been developed. These, at the minimum, have to provide accurate fitting functions to experimental data. However, for the purpose of this table, the empirical Tait equation along with a polynomial expression forthe zero pressure isobar is used. This equation is able to represent the experimental data for the melt state within the limits of experimental errors, i.e., the maximum deviations between measured and calculated specific volumes are about 0.001-0.002 cm /g. 

The reactivity effect of this enlargement depends upon the details of the way in which it occurs, and this goes beyond the scope of the Bethe-Tait approximation dealt with in this chapter. However, for the sake of completeness, an expression for this reactivity effect is derived below for the simple case of a spherical reactor. 

The Tail equation is a four-parameter representation of the P-V-T behavior of polymers. The four parameters are the zero pressure isotherm, Vq. Tait parameter, B, thermal expansion coefficient, a, and activation energy, In some industrial systems polynomial expressions are used for the zero-pressure isotherm and Tait parameter as follows ... 

The zero-isotherm and Tait parameter for some polymer systems were provided for 56 polymers by Rodgers [9]. The values for some systems are given in Table 2.1. For a few polymers, the temperature, T, is expressed as °C. 

EOS theories for polymer liquids were grouped into three categories (1) lattice-fluid theory, (2) the hole model, and (3) the cell model. The Tait equation was first developed 121 years ago in order to fit compressibility data of freshwater and seawater. The Tait equation is a four-parameter representation of PVT behavior of polymers. Expressions for zero pressure isotherms and Tait parameters were provided, and values of Tait parameters for 16 commonly used polymers were tabulated. 

Blankenberg FG, Katsikis PD, Tait JF, Davis RE, Naumovski L, Ohtsuki K, Kopiwoda S, Abrams MJ, Darkes M, Robbins RC, Maecker HT, Strauss HW. In vivo detection and imaging of phosphatidylserine expression during programmed cell death. PNAS 1998 95 6349-6354. 

The Tait equation is one of the simplest and yet more accurate empirical equations for fitting liquid density data of pure components over wide ranges of temperature and pressure. The general expression for this equation in terms of density along an isotherm is... 

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