Characteristic volume

VSTR = O Connell characteristic volume parameter, cm /g-mol ZRA = Rackett equation parameter RD = mean radius of gyration, A DM = dipole moment, D R = UNIQUAC r Q = UNIQUAC q QP = UNIQUAC q ... 

Equatioa-of-state theories employ characteristic volume, temperature, and pressure parameters that must be derived from volumetric data for the pure components. Owiag to the availabiHty of commercial iastmments for such measurements, there is a growing data source for use ia these theories (9,11,20). Like the simpler Flory-Huggias theory, these theories coataia an iateraction parameter that is the principal factor ia determining phase behavior ia bleads of high molecular weight polymers. 

An afternate method with approximately the same accuracy as the Rackett method is the COSTALD metnod of Hanldnson and Thomson.The critical temperature, a characteristic volume near the critical volume, and an acentric factor optimized for vapor pressure prediction by the Soave equation of state are required input parameters. The method is detailed in the Technical Data Book ... 

This example illustrates the simplified approach to film blowing. Unfortunately in practice the situation is more complex in that the film thickness is influenced by draw-down, relaxation of induced stresses/strains and melt flow phenomena such as die swell. In fact the situation is similar to that described for blow moulding (see below) and the type of analysis outlined in that section could be used to allow for the effects of die swell. However, since the most practical problems in film blowing require iterative type solutions involving melt flow characteristics, volume flow rates, swell ratios, etc the study of these is delayed until Chapter 5 where a more rigorous approach to polymer flow has been adopted. 

The CMC also varies logarithmically with the characteristic volume of the monomeric surfactant molecule. Thus, Eq. 13, developed by Sowada and McGowan [91], can be used to predict the CMC ... 

The characteristic volume V/105 in m3/mol of the sodium sulfate ion is 4.966. The characteristic volume V/105 of the linear alkyl chain can be evalu-... 

In this equation E (R2) is the excess molar refraction, S (tt ) is the solute dipolarity-polarizabiUty, A (2a ) and B(2 3 ) are the solute H-bond acidity and basicity, respectively, and Vis the McGowan characteristic volume (in cm mol /100). The solute size, V, (molecule favors octanol) together with solute H-bond basicity, B, (favors water) are the dominating parameters of this equation. The use of Bo(2P ) resulted in equation... 

Numerous models have been proposed to interpret pore diffusion through polymer networks. The most successful and most widely used model has been that of Yasuda and coworkers [191,192], This theory has its roots in the free volume theory of Cohen and Turnbull [193] for the diffusion of hard spheres in a liquid. According to Yasuda and coworkers, the diffusion coefficient is proportional to exp(-Vj/Vf), where Vs is the characteristic volume of the solute and Vf is the free volume within the gel. Since Vf is assumed to be linearly related to the volume fraction of solvent inside the gel, the following expression is derived ... 

Abraham MH, McGowan JC (1987) The use of characteristic volumes to measure cavity terms in reversed phase liquid chromatography. Chromatographia 23 243-246. 

Zhao and coworkers [53] also constructed a linear model using the Abraham descriptors. The MLR model possesses good correlation and predictability for external data sets. In this equation, E is an excess molar refraction (cm3/mol/ 10.0) and S the dipolarity/polarizability, A and B are the hydrogen bond acidity and basicity, respectively, and V is the McGowan characteristic volume (cm3/ mol/100). The large coefficients of A and B indicate too polar molecules having poor absorption. 

Here E is the solute excess molar refractivity, S is the solute dipolarity/ polarizability A and B are the overall or summation hydrogen-bond acidity and basicity, respectively and V is the McGowan characteristic volume lower-case letters stand for respective coefficients which are characteristic of the solvent, c is the constant. By help of sfafisfical methods like the principal component analysis and nonlinear mapping, the authors determined the mathematical distance (i.e., measure of dissimilarify) from an IL fo seven conventional solvents immiscible with water. It appears that the closest to the IL conventional solvent is 1-octanol. Even more close to IL is an aqueous biphasic system based on PEG-200 and ammonium sulfate (and even closer are ethylene glycol and trifluoroethanol, as calculated for hypofhefical water-solvenf sysfems involving fhese solvenfs). 

Any changes in the load size, load configuration, or container characteristics (volume, geometry, etc.) must be accompanied by repeat validation studies to prove that the cool spot location has not changed or, if it has, that it receives the design F0 time exposure from the sterilization cycle used. 

In order to compare the results from PD with the simulations, the input properties, and silo geometry have to be the same. As the results of PD in the previous section are based on a first order negative exponential correlation function, this function was used as well for the simulations. Three different input properties were used with different characteristic volumes (Vci) 40 and 400 m3. The silo volume was approximately 40,000 m3, with a height of 50 m and a diameter of 32 m. This relatively high silo was chosen because constant angles over the silo height are required (as indicated in Fig. 1) for a thorough comparison with PD. As the input properties are realizations of a stochastic process 400 repetitions were done per simulation. 

A better correlated input signal will leave less space for improvement compared to the previous. Fig. 3 shows the improvement of the auto correlation functions for Vc = 400 m3. It follows that the characteristic volume of the output property (Fco) is just slightly higher compared to Vci = 40 m3 Vco 3400 m3 versus Vco 3200 m3 for a = 0° and /S = 30°. 

Tables 1 and 2 both show the reduction of the standard deviations relative to the mean value of the input calculated by the simulations and PD for different stacking (a) and reclaiming (f ) angles. I cj in the upper left of the tables indicates the characteristic volume of the input property used for the calculations and simulations.

Young fish that has not started its reproductive cycle with the absence of secondary sexual characteristics. Volume 1(14). 

The simplest model of the condensed phase is represented by the lattice-gas model [50]. It reflects two major features of the any species in the condensed phase, viz., their characteristic volume and species interactions. The volume of a crystalline solid is characterized by its natural lattice. With a good approximation, one can consider that the subsurface region of a solid is... 

So, at any site there must be a particle of one species or another Y i= ff — First, let us consider the ideal models that take into account a characteristic volume of the adspecies only, and the ideas of the lateral interactions between the adspecies. 

As described in Sect. 4.4.1, this rate can also be expressed in terms of the characteristic volume by using the specific surface of mass transfer (4.22)... 

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