Effective molecular volume

From equation (6-2), one can conclude that intrinsic viscosity is proportional to the polymer molecular volume. On the other hand, the effective molecular volume is also the function of the molecular weight and the type of used solvent (or the nature of the solvent-polymer and polymer-polymer interactions). The intrinsic viscosity is an exponential function of the molecular weight with fixed coefficients for any specific polymer and solvent. 

Rawitch (1972) reported a difference in the rate of rotational diffusion, determined from the polarization of fluorescence, which suggested that the effective molecular volume of a-lactalbumin in solution is larger than for lysozyme, and this difference suggests conformational differences. 

Rawitch (1972) found a difference in rotational diffusion of these two proteins and concluded that the effective molecular volume of a-lactalbumin is greater than that of domestic hen lysozyme. 

When this quantity is calculated for each solvent and plotted against 1/r, it apparently shows a decreasing trend with increasing r. The trend in the excess friction of the solutes studied herein may be accounted for by the following model. First we consider that the radical is diffusing accompanied with several solvent (or other solute) molecules and the effective molecular volume of the radical is defined by including the attached solvent molecules around the radical. Next we assume that an unpaired electron has the capability of increasing the effective molecular volume only by a certain amount V. Then we obtain a simple relation between Af and r as,... 

It is a logical requirement that equations of state approach the ideal gas equation at the limit of low pressures. As the pressure decreases, the volume increases so that at very low pressures a/V P and V. If these terms are dropped from the van der Waals equation, it reduces to the ideal gas form. The terms and b account for intermolecular forces and molecular volume. The parameters a and b are called the attraction and repulsion parameters, respectively. The parameter b is also referred to as the effective molecular volume. 

The preceding qualitative observations about the temperature dependence of Ch and Vg — V, can be extended to a quantitative statement in cases for which the effective molecular volume of the penetrant in the sorbed state can be estimated. As a first approximation, one may assume that the effective molecular volume of a sorbed CO2 molecule is 80 A in the range of temperatures from 25 to 85 C. This molecular volume corresponds to an effective molar volume of 49 cmVmol of CO2 molecules and te similar to the partial molar volume of CO2 in various solvents, in several zeolite environments, and even as a pure subcritical liquid (see Tables 20.4-4 and 20.4-5). The implication here is not that mote than one COi molecule exists in each molecular-scale gap, but rather that the effective volume occupied by a CO2 molecule is roughly the same in the polymer sorbed state, in a saturated zeolite sorbed state, and even in a dissolved or liquidiike state since all these volume estimates tend to be similar for materials that are not too much above their critical temperatures. With the above approximation, the predictive expression given below for Cw can be compared to independently measured values for this parameter from sorption measurements ... 

Application of Eq. (20.4-12) to highly supercritical gases is somewhat ambiguous since the effective molecular volume of sorbed gases under these conditions is not estimated easily. A similar problem exists in a priori estimates of partial molar volumes of supercritical components even in low-molecular-weight iiqui. The principle on which Eq. (20.4-12) is ba remains valid, however, and while the total amount of unrelaxed volume may be available for a penetrant, the magnitude of Cj, depends strongly on how condensable the penetrant is, since this factor determines the relative efficiency with which the component can use the available volume. 

With nonpolar sorbates an increase in heat of adsorption with coverage is commonly observed, as illustrated in Figure 4.5 and this is commonly attributed to the effect of intermolecular attraction forces. The statistical model isotherm, however, suggests an alternative explanation. If the effective molecular volume increases with temperature, as it generally does, the isosteric heats... 

The extension of the simple statistical model to adsorption of a binary mixture is given by Eq. (3.102) and further extension to multicomponent systems follows naturally. " The parameters of the model (the Henry con-stant and effective molecular volume for each component) are derived from the single-component isotherms so that an a priori prediction of the mixture... 

Azeotrope formation and selectivity reversal appear to be fairly common features of binary adsorption equilibrium behavior but are not predicted by most of the simpler models such as Eqs. (4.11) or (4.16). Such behavior is predicted by Eq. (3.102) when the effective molecular volumes of the components are different and the component with the smaller volume also has the smaller Henry constant but only at relatively high sorbate concentrations. The experimental data for C2H4-CjHg in 5A show that selectivity reversal occurs even at relatively low loading (high temperatures) and is much more... 

The development of rigorous theoretical treatments for the elution behavior of small molecules has been largely ignored due to the adequacy of predictive ability of log M, log effective molecular length (ref. 9) or log effective molecular volume models (ref. 10). However, the calculation of these parameters for macromolecular solutes with the same degree of confidence is not yet possible. 

The above mentioned formulae are based on the assumption that a vdW interaction of the atoms at any distance do not affect their polarizabilities. In fact, the observed polarizabilities of rare gases and molecular substances vary, depending on the aggregate state. The relative variations range from 0.3 % for Ar to 16.8 % for I2 [19]. On condensation of molecules, the polarizability can decrease (e.g., by 3.2 % for CF4 or SnBr4) or increase (by 3.0 % for CI2, 6.6 % for Br2, 16.8 % for I2) [20]. Given that the effective molecular volume always decreases on condensation, this increase of polarizability can be caused only by accumulation of electron density between molecules. Some clue can be provided by the so-called Muller s factor, the ratio between the (relative) changes of refraction, E, and of volume, V [21],... 

The final model was obtained by linear regression on a set of 320 different molecules [2]. Since the effective molecular volumes used gave a practically zero intercept, we imposed a zero intercept and obtained a consistent model with only three adjustable parameters ... 

A more recent study on 28 compounds reinforced this observation [77]. It showed that molecular size alone, as measured by calculated effective molecular volume (K) [2] on AMI [33] optimized structures, accounts for -70% of the variance in the pA2 values measured by guinea pig ileum assay (Figure 4) ... 

The relation between the cube root of the effective molecular volume of oxides (VJJ) and the radius of resp>ective cations (rm) is plotted in Fig. 5 for a series of oxides. The volume of the molecule of M jO oxide was calculated dividing the imit cell volume by the number of molecules (Z) and by the munber of oxygen atoms (b) in the MaOb oxide. It will be further called the effectioe molecular volume ( (Vj j /Z)/b = ) (Stoklosa Laskowska, 2008b). As... 

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