Volume, excluded measurement

Several catalyst densities are used in the literature. True density may be defined as the mass of a powder or particle divided by its volume excluding all pores and voids. In a strict physical sense, this density can be calculated only through X-ray or neutron diffraction analysis of single crystal samples. The term apparent density has been used to refer to the mass divided by the volume including some portion of the pores and voids, and so values are always smaller than the true density. This term should not be used unless a clear description is given of what portion of the pores is included in the volume. So-called helium densities determined by helium expansion are apparent densities and not true densities since the measurement may exclude closed pores. 

As we begin to add structural features like atoms onto crystal lattice sites, we have to pay attention to the size of the features. How efficiently can we pack atoms onto a lattice We have already discussed two measures of the size of an atom or molecule. In Section 9.7, the van der Waals parameter b was related to the volume excluded per mole of molecules, so blNp is one measure of molecular size. In... 

McCabe and Fisher (1965) have measured the excluded volume of protein molecules by means of differential spectroscopy in the near-infrared region. The excluded specific volumes of bovine serum albumin and lysozyme were found to be 0.74 ml/g and 0.68 ml/g, respectively, values which are close to the values of apparent specific volume reported in the literature (Dayhoff et al., 1952 Sophianopoulos et al, 1962). The authors suggested that excluded specific volume as measured by their method is closely associated with the partial specific volume of the protein molecule. 

Because the definition of the adjusted retention volume was given above, and a related definition of the corrected retention volume was given in Chapter 2 (equation 4), we ought to make sure that these two are not confused with one another. Each has its own particular definition the adjusted retention volume, Fr is the retention volume excluding the void volume (measured from the methane or air peak) as shown in equation 9 the corrected retention volume, Vg, is the value correcting for the compres-... 

In molecular exclusion chromatography, the volume of mobile phase (the solvent) in the column outside the stationary phase is called the void volume, Vq. Large molecules that are excluded from the stationary phase are eluted in the void volume. Void volume is measured by passing through the column a molecule that is too large to enter the pores. The dye Blue Dextran (2 X 10 Da) is commonly used. 

The van der Waals parameter b is a measure of the volume excluded due to the finite size of the molecules. Estimate the size of a single molecule from the data in Table 1.1. 

Equation (8.97) shows that the second virial coefficient is a measure of the excluded volume of the solute according to the model we have considered. From the assumption that solute molecules come into surface contact in defining the excluded volume, it is apparent that this concept is easier to apply to, say, compact protein molecules in which hydrogen bonding and disulfide bridges maintain the tertiary structure (see Sec. 1.4) than to random coils. We shall return to the latter presently, but for now let us consider the application of Eq. (8.97) to a globular protein. This is the objective of the following example. 

We saw in Chap. 1 that the random coil is characterized by a spherical domain for which the radius of gyration is a convenient size measure. As a tentative approach to extending the excluded volume concept to random coils, therefore, we write for the volume of the coil domain (subscript d) = (4/3) n r, and combining this result with Eq. (8.90), we obtain... 

The parameter a which we introduced in Sec. 1.11 to measure the expansion which arises from solvent being imbibed into the coil domain can also be used to describe the second virial coefficient and excluded volume. We shall see in Sec. 9.7 that the difference 1/2 - x is proportional to. When the fully... 

The result of this equation describes the quality of the separation on the basis of an ideal size exclusion mechanism with a given pore volume distribution. The quality of the packing is deliberately excluded from this consideration. This parameter should be measured separately and judged by the plate number. The ASTM standard method for HPSEC of polystyrene (4) contains the following equation for resolution (R,) ... 

By definition, the e]q>erlmentally determined average mobile phase velocity Is equal to the ratio of the column length to the retention time of an unretalned solute. The value obtained will depend on the ability of the unretalned solute to probe the pore volume. In liquid chromatography, a value for the Interstitial velocity can be obtained by using an unretalned solute that Is excluded from the pore volume for the measurement (section 4.4.4). The Interstitial velocity Is probably more fundamentally significant than the chromatographic velocity in liquid chromatography (39). 

Vlugt, T. J. H., Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states, Mol. Phys. 2002, 100, 2763-2771... 

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