Measurement of Void Volume

Measurement of Void Volume. It is generally believed that the injection of so-called unretained component can be used for the measurement of the column void volume. The biggest challenge is to find a compound that is really unretained. In the last 40 years, many different analytes have been... 

The retention factor, Eq. (7.2), for each species / is calculated knowing the dead time, t(), and the retention time of species i at infinite dilution, /r,./- There are known methods in the literature for calculating the dead time or retention time for a non-retained peak in normal-phase, reversed-phase and ion-exchange chromatography [67]. For example, in normal-phase chromatography, pentane in 95 5 hexane-acetone is unretained. In reversed-phase chromatography, a common measure of void volume is from the refractive index response obtained when the sample solvent composition is different from the mobile-phase composition. 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

The volume of the solid phase Vp is usually measured by a pycnometric technique, which measures the excluded volume of a pycnometric fluid, whose molecules cannot penetrate the solid phase of PS. A simple example of a pycnometric fluid is helium [55], The pycnometric fluid fill in all void space (pores) accessible to it, and presumably do not adsorb on the surface of PS. In the case of microporous PSs, measurement of the volume accessible for guests with various sizes allows the determination of a distribution of micropores volume vs. the characteristic size of guest molecules. This approach lays the basis of the method of molecular probes. The essence of this method is in the following we have a series of probe molecules with different mean sizes (dl>d2>d3>---). The pycnometric measurements of the excluded volume will give a series The difference A V=Vpi-Vpi(i>j) corresponds to the volume of micropores with pycnometric sizes of d in a range dt[Pg.283]

Clearly by working with typical spatial resolutions of approximately 30-50 pm, individual pores within the material are not resolved. However, a wealth of information can be obtained even at this lower resolution (53,54,55). Typical data are shown in Fig. 20, which includes images or maps of spin density, nuclear spin-lattice relaxation time (Ti), and self-diffusivity of water within a porous catalyst support pellet. In-plane spatial resolution is 45 pm x 45 pm, and the image slice thickness is 0.3 mm. The spin-density map is a quantitative measure of the amount of water present within the porous pellet (i.e., it is a spatially resolved map of void volume). Estimates of overall pellet void volume obtained from the MR data agree to within 5% with those obtained by gravimetric analysis. 

The void volume can be determined by displacement in water. This is problematic when investigating a hydrophilic polymer or when accurate measurements are required. A good estimate of void volume can be obtained by comparing the absolute density of the polymer with the bulk density determined via ASTM D3574-95. For instance, let us assume that isocyanate and the polyol have specific gravities of 1.0. If a polyurethane is made of this combination, the absolute density of the polymer... 

C. A. Rimmer, C. R. Simmons, and J. G. Dorsey,The measurement and meaning of void volumes in reversed-phase liquid chromatography, J. Chromatogr. A 965 (2002), 219-223. 

A peak close to the origin may be due to non-retained sample molecules, flowing at the same rate as the mobile phase, or to artefacts, e.g. air (GC) or solvent (HPLC) in the sample. Whatever its origin, this peak can be used to measure the void volume and dead time of the column (p. 207). No peaks from genuine sample components should appear before this type of peak. 

When the major catalytic surface is in the interior of a solid particle, the resistance to transport of mass and energy from the external surface to the interior can have a significant effect on the global rate of reaction. Quantitative treatment of this problem is the objective in Chap. 11. It is sufficient here to note that this treatment rests on a geometric model for the extent and distribution of void spaces within the complex porous structure of the particle. It would be best to know the size and shape of each void space in the particle. In the absence of this information the parameters in the model should be evaluated from reliable and readily obtainable geometric properties. In addition to the surface area, three other properties fall into this classification void volume, the density of the solid material in the particle, and the distribution of void volume according to void size (pore-volume distribution). The methods of measurement of these four properties are considered in Secs. 8-5 to 8-7. 

A more accurate procedure is the helium-mercury method. The volume of helium displaced by a sample of catalyst is measured then the helium is removed, and the volume of mercury displaced is measured. Since mercury will not fill the pores of most catalysts at atmospheric pressure, the difference in volumes gives the pore volume of the catalyst sample. The volume of helium displaced is a measure of the volume occupied by the solid material. From this and the weight of the sample, the density of the solid phase, P5, can be obtained. Then the void fraction, or porosity, of the particle, p, may be calculated from the equation... 

In the absence of experimental data it is necessary to estimate from the physical properties of the catalyst. In this case the first step is to evaluate the diffusivity for a single cylindrical pore, that is, to evaluate D from Eq. (11-4). Then a geometric model of the pore system is used to convert D to for the porous pellet. A model is necessary because of the complexity of the geometry of the void spaces. The optimum model is a realistic representation of the geometry of the voids, with tractable mathematics, that can be described in terms of easily measurable physical properties of the catalyst pellet. As noted in Chap. 8, these properties are the surface area and pore volume per gram, the density of the solid phase, and the distribution of void volume according to pore size. 

Positron Annihilation Lifetime Spectroscopy (PALS) provides a measure of free volume holes or voids, free volume, and free volume distribution, at an atomic scale. The technique exploits the fact that the positively charged positron (e" ), the antiparticle to the electron, preferentially samples regions of low positive charge density. When injected in a polymer matrix, thermalized positrons can combine with an electron to form a bound state, known as positronium (Ps). This species can only exist in a void and it rapidly annihilates on contact with the electron cloud of a molecule. For polymer studies using PALS, it is ortho-positronium (oPs, a triplet state) which is of interest. The oPs spin exchanges with electrons of opposite spin on the walls of the cavity and it is annihilated. Thus, the oPs lifetime, 13, gives a measure of the mean free volume cavity radius, whereas the relative intensity of... 

Pore-volume distribution, distribution of void volume according to pore size or radius of pore mouth, is measured by N2 adsorption-desorption experiments [5, 8]. 

In a recent publication reviewing the status of research into intrinsic oscillations in solid-catalyzed reactions (l ), we emphasized the potential exploitation of combined theoretical and experimental studies of oscillatory behavior for obtaining new insights into catalytic reaction mechanisms and kinetics. In the present paper, we elaborate further on the subject of formulating and analyzing kinetic models which account for oscillatory behavior, and we present some new experimental information for the oscillatory oxidation of CO on a platinum foil. As in reference 1, the analysis here is applied to models describable by two first-order differential equations. The laboratory data reported were obtained from an isothermal gradientless CSTR of void volume h60 cm3 into which there was inserted a platinum foil of area 200 cm2. Continuous measurements were made of the CO2 concentration in the effluent stream. The experimental system is described in detail elsewhere (, . ... 

Therefore, a somewhat arbitrary reference pressure must be chosen for defining the total volume. The void volume of carbon black at a pressure of 0.18 MPa was chosen to be the reference in this case. This level for the reference pressure has a practical significance in that it is lower by one order of magnitude than the pressure exerted by the rotor blade of an internal mixer. Accepting this definition of void volume, the degree of penetration into the void volume, PEN, in Table 3.3, becomes a good measure of the degree of compaction. Under the present set of experimental conditions 30-35% of the void volume was penetrated by the elastomer. 

It is likely that volumetric measures were used for quantity deterrnination when commodities were first bartered however, it has been established with certainty that weighing scales or balances have been in use for at least 7,000 years (1). Measuring by weight instead of by volume eliminates some very considerable inaccuracies from, for example, changes in specific gravity of liquids with temperature, or changes in density of solids owing to voids. 

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