Separation factor parameters

The Smith-Brinkley Method uses two sets of separation factors for the top and bottom parts of the column, in contrast to a single relative volatility for the Underwood Method. The Underwood Method requires knowing the distillate and bottoms compositions to determine the required reflux. The Smith-Brinkley Method starts with the column parameters and calculates the product compositions. This is a great advantage in building a model for hand or small computer calculations. Starting with a base case, the Smith-Brinkley Method can be used to calculate the effect of parameter changes on the product compositions. 

Calculations for Rp as a function of the relevant experimental parameters (eluant ionic species concentration-including surfactant, packing diameter, eluant flow rate) and particle physical and electrochemical properties (Hamaker constant and surface potential) show good agreement with published data (l8,19) Of particiilar interest is the calculation which shows that at very low ionic concentration the separation factor becomes independent of the particle Hamaker constant. This result indicates the feasibility of xmiversal calibration based on well characterized latices such as the monodisperse polystyrenes. In the following section we present some recent results obtained with our HDC system using several, monodisperse standards and various surfactant conditions. 

Having chosen the test mixture and mobile diase composition, the chromatogram is run, usually at a fairly fast chart speed to reduce errors associated with the measurement of peak widths, etc.. Figure 4.10. The parameters calculated from the chromatogram are the retention volume and capacity factor of each component, the plate count for the unretained peak and at least one of the retained peaks, the peak asymmetry factor for each component, and the separation factor for at least one pair of solutes. The pressure drop for the column at the optimum test flow rate should also be noted. This data is then used to determine two types of performance criteria. These are kinetic parameters, which indicate how well the column is physically packed, and thermodynamic parameters, which indicate whether the column packing material meets the manufacturer s specifications. Examples of such thermodynamic parameters are whether the percentage oi bonded... 

The chiral recognition ability of a CSP is quantitatively evaluated from the results of chromatographic separation of enantiomers. Figure 3.4 shows a chromatogram of the resolution of benzoin (19) on cellulose tris(3,5-dimethylphenylcarbamate). The (+)-isomer elutes first followed by the (—)-isomer complete baseline separation is achieved. The results of the separation can be expressed by three parameters—capacity factors (k1), separation factor (a), and resolution factor (Rs)—defined as follows ... 

The resolution can be improved by increasing the column plate number, N, and/ or the separation factor, a (a = the ratio of the retention factors of the two compounds). N is the physical parameter and a is the chemical parameter for the separation. Higher N and a values give a better separation. 

To verify such a steric effect a quantitative structure-property relationship study (QSPR) on a series of distinct solute-selector pairs, namely various DNB-amino acid/quinine carbamate CSPpairs with different carbamate residues (Rso) and distinct amino acid residues (Rsa), has been set up [59], To provide a quantitative measure of the effect of the steric bulkiness on the separation factors within this solute-selector series, a-values were correlated by multiple linear and nonlinear regression analysis with the Taft s steric parameter Es that represents a quantitative estimation of the steric bulkiness of a substituent (Note s,sa indicates the independent variable describing the bulkiness of the amino acid residue and i s.so that of the carbamate residue). For example, the steric bulkiness increases in the order methyl < ethyl < n-propyl < n-butyl < i-propyl < cyclohexyl < -butyl < iec.-butyl < t-butyl < 1-adamantyl < phenyl < trityl and simultaneously, the s drops from -1.24 to -6.03. In other words, the smaller the Es, the more bulky is the substituent. The obtained QSPR equation reads as follows ... 

FIGURE 1.11 Systematic optimization of structural binding and stereorecognition increments of amino acid side chain (Rsa) carbamate residue (Rso)- Dependency of separation factors on the steric bulkiness of amino acid and carbamate residues as quantified by their corresponding Taft s steric parameters Es sa Eg so- (1) ionic interaction (2) jr-jr-interaction (3) hydrogen bonding (4) steric interaction. (Reproduced from M. Lammerhofer et al., J. Sep. ScL, 29 1486 (2006). With permission.)... 

There are few studies in literature reporting pure gas permeabilities as well as separation factors of mixtures. Vuren et al. (1987) reported Knudsen diffusion behavior of pure gases for y-alumina membranes with a mean pore radius of 1.2 nm. Separation experiments with a 1 1 H2/N2 mixture showed, that the theoretical Knudsen separation factor [of 3.7, Equation 6.4)j for this mixture could be obtained (Keizer et al. 1988 see also Figure 6.2). In Figure 6.2, the effect of process parameters is also demonstrated. The separation factor is a function of the pressure ratio over the membrane, which is the ratio of the pressure on the permeate-side to that on the feed-side. For pressure ratios approaching unity, which means the pressure on both sides of the... 

When the membrane performs only a separation function and has no catalytic activity, two membrane properties arc of importance, the permeability and the selectivity which is given by the separation factor. In combination with a given reaction, two process parameters are of importance, the ratio of the permeation rate to the reaction rate for the faster permeating component (c.g. a reaction product such as hydrogen in a dehydrogenation reaction) and the separation factors (permselectivities) of all the other components (in particular those of the reactants) relative to the faster permeating gas. These permselectivities can be expressed as the ratios of the permeation rates of... 

On the other hand, model calculations varying parameters, show clearly that the smaller diameter capillaries, representative of the porous matrix, do play a controlling role In the separation factor behavior. 

The presence of the pores adds two parameters - the pore volume fraction and the pore radius. The predicted Rp Increases as the pore radius decreases suggesting a preference tor small pore packings. However, for a small pore radius of 1.0 pm a single value of the separation factor corresponds to two values of the particle diameter (13). Such double-valued behavior Is of course undesirable In an analytic technique. 

Figure 3. Separation factor-particle diameter behavior computed from the pore-partitioning model showing the effect of the Hamaker constant at a low eluant ionic strength (O.OOl M). Other parameters are = 0.60, interstitial capillary radius = l6 fim, pore radius = fim,...

Figure 5. Separation factor-particle diameter behavior as a function of the pore radius for the pore-partioning model. Hamaker constant = 0.05 pico-erg all other parameters are the same as in Figure 3.

Figure 6. Separation factor-particle diameter tehavior as a function of packing diameter for the pore-partitioning model. Parameters are the same as in Figure 3 with the exception of the interstitial capillary radius which was computed from the hed hydraulic radius (Equation 11 (7.) with void fraction = 0.358).

When studying a new separation, the separation factors applicable to the considered medium are first determined in our laboratories. Then the various parameters are fed into a computer which uses a program similar to the one used in fractional distillation. The data obtained are usually in excellent agreement with the results of commercial scale operations. 

Factor Analyses. In an attempt to identify sources of the various elements, factor analyses were carried out separately on two data sets representing 1) filters exposed face down under an inverted funnel rain shield, and 2) filters exposed in a vane sampler continuously facing into the wind. Within each data set, separate factor analyses were performed on the data expressed as 1) concentrations in air (ng m ) and 2) abundances (percent of total mass). Rain amount, rain duration, and soil moisture data were included in early analyses, but these parameters were later dropped from the data sets because they had no significant relationship to any of the elements. Wind direction frequencies were included in the data sets throughout the analyses, however. 

The parameter La is also called the separation factor and provides a quantitative description of the equilibrium regions La = 0 for irreversible, La< 1 for favorable, La = 1 for lineal-, and La > 1 for unfavorable adsorption. The same holds for Fr in Freundlich s isotherm. 

The separation efficiency for a given membrane with a particular binary gas mixture will be dependent mainly upon three factors gas composition, the pressure ratio between feed and permeate gas, and the sepration factor for the two components. A higher separation factor gives a more selective membrane, resulting in a greater separation efficiency. This parameter is a function of the membrane material and is determined by the individual gas permeation rates. 

In this equation i represents the first eluting peak of a peak pair and j the last eluting peak. Hence, by definition a is always larger than unity. Sometimes a is called the separation factor, which is somewhat unfortunate terminology because separation is influenced by other factors than just a (see section 1.3). a is the chromatographic parameter that is most directly related to the selectivity of the phase system. In this book, therefore, the word selectivity will often be associated with a. Using eqns.(1.7) and (1.10) we can write two other equations for a, . 

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