Expression in terms of retentions

Enantioseparation is typically achieved as a result of the differences in interaction energies A(AG) between each enantiomer and a selector. This difference does not need to be very large, a modest A(AG) = 0.24 kcal/mol is sufficient to achieve a separation factor a of 1.5. Another mechanism of discrimination of enantiomers involves the preferential inclusion of one into a cavity or within the helical structure of a polymer. The selectivity of a selector is most often expressed in terms of retention of both enantiomers using the separation factor a that is defined as ... 

Provided the annealing process described above leads to retention (the re-formation of the parent compound, or a species which produces the parent compound on chemical analysis), Eq. (3) can be expressed in terms of retentions as follows... 

It was pointed out earlier that the velocity of migration of a species through the FFF channel is determined by the level of compression of that species against the accumulation wall by the applied driving force. More specifically, the migration velocity depends upon the effective thickness I of the compressed layer of molecules. Migration velocity v is most often expressed in terms of retention ratio jR, where R = vl<[v > here < t > is equal to the mean flow velocity of the carrier liquid in the channel. Clearly, the higher the values of v and JR, the shorter the retention time and the smaller the retention volume V. This inverse relationship is expressed by... 

Resolution also may be expressed in terms of retention indices of two components ... 

RETENTION EXPRESSED IN TERMS OF VOLOHE weight of liquid phase in the colvnm... 

In Equation 1.15, q represents the adsorbed amount of solute, ns and qs are the saturation capacities (number of accessible binding sites) for site 1 (nonstereoselect-ive, subscript ns) and site 2 (stereoselective, subscript s), and fens and bs are the equilibrium constants for adsorption at the respective sites [54]. It is obvious that only the second term in this equation is supposed to be different for two enantiomers. Expressed in terms of linear chromatography conditions (under infinite dilution where the retention factor is independent of the loaded amount of solute) it follows that the retention factor k is composed of at least two distinct major binding increments corresponding to nonstereoselective and stereoselective sites according to the following... 

Typically, the liquid permeabilities are obtained with water being the permeate and expressed in terms of L/h-m -bar. The gas permeabilities are often expressed in terms of air or nitrogen permeabilities. The retention characteristics can be generally and generically obtained by using some model molecules. The most commonly used model molecules are polyethylene glycol (PEG) polymers which are linear and flexible in nature, and... 

Therefore, the retention volume is expressible in terms of the two measurable quantities... 

In common with all other interactive modes of chromatography, the relative retention of a peptide in RPC can be expressed in terms of the equilibrium association constant, K.dSS0C, the concentrations (in moTL-1) of the peptide present in the stationary and mobile phases, i.e. [A]s and [T]m, and the volumes of the stationary and mobile phases, Vs and Vm respectively, within a column of length L and internal diameter dc Since KdSS0C is the ratio [A]s/[A]m, whilst... 

As the Gibbs standard free energy for the peptide-nonpolar ligand interaction decreases, and AGassoci becomes increasingly negative, enhanced retention will occur. The relationship between the relative retention of a specific peptide in a RPC separation process carried out at constant pressure, P, and constant molar volume, V, can thus be expressed in terms of the following well-known, fundamental thermodynamic relationship ... 

Equilibria may be expressed in terms of activity, instead of concentrations. The expression that relates the relative retention volume to the association constant is given by the following equation ... 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

The extent of separation can be quantified in terms of the resolution obtained between two consecutive chromatographic peaks. This resolution can be expressed in terms of three elemental characteristics of chromatographic separation retention, selectivity and efficiency. The influence of each of these three factors on resolution will be discussed. 

The capacity factor k to be discussed shortly, is an alternate measure of retention. While k is used more often than R in chromatography, the use of R is advantageous because (i) it is directly proportional to peak migration velocity and is thus a more direct measure of retention than k (ii) most equations describing chromatography are simpler when expressed in terms of R rather than k and (iii) R is a more universal measure of retention R but not k applies to other perpendicular flow methods such as field-flow fractionation. 

As is evident from the preceding discussion, the retention behavior of a polypeptide or protein P- expressed in terms of the capacity factor k is governed by thermodynamic considerations. Peak dispersion, on the other hand, arises from time-dependent kinetic phenomena, which are most conveniently expressed in terms of the reduced plate height he, . When no secondary effects, i.e., when no temperature effects, conformational changes, slow chemical equilibrium, pH effects, etc. occur as part of the chromatographic distribution process, then the resolution Rs, that can be achieved between adjacent components separated under these equilibrium or nearequilibrium conditions can be expressed as... 

Equations (105) and (106) provide an important linkage between the three essential parameters that dictate the overall quality of the chromatographic resolution, namely, the relative retention, expressed in terms of the capacity factor k the relative selectivity a, and the extent of peak dispersion Nt or he i. Higher system performances and thus larger values of Rs, per unit time... 

In view of Eq. (1), the retention factor in HPLC can be expressed in terms of the two virtual length components as [1]... 

Solute retention is usually expressed in terms of the capacity factor A, and this can be directly related to the equilibrium constant using Eq. (2). The dependence of the capacity factor A ( of a solute Sj on AT is thus given... 

Because the physicochemical basis of chromatographic retention on hydrocarbonacous stationary phases with aqueous eluents and the liquid-liquid partition of solutes between nonpolar organic solvents, e.g., /i-octanol, and aqueous solvents are similar, selectivities can be expressed in terms of partition coefficients by the relationship... 

Here, N is the column efficiency expressed in term of plate number, zu = A /Ai is the separation factor, which characterises the selectivity of separation, and k is the average retention factor of the two sample compounds 1 and 2 (or. to first approximation, the retention factor of the earlier-eluted compound 1). This expression is convenient for separation development and optimisation, as the three terms contributing to the resolution depend on many experimental conditions and the conditions can be adjusted to control each term more or less independently of the other two. (This does not fully apply for the last two terms, as the retention usually changes to some extent when the selectivity is manipulated.)... 

The membrane is the most important part in separation processes since its performance controls the efficiency and the selectivity of the process. Both flux and selectivity expressed in terms of separation or retention factors determine the process economics and usability, and finally the costs of the installation. 

In terms of retentions the Fletcher-Brown expression, Eq. (11), becomes... 

Hence retention volume can be expressed in terms of two measurable quantities Fq and Ft, and Ksec which is a function of solute molecular size and of the column packing pore size. In SEC, it can only vary between zero (total exclusion) and unity (total permeation). 

Resolution also is expressed in terms of time, with V lA) and V,.(B) being replaced with retention times t A) and and w(A) and w(B) being expressed in units of time. 

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