Retention volume, dependence

In adsorption chromatography, the energy of the interaction of a certain substance X with the pore surface and the variation of retention volumes depending on the polarity of the mobile phase are commonly assessed using Snyder s correlative approach 64). According to this approach, the energy of the interaction of substance X with adsorbent surface A from solvent S can be written as... 

For a given polymer with fixed X0 and Ax, Eqs. (3.15) and (3.16) describe a non-linear but monotonous variation of 0 with the composition of the mobile phase Cb (Fig. 10). The procedure of finding the critical conditions then becomes very simple it is necessary to find two solvents, in one of which (a) the adsorption and in the other one (b) the exclusion mode is operative and then, by changing their ratio, to find the point C where there is no retention volume dependence on the molecular weight of the polymer. The only requirement imposed on the choice of the solvents is that they both should be good solvents. In practice, however, it is... 

C higher than room temperature, the mobile phase (temperature of the mobile phase is supposed to be the same as room temperature in this case) will expand about 1% from when it entered the columns, resulting in an increase in the real flow rate in the column due to the expansion of the mobile phase and the decrease in the retention volume. The magnitude of the retention-volume dependence on the solvent expansion is evaluated to be about one-half of the total change in the retention volume. The residual contribution to the change in retention volume is assumed to be that due to gel-solute interactions such as adsorption. 

Finite Concentration. In this concentration range, surface adsorption results in nonlinear isotherms in which partition coefficients and retention volumes are dependent upon the adsorbate concentration in the gas phase. This means that a single partition coefficient, Ks (= T/c), is insufficient to characterize the process and the differential (3r/3c)T is required. Here, T is the surface excess of adsorbate expressed in mol m z, c Is the gas phase adsorbate concentration, and T is the column temperature. Nonlinear Isotherms give asymmetric peaks, whose shapes and retention volumes depend on the concentration of the probe. 

Thus, the specific retention volume depends on only two factors in a given solvent (MWs is assumed constant) the saturation vapor pressure of the solute P° and the activity coefficient y, of the solute. 

As a rule, a modifying agent is both a component of the carrier gas and a constituent of the stationary phase (surface layer of adsorbent). The situation is somewhat reminiscent of the retention in liquid chromatography, where the surface properties depend on the concentration of the modifier in the mobile phase. Analyte retention volume depends on the nature and partial pressure of the carrier gas additive as well as on the nature of adsorbent surface. Therefore the use of a phase system composed of a (modifier-carrier gas) mixture as mobile phase offers the possibility of fine tuning of selectivity and retention by adjusting the modifier content of both phases [10]. 

The basic assumption in any chromatographic theory is that retention is determined by the thermodynamic factors. In such a way, mobile and stationary phases are interpreted as true thermodynamic phases with volumes Vm and Vs, respectively, so that retention volume depends on the partition (distribution) equilibrium coefficient A" of the solute in these two phases Vr = Vm +KVs-By definition, all enthalpic and entropic interactions between the macromolecules and the chromatographic surface occur in the stationary phase. If the size of macromolecules in solution is comparable with the internal diameter of pores, the entire pore volume represents the stationary phase. Vs = Vp, yet the mobile phase is formed by the interstitial volume only, Vm = Vq. This is not always the case for... 

In liquid-liquid chromatography the retention volume depends on the ratio of activities of the component in the two phases at equilibrium i.e., on the ratio of the activity coefficients at infinite dilution. As liquid-liquid chromatography has been little used so far (because of instability of the chromatographic system), and activity coefficients are not easily accessible, this relationship has not been extensively explored. 

In reversed-pha.se chromatography the retention volume depends very much on the molecular mass of the analyte. Methylene selectivity (i.e., the relative retention of two successive homologues) varies over a much wider range in reversed-phase LC than in GC, and can be quite large [45],... 

Figure 9.1 illustrates the different modes of chromatography and shows the retention volume dependence of the molar mass. 

The yield of each of these fractions will depend on their retention volume which in turn wiil depend on the adsorbent selected and the eluting force of the solvents. 

The second important parameter is the chromatographic peak s width at the baseline, w. As shown in Figure 12.7, baseline width is determined by the intersection with the baseline of tangent lines drawn through the inflection points on either side of the chromatographic peak. Baseline width is measured in units of time or volume, depending on whether the retention time or retention volume is of interest. 

It is seen that, as predicted, the function for the retention volume is indeed simple and depends solely on the distribution coefficient and the volumes of the two phases that are present in the column. 

An eluted solute was originally identified from its corrected retention volume which was calculated from its corrected retention time. It follows that the accuracy of the measurement depended on the measurement and constancy of the mobile phase flow rate. To eliminate the errors involved in flow rate measurement, particularly for mobile phases that were compressible, the capacity ratio of a solute (k ) was introduced. The capacity ratio of a solute is defined as the ratio of its distribution coefficient to the phase ratio (a) of the column, where... 

In general, (Q) and ( ) will be equal, but the general case is assumed, where they are not. Equation (37) gives an explicit and accurate expression for the retention volume of a solute. The importance of each function in the expression will depend on the physical properties of the chromatographic system. At one extreme, using an open tubular column in GC, then... 

If the relationship between retention volume and temperature is known, as well as its dependence on solvent composition, then the combined effect of both solvent... 

The simplest mode of IGC is the infinite dilution mode , effected when the adsorbing species is present at very low concentration in a non-adsorbing carrier gas. Under such conditions, the adsorption may be assumed to be sub-monolayer, and if one assumes in addition that the surface is energetically homogeneous with respect to the adsorption (often an acceptable assumption for dispersion-force-only adsorbates), the isotherm will be linear (Henry s Law), i.e. the amount adsorbed will be linearly dependent on the partial saturation of the gas. The proportionality factor is the adsorption equilibrium constant, which is the ratio of the volume of gas adsorbed per unit area of solid to its relative saturation in the carrier. The quantity measured experimentally is the relative retention volume, Vn, for a gas sample injected into the column. It is the volume of carrier gas required to completely elute the sample, relative to the amount required to elute a non-adsorbing probe, i.e. 

As known, SEC separates molecules and particles according to their hydro-dynamic volume in solution. In an ideal case, the SEC separation is based solely on entropy changes and is not accompanied with any enthalpic processes. In real systems, however, enthalpic interactions among components of the chromatographic system often play a nonnegligible role and affect the corresponding retention volumes (Vr) of samples. This is clearly evident from the elution behavior of small molecules, which depends rather strongly on their chemical nature and on the properties of eluent used. This is the case even for... 

Scott and Reese chose to monitor retention volume as opposed to retention time, as retention volume is always the primary dependent variable in LC. Retention time is not a primary measurement because it must also include the reproducibility of the flow-rate delivered by... 

The extra-column dispersion governs the dimensions of the column that we use. In the calculation above, the dispersion is increased by about 8% by the extra-column effects. If we want the dispersion to be increased by no more than this, then should not be any smaller than the value calculated above. This in turn limits the retention volume, and thus the volume of the column itself. The minimum column volume we can use will depend on the amount of extracolumn dispersion and on what we consider to be an acceptable increase in peak width that is produced by extra-column effects. In practice, this acceptable increase is taken as 10%, based on an unretained solute, and if we take 50 (i as a typical figure for extracolumn dispersion then the minimum column diameter works out at about 4.5 mm for a column 25 cm long. 

In Fig. 3.4d the relative molecular mass of the solute, Mr, is plotted on a log scale against the retention volume. The interstitial volume, which represents the volume range within which separations occur, and the size range of solutes that are eluted in this volume range, depend on the sort of material that is used for the stationary phase. Because for a given separation, F0 and V are constant, we can reliably predict the total volume of solvent or the time taken for a particular analysis. The calibration curve is established by determining the retention volume for standards of known Mr. 

Our system provides for several forms of calibration function, but we generally use "universal" calibration (5) and represent the dependence of the logarithm of hydrodynamic volume on retention volume by a polynomial, as in Figure 6. Note that the slope of the function changes dramatically near the ends of the range of applicability. The calibrants at the ends of the range exert a dramatic influence on the form of the fitted polynomial. This behavior demonstrates that the column set must be carefully chosen to fractionate the desired range of molecular sizes. 

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