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Vr= V|(m) + S'VKs) + OVp(i) + nK2Vp(2) + fcK3Vs(A) ............................. (13)
where, (40 Is that fraction of the static interstitial volume accessible to the solute,
(Ï) is that fraction of the pore volume accessible to the solute, and (?) is the fraction of the stationary phase accessible to the solute.
Under some circumstances (Ï) and (?) can be equal, but the general case will be assumed, where they are not equal.
There are two 'dead volumes’ that are chromatographically important, viz,
tÜë L* /»> ÍëîÍ waIi 1ãëë ëëÈ 1Üë i’/' Íëîã! »«*÷1» iivb/4 ÒÊë f ëãã^ëã
uiv aw¹i/t u^cj\j vuiumt; cjiiu urc uittuiuu/itciutti* ucau vviunic. me ivmmci þ
used in the study of peak variance. It is used to calculate the linear velocity of the mobile phase for use in equations that describe the variance per unit length of a column for any given solute. The latter is used for determining the thermodynamic properties of a particular solute from retention data.
The kinetic dead volume is represented in equation (13) by (Vj(m)), and is solely that volume of mobile phase in the column that is moving. The thermodynamic dead volume is given, in equation (13), by,
V|(m) + Wks) + nVp( i)
The thermodynamic dead volume includes those static fractions of the mobile phase that have the same composition as the moving phase, and thus do not contribute to solute retention by differential interaction in a similar manner to those with the stationary phase. It is seen that, in contrast to the kinetic dead volume, which by definition can contain no static mobile phase, and as a consequence is independent of the solute chromatographed, the thermodynamic dead volume will vary from solute to solute depending on the size of the solute molecule (i.e. is dependent on both Wand to). Moreover, the amount of the stationary phase accessible to the solute will also vary with the size of the molecule (I.e. is dependent on (?)). It follows, that for a given stationary phase, It is not possible to compare the retentive properties of one solute with those of another in thermodynamic terms, unless (?), (Ø and (?) are known accurately for each solute. This Is particularly important if the two solutes differ significantly in molecular volume. The experimental determination of (S'), to) and(fc) would be extremely difficult, if not impossible in practice, as it would be necessary to carry out a separate series of exclusion measurements for each solute which, at best, would be lengthy and tedious.
The two functions involving either «2 or K3 , or both, in equation (13) can, in theory, contribute to solute retention. This will depend on whether the solute interacts with the absorbed component of the mobile phase on the surface or penetrates the layer and Interacts with the stationary phase proper. In either case, the accessibility of the solute to the retentive phase is governed by the magnitude of to) and (?) Another important aspect of equation (13) Is its implication on the accuracy with which the capacity factor k‘ can be measured. Now, (k‘), is normally calculated in the following way,
_ (vl(m) + »V|(s) + QVp(1) + n*<2vp(2) + ?K5Vs(a)~Vj (m)- Wl(s)~»Óð(1)
_ ïêãóð,à iWto ....................
V.^\ + wVi/-\ +nV„m
It can be seen from equation (14) that the value calculated for (Þ will carry the same errors as those associated with the measurement of the dead volume which will change with the size of the solute molecule.
However, providing that,
nK2Vp(2)+ ?«3Vs(a)» V|(m) + S'VKs) + OVpd)
Then, the 'corrected retention volume' can be employed for thermodynamic measurements, or correlated with solvent composition, with acceptably low errors.
Some of the characteristic column volumes outlined In the previous argument were determined by Alhedai et at (11) in the examination of a commercially available reverse phase column packing, Zorbax Ce. These authors examined the exclusion properties of the interstitial volume of the column by measuring the retention volume of a number of salts of different molecular volume.The substances used, in ascending order of ion volume, were as follows,
Data Used for the Determination of the Interstitial Volume of the
Substance Retention Volume (ml)
Sodium Nitrate 1.85
Sodium Sulfite 1.87
Sodium Thiosulfate 1.83
Sodium Nltroprusslde 1.64
Potassium Dichromate 1.62
The results obtained are shown as graphs relating retention volume against Ion volume in figure (1). The slope of the curve shown in figure (1) clearly indicates the exclusion properties of the interstitial volume. It is also seen that the charge on the Ion, be It double or single, has little effect on the retention. Extrapolation of the linear curve to zero ion volume gives the value of the total interstitial volume
It is seen that the closest measured value to the moving portion of the interstitial volume is obtained from the retention volume of sodium
dichromate but this is very little different from the retention volume of sodium nitro-prusside.