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# liquid chromatography column - Scott R.P.W.

Scott R.P.W. liquid chromatography column - John Wiley & Sons, 2001. - 144 p.
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The interstitial volume of the column is also made up of two parts: that fraction of the interstitial volume that is moving (V|(m)), and that fraction that Is close to the points of contact between the individual particles and away from the flow-stream that is essentially static (V|(S))
Hence,
Vi = V|(m) + Vj(s) ..................................................(5)
When mixed solvents are employed as the mobile phase, it has been shown
(10) that one solvent can be absorbed preferentially on, or associated with, the surface of the stationary phase. Consequently, some of the solvent contents of the pore, in close proximity with the stationary phase, will not necessarily have the same composition as that of the original mobile phase.
Therefore,
Vp - Vp(i) * Vp(2) .................................................... (6)
where, (Vp( i)) is that volume of the pore that contains solvent having the same composition as the original mobile phase, and (Vp(2)) Is that fraction of the pore volume having a different composition from that of the mobile phase.
Substituting for (Vi) and (Vp) from equations (5) and (6) in equation (4),
Vm = V|(m) + V|(s) + Vp(i) + Vp(2).................................... (7)
It is now necessary to consider the volume of stationary phase in the column. Owing to the nature of the majority of bonded phases and as a result of their method of manufacture, some of the smaller pores may become completely blocked by the stationary phase itself, and thus some stationary phase may become chromatographically unavailable.
It follows that, Vs = Vs(a) + Vs(u)
(8)
where, (Vs(a)) is the volume of chromatographically available stationary phase,
and (Vs(u)) is the volume of chromatographically unavailable stationary phase.
Substituting for (Vm) and (V\$) from equations (7) and (8) in equation (1),
Vc = V|(m) + V|(s) + Vp( 1) + Vp(2) + Vs(A) + Vs(U) +Vsi .......................(9)
Now from the plate theory, for solute (A), the retention volume is given by,
Vr(A) “ Vo + KA Vs.................................................................... (10)
where (Vr(A)) is the retention volume of solute (A),
(Êä) is the distribution coefficient of solute (A) between the two phases,
and (V0) and (Vs) have the meanings previously ascribed to them (Vs) can be considered to be (Adf), if adsorption is considered to be taking place as opposed to partition between two liquids.
It can be clearly seen from equation (9) that the expression for the retention volume of a solute, although generally correct, is grossly over simplified if accurate measurements of retention volumes are required. Some of the stationary phase may not be chromatographically available and not all the pore contents have the same composition as the mobile phase and, therefore, being static, can act as a second stationary phase. This situation is akin to the original reverse phase system of Martin and Synge where a dispersive solvent was absorbed into the pores of support to provide a liquid/liquid system. As a consequence a more accurate form of the retention equation would be,
vr= V|(m) + KV|(s) + KiVp(i) + K2Vp(2) + l<3Vs(A) ........................ (11)
where, (Þ is the distribution coefficient of the solute between the moving phase and the static portion of the interstitial volume,
(Kj) is the distribution coefficient of the solute between the moving phase and the static pore contents, (Vp( i))
(Êã) is the distribution coefficient of the solute between the moving phase and the static pore contents,(Vp(2)) and (K3) is the distribution coefficient of the solute between the moving phase and the available stationary phase (Vs(a))
All static phases will contribute to retention and, as seen from equation
(II), there are a number of distribution coefficients effecting the retention of the solute. However, the the static interstitial volume (Vj(S)) and the pore volume fraction (Vp(i)), contain mobile phase having the same composition as the moving phase and thus,
K = Ki = 1 Thus, equation (11) reduces to ,
Vr= V|(m) + V|(s)+ Vp(i) ¦ K2Vp(2) + K3Vs(A) ............................(12)
Unfortunately, even this modified equation does not describe the true practical situation in LC, as it is complicated by the fact that all silica-based materials exhibit exclusion properties. The pore diameter of silica-based stationary phases can range from, perhaps, 2-3 Angstrom to as much as 1000-2000 Angstrom. Consequently, some, otherwise open pores, are accessible to the solute while others are not, depending on the size of the molecule. Therefore, only those pores that have a diameter equal to, or greater than, that of the solute molecules are accessible and only the stationary phase within those pores can effect retention. In addition, the static interstitial volume between the particles can also exhibit exclusion properties and some of the static interstitial volume may also be inaccessible to the larger solutes. As a consequence, equation (12) must be further modified to give,
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