Plate Theory and Extensions - The Column Dead Volume > Page 30

Initially, (VM) will be divided into two parts, that contained in the pores (Vp) and that contained in the interstitial volume (VI), thus,

                                       VM  = VI + Vp                                 (30)

 

The interstitial volume can also be divided into two parts, the interstitial volume that is actually moving (VI(m)) and that portion of the interstitial volume close to the points of contact of the particles that is static (VI(s)).

Hence,                           VI = VI(m) + VI(S)                              (31)

If the mobile phase is a solvent mixture, the pore contents will not be homogeneous. On component (that with stronger interactions with the stationary phase) will be preferentially adsorbed on the surface [10] relative to the other. Thus, although the bulk of the pore contents (Vp(1)), will have the same composition as the mobile phase, the pore contents close to the surface, (Vp(2)), will have a composition that differs from the bulk mobile phase.

Hence,                           Vp = Vp(1) + Vp(2)                             (32)

 Substituting for (Vi) and (Vp) from  (31) and (32) in (30), a more informative distribution of the mobile phase becomes apparent,

                 VM  =   VI(m) + VI(S) +  Vp(1) + Vp(2)                   (33)

The stationary phase can be apportioned in a similar manner. For  a bonded phase, as the support is porous, some of the pores will be blocked with stationary phase and the total amount of stationary phase can be divided into that which is chromatographically available (VS(A)) and that which is chromatographically unavailable (VS(U)).

 It follows that,

                                 VS = VS(A) + VS(U)                                 (34)

Substituting for (VM) and (VS) from equations (33) and (34) in equation (25), an expression for the total column volume can be obtained,

    Vc =  VI(m) + VI(s) +  Vp(1) + Vp(2) +  VS(A) + VS(U) +VSi   (35)