# Plate Theory and Extensions - The Column Dead Volume > Page 32

All static
phases will contribute to retention and, consequently, a number of different
distribution coefficients will contribute to the solute retention. Some
simplification is possible The static interstitial volume (V_{I(s)}) and the pore volume fraction (V_{p}_{(1)}) will contain mobile phase that has
the same composition as the moving phase and, consequently,

K = K_{1} = 1

Thus, equation (37) will be reduced to

V_{r} = V_{I(m)} +
V_{I(s)} + V_{p}_{(1)} + K_{2}V_{p}_{(2)} + K_{3}V_{S(A)} (38)

Equation (38) is more precise than equation (36) but does not account for any exclusion that the support may introduce. In addition, as the particles are close-packed and touching some additional exclusion may take place in the interstitial volume, around the points of contact. The pore size can range from about 1-3 Å to several thousand angstrom and, thus, may partially exclude some components of a mixture particularly if the components cover a wide range of molecular weights. It follows that equation (38) must be further modified,

V_{r} = V_{I(m)} + YV_{I(s)} + WV_{p}_{(1)} + WK_{2}V_{p}_{(2)} + xK_{3}V_{S(A)} (39)

where (Y) | is that fraction of the static interstitial volume accessible to the solute, |

(W) | is that fraction of the pore volume accessible to the solute, |

and (x) | is the fraction of the stationary phase accessible to the solute. |

In most cases, (W) and (x) are likely to be equal, but, in equation (39) the general case is assumed. Equation (39) is an explicit and accurate expression for the retention volume of a solute. The significance of each function will depend on the physical properties of the chromatographic system. At one extreme, using an open tubular column in GC, then

V_{I(s)} =_{ }V_{p
}= 0_{ }_{ }

Thus, in this
case the simple form of equation (36) is quite adequate. Conversely, for a wide
pore silica base, separating small molecular weight materials using a single
solvent mobile phase, the contents of the pores will be homogeneous so K_{2} =1, and as there will be little or no exclusion, W = x = 1

and
V_{r} = V_{I(m)} + YV_{I(s)} + V_{p}
+ K_{3}V_{S(A)}

Clearly, equation (39) must be modified to suit the experimental conditions chosen for measurement.