Nonexclusion effects in the GPC of poly(N-vinyl-3,6-dibromocarbazole) ) in tetrahydrofuran, at 25 "C, using cross-linked polystyrene (PS) as the gel phase, are analyzed by use of the universal calibration method. The first point in order to determine such nonexclusion effects is to use values for the hydrodynamic volume and the elution volume truly representative of the samples. We show that an adequate set of average magnitudes is the weight-average intrinsic viscosity of the sample, the viscosity-average molecular weight, and the elution volume defined as the viscosity average by means of vv, = log {J3?,(V)[l(P1v] dVJ('/OAL), where H,( V) represents the relative weight of the normalized chromatogram for sample i at elution volume V , a is the exponent in the Mark-Houwink equation for the system under study, and A, is the coefficient of the linear term in the log M vs. V calibration of GPC valid for samples constituted of monomolecular species. The early elution of PVK-3,6-Br2 in THF, as compared with PS standards, can be represented by the equationwhere V , is the retention volume, V,, the interstitial volume, V , the solvent volume within the gel, KD the distribution coefficient for steric exclusion, which is given by KD = -A log ([TIM) + B (A and B are constants), and K is a distribution coefficient for solute-gel interactions. The values of K , found in the present system are gelow unity, and their molecular weight dependence can be represented by -In K, -X,, where X, is the degree of polymerization of the polymer molecule in the mobile phase. In the formulation of Dawkins this corresponds to incompatibility between eluted polymer (2) and gel (3), and -In K,/X, = @3(l + x23), where @3 is the volume fraction of the gel in the stationary phase and ~2 3 the polymer-gel interaction parameter per polymer repeating unit. The compatibility of PVK-3,6-Br2 with PS in THF solution is studied by determining the phase-separation diagram of the ternary system THF (1) + PVK-3,6-Br, (2) + linear PS(3), from which a value of xB at the plait point is determined. The equilibrium distribution of solute polymer (2) between the mobile phase and the gel is treated thermodynamically as a problem in preferential sorption in a ternary system (selective adsorption or desorption of 2 by 3 from the 1 + 2 solution). The result of this thermodynamic treatment is -In K,/X, = b3(l + g23 -g12 -g13), which is similar to the one given by Dawkins, but now it includes the additional contribution of the polymersolvent and gel-solvent interaction parameters g,, and g13. These g,'s and the x,,'s defined on the basis of chemical potential are connected through xi, = g,, -(1 -@,)(dg,,/d@,). The value of gl, + g13 can be of the order of unity so that (1 -g12 -g13) can approximately cancel. This expression gives thus the conditions under which K, can be unity or differ from unity depending on the balance of the interaction parameters.
IntroductionAs has been recognized for a long time, steric exclusion from a theoretical point of view is the only...