Gel permeation chromatography of poly(N-vinyl-3,6-dibromocarbazole). Universal calibration, nonexclusion effects, and incompatibility

Abstract

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...

Theoretical evaluation ofKp in size-exclusion chromatography from a thermodynamic viewpoint

“…A similar equation differing only in the two last terms has already been derived by Barrales-Rienda et al [39] and Tejero et al [40] Chromatographic evaluation of K p In size exclusion chromatography (SEC) on organic packings, the universal calibration concept [41] is well established for different polymers and solvents providing that the solvents are good for the polymers. However, when polymers are eluted in poor or "theta" solvents, solute-gel interactions become important and secondary mechanisms appear.…”

“…On the contrary, due to the incompatibility between polymeric solute and gel the V e values are shifted towards smaller retention volumes. [39] Therefore, a theoretical expression for the distribution coefficient of the solute between the solvent and the gel, K p , has been previously derived. [39,40] In this paper we present a more extended theoretical procedure to evaluate K p from chromatographic measurements.…”

“…(4), the quotient b 2 /b 20 can be referred as the partition coefficient K p . [39,[44][45][46] In this equation, b 20 tends to zero as it is usual in chromatographic experiments (note that V e is determined when b 20 e 0) Eq. (4) can thus be transferred into Eq.…”

Size‐Exclusion Chromatography in Single and Mixed Eluents: Effects of Sorption of Solvent and Polymer Solutes on Novel TSK‐Gel Super AW Columns

“…1 values with hydrodynamic size are related to polymer -gel adsorption, [7,33] whereas K p , 1 decreasing values with rising size suggest repulsions between polymer and gel. (9), the corresponding K p coefficients for all the systems under study (values not shown).…”

“…2a) or CHCl 3 (Fig. The magnitude of these shifts must be a function of polymer size, through the K p dependence on molar mass, [7,33] that can result in different "shapes" of the log M[h] vs. V e plots. The above findings can also be explained through thermodynamic considerations.…”