Universal Calibration and Molecular Weight Averages in Gel Permeation Chromatography Illustrated by Cellulose Nitrate and Poly(oxypropylene)

Abstract

Abstract The nature of the averaging process in the analysis of gel permeation chromatograms was examined for cases where the molecules in the detector cell of the apparatus were of different molecular weight and of the same molecular weight. When the molecules have the same molecular weight, the hydrodynamic volume (1), [⌉]M, averaged across a chromatogram was found to become KMa+1 for any molecular weight average at the elution volume corresponding to that average. [η] is intrinsic viscosity, M is molecular weight, and K and a are the appropriate Mark-Houwink constants. Thus when size separation is by molecular weight, the universal GPC calibration functions include KMn a+1 where Mn is the number average molecular weight. Cellulose nitrate and poly(oxypropylene) were analyzed using three sets of columns and two GPC instruments. KMn a+1, KMw a+1, and [η]Mw were found to represent the hydrodynamic volume since these functions fell on the universal calibration plot for nearly nono-disperse polystyrene standards. The function [η]Mn was displaced from the polystyrene universal calibration plot by factor which equaled Mw/Mn. The slopes and intercepts of the universal calibration plots were found to be completely consistent with the slopes and intercepts of the molecular weight calibration plots showing that the Mark-Houwink constants were correct. Intrinsic viscosity - molecular weight relations were presented for 12.0–12.6%N cellulose nitrate and for low molecular weight poly(oxypropylene), the latter relation being a correction of that of Sholtan and Lie (18).