Methods for Characterizing Branching Distribution in Polymers

A method of polymer analysis comprising:

• a) providing first and second chromatographic columns in series, at least one of which elutes polymer as a function of crystallizability, as represented by crystallization temperature, melting temperature, or dissolution temperature (T);
• and the other column elutes polymer as a function of its molecular weight (M) characteristics;
• b) eluting a polymer through the first column to form elution fractions, followed by eluting each of the fractions from the first column, in any order, through the second column to obtain an independent analysis by the second column for each of the fractions from the first;
• c) detecting the polymer exiting the second column and calculating the molecular weight distributions of the polymer fractions from the first column;
• d) calculating a two dimensional mass distribution of the polymer molecules with an axis for the crystallizability (T) and an M axis;
• e) calculating the Covariance of the eluting fractions by:
• Covariance=∫∫0,0∞,∞(T−Tw)(M−Mw)wM(T,M)dTdM
• wherein:
• T is the gradient (dissolution temperature or solubility) at which the polymer fraction dissolves;
• Tw is the weight-average dissolution temperature of the whole polymer;
• M is the molecular weight of a polymer fraction;
• Mw is the weight-average molecular weight of the whole polymer;
• wM (T, M) is the bivariate mass distribution (BVMD) of the crystalline portion of the polymer;
• and
• f) wherein the Covariance is calculated for each polymer as integrated over all the BVMD.