MODELING THE FRACTIONATION PROCESS IN TREF SYSTEMS .2. NUMERICAL-ANALYSIS

Temperature raising elution fractionation (TREF) allows qualitative sh ort chain branching (SCB) analysis in copolymers. In order to make the analysis quantitative, information on how such fractionation occurs m ust be incorporated into the interpretation of TREF spectra. In a prev ious work a model of the fractionation was proposed and some prelimina ry results given. In this article a rigorous mathematical analysis of the solution of the fractionation model is presented by defining two p roblems. The direct problem, of little practical use, helps to underst and the fractionation process. The inverse problem consists in obtaini ng the distribution of crystallizable lengths (DCL) (directly related to the SCB distribution) from the TREF spectrum. This last problem (i. e., the main interest of this work) is explained in detail. TREF exper iments are simulated solving the so-called direct problem using DC Ls of different shapes. The synthetic TREF spectra are then processed usi ng the inverse algorithm. The synthetic experiments demonstrate the ad equacy of the proposed algorithm as a tool of analysis. A linear ethyl ene polymer was used to test, experimentally, the numerical procedure. The results obtained are in agreement with those obtained in earlier studies on the same sample by Raman spectroscopy. (C) 1996 John Wiley & Sons, Inc.