General description of the structure of branched polymers

A multidimensional distribution function is defined to describe the branching structure of branched homopolymers such as starch and polyacrylates. Averages of this function give distributions which can be measured using, for example, the number and weight distributions as a function of hydrodynamic volume from size‐exclusion chromatography and field‐flow fractionation, and two‐dimensional separation methods. This provides means to plot data to obtain physically meaningful quantities, and to test mechanistic postulates for the (bio)synthesis, of branched polymers. A simple enzyme‐kinetic model for a reduced form of this multidimensional distribution for starch biosynthesis is derived and solved. One application is to derive number distributions for the molecular weight distribution of debranched glycogen. Fitting this to experiment gives estimates of this ratio for two forms of glycogen. We propose that number distributions from size separation for starch (which, it is pointed out, are obtained directly from in‐line viscometric detection) have a simple and meaningful form when plotted as ln(number distribution) against V_h^p, where V_h is hydrodynamic volume, and p a parameter of order unity determined from multiple‐detection size separation measurements. The new function is also used to propose a two‐dimensional experiment which can yield an unambiguous measurement of the amylose: amylopectin ratio in starch. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3914–3930, 2009