General description of the structure of branched polymers

Abstract

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 Vhp, where Vh 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

Characterization Methods for Starch-Based Materials: State of the Art and Perspectives

“…[69] Level 2: Whole Branched Molecules Complete specification of Level 2 structure requires a complicated distribution function which expresses the number of molecules in which a branch is found at DP X 1 from the reducing end, and then after x 1 monomer units there starts a secondary branch of DP X 11 , from which there is a branch x 11 units from its end of DP X 111 , etc., while the original chain has a second branch point x 2 units from the previous branch, the new branch having DP X 12 , and so ad infinitum. [1] This infinitely hierarchical distribution is denoted N(X 1 , x 1 , X 11 , x 11 , X 12 ,y, X 111 ,y, x 111 , X 12 , y; B), where B is the total number of chains in that molecule; see Fig. 4.…”

“…a solubilization procedure involving alkaline solution at elevated temperature can cause systematic loss of longer glucan chains, compared with solubilization using dimethyl sulfoxide solution. The long glucan chains may be cleaved by hydrolysis of a- (1)(2)(3)(4) linkages. In principle, hydrolysis can be observed using NMR spectroscopy to find the relative number of a-and b-glucose reducing ends to the number of total a-(1-4) linkages in a sample before and after the pretreatment.…”

“…Instead, various experimentally measurable 'projections' of this can be obtained, all of which can be written as appropriate integrals of the complete distribution function. [1] Techniques and Assumptions An essential requirement for characterizing the whole-molecule (fully branched) structure of a starchy material is that one has complete molecular dissolution without aggregation or degradation. This is not trivial: for example, starch from a grain is easy to dissolve fully in basic aqueous solution, but this can readily cause degradation, to a degree which depends on the pH.…”

“…[16] While the former is what is frequently used for presenting CLD data in the literature, the logarithmic representation of the same data brings out features at higher DPs which are not obvious in the conventional presentation (CLD of higher DPs is at least one to two orders of magnitude less than of the lowest DPs), as well as being a form based on mechanistic precepts. [1,[16][17][18] The conventional treatment of N de (X) is the difference plot, where one CLD is subtracted from another. However, difference plots require particular care not to introduce artefacts from incorrect normalization.…”

“…[1] Moreover, the complexity does not end there. Overall, starch has extraordinary structural complexity, with multiple hierarchical CSIRO PUBLISHING levels of structure on many different distance scales.…”