Pseudostationary Pulsed Laser Polymerization: A Simple Method for the Direct Determination of Axial Dispersion as Occurring in Size Exclusion Chromatography

• Published in: Macromolecular theory and simulations Vol. 12; no. 4; pp. 259 - 269
• Main Authors: Kornherr, Andreas, Olaj, Oskar Friedrich, Schnöll-Bitai, Irene, Zifferer, Gerhard
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.05.2003; WILEY‐VCH Verlag; Wiley
• Subjects: Applied sciences; chain length distribution; Chains; chromatography; Criteria; Dispersions; Exact sciences and technology; Mathematical analysis; Organic polymers; Physicochemistry of polymers; Poisson distributions; Polymerization; Preparation, kinetics, thermodynamics, mechanism and catalysts; Propagation (polymerization); pulsed laser polymerization; radical polymerization; Termination (polymerization); Free radical polymerization; Molecular weight distribution; Pulsed laser; Theoretical study; Kinetics; Rate constant; Computing method; Reaction propagation; Gel permeation chromatography
• ISSN: 1022-1344; 1521-3919
• DOI: 10.1002/mats.200390027

Theoretical distribution curves were calculated for several values of pulse separation t0 and concentrations of initiating radicals ρ formed by each pulse for both types of termination (disproportionation and combination). The absolute and relative peak widths of the additional peaks for the number, molar mass, and hyperdistribution were determined and compared. In all cases, the peak widths of these different distributions became the same with increasing values of C = ktρt0 and/or L0 = kp[M]t0, with [M] = monomer concentration and kt and kp are the rate constants of termination and propagation, respectively. This is similar to the behavior of Poisson distributions if only the degrees of polymerization are fairly high (P̄n ≥ 50). The analogy is further supported by the finding that under the same conditions the peak widths themselves approach the theoretical ones for Poisson distributions. Thus, the fulfilment of these two criteria suggests that the various peaks in multimodal distributions should be treated in the same formal way as Poissonian peaks although they clearly originate from a superposition of adjacent Poissonian peaks of different amplitude and, on the whole have a peak width somewhat in excess of the theoretical one of true Poisson peaks of the same P̄n. The point of inflection can be used as a measure of L0 without reservation only if the first criterion is not fulfilled. The influence of axial dispersion on the location of the extrema was calculated by use of standard deviations σad,k (0.05 and 0.025) to give “experimental curves” for which a pronounced increase in the absolute and relative peak widths was observed. Based on an assumed additivity of the peak variances, a simple procedure was tested for the direct determination of σad,k. The accuracy increased with increasing peak chain lengths and C values for those values determined from the first peak. The values determined from the second peak in the chain length region between 400–700 were closest to the input value. The points of inflection on the low and high molecular weight side of the additional first three peaks are given as a function of the peak maximum. The lower and upper lines were calculated with Equation (11) and (12), respectively.