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Pseudostationary Pulsed Laser Polymerization: A Simple Method for the Direct Determination of Axial Dispersion as Occurring in Size Exclusion Chromatography
Author(s) -
Kornherr Andreas,
Olaj Oskar Friedrich,
SchnöllBitai Irene,
Zifferer Gerhard
Publication year - 2003
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.200390027
Subject(s) - inflection point , chemistry , poisson distribution , dispersion (optics) , amplitude , polymerization , analytical chemistry (journal) , flattening , molecular physics , thermodynamics , physics , quantum mechanics , mathematics , chromatography , statistics , geometry , organic chemistry , polymer , astronomy
Theoretical distribution curves were calculated for several values of pulse separation t 0 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 = k t ρt 0 and/or L 0 = k p [ M ] t 0 , with [ M ] = monomer concentration and k t and k p 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 ( P̄ n ≥ 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 P̄ n . The point of inflection can be used as a measure of L 0 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 σ ad,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 σ ad,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.