Cover Picture: Macromol. Theory Simul. 6/2004

Kornherr, Andreas; Olaj, Oskar Friedrich; Schnöll‐Bitai, Irene; Zifferer, Gerhard

doi:10.1002/mats.200490010

Cited by 16 publications

(33 citation statements)

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“…A more detailed analysis of theoretical distribution curves will be necessary to elucidate the reason for this observation. [37] The values for the points of inflection (Table 4) do not give rise to a downward curvature as observed in Figure 1. No clear statement can still be made with respect to a chainlength-dependent k p value or a decrease in the monomer concentration due to monomer consumption during polymerization.…”

Section: Resultsmentioning

confidence: 56%

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

Schnöll‐Bitai

Pfeisinger

2003

Macro Chemistry & Physics

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Styrene was polymerized by intermittent photoinitiation (at a constant sector speed and a light to dark ratio of 1:5) in microemulsion. The molecular weight distribution was measured by size‐exclusion chromatography and turned out to be extremely well structured. When the points of inflection were used for the calculation of the rate constant of propagation in analogy to pulsed‐laser polymerization/size‐exclusion chromatography (PLP‐SEC), values were obtained which were lower than those accepted for bulk polymerization but good agreement was achieved with a slightly modified equation. The absolute peak width (introduced as the difference between two successive points of inflection) turned out to be an invariant quantity no matter which type of distribution curve (number, molar mass, or hyper distribution) was analyzed, thus demonstrating the Poissonian character of the peaks. Furthermore, the relative peak widths (defined as the ratio of two successive points of inflection) for the first peak scattered between 1.35–1.45, those for the second peak between 1.26–1.30. After subtracting the respective value for the theoretical peak width, the same value for the first and second peaks was obtained for all experiments over a broad range of experimental parameters. As the appearing peaks are well resolved and narrow, the influence of axial dispersion on the results is, therefore, conclusively demonstrated. A simple procedure for the direct determination of axial dispersion is presented based on the relative peak widths and the additivity of the peak variances. The invariance of the peak widths is an easily verifiable theoretical and experimental prerequisite for this procedure.

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Section: Resultsmentioning

confidence: 56%

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

Schnöll‐Bitai

Pfeisinger

2003

Macro Chemistry & Physics

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“…Its estimation -based on the properties of the distributions with axial dispersion -will be the subject of further efforts. [34] The broadening influence of the axial dispersion on the additional peaks was demonstrated by comparison of the determined extraordinary points and the derived absolute and relative peak widths. The applicability of a simple method for the direct determination of the axial dispersion was set forth.…”

Section: Resultsmentioning

confidence: 99%

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

Kornherr¹,

Olaj²,

Schnöll‐Bitai³

et al. 2003

Macro Theory & Simulations

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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.imageThe 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.

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“…Based on the peak width, a qualitative criterion that indicates the case when the PI is to be recommended as a measure of L 0 was recently derived. [13] However, there is no doubt that a quantitative relation would be preferable. The main goal of this study, therefore, is to prepare (model)…”

Section: If Present) In Ourmentioning

confidence: 98%

“…Finally, the influence of axial dispersion on all CLDs was taken into account [11,13] when transforming the original distribution into the SEC distribution w SEC [Equation (3)]. Table 1.…”

Section: Simulation Proceduresmentioning

confidence: 99%

A Method of Improving the Theoretical Basis of k_p Determination from PLP‐SEC Measurements

Kornherr

Olaj

Schnöll‐Bitai

et al. 2003

Macro Theory & Simulations

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Making use of hitherto ignored features (such as the peak width) contained in the chain‐length distributions of polymers prepared by pulsed‐laser polymerization (PLP), corrections are calculated from simulated chain‐length distributions for improving the accuracy of the “characteristic chain length” L0 data on which the evaluation of the propagation rate constant kp is based. These corrections refer to a wide range of chain lengths and primary radical production, slightly chain‐length‐dependent termination by disproportionation or combination, and a reasonable extent of axial dispersion introduced by the chromatographic device used in the evaluation of the chain‐length distribution. They can be applied to the point of inflection on the low‐molecular‐weight side of the extra peaks as well as to the peak maximum. The remaining mean error which, of course, concerns the evaluation of L0 only, is shown to be of the order of 1.0–1.5%, if the mode of termination is unknown, and comes down to about half that value if information on the mode of termination is available. Although all the other errors inherent in the size exclusion chromatography (SEC) method are still present, this method constitutes substantial progress with respect to the accuracy of determining kp data from PLP experiments followed by chromatographic analysis.Hyper mass distributions calculated for L0 = 200, C = 5 and b = 0.16 for termination by disproportionation considering Poissonian and Gaussian broadening.imageHyper mass distributions calculated for L0 = 200, C = 5 and b = 0.16 for termination by disproportionation considering Poissonian and Gaussian broadening.

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Cover Picture: Macromol. Theory Simul. 6/2004

Abstract: Cover:The picture on the cover shows theoretical PLP-SEC-distributions (characteristic parameters as indicated) assuming various extents of axial dispersion (small: red; moderate: green and large: blue).

Cited by 16 publications

References 0 publications

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

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

A Method of Improving the Theoretical Basis of k_p Determination from PLP‐SEC Measurements

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Cover Picture: Macromol. Theory Simul. 6/2004

Abstract: Cover:The picture on the cover shows theoretical PLP-SEC-distributions (characteristic parameters as indicated) assuming various extents of axial dispersion (small: red; moderate: green and large: blue).

Cited by 16 publications

References 0 publications

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

Investigation of the Peak Width of Polystyrene Prepared by Rotating‐Sector Polymerization in Microemulsion

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

A Method of Improving the Theoretical Basis of kp Determination from PLP‐SEC Measurements

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A Method of Improving the Theoretical Basis of k_p Determination from PLP‐SEC Measurements