General Solution to the Band-Broadening Problem in Polymer Molecular Weight Distributions*
Jeffrey V. Castro A , Kim Y. van Berkel B , Gregory T. Russell B and Robert G. Gilbert A CA Key Centre for Polymer Colloids, School of Chemistry, University of Sydney, Sydney NSW 2006, Australia.
B Department of Chemistry, University of Canterbury, Christchurch, New Zealand.
C Corresponding author. Email: gilbert@chem.usyd.edu.au
Australian Journal of Chemistry 58(3) 178-181 https://doi.org/10.1071/CH05002
Submitted: 5 January 2005 Accepted: 29 January 2005 Published: 15 March 2005
Abstract
A method is developed for overcoming the problem of band broadening (where a sample which is monodisperse in molecular weight elutes over a range of elution volumes) in order to obtain accurate molecular weight distributions of polymers using size exclusion chromatography (SEC). It is proved that the SEC signal from an exponential number distribution (as obtained from free-radical polymerization under certain conditions) has the same functional form at the maximum, irrespective of band broadening. This leads to a method for quantifying the band broadening from any SEC trace, and hence for deconvoluting the trace to obtain the true distribution—by free-radical polymerization one should synthesize ‘standards’ which have exponential distributions and then carry out least-squares fitting to find the corresponding broadening function. The new method opens the way for mechanistic understanding and rate parameters to be obtained from the full detail that has hitherto been inaccessible in molecular weight distributions.
Acknowledgments
The Key Centre for Polymer Colloids is established and supported under the Australian Research Council Research Centres program. K.Y.v.B. gratefully acknowledges the support of a New Zealand Foundation for Research Science and Technology Bright Future Scholarship, of the P. A. Rolfe Scholarship Fund, and also a Shirtcliffe Fellowship. J.V.C. is supported by an Australian Postgraduate Award and by the Cooperative Research Centre for Sustainable Rice Production.
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* This paper is dedicated to Prof. David Solomon on the occasion of his 75th birthday.
† The instantaneous distribution is that which is formed at a particular conversion, which can always be found experimentally by subtracting the cumulative distributions obtained by sampling at different conversions—the single exponential with combination and disproportionation arises because termination is predominantly between short and long radicals,[1] and model calculations shows the instantaneous MWD should be single exponential for M ≥ ∼105.
