Abstract
AN expression for the mean square radius of a randomly coiled long-chain polymer, that is, for the mean square distance of its constituent groups from their centre of mass, was first derived by Debye1. Debye's formula applies only to very long chains; the following simple derivation is valid for any unbranched chain, provided the correlation between two atoms depends only on the number of links separating them (this implies neglect of the excluded volume effect).
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References
Debye, P., J. Chem. Phys., 14, 639 (1946).
Lagrange, J.-L., Oeuvres, 5, 535 (Paris, 1870). Cf. Lamb, H., “Statics”, 3rd edit., 166 (Cambridge, 1928).
Wall, F. T., J. Chem. Phys., 11, 67 (1943).
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SACK, R. Mean Square Radius of randomly coiled Molecular Chains. Nature 171, 310 (1953). https://doi.org/10.1038/171310a0
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DOI: https://doi.org/10.1038/171310a0
