Premium
Form Factor of an Isolated Chain with Excluded Volume
Author(s) -
Freire Juan J.,
Álvarez Gabriel,
Bishop Marvin
Publication year - 2002
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 - 10.1002/1521-3919(20020101)11:1<11::aid-mats11>3.0.co;2-6
Subject(s) - asymptotic expansion , mathematics , function (biology) , chain (unit) , debye function , form factor (electronics) , debye , simple (philosophy) , series expansion , structure factor , yield (engineering) , mathematical analysis , physics , thermodynamics , debye length , quantum mechanics , condensed matter physics , ion , philosophy , epistemology , evolutionary biology , biology
The form factor of isolated chains with excluded volume, S ( x ), can be derived from the des Cloizeaux form of the distribution of internal distances between chain units (ignoring end effects). Using this approach, we have obtained numerical results of S ( x ). Also, we have considered an asymptotic expansion of this function at large values of the scaled scattering variable x . Considering only the first four terms, this asymptotic expansion is shown to yield a good estimation of form factor for values of x as small as x = 3.5. It is also shown that the S ( x ) is adequately described by the Debye function for x < 3.5. At x = 3.5 the truncated asymptotic expansion and the Debye function are equal and overestimate the exact result by about 2%. Therefore, the simple low x and high x descriptions are accurate, and their appropriate use produces a maximum error of 2% located at x = 3.5 with respect to the numerical value of the form factor resulting from this approach with the des Cloizeaux function.