TY - JOUR

T1 - Renormalized one-loop theory of correlations in disordered diblock copolymers

AU - Qin, Jian

AU - Grzywacz, Piotr

AU - Morse, David C.

PY - 2011/8/28

Y1 - 2011/8/28

N2 - A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)]10.1103/ PhysRevE.76.061802 is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q *), peak position q*, and single-chain statistics for symmetric and asymmetric copolymers as functions of X eN, where Xe is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q) upon XeN for symmetric diblock copolymers in the limit of strong scattering, or large XeN, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q) and a decrease of q for large values of XeN, relative to the RPA predictions, but an enhancement of S(q) and an increase in q for small X eN. The decrease in q near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q at small values of X eN is a direct result of non-Gaussian single-chain statistics.

AB - A renormalized one-loop (ROL) theory developed in previous work [P. Grzywacz, J. Qin, and D. C. Morse, Phys. Rev E. 76, 061802 (2007)]10.1103/ PhysRevE.76.061802 is used to calculate corrections to the random phase approximation (RPA) for the structure factor S(q) in disordered diblock copolymer melts. Predictions are given for the peak intensity S(q *), peak position q*, and single-chain statistics for symmetric and asymmetric copolymers as functions of X eN, where Xe is an effective Flory-Huggins interaction parameter and N is the degree of polymerization. The ROL and Fredrickson-Helfand (FH) theories are found to yield asymptotically equivalent results for the dependence of the peak intensity S(q) upon XeN for symmetric diblock copolymers in the limit of strong scattering, or large XeN, but to yield qualitatively different predictions for symmetric copolymers far from the ODT and for asymmetric copolymers. The ROL theory predicts a suppression of S(q) and a decrease of q for large values of XeN, relative to the RPA predictions, but an enhancement of S(q) and an increase in q for small X eN. The decrease in q near the ODT is shown to be unrelated to any change in single-chain statistics, and to be a result of inter-molecular correlations. Conversely, the predicted increase in q at small values of X eN is a direct result of non-Gaussian single-chain statistics.

UR - http://www.scopus.com/inward/record.url?scp=80052392976&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052392976&partnerID=8YFLogxK

U2 - 10.1063/1.3609758

DO - 10.1063/1.3609758

M3 - Review article

C2 - 21895217

AN - SCOPUS:80052392976

VL - 135

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084902

ER -