“Simulating the Fluctuation-Induced Suppression of the Order-Disorder Transition in an Asymmetric Diblock Copolymer Melt”
Diblock copolymers self-assemble into a rich variety of nanoscale ordered structures that are suitable for applications including energy conversion, data storage, nanolithography, and drug delivery. Mean-field theory predicts the phase behaviour of block copolymers with a great deal of success, however it systematically overestimates the order-disorder temperature (ODT) due to its inaccurate treatment of fluctuations in the disordered phase. There has been extensive work with compositionally symmetric diblock copolymer systems in developing fluctuation-corrections to mean field models that demonstrate a suppression of the ODT to lower temperatures with increased fluctuation strength. Systems of asymmetric diblock copolymers exhibit a similar suppression of the ODT, however have been less well-studied due to the existence of a disordered liquid of micelles in the low temperature regime of the disordered phase that is difficult to describe theoretically. We use Monte Carlo simulation to sample density field configurations weighted by a Landau-Brazovskii effective Hamiltonian and systematically investigate the fluctuation-induced suppression of the ODT in an asymmetric diblock copolymer melt as we decrease the invariant degree of polymerization N¯ from 106 to 105. We access the thermodynamic Helmholtz free energy through Monte Carlo averages which are related to derivatives of the Helmholtz free energy. Using thermodynamic integration, we compare the ordered BCC sphere phase free energy to that of the disordered phase to locate the ODT. Turning on a BCC-ordering field enables us to define a continuous integration path from order to disorder, bypassing the discontinuity at the ODT. We find that the BCC free energy is relatively insensitive to fluctuations. However, in the low-temperature regime of disorder, we observe and characterize a disordered liquid of micelles that is stabilized by the inclusion of fluctuations in our simulation. To accurately locate the ODT, we develop sophisticated methods to ensure that the disordered micelles are equilibrated. We find that decreasing N¯ from 106 to 105 causes a suppression of the ODT from T=0.0163 to T=0.0122. This result is in good agreement with a theory where fluctuations are incorporated on a single-mode Hartree level.
- Dr. Vladimir Ladizhansky, Chair
- Dr. Robert Wickham, Advisor
- Dr. John Dutcher
- Dr. Bill Smith