Abstract
A molecular model of the orientationally ordered lamellar phase exhibited by asymmetric rod-coil-rod triblock copolymers has been developed using the density-functional approach and generalizing the molecular-statistical theory of rod-coil diblock copolymers. An approximate expression for the free energy of the lamellar phase has been obtained in terms of the direct correlation functions of the system, the Flory-Huggins parameter and the Maier-Saupe orientational interaction potential between rods. A detailed derivation of several rod-rod and rod-coil density-density correlation functions required to evaluate the free energy is presented. The orientational and translational order parameters of rod and coil segments depending on the temperature and triblock asymmetry have been calculated numerically by direct minimization of the free energy. Different structure and ordering of the lamellar phase at high and low values of the triblock asymmetry is revealed and analyzed in detail. Asymmetric rod-coil-rod triblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter and for several values of the triblock asymmetry. It has been found that the lamellar phase appears to be the most stable one at strong segregation. The density distribution of the coil segments and the segments of the two different rods have been determined for different values of the segregation strength. The simulations confirm the existence of a weakly ordered lamellar phase predicted by the density-functional theory, in which the short rods separate from the long ones and are characterized by weak positional ordering.
Highlights
Rod-coil block copolymers are very interesting soft matter systems which combine the properties of coil-coil block copolymers and liquid crystals
The system of linear equations for the expansion coefficients of the direct correlation functions, presented in Appendix C, is solved numerically and the results are substituted in the expression for the free energy
We have developed a molecular-statistical theory of orientationally ordered rod-coil-rod triblock copolymers using the density-functional approach which has been applied by the authors before to the theory of rod-coil diblock copolymers [43]
Summary
Rod-coil block copolymers are very interesting soft matter systems which combine the properties of coil-coil block copolymers and liquid crystals. The theory employs the density-density correlation functions for Gaussian chains which are used in the Landau—de Gennes theory of rod-coil block copolymers [46] Such a density functional theory is not as precise as the full SCFT, but it is much less computationally challenging and can be used to calculate detailed orientational and translational order parameter profiles in an efficient way [43,44].
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