A Strong Segregation Theory for Ring Block Copolymers
Received date: 2017-05-29
Online published: 2017-08-07
Supported by
Project supported by the National Natural Science Foundation of China (Nos. 21320102005, 21304020).
Due to the ring structure with no free ends, the traditional strong-segregation theory for linear chains is not adequate for ring block copolymers. We developed the strong-segregation theory for ring block copolymers (SST-ring), by modifying both the entropic free energy term and the interfacial energy term. The ring block copolymer can only form two types of conformations, i.e., the loops on one side of an interface and the bridges connecting two interfaces. For the entropic energy originating from the stretching of the chain conformation under strong-segregation limit, we employ the strategy for calculating the entropic energy of looping and bridging chains connecting interfaces. Since the mixing of components is unavoidable for the ring triblock copolymers to adapt to the classical morphologies, we start from the propagating function of the self-consistent field theory, and deduce the formula of the interfacial energy between two two-component domains under the strong-segregation limit. The formula is reminiscent to the interfacial energy between two single-component domains, except that the Flory-Huggins parameter χAB between two components on each side of the interface is replaced by an effective parameter, χeff, which is a function of the composite fractions and the Flory-Huggins parameters between each components. The application of SST-ring to ring diblock copolymers is successful to describe the decreased characteristic length and the lifted order-disorder transition point, compared with the corresponding linear diblock copolymers with the same segment number N. We find that the critical χABN value of the ordered-disordered transition is 1.59 times that of the linear diblock polymers, and the characteristic lengths of the ring diblock copolymers are always 0.63 times of those of linear diblock copolymers. This agrees qualitatively with the predictions of the self-consistent theory, with slight quantitative difference originating from the strong-segregation limit assumption. For the SST-ring calculations for ring triblock copolymers in two-dimensions, corresponding to the film with the thickness much smaller than the radius of gyration of the polymer, we consider two types of micro phase structures:the classical morphologies (lamellae and cylinders) with multi-component domains, and the tiling-brick structures ([6,6,6] and[8,8,4], where the numbers denote the side numbers of the bricks) consisting of the single-component domains. SST-ring predicts that the ternary diagram consists of both types of the micro phase structures. When the Flory-Huggins parameters between any two components are equal, the phase diagram has a three-fold rotational symmetry to the center of the regular triangle, and three mirror symmetric axis crossing three vertices of the triangle, respectively. Our SST-ring theory is easy to be applied to different morphologies of ring block copolymers.
Liu Ming , Yang Yingzi , Qiu Feng . A Strong Segregation Theory for Ring Block Copolymers[J]. Acta Chimica Sinica, 2017 , 75(9) : 884 -892 . DOI: 10.6023/A17050235
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