Computer Simulation of Micellization for Ring-like Block Copolymers†

doi:10.7503/cjcu20130719

Abstract

Abstract:

The micellization behaviour of ring-like AB diblock copolymers in a selective solvent was compared with the corresponding linear ABA triblock copolymers via Monte Carlo simulation. The simulation results show that the difference in the critical micellization concentration(cmc) values between ring-like copolymers and linear copolymers with same compositions is closely related to the content of A blocks, f_A, and the strength of attractive interaction between B monomers, ε. When f_A is relatively small and ε is big, the cmc values of ring-like block copolymers are smaller than those of the corresponding linear ones; whereas when f_A is big and ε is small, the cmc values of triblock copolymers are smaller than those of the corresponding ring-like ones. To further understand the effect of f_A and ε on the micellization behavior, we calculated the entropy and the potential energy contributions to the micellization free energy, respectively. The results show that in the studied range of f_A and ε, the entropy loss in micellization for ring-like block copolymers is always smaller than that for triblock copolymers, so it seems that the micellization of ring-like block copolymers is always easier than that of the linear ones if we only consider the entropy contributions to the free energy. But if we calculate the potential energy contributions to the free energy, it can be found when f_A is relatively small and ε is big, the potential energy decreases greatly during the micellization of ring-like block copolymers. Considering the less unfavorable contribution of entropy part to the free energy for ring-like block copolymers, the micellization of ring-like block copolymers should be much easier than that of the linear ones. When f_A is big and ε is small, the potential energy decreases greatly when the micelles form for linear block copolymers. Although the entropic contribution to the free energy is unfavorable for linear ones, the potential energy still shows the dominative contribution to the free energy and therefore the micellization of linear block copolymers is much easier than the ring-like ones. The above analysis of the free energy will help us understand the micellization behavior of ring-like block copolymers and linear block copolymers.

Key words: Ring-like block copolymer, Micellization, Monte Carlo simulation

CLC Number:

O631

TrendMD:

LI Liangyi, LI Zhanwei, FU Cuiliu, SUN Zhaoyan, AN Lijia. Computer Simulation of Micellization for Ring-like Block Copolymers^†[J]. Chem. J. Chinese Universities, 2014, 35(1): 168.

Figures/Tables 6

Fig.1 Concentration of free copolymers(ϕf) versus the total copolymer concentration(ϕ) for different copolymer compositionsa1—f1 and a2—f2 denote the ring-like block copolymers and linear block copolymers with different chain compositions, respectively. a1. A12B11; b1. A16B11; c1. A20B11; d1. A24B11; e1. A28B11; f1. A32B11; a2. A6B11A6; b2. A8B11A8; c2. A10B11A10; d2. A12B11A12; e2. A14B11 A14; f2. A16B11 A16.

Fig.2 cmc values for ring-like(a1—d1) and linear block(a2—d2) copolymers with different compositions(fA) and different interaction parameters(ε)The big squares show the cmc values for different architectures are almost equal. ε: Ring-like block colymers: a1.0.84kBT; b1. 0.88kBT; c1. 0.92kBT; d1.0.96kBT. Linear block colymers: a2.0.84kBT; b2. 0.88kBT; c2. 0.92kBT; d2.0.96kBT.

Fig.3 Probability distributions of the distance from central bead to each junction at free state(ϕ=0.0015σ-3) and micellar state(ϕ=0.08σ-3), respectively, for linear A16B11A16 block copolymers(A) and ring-like A32B11 block copolymers(B)ε=0.9kBT. (A) a. L-A16B11A16-unimer; b. L-A16B11A16-micelle; (B) a. R-A32B11-unimer; b. R-A32B11-micelle.

Fig.4 Entropy related free energy change difference between linear block copolymers and ring-like block copolymers(ΦL-ΦR), as a function of fA

Fig.5 Difference in potential energy change between linear triblock copolymers and ring-like copo-lymers(ΔUL-ΔUR) as a function of fA Four parallel samples are used to generate the error bars, and in each sample 1000 snapshots(micellar state) or 5000 snapshots(free state) are analyzed.ε: a. 0.82kBT; b. 0.86kBT; c. 0.90kBT; d. 0.94kBT.

Fig.6 Fraction[f(n)] of micelles plotted as a function of chains per micelle, n, at ϕ=0.08σ-3 (A) Ring-like A12B11 block copolymers; (B) linear A6B11A6 block copolymers; (C) ring-like A32B11 block copolymers; (D) linear A16B11A16 block copolymers. ε: a. 0.84kBT; b. 0.88kBT; c. 0.92kBT; d. 0.96kBT.

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