^{1,2}, Yu Ma

^{1,2}, Juan Li

^{1,2}, Xiaoming Jiang

^{1,2}and Wenbing Hu

^{1,2,a)}

### Abstract

We report dynamic Monte Carlo simulations of microphase separated diblock copolymers, to investigate how crystallization of one species could accelerate the subsequent crystallization of another species. Although the lattice copolymer model brings a boundary constraint to the long periods of microdomains, the single-molecular-level force balance between two blocks and its change can be revealed in this simple approach. We found two contrastable acceleration mechanisms: (1) the metastable lamellar crystals of one species become thicker at higher crystallization temperatures, sacrificing its microphase interfacial area to make a larger coil-stretching of another amorphous species and hence to accelerate subsequent crystallization of the latter with a more favorable conformation. (2) While in the case allowing chain-sliding in the crystal, the equilibrated lamellar crystals of one species become thinner at higher temperatures, sacrificing its thermal stability to gain a higher conformational entropy of another amorphous species and hence to accelerate subsequent crystallization of the latter with a stronger tension at the block junction. Parallel situations of experiments have been discussed.

W.H. thanks the stimulating discussions from Professor Hsin-Lung Chen at National Tsinghua University and Professor Lei Zhu at Case Western Reserve University. The Financial support from National Natural Science Foundation of China (Grant No. 20825415) and from the National Basic Research Program of China (Grant No. 2011CB606100) is appreciated.

I. INTRODUCTION

II. SIMULATION TECHNIQUES AND SAMPLE PREPARATION

III. RESULTS AND DISCUSSION

A. The first case allows chain-sliding diffusion in the crystal

B. The second case forbids chain-sliding diffusion in the crystal

C. Structure analysis of the samples made in the first stage

IV. CONCLUSION

### Key Topics

- Crystallization
- 64.0
- Polymers
- 17.0
- Block copolymers
- 14.0
- Diffusion
- 13.0
- Nucleation
- 8.0

##### B01D9/00

## Figures

Snapshot of the symmetric diblock copolymer system with the lamellar microdomains generated by microphase separation in a cooling process till to *T* = 4.2, as described in the text. The bonds of two species (drawn as small cylinders) are colored with blue and yellow, respectively.

Snapshot of the symmetric diblock copolymer system with the lamellar microdomains generated by microphase separation in a cooling process till to *T* = 4.2, as described in the text. The bonds of two species (drawn as small cylinders) are colored with blue and yellow, respectively.

Time-evolution curves of C1 crystallinity in the first stage of temperature quenching with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion) upon isothermal crystallization at various high temperatures denoted nearby.

Time-evolution curves of C1 crystallinity in the first stage of temperature quenching with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion) upon isothermal crystallization at various high temperatures denoted nearby.

Snapshots on the XZ planes of the symmetric diblock copolymer systems with *E* _{ f }/*E* _{ c } = 0 after isothermal crystallization for a period of 300 000 Monte Carlo cycles at (a) *T* = 4.1, (b) *T* = 4.0, (c) *T* = 3.8, and (d) *T* = 3.6. The bonds of two species (drawn as small cylinders) are colored with blue for C1 and yellow for C2, respectively.

Snapshots on the XZ planes of the symmetric diblock copolymer systems with *E* _{ f }/*E* _{ c } = 0 after isothermal crystallization for a period of 300 000 Monte Carlo cycles at (a) *T* = 4.1, (b) *T* = 4.0, (c) *T* = 3.8, and (d) *T* = 3.6. The bonds of two species (drawn as small cylinders) are colored with blue for C1 and yellow for C2, respectively.

Time-evolution curves of C2 crystallinity with *E* _{ f }/*E* _{ c } = 0 upon isothermal crystallization at the same low temperatures *T* = 2.2 for the samples made by isothermal crystallization at various high temperatures denoted nearby.

Time-evolution curves of C2 crystallinity with *E* _{ f }/*E* _{ c } = 0 upon isothermal crystallization at the same low temperatures *T* = 2.2 for the samples made by isothermal crystallization at various high temperatures denoted nearby.

Snapshots on the XZ planes of the symmetric diblock copolymer systems with *E* _{ f }/*E* _{ c } = 0 after isothermal crystallization for a period of 300 000 Monte Carlo cycles at *T* = 2.2, for the samples made in the first stage at (a) *T* = 4.1, (b) *T* = 4.0, (c) *T* = 3.8, and (d) *T* = 3.6, as shown parallel in Fig. 3. The small cylinders with the blue color stands for those bonds of block C1, and the yellow for C2.

Snapshots on the XZ planes of the symmetric diblock copolymer systems with *E* _{ f }/*E* _{ c } = 0 after isothermal crystallization for a period of 300 000 Monte Carlo cycles at *T* = 2.2, for the samples made in the first stage at (a) *T* = 4.1, (b) *T* = 4.0, (c) *T* = 3.8, and (d) *T* = 3.6, as shown parallel in Fig. 3. The small cylinders with the blue color stands for those bonds of block C1, and the yellow for C2.

Avrami indexes (n) and kinetic constants (log_{10}K) obtained from the isothermal crystallization process of C2 at *T* = 2.1 for the samples prepared at various high temperatures (shown as X-axis) in the previous stage. The error bars were obtained from several simulations of parallel systems (the same in the following figures).

Avrami indexes (n) and kinetic constants (log_{10}K) obtained from the isothermal crystallization process of C2 at *T* = 2.1 for the samples prepared at various high temperatures (shown as X-axis) in the previous stage. The error bars were obtained from several simulations of parallel systems (the same in the following figures).

Time evolution curves of (a) C1 crystallinity upon isothermal crystallization at various high temperatures denoted nearby, with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion); (b) C2 crystallinity upon isothermal crystallization at the same low temperatures *T* = 2.6 for the samples made by isothermal crystallization at various high temperatures denoted nearby with *E* _{ f }/*E* _{ c } = 0.3.

Time evolution curves of (a) C1 crystallinity upon isothermal crystallization at various high temperatures denoted nearby, with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion); (b) C2 crystallinity upon isothermal crystallization at the same low temperatures *T* = 2.6 for the samples made by isothermal crystallization at various high temperatures denoted nearby with *E* _{ f }/*E* _{ c } = 0.3.

(a) Stem-length distributions in C1 crystals made at various high temperatures (as denoted) in the first stage. The stem length is defined as the number of continuously collinear-connected crystalline bonds, while each crystalline bond contains more than five parallel neighbors of the same species. The dashed line separates those longer stems made used to calculate the mean stem lengths. (b) Mean stem lengths in C1 crystals versus crystallization temperatures in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion).

(a) Stem-length distributions in C1 crystals made at various high temperatures (as denoted) in the first stage. The stem length is defined as the number of continuously collinear-connected crystalline bonds, while each crystalline bond contains more than five parallel neighbors of the same species. The dashed line separates those longer stems made used to calculate the mean stem lengths. (b) Mean stem lengths in C1 crystals versus crystallization temperatures in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion).

(a) Distributions curves for square radius of gyration of C2 blocks made at various high temperatures (as denoted) in the first stage. (b) Mean square radius of gyration of C2 blocks versus crystallization temperatures of C1 blocks in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion).

(a) Distributions curves for square radius of gyration of C2 blocks made at various high temperatures (as denoted) in the first stage. (b) Mean square radius of gyration of C2 blocks versus crystallization temperatures of C1 blocks in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0 (allowing chain-sliding diffusion).

(a) Stem-length distributions in C1 crystals made at various high temperatures (as denoted) in the first stage. The dashed line separates those longer stems made used to calculate the mean stem lengths. (b) Mean stem lengths in C1 crystals versus crystallization temperatures in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion).

(a) Stem-length distributions in C1 crystals made at various high temperatures (as denoted) in the first stage. The dashed line separates those longer stems made used to calculate the mean stem lengths. (b) Mean stem lengths in C1 crystals versus crystallization temperatures in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion).

(a) Distributions curves for square radius of gyration of C2 blocks made at various high temperatures (as denoted) in the first stage. (b) Mean square radius of gyration of C2 blocks versus crystallization temperatures of C1 blocks in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion).

(a) Distributions curves for square radius of gyration of C2 blocks made at various high temperatures (as denoted) in the first stage. (b) Mean square radius of gyration of C2 blocks versus crystallization temperatures of C1 blocks in the first stage for the sample systems with *E* _{ f }/*E* _{ c } = 0.3 (forbidding chain-sliding diffusion).

Article metrics loading...

Full text loading...

Commenting has been disabled for this content