Connectivity and topology of a phase-separating bicontinuous structure in a polymer mixture: Direct measurements of coordination number, inter-junction distances and Euler characteristic

Journal of Chemical Physics

Volumn 119, Issue 14, 2003, Pages 7554-7559

  Jinnai, Hiroshi ^a   Watashiba, Hideyuki ^a   Kajihara, Takashi ^a   Takahashi, Masaoki ^a  

^a KYOTO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTER SIMULATION; COORDINATION REACTIONS; CRYSTALLOGRAPHY; DECOMPOSITION; MIXTURES; MOLECULAR STRUCTURE; MORPHOLOGY; PHASE SEPARATION; PHASE TRANSITIONS; PROBABILITY DENSITY FUNCTION;

BICONTINUOUS STRUCTURE; EULER CHARACTERISTICS; INTERJUNCTION DISTANCES; MORPHOLOGICAL TRANSITION; POLYMER MIXTURE;

ORGANIC POLYMERS;

EID: 0142211221     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1607912     Document Type: Article

References (24)

1. T. Hashimoto, in Structure and Properties of Polymers, edited by R. W. Cahn, P. Haasen, and E. J. Kramer (VCH, Weinheim, 1993), Vol. 12, of Materials Science and Technology, p. 251.
2. H. Jinnai, Y. Nishikawa, T. Koga, and T. Hashimoto, Macromolecules 28, 4782 (1995).
3. H. Jinnai, T. Koga, Y. Nishikawa, and T. Hashimoto, Phys. Rev. Lett. 78, 2248 (1997).
4. H. Jinnai, Y. Nishikawa, H. Morimoto, T. Koga, and T. Hashimoto, Langmuir 16, 4380 (2000).
5. J. Kabel, A. Odgaard, B. van Rietbergen, and R. Huiskes, Bone 24, 115 (1999).
6. H. Jinnai, T. Kajihara, Y. Nishikawa, M. Ito, S. D. Smith, D. A. Agard, and R. J. Spontak, Adv. Mater. (Weinheim, Ger.) 14, 1615 (2002).
7. M. Fialkowski, A. Aksimentiev, and R. Holyst, Phys. Rev. Lett. 86, 240 (2001).
8. A. Aksimentiev, M. Fialkowski, and R. Holyst, Adv. Chem. Phys. 121, 141 (2002).
9. S. Hyde, S. Andersson, K. Larsson, Z. Blum, T. Landh, S. Lidin, and B. W. Niham, The Language of Shape (Elsevier, Amsterdam-Lausanne-New York-Oxford-Shannon-Tokyo, 1997).
10. P. J. Flory, Principles of Polymer Chemistry (Cornell University, New York, 1953).
11. T. Hashimoto, T. Izumitani, and M. Takenaka, Macromolecules 22, 2293 (1989).
12. W. E. Lorensen and H. E. Cline, Comput. Graphics 21, 163 (1987).
13. T. Saito and J. Toriwaki, IEICE Trans. Inf. Syst. E77-D, 1005 (1994).
14. J. Toriwaki and K. Mori, in Digital and Image Geometry, edited by G. Bertrand, A. Imiya, and R. Klette (Springer-Verlag, Berlin-Heidelberg, 2001), Vol. 2243 of LNCS, p. 412.
15. Y. Nishikawa, H. Jinnai, and H. Hasegawa, Kobunshi Ronbunshu 58, 13 (2000).
16. T. Saito and J. Toriwaki, Pattern Recogn. 27, 1551 (1994).
17. If there are multiple candidate for a junction, we used the following rule to determine the position of the junction. (i) Take one of the multiple junctions and check the length of the branches (network strands emerging from the junction). If one of the branches of this junction (junction 1) is shorter than L, look at the adjacent junction (junction 2) attaching to this short branch. Check the length of the branches of the junction 2. If these two junctions share the same short branch and their other branches are longer than L, place a junction at the middle of the two junction (on the short branch). (ii) In the above rule, if the junction 2 has more than one short branches attached to it, junction 1 transfers its right as a junction to junction 2 (so that junction 1 is not a junction any more). Repeat the two conditions until a single junction can be found.
18. Note that the resolution of the model is comparable to that of the 3D images of the DPB/PB phase-separating morphologies and thus the results can be directly applicable to the SD morphologies in the present study.
19. H. Jinnai, Y. Nishikawa, R. J. Spontak, S. D. Smith, D. A. Agard, and T. Hashimoto, Phys. Rev. Lett. 84, 518 (2000).
20. H. Jinnai, T. Kajihara, H. Watashiba, Y. Nishikawa, and R. J. Spontak, Phys. Rev. E 64, 010803(R) (2001).
21. H. Jinnai, T. Kajihara, H. Watashiba, Y. Nishikawa, and R. J. Spontak, Phys. Rev. E 64, 069903(E) (2001).
22. S. T. Hyde and S. Ramsden, in Discrete Mathematical Chemistry: DIMACS Workshop Discrete Mathematical Chemistry, edited by P. Hansen, P. Fowler, and M. Zheng (American Mathematical Society, Providence, 2000), Vol. 51 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, p. 203.
23. total and thus on N and B contained in the volume used for the measurements.
24. cell and B decreased.