搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

在光敏性三元聚合物混合物中构造 多尺度有序图案

郭宇琦 潘俊星 张进军 孙敏娜 王宝凤 武海顺

引用本文:
Citation:

在光敏性三元聚合物混合物中构造 多尺度有序图案

郭宇琦, 潘俊星, 张进军, 孙敏娜, 王宝凤, 武海顺

Multi-scale ordered patterns in photosensitive ternary polymer mixtures

Guo Yu-Qi, Pan Jun-Xing, Zhang Jin-Jun, Sun Min-Na, Wang Bao-Feng, Wu Hai-Shun
PDF
导出引用
  • 由多组分聚合物混合物所形成的多尺度有序结构能够展现出许多新奇的物理化学性质, 从而使其在材料工程领域具有十分重要的潜 在应用价值. 本文通过计算机模拟, 在光敏性不相容三元混合物体系中创建了多尺度有序结构. 通过调节光照区域和掩膜形状, 获得了棋盘形、箭靶状等十分独特的形貌, 并且这些结构可以在实验上通过在适当的时间淬火而稳定较长的时间. 详细探讨了组分比、掩膜宽度、间距以及光照强度对体系的影响, 从而为实现多尺度长程序花样薄膜的制备提供了一个简便的途径, 同时也为纳米器件的制备提供了一定的指导.
    Multi-scale ordered patterns of multi-component polymer mixtures can reveal many peculiar chemical and physical properties, which makes these systems have very important potential applications in materials engineering. Via computer simulation, we create interesting ordered multi-scale structures in photosensitive and immiscible polymer mixtures. The system that we employed comprises a ternary, molten A/B/C polymer blends and the three components are mutually immiscible. Polymer C is non-optically active, while polymers A and B can exhibit reversible chemical reaction A ⇆ B induced by light. Firstly, we investigate the phase behavior of the ternary blend guided by cross-stripy mask and light, and find that a chessboard-like ordered pattern forms in the mixture before removing the mask. In the illuminated regions, the A and C components gather into ellipsoidal core-shell structures in the uncrossed illuminated area, while the A and B components gather into star structures in the crossed stripes regions. When we remove the mask, the entire system becomes illuminated, and the reaction A ⇆ B occurs throughout the film: the ellipsoidal core-shell structures of A and C components turn to spherical structures, and the star structures of A and B components turn into concentric square ring structures. Then we show the influences of the number of cross stripes and the initial composition on the formation of structure. The average spatial volume fraction of C component first increases and then decreases with the stripy number increasing and the C component net lattices play an important role in the stability of ordered structures. Secondly, when the blend is covered by the annular mask, the C component gathers to the illuminated regions and the A and B components are in radial arrangement. As a result, the mixture forms an interesting dartboard-like pattern. However, when the mask is removed, the photochemical reactions occur in the A and B components of the whole region, the increasing of free energy induces the dartboard-like pattern to be broken and to change into dots-ring structure and then it forms a perfect concentric ring pattern and the target-like pattern. And also, we show the effects of initial composition ratio of C component, the distance between two adjacent rings D, the ring width d, and the illumination intensity on the evolution of ordered structure. The larger the initial composition ratio of C component, the more easily the ordered target-like pattern forms; the larger the distance D and the smaller the width d, the better the pinning effect of C component is. The illumination intensity has little influence on the ordered morphology of the ternary system. We provide a simple approach to creating multi-scale patterned films with long-range order, which could guide us in fabricating nanoscale devices.
      通信作者: 潘俊星, panjunxing2007@163.com;zhangjinjun@sxnu.edu.cn ; 张进军, panjunxing2007@163.com;zhangjinjun@sxnu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 21373131)、教育部高等学校博士点专项基金(批准号: 20121404110004)、山西省自然科学基金(批准号: 2015011004)、山西省人社厅优秀人才专项基金和山西省高校科技创新项目资助的课题.
      Corresponding author: Pan Jun-Xing, panjunxing2007@163.com;zhangjinjun@sxnu.edu.cn ; Zhang Jin-Jun, panjunxing2007@163.com;zhangjinjun@sxnu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 21373131), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20121404110004), the Provincial Natural Science Foundation of Shanxi, China (Grant No. 2015011004), the Research Foundation for Excellent Talents of Shanxi Provincial Department of Human Resources and Social Security, China, and the Provincial Science and Technology Innovation Project Foundation of Shanxi, China.
    [1]

    Sun M N, Zhang J J, Wang B F, Wu H S, Pan J X 2011 Phys. Rev. E 84 011812

    [2]

    Jang S G, Khan A, Dimitriou M D, Kim B J, Lynd N A, Kramer E J, Hawker C J 2011 Soft Matter 7 6255

    [3]

    Parnell A J, Pryke A, Mykhaylyk O O, Howse J R, Adawi A M, Terrill N J, Fairclough J P A 2011 Soft Matter 7 3721

    [4]

    Hong S W, Gu X D, Huh J, Xiao S G, Russell T P 2011 ACS Nano 5 2855

    [5]

    Bates F S, Maurer W, Lodge T P, Schulz MF, Matsen M W, Almdal K, Mortensen K 1995 Phys. Rev. Lett. 75 4429

    [6]

    Zhang J J, Jin G J, Ma Y Q 2006 J. Phys.: Condens. Matter 18 837

    [7]

    Ruokolainen J, Mäkinen R, Torkkeli M, Mäkelä T, Serimaa R, ten Brinke G, Ikkala O 1998 Science 280 557

    [8]

    Ruokolainen J, Saariaho M, Ikkala O 1999 Macromolecules 32 1152

    [9]

    Travasso R D M, Kuksenok O, Balazs A C 2005 Langmuir 21 10912

    [10]

    Kuksenok O, Travasso R D M, Balazs A C 2006 Phys. Rev. E 74 011502

    [11]

    Travasso R D M, Kuksenok O, Balazs A C 2006 Langmuir 22 2620

    [12]

    Puri S, Kumar D 2004 Phys. Rev. E 70 051501

    [13]

    Lakshmi K C, Kumar P B S 2003 Phys. Rev. E 67 011507

    [14]

    Tafa K, Puri S, Kumar D 2001 Phys. Rev. E 64 056139

    [15]

    Ma Y Q 2001 J. Chem. Phys. 114 3734

    [16]

    Huang C, de la Cruz M O, Swift B W 1996 Macromolecules 28 7996

    [17]

    Zhang L C, Sun M N, Pan J X, Wang B F, Zhang J J, Wu H S 2013 Chin. Phys. B 22 096401

    [18]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. B 22 026401

    [19]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. Lett. 30 046401

    [20]

    Pinna M, Hiltl S, Guo X H, Böker A, Zvelindovsky A V 2010 ACS Nano 4 2845

    [21]

    Chen H Y, Peng C J, Sun L, Liu H L, Hu Y 2007 Langmuir 23 11112

    [22]

    Chen H Y, Chen X Q, Ye Z C, Liu H L, Hu Y 2010 Langmuir 26 6663

    [23]

    Hao Q H, Miao B, Song Q G, Niu X H, Liu T J 2014 Polymer 55 4281

    [24]

    Xu Y C, Li W H, Qiu F, Lin Z Q 2014 Nanoscale 6 6844

    [25]

    Li M, Zhu Y J 2008 Acta Phys. Sin. 57 7555 (in Chinese) [李明, 诸跃进 2008 物理学报 57 7555]

    [26]

    Tong H P, Zhang L X 2012 Acta Phys. Sin. 61 058701 (in Chinese) [仝焕平, 章林溪 2012 物理学报 61 058701]

    [27]

    Zhang J J, Jin G J, Ma Y Q 2005 Phys. Rev. E 71 051803

    [28]

    Pinna M, Zvelindovsky A V 2008 Soft Matter 4 316

    [29]

    Xu T, Craig J H, Russell T P 2003 Macromolecules 36 6178

    [30]

    Böker A, Schmidt K, Knoll A, Zettl H, Hansel H, Urban V, Abetz V, Krausch G 2006 Polymer 47 849

    [31]

    Schmidt K, Böker A, Zettl H, Schubert F, Hänsel H, Fischer F, Weiss T M, Abetz V, Zvelindovsky A V, Sevink G J A, Krausch G 2005 Langmuir 21 11974

    [32]

    Hong Y R, Admson D H, Chainkin P M, Register R A 2009 Soft Matter 5 1687

    [33]

    Chen K, Ma Y Q 2002 J. Chem. Phys. 116 7783

    [34]

    Morozov A N, Zvelindovsky A V, Fraaije J G E M 2001 Phys. Rev. E 64 051803

    [35]

    Morozov A N, Fraaije J G E M 2002 Phys. Rev. E 65 031803

    [36]

    You L Y, Chen L J, Qian H J, Lu Z Y 2007 Macromolecules 40 5222

    [37]

    Pan Z Q, He L L, Zhang L X, Liang H J 2011 Polymer 52 2711

    [38]

    Nikoubashman A, Davis R L, Michal B T, Chaikin P M, Register R A, Panagiotopoulos A Z 2014 ACS Nano 8 8015

    [39]

    Nikoubashman A, Register R A, Panagiotopoulos A Z 2013 Soft Matter 9 9960

    [40]

    Guo Y Q, Zhang J J, Wang B F, Wu H S, Sun M N, Pan J X 2015 Condens. Matter Phys. 18 23801

    [41]

    Peng G W, Qiu F, Ginzburg V V, Jasnow D, Balazs A C 2000 Science 288 1802

    [42]

    Deng Z Y, Zhang L X 2015 Acta Phys. Sin. 64 0168201 (in Chinese) [邓真渝, 章林溪 2015 物理学报 64 0168201]

    [43]

    Chen K, Ma Y Q 2002 Phys. Rev. E 65 041501

    [44]

    Zhu Y J, Ma Y Q 2003 Chin. Phys. Lett. 20 703

    [45]

    Zhang J J, Jin G J, Ma Y Q 2005 Eur. Phys. J. E 18 359

    [46]

    Liu Y, Kuksenok O, Balazs A C 2013 Langmuir 29 750

    [47]

    Dayal P, Kuksenok O, Balazs A C 2008 Langmuir 24 1621

    [48]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. Lett. 30 076401

    [49]

    Grzybowski B A, Campbell C J 2007 Mater. Today 10 38

    [50]

    Glotzer S C, Stauffer D, Jan N 1994 Phys. Rev. Lett. 72 4109

    [51]

    Qiu T C, Kawai J J, Endoh K 1999 Chaos 9 298

    [52]

    Colvin V L, Larson R G, Harris A L, Schilling M L 1997 J. Appl. Phys. 81 5913

    [53]

    Kellogg G J, Walton D G, Mayes A M 1996 Phys. Rev. Lett. 76 2503

    [54]

    Christensen J J, Elder K, Fogedby H C 1996 Phys. Rev. E 54 R2212

    [55]

    Glotzer S C, Marzio E A Di, Muthukumar M 1995 Phys. Rev. Lett. 74 2034

    [56]

    Purit S, Frisch H L 1994 J. Phys. A: Math. Gen. 27 6027

    [57]

    Tran C Q, Kawai J J, Nishikawa Y, Jinnai H 1999 Phys. Rev. E 60 R1150

    [58]

    Nishioka H, Kida K, Yano O, Tran C Q 2000 Macromolecules 33 4301

    [59]

    Liu B, Tong C H, Yang Y L 2001 J. Phys. Chem.B 105 10091

    [60]

    Tong C H, Yang Y L 2002 J. Chem. Phys. 116 1519

    [61]

    Tong C H, Zhang H D, Yang Y L 2002 J. Phys. Chem. B 106 7869

    [62]

    Zhu Y J, Ma Y Q 2003 Phys. Rev. E 67 021804

    [63]

    Okuzono T, Ohta T 2003 Phys. Rev. E 67 056211

    [64]

    Good K, Kuksenok O, Buxton G A, Ginzburg V V, Balazs A C 2004 J. Chem. Phys. 121 6052

    [65]

    Nakanishi H, Satoh M, Norisuye T, Tran C Q 2004 Macromolecules 37 8495

    [66]

    Oono Y, Puri S 1987 Phys. Rev. Lett. 58 836

    [67]

    Puri S, Oono Y 1988 Phys. Rev. A 38 1542

    [68]

    Oono Y, Puri S 1988 Phys. Rev. A 38 434

    [69]

    Travasso R D M, Buxton G A, Kuksenok O, Good K, Balazs A C 2005 J. Chem. Phys. 122 194906 ten Brinke G, Ikkala O 1998 Science 280 557

  • [1]

    Sun M N, Zhang J J, Wang B F, Wu H S, Pan J X 2011 Phys. Rev. E 84 011812

    [2]

    Jang S G, Khan A, Dimitriou M D, Kim B J, Lynd N A, Kramer E J, Hawker C J 2011 Soft Matter 7 6255

    [3]

    Parnell A J, Pryke A, Mykhaylyk O O, Howse J R, Adawi A M, Terrill N J, Fairclough J P A 2011 Soft Matter 7 3721

    [4]

    Hong S W, Gu X D, Huh J, Xiao S G, Russell T P 2011 ACS Nano 5 2855

    [5]

    Bates F S, Maurer W, Lodge T P, Schulz MF, Matsen M W, Almdal K, Mortensen K 1995 Phys. Rev. Lett. 75 4429

    [6]

    Zhang J J, Jin G J, Ma Y Q 2006 J. Phys.: Condens. Matter 18 837

    [7]

    Ruokolainen J, Mäkinen R, Torkkeli M, Mäkelä T, Serimaa R, ten Brinke G, Ikkala O 1998 Science 280 557

    [8]

    Ruokolainen J, Saariaho M, Ikkala O 1999 Macromolecules 32 1152

    [9]

    Travasso R D M, Kuksenok O, Balazs A C 2005 Langmuir 21 10912

    [10]

    Kuksenok O, Travasso R D M, Balazs A C 2006 Phys. Rev. E 74 011502

    [11]

    Travasso R D M, Kuksenok O, Balazs A C 2006 Langmuir 22 2620

    [12]

    Puri S, Kumar D 2004 Phys. Rev. E 70 051501

    [13]

    Lakshmi K C, Kumar P B S 2003 Phys. Rev. E 67 011507

    [14]

    Tafa K, Puri S, Kumar D 2001 Phys. Rev. E 64 056139

    [15]

    Ma Y Q 2001 J. Chem. Phys. 114 3734

    [16]

    Huang C, de la Cruz M O, Swift B W 1996 Macromolecules 28 7996

    [17]

    Zhang L C, Sun M N, Pan J X, Wang B F, Zhang J J, Wu H S 2013 Chin. Phys. B 22 096401

    [18]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. B 22 026401

    [19]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. Lett. 30 046401

    [20]

    Pinna M, Hiltl S, Guo X H, Böker A, Zvelindovsky A V 2010 ACS Nano 4 2845

    [21]

    Chen H Y, Peng C J, Sun L, Liu H L, Hu Y 2007 Langmuir 23 11112

    [22]

    Chen H Y, Chen X Q, Ye Z C, Liu H L, Hu Y 2010 Langmuir 26 6663

    [23]

    Hao Q H, Miao B, Song Q G, Niu X H, Liu T J 2014 Polymer 55 4281

    [24]

    Xu Y C, Li W H, Qiu F, Lin Z Q 2014 Nanoscale 6 6844

    [25]

    Li M, Zhu Y J 2008 Acta Phys. Sin. 57 7555 (in Chinese) [李明, 诸跃进 2008 物理学报 57 7555]

    [26]

    Tong H P, Zhang L X 2012 Acta Phys. Sin. 61 058701 (in Chinese) [仝焕平, 章林溪 2012 物理学报 61 058701]

    [27]

    Zhang J J, Jin G J, Ma Y Q 2005 Phys. Rev. E 71 051803

    [28]

    Pinna M, Zvelindovsky A V 2008 Soft Matter 4 316

    [29]

    Xu T, Craig J H, Russell T P 2003 Macromolecules 36 6178

    [30]

    Böker A, Schmidt K, Knoll A, Zettl H, Hansel H, Urban V, Abetz V, Krausch G 2006 Polymer 47 849

    [31]

    Schmidt K, Böker A, Zettl H, Schubert F, Hänsel H, Fischer F, Weiss T M, Abetz V, Zvelindovsky A V, Sevink G J A, Krausch G 2005 Langmuir 21 11974

    [32]

    Hong Y R, Admson D H, Chainkin P M, Register R A 2009 Soft Matter 5 1687

    [33]

    Chen K, Ma Y Q 2002 J. Chem. Phys. 116 7783

    [34]

    Morozov A N, Zvelindovsky A V, Fraaije J G E M 2001 Phys. Rev. E 64 051803

    [35]

    Morozov A N, Fraaije J G E M 2002 Phys. Rev. E 65 031803

    [36]

    You L Y, Chen L J, Qian H J, Lu Z Y 2007 Macromolecules 40 5222

    [37]

    Pan Z Q, He L L, Zhang L X, Liang H J 2011 Polymer 52 2711

    [38]

    Nikoubashman A, Davis R L, Michal B T, Chaikin P M, Register R A, Panagiotopoulos A Z 2014 ACS Nano 8 8015

    [39]

    Nikoubashman A, Register R A, Panagiotopoulos A Z 2013 Soft Matter 9 9960

    [40]

    Guo Y Q, Zhang J J, Wang B F, Wu H S, Sun M N, Pan J X 2015 Condens. Matter Phys. 18 23801

    [41]

    Peng G W, Qiu F, Ginzburg V V, Jasnow D, Balazs A C 2000 Science 288 1802

    [42]

    Deng Z Y, Zhang L X 2015 Acta Phys. Sin. 64 0168201 (in Chinese) [邓真渝, 章林溪 2015 物理学报 64 0168201]

    [43]

    Chen K, Ma Y Q 2002 Phys. Rev. E 65 041501

    [44]

    Zhu Y J, Ma Y Q 2003 Chin. Phys. Lett. 20 703

    [45]

    Zhang J J, Jin G J, Ma Y Q 2005 Eur. Phys. J. E 18 359

    [46]

    Liu Y, Kuksenok O, Balazs A C 2013 Langmuir 29 750

    [47]

    Dayal P, Kuksenok O, Balazs A C 2008 Langmuir 24 1621

    [48]

    Pan J X, Zhang J J, Wang B F, Wu H S, Sun M N 2013 Chin. Phys. Lett. 30 076401

    [49]

    Grzybowski B A, Campbell C J 2007 Mater. Today 10 38

    [50]

    Glotzer S C, Stauffer D, Jan N 1994 Phys. Rev. Lett. 72 4109

    [51]

    Qiu T C, Kawai J J, Endoh K 1999 Chaos 9 298

    [52]

    Colvin V L, Larson R G, Harris A L, Schilling M L 1997 J. Appl. Phys. 81 5913

    [53]

    Kellogg G J, Walton D G, Mayes A M 1996 Phys. Rev. Lett. 76 2503

    [54]

    Christensen J J, Elder K, Fogedby H C 1996 Phys. Rev. E 54 R2212

    [55]

    Glotzer S C, Marzio E A Di, Muthukumar M 1995 Phys. Rev. Lett. 74 2034

    [56]

    Purit S, Frisch H L 1994 J. Phys. A: Math. Gen. 27 6027

    [57]

    Tran C Q, Kawai J J, Nishikawa Y, Jinnai H 1999 Phys. Rev. E 60 R1150

    [58]

    Nishioka H, Kida K, Yano O, Tran C Q 2000 Macromolecules 33 4301

    [59]

    Liu B, Tong C H, Yang Y L 2001 J. Phys. Chem.B 105 10091

    [60]

    Tong C H, Yang Y L 2002 J. Chem. Phys. 116 1519

    [61]

    Tong C H, Zhang H D, Yang Y L 2002 J. Phys. Chem. B 106 7869

    [62]

    Zhu Y J, Ma Y Q 2003 Phys. Rev. E 67 021804

    [63]

    Okuzono T, Ohta T 2003 Phys. Rev. E 67 056211

    [64]

    Good K, Kuksenok O, Buxton G A, Ginzburg V V, Balazs A C 2004 J. Chem. Phys. 121 6052

    [65]

    Nakanishi H, Satoh M, Norisuye T, Tran C Q 2004 Macromolecules 37 8495

    [66]

    Oono Y, Puri S 1987 Phys. Rev. Lett. 58 836

    [67]

    Puri S, Oono Y 1988 Phys. Rev. A 38 1542

    [68]

    Oono Y, Puri S 1988 Phys. Rev. A 38 434

    [69]

    Travasso R D M, Buxton G A, Kuksenok O, Good K, Balazs A C 2005 J. Chem. Phys. 122 194906 ten Brinke G, Ikkala O 1998 Science 280 557

  • [1] 张银胜, 童俊毅, 陈戈, 单梦姣, 王硕洋, 单慧琳. 基于多尺度特征增强的合成孔径光学图像复原. 物理学报, 2024, 73(6): 064203. doi: 10.7498/aps.73.20231761
    [2] 侯凤贞, 黄晓林, 庄建军, 霍铖宇, 宁新宝. 多尺度策略和替代数据检验——HRV时间不可逆性分析的两个要素. 物理学报, 2012, 61(22): 220507. doi: 10.7498/aps.61.220507
    [3] 何建平, 吕文中, 汪小红. Ba0.5Sr0.5TiO3有序构型的第一性原理研究. 物理学报, 2011, 60(9): 097102. doi: 10.7498/aps.60.097102
    [4] 陆怀宝, 黎军顽, 倪玉山, 梅继法, 王洪生. 体心立方金属钽Ⅱ型裂纹尖端缺陷萌生的多尺度分析. 物理学报, 2011, 60(10): 106101. doi: 10.7498/aps.60.106101
    [5] 曹功勋, 张晓青, 孙转兰, 王学文, 娄可行, 夏钟福. 人工调控微结构压电驻极体的热稳定性和电荷动态特性. 物理学报, 2010, 59(9): 6514-6520. doi: 10.7498/aps.59.6514
    [6] 孙转兰, 张晓青, 曹功勋, 王学文, 夏钟福. 有序结构氟聚合物压电驻极体的制备和压电性研究. 物理学报, 2010, 59(7): 5061-5066. doi: 10.7498/aps.59.5061
    [7] 邢真慈, 徐伟, 戎海武, 王宝燕. 有界噪声激励下带有时滞反馈的随机Mathieu-Duffing系统的响应. 物理学报, 2009, 58(2): 824-829. doi: 10.7498/aps.58.824
    [8] 龚志强, 周 磊, 支 蓉, 封国林. 1—30d尺度温度关联网动力学统计性质研究. 物理学报, 2008, 57(8): 5351-5360. doi: 10.7498/aps.57.5351
    [9] 杨小冬, 宁新宝, 何爱军, 都思丹. 基于多尺度的人体ECG信号质量指数谱分析. 物理学报, 2008, 57(3): 1514-1521. doi: 10.7498/aps.57.1514
    [10] 雷佑铭, 徐 伟. 有界噪声和谐和激励联合作用下一类非线性系统的混沌研究. 物理学报, 2007, 56(9): 5103-5110. doi: 10.7498/aps.56.5103
    [11] 宋庆功, 姜恩永, 裴海林, 康建海, 郭 英. 插层化合物LixTiS2中Li离子-空位二维有序结构稳定性的第一性原理研究. 物理学报, 2007, 56(8): 4817-4822. doi: 10.7498/aps.56.4817
    [12] 张永炬, 余森江, 葛洪良, 邬良能, 崔玉建. 硅油基底表面铁薄膜的生长机理及表面有序结构. 物理学报, 2006, 55(10): 5444-5450. doi: 10.7498/aps.55.5444
    [13] 夏阿根, 杨 波, 金进生, 张亦文, 汤 凡, 叶高翔. 液体基底表面金薄膜中的有序结构和自组装现象. 物理学报, 2005, 54(1): 302-306. doi: 10.7498/aps.54.302
    [14] 张永炬, 余森江. 准自由支撑铝薄膜中有序表面结构的自组织生长. 物理学报, 2005, 54(10): 4867-4873. doi: 10.7498/aps.54.4867
    [15] 胡隐樵. 强迫耗散系统的有序结构和系统的发展(Ⅱ),广义能量极小值原理和系统的发展. 物理学报, 2003, 52(6): 1354-1359. doi: 10.7498/aps.52.1354
    [16] 胡隐樵. 强迫耗散系统的有序结构和系统的发展(Ⅰ),最小熵产生原理和有序结构. 物理学报, 2003, 52(6): 1379-1384. doi: 10.7498/aps.52.1379
    [17] 姜泽辉, 陆坤权, 厚美瑛, 陈 唯, 陈相君. 振动颗粒混合物中的三明治式分离. 物理学报, 2003, 52(9): 2244-2248. doi: 10.7498/aps.52.2244
    [18] 马坚伟, 杨慧珠, 朱亚平. 多尺度有限差分法模拟复杂介质波传问题. 物理学报, 2001, 50(8): 1415-1420. doi: 10.7498/aps.50.1415
    [19] 宋庆功, 丛选忠, 张庆军, 莫文玲, 戴占海. 六角蜂窝晶格的有序结构. 物理学报, 2000, 49(10): 2011-2016. doi: 10.7498/aps.49.2011
    [20] 宋庆功, 戴占海, 丛选忠, 魏 环, 张庆军. 六方密堆二元合金的有序结构. 物理学报, 2000, 49(11): 2201-2209. doi: 10.7498/aps.49.2201
计量
  • 文章访问数:  5678
  • PDF下载量:  160
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-09-28
  • 修回日期:  2015-12-21
  • 刊出日期:  2016-03-05

/

返回文章
返回