A summary of soft matter theories

Wu Chen-Xu; Yan Da-Dong; Xing Xiang-Jun; Hou Mei-Ying

doi:10.7498/aps.65.186102

Abstract

This paper summarizes some theories widely used in soft matter systems, such as elastic theory, phase transition theory, scaling law, theory of granular particles, self-consistent field theory, etc. The role entropy plays in softmatter systems is also discussed. Other dynamic theories like adhesion, diffusion, wave motion, etc. are not included here.

Keywords:

Authors and contacts

1.
Research Institute for Biomimetics and Soft Matter, College of Physics and Technology, Xiamen University, Xiamen 361005, China;
2.
Department of Physics, Beijing Normal University, Beijing 100875, China;
3.
Department of Physics and Astrophysics, Shanghai Jiaotong University, Shanghai 200240, China;
4.
Key Laboratory of Soft Matter Physics, Beijing National Laboratory for Condense Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Wu Chen-Xu, cxwu@xmu.edu.cn;yandd@bnu.edu.cn;xxing@sjtu.edu.cn;mayhou@aphy.iphy.ac.cn ; Yan Da-Dong, cxwu@xmu.edu.cn;yandd@bnu.edu.cn;xxing@sjtu.edu.cn;mayhou@aphy.iphy.ac.cn ; Xing Xiang-Jun, cxwu@xmu.edu.cn;yandd@bnu.edu.cn;xxing@sjtu.edu.cn;mayhou@aphy.iphy.ac.cn ; Hou Mei-Ying, cxwu@xmu.edu.cn;yandd@bnu.edu.cn;xxing@sjtu.edu.cn;mayhou@aphy.iphy.ac.cn

References

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[2]	Helfrich W 1973 Z. Naturforsch. C 28 693
[3]	de Gennes P G 1969 Phys. Lett. A 30 454
[4]	de Gennes P G 1969 J. Phys. (Paris) 30 C4
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[8]	Kaplan J I, Drauglis E 1971 Chem. Phys. Lett. 9 645
[9]	Chandrasekhar S, Madhusudana N V 1970 Mol. Cryst. Liq. Cryst. 10 151
[10]	Onsager L 1949 Ann. NY Acad. Sci. 51 627
[11]	Straley J P 1973 Phys. Rev. A 5 2181
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[13]	Zocher H 1933 Trans. Faraday Soc. 29 945
[14]	Oseen C W 1933 Trans. Faraday Soc. 29 883
[15]	Frank F C 1958 Discuss. Faraday Soc. 25 19
[16]	Fredericksz V, Zona V 1931 Z. Krisrallogr. 79 225
[17]	Smalyukh I I, Lansac Y, Clark N A, Trivedi R P 2010 Nature Mater 9 1392010
[18]	Poulin P, Stark H, Lubensky T C, Weitz D A 1997 Science 275 1770
[19]	Terentjev E M 1995 Phys. Rev. E 51 1330
[20]	Ravnik M, Zǔmer S 2009 Soft Matter 5 269
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[24]	Bouligand Y, Kleman M 1970 J. Phys. (Paris) 31 1041
[25]	Cladis P E 1972 Phys. Rev. Lett. 28 1629
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[29]	Harris A B, Kamien R D, Lubensky T C 1999 Rev. Mod. Phys. 71 1745
[30]	Dupuis A, Marenduzzo D, Yeomans J M 2005 Phys. Rev. E 71 011703
[31]	Peng H G, Zhou Z, Merlitz H, Wu C X 2016 Chem. Phys. Lett. 653 196
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[46]	Izumi K, Laachi N, Man X, Delaney K T, Fredrickson G H 2014 Proc. SPIE 9049 904922
[47]	Izumi K, Laachi N, Delaney K T, Fredrickson G H 2015 J. Photopol. Sci. Technol. 28 689
[48]	Ginzburg V V, Weinhold J D, Hustad P D, Trefonas P, Kim B, Laachi N, Fredrickson G H 2015 Directed Self-Assembly of Block Copolymers for Nano-Manufacturing (in Grohheid R, Nealey P, Eds.) pp67-95 (Elsevier: Woodhead Publishing)
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[51]	Brown S, Szamel G 1998 J. Chem. Phys. 109 6184
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[53]	Muller M, Wittmer J P, Barrat J L 2000 Europhys. Lett. 52 406
[54]	Vettorel T, Grosberg A Y, Kremer K 2009 Phys. Biol. 6 025013
[55]	Takano A 2007 Polm. Prepr. Jpn. 56 2424
[56]	Sakaue T 2011 Phys. Rev. Lett. 106 167802
[57]	Bagnold R A 1954 Proc. R. Soc. London Ser. A 225 49
[58]	Midi D R 2004 Eur. Phys. J. E 14 341
[59]	Jop P, Forterre Y, Pouliquen O 2006 Nature 441 727
[60]	Goyon J, Colin A, Ovarlez G, Ajdari A, Bocquet L 2008 Nature 454 84
[61]	Argon A S 1979 Acta. Met. 27 749
[62]	Bi D, Zhang J, Chakraborty B, Behringer R 2011 Nature 480 355
[63]	Jiang Y M, Liu M 2009 Granular Matter 11 139
[64]	Roscoe K H, Schofield A N, Wroch C P 1958 Geotechnique 8 22
[65]	Roscoe K H, Schofield A N, Thurairajah A 1963 Geotechnique 13 211
[66]	Roscoe K H, Barland T B 1968 (in Heyman J, Lechies F A, Engineering Plasticity (Cambridge: Cambridge University Press) pp535-609
[67]	Andelman D 1995 Handbook of Biological Physics 1 603
[68]	Han M, Xing X 2013 J. Statist. Phys. 151 1121
[69]	Tata B V R, Mohanty P S, Valsakumar M C 2008 Solid State Communications 147 360
[70]	Boroudjerdi H, Kim Y W, Naji A, Netz R R, Schlagberger X 2005 Serr A. Phys. Rep. 416 129
[71]	Wang Z G 2010 Phys. Rev. E 81 021501
[72]	Borukhov I, Andelman D, Orland H 1997 Phys. Rev. Lett. 79 435
[73]	Ding M, Liang Y, Lu B S, Xing X 2015 arXiv preprint arXiv: 1502 06687
[74]	Kunz W 2010 Current Opinion in Colloid and Interface Science 15 34
[75]	Hansen J P, McDonald I R 2013 Theory of Simple Liquids (New York: Academic Press)
[76]	Cai W 2013 Computational Methods for Electromagnetic Phenomena: Electrostatics in Solvations, Scattering, and Electron Transport (London: Cambridge University Press)
[77]	Lin Y, Baumketner A, Deng S, Xu Z, Jacobs D, Cai W 2009 J. Chem. Phys. 131 154103
[78]	Liang Y, Xu Z, Xing X 2015 New J. Phys. 17 083062
[79]	Greengard L, Vladimir R 1987 J. Comp. Phys 73 325
[80]	Tubiana L, Orlandini E, Micheletti C 2011 Phys. Rev. Lett. 107 188302
[81]	Grosberg A Y, Rabin Y, Havlin S, Neer A 1993 Europhys. Lett. 23 373
[82]	Lieberman-Aiden E, van Berkum N L, Williams L, Imakaev M et al. 2009 Science 326 289
[83]	Rosa A, Everaers R 2008 PloS Comput. Biol. 4 e1000153
[84]	Jun S, Muller B 2006 Proc. Natl. Acad. Sci. USA 103 12388
[85]	Arsuaga J, Vazquez M, McGuirk P, Trigueros S, Sumners D W, Roca J 2005 Proc. Natl. Acad. Sci. USA 102 9165
[86]	Marenduzzo D, Orlandinib E, Stasiakc A, Sumners D W, Michelettie C 2009 Proc. Natl. Acad. Sci. USA 106 22269
[87]	Micheletti C, Marenduzzo D, Orlandini E, Sumners D W 2006 J. Chem. Phys. 124 064903
[88]	Nepal M, Yaniv A, Shafran E, Krichevsky O 2013 Phys. Rev. Lett. 110 058102
[89]	Walter J C, Baiesi M, Barkema G T, Carlon E 2013 Phys. Rev. Lett. 110 068301
[90]	Zhulina E B, Vilgis T A 1995 Macromolecules 28 1008
[91]	Kroeger M, Peleg O, Halperin A 2010 Macromolecules 43 6213
[92]	Merlitz H, Wu C X, Sommer J U 2011 Macromolecules 44 7043
[93]	Polotsky A A, Gillich T, Borisov O V, Leermakers F A M, Textor M, Birstein T M 2010 Macromolecules 43 9555
[94]	Cui W, Su C, Wu C X, Merlitz H, Sommer J U 2013 J. Chem. Phys. 139 134910
[95]	Merlitz H, He G L, Wu C X, Sommer J U 2009 Phys. Rev. Lett. 102 115702
[96]	Edwards S F, Oakeshott R B S 1989 Physica A 157 1080
[97]	Falk M L, Langer J S 1998 Phys. Rev. E 57 7192
[98]	Hansen J P, Lowen H 2000 arXiv preprint cond-mat/0002295

Cited By

[1]	Landau L D, Lifshitz E M 2013 Statistical Physics (New Delhi: Addison-Wesley)
[2]	Helfrich W 1973 Z. Naturforsch. C 28 693
[3]	de Gennes P G 1969 Phys. Lett. A 30 454
[4]	de Gennes P G 1969 J. Phys. (Paris) 30 C4
[5]	Maier W, Saupe A 1958 Z. Naturforsch A 13 564
[6]	Maier W, Saupe A 1959 Z. Naturforsch A 14 882
[7]	Maier W, Saupe A 1960 Z. Naturforsch A 15 287
[8]	Kaplan J I, Drauglis E 1971 Chem. Phys. Lett. 9 645
[9]	Chandrasekhar S, Madhusudana N V 1970 Mol. Cryst. Liq. Cryst. 10 151
[10]	Onsager L 1949 Ann. NY Acad. Sci. 51 627
[11]	Straley J P 1973 Phys. Rev. A 5 2181
[12]	Straley J P 1973 Mol. Cryst. Liq. Cryst. 22 333
[13]	Zocher H 1933 Trans. Faraday Soc. 29 945
[14]	Oseen C W 1933 Trans. Faraday Soc. 29 883
[15]	Frank F C 1958 Discuss. Faraday Soc. 25 19
[16]	Fredericksz V, Zona V 1931 Z. Krisrallogr. 79 225
[17]	Smalyukh I I, Lansac Y, Clark N A, Trivedi R P 2010 Nature Mater 9 1392010
[18]	Poulin P, Stark H, Lubensky T C, Weitz D A 1997 Science 275 1770
[19]	Terentjev E M 1995 Phys. Rev. E 51 1330
[20]	Ravnik M, Zǔmer S 2009 Soft Matter 5 269
[21]	Dzyaloshinskii I E 1970 Sov. Phys. JETP 31 773
[22]	Friedel J, de Gennes P G 1969 C. R. Scad. Sci. B 268 257
[23]	Kleman M, Friedel J 1969 J. Phys. (Paris) 30 C4
[24]	Bouligand Y, Kleman M 1970 J. Phys. (Paris) 31 1041
[25]	Cladis P E 1972 Phys. Rev. Lett. 28 1629
[26]	Coleman S 1975 Phys. Rev. D 11 2088
[27]	Polyakov A M 1974 ZhETF Pis. Red. 20 430
[28]	Priest R G, Lubensky T C 1974 Phys. Rev. A 9 893
[29]	Harris A B, Kamien R D, Lubensky T C 1999 Rev. Mod. Phys. 71 1745
[30]	Dupuis A, Marenduzzo D, Yeomans J M 2005 Phys. Rev. E 71 011703
[31]	Peng H G, Zhou Z, Merlitz H, Wu C X 2016 Chem. Phys. Lett. 653 196
[32]	Helfrich W 1973 Zeitschrift fr Naturforschung C 28 693
[33]	Ouyang Z C, Helfrich W 1987 Phys. Rev. Lett. 59 2486
[34]	Ouyang Z C, Helfrich W 1989 Phys. Rev. A 39 5280
[35]	Bausch A R, Kroy K 2006 Nat. Phys. 2 231
[36]	Fletcher D A, Mullins R D 2010 Nature 463 485
[37]	Kratky O, Porod G 1949 Recl. Trav. Chim. 68 1106
[38]	Heussinger C, Bathe M, Frey E 2007 Phys. Rev. Lett. 99 048101
[39]	Taute K M, Pampaloni F, Frey E, Florin E L 2008 Phys. Rev. Lett. 100 028102
[40]	Edwards S F 1965 Proc. Phys. Soc. 85 613
[41]	Matsen M W, Schick M 1994 Phys. Rev. Lett. 72 2660
[42]	Fredrickson G H 2006 The Equilibrium Theory of Inhomogeneous Polymers (Oxford: Clarendon Press)
[43]	Lennon E M, Katsov K, Fredrickson G H 2008 Phys. Rev. Lett. 101 138302
[44]	Man X K, Delaney K, Villet M, Orland H, Fredrickson G H 2014 J. Chem. Phys. 140 024905
[45]	Villet M C, Fredrickson G H 2014 J. Chem. Phys. 141 224115
[46]	Izumi K, Laachi N, Man X, Delaney K T, Fredrickson G H 2014 Proc. SPIE 9049 904922
[47]	Izumi K, Laachi N, Delaney K T, Fredrickson G H 2015 J. Photopol. Sci. Technol. 28 689
[48]	Ginzburg V V, Weinhold J D, Hustad P D, Trefonas P, Kim B, Laachi N, Fredrickson G H 2015 Directed Self-Assembly of Block Copolymers for Nano-Manufacturing (in Grohheid R, Nealey P, Eds.) pp67-95 (Elsevier: Woodhead Publishing)
[49]	de Gennes P G 1979 Scaling Concepts in Polymer Physics (Ithaca: Cornell University Press)
[50]	Pakula T, Geyler S 1998 Macromolecules 21 1665
[51]	Brown S, Szamel G 1998 J. Chem. Phys. 109 6184
[52]	Muller M, Wittmer J P, Cates M E 2000 Phys. Rev. E 61 4078
[53]	Muller M, Wittmer J P, Barrat J L 2000 Europhys. Lett. 52 406
[54]	Vettorel T, Grosberg A Y, Kremer K 2009 Phys. Biol. 6 025013
[55]	Takano A 2007 Polm. Prepr. Jpn. 56 2424
[56]	Sakaue T 2011 Phys. Rev. Lett. 106 167802
[57]	Bagnold R A 1954 Proc. R. Soc. London Ser. A 225 49
[58]	Midi D R 2004 Eur. Phys. J. E 14 341
[59]	Jop P, Forterre Y, Pouliquen O 2006 Nature 441 727
[60]	Goyon J, Colin A, Ovarlez G, Ajdari A, Bocquet L 2008 Nature 454 84
[61]	Argon A S 1979 Acta. Met. 27 749
[62]	Bi D, Zhang J, Chakraborty B, Behringer R 2011 Nature 480 355
[63]	Jiang Y M, Liu M 2009 Granular Matter 11 139
[64]	Roscoe K H, Schofield A N, Wroch C P 1958 Geotechnique 8 22
[65]	Roscoe K H, Schofield A N, Thurairajah A 1963 Geotechnique 13 211
[66]	Roscoe K H, Barland T B 1968 (in Heyman J, Lechies F A, Engineering Plasticity (Cambridge: Cambridge University Press) pp535-609
[67]	Andelman D 1995 Handbook of Biological Physics 1 603
[68]	Han M, Xing X 2013 J. Statist. Phys. 151 1121
[69]	Tata B V R, Mohanty P S, Valsakumar M C 2008 Solid State Communications 147 360
[70]	Boroudjerdi H, Kim Y W, Naji A, Netz R R, Schlagberger X 2005 Serr A. Phys. Rep. 416 129
[71]	Wang Z G 2010 Phys. Rev. E 81 021501
[72]	Borukhov I, Andelman D, Orland H 1997 Phys. Rev. Lett. 79 435
[73]	Ding M, Liang Y, Lu B S, Xing X 2015 arXiv preprint arXiv: 1502 06687
[74]	Kunz W 2010 Current Opinion in Colloid and Interface Science 15 34
[75]	Hansen J P, McDonald I R 2013 Theory of Simple Liquids (New York: Academic Press)
[76]	Cai W 2013 Computational Methods for Electromagnetic Phenomena: Electrostatics in Solvations, Scattering, and Electron Transport (London: Cambridge University Press)
[77]	Lin Y, Baumketner A, Deng S, Xu Z, Jacobs D, Cai W 2009 J. Chem. Phys. 131 154103
[78]	Liang Y, Xu Z, Xing X 2015 New J. Phys. 17 083062
[79]	Greengard L, Vladimir R 1987 J. Comp. Phys 73 325
[80]	Tubiana L, Orlandini E, Micheletti C 2011 Phys. Rev. Lett. 107 188302
[81]	Grosberg A Y, Rabin Y, Havlin S, Neer A 1993 Europhys. Lett. 23 373
[82]	Lieberman-Aiden E, van Berkum N L, Williams L, Imakaev M et al. 2009 Science 326 289
[83]	Rosa A, Everaers R 2008 PloS Comput. Biol. 4 e1000153
[84]	Jun S, Muller B 2006 Proc. Natl. Acad. Sci. USA 103 12388
[85]	Arsuaga J, Vazquez M, McGuirk P, Trigueros S, Sumners D W, Roca J 2005 Proc. Natl. Acad. Sci. USA 102 9165
[86]	Marenduzzo D, Orlandinib E, Stasiakc A, Sumners D W, Michelettie C 2009 Proc. Natl. Acad. Sci. USA 106 22269
[87]	Micheletti C, Marenduzzo D, Orlandini E, Sumners D W 2006 J. Chem. Phys. 124 064903
[88]	Nepal M, Yaniv A, Shafran E, Krichevsky O 2013 Phys. Rev. Lett. 110 058102
[89]	Walter J C, Baiesi M, Barkema G T, Carlon E 2013 Phys. Rev. Lett. 110 068301
[90]	Zhulina E B, Vilgis T A 1995 Macromolecules 28 1008
[91]	Kroeger M, Peleg O, Halperin A 2010 Macromolecules 43 6213
[92]	Merlitz H, Wu C X, Sommer J U 2011 Macromolecules 44 7043
[93]	Polotsky A A, Gillich T, Borisov O V, Leermakers F A M, Textor M, Birstein T M 2010 Macromolecules 43 9555
[94]	Cui W, Su C, Wu C X, Merlitz H, Sommer J U 2013 J. Chem. Phys. 139 134910
[95]	Merlitz H, He G L, Wu C X, Sommer J U 2009 Phys. Rev. Lett. 102 115702
[96]	Edwards S F, Oakeshott R B S 1989 Physica A 157 1080
[97]	Falk M L, Langer J S 1998 Phys. Rev. E 57 7192
[98]	Hansen J P, Lowen H 2000 arXiv preprint cond-mat/0002295

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