Theory of wormlike polymer chains in confinement

Progress in Polymer Science

Volumn 54-55, Issue , 2016, Pages 3-46

  Chen, Jeff Z Y ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Computation; Physics; Polymers

Indexed keywords

CALCULATIONS; COMPUTATION THEORY; CRYSTAL ORIENTATION; DEGREES OF FREEDOM (MECHANICS); FREE ENERGY; LIQUID CRYSTALS; MEAN FIELD THEORY; MOLECULAR ORBITALS; PHYSICS; POLYMERS; POTENTIAL ENERGY; SURFACE DEFECTS;

CONFINED LIQUID CRYSTALS; CONFORMATIONAL PROPERTIES; MATHEMATICAL TREATMENTS; ORIENTATIONAL DEFECTS; ORIENTATIONAL DEPENDENCE; SELF CONSISTENT FIELD THEORY; SEMI-FLEXIBLE POLYMERS; WORM-LIKE CHAIN MODELS;

CHAINS;

EID: 84961339328     PISSN: 00796700     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.progpolymsci.2015.09.002     Document Type: Review

References (157)

1. M. Doi, and S.F. Edwards The theory of polymer dynamics 1988 Oxford University Press New York 391
2. G.H. Fredrickson The equilibrium theory of inhomogeneous polymers 2006 Clarendon Press Oxford 456
3. O. Kratky, and G. Porod Röntgenuntersuchung Gelöster Fadenmoleküle Recl. des Trav. Chim. des Pays-Bas 68 12 1949 1106 1122
4. N. Saitô, K. Takahashi, and Y. Yunoki The statistical mechanical theory of stiff chains J Phys Soc Jpn 22 1 1967 219 226
5. Z.Y. Chen Continuous isotropic-nematic transition of partially flexible polymers in two dimensions Phys Rev Lett 71 1 1993 93 96
6. Z.Y. Chen Nematic ordering in semiflexible polymer chains Macromolecules 26 13 1993 3419 3423
7. K.F. Freed Functional integrals and polymer statistics Adv Chem Phys 22 1 1972 1 128
8. Q. Liang, J. Li, P. Zhang, and J.Z.Y. Chen Modified diffusion equation for the wormlike-chain statistics in curvilinear coordinates J Chem Phys 138 24 2013 244910/1-6
9. Y. Jiang, and J.Z.Y. Chen Self-consistent field theory and numerical scheme for calculating the phase diagram of wormlike diblock copolymers Phys Rev E 88 4 2013 042603/1-14
10. M. Doi Soft matter physics 2013 Oxford University Press New York 312
11. Y. Yang, T.W. Burkhardt, and G. Gompper Free energy and extension of a semiflexible polymer in cylindrical confining geometries Phys Rev E 76 2007 011804/1-7
12. T.W. Burkhardt, Y. Yang, and G. Gompper Fluctuations of a long, semiflexible polymer in a narrow channel Phys Rev E 82 2010 041801/1-9
13. Z. Benkova, and P. Cifra Simulation of semiflexible cyclic and linear chains moderately and strongly confined in nanochannels Macromolecules 45 5 2012 2597 2608
14. G. Morrison, and D. Thirumalai Semiflexible chains in confined spaces Phys Rev E 79 2009 011924/1-14
15. J.Z.Y. Chen Free energy and extension of a wormlike chain in tube confinement Macromolecules 46 24 2013 9837 9844
16. J. Gao, P. Tang, Y. Yang, and J.Z.Y. Chen Free energy of a long semiflexible polymer confined in a spherical cavity Soft Matter 10 2014 4674 4685
17. N.V. Hud Double-stranded DNA organization in bacteriophage heads: an alternative toroid-based model Biophys J 69 4 1995 1355 1362
18. Y.-F. Wei, and P.-Y. Hsiao Role of chain stiffness on the conformation of single polyelectrolytes in salt solutions J Chem Phys 127 6 2007 064901/1-14
19. A.J. Spakowitz, and Z.-G. Wang Semiflexible polymer confined to a spherical surface Phys Rev Lett 91 2003 166102/1-4
20. C.-H. Lin, Y.-C. Tsai, and C.-K. Hu Wrapping conformations of a polymer on a curved surface Phys Rev E 75 2007 031903/1-11
21. I. Gurevitch, and S. Srebnik Conformational behavior of polymers adsorbed on nanotubes J Chem Phys 128 14 2008 144901/1-9
22. D.G. Angelescu, P. Linse, T.T. Nguyen, and R.F. Bruinsma Structural transitions of encapsidated polyelectrolytes Eur Phys J E 25 3 2008 323 334
23. W.-Y. Zhang, and J.Z.Y. Chen Tennis-ball state of a self-avoiding wormlike polymer on a spherical surface EPL (Europhys Lett) 94 4 2011 43001/1-6
24. W.-Y. Zhang, Y. Jiang, and J.Z.Y. Chen Onsager model for the structure of rigid rods confined on a spherical surface Phys Rev Lett 108 2012 057801/1-5
25. W.-Y. Zhang, Y. Jiang, and J.Z.Y. Chen Solution of the Onsager model for the structure of rigid rods confined on a spherical surface Phys Rev E 85 6 2012 061710/1-6
26. Q. Liang, S. Ye, P. Zhang, and J.Z.Y. Chen Rigid linear particles confined on a spherical surface: phase diagram of nematic defect states J Chem Phys 141 24 2014 244901/1-10
27. G.B. Arfken, H.-J. Weber, and L. Ruby Mathematical methods for physicists 1985 Academic Press New York 1029
28. M.G. Bawendi, and K.F. Freed A Wiener integral model for stiff polymer chains J Chem Phys 83 5 1985 2491 2496
29. J.B. Lagowski, J. Noolandi, and B. Nickel Stiff chain model functional integral approach J Chem Phys 95 2 1991 1266 1269
30. K. Ghosh, and M. Muthukumar Scattering properties of a single semiflexible polyelectrolyte J Polym Sci B: Polym Phys 39 21 2001 2644 2652
31. A.L. Kholodenko Analytical calculation of the scattering function for polymers of arbitrary flexibility using the dirac propagator Macromolecules 26 16 1993 4179 4183
32. A.J. Spakowitz, and Z.-G. Wang Exact results for a semiflexible polymer chain in an aligning field Macromolecules 37 15 2004 5814 5823
33. S. Stepanow Statistical mechanics of semiflexible polymers Eur Phys J B 39 4 2004 499 512
34. S. Stepanow On the behaviour of the short Kratky-porod chain J Phys: Condens Matter 17 20 2005 S1799 S1807
35. X. Zhang, Y. Jiang, B. Miao, Y. Chen, D. Yan, and J.Z.Y. Chen The structure factor of a wormlike chain and the random-phase-approximation solution for the spinodal line of a diblock copolymer melt Soft Matter 10 2014 5405 5416
36. W. Reisner, J.N. Pedersen, and R.H. Austin DNA confinement in nanochannels: physics and biological applications Rep Prog Phys 75 2012 106601/1-34
37. T. Odijk The statistics and dynamics of confined or entangled stiff polymers Macromolecules 16 8 1983 1340 1344
38. T. Odijk Theory of lyotropic polymer liquid crystals Macromolecules 19 9 1986 2313 2329
39. T.W. Burkhardt Free energy of a semiflexible polymer in a tube and statistics of a randomly-accelerated particle J Phys A-Math Gen 30 7 1997 L167 L172
40. T.W. Burkhardt Free energy of a semiflexible polymer confined along an axis J Phys A: Math Gen 28 24 1995 L629
41. D.J. Bicout, and T.W. Burkhardt Simulation of a semiflexible polymer in a narrow cylindrical pore J Phys A: Math Gen 34 29 2001 5745/1-10
42. M. Dijkstra, D. Frenkel, and H.N. Lekkerkerker Confinement free energy of semiflexible polymers Phys A: Stat Mech Appl 193 3-4 1993 374 393
43. P.G. de Gennes Scaling concepts in polymer physics 1979 Cornell University Press Ithaca 319
44. E.F. Casassa Comments on exclusion of polymer chains from small pores and its relation to gel permeation chromatography Macromolecules 9 1 1976 182 185
45. M.R. Smyda, and S.C. Harvey The entropic cost of polymer confinement J Phys Chem B 116 35 2012 10928 10934
46. J.Z.Y. Chen, and D.E. Sullivan Free energy of a wormlike polymer chain confined in a slit: crossover between two scaling regimes Macromolecules 39 22 2006 7769 7773
47. A.Y. Grosberg, A.R. Khokhlov, and Y.A. Atanov Statistical physics of macromolecules 1994 AIP New York 350
48. Z.Y. Chen, and S.-M. Cui Orientational wetting layer of semiflexible polymers near a hard wall Phys Rev E 52 1995 3876 3880
49. T. Odijk Scaling theory of DNA confined in nanochannels and nanoslits Phys Rev E 77 6 2008 060901/1-4
50. Y. Wang, D.R. Tree, and K.D. Dorfman Simulation of DNA extension in nanochannels Macromolecules 44 16 2011 6594 6604
51. D.R. Tree, Y. Wang, and K.D. Dorfman Mobility of a semiflexible chain confined in a nanochannel Phys Rev Lett 108 2012 228105/1-4
52. D.R. Tree, Y. Wang, and K.D. Dorfman Extension of DNA in a nanochannel as a rod-to-coil transition Phys Rev Lett 110 2013 208103/1-4
53. L. Dai, D.R. Tree, J.R.C. van der Maarel, K.D. Dorfman, and P.S. Doyle Revisiting blob theory for DNA diffusivity in slitlike confinement Phys Rev Lett 110 2013 168105/1-4
54. L. Onsager The effects of shape on the interaction of colloidal particles Ann N Y Acad Sci 51 4 1949 627 659
55. R. Pathria Statistical mechanics 1996 Butterworth Heinemann Oxford, UK 529
56. A. Khokhlov, and A. Semenov Liquid-crystalline ordering in the solution of partially flexible macromolecules Phys A 112 3 1982 605 614
57. G.J. Vroege, and H.N.W. Lekkerkerker Phase transitions in lyotropic colloidal and polymer liquid crystals Rep Prog Phys 55 8 1992 1241 1309
58. G. Lasher Nematic ordering of hard rods derived from a scaled particle treatment J Chem Phys 53 11 1970 4141 4146
59. R. Kayser, and H. Raveché Bifurcation in onsager's model of the isotropic-nematic transition Phys Rev A 17 1978 2067 2072
60. H.N.W. Lekkerkerker, P. Coulon, R. Van Der Haegen, and R. Deblieck On the isotropic liquid crystal phase separation in a solution of rodlike particles of different lengths J Chem Phys 80 7 1984 3427 3433
61. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannary Numerical recipes in C 2nd ed. 1992 Cambridge University Press
62. Y. Jiang, and J.Z.Y. Chen Isotropic-nematic interface in a lyotropic system of wormlike chains with the onsager interaction Macromolecules 43 24 2010 10668 10678
63. G.J. Vroege, and T. Odijk Induced chain rigidity splay modulus and other properties of nematic polymer liquid crystals Macromolecules 21 9 1988 2848 2858
64. J.C. Adams, and P.N. Swarztrauber Computer code SPHEREPACK 3.2 2009 http://www.cisl.ucar.edu/css/software/spherepack/
65. P.N. Swarztrauber, and W.F. Spotz Generalized discrete spherical harmonic transforms J Comput Phys 159 2 2000 213 230
66. M. Tygert Fast algorithms for spherical harmonic expansions, {III} J Comput Phys 229 18 2010 6181 6192
67. T.L. Chantawansri, A.W. Bosse, A. Hexemer, H.D. Ceniceros, C.J. Garcia-Cervera, E.J. Kramer, and G.H. Fredrickson Phys Rev E 75 2007 031802/1-17
68. R.A. Pelcovits Cholesteric pitch of rigid and semi-flexible chiral liquid crystals Liq Cryst 21 3 1996 361 364
69. T. Hino, and J.M. Prausnitz Hard-sphere-chain equations of state for lyotropic polymer liquid crystals Polymer 40 5 1999 1241 1250
70. G.T. Pickett, and K.S. Schweizer Liquid-state theory of anisotropic flexible polymer fluids J Chem Phys 110 14 1999 6597 6600
71. K.M. Jaffer, S.B. Opps, D.E. Sullivan, B.G. Nickel, and L. Mederos The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids J Chem Phys 114 7 2001 3314 3324
72. P.P.F. Wessels, and B.M. Mulder Nematic homopolymers: from segmented to wormlike chains Soft Mater 1 3 2003 313 342
73. S. Fraden, G. Maret, and D.L.D. Caspar Angular correlations and the isotropic-nematic phase transition in suspensions of tobacco mosaic virus Phys Rev E 48 1993 2816 2837
74. J. Tang, and S. Fraden Isotropic-cholesteric phase transition in colloidal suspensions of filamentous bacteriophage fd Liq Cryst 19 4 1995 459 467
75. W.-l. Chen, T. Sato, and A. Teramoto Interfacial tension between coexisting isotropic and nematic phases for a lyotropic polymer liquid crystal: poly(n-hexyl isocyanate) solutions Macromolecules 31 19 1998 6506 6510
76. K.R. Purdy, and S. Fraden Isotropic-cholesteric phase transition of filamentous virus suspensions as a function of rod length and charge Phys Rev E 70 2004 061703/1-8
77. J. Herzfeld Crowding-induced organization in cells: spontaneous alignment and sorting of filaments with physiological control points J Mol Recognit 17 5 2004 376 381
78. Y. Dong, Y. Wu, J. Wang, and M. Wang Influence of degree of molar etherification on critical liquid crystal behavior of hydroxypropyl chitosan Eur Polym J 37 8 2001 1713 1720
79. Y. Dong, H. Wang, W. Zheng, Y. Zhao, D. Bi, L. Zhao, and X. Li Liquid crystalline behaviour of chitooligosaccharides Carbohydr Polym 57 3 2004 235 240
80. K. Kassapidou, W. Jesse, J.A.P.P. van Dijk, and J.R.C. van der Maarel Liquid crystal formation in DNA fragment solutions Biopolymers 46 1 1998 31 37
81. M. Dijkstra, and D. Frenkel Simulation study of the isotropic-to-nematic transitions of semiflexible polymers Phys Rev E 51 1995 5891 5898
82. H. Fynewever, and A. Yethiraj Phase behavior of semiflexible tangent hard sphere chains J Chem Phys 108 4 1998 1636 1644
83. X. Lu, and J.T. Kindt Monte carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers J Chem Phys 120 21 2004 10328 10338
84. G. Cinacchi, and L. De Gaetani Phase behavior of wormlike rods Phys Rev E 77 2008 051705/1-4
85. V. Ivanov, J. Martemyanova, A. Rodionova, and M. Stukan Computer simulation of stiff-chain polymers Polym Sci Ser C 55 1 2013 4 22
86. M. Dennison, M. Dijkstra, and R. van Roij Phase diagram and effective shape of semiflexible colloidal rods and biopolymers Phys Rev Lett 106 2011 208302/1-4
87. S.-M. Cui, and Z.Y. Chen Columnar and smectic order in binary mixtures of aligned hard cylinders Phys Rev E 50 1994 3747 3754
88. R.C. Hidalgo, D.E. Sullivan, and J.Z.Y. Chen Smectic ordering of homogeneous semiflexible polymers Phys Rev E 71 2005 041804/1-9
89. J.A. Cuesta, C.F. Tejero, and M. Baus Isotropic-nematic transition of hard ellipses Phys Rev A 39 1989 6498 6506
90. D. Frenkel, and R. Eppenga Evidence for algebraic orientational order in a two-dimensional hard-core nematic Phys Rev A 31 1985 1776 1787
91. M.C. Lagomarsino, M. Dogterom, and M. Dijkstra Isotropic-nematic transition of long, thin, hard spherocylinders confined in a quasi-two-dimensional planar geometry J Chem Phys 119 2003 3535
92. J. Galanis, D. Harries, D.L. Sackett, W. Losert, and R. Nossal Spontaneous patterning of confined granular rods Phys Rev Lett 96 2006 028002/1-4
93. J. Galanis, R. Nossal, W. Losert, and D. Harries Nematic order in small systems: measuring the elastic and wall-anchoring constants in vibrofluidized granular rods Phys Rev Lett 105 2010 168001/1-4
94. M. Soares e Silva, J. Alvarado, J. Nguyen, N. Georgoulia, B.M. Mulder, and G.H. Koenderink Self-organized patterns of actin filaments in cell-sized confinement Soft Matter 7 2011 10631 10641
95. C. Tsakonas, A. Davidson, C. Brown, and N. Mottram Multistable alignment states in nematic liquid crystal filled wells Appl Phys Lett 90 2007 111913/1-10
96. J. Dzubiella, M. Schmidt, and H. Löwen Topological defects in nematic droplets of hard spherocylinders Phys Rev E 62 2000 5081 5091
97. D. de las Heras, E. Velasco, and L. Mederos Topological defects in a two-dimensional liquid crystal confined in a circular nanocavity Phys Rev E 79 2009 061703/1-10
98. F.C. Frank I. Liquid crystals. On the theory of liquid crystals Discuss Faraday Soc 25 1958 19 28
99. C. Luo, A. Majumdar, and R. Erban Multistability in planar liquid crystal wells Phys Rev E 85 2012 061702/1-15
100. J.Z.Y. Chen Structure of two-dimensional rods confined by a line boundary Soft Matter 9 45 2013 10921 10930
101. T.C. Lubensky, and J. Prost Orientational order and vesicle shape J Phys II (France) 2 3 1992 371 382
102. D.R. Nelson Defects and geometry in condensed matter physics 2002 Cambridge University Press 392
103. M.J. Bowick, and L. Giomi Two-dimensional matter: order, curvature and defects Adv Phys 58 5 2009 449 563
104. A.M. Turner, V. Vitelli, and D.R. Nelson Vortices on curved surfaces Rev Mod Phys 82 2 2010 1301 1348
105. A. Poniewierski, and R. Holyst Nematic alignment at a solid substrate: The model of hard spherocylinders near a hard wall Phys Rev A 38 1988 3721 3727
106. M.A. Bates, and D. Frenkel J Chem Phys 112 2000 10034 10041
107. A. Khokhlov, and A. Semenov On the theory of liquid-crystalline ordering of polymer chains with limited flexibility J Stat Phys 38 1-2 1985 161 182
108. L. Wu, E.A. Muller, and G. Jackson Understanding and describing the liquid-crystalline states of polypeptide solutions: a coarse-grained model of PBLG in DMF Macromolecules 47 4 2014 1482 1493
109. A. Arsenault, S. Fournier-Bidoz, B. Hatton, H. Miguez, N. Tetreault, E. Vekris, S. Wong, M. Yang, V. Kitaev, and G.A. Ozin Towards the synthetic all-optical computer: science fiction or reality? J Mater Chem 14 2004 781 794
110. F. Li, W.C. Yoo, M.B. Beernink, and A. Stein Site-specific functionalization of anisotropic nanoparticles: from colloidal atoms to colloidal molecules J Am Chem Soc 131 51 2009 18548 18555 PMID: 19954228
111. A. Fernández-Nieves, V. Vitelli, A.S. Utada, D.R. Link, M. Márquez, D.R. Nelson, and D.A. Weitz Novel defect structures in nematic liquid crystal shells Phys Rev Lett 99 2007 157801/1-4
112. T. Lopez-Leon, V. Koning, K.B.S. Devaiah, V. Vitelli, and A. Fernandez-Nieves Frustrated nematic order in spherical geometries Nat Phys 7 5 2011 391 394
113. M. Huber, and H. Stark Tetravalent colloids by nematic wetting EPL (Europhys Lett) 69 1 2005 135
114. H.-L. Liang, J. Noh, R. Zentel, P. Rudquist, and J.P. Lagerwall Tuning the defect configurations in nematic and smectic liquid crystalline shells Philos Trans R Soc Lond A: Math Phys Eng Sci 371 1988
115. D.R. Nelson Toward a tetravalent chemistry of colloids Nano Lett 2 10 2002 1125 1129
116. G. Skačej, and C. Zannoni Controlling surface defect valence in colloids Phys Rev Lett 100 2008 197802/1-4
117. H. Shin, M. Bowick, and X. Xing Topological defects in spherical nematics Phys Rev Lett 101 3 2008 037802/1-4
118. M.A. Bates Nematic ordering and defects on the surface of a sphere: a Monte Carlo simulation study J Chem Phys 128 10 2008 104707/1-5
119. S. Dhakal, F.J. Solis, and M. Olvera de la Cruz Nematic liquid crystals on spherical surfaces: control of defect configurations by temperature, density, and rod shape Phys Rev E 86 2012 011709/1-9
120. P.-G. de Gennes, and J. Prost The physics of liquid crystals 1995 Oxford University Press New York
121. D. Seč, T. Lopez-Leon, M. Nobili, C. Blanc, A. Fernandez-Nieves, M. Ravnik, and S. Zumer Defect trajectories in nematic shells: role of elastic anisotropy and thickness heterogeneity Phys Rev E 86 2012 020705/1-4
122. V. Vitelli, and D.R. Nelson Nematic textures in spherical shells Phys Rev E 74 2006 021711/1-18
123. J.P. Straley Frank elastic constants of the hard-rod liquid crystal Phys Rev A 8 1973 2181 2183
124. T. Sato, and A. Teramoto On the Frank elastic constants of lyotropic polymer liquid crystals Macromolecules 29 11 1996 4107 4114
125. A. Akinchina, and P. Linse Monte Carlo simulations of polyion-macroion complexes. 1. Equal absolute polyion and macroion charges Macromolecules 35 13 2002 5183 5193
126. S. Stoll, and P. Chodanowski Polyelectrolyte adsorption on an oppositely charged spherical particle. chain rigidity effects Macromolecules 35 25 2002 9556 9562
127. R.F. Bruinsma Physics of RNA and viral assembly Eur Phys J E 19 3 2006 303 310
128. I. Kusner, and S. Srebnik Vector imitation model of semiflexible polymers: application to polymer adsorbed on a spherical particle Macromolecules 40 17 2007 6432 6438
129. H.-L. Liang, S. Schymura, P. Rudquist, and J. Lagerwall Nematic-smectic transition under confinement in liquid crystalline colloidal shells Phys Rev Lett 106 2011 247801/1-4
130. V. Koning, T. Lopez-Leon, A. Fernandez-Nieves, and V. Vitelli Bivalent defect configurations in inhomogeneous nematic shells Soft Matter 9 2013 4993 5003
131. R.M. Evans Phase diagrams for deformable toroidal and spherical surfaces with intrinsic orientational order J Phys II 5 4 1995 507 530
132. R.L.B. Selinger, A. Konya, A. Travesset, and J.V. Selinger Monte Carlo studies of the XY model on two-dimensional curved surfaces J Phys Chem B 115 48 2011 13989 13993
133. Y. Li, H. Miao, H. Ma, and J.Z.Y. Chen Defect-free states and disclinations in toroidal nematics RSC Adv 4 2014 27471 27480
134. T.-S. Nguyen, J. Geng, R.L.B. Selinger, and J.V. Selinger Nematic order on a deformable vesicle: theory and simulation Soft Matter 9 34 2013 8314 8326
135. J.Z.Y. Chen, D.E. Sullivan, and X. Yuan Model for wormlike polymers confined between hard walls Europhys Lett 72 1 2005 89
136. J.Z.Y. Chen, D.E. Sullivan, and X. Yuan Surface-induced liquid crystal transitions of wormlike polymers confined in a narrow slit. A mean-field theory Macromolecules 40 4 2007 1187 1195
137. A. Leferink op Reinink, E. van den Pol, A. Petukhov, G. Vroege, and H. Lekkerkerker Phase behaviour of lyotropic liquid crystals in external fields and confinement Eur Phys J Special Top 222 11 2013 3053 3069
138. P. Sheng Phase transition in surface-aligned nematic films Phys Rev Lett 37 1976 1059 1062
139. P. Sheng Boundary-layer phase transition in nematic liquid crystals Phys Rev A 26 1982 1610 1617
140. T.J. Sluckin, and A. Poniewierski Novel surface phase transition in nematic liquid crystals: Wetting and the Kosterlitz-Thouless transition Phys Rev Lett 55 1985 2907 2910
141. A.K. Sen, and D.E. Sullivan Landau de Gennes theory of wetting and orientational transitions at a nematic-liquid substrate interface Phys Rev A 35 1987 1391 1403
142. K. Shundyak, and R. van Roij Hard colloidal rods near a soft wall: wetting drying and symmetry breaking EPL (Europhys Lett) 74 6 2006 1039
143. A.V. Emelyanenko, S. Aya, Y. Sasaki, F. Araoka, K. Ema, K. Ishikawa, and H. Takezoe Two transitions between isotropic and nematic phases in confined liquid crystals Phys Rev E 84 2011 041701/1-4
144. M. Dijkstra, R. van Roij, and R. Evans Wetting and capillary nematization of a hard-rod fluid: a simulation study Phys Rev E 63 2001 051703/1-7
145. V.A. Ivanov, A.S. Rodionova, E.A. An, J.A. Martemyanova, M.R. Stukan, M. Müller, W. Paul, and K. Binder Orientational ordering transitions of semiflexible polymers in thin films: a Monte Carlo simulation Phys Rev E 84 2011 041810/1-15
146. V.A. Ivanov, A.S. Rodionova, J.A. Martemyanova, M.R. Stukan, M. Muller, W. Paul, and K. Binder Wall-induced orientational order in a thermal semidilute solutions of semiflexible polymers: Monte Carlo simulations of a lattice model J Chem Phys 138 23 2013 234903/1-20
147. V.A. Ivanov, A.S. Rodionova, J.A. Martemyanova, M.R. Stukan, M. Muller, W. Paul, and K. Binder Conformational properties of semiflexible chains at nematic ordering transitions in thin films: a Monte Carlo simulation Macromolecules 47 3 2014 1206 1220
148. R. van Roij, M. Dijkstra, and R. Evans Orientational wetting and capillary nematization of hard-rod fluids Europhys Lett 49 3 2000 350 356
149. R.A. van Roij, M. Dijkstra, and R. Evans Interfaces, wetting, and capillary nematization of a hard-rod fluid: theory for the Zwanzig model J Chem Phys 113 17 2000 7689 7701
150. R. Zwanzig First order phase transition in a gas of long thin rods J Chem Phys 39 7 1963 1714 1721
151. A. Chrzanowska, P.I.C. Teixeira, H. Ehrentraut, and D.J. Cleaver Ordering of hard particles between hard walls J Phys: Condens Matter 13 21 2001 4715
152. A. Chrzanowska Application of Gaussian quadratures to density functional (df) theories of confined liquid crystals J Comput Phys 191 1 2003 265 281
153. D. de las Heras, E. Velasco, and L. Mederos Effects of wetting and anchoring on capillary phenomena in a confined liquid crystal J Chem Phys 120 10 2004 4949 4957
154. S. Varga, Y. Marttnez-Rattn, and E. Velasco Competition between capillarity layering and biaxiality in a confined liquid crystal Eur Phys J E 32 1 2010 89 101
155. S. Varga, Y. Marttnez-Rattn, and E. Velasco Hard rods in a cylindrical pore: the nematic-to-smectic phase transition J Phys: Condens Matter 26 7 2014 075104/1-7
156. M. Abramowitz, and I. Stegun Handbook of mathematical functions 1970 Dover Publishing Inc. New York 1046
157. J. Hubbard Calculation of partition functions Phys Rev Lett 3 1959 77 78