Thermal fluctuations and effective bending stiffness of elastic thin sheets and graphene: A nonlinear analysis

Abbena, 2006 Ahmadpoor, 2017, A perspective on the statistical mechanics of 2d materials, Extreme Mech. Lett., 14, 38, 10.1016/j.eml.2016.12.007 Ahmadpoor, 2015, Flexoelectricity in two-dimensional crystalline and biological membranes, Nanoscale, 7, 16555, 10.1039/C5NR04722F Ahmadpoor, 2016, Thermal fluctuations of vesicles and nonlinear curvature elasticity – implications for size-dependent renormalized bending rigidity and vesicle size distribution, Soft Matter, 12, 2523, 10.1039/C5SM02769A Akinwande, 2017, A review on mechanics and mechanical properties of 2d materials – graphene and beyond, Extreme Mech. Lett, 10.1016/j.eml.2017.01.008 Aleksandr, 1949 Amit, 2005 Aronovitz, 1988, Fluctuations of solid membranes, Phys. Rev. Lett., 60, 2634, 10.1103/PhysRevLett.60.2634 Auth, 2007, Fluctuations of coupled fluid and solid membranes with application to red blood cells, Phys. Rev. E, 76, 051910, 10.1103/PhysRevE.76.051910 Bhimanapati, 2015, Recent advances in two-dimensional materials beyond graphene, ACS Nano, 9, 11509, 10.1021/acsnano.5b05556 Boal, 2012 Brenner, 2002, A second-generation reactive empirical bond order (rebo) potential energy expression for hydrocarbons, J. Phys. Condens. Matter, 14, 783, 10.1088/0953-8984/14/4/312 Butler, 2013, Progress, challenges, and opportunities in two-dimensional materials beyond graphene, ACS Nano, 7, 2898, 10.1021/nn400280c Canham, 1970, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell, J. Theor. Biol., 26, 61, 10.1016/S0022-5193(70)80032-7 Deserno, M., 2007. Fluid Lipid Membranes – A Primer. See http://www.cmu.edu/biolphys/deserno/pdf/membrane_theory.pdf. Dimova, 2014, Recent developments in the field of bending rigidity measurements on membranes, Adv. Colloid Interface Sci., 208, 225, 10.1016/j.cis.2014.03.003 Doussal, 1992, Self-consistent theory of polymerized membranes, Phys. Rev. Lett., 69, 1209, 10.1103/PhysRevLett.69.1209 Engelhardt, 1985, Bilayer bending elasticity measured by fourier analysis of thermally excited surface undulations of flaccid vesicles, J. Phys. Lett., 46, 395, 10.1051/jphyslet:01985004608039500 Farago, 2005, Pore formation in fluctuating membranes, J. Chem. Phys., 122, 044901, 10.1063/1.1835952 Fasolino, 2007, Intrinsic ripples in graphene, Nat. Mater., 6, 858, 10.1038/nmat2011 Faucon, 1989, Bending elasticity and thermal fluctuations of lipid membranes. Theoretical and experimental requirements, J. Phys., 50, 2389, 10.1051/jphys:0198900500170238900 Feng, 2011, Graphene based gene transfection, Nanoscale, 3, 1252, 10.1039/c0nr00680g Fisher, 1993, Force between biological surfaces, J. Chem. Soc. Faraday Trans., 89, 2567, 10.1039/ft9938902567 Freund, 2013, Entropic pressure between biomembranes in a periodic stack due to thermal fluctuations, Proc. Natl. Acad. Sci., 110, 2047, 10.1073/pnas.1220968110 Gao, 2014, Probing mechanical principles of cell-nanomaterial interactions, J. Mech. Phys. Solids, 62, 312, 10.1016/j.jmps.2013.08.018 Gao, 2014, Thermomechanics of monolayer graphene: rippling, thermal expansion and elasticity, J. Mech. Phys. Solids, 66, 42, 10.1016/j.jmps.2014.01.011 Goldenfeld, N, 1992. Lectures on Phase Transitions and the Renormalization Group. Gurtin, 2010 Helfrich, 1973, Elastic properties of lipid bilayers: theory and possible experiments, Z. Naturforschung C, 28, 693, 10.1515/znc-1973-11-1209 Helfrich, 1986, Size distributions of vesicles: the role of the effective rigidity of membranes, J. Phys., 47, 321, 10.1051/jphys:01986004702032100 Huang, 2017, Formation and size distribution of self-assembled vesicles, Proc. Natl. Acad. Sci., 114, 2910, 10.1073/pnas.1702065114 Kalbacova, 2010, Graphene substrates promote adherence of human osteoblasts and mesenchymal stromal cells, Carbon, 48, 4323, 10.1016/j.carbon.2010.07.045 Kim, 2009, Large-scale pattern growth of graphene films for stretchable transparent electrodes, Nature, 457, 706, 10.1038/nature07719 Kit, 2012, Twisting graphene nanoribbons into carbon nanotubes, Phys. Rev. B, 85, 085428, 10.1103/PhysRevB.85.085428 Kittel, 2004 Kleinert, 2009 Koskinen, 2010, Approximate modeling of spherical membranes, Phys. Rev. B, 82, 235420, 10.1103/PhysRevB.82.235420 Kostarelos, 2014, Exploring the interface of graphene and biology, Science, 344, 261, 10.1126/science.1246736 Kudin, 2001, C 2 f, bn, and c nanoshell elasticity from ab initio computations, Phys. Rev. B, 64, 235406, 10.1103/PhysRevB.64.235406 Kuila, 2011, Recent advances in graphene-based biosensors, Biosens. Bioelectron., 26, 4637, 10.1016/j.bios.2011.05.039 Landau, 1959, Course of theoretical physics, 7 Li, 2013, Graphene microsheets enter cells through spontaneous membrane penetration at edge asperities and corner sites, Proc. Natl. Acad. Sci., 110, 12295, 10.1073/pnas.1222276110 Liang, 2016, A fluctuating elastic plate and a cell model for lipid membranes, J. Mech. Phys. Solids, 90, 29, 10.1016/j.jmps.2016.02.019 Liang, 2016, A fluctuating elastic plate model applied to graphene, J. Appl. Mech., 83, 081008, 10.1115/1.4033681 Lindsay, 2011, Flexural phonons and thermal transport in multilayer graphene and graphite, Phys. Rev. B, 83, 235428, 10.1103/PhysRevB.83.235428 Lipowsky, 1986, Unbinding transitions of interacting membranes, Phys. Rev. Lett., 56, 2541, 10.1103/PhysRevLett.56.2541 Lipowsky, 1991, Adhesion of vesicles and membranes, Mol. Cryst. Liquid Cryst., 202, 17, 10.1080/00268949108035656 Lu, 2009, Elastic bending modulus of monolayer graphene, J. Phys. D: Appl. Phys., 42, 102002, 10.1088/0022-3727/42/10/102002 Lu, 2009, Nonlinear mechanics of single-atomic-layer graphene sheets, Int. J. Appl. Mech., 1, 443, 10.1142/S1758825109000228 Mermin, 1968, Crystalline order in two dimensions, Phys. Rev., 176, 250, 10.1103/PhysRev.176.250 Meyer, 2007, The structure of suspended graphene sheets, Nature, 446, 60, 10.1038/nature05545 Morozov, 2008, Giant intrinsic carrier mobilities in graphene and its bilayer, Physical Rev. Lett., 100, 016602, 10.1103/PhysRevLett.100.016602 Nayak, 2011, Graphene for controlled and accelerated osteogenic differentiation of human mesenchymal stem cells, ACS Nano, 5, 4670, 10.1021/nn200500h Nelson, 1987, Fluctuations in membranes with crystalline and hexatic order, J. Phys., 48, 1085, 10.1051/jphys:019870048070108500 Nelson, 2004 Nelson, 2004 Neto, 2009, The electronic properties of graphene, Rev. Mod. Phys., 81, 109, 10.1103/RevModPhys.81.109 Novoselov, 2005, Two-dimensional atomic crystals, Proc. Natl. Acad. Sci. USA, 102, 10451, 10.1073/pnas.0502848102 Paczuski, 1988, Landau theory of the crumpling transition, Phys. Rev. Lett., 60, 2638, 10.1103/PhysRevLett.60.2638 Pécréaux, 2004, Refined contour analysis of giant unilamellar vesicles, Eur. Phys. J. E, 13, 277, 10.1140/epje/i2004-10001-9 Phillips, 2012 Plimpton, 1995, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys., 117, 1, 10.1006/jcph.1995.1039 Roldán, 2011, Suppression of anharmonicities in crystalline membranes by external strain, Phys. Rev. B, 83, 174104, 10.1103/PhysRevB.83.174104 Safran, 1994, 90 Seifert, 1997, Configurations of fluid membranes and vesicles, Adv. Phys., 46, 13, 10.1080/00018739700101488 Sharma, 2013, Entropic force between membranes reexamined, Proc. Natl. Acad. Sci., 110, 1976, 10.1073/pnas.1222033110 Sun, 2008, Nano-graphene oxide for cellular imaging and drug delivery, Nano Res., 1, 203, 10.1007/s12274-008-8021-8 Tuckerman, 1992, Reversible multiple time scale molecular dynamics, J. Chem. Phys., 97, 1990, 10.1063/1.463137 Wan, D., Nelson, D. R., Bowick, M. J., 2017. Thermal Stiffening of Clamped Elastic Ribbons. ArXiv preprint arXiv:1702.01863. Wang, 2013, Cellular entry of graphene nanosheets: the role of thickness, oxidation and surface adsorption, RSC Adv., 3, 15776, 10.1039/c3ra40392k Wei, 2012, Bending rigidity and gaussian bending stiffness of single-layered graphene, Nano Lett., 13, 26, 10.1021/nl303168w Weiner, 2012 Xu, 2010, Geometry controls conformation of graphene sheets: membranes, ribbons, and scrolls, ACS Nano, 4, 3869, 10.1021/nn100575k Yang, 2011, Multi-functionalized graphene oxide based anticancer drug-carrier with dual-targeting function and ph-sensitivity, J. Mater. Chem., 21, 3448, 10.1039/C0JM02494E Zakharchenko, 2010, Self-consistent screening approximation for flexible membranes: application to graphene, Physical Review B, 82, 125435, 10.1103/PhysRevB.82.125435 Zhong-Can, 1989, Bending energy of vesicle membranes: general expressions for the first, second, and third variation of the shape energy and applications to spheres and cylinders, Phys. Rev. A, 39, 5280, 10.1103/PhysRevA.39.5280 Zhu, 2016, Nanomechanical mechanism for lipid bilayer damage induced by carbon nanotubes confined in intracellular vesicles, Proc. Natl. Acad. Sci., 113, 12374, 10.1073/pnas.1605030113