Abstract.
Many natural composites exhibit an architecture known as twisted plywood which imparts to them a superior set of physical properties. The origin of this structure is complex and not yet understood. However, it is thought to involve a lyotropic chiral nematic liquid-crystalline mesophase. Indeed, striking structural similarities have been observed and reported between biological fibrous composites and ordered fluids. In this work, a mathematical model based on the Landau-de Gennes theory has been developed to investigate the role played by constraining surfaces in the structural development of a composite material that experiences a liquid-crystalline state during the early steps of its morphogenesis. The goal of this study is to verify the need for an initial constraining surface in the formation of monodomain twisted plywoods as hypothesized by Neville (Tissue & Cell 20, 133 (1988); Biology of Fibrous Composites (Cambridge University Press, 1993)). The numerical simulations qualitatively confirm this theory and highlight the important role that modelling of liquid-crystalline self-assembly plays in the study of tissue morphogenesis.
Similar content being viewed by others
References
C. Neville, Biology of Fibrous Composites (Cambridge University Press, 1993).
Y. Bouligand, Liquid crystalline order in biological materials, in Liquid Crystalline Order in Polymers, edited by A. Blumstein (Academic Press, New York, 1978).
M. Elices, Structural Biological Materials: Design and Structure-Property Relationships (Pergamon, 2000).
M.M. Giraud-Guille, Int. Rev. Cytol. 166, 59 (1996).
M.M. Giraud-Guille, Calcif. Tissue Int. 42, 167 (1988).
S.C. Cowin, J. Biomed. Eng. 122, 533 (2000).
C. Neville, Tissue & Cell 20, 133 (1988).
P.G. de Gennes, J. Prost, The Physics of Liquid Crystals, 2nd edition (Oxford University Press, 1993).
D.C. Wright, N.D. Mermin, Rev. Mod. Phys. 61, 385 (1989).
M. Doi, S.F. Edwards, Theory of Polymer Dynamics (Oxford University Press, 1987).
A.D. Rey, M.M. Denn, Annu. Rev. Fluid Mech. 34, 233 (2002).
P.J. Van der Houwen, Appl. Numer. Math. 20, 261 (1996).
A. Sonnet, A. Kilian, S. Hess, Phys. Rev. E 52, 718 (1995).
T.W.B. Kibble, J. Phys. A Gen. Phys. 9, 1387 (1976).
T. Tsuji T., A.D. Rey, Macromol. Theor. Simul. 7, 623 (1998).
P. Crooker, in Chirality in Liquid Crystals, edited by H.-S. Kitzerow, C. Bahr (Springer-Verlag, New York, 2001).
O.D. Lavrentovich, M. Kleman, in Chirality in Liquid Crystals, edited by H.-S. Kitzerow, C. Bahr (Springer-Verlag, New York, 2001).
R.D. Kamien, J.V. Selinger, J. Phys. Condens. Matter 13, R1 (2001).
G.A. Hinshaw, R.G. Petscheck, Phys. Rev. Lett. 60, 1864 (1988).
S. Faetti, Phys. Rev. A 36, 408 (1987).
D.W. Berreman, Phys. Rev. Lett. 28, 1983 (1972).
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 15 September 2003, Published online: 11 November 2003
PACS:
61.30.-v Liquid crystals - 61.30.Dk Continuum models and theories of liquid crystal structure - 61.30.Mp Blue phases and other defect-phases - 61.30.St Lyotropic phases
Rights and permissions
About this article
Cite this article
De Luca, G., Rey, A.D. Monodomain and polydomain helicoids in chiral liquid-crystalline phases and their biological analogues. Eur. Phys. J. E 12, 291–302 (2003). https://doi.org/10.1140/epje/i2002-10164-3
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2002-10164-3