Abstract
Quantum mechanics (QM) and molecular mechanics (MM) calculations were performed to elucidate Young’s moduli for a series of cellulose Iβ models. Computations using the second generation empirical force field MM3 with a disaccharide cellulose model, 1,4′-O-dimethyl-β-cellobioside (DMCB), and an analogue, 2,3,6,2′,3′,6′-hexadeoxy-1,4′-O-dimethyl-β-cellobioside (DODMCB), that cannot make hydrogen bonds reveal a considerable contribution of intramolecular hydrogen bonding to the molecular stiffness of cellulose Iβ; the moduli for DMCB and DODMCB being 85.2 and 37.6 GPa, respectively. QM calculations confirm this contribution with modulus values of 99.7 GPa for DMCB and 33.0 GPa for DODMCB. However, modulus values for DMCB were considerably lower than values previously reported for cellulose Iβ. MM calculations with extended cellulose chains (10–40 glucose units) resulted in modulus values, 126.0–147.5 GPa, more akin to the values reported for cellulose Iβ. Comparison of the cellodecaose model, 1,4′-O-dimethyl-β-cellodecaoside (DMCD), modulus with that of its hydrogen bonding-deficient analogue, 2,3,6,2′,3′,6′-hexadeoxy-1,4′-O-dimethyl-β-cellodecaoside (DODMCD), corroborates the observed stiffness conferred by intramolecular hydrogen bonds; the moduli for DMCD and DODMCD being 126.0 and 63.3 GPa, respectively. Additional MM3 determinations revealed that modulus values were not strongly affected by intermolecular hydrogen bonding, with multiple strand models providing values similar to the single strand models; 87.5 GPa for a 7-strand DMCB model and 129.5 GPa for a 7 strand DMCD model.
Similar content being viewed by others
References
Cael JJ, Gardner KH, Koenig JL, Blackwell J (1975) Infrared and Raman spectroscopy of carbohydrates. Paper V. Normal coordinate analysis of cellulose I. J Chem Phys 62:1145–1154
Eichhorn SJ, Davies GR (2006) Modelling the crystalline deformation of native and regenrated cellulose. Cellulose 13:291–307
Eichhorn SJ, Young RJ, Davies GR (2005) Modeling crystal and molecular deformation in regenerated cellulose fibers. Biomacromolecules 6:507–513
Finkenstadt VL, Millane RP (1998) Crystal structure of Valonia cellulose I β. Macromolecules 31:7776–7783
French AD, Johnson GP (2004) Advanced conformational energy surfaces for cellobiose. Cellulose 11:449–462
French AD, Johnson GP (2009) Cellulose and the twofold screw axis: modeling and experimental arguments. Cellulose 16:959–973
Gardner KH, Blackwell J (1974) The structure of native cellulose. Biopolymers 13:1975–2001
Lyons WJ (1959) Theoretical value of the dynamic stretch modulus of cellulose. J Appl Phys 30:796–797
Matsuo M, Sawatari C, Iwai Y, Ozaki F (1990) Effect of orientation and crystallinity on the measurement by X-ray diffraction of the crystal lattice moduli of cellulose I and II. Macromolecules 23:3266–3275
Meyer KH, Lotmar W (1936) The elasticity of cellulose. IV. The constitution of the crystallized cellulose portion. Helv Chim Acta 19:68–86
Meyer KH, Mark H (1928) Über den bau des krystallinsierten anteils der cellulose. Ber Dtsch Chem Ges 61:593–614
Nishino T, Takano K, Nakamae K (1995) Elastic modulus of the crystalline regions of cellulose polymorphs. J Polym Sci Part B Polym Phys 33:1647–1651
Nishiyama Y, Langan P, Chanzy H (2002) Crystal structure and hydrogen-bonding system in cellulose Iβ from synchrotron X-ray and neutron fiber diffraction. J Am Chem Soc 124:9074–9082
Nishiyama Y, Johnson GP, French AD, Forsyth VT, Langan P (2008) Neutron crystallography, molecular dynamics, and quantum mechanics studies of the nature of hydrogen bonding in cellulose Iβ. Biomacromolecules 9:3133–3140
Sakurada I, Nukushina Y, Ito T (1962) Experimental determination of the elastic modulus of crystalline regions in oriented polymers. J Polym Sci 57:651–660
Šturcová A, Davies GR, Eichhorn SJ (2005) Elastic modulus and stress-transfer properties of tunicate cellulose whiskers. Biomacromolecules 6:1055–1061
Tanaka F, Iwata T (2006) Estimation of the elastic modulus of cellulose crystal by molecular mechanics simulation. Cellulose 13:509–517
Tashiro K, Kobayashi M (1991) Theoretical evaluation of three-dimensional elastic constants of native and regenerated celluloses: role of hydrogen bonds. Polymer 32:1516–1526
Treloar LRG (1960) Calculations of elastic moduli of polymer crystals: III. Cellulose. Polymer 1:290–303
Acknowledgments
The Agricultural Research Service funded this work; CRIS project 44000-6435-070-00D. The authors wish to acknowledge Dr. Michael K. Dowd, Dr. Ryan P. Slopek, and Dr. Melisa M. Cherney for helpful comments on the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Santiago Cintrón, M., Johnson, G.P. & French, A.D. Young’s modulus calculations for cellulose Iβ by MM3 and quantum mechanics. Cellulose 18, 505–516 (2011). https://doi.org/10.1007/s10570-011-9507-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10570-011-9507-1