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Journal of Nanomaterials
Volume 2013 (2013), Article ID 409676, 10 pages
Interaction Effects between Cellulose and Water in Nanocrystalline and Amorphous Regions: A Novel Approach Using Molecular Modeling
Département de Chimie et Physique, Centre de Recherche sur les Matériaux Lignocellulosiques (CRML), Université du Québec à Trois-Rivières (UQTR), 3351 Boul. des Forges, C.P. 500 Trois-Rivières, QC, G9A 5H7, Canada
Received 16 January 2013; Revised 14 April 2013; Accepted 14 April 2013
Academic Editor: Sheng-Rui Jian
Copyright © 2013 Ali Chami Khazraji and Sylvain Robert. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The hydrophilic/hydrophobic nature of cellulose is based on its structural anisotropy. Cellulose chains are arranged in a parallel manner and are organized in sheets stabilized by interchain OH–O hydrogen bonds, whereas the stacking of sheets is stabilized by both van der Waals (vdW) dispersion forces and weak CH–O hydrogen bonds. Cellulose has a strong affinity to itself and materials containing hydroxyls, especially water. Based on the preponderance of hydroxyl functional groups, cellulose polymer is very reactive with water. Water molecular smallness promotes the reaction with the cellulose chains and immediately formed hydrogen bonds. Besides that, vdW dispersion forces play an important role between these two reactive entities. They stabilize the cellulose structure according to the considerable cohesive energy in the cellulose network. Hydrogen bonding, electrostatic interactions, and vdW dispersion forces play an important role in determining the cellulose crystal structure during the cellulose-water interactions. As a result of these interactions, the volume of cellulose undergoes a meaningful change expressed not only by an exponential growth in amorphous regions, but also by an expansion in nanocrystalline regions. In addition, the volume change is associated with the swelling material expressed as a weight gain of the cellulose polymer. Molecular modeling using Accelrys Materials Studio allowed us to open a new horizon and is helpful for understanding cellulose-water interactions.
Objective of This Study. In this paper, we studied the behavior of amorphous and nanocrystalline Iα regions of cellulose when these two regions interact with water molecules. Further more, we highlighted the mechanism that governs their interactions.
Cellulose is a polymer of β-D-glucose units linked together by (1→4) glycosidic bonds to form cellobiose residues that are the repeating units in the cellulose chain (Figure 1) . Several reviews have already been published reporting the state of knowledge of this fascinating polymer [2–13].
The cellulose structure favors organization into bundles with the crystalline order held together by hydrogen bonds and disordered or amorphous regions (Figure 2). In a previous study [14, 15], Flory stated that a polymer in a condensed amorphous state exists in a nonperturbed conformation in the conformational analysis of the polymer .
Native crystalline cellulose is generally found as a mixture of cellulose Iα and cellulose Iβ polymorphic forms. The proportions of the two allomorphs of crystalline cellulose vary depending on the source of the cellulose. Higher plants such as trees and corn are believed to have a higher proportion of cellulose Iβ. Studies have determined that cellulose Iβ is more stable than cellulose Iα, and the conversion from type Iα to Iβ is irreversible. Electron diffraction patterns show type Iα to have a triclinic unit cell and type Iβ to have a monoclinic unit cell. In both phases, the cellulose chains are organized in a parallel-up fashion. The Iα phase has cell dimensions a = 0.674 nm, b = 0.593 nm, c = 1.036 nm (chain axis), α = 117°, β = 113°, and γ = 81° and one cellobiose moiety per unit cell . The Iβ phase is very similar to the model by Sarko and Muggli , with the cell dimensions a = 0.801 nm, b = 0.817 nm, c = 1.036 nm (chain axis), α = β = 90°, and γ = 97.3° and two cellobiose moieties per unit cell. The number of glucose units or the degree of polymerization (DP) is up to 20 000, but shorter cellulose chains can occur and are mainly localized in the primary cell walls .
2. Computational Methods
In this study, we used Accelrys Materials Studio 6.0 software . In order to study the behavior of water in the disordered part of cellulose’s so-called amorphous regions, we used the Amorphous Cell MS 6.0 module. This is a module to create 3D periodic structures composed of small molecules, polymers, and so forth. We construct a cell based on the density and the number and length of the chains. In the Amorphous Cell Construction, lattice type is cubic and lengths are the values of the lattice parameters a (Å), b (Å), and c (Å). Ramp density from: allows construction of the cell at the specified density, in g/cc, after which the density will be ramped up to its final value as specified on the setup tab using a succession of geometry optimization and dynamics steps.
In addition, we used another module from Accelrys Materials Studio 6.0 called DMol3. This module helps us display electronic properties in amorphous cells of cellulose after interacting with water molecules. DMol3 is a modeling program that uses density functional theory (DFT) to simulate chemical processes and predict properties of materials both rapidly and accurately. The theoretical foundation is based on Schrödinger’s equation. The Hamiltonian operates on wavefunctions of all electronic degrees of freedom. In practice, wave functions are expressed in terms of one particle function. The density functional theory is based on the Hohenberg-Kohn theorem, Kohn-Sham theorem, and Kohn-Sham equations.
We also used Forcite module from Accelrys Materials Studio 6.0. This module is an advanced classical mechanics tool that enables energy calculations, geometry optimizations, and dynamics simulations. We used this tool to calculate the cell parameters when cellulose chains in the ordered regions interact with water molecules. For cellulose polymers, using Forcite Plus with the COMPASS force field enables the prediction of properties such as mechanical properties, density, diffusion, and solubility parameters.
3. Results and Discussion
3.1. First Part of Study
Molecular modeling is a well-adapted technique to investigate the organization of the cellulose chains within the material . Here again, most of the efforts have been devoted to modeling the crystal phases and performing the cellulose-water interactions. Modeling protocols go from simple minimization of finite-sized systems (without periodic boundary conditions) to molecular dynamics experiments performed on infinite solids with periodic boundary conditions. Former studies, called minicrystals, allowed prediction of the relative stability of the different cellulosic allomorphs [21–23]. Molecular modeling has been performed on three cellulosic systems: the amorphous phase and the two native crystalline phases (Iα and Iβ).
The cellulose chains are composed of ordered regions (nanocrystals) and disordered regions (amorphous). We will start our study by interacting water molecules with cellulose chains in the amorphous regions and then in the nanocrystalline regions.
3.1.1. Creating a Cellobiose Molecule and a Water Molecule
We will build an amorphous cell model in which there are cellulose chains and water molecules. The cellulose chain is composed of one cellobiose unit. The first task is to open a new 3D atomistic document in which we sketched a structure. Then, we have to draw a cellobiose unit and a water molecule in the corresponding files (Figures 3 and 4).
Now that our structures of cellobiose unit and water molecule are ready, we may start building an amorphous cell. In order to get a cell which is approximately 38.5 × 38.5 × 38.5 Å, we used the Amorphous Cell MS Builder of Accelrys Materials Studio 6.0.
In the amorphous cell calculation dialog, the setup tab contains a construction task, the quality is medium, the density is 1 g/cc, and the output is 10 frames. The composition table, including cellobiose unit and water molecules, is represented in Table 1. Each experiment between cellulose chains and water molecules in this table is independent of the other.
At the beginning, we set the number of cellulose chains, and we varied the number of water molecules. We started the modeling with 100 cellulose chains, and in each chain, there is one repeating unit (cellobiose) and one water molecule. We loaded them into amorphous cell. After that, we varied only the number of water molecules as shown in the following Table 1.
Amorphous cell is a comprehensive model building tool for creating a wide range of amorphous materials. Its flexible approach to force field choice, combined with several different construction techniques, enables the building of bulk structures of a wide range of systems including polymers and glasses, as well as nanostructures. Amorphous cell can also be used to generate layered structures to enable calculations on interfaces.
In the energy tab of the amorphous cell calculation dialog, we change the force field to COMPASS. After running the calculation, we obtained something like the model shown in Figure 5 as an example, including 100 cellulose chains and one water molecule.
COMPASS is a powerful force field that supports atomistic simulation of condensed phase materials. COMPASS stands for condensed-phase optimized molecular potentials for atomistic simulation studies. The COMPASS force field aims to achieve high accuracy in prediction for a broad range of systems. The goal is to be able to predict properties of molecules, both in isolation and in the condensed phase, with accuracy comparable to an experiment. It is an ab initio force field because most parameters are initially derived based on ab initio data. Following this step, parameters are optimized to yield good agreement with experimental data. In particular, thermophysical data for molecular liquids and crystals are used to refine the nonbonding parameters by using molecular dynamics simulations.
When this experiment ended, we repeated the same experiment by changing the number of water molecules and keeping the number of cellulose chains fixed at 100 as shown in Table 2. This table represents the cubic cell parameters. The experiments were done on systems with 100 cellulose chains composed of one cellobiose unit and progressive amounts of water molecules.
We repeated the same procedure, but now we increased the polymerization degree of the cellulose chains. This time, we took a chain cellulosic that contains five repeating units of cellobiose. The cubic cell composition including cellobiose unit and water molecules is represented in Table 3.
After running the calculation, we obtain the model shown in Figure 6 as an example representing 100 cellulose chains which are formed by five repeating units or cellobiose and 6400 water molecules.
We set the number of cellulose chains, and we varied the number of water molecules. Table 4 shows the results of the experiments that were performed with 100 cellulose chains composed of five repeating units or cellobiose with a varying number of water molecules.
Analysis of the results is presented in Figure 7. This graph shows what happens when water molecules interact with cellulose in amorphous regions. These regions are influenced by the presence of water molecules. Consequently, the volumes of the amorphous regions undergo an exponential growth.
Now, look what happened to the electronic levels. In general, carbohydrates are hydrophilic and tend to strongly interact with water. Water can act as a plasticizing agent changing the key mechanical properties and depressing the glass transition temperature of an amorphous carbohydrate. Figure 7 clearly shows the volume variation of the amorphous regions of cellulose as a function of the water molecules variation. The amorphous regions are unstable when they interact with the water molecules.
In order to elucidate the mechanism that governs the interactions between the cellulose chains and water in the amorphous regions, we reacted only few molecules (Figure 8). The water molecules are interacting with the cellulose chains. Consequently, we found an immediate formation of a hydrogen bonding network occurring between cellobiose and water molecules dispersed in the amorphous regions. The polar bonding can occur between cellobiose (intermolecularly), within different parts of a single cellobiose (intramolecularly), or between cellobiose and water molecules. The hydrogen bond is often described as an electrostatic dipole-dipole interaction. However, it also has some features of covalent bonding. It is directional and strong, producing interatomic distances shorter than sum of the van der Waals radii.
Within the plant cell wall matrix, water molecules are subjected to a number of interactions caused by the chemical and physical composition of the cell wall. Structure and composition of the cell wall produce states and locations of water molecules. Further, cellulose chains have a strong affinity toward themselves and toward materials containing hydroxyl groups. Cellulose chains are inter-connected by OH–O-type hydrogen bonds to form flat sheets with CH–O hydrogen bonds. Nonbonding interactions are involved in these interactions, especially electrostatic, hydrogen bonds, and van der Waals dispersion forces. Water is a good polar solvent. Among its properties, water molecules are solvent ionizing and dissociating molecules. Cellulose polymer is hydrophilic and tends to strongly interact with water. Also, water molecules interact easily with cellulose chains. At the cellulose chain interface, several hydrogen bonds are lost. However, these losses of intermolecular hydrogen bonds within the cellulose chains are compensated with new hydrogen bonds from water molecules. Large anti-bonding electron clouds exist around the glycosidic bonds in the cellulose polymer. These anti-bonding electron clouds produce an induced polarization at the approach of the water molecules. Electron clouds can be distorted and thus create an electrostatic dipole. From the concept of polarizability, a wave dipole is created. The properties of the hydrocarbon chains dominate and define the interactions. A repulsion component resulting from the Pauli principle prevents the collapse of the chains. Different types of interactions could exist—attractive or repulsive interactions between permanent dipoles within the cellulose polymer and water molecules, induction interactions between permanent poles of water molecules and induced multipoles of cellulose chains, and any pairs of molecules arising from the interactions on instantaneous multi-poles.
Water molecules could penetrate between the fibers through capillary forces and interact with the cellulose chains. Formation of hydrogen bonds at the water/cellulose interface is shown to depend sensitively on the adsorption site, for example, above the equatorial hydroxyls or OH moieties pointing out of the cellulose chains. Also, the van der Waals dispersion forces contribute significantly to the adsorption energy. All intermolecular/van der Waals dispersion forces in the cellulose polymer are anisotropic. Electrostatic interactions change sign upon rotation of the molecules. Electrostatic forces can be attractive or repulsive depending on the mutual orientation of the molecules. Moreover, weak interactions also allow the dispersion of cellulose chains in water.
In addition, we must consider another factor which is the swelling. The term swelling is usually associated with volume increase of the material due to liquid uptake. This term is expressed as weight gain of the cellulose material.
Each molecule from cellulose and water has an electron density that measures the probability of an electron being present at a specific location. We reacted a few molecules of cellulose and water so that we can show clearly their reactive effects that occur between them. Through their valence electrons, we can show the effects using molecular modeling software DMol3 from Accelrys Materials Studio 6.0.
3.1.2. Modeling Interactions between Cellulose and Water Using Quantum Mechanics
We used DMol3 tool from Accelrys Materials Studio 6.0 to display electronic properties after interactions between cellulose chains and water molecules. We set the Task to Geometry Optimization. The Quality is set to Medium. The Functional is set to GGA and BLYP. In the Electronic Tab we set the Basis Set to DNP.
Electron clouds are often found around atoms. Molecular modeling software provides graphical images of electron density (Figure 9). Graphically, the electron density surface also serves as a canvas upon which other electronic properties can be displayed. The electrostatic potential map provides an indicator for charge distribution in cellulose and water molecules (Figure 10). The electrostatic potential is mapped onto the total charge density isosurface using color to represent the variation. Conversely, we have built an interactive model between these two entities cellulose-water interactions. Consequently, in this region, cellulose and water molecules can interact easily between themselves, and they finish by forming one entity with the electronic clouds mixed up together.
The Amorphous Cell module from Accelrys Materials Studio 6.0 allows us to highlight a way in which the cellulose and water react. The Ewald summation method is for both electrostatic and van der Waals nonbonds terms. In other words, the default methods are Ewald summation for van der Waals interacting and for Coulombic interactions (Figure 11).
This experiment clearly shows what happens when cellulose chains and water molecules get together—cellulose chains and water molecules react quickly and without any obstacles. In other words, cellulose is a hydrophilic interface. In addition to the hydrogen bonds, van der Waals dispersion forces are present during the cellulose-water interactions.
In our previous papers, we showed in detail several phenomena that govern the interactions between cellulose and water.
3.2. Second Part of the Study
In the second part of this work, we will study the cellulose chains in the nanocrystalline regions when they interact with water molecules using molecular modeling from Accelrys Materials Studio.
3.2.1. Building and Optimizing the Iα Structure of Cellulose
In the Iα structure, cellulose chains adopt parallel configurations. We built a model of nanocrystalline cellulose Iα. We used the Forcite Molecular Modeling of Accelrys Materials Studio 6.0. The first structure of nanocrystalline cellulose I is without water molecules (Figure 12). The lattice parameters are defined as following. The lattice type is 3D triclinic 1 P1 (a = 91.031 Å, b = 54.677 Å, c = 84.934 Å, α = 128.610°, β = 115.950°, and γ = 80.470°). In the second structure of nanocrystalline cellulose Iα, we inserted water molecules (Figure 13). We also defined the follows lattice parameters of the crystal. The lattice type is 3D triclinic 1 P1 (a = 90.444 Å, b = 54.788 Å, c = 85.189 Å, α = 128.150°, β = 115.770°, and γ = 80.580°). After that, we compared the effects of water molecules in these two models of nanocrystalline cellulose Iα. From Forcite calculation, in the setup tab the task is geometry optimization, and in the energy tab the force field is COMPASS.
The results that we obtained are presented in Figure 14. We find that the effects of water molecules on the cellulose chains are not negligible on the volume. The nanocrystalline cellulose Iα regions undergo a meaningful expansion. In the global volume, there is much change. However, these changes in volume did not prevent a slight variation along all the sides of the cube. The volumes of nanocrystalline cellulose Iα have been changed undergoing narrowing or enlargement of their sides, as shown in Table 5. All the sides varied so that the whole crystal volumes do not remain constant.
We have only taken a low polymerization degree because the reaction takes a long time and, in the end, did not lead to completion. We will try in the next work to increase the polymerization degree according to the performance of the molecular modeling in Accelrys Materials Studio 6.0.
Using the Accelrys Materials Studio 6.0 allows us to formulate the following approach (Figure 15). Molecular modeling allowed us to demonstrate in this experiment, for example, that water molecules could penetrate through cellulose fibers that consist of multiple cellulose chains. These cellulose chains interact through hydrogen bonds, van der Waals (vdW), and electrostatic interactions. Cellulose chains have a strong affinity toward themselves and toward materials containing hydroxyl groups. At the surface of chains, several intermolecular hydrogen bondings are lost, but they are compensated by water molecules hydrogen bonds. Hydrogen bonding and vdW dispersion forces stabilize the cellulose chain structures in the water media. Hydrogen bonds dominate interchain energy, and vdW dispersion forces are mostly responsible for holding the chains together, although with relatively weak CH–O interactions. The large antibonding electron clouds surrounding the glycosidic bonds in the cellulose chains produce an induced polarization at the approach of water molecules. Electrostatic potential added to electronic density gives an insight into the cellobiose and water molecules. In other words, water molecules cannot enter between the cellulose chains because the chains form strong aggregations. On the contrary, water molecules could seep between the fiber bundles. Water molecules may surround cellulose chains forming at least one layer of water.
We seek to understand the interactions between water molecules and cellulose polymer. This study takes us a little closer to reality. The following images help us a little to clarify the phenomenon of the behavior of water molecules when they come close to the cellulose polymer. That is to say, how they might behave in the fiber matrix. These images allow us to explain our approach.
The cellulose chains have a hydrophilic character and tend to aggregate with other cellulose chains as shown in Figures 16, 17, 18, and 19. Water molecules have the tendency or power to enter into the cellulose fibers, for example, through capillary attraction, capillarity, or capillary motion. However, it is so difficult or almost impossible for water molecules to break the strong bonds that exist between the cellulose chains, except perhaps by an external effect which could weaken such strong chemical bonds. On the contrary, the water molecules are largely free of interactions with the external cellulose chains.
Table 5 shows the cubic cell parameters of the volume of cellulose Iα into the nanocrystalline regions when the cellulose chains have been interacting with water molecules. These cells parameters show that the volumes of nanocrystalline cellulose changed after interacting with water molecules. As the water molecules increase, the volumes of nanocrystalline cellulose regions increase. Therefore, the water is able to react with cellulose chains in these regions, causing an increasing in the volume.
We tried to produce patterns through changes in the volume of the cellulose chain sheath-binder when they interact with water molecules. We achieved this diagram in which it shows the approximate change in the volume of the polymer cellulose when it comes into contact with water. We wanted to show pattern variations in volume when the cellulose chains and water molecules react with each other. Figure 20 shows the expansion of the cubic cell parameters from the initial structure to the final structure of nanocrystalline cellulose Iα when the cellulose chains and the water molecules interact.
We note that this work is a continuation of two previous studies. The one study is entitled “Molecular modeling of cellulose-water interactions: qualitative studies of water on cellulose structure and properties”. other study is entitled “Self-assembly and intermolecular forces when cellulose and water interact using molecular modeling”. All these studies showed the phenomena that may exist in the interactions between cellulose when it comes into contact with water.
In summary, understanding the interactions of cellulose with water and the state of water in cellulose are of a great interest. This study shows, using molecular modeling software from Accelrys Materials Studio, the hydrophilic nature of the cellulose polymer, especially, in aqueous media. Cellulose polymer is formed of several chains packed together. Such cellulose chains are strongly bonded between them, and it is so difficult for water molecules to break these bonds.
In fact, water molecules interact rapidly with cellulose chains either in nanocrystalline cellulose Iα regions outside of the chains or in the amorphous regions. After interacting, these two reactive species form one single entity together. However, this new state has an effect on cellulose structures, especially, in volume. The nanocrystalline cellulose Iα and amorphous regions are influenced after the interactions with water molecules. Consequently, this effect is reflected in the volume change in these two cellulose regions that are amorphous and nanocrystalline Iα.
The volume change of both nanocrystalline cellulose Iα and amorphous regions is manifested in its dimensions. Their volumes become larger. Consequently, this change in volume is the result of the interactions between cellulose and water molecules. Besides that, the interactions between the water molecules and the cellulose chains result in the electronic reactions. These reactions between the cellulose and water lead to the formation of hydrogen bond networks between water molecules and cellulose chains, perfect fusion of electron densities of these two reactive species, and creation of single electrostatic potential fields that can combine these matters into one reactive entity. In the amorphous regions, when water molecules come into contact with cellulose chains, it produces a molecular orbital combination of the cellulose chains with those of water molecules according to the linear combination of atomic orbitals (LCAO) theory. In addition, the swelling factor following the interaction with the water molecules is another factor that causes the increase in the volume of the cellulose chains. In other words, the swelling factor is usually associated with volume increase of the material due to liquid uptake (expressed as weight gain of the material).
The authors would like to thank NSERC (National Sciences and Engineering Research Council of Canada), the Innovative Green Wood Fibre Products Network, and the CQMF (Centre Québécois sur les Matériaux Fonctionnels) for financial support. They also thank the Compute Canada network and Calcul Québec for their computational resources.
- R. J. Moon, A. Martini, J. Nairn, J. Simonsen, and J. Youngblood, “Cellulose nanomaterials review: structure, properties and nanocomposites,” Chemical Society Reviews, vol. 40, no. 7, pp. 3941–3994, 2011.
- A. D. French, N. R. Bertoniere, R. M. Brown et al., “Cellulose,” in Kirk-Othmer Encyclopedia of Chemical Technology, A. Seidel, Ed., vol. 5, John Wiley & Sons, New York, NY, USA, 5th edition, 2004.
- R. H. Atalla, “3.16—celluloses,” Comprehensive Natural Products Chemistry, vol. 3, pp. 529–598, 1999.
- R. H. Atalla, “The individual structures of native celluloses,” Lenzinger Berichte, vol. 79, p. 5, 2000.
- R. H. Atalla, J. W. Brady, J. F. Matthews, S.-Y. Ding, and M. E. Himmel, “Structures of plant cell wall celluloses,” in Biomass Recalcitrance: Deconstructing the Plant Cell Wall for Bioenergy, pp. 188–212, Blackwell Publishing, Oxford, UK, 2009.
- D. Fengel and G. Wegener, Wood, Chemistry, Ultrastructure, Reactions, Walter de Gruyter, New York, NY, USA, 1983.
- D. N.-S. Hon and N. Shiraishi, Wood and Cellulosic Chemistry, Marcel Dekker, New York, NY, USA, 1991.
- R. H. Marchessault and P. R. Sundararajan, “Cellulose,” in The Polysaccharides, G. O. Aspinall, Ed., Academic Press, New York, NY, USA, 1983.
- A. C. O’Sullivan, “The structure slowly unravels,” Cellulose, vol. 4, no. 3, pp. 173–207, 1997.
- A. Sarko, in Wood and Cellulosics: Industrial Utilisation, Biotechnology, Structure, and Properties, J. F. Kennedy, Ed., Ellis Horwood, Chichester, UK, 1987.
- S. Salmon and S. M. Hudson, “Crystal morphology, biosynthesis, and physical assembly of cellulose, chitin, and chitosan,” Journal of Macromolecular Science, Part C, vol. 37, no. 2, pp. 199–276, 1997.
- D. Klemm, B. Heublein, H. P. Fink, and A. Bohn, “Cellulose: fascinating biopolymer and sustainable raw material,” Angewandte Chemie—International Edition, vol. 44, no. 22, pp. 3358–3393, 2005.
- R. D. Preston, “Natural celluloses,” in Cellulose: Structure, Modification and Hydrolysis, R. A. Young and R. M. Rowell, Eds., John Wiley and Sons, New York, NY, USA, 1986.
- P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, NY, USA, 1953.
- P. J. Flory, Statistical Mechanics of Chain Molecules, Interscience, New York, NY, USA, 1969.
- K. Mazeau and L. Heux, “Molecular dynamics simulations of bulk native crystalline and amorphous structures of cellulose,” Journal of Physical Chemistry B, vol. 107, no. 10, pp. 2394–2403, 2003.
- A. P. Heiner and O. Teleman, “Interface between monoclinic crystalline cellulose and water: breakdown of the odd/even duplicity,” Langmuir, vol. 13, no. 3, pp. 511–518, 1997.
- A. Sarko and R. Muggli, “Packing analysis of carbohydrates and polysaccharides. III. Valonia cellulose and cellulose II,” Macromolecules, vol. 7, no. 4, pp. 486–494, 1974.
- Y. Habibi, L. A. Lucia, and O. J. Rojas, “Cellulose nanocrystals: chemistry, self-assembly, and applications,” Chemical Reviews, vol. 110, no. 6, pp. 3479–3500, 2010.
- Accelrys Software Inc., Material Studio Modeling Environment, Release 6, Accelrys Software Inc., San Diego, Calif, USA, 2011.
- A. Aabloo, A. D. French, R. H. Mikelsaar, and A. J. Pertsin, “Studies of crystalline native celluloses using potential energy calculations,” Cellulose, vol. 1, no. 2, pp. 161–168, 1994.
- A. D. French, D. P. Miller, and A. Aabloo, “Miniature crystal models of cellulose polymorphs and other carbohydrates,” International Journal of Biological Macromolecules, vol. 15, no. 1, pp. 30–36, 1993.
- A. P. Victor, K. Mazeau, M. Lakin, and S. Pérez, “A priori crystal structure prediction of native celluloses,” Biopolymers, vol. 54, no. 5, pp. 342–354, 2000.