+
+
Langmuir 1997, 13, 511-518
511
Interface between Monoclinic Crystalline Cellulose and Water: Breakdown of the Odd/Even Duplicity Andreas P. Heiner* and Olle Teleman VTT Biotechnology and Food Research, POB 1500, FIN-02044 Espoo, Finland Received September 11, 1996. In Final Form: December 10, 1996X The interface between the (110) crystal face of cellulose Iβ and water was studied by molecular dynamics simulation with cellulose coordinates refined from electron diffraction data as a starting point. Potential energies, pucker parameters, torsion angles, and hydrogen bonding have been used for the characterization. Only the topmost layer in the cellulose differs in terms of structure and dynamics from the crystal bulk, but even these difference are small. At the surface approximately half of the cellulose intermolecular hydrogen bonding is lost, but this is compensated by hydrogen bonds with water molecules. Much of the difference between even and odd (200) planes disappears at the interface, except for the orientation of the glucose ring plane. Water dynamics is retarded by a factor of 2-3 close to the surface. The potential energy of water molecules in the first hydration layer is lower by 2 kJ/mol. The cellulose surface contains about five exposed hydroxyl groups per square nanometer, which accounts for the good hydration of the surface.
Introduction Natural cellulose consists of long, parallel homopolymers of (1 f 4)-β-linked D-glucose monomers. Despite its importance in a number of industrial applications, a detailed picture of cellulose structure at the microscopic level was achieved only recently. Using electron diffraction techniques on fibers, Sugiyama et al. were able to determine the unit cells of both native crystalline cellulose phases and obtained approximate coordinates from models built to fit the fiber diffraction data.1 In both phases the cellulose chains are organized in a parallel-up fashion. The IR phase is triclinic with cell dimensions a ) 0.674 nm, b ) 0.593 nm, c ) 1.036 nm (chain axis), R ) 117°, β ) 113°, γ ) 81°, and one cellobiose moiety per unit cell. The Iβ phase is monoclinic and very similar to the model by Sarko and Muggli,2 with cell dimensions a ) 0.801 nm, b ) 0.817 nm, c ) 1.036 nm (chain axis), R ) β ) 90°, γ ) 97.3°, and two cellobiose moieties per unit cell. The densities are 1.582 and 1.599 g cm-3. The coordinates have received corroboration from atomic force microscopic studies of crystalline cellulose from Valonia macrophysa.3 In an earlier communication, we attempted to refine the atomic coordinates for crystalline cellulose.4 Both phases (27 and 72 unit cells) were subjected to molecular dynamics simulation for 1 ns under the periodic boundary conditions appropriate for the two crystal forms. The simulations resulted in minor changes in atomic coordinates. In agreement with experimental data, the Iβ phase was found to be more stable than the IR phase. It was also found that the χ torsion angle determines the C-6 13C CP-MAS NMR chemical shift, while no simple geometric explanation could be found for the shifts of C-1 and C-4.5 The most striking property of the monoclinic phase, however, is the angle of 9.6° that is found between glucose ring planes in alternate (200) crystal planes. We labeled * Corresponding author: Telephone +358-9-456 51 05. Fax: +358-9-455 21 03. E-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, February 1, 1997. (1) Sugiyama, J.; Vuong, R.; Chanzy, H. Macromolecules 1991, 24, 4168-4175. (2) Sarko, A.; Muggli, R. Macromolecules 1974, 7, 486-494. (3) Kuutti, L.; Peltonen, J.; Pere, J.; Teleman, O. J. Microsc. 1995, 178, 1-6. (4) Heiner, A. P.; Sugiyama, J.; Teleman, O. Carbohydr. Res. 1995, 273, 207-223. (5) Heiner, A. P.; Teleman, O. Pure Appl. Chem., in press.
these alternating planes even and odd, and their cellulose molecules have different properties, as exemplified by hydrogen bond patterns and pucker parameters.5 All biologically and technically important processes involving cellulose occur at the interface between cellulose and water. Only a few experimental studies have dealt with crystalline cellulose surfaces. These include electron microscopic studies of cellulose and other polysaccharides,6-8 atomic force microscopy,3,9,10 and adsorption studies.11 Chanzy and co-workers were also able to observe preferential adsorption of a cellulase, cellobiohydrolase I, to one of the crystalline surfaces.12 In all these studies the resolution has been at the molecular level at best. The presence of solvent is known to affect the structure of carbohydrates. In water, the ratio between the R- and β-anomer of glucose is approximately 0.65:0.35 in favor of the β-anomer; in DMSO at lower temperatures the preference is reversed in favor of the R-anomer.13 Whether the anomeric effect is of intramolecular nature14,15 or is a solvation induced effect16-18 is still unresolved. In vacuum, the exocyclic hydroxymethyl group of β-Dglucose invariably adopts the tg conformation19 due to the formation of an intramolecular hydrogen bond O6(6) Chanzy, H. D.; Henrissat, B. FEBS Lett. 1985, 184, 285-288. (7) Chanzy, H. D.; Grosrenaud, A.; Joseleau, J. P. Biopolymers 1982, 21, 301-319. (8) Helbert, W.; Chanzy, H. Carbohydr. Polym. 1994, 24, 119-122. (9) Hanley, S. J.; Giasson, J.; Revol, J.-F.; Gray, D. G. Polymer 1992, 21, 4639. (10) Hanley, S. J.; Gray, D. Holzforschung 1994, 48, 29-34. (11) Reinikainen, T.; Teleman, O.; Teeri, T. Proteins: Struct., Funct., Genet. 1995, 22, 392-403. (12) Chanzy, H. D.; Henrissat, B.; Vuong, R. FEBS Lett. 1984, 172, 193-197. (13) Franks, F. Pure Appl. Chem. 1987, 59, 1189-1202. (14) Cramer, C. J.; Truhlar, D. G. J. Am. Chem. Soc. 1993, 115, 57455753. (15) van Eijck, B. P.; Hooft, R. W. W.; Kroon, J. J. Phys. Chem. 1993, 97, 12093-12099. (16) Schmidt, R. K.; Karplus, M.; Brady, J. W. J. Am. Chem. Soc. 1996, 118, 541-546. (17) Tvaroska, I.; Kozar, T. Theor. Chim. Acta 1986, 70, 99. (18) Ha, S.; Gao, J.; Tidor, B.; Brady, J. W.; Karplus, M. J. Am. Chem. Soc. 1991, 113, 1553. (19) The conformation of the hydroxymethyl group is defined by two characters. The first refers to the O5-C5-C6-O6 (ω) torsion angle (g ) gauche, t ) trans), and the 2nd refers to the χ C4-C5-C6-O6 torsion angle. The tg conformation ranges from χ ) -120° to χ ) 0°, the gt conformation ranges from χ ) -120° to χ ) 120°, and the gg conformation ranges from χ ) 0° to χ ) 120°.
+
512
+
Langmuir, Vol. 13, No. 3, 1997
H6‚‚‚O4. This interaction is absent in (mildly) polar solvents, and the ratio between the three staggered conformations gg:gt:tg is approximately 0.5:0.5:0. Both high-level quantum mechanical calculations15 and molecular dynamics simulations20 have shown that the orientation of the hydroxymethyl group is determined by solvation effects. Similarly, the intramolecular hydrogen bond O3-H3‚‚‚O5 over the glycosidic linkage in methyl β-cellobioside is present in apolar solvents but absent in polar solvents.21 In a recent NMR study Jiminez-Barbero et al.22 showed that the stability of carbohydrate complexes is strongly influenced by the orientation of hydroxyl groups of both substrate and ligand. The hydroxyl groups of the substrate may reorient on binding, even when they are not directly hydrogen bonded to the ligand. This is caused by solvation/desolvation processes of the hydroxyl groups. In summary, solute-solvent hydrogen bonds are often energetically favored over solute-solute hydrogen bonds, resulting in different hydroxyl conformations for wellhydrated carbohydrates compared to carbohydrates in vacuum or an apolar environment. In cellulose, a tg conformation for the hydroxymethyl group permits formation of an intramolecular hydrogen bond O2-H2‚‚‚O6 over the glycosidic linkage. If present, the tensile strength is approximately 50GPa higher than that with the single O3-H3‚‚‚O5 hydrogen bond over the glycosidic linkage found in cellulose II.23,24 At the surface these intramolecular hydrogen bonds have to compete with solvent interactions. The presence of a flat surface presents restrictions on the location of the solvent, which may limit the hydration of the hydroxyl groups. Here, we give an atomic-level characterization of the cellulosewater interface, based on molecular dynamics simulation of our previous cellulose coordinates in the presence of water. Methods Six cellulose layers, each layer consisting of six chains of three cellobiose units, were placed in the center of a monoclinic periodic box with dimensions Lx ) 3.6394 nm, Ly ) 3.1080 nm, Lz ) 3.21101 nm, with the normal of the monoclinic (110) surface parallel to the Z-axis; the c-axis was chosen parallel to the Y-axis (see Figure 1). The angle between the Lx and Lz sides is equal to the angle between the crystal 1,1,0 and 1,-1,0 vectors, i.e. ζ ) 88.858°. The initial cellulose conformation was obtained by applying crystal symmetry operations on the average structure over 500 ps of a previous cellulose Iβ simulation,4 on the basis of electron diffraction data by Sugiyama et al.1 To prevent a bias toward the initial average crystal structure, side group dihedrals of the glucose moieties were randomized followed by a short simulation using full periodic boundary conditions. Lz was then increased to 6.211 01 nm (cf. Figure 1), and the additional space was filled with 1132 SPC/E water molecules,25 equivalent to a density of 0.998 g/cm3. The complete system consists of 3024 cellulose (united) atoms and 3396 water atoms. The system was energy minimized and subsequently thermalized at 300 K while restraining the cellulose chains to their initial position using a force constant of 3000 kJ‚nm-2 during the first 10 ps. After the position restraints were removed, the system was equilibrated at 300 K for 120 ps. During the first 5 ps of the equilibration the interplanar distance (0.5352 nm in the crystal structure) (20) Kroon-Batenburg, L. M. J.; Kroon, J. Biopolymers 1990, 29, 1243-1248. (21) Leeflang, B. R.; Vliegenthart, J. F. G.; Kroon-Batenburg, L. M. J.; van Eijck, B. P.; Kroon, J. Carbohydr. Res. 1992, 230, 41-61. (22) Jiminez-Barbero, J.; Junquera, E.; Martin-Pastor, M.; Sharma, S.; Vicent, C.; Penades, S. J. Am. Chem. Soc. 1995, 117, 11198-11204. (23) Reiling, S.; Brickmann, J. Macromol. Theory Simul. 1995, 4, 725-743. (24) Kroon-Batenburg, L. M. J.; Kroon, J.; Nordholt, M. G. Polym. Commun. 1986, 27, 290. (25) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, J. P. J. Phys. Chem. 1987, 91, 6269.
Heiner and Teleman decreased by 3.3% to 0.5174 nm. The length of the c-axis was decreased linearly to 6.11 nm during the next 60 ps, to compensate for the reduced solvent density (final solvent density was 0.974 g‚cm-3). The system was simulated in an NVT ensemble using the GROMOS87 force field26 in conjunction with a locally adapted GROMOS87 program suit.27 The temperature of cellulose and water was controlled separately using the Berendsen thermostat with a coupling constant of τbath ) 0.4 ps.28 A time step of 1.25 fs was used, and bond lengths were constrained using the SHAKE algorithm with a relative tolerance of 10-8. Nonbonded interactions were calculated using the twin-range cutoff procedure with radii of 0.9 and 1.1 nm, respectively. The nonbonded pair list was updated every 12.5 fs, which is sufficient for solvated systems. Configurations were saved every 0.2 ps. The simulation extended over 500 ps and was run on an IBM-RS6000/390 work station in double precision. Pucker parameters were analyzed according to Cremer and Pople.29 Examples of puckered conformations as a function of the Q,Θ,Φ parameters can be found in ref 30.
Results and Discussion A snapshot from the end of the simulation has been drawn in Figure 1b. In order to simplify the presentation of results, a number of specific terms will be used. The cellulose layers II and III (in total four layers, cf. Figure 1a) will be referred to as bulk, while the simulation of ref 4 performed under crystal periodic boundary conditions will be referred to as the crystal. Odd and even indicate that something is part of an odd or even (200) plane. In the interface, glucose moieties are oriented in two ways, with the hydroxymethyl either protruding into the water or buried into the cellulose. These will be indicated as C6-outward and C6-inward, respectively. Overall Structure. The (110) interplanar distance decreases by approximately 3.7% from 0.5352 nm to 0.5174 nm. The unit cell parameters calculated from the ring centers of the four central layers showed the largest changes for the a vector (-3.6%, 0.772 nm) and γ (+1.7%, 99.0°), whereas the b vector, which is approximately parallel to the interchain hydrogen bonds, was hardly affected (+0.5%, 0.821 nm). The unit cell parameters of cellulose Iβ vary with cellulose origin, but in most cases the variations are such as to keep the interplanar distances d1,1,0 and d1,-1,0 constant. The simulated unit cell parameters are well within the range of reported experimental parameters,31,32 except for γ, which is approximately 3° too large. The latter is probably a consequence of the constant volume simulation, which constrains the coordinate component parallel to (1,-1,0). The united atom GROMOS force field has been applied also to other saccharides. Kouwijzer et al. found an average volume decrease of 2-3% for the standard GROMOS force field for a number of monosaccharides33 but also that the inter- and intramolecular structure was preserved well. The observed small contraction may therefore be a consequence of the choice of force field. We will compare the properties of the four central layers with those of the (26) Koehler, J. E. H.; Saenger, W.; van Gunsteren, W. F. Eur. Biophys. J. 1987, 15, 197-210. (27) van Gunsteren, W. F.; Berendsen, H. J. C. Groningen Molecular Simulation (GROMOS) Library Manual, Biomos, Nijenborgh 4, Groningen, The Netherlands. (28) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684-3690. (29) Cremer, D.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 1354-1358. (30) Dowd, M. K.; French, A. D.; Reilly, P. J. Carbohydr. Res. 1994, 264, 1-19. (31) French, A. D.; Roughead, W. A.; Miller, D. P. ACS Symp. Ser. 1987, 340, 15-37. (32) Wada, M.; Okano, T.; Sugiyama, J.; Horii, F. Cellulose 1995, 5, 223-233. (33) Kouwijzer, M. C. L. E.; van Eijck, B. P.; Kroes, S. J.; Kroon, J. J. Comput. Chem. 1993, 14, 1281-1289.
+
Monoclinic Crystalline Cellulose and Water
+
Langmuir, Vol. 13, No. 3, 1997 513
Figure 1. (a, top left) Schematic placement of monoclinic crystalline cellulose in the periodic simulation box. Each cellulose layer has been numbered. All properties have been averaged over both layers; i.e., a surface layer property has been averaged over both layers I. For analysis purposes, the water has been divided into slabs of 0.25 nm thickness. During the initial equilibration the box was shorter and only contained the cellulose. Please note that the odd/even labeling unfortunately was interchanged in Figure 4 of ref 4. (b, top right) As for part a but a snapshot from the end of the simulation (130 + 500 ps) drawn with a CPK representation. Cellulose carbon atoms are yellow, oxygen atoms red, and water oxygen atoms are blue. Hydrogen atoms have not been drawn. (c, bottom) One of the surfaces en face. Polar hydrogens in the cellulose are white. The picture shows the water in layer 2 and about half of the water in layer 3 (blue sticks).
+
+
514
Langmuir, Vol. 13, No. 3, 1997
Heiner and Teleman
Table 1. Camber of Glucose Ring Planes with Respect to the 200 Plane layer
orientation
even molecules
odd molecules
I I II II III III
C6-inward C6-outward C6-inward C6-outward C6-inward C6-outward
-8.9° -7.8° -7.4° -8.0° -7.0° -7.2°
0.5° 7.5° 1.3° 1.3° 0.4° 0.6°
Figure 2. Distribution of the Φ pucker parameter for crystal (full curves), bulk (dashed curves), and surface (dotted curves) glucose rings. Bold and thin curves denote the even and odd subphases. Only C6-outward glucose units have been taken into account for the surface curves.
previous bulk simulation to ensure that the contraction does not entail other artifacts. The backbone torsion angle distributions of layers II and III are similar to those of the crystal simulation (〈φ〉 ) 21.2° (even), 23.0° (odd); 〈ψ〉 ) -18.0° (even), -19.4° (odd)). For the surface layers, the distributions are slightly wider. The differences in average torsion angles between C6-inward and C6-outward glucose rings are small (approximately 3°), except for 〈ψ〉 in the odd phase, where it is about 8°. The two chains in the monoclinic unit cell can be identified as “odd” or “even” by their angle to the (200) crystal plane. This angle can be divided into pitch and camber angles, where the camber is the angle between the glucose ring plane and the (200) plane as drawn in Figure 1a. The camber angles are given in Table 1. In layers II and III the camber differs between odd and even molecules by 8.3°, close to the full crystal simulation. In layer I odd molecules, the camber increases to +7.5° for C6-outward glucose rings. The latter is believed to be a consequence of the asymmetry of the hydrogen bond network of cellulose chains at the surface. Pucker parameters are useful descriptors of the glucose ring conformations.5 This applies in particular to the puckering azimuth (Φ), which describes toward what ring shape the 4C1 ring conformation deviates. As the glucose moieties are always close to the 4C1 conformation, the Φ parameter describes the shape of the potential well rather than other conformations. For the interior layers, the Φ pucker distribution agrees with that of the crystal simulation (cf. Figure 2). For the surface layers the Φ pucker distribution is neither “odd” nor “even” but has features similar to those of rings in the triclinic phase (Φ maximum at -30°, Θ distribution between odd and even). The Φ distribution differs to some extent also for C6inward and C6-outward moieties. While the Θ distributions for odd and even are distinct in the crystal, they superimpose for even and odd surface glucose rings. The pucker amplitude (Q) is similar in all cases (data not shown). Sidegroups and Hydrogen Bonding. The torsion angle distribution (χ: C4-C5-C6-O6) for the C6-outward
Figure 3. Torsion angle distributions: (a) χ (C4-C5-C6O6); (b) τ2 (C1-C2-O2-H2); (c) τ3 (C2-C3-O3-H3); (d) τ6 (C5-C6-O6-H6). Bold and thin curves denote the even and odd subphases. Full curves refer to the crystal simulation. Dashed curves are the bulk layers, which approximate the crystal in all cases. Dotted curves describe the surface glucose rings where the relevant hydroxyl group is solvent exposed, i.e. C6-outward for parts a and d and C6-inward for parts b and c.
hydroxymethyl groups in layer I is quite distinct from that in the bulk (Figure 3a). For even chains, the gt conformation is favored over the tg conformation and a minor gg population (gt:gg:tg ) 0.65:0.08:0.27). In odd chains the gt and gg conformations are approximately equally populated, while tg is less populated (gt:gg:tg ) 0.48:0.35:0.17). The χ distribution in the bulk is similar to that in the crystal, with only slightly different populations of the gg and gt states. A lifetime analysis based on Markov chains shows that χ dynamics is faster for C6outward rings, particularly for even chains. The τ2 (C1-C2-O2-H2), τ3 (C2-C3-O3-H3) and τ6 (C5-C6-O6-H6) distributions (Figure 3b-d) for the bulk are very similar to those of the crystal simulation. This includes the typical distinction between odd and even planes observed in the τ2 and τ6 distributions. The lifetime analysis shows that solvent-exposed torsion angles rotate at least one order of magnitude faster than inward hydroxyl groups. In layer I C6-inward glucose rings, the τ2 dihedral is solvent-exposed (Figure 3b) and, as a result, shows a
+
+
Monoclinic Crystalline Cellulose and Water
Langmuir, Vol. 13, No. 3, 1997 515
Table 2. Cellulose Intramolecular Hydrogen Bondsa layer I; even bond solv expc bond buriedc layer I; odd bond solv expc bond buriedc layer II; even layer II; odd layer III; even layer III; odd crystal; even crystal; odd
O2‚‚‚O6b
O3‚‚‚O5b
O6‚‚‚O2
0.484 0.050 0.918 0.445 0.073 0.817 0.929 0.826 0.833 0.832 0.951 0.801
0.614 0.517 0.710 0.714 0.716 0.711 0.697 0.879 0.678 0.852 0.733 0.883
0.072 0.143 0 0.120 0.134 0.105 0.044 0.099 0.096 0.097 0 0.105
Table 4. Hydrogen Bonds between Cellulose and Watera layer I; even O2 O3 O4 O5 O6
layer I; odd
donor
accept
total
donor
accept
total
0.784 0.100 0.000 0.000 0.580
0.420 0.602 0.260 0.031 0.786
1.20 0.70 0.26 0.03 1.35
0.800 0.170 0.000 0.000 0.700
0.498 0.693 0.170 0.007 0.832
1.30 0.86 0.17 0.01 1.53
a The number listed is the occupancy, but only taking into account the glucose moieties in which the relevant oxygen atom is exposed (C6-inward for O2, O3, and O4; C6-outward for O5 and O6). In the buried orientation, no hydrogen bonds are formed to water molecules.
a The number listed is the occupancy, i.e. the probability of existence for the hydrogen bond. Only hydrogen bonds with a maximum occupancy above 0.05 are reported. The donor is given first. An occasional O6‚‚‚O3 hydrogen bond was also observed (maximum occ ≈ 0.05). b Strong hydrogen bond in the crystal. c The bond is solvent exposed when the O5- or O6-containing glucose is C6-outward and the O2- or O3-containing glucose is C6-inward.
Table 3. Cellulose Intermolecular Hydrogen Bondsa layer I; even bond solv expc bond buriedc layer I; odd bond solv expc bond buriedc layer II; even layer II; odd layer III; even layer III; odd crystal; even crystal; odd
O3‚‚‚O6
O6‚‚‚O2
O6‚‚‚O3b
O6‚‚‚O4
0.024 0.003 0.044 0.083 0 0.166 0.018 0.043 0.045 0.083 0 0.034
0.079 0 0.157 0.094 0.078 0.110 0.137 0.070 0.110 0.090 0.175 0.115
0.414 0.012 0.817 0.336 0 0.672 0.828 0.686 0.768 0.743 0.874 0.712
0.043 0.087 0 0.016 0 0.032 0 0.055 0 0.011 0.011 0.011
a The number listed is the occupancy. Only hydrogen bonds with a maximum occupancy above 0.05 are reported. The donor is given first. Occasional hydrogen bonds were also observed for O2‚‚‚O3 (maximum occ ≈0.04) and O6‚‚‚O5 (≈0.04). b Strong hydrogen bond in the crystal. c The bond is solvent exposed when the O5- or O6containing glucose is C6-outward and the O2- or O3-containing glucose is C6-inward.
different torsion angle distribution. The difference between the odd and even planes disappears. The gauche maximum at 60° is shifted to 80°, but its population decreases to 30% while the trans state increases to a 70% population. Solvent exposure affects the τ3 dihedral only little. The trans conformation loses some 15% population, mostly to the gauche state at +60° (Figure 3c). By contrast, solvent-exposed τ6 dihedrals become more or less freely rotating (Figure 3d). In the odd planes the trans state and two gauche states are equally populated, while the gauche state is slightly disfavored in the even planes. This indicates that the intrachain hydrogen bond O3H3‚‚‚O5 is preserved quite well on the surface, whereas the O2-H2‚‚‚O6 intrachain hydrogen bond is almost completely lost. A hydrogen bond was considered to exist, when the hydrogen-acceptor distance is less than 0.25 nm and the acceptor-hydrogen donor angle exceeds 135°. Tables 2-4 summarize intramolecular, intermolecular, and cellulosewater hydrogen bonds. The intramolecular hydrogen bonds are well preserved both in the bulk and when not solvent exposed. The O3‚‚‚O5 bond is preserved even at the surface (even, 0.517; odd, 0.716). In dissolved methyl β-cellobioside this hydrogen bond is lost in polar solvents.20 When solvent-exposed, the O2‚‚‚O6 hydrogen bond is partially replaced by a hydrogen bond between O6 and O2, but the sum of these interactions is only one fifth of that in the bulk (even, 0.193; odd, 0.217). The latter fraction is larger than the occupancy of the tg conformer
Figure 4. Density profiles and water dynamics. The density profiles (g/cm3) refer to the left y scale. The translational diffusion coefficient (D, circles) and second-order rotational correlation times for the water dipole vector (τ2, diamonds) refer to the right y scale. The rotational correlation time was from a single-exponential fit to the second-order Legendre polynomial of cos θ(∆), where θ(∆) is the angle between the dipole vector at time t and that at time t + ∆. The translational diffusion coefficient was obtained from a linear fit to the mean square displacement as a function of time.
(0.17), which means that a hydrogen bond between O2 and O6 can be formed in the gg or the gt conformer. The lower occurrence of the O2‚‚‚O6 hydrogen bond is obviously consistent with the preference for other than the tg conformer on solvent exposure, but the rapid rotation of the χ dihedral may also play a role. The intermolecular O6‚‚‚O3 bond, which connects adjacent molecules in the same (200) plane, is conserved in the bulk. In layers I, half of it is lost, since there is no outside molecule with which to form the bond. Hydration and Solvent Properties. The cellulose and water density profiles are given in Figure 4. The cellulose atomic positions fluctuate only little even at room temperature, as the crystal is very stiff. For this reason the cellulose density profile was made smoother by using a large bin size (0.05 nm). The higher cellulose macroscopic density is also clearly visible (1.6 g/cm3). There is a marked first and second hydration layer, outside of which the water density approaches bulk density. Away from the cellulose, both water structure and dynamics are similar to what is obtained for pure SPC/E water. Recently Grigera et al.34 described the interface with SPC/E water for a hydrophilic (ice in the Ih structure) and a hydrophobic (similar structure, but atoms without partial charges) crystal. Outside the hydrophilic crystal they observed three hydration peaks, but they observed none outside the hydrophobic crystal. The first hydration (34) Grigera, J. R.; Kalko, S. G.; Fischbarg, J. Langmuir 1996, 12, 54-158.
+
516
+
Langmuir, Vol. 13, No. 3, 1997
Figure 5. Hydration of cellulose: (a) radial distribution of water oxygen atoms around the O2 cellulose oxygen atoms; (b) similar to part a but with respect to O3; (c) similar to part a but with respect to O6. Bold and thin curves denote the even and odd subphases. The radial distribution functions are normalized to correspond to bulk water density in grams per cubic centimeter.
shell in Figure 4 is not as pronounced as theirs, and the assent to the first peak is slower (resembling a hydrophobic wall), but both phenomena are probably caused by the greater roughness of the cellulose crystal surface. From this comparison the cellulose seems to behave like a hydrophilic crystal. The cellulose hydration is described by a number of radial distribution functions around cellulose hydroxyl groups (Figure 5). There is a distinct difference between odd and even for all three oxygen atoms. This difference is the least noticeable for O6, as it protrudes further into the solvent than O2 or O3. The radial distribution functions converge toward a density around 0.6 g/cm3, as the interface cellulose experiences a half-space of water. That the asymptote is above half the bulk density indicates that the reference hydroxyls protrude somewhat into the solvent and slightly more so for odd planes. Exposed hydroxyl groups form hydrogen bonds with water molecules (Table 4). The strongest hydration is formed by O2 and O6. For each C6-inward glucose ring O2 forms about 1.25 hydrogen bonds to water molecules, 0.8 as donor and half as acceptor. In β-D-glucose O2 forms 1.98 hydrogen bonds to water, in equal amounts as acceptor and donor. To assess the influence of the surface, the hydrogen bonds with cellulose have to be considered as well. This gives an extra 0.06 as a donor and 0.17 as an acceptor, and the total number of hydrogen bonds formed by O2 is approximately 0.5 lower than that in free glucose.35 Likewise, each solvent-exposed O6 hydroxyl forms 1.5 hydrogen bonds to water molecules, but this hydroxyl is a stronger acceptor than donor. Including the intracellulose hydrogen bonds, the O6-hydroxyl forms 0.99 hydrogen bonds as an acceptor and 0.87 hydrogen bonds as a donor. This is approximately 0.35 hydrogen bonds less than for β-D-glucose.35 O3 is slightly more weakly hydrated with a total of about 0.75 hydrogen bonds. O5 (35) van Eijck, B. P.; Kroon-Batenburg, L. M. J.; Kroon, J. J. Mol. Struct. 1990, 237, 315-325.
Heiner and Teleman
is only marginally exposed, and O4 in the glycosidic linkage is not very well exposed. Figure 1c shows the water molecules closest to the surface. Hydrogen bonds with the water are easily found from the picture, including cases where two C6 hydroxyl groups are bridged by hydrogen bonds to the same water molecule. The cellulose surface contains about 4.8 well exposed hydroxyl groups per square nanometer, which form about 5.8 hydrogen bonds with the water. Since the geometric cross section of a water molecule is 0.1 nm2, almost two thirds of the water molecules in the first layer will form a hydrogen bond to the cellulose. In this crude sense the cellulose surface appears relatively well hydrated. The density of the water closest to the cellulose is given in Figure 6. There is one localized water molecule per cellobiose unit in the surface, located close to the O2 and O3 hydroxyls of the C6-inward glucose moiety. The cellulose surface affects the water dynamics close to the surface. Figure 4 also gives the rotational correlation time and translational diffusion coefficient as functions of distance from the cellulose. The presence of the solid surface retards solvent dynamics by a factor of 2-3 for the innermost layer, in keeping with results obtained for other surfaces.34,36,37 Bulk behavior is observed from layer 6 and outward. Energetics. The potential energies are given in Table 5 for the cellulose and in Table 6 for the solvent. The bulk van der Waals and electrostatic potential energies are similar to those obtained from the bulk simulation. Of the cellulose-cellulose intermolecular interaction the cellulose in layers I loses one third of the van der Waals contribution and half of the Coulombic interaction. This is to some extent but not completely compensated by interactions with the water. In the hydration layer (layers 1-5) the water potential energy is on average -44.36 kJ/mol, lower than the bulk value of -43.24 kJ/mol (layers 6-8), which is close to that of pure SPC/E water.25 This suggests that the (110) crystalline surface is mildly hydrophilic, in contrast to what has been assumed so far. The relevant criterion is obviously the free energy of hydration, which can be estimated from the integral over space of density and chemical potential, viz.
∫
∆Ghydr ) -RT vn(r b) µ(r b) dr b)
∫
( )
b) ln -RT vn(r
n(r b) dr b nbulk
where µ is the local chemical potential and n the local density. In contrast to the chemical potential, ∆Ghydr can be determined accurately, since the integrand is well behaved for small n. In determining the grid size to calculate ∆Ghydr two conflicting criteria have to be met.38 In order to reproduce surface detail the grid has to be as fine as possible while good statistics calls for a large grid size. By averaging over all nine cellulose unit cells in the cellulose water interface, an nbulk ≈ 68 was obtained for a grid cell of ∆x ) 0.067 397 nm, ∆y ) 0.069 067 nm, and ∆z ) 0.02 nm. The calculation was performed separately for the two interfaces for a multitude of grid sizes. The obtained ∆Ghydr values converge with decreasing grid size before insufficient statistics restricts accuracy. This means that there is a grid size range that offers sufficient statistics and reproduces surface detail. (36) Ahlstro¨m, P.; Teleman, O.; Jo¨nsson, B. Chem. Scr. 1989, 29A, 97-102. (37) Rossky, P. J.; Hi Lee, S. Chem. Scr. 1989, 29A, 93-96. (38) Edholm, O.; Berendsen, H. J. C. Mol. Phys. 1984, 51, 10111028.
+
Monoclinic Crystalline Cellulose and Water
+
Langmuir, Vol. 13, No. 3, 1997 517
The resulting ∆Ghydr/∆z and its integral are shown in Figure 7. After subtraction of the base line in layers 6-8 the final estimate of ∆Ghydr for the hydration layer (layers 1-5) is -12.7 ( 1.4 kJ/nm2 or -0.44 ( 0.05 kJ/mol of water. A large contribution to this arises from the localized water molecules shown in Figure 6. Using the enthalpy (Table 6) we obtain an associated entropy loss -T∆Ssolv due to hydration of 0.68 ( 0.05 kJ/mol. This can be compared to the entropy loss of 8.4 kJ/mol on transferring a water molecule from the bulk into immobile environments such as ice or strongly hydrated salts at 300 K.39 In zeolites -T∆Ssolv is around 2.7 kJ/mol. Assuming that the energy gain and entropy loss are concentrated in the first hydration layer, ∆Esolv ≈ 3.23 kJ/mol, -T∆Ssolv ≈ 1.96 kJ/mol, which is still much less than the entropy loss on freezing. To ascertain the overall stability of the interface, the ∆Gcell has to be calculated as well. The wider dihedral distribution functions of the surface layer suggest an entropy gain. Entropies can be evaluated from the torsion angle distribution.40-42 The entropy gain in interface molecules is given in Table 7 for the torsion angles with the largest differences between bulk and interface. As expected the major contribution is due to the hydroxymethyl side group. The average total entropy gain is -T∆Scell ) -9.4 kJ/mol of cellobiose in layers I. This value is an upper limit, as correlations between the degrees of freedom were neglected. Table 8 summarizes the surface energetics. The total surface free energy is positive by at least 23.1 kJ/nm2, which thus disfavors surface formation. In principle, this means that cellulose systems will tend to minimize the surface area, i.e. form as large microfibrils as possible. Owing to the polymeric nature of cellulose and the stiffness of the crystal, microfibril reformation may be so slow that the tendency to minimize the microfibril surface lacks practical importance. Conclusion
Figure 6. Hydration of cellulose. (a,top) En face view of the cellulose surface showing the water density of the first hydration shell. The water density was averaged over layers 1 and 2 and half of 3 and divided by the bulk water density. Contours are plotted every 0.2Fbulk ≈ 0.2 g/cm3, and the maximum density (≈2.0) is found between the glycosidic linkage of one molecule and the O2 and O3 hydroxyls of the adjacent molecule. The portion of the glucose rings that point into the cellulose has not been drawn. The dotted rectangle indicates the unit cell, which contains one cellobiose moiety each from an even and an odd molecule. (b, bottom) Cross section of the interface with cellulose to the left (thicker contours). The distance between cellulose density contours is 1.5 g/cm3, and that for water is 0.25 g/cm3. The cellulose density peaks are artificially sharp, since the density was calculated using point atoms. Total densities as a function of z are shown at the top.
Only the topmost surface layer of the crystalline cellulose is structurally affected by the water outside the surface, which reflects the strength and rigidity of the cellulose crystal. This observation is consistent with findings based on solid state 13C CP-MAS NMR spectra, from which the effective surface component could be identified and found to correspond to one layer only (ref 43 and Dr. T. Iversen, personal communication). The structure of the surface layer is only mildly different from that of the bulk. Differences are found for the hydroxymethyl and hydroxyl groups. The surface glucose moieties are more glucose like, and the odd/even duplicity is practically absent from the surface layer. Whether the hydration is even better for the (1,-1,0) surface remains to be seen. Its density of hydroxyl groups is about 13% higher, but the tighter packing may also impose constraints. Work in our laboratory is in progress to describe this and the two triclinic surfaces in a similar manner. They will be compared to the (1,1,0) surface and the results used in the interpretation of AFM micrographs Cellulose is the main strength provider in most plants. In this role it interacts with a number of other polymeric (39) Dunitz, J. D. Science 1994, 264, 670. (40) Edholm, O.; Berendsen, H. J. C.; van der Ploeg, P. Mol. Phys. 1983, 48, 379-388. (41) di Nola, A.; Berendsen, H. J. C.; Edholm, O. Macromolecules 1984, 17, 2044-2050. (42) Edholm, O.; Berendsen, H. J. C. Mol. Phys. 1984, 51, 10111028. (43) Newman, R. H.; Hemmingson, J. A. Cellulose 1994, 2, 95-110. (44) Finkenstadt, V. L.; Hendrixson, T. L.; Millane, R. P. J. Carbohydr. Chem. 1995, 14, 601-611.
+
+
518
Langmuir, Vol. 13, No. 3, 1997
Heiner and Teleman
Table 5. Potential Energies for the Cellulose (kJ/mol)a energy contribution
layer I: odd
layer I: even
layer II: odd
layer II: even
layer III: odd
layer III: even
intramolecular, bonded bond angles torsion angles improper torsions intramolecular, nonbonded van der Waals contr Coulombic contr intramolecular, w cellul van der Waals contr Coulombic contr intramolecular, w water van der Waals contr Coulombic contr total potential energyb total van der Waals total Coulombic
129.8 45.0 78.7 6.1 437.3 -33.8 471.1 -163.4 -119.4 -44.0 -74.7 -21.1 -53.7 329.0 -174.3 373.5
135.9 50.6 77.7 7.6 437.5 -34.5 472.0 -171.0 -121.2 -49.8 -70.0 -21.4 -48.6 332.4 -177.1 373.6
131.5 46.9 79.2 5.4 429.7 -29.5 459.2 -256.9 -176.0 -80.8 -1.0 -0.5 -0.4 303.3 -206.1 377.9
134.0 49.2 78.6 6.2 431.3 -30.9 462.1 -260.2 -175.6 -84.6 -0.3 -0.4 0.0 304.7 -206.8 377.6
122.1 40.5 76.6 5.0 428.9 -29.2 458.2 -256.5 -176.1 -80.4 0.0 0.0 0.0 294.5 -205.3 377.7
131.2 46.2 77.4 7.7 429.3 -31.9 461.2 -257.3 -176.6 -80.7 0.0 0.0 0.0 303.1 -208.4 380.4
a The energies are given per cellobiose unit. Pair interactions have been attributed with 50% to each interagent. b Sum of van der Waals, Coulombic, and bonded contributions.
Table 6. Water Potential Energies in kJ/mola intermolecular interaction within the layer van der Waals contr Coulombic contr with other water layers van der Waals contr Coulombic contr with the cellulose van der Waals contr Coulombic contr total energy van der Waals contr Coulombic contr no. of waters in layer
layer 1b
layer 2
layer 3
layer 4
layer 5
layer 6
layer 7
layer 8
-0.1 0.0 -0.1 -17.2 3.7 -20.9 -24.5 -3.0 -21.5 -41.8 0.8 -42.6 0.0
-10.1 2.6 -12.7 -20.8 3.3 -24.0 -15.0 -3.4 -11.7 -46.0 2.5 -48.4 42.5
-18.6 4.2 -22.8 -20.6 3.1 -23.7 -6.1 -2.1 -4.0 -45.2 5.2 -50.4 98.2
-17.2 3.9 -21.2 -25.7 3.2 -29.0 -0.7 -0.4 -0.3 -43.7 6.8 -50.5 93.8
-16.7 3.8 -20.6 -26.6 3.2 -29.8 -0.1 0.0 -0.1 -43.4 7.0 -50.4 91.7
-16.7 3.8 -20.5 -26.6 3.2 -29.9 0.0 0.0 0.0 -43.3 7.0 -50.3 91.7
-16.6 3.8 -20.4 -26.6 3.2 -29.8 0.0 0.0 0.0 -43.2 7.0 -50.2 91.6
-10.3c 2.4 -12.7 -32.9 4.6 -37.5 0.0 0.0 0.0 -43.2 7.0 -50.2 56.5
a The energies are given per water molecule. Pair interactions have been attributed with 50% to each interagent. b Since layer 1 is very scarcely populated, the layer internal interaction is weak and the uncertainties large. c Layer 8 is the remainder of the periodic box at the edge and therefore thinner. This is the reason for the lower internal interaction.
Table 7. Entropy Gain in Surface Cellulose Moleculesa T∆Sb (kJ/mol cellobiose) main chain φ ψ Φ (ring) Θ (ring) Q (ring) side groups χ τ2 τ3 τ6 total
1.53 0.39 0.33 0.31 0.29 0.21 7.83 2.79 0.27 1.62 3.15 9.36
a Upper limit since correlations were neglected. b Average of odd and even chains.
Table 8. Total Cellulose Surface Energetics
Figure 7. Surface free energy for the water outside cellulose. Both ∆Ghydr/∆z and its integral (inset) are shown. The curves have been calculated independently for the two interfaces. That the two curves follow each other closely indicates adequate statistics.
compounds such as xyloglucan,44 different hemicelluloses, and lignin. With the polyoses this interaction will consist of a mixture of hydrogen bonding and a hydrophobic effect, in similarity to the forces that hold together the cellulose crystal but for geometric reasons are much weaker. In the future we will attempt to characterize these interactions at a molecular level.
cellulose solvent a
∆Ha (kJ/nm2)
-T∆S (kJ/nm2)
∆G (kJ/nm2)
+50.7 -32.3 +18.4
>-14.9 +19.6 >+4.7
>+35.8 -12.7 >+23.1
Since ∆V ) 0 in a constant volume simulation ∆H ) ∆U.
Acknowledgment. We are grateful to Mr. Lauri Kuutti for valuable discussion and to the European Commission for financial support under the Human Capital and Mobility programme (Grant No. ERBCHICT941552). LA960886D
