Interactions Binding Mineral and Organic Phases in Nanocomposites

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Interactions Binding Mineral and Organic Phases in Nanocomposites Based on Bacterial Cellulose and Calcium Phosphates D. A. Tolmachev and N. V. Lukasheva* Institute of Macromolecular Compounds, Russian Academy of Sciences, Bol’shoi pr. 31, St. Petersburg, 199004 Russia S Supporting Information *

ABSTRACT: The interactions responsible for the adhesion of calcium phosphate (CP) nanocrystals and bacterial cellulose (BC) nanofibrils in the composite material obtained by mixing aqueous suspensions of presynthesized CP and BC and the dependence of these interactions on the CP morphology and chemical structure have been elucidated by molecular mechanics calculations of the CP−BC interfacial structures. The interactions between the superficial CP and BC crystal layers have been simulated. Two crystalline CP structures (i.e., hydroxyapatite (HAP) and whitlockite) with two morphologies (plateshaped and rod-shaped) were considered. Electrostatics has been found to be the major contributor to the adhesion of the CP crystallites and BC nanofibers, and the formation of interfacial hydrogen bonds makes a minor contribution to the interaction energy. It has also been found that, in general, the energy gain resulting from whitlockite−BC binding is greater than that for HAP−BC binding, and the binding of the rod-shaped crystallites of whitlockite with BC is the most profitable. The energy loss and entropy gain upon replacement of the BC−water and CP−water contacts by the BC−CP contacts have been estimated.

I. INTRODUCTION In recent years, new hybrid organic−inorganic materials that can be widely used in medical practice, particularly in the field of prosthetics (for bone grafts), have been intensively developed. Bone tissue is a natural composite formed as a result of the growth of calcium phosphate (CP) crystals in an organic (collagen) matrix. The binding strength of these two phases is provided by strong electrostatic interactions between mineral ions and charged groups of collagen molecules ionized under normal physiological conditions. Organic−mineral composites are the most promising materials for implants intended to replace bones; therefore, their properties should be similar to those of bones. These materials are often produced by mimicking the natural process of mineralization (bioimitation), namely, by soaking an organic matrix with ionizable molecules in a simulated body fluid1−4 or by alternately soaking this matrix in Ca2+- and PO43−-containing solutions.5 Mineral ions from the solution precipitate on charged molecules of the organic matrix, thereby forming CP crystallites. Bacterial cellulose (BC) is successfully applied in different areas of tissue engineering, including its use as an organic matrix in composite materials for bone implants.6−8 Cellulose produced by bacteria has unique properties, such as chemical purity (free of lignin and hemicellulose), which distinguishes it from other forms of cellulose. It is also characterized by high biocompatibility, an ultrafine network structure, a high water holding capacity, a high degree of polymerization, a high crystallinity, and a high mechanical strength.9,10 BC possesses unique sorption properties because of its network structure consisting of ribbons with nanoscale © 2012 American Chemical Society

thicknesses. Every ribbon is built from a large number (10− 100) of crystalline nanofibrils separated by nanochannels, and all surfaces are covered with hydrophilic OH groups. Figure 1 shows the BC ribbon structure (on different scales). A large numer of investigations are concerned with the use of the bioimitation procedure to create composite materials based on bacterial cellulose for bone implants.13−20 Primary hydroxyl groups of cellulose do not have a high enough reactivity to grow CP crystals.21 Though oxygen atoms of primary hydroxyl groups have negative partial atomic charges, the interactions between them and Ca2+ ions (ion−polar interactions) in water solutions are very weak and probably cannot compensate for entropy losses. It is established18 that the apatite nucleation rate on BC ribbons is enhanced when ionizable groups are formed on their surfaces. To achieve this, BC must be chemically modified,14,21 but as a consequence of modification, cellulose can contain different chemical impurities that can adversely affect the biological properties of the final material. In addition, the growth of mineral crystals is long and lasts for more than 1 week, which has a destructive effect on the organic matrix. Recent studies12,22 have shown that promising composites for the creation of bone grafts can be obtained by mixing aqueous suspensions of presynthesized components: chemically pure BC and CP nanocrystals, which are analogues of the mineral component of natural bone. The preparation of BC− CP composite materials by mixing presynthesized components Received: June 14, 2012 Revised: August 10, 2012 Published: August 10, 2012 13473

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Figure 1. Schematic representation of (left) a nanosized ribbon consisting of nanofibrils and (right) the packing model of cellulose chains in nanofibril−nanocrystalline subunits.11,12

allows the use of multimineral CP. Owing to their structural flexibility, CP can be prepared in a variety of morphologies, on most occasions in the form of plate-shaped or rod-shaped (needle-shaped) nanocrystals25,26 having well-defined plane surfaces. Surfaces of such particles are formed by various crystallographic planes that can interact in different fashions with the organic matrix because of differences in their structures. Moreover, the interactions between the organic and mineral phases depend on the CP chemical structure. In ref 22, composite materials were prepared on the basis of BC gel films (cellulose produced by Acetobacter xylinum (CAX)) and two-component synthetic calcium phosphate comprising HAP (Ca 5 (PO 4 ) 3 OH) and whitlockite (Ca2.6Mg0.4(PO4)2) by mixing CP and BC aqueous suspensions. These CP components were chosen because HAP is a direct analogue of the mineral part of bone, and magnesiumcontaining β-tricalcium phosphate can provide increasing bioactivity and a longer implant lifetime.23,24 The CP paste crystallites had plate-shaped structures. Thus, both components had highly developed plane surfaces on the nanolevel. Such surfaces promote the formation of a maximum number of energetically favorable contacts between two phases. It was found that the composite material was formed via the adsorption of CP nanoparticles on BC ribbon surfaces, but CPs differing in their chemical structures were adsorbed to different extents. Namely, the whitlockite nanocrystals were adsorbed to a greater degree than HAP. In contrast to the composites obtained by imitating the biomineralization process, for which electrostatics plays the main role in structure formation, the type of the interaction responsible for the interfacial binding in the material obtained from ready-made presynthesized components (BC and CP) is unclear. The properties of synthesized composite materials directly depend on the binding strength of the organic and mineral phases, which in turn is determined by the intermolecular interactions at phase boundaries. The problem of major importance in the development of composite materials is to gain insight into the nature of interactions between their mineral and organic constituents. An efficient tool in the identification of the interactions responsible for the formation of interfacial regions and their structure is computer simulation using an atomistic description of the system. No computer modeling of the systems, such as CP−BC interfacial regions, has been carried out so far. The studies reported in the literature focus on the modeling of interactions of individual organic molecules with various surfaces27−35 of the HAP crystals that have already been formed and that are growing. Organic molecules such as poly(acrylic acid),27 chitosan,28

amino acids and proteins (BMP7, collagen and its models),29−32 citric acid,33,34 and glycosaminoglycan saccharides35 have been investigated. As a rule, HAP surfaces with low Miller indices of (001), (010) are considered because these surfaces have the largest interplanar spacings and, as a result, are generally the most stable. Estimations of the surface energies29,33,34 indicate that the (001) surface is more stable than the (010) surface. Simulations show that the strength of interaction between molecules and HAP surfaces depends on the Ca/P ratios on the HAP surfaces and on the type of active groups in organic molecules. The interactions that provide the binding of neutral organic molecules with HAP are (i) hydrogen bonding between hydrogen atoms of hydroxyl groups of organic molecules and oxygen atoms of phosphate and hydroxyl groups of HAP and (ii) the electrostatic interaction between oxygen atoms (having a relatively large negative partial atomic charge) of organic hydroxyl groups and Ca ions of HAP. In the case of the organic molecules charged by the deprotonation and/or protonation of COOH and/or NH2 groups, they are bound to HAP by strong electrostatic interactions. A majority of the investigations mentioned above have revealed that the studied molecules interact more strongly with the less-stable (010) surface. The goal of our study was to reveal which interactions are responsible for the adhesion of components of composite materials obtained by mixing aqueous suspensions of presynthesized CP and BC and also how these interactions depend on the morphology and chemical structure of CP crystallites. To this end, we used quantum chemical and molecular mechanics methods. Two CP crystalline structures (HAP and whitlockite) with two morphologies (plate-shaped and rod-shaped) were considered. This article is organized as follows. Simulation models and the procedure and methods are described in Sections IIA and B, respectively. Results are given in Section III, which contains a short analysis of a single cellulose molecule (Section IIIA), the results of calculations for HAP−BC (Section IIIB) and whitlokite−BC (Section IIIC) interfacial structures, and characteristics of the structural changes of cellulose molecules (Section IIID). Section IV is concerned with a discussion of our results: the dependence of the interaction energy between phases on the mineral surface structure (Section IVA) and the potential energy gain due to the association of BC with different CPs (Section IVB). In Section IVC, we discuss whether there is any gain in free energy when the cellulose− water and mineral−water contacts are replaced by the cellulose−mineral contacts. Section V contains conclusions. 13474

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plane. Active surfaces of the rod-shaped crystallites are parallel to the (100) and (010) crystallographic planes. There is no direct information in the literature regarding whitlockite crystallites. For this reason, we assumed that active surfaces of whitlockite nanocrystals were similar to those of HAP. Thus, to simulate the interfacial contacts, the topmost layers parallel to the (001) (ab surface), (010) (bc surface), and (100) (ac surface) crystallographic planes of the HAP and whitlockite crystallites were taken. It should be pointed out that the ac and bc whitlockite surfaces are equivalent to each other whereas there are some differences between the ac and bc surfaces of monoclinic HAP because of different orientations of the OH groups. These groups change their direction to the opposite one every 0.94 nm on the ac surface, but on the bc surface, all OH groups are oriented in the same direction. Our preliminary calculations showed that these differences have a negligible impact on the results. For this reason, we assumed that the (010) and (100) surfaces were equivalent to each other (for HAP and whitlockite), and below we present results only for the (001) and (010) surfaces. Surfaces sizes of the plate-shaped crystallites were taken to be s = 2ab for HAP and s = 2a2b for whitlockite. Surfaces sizes of the rod-shaped crystallites were assumed to be close to those of the plate-shaped crystallites. The thicknesses of all of the layers were chosen to be equal to each other and close to the unit cell parameter c of HAP. All layers were constructed so that they were electrically neutral. During the minimization of the potential energy of the CP−BC system, the relative positions of the atoms in the CP layer were fixed in accordance with their locations in the crystal structure, but the position of the CP crystallite as a whole relative to the cellulose surface was varied. ii. Bacterial Cellulose. It was established12,22 that the CAX molecules in nanofibrils form the Iβ crystal structure. Cellulose Iβ has a monoclinic unit cell, and its (−110) crystallographic plane (Figure 5a) is parallel to the nanofibril surface (Figure 1c). Unit cell parameters obtained for CAX38 are a = 0.817, b = 0.801, and c = 1.036 nm, α = β = 90°, and γ = 96°. Cellulose molecules are organized into sheets arranged parallel to the ac plane. It is believed that the Iβ structure contains two types of sheets for the corner and center molecules, the so-called odd and even planes.39−41 These sheets are distinguished by the 5° difference in the orientations of the constituent cellulose molecules. Each molecule in the sheet is bonded to the adjacent ones by hydrogen bonds between primary and secondary hydroxyl groups. Hydrogen bonds can also occur between neighboring sheets. CP nanocrystals are adsorbed on the BC nanofiber surface formed by the (−110) face of the monoclinic cell (Figure 4a). We constructed a simplified model of the superficial layer of the BC nanofiber. The cellulose surface layer was represented by eight oligomer cellulose chains consisting of eight glucose residues (Figure 4b). MD simulations of the interface between monoclinic crystalline cellulose (face (−110)) and water42 have demonstrated that there is no difference between the odd and even planes in the surface layer. For this reason, all of the chains were located at the same angle of inclination (Figure 4c). The chains in this layer are shifted relative to each other along the chain long axis (Figure 4d). To take into account the intracrystalline hydrogen bonds between molecules of neighboring layers of the cellulose crystal and the effect of the supermolecular organization, the coordinates of the atoms involved in the formation of the intracrystalline hydrogen bonds and also chain conformations

Some explanatory and additional information is given in the Supporting Information.

II. SIMULATION MODELS, PROCEDURE, AND METHOD A. Models. We limited our calculations to simulating the interactions between the superficial layers of the CP and BC crystals alone. i. HAP and Whitlockite. The CP paste used in ref 22 to prepare the CP−BC composite material was a mixture of two crystalline phases: a monoclinic phase of hydroxyapatite and a trigonal phase of magnesium-containing tricalcium phosphate (whitlockite). These phases have the following crystal lattice parameters: a = 0.94 nm, b = 2a, c = 0.64 nm; a = b = 1.03 nm and c = 3.71 nm for HAP and whitlockite, respectively. Unitcell angles are α = β = 90° and γ = 120° for both phases. The CP crystal structures were constructed by using the atomic coordinates given for HAP36 and whitlockite.37 The atomistic models of the crystal structures of HAP and whitlockite were constructed by using the program Atoms 51. These models are depicted below in the ab and ac projections (Figures 2 and 3, where the sizes are in nanometers).

Figure 2. Atomic model of the crystalline structure of hydroxyapatite in the (a) ab and (b) ac projections. The sizes are in nanometers (Ca, white; O, red; P, yellow; and H, gray).

Figure 3. Atomic model of the crystalline structure of whitlockite in the (a) ab and (b) ac projections. The sizes are in nanometers (Ca, white; Mg, cyan; O, red; and P, yellow).

It is established for HAP26 that active surfaces of the plateshaped crystallites are parallel to the (001) crystallographic 13475

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Figure 4. (a) Supermolecular structure of the Iβ cellulose unit cell (the (−110) crystallographic plane is shown by the dashed line). (b) Cellulose molecule in the superficial layer. (c) Layer projection onto the plane orthogonal to the long axes of the molecules. (d) Layer projection on the plane parallel to the surface layer.

at the monomolecular layer edges were fixed. The fixed atoms and molecules are shown in green in Figure 4c,d. At the same time, the positions of other atoms were not fixed (i.e., all of the internal degrees of freedom for the remaining chains were varied). iii. CP Crystallites on the BC Surface. In the starting configuration, the CP crystallites were located some distance away from the bacterial cellulose surface. Four options for the CP orientations on the cellulose surface were considered (Figure 5): a, b (b, c) axes and long and short diagonals of the

because the active surfaces of the model structures of the CP crystallites were taken to be smaller than the model cellulose surface. In the first position, the geometric center of the crystallite was located immediately above the geometric center of the cellulose surface for each crystallite orientation. Then the calculations were executed for other starting positions of the CP crystallites in order to cover the entire cellulose surface. The energies obtained for the BC−CP interfacial structures minimized from different starting positions of the CP crystallite were averaged. In addition, the results obtained for orientations 1 and 2 of the plate-shape crystallites and for orientations 3 and 4 of the rod-shape crystallites were averaged as well. This was done because orientations 1 and 2 of the plate-shaped crystallites for whitlockite having a hexagonal unit cell were equivalent. As for monoclinic HAP, the results for these orientations were expected to be different because of differences in the OH group orientations along the a and b axes of the unit cell. However, as estimates showed, the energy differences were negligible. Orientations 3 and 4 for the rodshaped crystallites are equivalent to each other because in both orientations the identical and identically spaced groups will interact with cellulose. B. Procedure and Method. The calculations were carried out in three stages. In the first stage, calculations were performed for a single cellulose molecule. Then the monomolecular layer composed of cellulose molecules in the conformation corresponding to the intramolecular energy minimum was constructed, and its energy was minimized. The obtained structure was taken as the initial structure of the cellulose surface layer. Finally, in the third stage, the calculations of the CP−BC interfacial structures were carried out. For calculations, the Firefly QC package,43 which is partially based on the GAMESS (US) 44 source code and the HyperChem-6 molecular modeling package, was used. The quantum chemical ab initio (HF/6-31G*) method and Mulliken population analysis were used to obtain partial atomic charges of the cellulose molecule. The molecular mechanics (MM) method was applied to calculate the minimum-energy conformation of the cellulose molecule as well as the cellulose

Figure 5. Schematic representation of the orientations of (a) plateshaped and (b) rod-shaped CP crystallites on the BC surface.

unit cell of the CP crystallites were oriented parallel to the long axes of the polymer chains (the structures are denoted as 1, 2, 3, and 4). It was found that the formation of the most favorable contacts between the CP and cellulose surfaces was accompanied by changes in the CP crystallite orientations on the cellulose surface as compared to their starting positions, but these changes were small (no more than 1−8°). Calculations were performed for a number of starting positions of the CP crystallites above the cellulose surface 13476

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same range as, for example, those obtained for the HAP− poly(acrylic acid) and HAP−collagen interfaces.27,29 Energy minimization was performed by the conjugate gradient method with a convergence criterion of 10−4 kJ/mol. To calculate the electrostatic contribution to the total energy, dielectric constant ε = 4 was used. When choosing the dielectric constant, we were guided by the Lichtenecker logarithmic law of mixing widely used for two-component composites58

layer structure and the interaction energies between the CP (whitlockite and hydroxyapatite) and BC crystal surfaces. The AMBER force field (HyperChem-6) with the ambers parameter set derived by Homans45 for oligosaccharides was used. His approach to developing the carbohydrate force field was to combine the parameters for monosaccharides46 with the results of ab initio calculations on model compounds relevant to the glycosidic linkage.47 Homans’ carbohydrate force field utilized charges and van der Waals parameters derived for monosaccharides in ref 46. The atom types and force-field parameters are listed in ref 45. To take into account changes in partial atomic charges when glucose units form the cellulose chain, we calculated (HF/631G*) atomic charges for a chain fragment consisting of three glucose units. The partial charges obtained were used in our calculations. Their values, together with the monosaccharide charges in ref 45, are presented in Supporting Information Table 1. The reliability of the approach we used was tested by comparing the conformational energy map (for the torsion angles defining the main chain conformation) calculated for a cellobiose molecule with the maps calculated by other authors with other force fields. We have found that the calculated conformational characteristics are very similar to those obtained in other studies48−50 (details in Supporting Information). Moreover, the torsion angles that define the cellulose main chain conformation and correspond to the lowest-energy minimum are very close to the angles obtained from the experimental and DFT data51,52 for the Iβ cellulose crystal structure. The constructed oligomer cellulose chain in the optimized structure was hydrogen bonded, as it must be in the Iβ crystal structure (details in Supporting Information). Because we modeled only the surface layer of the cellulose crystal by simulating the constraints imposed by the crystal packing and intercrystal hydrogen bonds, the conformational changes were of major importance. The CP parameters were taken from refs 27 and 53. In the simulations, the positions of all atoms in CP were fixed, so we needed only interatomic interaction parameters. In ref 27, the van der Waals parameters (for the Lennard-Jones potential) for HAP were obtained from the Hauptmann potential energy function of apatites.54 We used these parameters for whitlockite as well, and the parameters for Mg were taken from ref 53. The values of the atomic charges were taken from ref 27. To calculate the interactions between BC and CP correctly, it was necessary to take into account the specific character of the interactions between organic and mineral phases. Considering this, we used the method of parameter calculation based on the unification of the parameters of two force fields (for mineral and organic compounds).55 The methods described in ref 55 rely on a systematic approach to generating the cross-term potentials between the organic and mineral components of the system. The parameters of the potential of intermolecular interactions between BC and CP were calculated by using this method. The reliability of the methodology used for the interface calculations was tested for the BC−water and HAP−water interfaces. We applied the ambers parameters for water. As discussed in Section IVB, the results of our calculations are in good agreement with the results obtained by other authors and also with the experimental data.42,56,57 In addition, the BC−CP interface interaction energies obtained in our study are in the

log ε = ν1 log ε1 + ν 2 log ε2

where v1, v2 and ε1, ε2 are the volume fractions and the dielectric constants of the components, respectively. By taking v1 = v2 = 0.5, ε1 = 1.6−1.9 (for bacterial cellulose),60 and ε2 = 7.1−7.5 (for HAP),59 we obtain ε = 3.4−3.8.

III. RESULTS A. Cellulose Molecule. Partial atomic charges calculated for a cellulose molecule fragment are shown in Figure 6.

Figure 6. Fragment of a cellulose molecule with the conventional numbering of atoms. Partial charges and designations of torsion angles are given.

B. HAP-BC. The formation of the energetically favorable interfacial contacts between CP and BC surfaces leads to the deformation of the cellulose surface layer (Figure 7). These deformations require energy. These energy costs were estimated as the difference between the cellulose layer energy in the initial structure (Figure 7a) and the energy of this layer in the optimized structure (Figure 7b). The interaction energy between CP and BC was estimated by subtracting the sum of self-energies of the components from the total energy of the system. The energies of different structures of the HAP−BC interfaces are presented in the histogram in Figure 8 together with the contributions of different (electrostatic, H-bonding, and nonbonding) interactions and the deformation energies of the cellulose layer. Here and below, the energies are given as the calculated value per unit area of 1 nm2, which is approximately equivalent to the area of the ab face of the whitlockite unit cell and to the area of a(1/2b) for HAP. An analysis of the contributions of different interactions to the total energy shows that the main contribution comes from electrostatics (∼59−63% for the plate-shaped and ∼50−56% for the rod-shaped crystallites). The van der Waals interactions are typically much weaker than the electrostatic ones, but because of a large number of nonpolar groups in the cellulose molecules involved in the interaction, this contribution is ∼33− 39% for the plate-shaped and ∼40−46% for the rod-shaped crystallites. The contribution to the total energy due to the formation of interfacial hydrogen bonds is minimal (∼2−7%). 13477

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C. Whitlockite−BC. The interaction energies of the whitlockite−BC interphase structures are presented in the histogram in Figure 9 together with different contributions to the total energy (electrostatic, H-bonding, and nonbonding interactions) and the deformation energy of the cellulose layer.

Figure 9. Histogram of the whitlockite−BC interaction and deformation energies of the BC layer.

For whitlockite, as for HAP, along with the electrostatic contribution (∼58−62% of the total energy for the plateshaped and ∼58−60% for the rod-shaped crystallites), the van der Waals interactions play an important role in the association of whitlockite with BC. The contribution of the van der Waals interactions for the plate-shaped crystallites is about 36−39%, and that for the rod-shaped crystallites it is about 39−41%. In contrast to HAP, the relative contributions of the electrostatic and van der Waals interactions for the plate-shaped and rodshaped crystallites are nearly the same. The contribution to the total energy due to the formation of the interfacial hydrogen bonds is even lower (∼1−3%) than for HAP. Opposite to HAP, the active surface of the rod-shaped crystallites (the (010) face) of whitlockite is most strongly attracted to the cellulose surface. The deformation energy of the cellulose layer is, on the average, lower than for HAP−BC and amounts to about 5− 17% of the interaction energy, and as for HAP, the changes in the conformation energy of the cellulose molecules give the main contribution to the deformation energy (Supporting Information Figure 4). D. Structural Changes in Cellulose Molecules. As noted above, to realize the most favorable interfacial contacts, changes in the cellulose layer are necessary, and these changes are mainly the intramolecular (conformational) rearrangements in the cellulose molecules. Figure 5 in Supporting Information shows different contributions to the intramolecular deformation energies (due to deformations of valence bonds and valence and torsion angles, changes in the nonbond interactions, and the destruction of H-bonds). In all cases, it is difficult to identify the major contribution. It is interesting to analyze the changes in the torsion angles (φOS, ΨOS, φOH, and ΨOH in Figure 6) that determine the relative arrangement of glucose residues in the cellulose molecule and the orientations of the primary hydroxyl groups. The average deviations of these angles from their values in the initial structure of the cellulose layer are presented in the histograms in Figure 10. Averaging was performed over all the orientations of the CP crystallites.

Figure 7. Atomistic model of the HAP(balls)−BC(balls and cylinders) system: (a) the initial structure and (b) the minimized structure .

Figure 8. Histogram of HAP−BC interaction and deformation energies of the BC layer.

It can be seen that the (001) face (the active surface of the plate-shaped crystallites) interacts with the cellulose surface more strongly than does the (010) face (rod-shaped crystallites). The interaction energies for different orientations of the plate-shaped crystallites differ only slightly, hence there is no preferred orientation. However, the preferred orientation for the (010) crystallographic face can be identified. It is the orientation of the crystallite c axis parallel to the long axes of the cellulose chains. A comparison of the interaction and deformation energies shows that the latter amounts to about 9−23% of the former. The deformation energy of the cellulose layer is the sum of the contributions resulting from changes in the intra- and intermolecular structures. (These contributions are given in Supporting Information Figure 3.) The changes in the intramolecular energy of cellulose molecules give the main contribution to the deformation energy. 13478

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Figure 10. Histograms of averaged deviations of torsion angles φOS, ΨOS, φOH, and ΨOH from their values in the initial structure of the cellulose layer: (a) for plate-shaped and (b) for rod-shaped CP crystallites.

Figure 11. Average numbers of atomic pairs (per nm2) as a function of the distance between constituent atoms for (a) BC−HAP(001), (b) BC− HAP(010)), and (c) BC−whitlockite (010). Designations in the frames: cellulose atoms on the left and CP atoms on the right.

A comparison of the results obtained for the CP−BC interfaces in the case of the plate-shaped crystallites shows that both types of torsion angles (those defining the cellulose backbone conformation and those determining the orientations of hydroxyl groups) vary to a lesser extent for whitlockite than for HAP. This difference is, in particular, due to a higher conformity of the cellulose and whitlockite crystal cell parameters, namely, the periodicity along cellulose chain c = 1.036 nm is almost identical to parameters a = b = 1.03 nm of the crystal cell of whitlockite. However, the changes in the orientation of hydroxyl groups for the rod-shaped crystallites are greater in the case of whitlockite, although the cellulose backbone conformation in this case varies less than for HAP. The estimate of the deviations of the valence angles, such as the valence angle of the glycosidic oxygen and the valence

angles of the primary and secondary hydroxyl groups, from their initial values showed that these deviations are small (Supporting Information and Section IIID). They are in the range 0.5−2.2°. This showed that the energetically most favorable interfacial contacts are carried out mainly because of the changes in the torsion angles. In general, the deformations of the valence angles were the smallest for the BC−whitlockite interface probably because of the higher conformity of the distributions of the active groups on the cellulose and whitlockite crystal surfaces.

IV. DISCUSSION A. Interaction Energy and Structure of Mineral Surfaces. All active groups of cellulose form multiple interactions with the CP surfaces. Among all atomic pairs 13479

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B. Gain in Potential Energy Due to CP−BC Interface Formation. The gain in potential energy due to the association of BC and CP surfaces was estimated as

that form energetically preferable close contacts, the oxygen atoms of the cellulose hydroxyl groups and the Ca ions of CP make the greatest contributions to the interaction energy. Figure 11 presents average numbers of different atomic pairs (per nm2) as a function of the distance between atoms: for the cellulose molecules and the (001) and (010) HAP surfaces and for the (010) surface of whitlockite. A comparison of the quantity of close contacts for different atomic pairs of the BC and HAP surfaces shows that the number of strongest contacts (OH6−Ca and OH−Ca) for the (001) HAP surface is greater than that for the (010) HAP surface. This explains the differences in the interaction energies obtained for these surfaces (Figure 8). Thus, in contrast to peptide molecules or other molecules with the same (as in peptides) active groups studied in refs 30 and 31 the molecules of the cellulose crystal surface layer interact more strongly with the (001) HAP surface than with the (010) surface. This is mainly because the peptide molecules, in addition to negatively charged (COO−) groups, have positively charged (NH3+) groups that interact strongly with PO43− ions of the HAP surface. The fraction of these ions, as compared to Ca ions, is higher for the (010) HAP surface than for the (001) surface (text below and Table 1). A

Eassociation = Etotal −

∑ Eiseparate component i

(1)

where Etotal is the total energy of the united system and ∑iEseparate i component is the sum of the self-energies of the individual components. This quantity is equivalent to the sum of the interaction and deformation energies of the system. The histogram of the energy gains for all HAP−BC and whitlockite−BC structures is presented in Figure 12.

Table 1. Averaged CP−BC Interaction Energies (in kJ/ mol·nm2) and Ratios between Numbers of Positive (Ca, Mg) and Negative (O) Charges per Unit Surface

Figure 12. Histograms of potential energy gains due to the HAP−BC and whitlockite−BC interphase structure formation.

For HAP, the gains in the potential energy are, on average, higher for the plate-shaped crystallites than for the rod-shaped ones. But for whitlockite, the binding of the rod-shaped crystallites with the cellulose crystal surface is more profitable. In general, the energy gain upon whitlockite−cellulose binding is greater than that upon HAP−cellulose binding, with the difference being most pronounced for the rod-shaped crystallites of whitlockite and HAP. The most favorable location of the plate-shaped crystallites on the cellulose surface is when the long diagonal of the ab face is parallel to the long axes of the cellulose molecules. The rod-shaped crystallites prefer to be oriented on the cellulose surface in such a manner that their c axes are along (for HAP) or across (for whitlockite) the long axes of the cellulose molecules. C. Gain in Free Energy Due to CP−BC Interface Formation. It is very important to understand whether the integration of components is profitable for the system or whether it would be more profitable for the system if they existed separately? To answer this question, it is necessary to bear in mind that the composite material is obtained by mixing

comparison of the numbers of close contacts for different atomic pairs of the BC−HAP and BC−whitlockite interfaces shows that the two most strongly interacting pairs (OH−Ca and OH6−Ca) form the largest number of close contacts for whitlockite. The predominant number of OH−Ca close contacts suggests that the distribution of OH groups on the cellulose surface is consistent with that of calcium ions on the whitlockite surface. The total energies of the BC−CP interfacial interaction differ appreciably for HAP and whitlockite (Figures 9 and 10) mainly because of differences in the electrostatic energies. This can be explained by different ratios between positive and negative charges per unit area of the active surface of the CP crystallites. This is evident from Table 1, where NCa and NO denote the numbers of positive (Ca, Mg) and negative (O) charges, respectively, per unit surface and E is the average CP−BC interaction energy (in kJ/mol·nm2). Averaging was performed over all orientations of the HAP and whitlockite crystals. It can be seen that the energies strongly correlate with the NCa/NO ratio (i.e., the greater the ratio, the stronger the interaction). 13480

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BC and CP water suspensions. Though the components are not soluble in water, both of them have hydrated surfaces. To form CP−BC interfacial regions, it is necessary to remove water molecules from the BC and CP surfaces. The water removal leads to energy loss, on one hand, and to a gain in the system’s entropy, on the other hand. To estimate the binding energy between water molecules and BC and CP surfaces, we calculated the potential energies of the BC(−110)−water and HAP(001)−water interfaces. The potential energy minimization was carried out for a layer (about 0.6 nm thick) of water molecules on the BC(−110) and HAP(001) surfaces. As in previous calculations, dielectric constants were estimated by using the Lichtenecker logarithmic law of mixing.58 Their values were 13 (for cellulose and water) and 24 (for HAP and water). It is reasonable to assume that the main part of the energy loss and entropy gain upon removal of water molecules from the surface is attributable to the first hydration layer. According to our estimates, about six water molecules can exist on 1 nm2 of the HAP and BC surfaces. This value is consistent with other calculations and experimental data.42,56,57 The potential energy losses are about 67 and 79.4 kJ/mol*nm2 because of water removal from the BC and HAP surfaces, respectively. Taking into account that the transfer of a water molecule from the immobile state on the surface to the bulk gives an entropy gain of ∼8.4 kJ/mol,61 we obtain free-energy losses for the transfer of six water molecules from the unit surface (1 nm2) of about 16.6 and 29.0 kJ/mol·nm2 for BC and HAP, respectively. The entropy losses due to the association of CP and BC crystallites can be ignored because they are insignificant, so we can subtract the above values from the values of the potential energy gain upon BC−CP association (Figure 11). The free-energy changes for the BC(−110)− HAP(001) binding in water were estimated to be −149.1, −149.9, and −174.3 kJ/mol·nm2 for different crystallite orientations. In all probability, the gain in free energy for whitlockite will be even greater. The negative free energies obtained mean that the BC−CP binding in a water suspension is profitable and that the interfacial interaction is attractive. Water, because of its strong interaction with the HAP and BC surfaces, cannot be treated only as a simple dielectric shield solvent. Experimental investigations and simulation results demonstrate62−64 that water has a special layered structure on the HAP and BC surfaces. On the HAP surface it has an icelike structure. Thus, immobile, highly structured water might influence the BC−CP aggregation kinetics. The composite materials that we studied were obtained by the high-speed mixing of aqueous suspensions of their components, which allowed kinetic limitations to be overcome. The interaction between surfaces of different materials depends on their types of constituent atoms. Thus, the types of interactions (nonpolar, i.e., dispersion, and polar, i.e., acid− base) between two interacting surfaces determine the strength of their adhesion. These interactions are mainly controlled by the interfacial surface tensions between two phases. The interaction between two materials suspended in water can be characterized by using surface tension energies65

ΔG132 = 2 ⎡ LW LW LW LW LW LW LW ⎤ ⎢ γ1 γ3 + γ2 γ3 − γ1 γ2 − γ3 +⎥ ⎢ ⎥ ⎢ ⎥ γ3+ γ1− + γ2− − γ3− + γ3− ⎢ ⎥ ⎢ ⎥ γ1+ + γ2+ − γ3+ − ⎢ ⎥ ⎢ ⎥ + − − + γ1 γ2 − γ1 γ2 ⎢⎣ ⎥⎦

(

)

(

)

(2)

where ΔG132 is the interaction energy between material 1 (BC) and material 2 (HAP) in water (indexed by 3), γ+ represents the acidic components, γ− represents the basic components of the surface tension, and γLW represents the Lifshitz−van der Waals (LW) surface tension components (apolar). The values of the surface tensions components for BC, HAP, and water were taken from refs 66−68. The calculated ΔG132 is about −5.4 × 10−24 kJ/nm2. Its negative value indicates that interactions between HAP and BC suspended in water have attractive character and the interfacial region formation is favorable. This confirms the conclusion inferred from our simulations. It is known that the competitive interactions between individual components in a polymer−filler composite material determine its structure. In other words, the ratios between the polymer−filler (BC−CP), polymer−polymer (BC−BC), and filler−filler (CP−CP) interaction energies determine whether a homogeneous mixture or two separate phases will be formed or whether a filler will coat a polymer and form (at high filler contents) a network within a polymer matrix.69 Our calculations of the BC(−110)−BC(−110) and HAP(001)− HAP(001) interaction energies and the estimates (taking into account energy losses and entropy gains resulting from water removal) yielded ΔGBC−BC ≈ −79 kJ/mol·nm2 and ΔGHAP−HAP ≈ −302 kJ/mol·nm2. The free energies calculated for all types of interactions can be arranged in the following sequence: ΔG BC − BC( −79 kJ/mol ·nm 2) < ΔG BC − HAP( −149 to−174 kJ/mol ·nm 2) < ΔG HAP − HAP( −302 kJ/mol ·nm 2)

Such estimates can also be made by using surface free energies. The free interaction energy between surfaces of particles of a material suspended in liquid can be described (by using the values of surface tension) as65

(

ΔG131 = −2 −

γ1LW − γ1+γ3− −

2

γ3LW

)

γ1−γ3+

)

(

−4

γ1+γ1− +

γ3+γ3− (3)

where BC or HAP is 1 and water is 3. The estimations yield ΔGC−C ≈ 13 × 10−24 and ΔGHAP−HAP ≈ −21 × 10−24 kJ/nm2 for BC−BC and HAP−HAP interactions, respectively, so the values obtained by using the surface energies can be arranged in the same manner as above: ΔGC − C(13 × 10−24 kJ/nm 2) < ΔGC − HAP( −5.4 × 10−24 kJ/nm 2) < ΔG HAP − HAP( −21 × 10−24 kJ/nm 2) 13481

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angles from their initial values. This material is available free of charge via the Internet at http://pubs.acs.org.

This means that the HAP crystallites can be adsorbed on the BC nanofibrils and stick to each other, thus forming a network within the BC matrix, especially at high filler contents. The influence of the secondary structure on the mechanical properties of the CP−BC composite materials and the identification of the effective fraction of the CP crystallites are important issues to be resolved.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

V. CONCLUSIONS An MM study of the interfacial structures formed by interacting BC and CP crystalline surfaces was carried out. Two CP crystalline structures (hydroxyapatite and whitlockite) with two morphologies (plate-shaped and rod-shaped) were considered. As revealed by our study, the BC surface layer is deformed when interacting with CP. The formation of energetically favorable contacts with the mineral crystal surface leads to conformational changes in cellulose molecules. The torsion angles determining the orientations of the primary hydroxyl groups vary most appreciably. The contribution to the interaction energy due to the formation of interfacial hydrogen bonds is minimal (∼2−7%). Electrostatics makes the major contribution to the energy of interaction between the organic (cellulose) and mineral (HAP and whitlockite) surfaces. The electrostatic contributions strongly correlate with the ratios between positive and negative charges per unit area of the active surfaces of the CP crystallites. For whitlockite, this ratio, and hence the fraction of positive charges, is higher than for HAP. For this reason, whitlockite interacts more strongly with cellulose than does HAP. The association of CP and BC suspended in water is energetically favorable, and their interaction is attractive. This profitability is greater for whitlockite than for HAP. This conclusion is consistent with the experimental data for the mixture of HAP and whitlockite plate-shaped crystallites,22 which showed that whitlockite was adsorbed to a greater extent than HAP. As our data indicate, the rod-shaped crystallites of whitlockite bind most strongly to BC; therefore, this mineral is promising for the creation of composite materials with improved mechanical properties. The topmost monomolecular layer of the cellulose crystal was considered in this study. No doubt, it would be more correct to model a multilayered system because changes must affect deeper layers of cellulose nanofibers. The surface layer in a multilayered system is likely to be deformed to a lesser extent because the strain distributes to deeper layers. To find out how many molecular layers of cellulose nanofibers are affected, what type of strain is predominant, and how the mobility of cellulose molecules changes upon the binding of CP crystallites to the nanofiber surface, it would be useful to execute MD simulations for a multilayered model of the cellulose crystal surface. Work along this line is in progress.

■

■

ACKNOWLEDGMENTS This work was supported by the Ministry of Education and Science of the Russian Federation (State Agreement no. 12.740.11.0025).

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Partial atomic charges calculated in the present study and taken from ref 45. Conformational energy maps calculated for cellobiose. Optimized structure of the oligomer molecule of cellulose. Histogram of the intermolecular and intramolecular contributions to the deformation energy of the BC layer in the HAP−BC interfacial structure. Histogram of the intermolecular and intramolecular contributions to the deformation energy of the BC layer in the whitlockite−BC interfacial structure. Histograms of the intramolecular deformation energy of the BC layer and different contributions. Deviations of the valence 13482

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