Article pubs.acs.org/Langmuir
Adsorption of Ethanol and Water on Calcite: Dependence on Surface Geometry and Effect on Surface Behavior K. S. Keller,† M. H. M. Olsson,*,† M. Yang,‡ and S. L. S. Stipp† †
Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark School of Material Science and Engineering, Southwest Petroleum University, Sichuan, China
‡
ABSTRACT: Molecular dynamics (MD) simulations were used to explore adsorption on calcite, from a 1:1 mixture of ethanol and water, on planar {10.4} and stepped, i.e. vicinal, surfaces. Varying the surface geometry resulted in different adsorption patterns, which would directly influence the ability of ethanol to control calcite crystal growth, dissolution, and adsorption/ desorption of other ions and molecules. Ethanol forms a wellordered adsorbed layer on planar faces and on larger terraces, such as between steps and defects, providing little chance for water, with its weaker attachment, to displace it. However, on surfaces with steps, adsorption affinity depends on the length of the terraces between the steps. Long terraces allow ethanol to form a well-ordered, hydrophobic layer, but when step density is high, ethanol adsorption is less ordered, allowing water to associate at and near the steps and even displacing pre-existing ethanol. Water adsorbed at steps forms mass transport pathways between the bulk solution and the solid surface. Our simulations confirm the growth inhibiting properties of ethanol, also explaining how certain crystal faces are more stabilized because of their surface geometry. The −O(H) functional group on ethanol forms tight bonds with calcite; the nonpolar, −CH3 ends, which point away from the surface, create a hydrophobic layer that changes surface charge, thus wettability, and partly protects calcite from precipitation and dissolution. These tricks could easily be adopted by biomineralizing organisms, allowing them to turn on and off crystal growth. They undoubtedly also play a role in the wetting properties of mineral surfaces in commercial CaCO3 manufacture, oil production, and contamination remediation.
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INTRODUCTION Some organisms produce minerals for protection or structural support.1−3 Biomineral growth is promoted and controlled with the help of organic compounds that engineer the size, shape, and properties of the material. Improved understanding about the controls on biomineralization would open new avenues for biomimetic mineral production, offering interesting implications for the medical community and industry. Deeper knowledge about the actual nanometer scale processes that take place at the interface between biominerals and organic molecules would also lead to benefits across a range of fields, including material design, nanoengineering, energy, environment sustainability, and health. Calcite, the rhombohedral polymorph of CaCO3, is one of the most abundant minerals in the earth’s crust4 and is the favored biomineral of organisms as diverse as oysters and some forms of unicellular algae called coccolithophorids. Calcareous deposits, such as limestone and chalk, host significant quantities of the world’s drinking water and oil, so deeper understanding about how organic compounds interact with calcite would also contribute to better contamination remediation strategies and enhanced oil recovery. Calcite’s most stable surface is the rhombic {10.4} face, which results from bonds broken between the Ca and CO3 ions.5 This surface has been investigated extensively in © 2015 American Chemical Society
experiment as well as in computational studies, but relatively few have explored the behavior and properties of other planes through the calcite atomic structure. All of calcite’s other faces are made from the basic rhombic face by combinations of steps and various lengths of terraces between them. Terraces separated by steps and edges have been simulated by setting up vicinal faces, with surfaces made of repeating acute steps, such as the {31.8} plane, or by repeated obtuse steps, such as {31̅.16} and {31.16}.6−9 When the bulk crystal structure is terminated by cleavage, dangling bonds are satisfied either by the surface restructuring, when it is exposed to vacuum, or by reacting with water, when it is exposed to air or aqueous fluids.10,11 Computational studies have also demonstrated that water adsorbs on all three surfaces: {10.1}, {31.8}, and {21.16}6,12 (the importance of water structure on surfaces has also been the subject elsewhere13−17). The atomistic simulations presented by Spagnoli et al.8 showed that calcite surface geometry has an influence on how well water can arrange itself. In contrast to their results, de Leeuw et al.6 reported that a calcite surface with obtuse steps is less stabilized by water than one composed of acute steps. That Received: November 5, 2014 Revised: February 12, 2015 Published: March 19, 2015 3847
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Freeman et al.28 We have used GROMACS29−31 for all simulations and VMD32 for analysis and visualization. To create the boxes of solvent for the simulations, we used the genbox function. The number of molecules was chosen depending on the surface size but keeping a constant volume ratio of 50% ethanol to 50% water and a density of approximately 540 g/L. First, the solvent box was initially energy minimized (EM) with the steepest decent algorithm and equilibrated by molecular dynamics (MD) simulation, using the leapfrog algorithm.33 Then the mineral and solvent systems were put together. We used this procedure to ensure that the solvent molecules near the calcite surface were mixed randomly and were in a low-energy configuration. Testing using the radial distribution function confirmed that solvent molecule positioning was random in the initial solvent box. The resulting simulation box contained the calcite surface with the solvent box on top with x and y dimensions determined by the calcite slab size. The z dimension, on the other hand, was extended to 250 Å. This extra vacuum volume was included to avoid interaction between the system and its images. In all simulations, we used three-dimensional periodic boundary conditions, and we froze the bottom half of the crystal to improve the representation for a bulk region. We used an Andersen thermostat and obtained a NVT canonical ensemble. For the simulation procedure of the combined system, we (1) found the energy minimum using steepest decent, (2) made a molecular dynamics simulation raising the temperature incrementally from 0 to 400 K over 2 ns, (3) decreased the temperature to 300 K over 0.5 ns, and finally (4) used molecular dynamics simulation at 300 K for 5−8 ns, depending on the system size, for analyzing the trajectory. The time step was set to 1 fs for the solvent box run and 0.5 fs for the whole system.
water preferentially adsorbs on some vicinal faces rather than others was supported by simulations on calcite in water− ethanol mixtures,9 and a consistent picture also emerged from experimental work with other CaCO3 polymorphs.18 One of the aims of our study was to define how variations in surface geometry affect adsorbate structuring. In 2008, Harding and colleagues19 published a thorough survey of computational techniques and programs used for simulating organic−inorganic interfaces. They also reported on work with selective inhibition of step growth by organic molecules, such as polysaccharides20 and peptides,21 which attach through one or more functional groups. Yu et al.22 showed that complex biomolecules in aqueous environments tend to attach through a single functional group whereas in vacuum, they favor maximizing interaction with a surface. Because ethanol is a simple organic molecule that has both a −CH3 group on one end and −O(H) on the other, it has previously been used to model interactions of organic compounds with the calcite surface. Cooke et al.13 and then Sand et al.9 simulated calcite interaction with pure ethanol, pure water, and in mixed solution, experimentally as well as with molecular dynamics simulations. They demonstrated that ethanol attaches more strongly to the calcite surface than water, that it forms an ordered layer, and that at steps the order is effectively disrupted. Our simulations extend that work, investigating the calcite− organic molecule interface in a mixed ethanol−water environment, on a range of calcite faces. We focus in particular on vicinal face behavior, where various terrace lengths separate the acute and obtuse steps because in biomineralization, as in inorganic crystal growth and dissolution, mass is added or lost predominantly at kinks and steps. On terraces, the energy required for nucleating new atomic layers or for forming etch pits is high and therefore less interesting for biomineralization. The purpose of our study was to demonstrate how ethanol adsorption depends on the spacing between steps and its concentration in the water−ethanol mixture and that adsorption on mineral surfaces can dramatically modify their wetting characteristics.
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RESULTS AND DISCUSSION The results can be divided into two topics: (1) adsorption properties and the behavior of the bulk solvent and (2) adsorption at steps and on the intermediate terraces. Adsorption, Ordering, and Bulk Behavior. Simulating the planar {10.4} surface in a 50% ethanol−water mixture results in a well-ordered layer adsorbed directly on calcite, dominated by ethanol, as shown in Figure 1. Because the calcite surface is highly hydrophilic and polar, the ethanol molecules bind through −O(H) rather than the hydrophobic −CH3 tail. Solvent molecules interact with the surface through (1) hydrogen bonds between O from carbonate and H from ethanol or water and (2) electrostatic interactions between calcium and OH from ethanol or water. These results, including the typical lengths of interaction derived with GROMACS, are completely consistent with the earlier study by Cooke et al., which was made with DL_POLY and the same force field.13 In general, ethanol attached more closely to the surface than water, which was also reported by Sand et al.9 Thus, as expected, ethanol dominates as the adsorbing molecule in the first layer, next to the calcite surface. Some water was also observed so during the time of the simulations ethanol could not dislodge all water. According to simulations of calcite in pure ethanol by Sand et al.,9 ethanol molecules in the adsorbed layer orient themselves over the surface carbonate groups, forming a well-ordered structure. They observed a domain where locally the orientation of the ethanol molecules was twisted because
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MODELING We created a number of calcite surfaces with Material Studio23 to represent the planar {10.4} terrace and several vicinal faces. We used three vicinal faces constructed with acute steps, namely, {31.8}, where 5 steps were separated by terraces 10 Å wide, {71.24}, with 3 steps at 22 Å and {11 1.40}, with 3 steps at 34 Å, and a {31̅.16} face with 4 obtuse steps approximately 10 Å apart. We also used surfaces constructed from the {31.16} face with 3 steps, which is similar to the obtuse, 19 Å apart and a surface with an etch pit that is 1 molecular layer deep on the {10.4} face. Thus, all surfaces except the planar {10.4} face had a minimum width of 45 Å in x and y and at least three steps. Our simulations on the planar face, the naturally occurring cleavage plane, served as a control, to compare with previous work9,13 to validate our setup and for use in making direct comparisons between the results for the various vicinal faces. The force field used in this study is a hybrid of the Amber and Pavese potentials, as previously used in Sand et al.9 Thus, we used the Pavese et al.24 potential to model calcite, the flexible TIP3P25 potential for water, and an ethanol potential derived from the Antechamber program in AMBER 9.0.26,27 The potential for the cross-terms are those proposed by 3848
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Figure 2. Orientations for ethanol and water on calcite in a 50% ethanol−water mixture. The figures were selected from a snapshot of the system at equilibrium.
Figure 1. A calcite {10.4} surface in a 50% water−ethanol mixture. Snapshot of the last MD frame after 5.5 ns. Calcium is represented by green; carbon, blue; oxygen, red; and hydrogen, white. In the lower part of the figure, we isolate and depict the ethanol (left) and water (right) molecules from the total picture. This trick of separating the solvents makes it clear how the phases distribute themselves in the 50% ethanol−50% water mixture.
some of the carbonate ions adsorbed two ethanol molecules. In our mixed ethanol−water simulations, we did not observe such double attachments but ethanol did not order itself as systematically when water was present. Water adsorbed but the carbonate ions were not able to attract more than one water. In simulations of calcite in pure water made by Perry et al.,34 the most common arrangement was double attachment to carbonate. The differences between our results and those previously published might originate from the force field used, or it might be that in water−ethanol mixtures local ethanol ordering is disrupted. It is more reasonable to form only one hydrogen bond to a carbonate ion because attachment of the first H decreases local negative charge over the carbonate O so its potential for forming a second hydrogen bond is diminished. Ordering observed in our simulations shows hydroxyl from ethanol pointing toward surface CO3, with CH3 pointing out from the surface, as shown in Figure 2a. Water coordinates with calcite in two ways: either with H directed toward CO3 or with O toward a Ca atom, as shown in Figure 2b. Figure 3 shows that ethanol is well ordered in the adsorbed layer near the calcite. Each part of the ethanol molecule, −OH, −CH2−, and −CH3, is represented by a peak in the density plot (red trace). The OH group, which is closest to the surface, has the best defined peak, indicating highest ordering. There is a second ethanol layer, but the parts of the molecule are not clearly distinguishable. The two possible orientations of water result in two peaks, slightly further from the surface. There are two more layers of water where orientation is visible and even a suggestion of a fourth layer, but by this distance, structure imposed by the surface has become diffuse (Figure 3). The first peak from the ethanol curve is closer to the surface than the first peak from the water curve, indicating that ethanol binds more strongly to calcite than water. The ethanol peak is
Figure 3. Density plots from the calcite surface (green) into bulk solution and vacuum at 30 Å, showing distances from the surface for adsorbed ethanol (red) and water (blue).
also sharper, indicating higher ordering. These observations match those previously reported.9 Figure 4 shows hydrogen bond distances between Ca and the adsorbing molecule. On average, ethanol forms shorter hydrogen bonds than water to calcite, but some water binds closer than some ethanol and there is more spread in the water−calcite distances, also suggesting disorder.
Figure 4. Hydrogen bond length between Ca and the adsorbing species: ethanol (red) and water (blue). 3849
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domains. This would cause very local differences in surface tension; thus wettability could vary dramatically. Structuring in the Bulk Solvent. In the setup for the simulations, if we were not careful to begin with randomly distributed solvent molecules, it could explain the observed tendency for phase separation. We could test if water and ethanol molecules were randomly distributed within the box of solvent by determining the radial distribution function (RDF) for each solvent pair: Owat−Owat, Oeth−Oeth, and Oeth−Owat (equal to Owat−Oeth). Figure 6 shows all three combinations, calculated over the last 500 ps of the initial solvent box MD simulation.
Both curves in Figure 3 show a low-density region after the first ordered layer, at a distance of 5.0−6.5 Å for ethanol and ∼4 Å for water. Both of these low-density zones can be understood in terms of a change in surface charge character. Once the first layer of ethanol molecules has attached to calcite, the remaining solvent molecules must interact with the hydrophobic −CH3 ends of the first layer. The solid surface is no longer hydrophilic. Interaction of the solvent molecules with the new, dominantly hydrophobic surface is weaker and less ordered than with the termination of the calcite structure. Once ethanol has formed a layer, the solid is no longer water wetting. Water adsorption is inhibited because of the hydrophobic environment created by the alkyl ends of ethanol. In domains on the surface, where water dominates, its structured layer is thinner because the water molecules are smaller, but after the density depleted region, the next layer of water is more ordered than the second layer of ethanol (Figure 3). Previous studies on pure and mixed water−ethanol−calcite systems, both experimental and modeling, also report such a density gap between adsorbed layers.9,35 In the bulk fluid, which we define for convenience as the region beyond the ordered adsorbed layer, there is a phase separation between water and ethanol molecules, as we see in Figures 3 and 1. Water is enriched in the center, and ethanol is enriched toward the solid−fluid and vacuum−fluid interfaces. The second layer of ethanol prefers to orient with its hydrophobic ends oriented toward the hydrophobic ends of the first layer as well as toward the vacuum where hydrophobic ends point away from the water. Water is enriched in the middle zone, structured within itself. Separation of the two phases is observed in all of the simulations after 5 ns. We can also examine the distribution of ethanol and water in the first adsorbed layer. Figure 5 shows the type and orientation
Figure 6. RDFs of the solvent box before putting it together with the calcite surface.
The first peaks of both Oeth−Oeth and Oeth−Ow RDF plots are located at ∼2.5 Å and the height of the peaks is similar, indicating similar probability for finding O from an ethanol or a water close to an ethanol molecule. If structuring were to be significant, one of the peaks for the Oeth−Ow RDF would be much lower, and the other would be shifted to a higher value. An example of significant structuring can be seen in the paper by Atamas and Atamas.36 Figure 6 only shows a slight enrichment of water in the first coordination sphere of the ethanol and a slight enrichment of ethanol in the second coordination sphere. The Ow−Ow RDF has a similar shape to the RDF curve of water in methanol observed by Dixit et al.,37 where the first peak also approaches a RDF of 4.5 and the shape otherwise resembles that for pure water. Thus, we concluded that there was no significant structuring in the bulk solvent at the beginning of the MD simulation. Adsorption on Viscinal Surfaces: Acute and Obtuse Steps and the Terraces Between. Figure 7 show ethanol and water from the final snapshot at 5.5 ns over a surface along the {31.8} plane, formed by acute steps, and along the {3 1̅.16} plane, formed by obtuse steps. A line shows the geometry of the underlying calcite in the bottom cross section. On the surface with acute steps, ethanol orders itself with OH toward calcite, but the adsorbed layer is not as ordered as on the {10.4} terraces. Ethanol and water form a coherent layer, but water dominates at the steps. There could be two reasons: (1) the smaller water molecules fit the surface geometry more easily or (2) an ethanol molecule bound at the inner corner through the OH group would present its hydrophobic side to interact with the step edge. Because the step edge is polar, it is energetically
Figure 5. Distribution of ethanol and water on {10.4} calcite, selectively separated from the final MD snapshot (taken after 5.5 ns) to illustrate the lateral distribution of domains.
of the adsorbed molecules from the last snapshot of the simulation. They form a patchwork of domains that are dominated by one or the other of the adsorbing molecules rather than a homogeneous or random coverage. This larger scale phase ordering also reflects the effect of preference for associations between hydrophobic and hydrophilic functional groups. Thus, on the ideal, planar, {10.4} calcite surface, in the absence of steps or defects, there is clear evidence for phase separation of ethanol and water both laterally, on the surface, and vertically, out into the fluid phase. On a real surface, where there are structural defects in the atomic lattice and substitution of foreign ions in the crystal, one or the other solvent molecule would be favored, enhancing the formation of adsorbent phase 3850
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our simulations, water associating exactly at steps also provides channels for water-soluble species to reach calcite. However, whether the obtuse edge is less stabilized than the acute, as de Leeuw et al.6 suggest, is difficult to conclude from our results. Influence of Terrace Length. Figure 7 shows that ethanol is able to form an ordered layer on 3 unit cell long terraces, separating obtuse steps on a {31̅.16} vicinal surface and 5 unit cell long terraces on a {31.16} vicinal surface but not on the 3 unit cell terraces that separate acute steps on a {31.8} surface. The stepped surfaces studied so far are different in the length of the terraces between steps as well as the angle. However, the {31.8} and {31̅.16} surfaces have very different ethanol coverage, in spite of almost identical step-to-step distances, which suggests that the terrace length is only a minor factor for the ethanol coverage. This might not be apparent, and the high step density of the {31.8} and {31̅.16} faces is rarely seen under natural conditions where large terraces of the {10.4} face dominates the calcite surface. Our next task was therefore to investigate whether the lack of ethanol ordering persists on vicinal faces with lower acute step density and whether it is the difference in the geometry and arrangement of atoms at the obtuse and acute steps that controls the degree of ordering or the length of the terraces between them. To explore the influence of terrace length on ethanol ordering, we created other viscinal surfaces. One, with Miller indices {7 1.24}, has acute steps that are separated by terraces that are 5 unit cells long. Figure 8 is a snapshot showing adsorbed water and ethanol.
Figure 7. Ethanol and water distributions of the adsorbed layer on {31.8}, {31.̅ 16}, and {31.16} calcite surfaces. The acute steps of the {31.8} surface are separated by terraces that are 3 calcite unit cells long, whereas the obtuse steps of the {31.̅ 16} and {31.16} surfaces are separated by terraces that are 3 and 5 calcite unit cells long.
Figure 8. Adsorbed water and ethanol on the calcite {7 1.24} vicinal surface where acute steps are separated by terraces that are 5 unit cells long. Ethanol is ordered on the terraces and water associates with the steps.
Compared with the {31.8} vicinal surface, where acute steps are separated by shorter terraces, the phases are more separated. Thus, surface geometry, i.e. step angle and spacing, has a definite influence on ethanol bonding, access to water and how well growth or dissolution are inhibited. We also ran simulations on surface {11 1.40}, which has acute steps separated by terraces that are approximately as long those on the {31.16} plane that is formed of obtuse faces. These terraces also order ethanol in a layer that is interrupted by water at the step edges. Ethanol Affinity for Stepped Surfaces. Our results from vicinal calcite surfaces in ethanol−water mixtures suggest that water very likely occupies the surface sites near the steps also on natural calcite. In the study of the {10.4} plane in mixed ethanol−water, Cooke et al.13 demonstrated that water was not likely to interrupt an adsorbed ethanol layer, if this had been there from the start of the simulation. However, the higher
more favorable to have two water molecules associated with it than one polar and one weak, hydrophobic interaction. On the surface with obtuse steps, ethanol forms a well-ordered layer on the terraces, but the layer is interrupted at the steps, where water is preferred. The amount of water that associates at the acute steps is larger than at the obtuse steps, and similarly, more water is associated at steps for the {3 1.16} surface compared with the {3 1̅.16} surface. On the planar surface and on each terrace between obtuse steps, a second layer of ethanol forms, with CH3 from each of the layers associated most closely, as was observed by Sand and colleagues.9 Previous reports of experiments and simulations have shown that steps are less stabilized by ethanol than terraces,6,8 thus leaving a pathway from the bulk fluid to the crystal surface, where water can pass through and react. Sand et al.9 demonstrated that a water bridge forms at step edges. In 3851
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dominates the terrace area outside the etch pit and to some extent the terrace in the etch pit center.
affinity for water at steps could be sufficient to interrupt an established ethanol layer on a stepped surface. To test if ethanol is likely to be replaced by water, thus providing less inhibition for water-based reactions, we constructed a model with an obtuse stepped surface and covered it with a layer of ethanol before we added the 50% by volume mixture of ethanol and water. All other simulation settings were identical to those previously described. Figure 9 presents the results. The ethanol
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CONCLUSIONS AND IMPLICATIONS Our results confirm that ethanol is favored over water on calcite surfaces. It forms an ordered layer on terraces that is disrupted at steps, where it is displaced by water. This leads to local domains in the plane of the surface where the phases are separated. Even on surfaces initially covered by a layer of ethanol, water displaces the ethanol adsorbed at and near the steps. The angle of the steps, i.e. acute or obtuse, is less of a controlling factor for water displacement than the length of the terraces that separate them. Inhibition of processes mitigated by water, such as adsorption or desorption of foreign ions, precipitation, or dissolution, is most effective on wide terraces. When water replaces ethanol at step edges, it forms a bridge between the solid surface and the bulk fluid, which allows mass transport to the surface. This local preference for one or the other molecule is a mechanism that could easily be adapted by biomineralizing organisms. By tailoring organic molecules to seek out or shun steps, an organism could create or disrupt an adsorbed layer, thus turning biomineralization on and off. This is an important result. Ethanol binds strongly through its −O(H) group, leaving the −CH3 tail to protrude into the fluid. A strongly ordered layer of ethanol changes the surface energy, rendering it hydrophobic. This change in charge properties induces a separation of phases in the direction perpendicular to the surface, out into the bulk fluid, such that ethanol is more abundant at the solid−fluid surface and at the fluid−vacuum surface, leaving water to occupy the middle region. This change of character of the solid surface by water-soluble organic compounds and the phase separation in the bulk could also be used by organisms to control surface properties, thus affinity for trace compounds, or simply for crystal growth. One could also assume that local phase separation would control the behavior of other organic compounds, such as in an oil reservoir, playing a role in determining which hydrocarbons are produced and which remain in the reservoir, affecting pore surface wettability.
Figure 9. Time sequence showing the evolution in adsorbed species at an obtuse step: (a) at the outset with a complete ethanol monolayer, (b) after 2.5 ns of MD simulation, and (c) after 5 ns. We show ethanol (top series) and water (bottom series) separately, and only Ca from the calcite surface is included. Water clearly displaces ethanol at the step edge with time.
layer on the terraces is highly ordered, but it is displaced by water at step edges, already after half of the simulation time has passed. More water has replaced ethanol by the end of the 5 ns, and aqueous bridges have been created. Ethanol attachment at acute and obtuse steps can also be examined by studying a one molecular layer deep etch pit on a {10.4} surface. Such an etch pit has 2 acute and 2 obtuse steps within the same simulation box, and the shape and extent of all terraces are therefore identical for either step type. A snapshot from such a simulation is presented in Figure 10, where we depict the distribution of ethanol (red) and water (blue) molecules as seen from the calcite surface. Water is again preferred at both the acute and obtuse steps, whereas ethanol
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected] (M.H.M.O.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by Maersk Oil & Gas and the Danish Advanced Technology Foundation through Nano-Chalk with a small contribution from the Engineering and Physical Sciences Research Council (EPSRC) through the MIB Consortium (Materials Interface with Biology (grant EP/I001514/1) and the European Community for the CarbFix Project, Grant Agreement FP7-283148. Computer resources were provided by the Danish Center for Scientific Computing (DCSC), now renamed to the Danish e-Infrastructure Coorporation (DeIC).
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Figure 10. Distribution of ethanol and water in a one molecule layer deep etch pit on a {10.4} face of calcite at the end of the simulation. Water (blue) is preferred over ethanol (red) at both acute and obtuse steps of the pit, whereas ethanol dominates the terraces outside and, to some extent, at the center of the etch pit. Water and ethanol adsorbed outside the etch pit are represented in metallic pastel shades.
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DOI: 10.1021/la504319z Langmuir 2015, 31, 3847−3853
