Langmuir 2002, 18, 2019-2023
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Surface Relief Grating Induced Colloidal Crystal Structures† Dong Kee Yi, Mi Jeong Kim, and Dong-Yu Kim* Department of Materials Science and Engineering, Kwang-Ju Institute of Science and Technology, Oryong-dong 1, Puk-gu, Kwang-Ju, 500-712, Republic of Korea Received August 22, 2001. In Final Form: January 2, 2002 A new template-directed method is described for controlling colloidal arrays by using capillary force. Surface relief gratings (SRGs) were used as a substrate for bottom layer induced crystal structure control. The crystal structure of each level of arrays was determined by the topology of SRGs and thermodynamic factors. The findings show that not only the ratio of SRG spacing to colloid diameter but also the ratio of SRG depth to colloid diameter affected the nature of the resulting crystal structure. When the ratio of SRG depth to colloid diameter was 0.74, a square array of colloids was well developed layer by layer. The second layer showed a unique dumbbell-like crystal structure. The method allows the formation of a well-organized body-centered cubic (bcc)-like bottom mono- and bilayer and a wide top area of hexagonal array at a ratio of 0.48. This new method permits the control of wide crystal arrays of colloid particles even with a small diameter (350 nm) in a short time.
Introduction A crystalline colloidal array has numerous applications in areas such as photonic crystals,1,2 sensing materials,3,4 and wavelength division multiplexing technology that has potential for use in optical communication systems.5 The following requirements must be met in order for crystalline colloids to be used in these applications: (1) colloid particles must be easily arrayed in two dimensions or three dimensions, (2) a wide crystalline domain (at least 1000 µm3) with few defects and dislocations must be formed, and (3) lattice parameters must be controlled. In addition, if the crystal structures, face-centered cubic (fcc) or body-centered cubic (bcc), could be precisely determined, then optical and mechanical properties could be controlled. Various strategies have been developed for constructing a colloidal assembly, including sedimentation on flat6,7 or patterned substrates8 by gravity, using capillary force,9-11 electrochemical growth,12 and other novel methods.13 Although the sedimentation method is typically used for achieving colloidal arrays, days or weeks are required to obtain a well-organized colloidal crystal structure. For this reason, a number of alternative methods have been * To whom correspondence should be addressed. Tel: +82-062970-2335. Fax: +82-062-970-2330. E-mail:
[email protected]. † This work was supported by the BK21 project and the Support Project of University Foundation Research supervised by IITA. (1) Tarhan, I. I.; Watson, G. H. Phys. Rev. Lett. 1996, 76, 315. (2) Li, Z. Y.; Zhang, Z. Q. Adv. Mater. 2001, 13, 433. (3) Holtz, J. H.; Asher, S. A. Nature 1997, 389, 829. (4) Weissman, J. M.; Sunkara, H. B.; Tse, A. S.; Asher, S. A. Science 1996, 274, 959. (5) Avrutsky, I.; Kochergin, V.; Zhao, Y. IEEE Photonics Technol. Lett. 2000, 12, 1647. (6) (a) Deutsch, M.; Vlasov, Y. A.; Norris, D. J. Adv. Mater. 2000, 12, 1176. (b) Pusey, P. N.; van Megen, W. Nature 1986, 320, 340. (7) Mayoral, R.; Requena, J.; Moya, J. S.; Lo´pez, C. L.; Cintas, A.; Mı´guez, H.; Meseguer, F.; Va´zquez, L.; Holgads, M.; Blanco, A. Adv. Mater. 1997, 9, 257. (8) Van Blaaderen, A.; Ruel, R.; Wiltzius, P. Nature 1997, 385, 321. (9) Denkov, N. D.; Velev, O. D.; Kralchevsky, P. A.; Ivanov, I. B.; Yoshimura, H.; Nagayama, K. Nature 1993, 361, 26. (10) Wei, Q. H.; Cupid, D. M.; Xu, X. L. Appl. Phys. Lett. 2000, 77, 1641. (11) Kralchevsky, P. A.; Nagayama, K. Langmuir 1994, 10, 23. (12) Braun, P. V.; Wiltzius, P. Nature 1999, 402, 603. (13) Velev, O. D.; Lenhoff, A. M.; Kaler, E. W. Nature 2000, 287, 2240.
developed.9-13 In contrast to the sedimentation method, a capillary force method can form a crystal structure more rapidly and the number of colloidal arrays can also be controlled.9-11,14 Tailoring of the crystal structures at will would be desirable for many practical applications. As one of these methods, the template surface-directed method has been reported. Park et al. demonstrated a replica molding technique for fabricating two-dimensional (2D) and threedimensional (3D) colloidal assemblies in a well-ordered pattern.15 They used a patterned photoresist, not only as a frame to fix the colloidal structure but also as a channel for separating water from the colloidal suspensions. This method shortened the time needed to array the colloidal particles on the substrate, but the control of crystal structure (fcc, bcc, etc.) remained difficult. Van Blaaderen et al. also reported on substrate-induced crystal arrays using gravity and the effects of lattice spacing on the crystal array.8 All of these studies used patterned photoresists as templates which have rectangular geometries; therefore, the diameter of the colloid particles and the dimensions of the photoresist patterns needed to be closely matched. Here, we report on a new template-induced crystal tailoring method employing surface relief gratings (SRGs) fabricated on polymer films, which show sinusoidal surface profiles. The round profile of the SRGs would be expected to increase the contact area between colloid particles and the SRG substrate enhancing the interaction between the two materials. In the case of other previously reported template methods, including imprinted substrates,16 the contact area of colloid particles and substrate is comparatively smaller than that of the case where the SRG is used as a substrate. We also assembled colloidal crystalline structures by the simultaneous use of gravity and capillary force for a faster process to obtain wellordered crystal arrays. We demonstrated that this method allows for the control of colloid assemblies into various (14) Tessier, P. M.; Velev, O. D.; Kalambur, A. T.; Lenhoff, A. M.; Rabolt, J. F.; Kaler, E. W. Adv. Mater. 2001, 13, 396. (15) Park, S. H.; Qin, D.; Xia, Y. Adv. Mater. 1998, 10, 1028. (16) Lin, K.; Crocker, J. C.; Prasad, V.; Schofield, A.; Weitz, D. A.; Lubensky, T. C.; Yodh, A. G. Phys. Rev. Lett. 2000, 85, 1770.
10.1021/la011340g CCC: $22.00 © 2002 American Chemical Society Published on Web 02/22/2002
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Figure 1. Schematic views of deformed spheres that are under the influence of the capillary forces in a tube: (a) shows larger deformation of spheres when the contact area between the particles and the substrate walls is large; however, (b) shows relatively small deformation when a small gap exists between the particles and the walls.
crystal structures through a change in template spacing and modulation depth. Theoretical Background Mason17 gave a good analysis for how the capillary force works between the two elastic spheres that are placed in a tube filled with liquid. Figure 1 shows that the thin liquid film was made between two particles. This film is formed when two particles are deformed. When the sum of the capillary pressure, Pc, and the surface tension pressure is more than the elastic pressure, Pg, keeping the particles round, the particles are deformed as in Figure 1. Mason showed that the capillary pressure, Pc, is given as
Pc ) 2σ/(2f/31/2 - 1)R
(1)
where σ is the air-water interfacial tension, f is the fractional compression of a particle, and R is the sphere radius. It was demonstrated that the capillary forces act in the direction not only parallel to the particles but also normal to the particles.18 The parallel capillary forces bring the particles closer to each other, and the normal capillary forces push the particles toward the substrates. In our experiments, colloidal dispersions were placed in the SRG grooves. As the water of the colloidal dispersions evaporates, the colloid concentration increases and the colloid particles are influenced by the capillary forces. In this case, the analyses of Mason and Sheetz18 can be applicable to understanding the results. Figure 1a is the case where the beads contact the SRG grooves, and Figure 1b is the case where a small gap exists between the colloids and the SRG groove walls. Experimental Section Our experimental setup is similar to that used by Lu et al.19 They reported that there was a limit in the bead size for a successful self-assembly process. Small beads, less than 500 nm in diameter, were self-assembled into polygonal or polyhedral clusters, and as a result, the structuring of a 3D crystal array was not achieved. Presumably, the size of the cylindrical hole (capturing polymer beads) based on the photoresist could not be easily controlled; therefore, there was a diameter limit for the application of capturing small beads. In our experiments, instead of photoresist patterning, SRGs fabricated on azo polymer films were used for easy control of surface topology such as depth modulation and spacing to form 3D crystal arrays. (17) Mason, G. Br. Polym. J. 1973, 5, 101. (18) Sheetz, D. P. J. Appl. Polym. Sci. 1965, 9, 3759. (19) Lu, Y.; Yin, Y.; Xia, Y. Adv. Mater. 2001, 13, 34.
Figure 2. A schematic view of the experimental setup. The grating groove direction is denoted as the X-Y direction. Colloid particles move down the substrate perpendicular to the grating grooves (denoted as the A-B direction): water evaporation makes menisci, capillary force and gravity force drive colloids arrayed, and spacers maintain the distance between the two glass substrates at 0.1 mm. Azo polymer films are known to form SRGs simply by exposure to an interference pattern of laser beams.20-22 SRG patterning using an azo polymer has several advantages over conventional lithographic patterning: (1) it is a single-step process which requires a relatively short time, (2) multiple patterns can be superimposed, and (3) it is thermally and optically erasable. Monodispersed polystyrene (PS) latex (diameter of 350 and 500 nm) and silica beads (diameter of 500 nm) were purchased from Polysciences Co. and Duke Scientific Co., respectively. An epoxy-based azo functional polymer was synthesized by condensation polymerization as previously reported.23 The ζ-potential of colloids and the azo functional polymer was measured by an electrophoretic light-scattering spectrophotometer, type ELS-800 (Otsuka Electrons, Osaka). Azo functional polymer was solubilized with cyclohexanone and spin-coated on the glass slide, and the films were dried under vacuum. The thickness of the film was about 1.2 µm. For SRG patterning, the polymer films were exposed to an interference pattern of Ar+ laser beams with an intensity of about 100 mW/ cm2 at a wavelength of 488 nm. By varying the interference angle, the SRGs’ spacing was controlled, and the modulation was monitored by measuring diffraction efficiency that can be obtained with a low power He-Ne laser. The spacing of the grating could be controlled by the Bragg equation: a grating spacing d is equal to λ/2 sin θ, where λ is the input laser wavelength and θ was the incident angle. Under the constant laser wavelength, the spacing is only dependent on the interference angle θ. Two SRGs with the spacings of 780 and 1100 nm were made. The modulation depth of SRG grooves was about 250 nm. Figure 2 shows a schematic view of the experimental setup. Α colloidal suspension (1.5 wt %) was dropped on the SRG substrate: (1) silica (diameter of 500 nm) on the substrate with spacing of 1100 nm and (2) PS (diameter of 350 and 500 nm) and silica (diameter of 500 nm) on the substrate with spacing of 780 nm and the substrate was covered with another glass plate. Spacers (Teflon) were placed between the glass plates to keep the distance at 0.1 mm. The suspension sandwiched by two glass plates was placed at a slope of 30° in an oven at 45 °C for 90 min. The tilted substrate enabled us to see the layer by layer development of colloid particles in a short time. When the contained colloidal suspensions evaporate, they are simultaneously affected by gravity and capillary force, and the evaporation is more vigorous in the margin of the glass substrates due to facing the air. After removing the cover glass, an iridescent sample (0.8 cm × 0.8 cm) was obtained that was dried for 8 h in an oven at 35 °C. Scanning electron microscope (SEM) images of gold-coated (20) Kim, D. Y.; Tripathy, S. K.; Li, L.; Kumar, J. Appl. Phys. Lett. 1995, 66, 1166. (21) Rochon, P.; Batalla, E.; Natansohn, A. Appl. Phys. Lett. 1995, 66, 136. (22) Jiang, X. L.; Li, L.; Kumar, J.; Kim, D. Y.; Shivshankar, V.; Tripathy, S. K. Appl. Phys. Lett. 1996, 68, 2618. (23) Kim, D. Y.; Li, L.; Jiang, X. L.; Shivshankar, V.; Kumar, J.; Tripathy, S. K. Macromolecules 1995, 28, 8835.
Surface Relief Grating Induced Crystal Structures Table 1. ζ-Potential Values for the Silica, Polystyrene Beads, and Azo Polymer SiO2
polymer substrate polystyrene
ζ-potential (mV)a -41.5 ( 3.1 -16.8 ( 1.4 a
-38 ( 2.8
Measured at room temperature.
Figure 3. AFM image of the SRG substrate, with the X-Y direction parallel to the grating grooves, showing a modulation depth of 240 nm and a spacing length of 780 nm. samples were obtained by a JEOL-5800 (JEOL Co.). Atomic force microscope (AFM) images were measured in noncontact mode by an Auto Probe CP (PSI Co.).
Results and Discussion Table 1 shows the values for the ζ-potential of the colloid particles and the polymer substrate in units of mV and clearly shows that the surfaces of the colloid particles and the polymer are negatively charged. Like-charged colloid particles have a long-range attraction force,24-27 the Hamaker force, which is induced by the additive effects of atom-atom dipoles between colloid particles. The Hamaker force effects occur in the hundred-nanometer range. The colloidal dispersions were sonicated for 10 min prior to use to disperse the sediment (which happened during the storage). Figures 3 and 4 show the images of an AFM and a SEM for the experiments involving silica beads (diameter of 500 nm). Figure 3 shows that the fabricated SRG template in this case has a surface modulation of 240 nm and a spacing of 780 nm. The homogeneity of surface modulation and spacing was also confirmed by an AFM depth profile. The ratio of the SRG spacing to the colloid diameter (hereafter denoted as S/D) was 1.56, and the ratio of modulation depth to the colloid diameter (hereafter denoted as Md/D) was 0.48. In the experiments, glass plates were sloped in the direction of A-B. The tilted condition makes the colloid particles array homogeneously and fast (the upper part of the sample dries faster than the lower part) in the SRG grooves even at the early stage of crystal structuring. Figure 4a shows the bottommost layer; the white balls are silica beads with a diameter of 500 nm. Silica beads were placed only in concave areas of the SRG template; in comparison with the case where the colloid particles and substrate are oppositely charged, the same charges on the colloid particles and the SRGs may have assisted to selectively array the colloid particles in the concave regions. The capillary force causes the silica beads to be arrayed in a tight line. It has been reported that the capillary (24) Hamaker, H. C. Physica 1937, 4, 1058. (25) Derjaguin, B. V. Theory of Stability of Colloids and Thin Liquid Films; Plenum Press: New York, 1989. (26) Israelachvili, J. N. Intermolecular and Surface Forces; Academic Press: London, 1992. (27) Hunter, R. J. Introduction to Modern Colloid Science; Oxford University Press: New York, 1993.
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force works as the main factor of the particle shrinkage.17,18,28 The calculated capillary pressure, Pc, is on the order of 106-107 Pa (σ is 36.3 mN/m, f is 1-0.9047, and R is 500 nm) by eq 1, and the capillary force, Pc multiplied by the contact area of beads, is about 10-8 N. Presumably, it is thought that the capillary force was high enough to get over the elastic property of silica beads for deforming the beads. An aqueous colloid might have a tensile strength less than that of pure water (40 kg/cm2).18 When we carried out the same experiment with PS beads (diameter of 500 nm), the shrinkage of beads was also observed. The mesoparticles have comparatively few numbers of molecules and thus have weak mechanical properties to be easily deformed under the small force (∼10-8 N). As the particles get smaller, capillary pressure, Pc, increases due to eq 1 and therefore the deformation of particles increases. In contrast, the silica bead near the vacancy retains a round shape due to not contacting the neighboring bead. However, the samples made under the free sedimentation condition do not experience the capillary force, and therefore no shrinkage of beads might be observed.16 The depth profile in the direction of X-Y shows that the height of the bead is about 410 nm, indicating that the silica beads are depleted into the SRG substrate by about 90 nm. The depletion of beads could be due to the normal capillary force acting in the direction perpendicular to the substrate, and the gravity also makes the beads imbedded in the substrate. This depletion is much larger when compared with the case of patterned photoresist templates. This deep depletion allows the silica beads to be fixed well on the SRG patterns to form a more thermodynamically stable colloidal array. In addition, the depth profile in the direction of A-B indicates that the silica bead protrudes over the top of the SRG pattern by about 170 nm. The angle of neighboring diagonal arrays is 58°. Although some vacancies were observed, silica beads were well organized in the X-Y direction and even in the A-B direction. It has been recently reported that one-dimensional (1D) ordering by an external force such as an optical field can induce 2D hexagonal ordering.29 It is believed that a similar longrange order interaction exists in our case, even though the spacing may be large enough to avoid twinning between adjacent layers. Further studies will be required for a complete understanding of the mechanisms. Figure 4b shows the crystal structure of the second bottom layer. The silica beads arrayed in the second layer are also shrunk in the X-Y direction, and a bcc {110}-like pattern is evident. The angle of the diagonal line is retained at about 58° confirming that the second-layer crystal structure was induced by the bottommost layer. Figure 4c shows the topmost layer and the cleaved facets. The crystal structure of the topmost layer is the {111} type. The topmost silica beads show an ordered hexagonal array with a large area (18 µm × 12 µm). From the cleaved facets, both {111} and {100} type orderings were observed; therefore, the crystal structure (at upper layers) can be identified as fcc structure, although {110} type arrays can be seen up to the third layer from the inset image. At the early stage, SRG-induced crystal structuring was dominant, and then bottom layers showed a {110} facet. At this time, the suspension was relatively dilute. The bcc crystal structure {110} is often observed in the dilute state, but as the concentration is increased during evaporation of the matrix medium, the more dense fcc structure (28) Scherer, G. W. J. Am. Ceram. Soc. 1990, 73, 3. (29) Wei, Q. H.; Bechinger, C.; Rudhardt, D.; Leiderer, P. Phys. Rev. Lett. 1998, 81, 2606.
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Figure 4. Monodispersed silica beads 500 nm in diameter were placed on the SRG substrate (spacing of 780 nm). SEM images and AFM depth profiles: (a) the substrate and the bottommost layer (S and 1 represent the substrate and the bottommost layer, respectively) and the depth profiles of the A-B and X-Y directions; (b) the bottommost and the second layer (1 and 2 indicate the bottommost and the second layer, respectively); (c) the topmost layer and a cleaved image, with {100} and {111} facets indicated in the cleaved image (1, 2, and 3 represent the bottom, second, and third layers, respectively).
becomes dominant.30 In terms of thermodynamics, a higher order state is a lower entropy state. The lower entropy state becomes favorable (lower free energy state) when the enthalpy decreases under constant temperature. As the colloidal suspensions become concentrated, the particle interactions increase (lower enthalpy state) and a more ordered state becomes thermodynamically stable. It has been reported that the fcc crystal structure is more stable than hexagonal close packing (hcp).31 Therefore, the crystal order pattern changes from a bcc-like order to fcc ordering rather than hcp as the layer grows and becomes concentrated. To further investigate the effects of SRG substrate geometries on the crystal structures, we arrayed smaller colloid particles (PS latex with 350 nm in diameter) on the SRG substrate (spacing of 780 nm and depth of 260 nm). In this case, the S/D was 2.22. Figure 5a shows a large area of the bottommost layer and second layer. Figure 5b clearly shows the crystal structure of the second layer with its unique “dumbbell” shape. The AFM depth profile at the bottommost layer shows that little part of the PS colloid particles protrudes over the SRGs’ convex parts, and this deep imbedding permitted the PS colloid particles to be arrayed so close to each other in the second layer. Furthermore, the convex area of the SRG plays a role in the separation of neighboring colloidal particles in the direction of A-B, producing dumbbell-type crystals. In comparison with the previous case where the S/D was 1.56, the shrinkage of beads was small when the S/D was 2.22. This may be due to the smaller capillary force acting in this case. When S/D was 1.56, the beads were so tightly put in the grooves that no clearance was seen between the beads and the groove walls (see Figure 4a and Figure 1a). It is assumed that when the beads contact with the groove walls, the area of the thin water layer between the beads increases due to the limited bead (30) Monovoukas, Y.; Gast, A. P. J. Colloid Interface Sci. 1989, 128, 533. (31) Woodcock, L. V. Nature 1997, 385, 141.
Figure 5. PS beads 350 nm in diameter were placed on the SRG substrate (spacing of 780 nm). SEM images and AFM depth profiles: (a) the bottommost and second layers in a wide area, where imbedded polystyrene colloids at the bottommost layer are seen in the circular area and the dumbbell-like second layer is seen over the first layer; (b) a close-up of the unique dumbbell-like second layer and the bottommost layer, where colloid particles are depleted in lengths of 100 nm, and little part is protruded over the top of SRG pattern (denoted as ]).
mobility leading to the larger contact area between the neighboring beads. But when the S/D was 2.22, there was a small gap between the beads and the groove walls; therefore, the beads were loosely placed in the grooves
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ing structure32 or square islands in a hexagonal matrix33 were reported. However, the bottom layers show a dumbbell-like array (dominantly at the second layer) or small domains of hexagonal array. This structural development is comparable with the case of 500 nm sized colloid particles previously discussed. In the previous case, the bottom layers were well-ordered {110} facets and the topmost layer showed a hexagonal pattern, a {111} facet. It is assumed that different S/D values made distinguishable bottom layer arrays between silica (500 nm in diameter) and PS (350 nm in diameter); the S/D was 1.56 and 2.22, respectively, under the same grating spacing. These different bottom layer arrays induced the unique topmost array, although thermodynamic factors also played a role as top layer forming factors. When silica 500 nm in diameter was placed on the SRGs with longer grating spacing (depth of 240 nm and spacing of 1.1 µm), the S/D (2.2) was similar to the case of PS latex 350 nm in diameter. However, no dumbbell-like order was seen, and the topmost layer was present as a hexagonal array. This can be attributed to the differences in the Md/D: 0.74 and 0.48 for PS and silica, respectively. When Md/D was 0.74, the colloid particles were imbedded deeply in the cavity made by SRGs. The SRG functions to separate the colloid particles in the direction of A-B, producing the dumbbell-like arrays. But when the Md/D was 0.48, dumbbell-like arrays were not achieved, and the topmost layer was controlled mainly by thermodynamic factors. From this, we realized that the ratio of grating modulation depth to colloid diameter, Md/D, also greatly affects the tailoring of the crystal assembly. Conclusions
Figure 6. PS beads 350 nm in diameter were placed on the SRG substrate (spacing of 780 nm). SEM images: (a) a wide area of well-developed dumbbell-like array (some hexagonal arrays are also seen in left corner); (b) development of layers from bottommost to topmost (bottommost layer is located in the left corner); (c) wide topmost area. The vacancy in the inset shows how a colloid was placed on the corner of four neighboring colloid particles; hexagonal arrays are denoted as circles.
(see Figure 5 and Figure 1b). This makes the beads more freely moving in the groove under the water atmosphere resulting in the smaller contact area between the beads along the grooves. Consequently, the capillary force has a lower value than the case of densely arrayed beads. Figure 6a shows a wide area of the second bottom layer containing well-developed dumbbell-type crystal structures. Figure 6b shows terraces of layers from the bottom to topmost layer (about the 10th layer) with the bottommost layer in the left corner. A square array dominates each terrace, including the topmost layer. The wide, topmost layer is seen in Figure 6c; though small domains of hexagonal array are present, the well-organized crystal structure of the square array is dominant (see the enlarged inset image). Interestingly, a square-hexagonal alternat-
We have demonstrated that when combined with capillary force, SRG patterns on azo polymers could be successfully employed as a substrate for a templatedirected crystal assembly due to the ease of control of spacing and depth of the grooves. Capillary force, depending on the substrate structure, worked as a driving force for making dense colloidal arrays. The large depletion of the colloid particles into the SRG template implies that the sinusoidal surface topology of SRGs is well suited for capturing colloidal spheres with the round shape. The 1D regularity of SRGs further induced even 2D and 3D orders with various crystalline structures that depend on the ratio of the spacing to the colloid diameter and the ratio of the modulation depth of SRG to the colloid diameter. Compared with previous substrate-induced crystal arrays (e.g., refs 8 and 19), we also accomplished 1D-induced 2D and 3D crystal assembly even with smaller colloids (,400 nm). In all cases, the topmost layer showed wide, wellorganized colloidal crystal structures in a hexagonal or square array. LA011340G (32) Pieranski, P.; Strzelecki, L.; Pansu, B. Phys. Rev. Lett. 1983, 50, 900. (33) Dushkin, C. D.; Nagayama, K.; Miwa, T.; Kralchevsky, P. A. Langmuir 1993, 9, 3695.
