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Colloidal photonic crystals obtained by the Langmuir–Blodgett technique
Applied Surface Science 246 (2005) 409–414 www.elsevier.com/locate/apsusc
Colloidal photonic crystals obtained by the Langmuir–Blodgett technique Ste´phane Reculusa, Serge Ravaine* Centre de Recherche Paul Pascal, CNRS, 115, Avenue du Dr. Schweitzer, 33600 Pessac, France Available online 7 January 2005
Abstract Monodispersed silica spheres with diameters of 220–1100 nm were prepared by hydrolysis of tetraethyl orthosilicate (TEOS) in an alcoholic medium in the presence of water and ammonia. By grafting vinyl or amine groups on silica surfaces using the coupling agents allyltrimethoxysilane and aminopropyltriethoxysilane, respectively, amphiphilic silica spheres were obtained and could be organized to form a stable Langmuir film at the air–water interface. The control led transfer of this monolayer of particles onto a solid substrate gave us the ability to build three-dimensional regular crystals with well-defined thickness and organization. These colloidal crystals diffract light in the UV, visible and the near-infrared (NIR) spectral regions, depending on the size of the silica spheres and according to the Bragg’s law. # 2004 Elsevier B.V. All rights reserved. Keywords: Colloidal crystals; Silica; Langmuir–Blodgett technique; Controlled architecture
1. Introduction For many years, colloidal crystals have drawn a considerable interest in the field of materials chemistry, both for theoretical and experimental considerations. Such nanostructured materials, consisted of a controlled assembly of monodisperse colloids in a highly regular structure (typically a facecentered cubic system), are indeed particularly interesting and perfectly adequate for the field of photonic crystals, i.e. dielectric materials with a one-, * Corresponding author. Tel.: +33 556845667; fax: +33 556845600. E-mail address: [email protected] (S. Ravaine).
two- or three-dimensional periodicity exhibiting peculiar interactions with light [1–4]. Several techniques have been developed for the creation of such materials, including colloidal self-assembly [5–10], 3D holography using multiple laser beams [11,12] and photolithography [13]. We have previously reported that colloidal crystals with a thickness controlled at the layer level can be synthesized by using the well-known Langmuir–Blodgett technique [14]. Here we report the elaboration of crystals with a perfectly controlled thickness starting with silica spheres with diameters ranging from 220 to 1100 nm, in order to elaborate SiO2 photonic crystals with diffraction wavelengths going from 500 to 2300 nm. In fact, it is the first report of the synthesis of high optical quality crystalline
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.11.066
410
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
spheres arrays with a well-defined thickness which operate in the near-infrared region, that is a challenge to fabricate practical optical devices for telecommunications. Reese and Asher [15] and Hamilton coworkers [16] have previously reported the elaboration of such materials but without the control of their thickness at the layer level.
2. Experimental 2.1. Materials Tetraethoxysilane (TEOS, Fluka), ammonia (29% in water, J.T. Baker), allyltrimethoxysilane (GelestABCR), aminopropyltriethoxysilane (Aldrich) were purchased in their reagent grade and used without further purification. Deionized water was obtained with a MilliQ system (Millipore) whereas ethanol (EtOH), methanol (MeOH) and chloroform (CHCl3) were purchased from Prolabo. 2.2. Methods 2.2.1. Synthesis of silica particles The methods employed for the synthesis and the functionalization of silica particles were similar to those described in a previous work where the syntheses of particles with diameters of 460 and 680 nm were detailed [14]. The amounts of reagents solutions employed for the synthesis of spheres of other diameters in the micron size range are given in Table 1. In some experiments, an alcoholic solution of TEOS was prepared separately and introduced continuously in the medium at a precise rate thanks to a single-syringe pump (see below).
2.2.2. Functionalization of silica particles Allyltrimethoxysilane or aminopropyltriethoxysilane was directly added into the nanoparticles dispersion. The amount of coupling agent was around ten times higher than the amount necessary to cover the inorganic surface with a monolayer (the theoretical amount for such a coverage being nominally 2 molecules nm2). After it was left to react overnight, the mixture was held at 80 8C for 1 h to promote covalent bonding of the organosilane to the surface of the silica nanoparticles. The choice of allyltrimethoxysilane and aminopropyltriethoxysilane was driven by the necessity to avoid the aggregation of the silica particles either in solution before their spreading at the air–water interface or just after this step. 2.2.3. Silica suspensions treatment In order to eliminate the remaining reagents, all the suspensions were dialyzed against water several times (for a small particle size) or submitted to several cycles of washing and centrifugation. The final concentration of the suspension was determined by measuring the mass of a dried extract and the measured value was always in agreement with the theoretical one (calculated assuming a complete conversion of TEOS into silica). 2.2.4. Silica particles size measurements Granulometry experiments were performed on a Malvern Mastersizer apparatus. 2.2.5. Formation of a 2D-array of particles A diluted suspension of functionalized silica particles in a 80%/20% (v/v) mixture of chloroform and ethanol was prepared according to a previously reported procedure [14]. After spreading on a pure water subphase (pH = 5.5), a stepwise compression of the 2D
Table 1 Experimental conditions corresponding to the synthesis of silica spheres with various diameters Reaction medium
Solution of TEOS
Volume of alcohol (mL)
Volume of ammonia (mL)
Volume of alcohol (mL)
Volume of TEOS (mL)
200 (EtOH) 100 (MeOH) 200 (EtOH)
15 20 20
0 20 (MeOH) 25 (EtOH)
5 20 25
a
TEOS was added at once.
Rate of addition (mL h1) a
20 8
Final particle size (nm)
220 360 1100
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
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particulate film was carried out under continuous dried nitrogen flow, at room temperature (20 1 8C), until a surface pressure of ca. 6 mN m1, that was the pressure chosen for the transfer. 2.2.6. Colloidal crystal synthesis After compression, the Langmuir film was transferred onto hydrophilic glass slides or silicon wafers. The slides were immersed quickly in the subphase (downstroke speed: 10 cm min1) and then slowly pulled up out of the water (upstroke speed: 0.1 cm min1). In these optimized conditions, for all sizes of particles, the deposition on the substrate only occurred during the upstroke with a transfer ratio close to unity, what allowed us to transfer a monolayer of particles at each cycle. 2.2.7. Scanning electron microscopy SEM observations were performed with a JEOL JSM-840A scanning electron microscope operating at 10 kV. The specimens were carbon-coated prior to examination.
Fig. 1. p–A isotherms of functionalized silica particles of different sizes (from left to right: 220 nm amine, 360 nm amine, 680 nm vinyl and 1100 nm amine).
by SEM (see Fig. 3) and a small incertitude on the value of the spheres diameters determined by granulometry can explain the slight difference between experimental and theoretical values. 3.2. Langmuir–Blodgett films
2.2.8. UV-visible/near IR spectroscopy Near-infrared spectra were recorded on a MagnaIR Spectrometer 750 from Nicolet and UV-visible spectra with a Unicam UV 4 spectrophotometer.
3. Results and discussion 3.1. p–A isotherms Typical surface pressure (p)/area (A) isotherms corresponding to the compression of the silica particles films are shown in Fig. 1. The slope of the curves is extremely steep, indicating a low compressibility of the films. The areas corresponding at the collapse of the films and those extrapolated to p = 0 mN m1 are listed in Table 2. These values are in good agreement with those predicted by assuming that area occupied by one silica sphere in a close-packed hexagonal arrangement is equal to: pffiffiffi 3 D2 2 where D is its diameter. The presence of a small number of defects and holes which can be observed
The transfer of the particles films onto a solid substrate was done at a surface pressure of ca. 6 mN m1. As shown in Fig. 2, the visual appearance of the LB films testifies to their high crystalline quality and their uniform thickness at the centimeter scale. The samples exhibit a brilliant color due to Bragg diffraction of visible light. A systematic change of the color can be seen by modifying the orientation of the substrate. Tentative transfers at surface pressure values higher than 6 mN m1 led to poor quality LB films, due to the high rigidity of the Langmuir films. In Fig. 3 are presented SEM side views of colloidal crystals obtained through the transfer of 10 layers of silica Table 2 Experimental and calculated values of the area per particle of the particulate monolayer for silica spheres with different sizes Diameter of the silica spheres (nm)
Predicted area (mm2)
Area at the collapse (mm2)
Area extrapolated to p = 0 mN m1 (mm2)
220 360 680 1100
0.042 0.112 0.400 1.048
0.055 0.161 0.430 1.280
0.058 0.170 0.430 1.340
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S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
Fig. 2. Optical pictures showing the evolution of the colors diffracted by a colloidal crystal made of a single layer of silica particles (diameter D = 680 nm) as a function of the orientation of the substrate (here a glass slide).
particles with various sizes. The close packed structure extends uniformly over the samples, whatever their thickness is. Even if typical defects such as sphere vacancies and vertical cracks can be observed every 100 mm on average, the top surface of the crystals is relatively smooth and the number of
deposited layers matches perfectly with the predefined value. The optical properties of the crystals have also been studied. Fig. 4 shows the dependence of the transmission spectra of 10 layers colloidal crystals as a function of the size of the silica particles. The sharp
Fig. 3. Side views of colloidal crystals consisting of 10 layers of silica particles with different sizes and surface functions: (a) 220 nm amine; (b) 360 nm amine; (c) 680 nm vinyl; (d) 1100 nm amine.
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
413
Table 3 Comparison of the average values of the silica particles diameters (nm) estimated with several techniques Granulometry Bragg peak position SWA model
Fig. 4. Experimental (continuous line) and predicted (dotted line) visible-NIR transmission spectra of colloidal crystals consisting of 10 layers of silica particles with various diameters (from bottom to top: 220, 360, 680 and 1100 nm). For better clarity, curves were shifted vertically.
peaks which can be observed in each spectrum result from the first-order Bragg diffraction of light by the crystals. The diffraction peak positions obey Bragg’s law: mlm ¼ lB ¼ 2ne dh k l sin aB
(1)
where m is an integer (corresponding to the diffraction order), lB the Bragg diffracted wavelength, ne the effective refractive index of the crystal, dh k l the distance between two consecutive lattice planes with Miller indices (h, k, l) and aB is the Bragg angle. In our experimental conditions, the diffracted intensity is measured in the same direction as the incident beam, which is itself perpendicular to the surface of the crystal. Consequently, assuming that we have a f.c.c. lattice, we are in the condition of the Bragg diffraction angle (aB = 908) for the lattice planes with Miller indices (1, 1, 1). Modifying Eq. (1), it comes that the main peak corresponding to the first order of diffraction (m = 1) is obtained when:
220 230 230
370 364 360
680 688 690
1100 1195 1070
Therefore, the particles diameter can be calculated from the Bragg peak position. The results given in Table 3 are in a good agreement with the values determined by granulometry. A quantitative study of the optical properties of the colloidal crystals based on the scalar wave approximation theory [17,18] has also been performed. The solving of Maxwell equation for an electric field propagation in a periodic medium leads to expressions of the transmission rate which have been used to fit the experimental UV-visible-NIR transmission spectra. Results of the fitting procedure, carried out with D as only adjustable parameter, are shown in Fig. 4. A good agreement between experimental and simulated spectra is achieved. The values of D resulting from the simulation are listed in Table 3 and are in agreement with those calculated by other techniques.
4. Conclusion Using the Langmuir–Blodgett technique, we have engineered colloidal crystals with a well-controlled thickness made of silica spheres with diameters of 220–1100 nm. These materials exhibit diffraction properties in UV, visible or NIR wavelength ranges, depending on the size of the silica particles. We are currently extending our strategy to engineer colloidal crystals with a more complex structural organization, based on precursors with different natures and morphologies.
l ¼ lB ¼ 2ne d1 1 1 In the case of a f.c.c. lattice consisted of spheres of a diameter D, the value of d1 1 1 is given by: rffiffiffi 2 D d1 1 1 ¼ 3
Acknowledgments We thank Be´ atrice Agricole (CRPP, Pessac) and Elisabeth Sellier (CREMEM, Talence) for Langmuir– Blodgett and SEM experiments, respectively.
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S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
References [1] J.M. Weissman, H.B. Sunkara, A.S. Tse, S.A. Asher, Science 274 (1996) 959. [2] G. Pan, R. Kesavamoorthy, S.A. Asher, Phys. Rev. Lett. 78 (1997) 3860. [3] J.H. Holtz, S.A. Asher, Nature 389 (1997) 829. [4] W. Lee, S.A. Pruzinsky, P.V. Braun, Adv. Mater. 14 (2002) 271. [5] S.G. Romanov, N.P. Johnson, A.V. Fokin, V.Y. Butko, H.M. Yates, M.E. Pemble, C.M. Sotomayor Torres, Appl. Phys. Lett. 70 (1997) 2091. [6] M. Egen, R. Zentel, Chem. Mater. 14 (2002) 2176. [7] H. Miguez, F. Meseguer, C. Lopez, A. Blanco, J. Moya, J. Requena, A. Mifsud, V. Fornes, Adv. Mater. 10 (1998) 480. [8] P. Jiang, J.F. Bertone, K.S. Hwang, V.L. Colvin, Chem. Mater. 11 (1999) 2132.
[9] J. Texter, CR Chimie 6 (2003) 1425. [10] Y.-H. Ye, F. LeBlanc, A. Hache, V.V. Truong, Appl. Phys. Lett. 78 (2001) 52. [11] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Nature 404 (2000) 53. [12] H.-B. Sun, S. Matsuo, H. Misawa, Appl. Phys. Lett. 74 (1999) 786. [13] I. Divliansky, T.S. Mayer, K.S. Holliday, V.H. Crespi, Appl. Phys. Lett. 82 (2003) 1667. [14] S. Reculusa, S. Ravaine, Chem. Mater. 15 (2003) 598. [15] C.E. Reese, S.A. Asher, J. Colloid Interf. Sci. 248 (2002) 41. [16] W. Wang, B. Gu, L. Liang, W.A. Hamilton, J. Phys. Chem. B 107 (2003) 12113. [17] W.-K. Shung, Y.C. Tsai, Phys. Rev. B 48 (1993) 11265. [18] D.M. Mittleman, J.F. Bertone, P. Jiang, K.S. Hwang, V.L. Colvin, J. Chem. Phys. 111 (1999) 345.
Colloidal photonic crystals obtained by the Langmuir–Blodgett technique Ste´phane Reculusa, Serge Ravaine* Centre de Recherche Paul Pascal, CNRS, 115, Avenue du Dr. Schweitzer, 33600 Pessac, France Available online 7 January 2005
Abstract Monodispersed silica spheres with diameters of 220–1100 nm were prepared by hydrolysis of tetraethyl orthosilicate (TEOS) in an alcoholic medium in the presence of water and ammonia. By grafting vinyl or amine groups on silica surfaces using the coupling agents allyltrimethoxysilane and aminopropyltriethoxysilane, respectively, amphiphilic silica spheres were obtained and could be organized to form a stable Langmuir film at the air–water interface. The control led transfer of this monolayer of particles onto a solid substrate gave us the ability to build three-dimensional regular crystals with well-defined thickness and organization. These colloidal crystals diffract light in the UV, visible and the near-infrared (NIR) spectral regions, depending on the size of the silica spheres and according to the Bragg’s law. # 2004 Elsevier B.V. All rights reserved. Keywords: Colloidal crystals; Silica; Langmuir–Blodgett technique; Controlled architecture
1. Introduction For many years, colloidal crystals have drawn a considerable interest in the field of materials chemistry, both for theoretical and experimental considerations. Such nanostructured materials, consisted of a controlled assembly of monodisperse colloids in a highly regular structure (typically a facecentered cubic system), are indeed particularly interesting and perfectly adequate for the field of photonic crystals, i.e. dielectric materials with a one-, * Corresponding author. Tel.: +33 556845667; fax: +33 556845600. E-mail address: [email protected] (S. Ravaine).
two- or three-dimensional periodicity exhibiting peculiar interactions with light [1–4]. Several techniques have been developed for the creation of such materials, including colloidal self-assembly [5–10], 3D holography using multiple laser beams [11,12] and photolithography [13]. We have previously reported that colloidal crystals with a thickness controlled at the layer level can be synthesized by using the well-known Langmuir–Blodgett technique [14]. Here we report the elaboration of crystals with a perfectly controlled thickness starting with silica spheres with diameters ranging from 220 to 1100 nm, in order to elaborate SiO2 photonic crystals with diffraction wavelengths going from 500 to 2300 nm. In fact, it is the first report of the synthesis of high optical quality crystalline
0169-4332/$ – see front matter # 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2004.11.066
410
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
spheres arrays with a well-defined thickness which operate in the near-infrared region, that is a challenge to fabricate practical optical devices for telecommunications. Reese and Asher [15] and Hamilton coworkers [16] have previously reported the elaboration of such materials but without the control of their thickness at the layer level.
2. Experimental 2.1. Materials Tetraethoxysilane (TEOS, Fluka), ammonia (29% in water, J.T. Baker), allyltrimethoxysilane (GelestABCR), aminopropyltriethoxysilane (Aldrich) were purchased in their reagent grade and used without further purification. Deionized water was obtained with a MilliQ system (Millipore) whereas ethanol (EtOH), methanol (MeOH) and chloroform (CHCl3) were purchased from Prolabo. 2.2. Methods 2.2.1. Synthesis of silica particles The methods employed for the synthesis and the functionalization of silica particles were similar to those described in a previous work where the syntheses of particles with diameters of 460 and 680 nm were detailed [14]. The amounts of reagents solutions employed for the synthesis of spheres of other diameters in the micron size range are given in Table 1. In some experiments, an alcoholic solution of TEOS was prepared separately and introduced continuously in the medium at a precise rate thanks to a single-syringe pump (see below).
2.2.2. Functionalization of silica particles Allyltrimethoxysilane or aminopropyltriethoxysilane was directly added into the nanoparticles dispersion. The amount of coupling agent was around ten times higher than the amount necessary to cover the inorganic surface with a monolayer (the theoretical amount for such a coverage being nominally 2 molecules nm2). After it was left to react overnight, the mixture was held at 80 8C for 1 h to promote covalent bonding of the organosilane to the surface of the silica nanoparticles. The choice of allyltrimethoxysilane and aminopropyltriethoxysilane was driven by the necessity to avoid the aggregation of the silica particles either in solution before their spreading at the air–water interface or just after this step. 2.2.3. Silica suspensions treatment In order to eliminate the remaining reagents, all the suspensions were dialyzed against water several times (for a small particle size) or submitted to several cycles of washing and centrifugation. The final concentration of the suspension was determined by measuring the mass of a dried extract and the measured value was always in agreement with the theoretical one (calculated assuming a complete conversion of TEOS into silica). 2.2.4. Silica particles size measurements Granulometry experiments were performed on a Malvern Mastersizer apparatus. 2.2.5. Formation of a 2D-array of particles A diluted suspension of functionalized silica particles in a 80%/20% (v/v) mixture of chloroform and ethanol was prepared according to a previously reported procedure [14]. After spreading on a pure water subphase (pH = 5.5), a stepwise compression of the 2D
Table 1 Experimental conditions corresponding to the synthesis of silica spheres with various diameters Reaction medium
Solution of TEOS
Volume of alcohol (mL)
Volume of ammonia (mL)
Volume of alcohol (mL)
Volume of TEOS (mL)
200 (EtOH) 100 (MeOH) 200 (EtOH)
15 20 20
0 20 (MeOH) 25 (EtOH)
5 20 25
a
TEOS was added at once.
Rate of addition (mL h1) a
20 8
Final particle size (nm)
220 360 1100
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
411
particulate film was carried out under continuous dried nitrogen flow, at room temperature (20 1 8C), until a surface pressure of ca. 6 mN m1, that was the pressure chosen for the transfer. 2.2.6. Colloidal crystal synthesis After compression, the Langmuir film was transferred onto hydrophilic glass slides or silicon wafers. The slides were immersed quickly in the subphase (downstroke speed: 10 cm min1) and then slowly pulled up out of the water (upstroke speed: 0.1 cm min1). In these optimized conditions, for all sizes of particles, the deposition on the substrate only occurred during the upstroke with a transfer ratio close to unity, what allowed us to transfer a monolayer of particles at each cycle. 2.2.7. Scanning electron microscopy SEM observations were performed with a JEOL JSM-840A scanning electron microscope operating at 10 kV. The specimens were carbon-coated prior to examination.
Fig. 1. p–A isotherms of functionalized silica particles of different sizes (from left to right: 220 nm amine, 360 nm amine, 680 nm vinyl and 1100 nm amine).
by SEM (see Fig. 3) and a small incertitude on the value of the spheres diameters determined by granulometry can explain the slight difference between experimental and theoretical values. 3.2. Langmuir–Blodgett films
2.2.8. UV-visible/near IR spectroscopy Near-infrared spectra were recorded on a MagnaIR Spectrometer 750 from Nicolet and UV-visible spectra with a Unicam UV 4 spectrophotometer.
3. Results and discussion 3.1. p–A isotherms Typical surface pressure (p)/area (A) isotherms corresponding to the compression of the silica particles films are shown in Fig. 1. The slope of the curves is extremely steep, indicating a low compressibility of the films. The areas corresponding at the collapse of the films and those extrapolated to p = 0 mN m1 are listed in Table 2. These values are in good agreement with those predicted by assuming that area occupied by one silica sphere in a close-packed hexagonal arrangement is equal to: pffiffiffi 3 D2 2 where D is its diameter. The presence of a small number of defects and holes which can be observed
The transfer of the particles films onto a solid substrate was done at a surface pressure of ca. 6 mN m1. As shown in Fig. 2, the visual appearance of the LB films testifies to their high crystalline quality and their uniform thickness at the centimeter scale. The samples exhibit a brilliant color due to Bragg diffraction of visible light. A systematic change of the color can be seen by modifying the orientation of the substrate. Tentative transfers at surface pressure values higher than 6 mN m1 led to poor quality LB films, due to the high rigidity of the Langmuir films. In Fig. 3 are presented SEM side views of colloidal crystals obtained through the transfer of 10 layers of silica Table 2 Experimental and calculated values of the area per particle of the particulate monolayer for silica spheres with different sizes Diameter of the silica spheres (nm)
Predicted area (mm2)
Area at the collapse (mm2)
Area extrapolated to p = 0 mN m1 (mm2)
220 360 680 1100
0.042 0.112 0.400 1.048
0.055 0.161 0.430 1.280
0.058 0.170 0.430 1.340
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S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
Fig. 2. Optical pictures showing the evolution of the colors diffracted by a colloidal crystal made of a single layer of silica particles (diameter D = 680 nm) as a function of the orientation of the substrate (here a glass slide).
particles with various sizes. The close packed structure extends uniformly over the samples, whatever their thickness is. Even if typical defects such as sphere vacancies and vertical cracks can be observed every 100 mm on average, the top surface of the crystals is relatively smooth and the number of
deposited layers matches perfectly with the predefined value. The optical properties of the crystals have also been studied. Fig. 4 shows the dependence of the transmission spectra of 10 layers colloidal crystals as a function of the size of the silica particles. The sharp
Fig. 3. Side views of colloidal crystals consisting of 10 layers of silica particles with different sizes and surface functions: (a) 220 nm amine; (b) 360 nm amine; (c) 680 nm vinyl; (d) 1100 nm amine.
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
413
Table 3 Comparison of the average values of the silica particles diameters (nm) estimated with several techniques Granulometry Bragg peak position SWA model
Fig. 4. Experimental (continuous line) and predicted (dotted line) visible-NIR transmission spectra of colloidal crystals consisting of 10 layers of silica particles with various diameters (from bottom to top: 220, 360, 680 and 1100 nm). For better clarity, curves were shifted vertically.
peaks which can be observed in each spectrum result from the first-order Bragg diffraction of light by the crystals. The diffraction peak positions obey Bragg’s law: mlm ¼ lB ¼ 2ne dh k l sin aB
(1)
where m is an integer (corresponding to the diffraction order), lB the Bragg diffracted wavelength, ne the effective refractive index of the crystal, dh k l the distance between two consecutive lattice planes with Miller indices (h, k, l) and aB is the Bragg angle. In our experimental conditions, the diffracted intensity is measured in the same direction as the incident beam, which is itself perpendicular to the surface of the crystal. Consequently, assuming that we have a f.c.c. lattice, we are in the condition of the Bragg diffraction angle (aB = 908) for the lattice planes with Miller indices (1, 1, 1). Modifying Eq. (1), it comes that the main peak corresponding to the first order of diffraction (m = 1) is obtained when:
220 230 230
370 364 360
680 688 690
1100 1195 1070
Therefore, the particles diameter can be calculated from the Bragg peak position. The results given in Table 3 are in a good agreement with the values determined by granulometry. A quantitative study of the optical properties of the colloidal crystals based on the scalar wave approximation theory [17,18] has also been performed. The solving of Maxwell equation for an electric field propagation in a periodic medium leads to expressions of the transmission rate which have been used to fit the experimental UV-visible-NIR transmission spectra. Results of the fitting procedure, carried out with D as only adjustable parameter, are shown in Fig. 4. A good agreement between experimental and simulated spectra is achieved. The values of D resulting from the simulation are listed in Table 3 and are in agreement with those calculated by other techniques.
4. Conclusion Using the Langmuir–Blodgett technique, we have engineered colloidal crystals with a well-controlled thickness made of silica spheres with diameters of 220–1100 nm. These materials exhibit diffraction properties in UV, visible or NIR wavelength ranges, depending on the size of the silica particles. We are currently extending our strategy to engineer colloidal crystals with a more complex structural organization, based on precursors with different natures and morphologies.
l ¼ lB ¼ 2ne d1 1 1 In the case of a f.c.c. lattice consisted of spheres of a diameter D, the value of d1 1 1 is given by: rffiffiffi 2 D d1 1 1 ¼ 3
Acknowledgments We thank Be´ atrice Agricole (CRPP, Pessac) and Elisabeth Sellier (CREMEM, Talence) for Langmuir– Blodgett and SEM experiments, respectively.
414
S. Reculusa, S. Ravaine / Applied Surface Science 246 (2005) 409–414
References [1] J.M. Weissman, H.B. Sunkara, A.S. Tse, S.A. Asher, Science 274 (1996) 959. [2] G. Pan, R. Kesavamoorthy, S.A. Asher, Phys. Rev. Lett. 78 (1997) 3860. [3] J.H. Holtz, S.A. Asher, Nature 389 (1997) 829. [4] W. Lee, S.A. Pruzinsky, P.V. Braun, Adv. Mater. 14 (2002) 271. [5] S.G. Romanov, N.P. Johnson, A.V. Fokin, V.Y. Butko, H.M. Yates, M.E. Pemble, C.M. Sotomayor Torres, Appl. Phys. Lett. 70 (1997) 2091. [6] M. Egen, R. Zentel, Chem. Mater. 14 (2002) 2176. [7] H. Miguez, F. Meseguer, C. Lopez, A. Blanco, J. Moya, J. Requena, A. Mifsud, V. Fornes, Adv. Mater. 10 (1998) 480. [8] P. Jiang, J.F. Bertone, K.S. Hwang, V.L. Colvin, Chem. Mater. 11 (1999) 2132.
[9] J. Texter, CR Chimie 6 (2003) 1425. [10] Y.-H. Ye, F. LeBlanc, A. Hache, V.V. Truong, Appl. Phys. Lett. 78 (2001) 52. [11] M. Campbell, D.N. Sharp, M.T. Harrison, R.G. Denning, A.J. Turberfield, Nature 404 (2000) 53. [12] H.-B. Sun, S. Matsuo, H. Misawa, Appl. Phys. Lett. 74 (1999) 786. [13] I. Divliansky, T.S. Mayer, K.S. Holliday, V.H. Crespi, Appl. Phys. Lett. 82 (2003) 1667. [14] S. Reculusa, S. Ravaine, Chem. Mater. 15 (2003) 598. [15] C.E. Reese, S.A. Asher, J. Colloid Interf. Sci. 248 (2002) 41. [16] W. Wang, B. Gu, L. Liang, W.A. Hamilton, J. Phys. Chem. B 107 (2003) 12113. [17] W.-K. Shung, Y.C. Tsai, Phys. Rev. B 48 (1993) 11265. [18] D.M. Mittleman, J.F. Bertone, P. Jiang, K.S. Hwang, V.L. Colvin, J. Chem. Phys. 111 (1999) 345.