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ISSN 19950780, Nanotechnologies in Russia, 2010, Vol. 5, Nos. 7–8, pp. 469–473. © Pleiades Publishing, Ltd., 2010. Original Russian Text © O.V. Rudenko, A.I. Korobov, B.A. Korshak, P.V. LebedevStepanov, S.P. Molchanov, M.V. Alfimov, 2010, published in Rossiiskie nanotekhnologii, 2010, Vol. 5, Nos. 7–8.

ARTICLES

SelfAssembly of ColloidalParticle Ensembles in an Acoustic Field O. V. Rudenko, A. I. Korobov, B. A. Korshak, P. V. LebedevStepanov, S. P. Molchanov, and M. V. Alfimov Photochemistry Center, Russian Academy of Sciences, ul. Novatorov 7a, Moscow, 119421 Russia email: [email protected] Received September 23, 2009

Abstract—This paper is devoted to experimental and theoretical studies of the formation of structured films from the ensembles of micro or nanoparticles in the drops of a colloidal solution placed on a support and subjected to acousticvibration effects. DOI: 10.1134/S1995078010070062

INTRODUCTION Arranged ensembles of micro and nanoparticles obtained by selfassembly from colloidal solutions are photoncrystaltype structures. They are used in opti cal devices, elements of chemosensors, as flexible pro tective layers for light diodes, etc. The selfassembly as a result of the solvent evapo ration occurs due to capillary forces, which shift the particles in the subsurface regions of the solution along with the reduction of its volume. The result of self assembly (the morphology of the solid phase) can be managed by setting the external parameters (pressure, temperature, and humidity) and the internal parame ters (the concentration of the solution, the support material and the particles, the type of solvent, and the shapes and sizes of the particles) of this process. A drop running dry on the support is an open dissi pative system, and, as the solvent evaporates [1], the processes of selforganization proceed along with the crystallization or precipitation of the dissolved sub stance, which results in the formation of ordered solidphase structures [2]. Studies of the dynamics of the drops which dry during time periods of from tens of hours to fractions of a second can be found [2–9]. For technological purposes, it is important to man age the process of nanoparticle arrangement. One such approach is structuring the support by the forma tion of a certain relief on its surface employing the methods of plasma etching and laser lithography. The typical sizes of the relief in the latter case are deter mined by the optical wavelength and usually are on the order of 1 μm. Another approach is the deposition of the first layer of the nanoparticles. In this process, the unevenness of the relief is associated with the type of packing and the sizes and shapes of the particles. The secondary layer is deposited on the surface of the first

one. The arrangement of the particles on it is deter mined by the relief of the primary layer and the extent of its attachment to the support; the secondary layer can cause some shift in the molecules in the first layer. The listed management approaches are not associ ated with the application of external fields to the sys tem and can be called ‘passive.’ Using a rotating sup port (spin coating and centrifugation) can be classified as the active method. This method makes it possible to use the inertia force to manufacture more even and uniform (in terms of thickness) films consisting of par ticles. The idea of using acoustic fields is the further development of instrumentation for the managed self assembly [10, 11]. Though the acoustic field is exten sively used for solution structuring, using an acoustic field for the management of the selfassembly in a drop of colloidal solution is a new approach [12, 13]. The following properties make the use of an acous tic field reasonable: (i) It is possible to intensify the selfassembly pro cess due to the vibration impact on the particles and the support. As a result of the agitation of the drying solution, the mobility of the nanoparticles and the probability that they will pack more densely increase. (ii) It is possible to create a standing acoustic wave (a periodic pressure field). As a result, the ensemble divides into groups with either a depleted or enriched concentration of particles. (iii) A directed transport can be implemented; i.e. the particles can be moved from one region of the sam ple to another. (iv) The wavelength and the intensity of the acous tic waves can be altered in a wide range in order to optimize the impact mode.

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drop on a solid surface (occupying the semispace z > 0) with a planar liquid layer (laying in the range –h < z < 0). The force (1) in twodimension regions (x, z), where the axis x is directed along the solid sur face, is expressed through the potential U: 2

Fig. 1. A drop of solution subjected to an acoustic field: (1) the surface of the drop, (2) the piezoelements respon sible for the acoustic field, and (3) the standing acoustic wave.

The following forces affect a particle in a colloidal solution [3]: the resultant force of the conservative forces from other particles; the force of interaction between the particle and the support; and the capillary force, which is associated with the interaction with the solvent and depends on the viscosity and the ratio of the densities of the particle and the solution. One more force which is associated with the acoustic impact will be discussed in more detail. The impact of the acoustic field is explained by Fig. 1. The piezoelements create counterrunning Ray leigh waves which form a standing wave. Oscillating (usually at the frequencies 10–100 MHz) pressure and vibration speed fields with fixed positions of the nodes and antinodes appear in the drop. The average acous tic pressure during the oscillation period is zero; there fore, slow movements and grouping of the particles occur under the impact of the radiation forces [14, 15], which are quadratic in the acoustic variables: 2 ∂ ε F i =  ⎛   〈 p' 〉 + ρ 〈 u i u k〉⎞ . (1) 2 ⎝ ⎠ ∂x k c ρ Here p', u are the acoustic fields of pressure and speed and c, ρ, ε are the sound speed, density, and the non linearity of the medium. The angle brackets imply averaging. To make the idea clear, let us replace a real (a)

F = – ∇U,

k U  = ( ε – 1 ) 20 cos 2kx cos 2r ( z + h ) A r

(2) 2 2 2 ⎛ k 0⎞ ( ε – 1 )k 0 + k +   cos 2r ( z + h ) – ⎜ 1 + ( ε – 1 ) 2 ⎟ cos 2kx. 2 ⎝ r r ⎠ Obviously, the potential relief is periodical along the support and the period is x∗ = π/k = cef/2f, which is twice as small as the wavelength. The designations in formula (2) are 2

2

2

r = k0 – k ,

k 0 = ω/c,

k = ω/c ef ,

ω = 2πf,

and cef is the effective speed of the propagation of the coupled acoustic Rayleigh mode, which is determined from the corresponding dispersion equation [16]. A is a constant and f is the frequency of the wave. It can be demonstrated [13] that, if the densities of the particle and the medium are close, the speed of the particle and the medium are nearly the same and the particle is hardly moved towards the liquid. Since the average movement of the liquid as a result of the acoustic impact is zero, the particles do not move either. The type of movement in the field of radiation forces (2) is more complicated. In addition, the acous tic impact affects the features of the hydrodynamic flows which appear in the drop; this can result in the development of convection and even turbulent flow in relatively large drops. (b)

Fig. 2. (a) Ca2CO3 powder: the drop diameter is 7 mm, the solvent is water, and the concentration of the solution is 4 wt %. (b) The 180 nm polystyrene particles: the drop diameter is 2.5–3 mm, the solvent is water, and the initial concentration is 4%. NANOTECHNOLOGIES IN RUSSIA

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According to the physical model, the greatest impact of the acoustic field on the particle ensemble should take place when the properties of the particles (first and foremost the density) differ significantly from the corresponding properties of the liquid. Indeed, the greatest impact of the acoustic field was observed for the particles, the density of which was sig nificantly different from the density of the solvent (water). The Ca2CO3 powder yielded the clearest results (Fig. 2a). It is well adsorbed on the support, where the theory predicts the highest intensity of the acoustic field should be. On the other hand, the density of polystyrene par ticles is 1.05 g/cm3, which is nearly the same with water. Therefore, the results of the impact of the acoustic field on such a system are hardly noticeable (Fig. 2b). The density of silica particles is nearly twice the density of water, although the presence of pores in these particles somewhat reduces the effective density. Nevertheless, the formations, the shape of which reproduces the intensity distribution in the standing wave, are easily noticeable on the edges of the drop (Fig. 3). The experimentally observed period of the structure on the support was twice as low as the acous tic wavelength; this effect was quadratic in amplitude. For the theoretical description of the system, two problems should be solved: (i) The evaporation of the drop or a film of the col loidal solution on a planar support. The drop of the considered sizes has the shape of a sphere segment, the parameters of which are determined by the contact angle between the support and the solution. The pro

Fig. 3. 6 µm SiO2 particles: the drop diameter is 2.5–3 mm and the solvent is water. The initial concentration of the solution is 4 wt %.

EXPERIMENTAL An experimental apparatus operating according to the scheme in Fig. 1 was used. The drops of the solu tion were placed on a lithium niobate support with an initial diameter of about 5 mm. The material of the nanoparticles was polystyrene or silica (SiO2). The density of polystyrene particles was about 1.05 g/cm3, and the density of silica particles was about 2 g/cm3. The powder of Ca2CO3 was studied as well; it con tained particles of a different dispersion (1–3 μm). Aqueous solutions were used for the experiment. The frequency of the acoustic oscillations was 15 MHz, the wavelength was 240 μm, the electrical power was about 0.64 W, and losses were about 10 dB.

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Fig. 4. Visualization of the distribution of 300 particles on the support after numerical experiments in the absence of an acoustic field (the left side) and in the presence of an acoustic field (the right side). NANOTECHNOLOGIES IN RUSSIA

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cess of the solvent evaporation is associated with the diffusion of the solvent vapors from the surface of the drop into the atmosphere. (ii) The movement of the nanoparticles in the bulk of the evaporating drop of the solution on the surface under the impact of the acoustic field. In order to solve this problem, methods of hydrodynamics and colloi dal chemistry were used to describe the nanoparticle interaction, in particular, the Derjaguin–Landau– Verwey–Overbeek (DLVO) theory, as well as the com puter methods of particledissipative dynamics [3, 17] (an analogue of molecular dynamics, which considers nanoparticles instead of molecules; the nanoparticles move in a continuous medium of the solvent which is characterized by a medium density, viscosity, and dielectric permittivity). A computer program was developed on the basis of the indicated physical model. The program calculated the multidimensional path of a system (an ensemble of particles) from the initial to the final state (the process and the result of the self assembly): r i = r i (t), i = 1, 2, …, N. At t = tmax, we obtain the resultant distribution of the particles in the support. The computation time of the system evolution from the initial to the final state strongly depends on the amount of the particles in the system. Therefore, while accounting for the abilities of conventional per sonal computers with a processor speed of 1–2 GHz and an admissible computation time of about 1 h, the proposed model makes it possible to consider about a hundred particles. The main features of the acoustic force impact on microdrops containing a small num ber of particles are reproduced. Figure 4 (the left side) demonstrates the result of a computation for 300 1μm silica particles obtained from a drop with an initial volume of 40 pl without subjection to the acoustic field. The visualization was implemented using VMD1.8 software. The diameter of the ensemble was 100 μm. Figure 4 (the right side) shows the ensemble in the drop, drying up under the managing impact of the acoustic field. The result of a simulation of the acous ticfield impact on the selfassembly is as follows: two domains appear which are situated in the minimums of acoustic pressure. CONCLUSIONS An experimental opportunity for the acoustic man agement of the selfassembly of a colloidalparticle ensemble has been demonstrated. The selfassembly effect can be managed by changing the configuration and power of the acoustic wave and altering the prop erties of the particles and the solvent. The physical model describes the major properties of the resultant structures: e.g., the space period and the dependence of the intensity of the acoustic impact on the particles

for different ratios of the densities of the particles and the solvent. As the analysis of the literature has revealed (see, for example, [10, 11] and their references), the state ment of the problem and the results of the present study are novel and do not have direct analogues. The acoustic field is being used for the synthesis of nano particles, but its application for managing the self assembly of nanoparticle assembly is a novel approach. Its closest analogues are polymer structuring on the support with a standing acoustic wave [11]. ACKNOWLEDGMENTS The authors are grateful to N.I. Odin, V.A. Gusev, M.Yu. Izosimov, Yu.N. Makov, and N.A. Chernyshov for their contribution to the project. This study was financially supported by the Federal Agency for Science and Innovation (state contract no. 02.513.12.3028). REFERENCES 1. G. Nicolis and I. Prigogine, SelfOrganization in Non equilibrium Systems: From Dissipative Structures to Ordering through Fluctuations (Wiley, New York, 1977; Mir, Moscow, 1979). 2. L. V. Andreeva, D. A. Ivanov, D. S. Ionov, A. V. Kosh kin, P. V. LebedevStepanov, O. Yu. Rybakov, A. S. Sinitsky, A. N. Petrov, and M. V. Alfimov, “Inves tigations of Crystallization of Solutions in Microdrop lets on an Affymetrix GMS 417 Arrayer Device,” Prib. Tekh. Eksp., No. 6, 127 (2006) [Instrum. Exp. Tech. 49 (6), 860 (2006)]. 3. L. V. Andreeva, A. V. Koshkin, P. V. LebedevStepanov, A. N. Petrov, and M. V. Alfimov, “Driving Forces of the Solute SelfOrganization in an Evaporating Liquid Microdroplet,” Colloids Surf., A 300, 300 (2007). 4. Yu. Yu. Tarasevich, “Mechanisms and Models of the Dehydration SelfOrganization in Biological Fluids,” Usp. Fiz. Nauk 174 (7), 779 (2004) [Phys.–Usp. 47 (7), 717 (2004)]. 5. H. Hu and R. G. Larson, Analysis of the Microfluid Flow in an Evaporating Sessile Droplet, Langmuir 21, 3972 (2005). 6. H. Hu and R. G. Larson, Analysis of the Effect of Marangoni Stresses on the Microflow in an Evaporat ing Sessile Droplet, Langmuir 21, 3972 (2005). 7. R. Deegan, “Pattern Formation in Drying Drops,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Inter discip. Top. 61, 475 (2000). 8. R. Deegan, O. Bakajin, T. Dupont, G. Huber, S. Nagel, and T. Witten, “Contact Line Deposits in an Evaporat ing Drop,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 62, 756 (2000). 9. M. V. Alfimov, R. M. Kadushnikov, N. A. Shturkin, V. M. Alievskii, and P. V. LebedevStepanov, “Imitated Modeling of the Processes of SelfOrganization of Nanoparticles,” Ross. Nanotekhnol. 1 (1–2), 127 (2006).

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SELFASSEMBLY OF COLLOIDALPARTICLE ENSEMBLES 10. A. Alvarez, J. Friend, and L. Y. Yeo, “Rapid Generation of Protein Aerosols and Nanoparticles via Surface Acoustic Wave Atomization,” Nanotechnology 19, 455 103 (2008). 11. A. Alvarez, J. Friend, and L. Y. Yeo, “Surface Vibration Induced Spatial Ordering of Periodic Polymer Patterns on a Substrate,” Langmuir 24, 10 629 (2008). 12. P. V. LebedevStepanov and S. A. Rybak, “Sound Absorption by a Solution of Nanoparticles,” Akust. Zh. 55 (3), 326 (2009) [Acoust. Phys. 55 (3), 329 (2009)]. 13. P. V. LebedevStepanov and O. V. Rudenko, “Sound Attenuation in a Liquid Containing Suspended Parti cles of Micron and Nanometer Dimensions,” Akust. Zh. 55 (6), 706 (2009) [Acoust. Phys. 55 (6), 329 (2009)].

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14. O. V. Rudenko and S. I. Soluyan, Theoretical Founda tions of Nonlinear Acoustics (Nauka, Moscow, 1975; Consultants Bureau, New York, 1977). 15. Z. A. Gol’dberg, “Acoustic Radiation Pressure,” in HighIntensity Ultrasonic Fields, Ed. by L. D. Rozen berg (Nauka, Moscow, 1968; Plenum, New York, 1971). 16. I. A. Viktorov, Surface Acoustic Waves in Solids (Nauka, Moscow, 1981) [in Russian]. 17. P. J. Hoogerbrugge and J. M. V. A. Koelman, “Simulat ing Microscopic Hydrodynamic Phenomena with Dis sipative Particle Dynamics,” Europhys. Lett. 19 (3), 155 (1992).

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