ЖУРНАЛ ФИЗИЧЕСКОЙ ХИМИИ, 2010, том 84, № 7, с. 1381-1382
КРАТКИЕ СООБЩЕНИЯ =
УДК 541.18
PREDICTION OF SILVER NANOPARTICLES SIZE SYNTHESIZED
IN MICROEMULSION SYSTEM
© 2010 г. A. Salabat
Chemistry Department, Arak University Iran E-mail: a-salabat@araku.ac.ir Received July 7, 2009
Abstract — Nanoparticle synthesis within the aqueous cores of water-in-oil reverse micelle systems is a viable method, which allows control over the size and shape of the particles. The intermicellar exchange rate is affected by the bulk solvent type, the contents dissolved within the core, and the size of the reverse micelle or the water content, referred to as the W value, where W is the molar ratio of the water to surfactant concentrations. In this study a soft sphere model was used to predict ultimate silver nanoparticle particle sizes obtained in AOT reverse micelle. In this model a total interaction energy is implemented to represent the attractive van der Waals forces acting between the metallic particles and the repulsive osmotic and elastic forces, which result from the surfactant tail—tail and solvent—tail interactions responsible for the steric stabilization of the metallic particles within the microemulsion. Result from the model accurately predicts the ultimate silver nanoparticle sizes.
INTRODUCTION
Nanoparticles, which are defined as particles with diameters of about 100 nm or less, are technologically significant, since they are utilized to fabricate structures, coatings, and devices that have novel and useful properties due to the very small dimensions of their particulate constituents. Nanoparticle synthesis in mi-croemulsions has been a hot research topic since the early 1980s, when the first colloidal solutions of platinum, palladium and rhodium metal nanoparticles were prepared [1]. The factors controlling the ultimate size and shape of particles grown within the reverse micelles remain an area of significant interest [2—5]. The work by Shah et al. [6] proposed a model that takes a soft sphere approach to balance the attractive van der Waals force with steric repulsive forces to determine the total interaction energy. This model was to study agglomeration stability of copper [7] and gold [8] nanoparticles in reverse micelle systems. To model the metallic nanoparticle synthesis within the reverse micellar system, the soft sphere approach was modeled as a spherical metallic nanoparticle surrounded by an anionic surfactant, Sodium ¿/s(2-ethylhexyl) sulfosuccinate (AOT), monolayer with the alkyl tails interacting with the bulk solvent. In this work, a similar theoretical approach is used to predict the ultimate silver nanoparticle size that can be synthesized and stabilized in the AOT reverse micelle system.
MODEL
In order to predict particles size, we studied the agglomeration stability of silver nanoparticles inside reverse micelles by calculating the total interaction ener-
gy O total between pairs of particles as a function of particle size. A soft sphere model was used in which the reverse micelle was replaced by a silver nanoparticle with an adsorbed monolayer of AOT suspended in hexane. In this way, the effect of water inside the reverse micelle was neglected as a first approximation. It is believed that after particle formation the water in the micelle mainly hydrates the surfactant head groups.
The total interaction energy O total between two reverse micelles containing silver nanoparticles can be calculated from the sum of the interactions which govern the stability of the nanoparticles. The van der Waals interaction is the dominant attraction, and is dependent on the particle radius R, the center to center separation distance d, and the Hamaker constant A131 which plays an important role in the description of the attraction energy between particles. Subscript 1 in the Hamaker constant refers to particles of the same material, separated by a continuous medium, represented through subscript 3. Under our conditions the Hamaker constant will always be positive and the van der Waals interaction (O vdW) is given by:
Ф
vdW
ЗШ 6
2R
2
_+ 2R2 + ln [ d2 - 4R2
d2 - 4R2 d2 ПI d2 у
(1)
iii2 - <) \
(2)
431 = (A
where R and d are particles radius and center to center separation, respectively; the term A11 represents the silver—silver nanoparticle interaction, taken here as 3.1 x 10-19 J, and A33 corresponds to the solvent interaction, which for hexane we take as 4.78 x 10-20 J.
Another important effect that contributes to the total interaction energy is the repulsive forces due to
1382
SALABAT
kT
-4
\
v 1 \
2 \
\
3
1 2 3
d, nm
Contributions to the total interaction energy model for silver nanoparticles coated with AOT dispersed in hexane:
(1) ®osm; (2) ®total; (3) OvdW; dis the separation distance.
overlapping of the surfactant tails covering the silver nanoparticles, and their interactions with the surrounding solvent molecules. These interactions can be modeled as an osmotic repulsion O osm, which depends on various thermodynamic properties of the system, such as the solubility of the surfactant molecules in the organic solvent, and the reaction temperature:
Oosm = ^^6ZI1 - x)(l -h)\ l < h < 2l. (3)
4 nRkT ф2 Д
v solv
Here k is Boltzmann's constant, vsolv is the molecular volume of the hexane, ^ is the volume fraction occupied by the AOT molecule, x is the Flory—Huggins interaction parameter, l is the chain length of the AOT, and h represents the particle—particle separation distance. The volume fraction and Flory—Huggins parameter may be calculated from:
3 R 2l
X =
$ = 0.9 -R-3 , (4)
+ l)3 -R3J
(83 -52)2, (5)
2 R. (6)
In equation (5), v 3 represents the molar volume of the hexane, R' is the gas constant, and 8/ are the Hilde-
V3
R T
h = d
brand solubility parameters, in which 83 corresponds to the hexane solubility, and 82 is related to the AOT solubility, which when calculated according to group contribution methods is equal to 12.26 MPa0 5 [7]. The total interaction is the sum of the van der Waals and osmotic contributions, which we calculate as a function of particle—particle separation distance and the size of the particles.
RESULTS AND DISCUSSION
Figure exhibits the results of the total interaction energy calculations for silver nanoparticles coated with AOT surfactant as a function of the separation distance and particle size in hexane. A local minimum is observed at 1.7 nm separation distance. The presence of such local minimum could lead to reversible flocculation of growing particles during synthesis. Therefore the change in interaction energy with increasing particle size was considered and compared the depth of the local energy well to — 1.5kT, for which thermal energy would not prevent agglomeration [9]. The model predicts silver particles diameter of 3.8 nm at lvalue of 10. The experimental particle sizes are reported as 3.9 nm [10]. Comparison of the experimental particle sizes and the model predictions shows good agreement in this system.
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ЖУРНАЛ ФИЗИЧЕСКОЙ ХИМИИ том 84 № 7 2010
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