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Intrinsically stable dispersions of silicon nanoparticles
Journal of Colloid and Interface Science 325 (2008) 173–178
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Intrinsically stable dispersions of silicon nanoparticles A. Reindl, W. Peukert ∗ Institute of Particle Technology, Friedrich-Alexander University, Cauerstr. 4, 91058 Erlangen, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 22 January 2008 Accepted 22 May 2008 Available online 28 May 2008
Stable suspensions of silicon nanoparticles (SiNP) were fabricated by dispersion in 1-butanol as well as ethanol without the application of an additive. In order to achieve an in-depth insight into the stabilizing mechanism, the particle–particle interactions need to be considered. In this respect the total interaction energy of the silicon nanoparticles in 1-butanol and ethanol was calculated for three model systems according to the DLVO theory: (1) two solid silicon spheres, (2) two spheres with a silicon core and an amorphous silicon dioxide shell, and (3) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules. The results of the calculations are evaluated and discussed with regard to experimental data obtained by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), high resolution transmission electron microscopy (HRTEM), and zeta potential measurements. © 2008 Elsevier Inc. All rights reserved.
Keywords: Silicon nanoparticles Stabilizing Dispersing DLVO theory Core–shell
1. Introduction Nanoparticles are of growing interest in many areas of the chemical, pharmaceutical, ceramic, and microelectronic industry from the scientific as well as the technological point of view. Applications range from pigments, nanocomposites, drug delivery and ceramic materials to the fabrication of thin semi-conductive films based on various printing technologies. Therefore a high industrial demand exists on stable suspensions (with regard to aggregation) of nanoparticles in aqueous as well as non-aqueous media. Besides the direct synthesis by chemical methods, wet grinding and dispersing are suitable methods for the production of nanoparticulate systems, since a high specific energy input is accomplished [1]. However, the stability of the dispersions is strongly influenced by particle–particle interactions. Particles in the order of 1 μm and below feature a high mobility due to Brownian diffusion, which leads to a high collision frequency between the particles. Nonstabilized nanoparticles usually tend to aggregate easily, especially when dispersed in an organic medium. Therefore the particle– particle interactions need to be understood in detail in order to tailor the properties of the nanoparticulate system according to specific needs. In this case stable suspensions of silicon nanoparticles (SiNP) in an organic solvent are required for the manufacture of electronic/optoelectronic devices using printing technologies. As reported recently [2,3], intrinsically stable suspensions of SiNP in 1-butanol were obtained by dispersing in a stirred media mill
*
Corresponding author. Fax: +49 9131 8529402. E-mail address: [email protected] (W. Peukert).
0021-9797/$ – see front matter doi:10.1016/j.jcis.2008.05.042
©
2008 Elsevier Inc. All rights reserved.
without the application of an additive. This work focuses on determining the particle–particle interactions of SiNP in 1-butanol and ethanol to achieve an in-depth insight into the stabilizing mechanism of the particulate system. In this regard the total interaction energy of the SiNP was calculated via DLVO theory for different models including core–shell approaches. The approach of describing colloidal stability with core–shell models has been reported in literature before [4–6]. The results of the calculations of this work are evaluated and discussed with regard to experimental data obtained by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), high resolution transmission electron microscopy (HRTEM) and zeta potential measurements. In literature a suspension is typically considered as stable [7,8], if the total interaction energy develops an energy barrier larger than 15kT . However, this approach explains the observed stability of the SiNP only for a limited range of particle sizes. The present work shows that one has to consider not only the height of the energy barrier but also the depth of the primary minimum of the total interaction energy, to achieve a detailed understanding of the particle interactions and the associated suspension stability. 2. Experimental 2.1. Materials Ethanol (absolute) and 1-butanol (p.a.) purchased from Aldrich and used as received. Silicon nanoparticles (SiNP) with a primary particle size of approximately 100 nm were obtained from Evonik Degussa GmbH (Evonik). Suspensions of 20 wt% SiNP in 1-butanol and in ethanol (volume fraction 0.080 and 0.078, respectively)
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were dispersed for 6 h using a stirred media mill. A detailed description of the dispersing procedure is reported elsewhere [2,3]. 2.2. Transmission electron microscopy (TEM) A suspension of SiNP was placed on an ultra thin carbon film on a 400 mesh Cu-grid and then dried in air. The HRTEM images were obtained using a Philips CM 300 UltraTwin microscope at an acceleration voltage of 300 kV in the bright-field mode. 2.3. Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) The DRIFT spectra of the SiNP were recorded on a Varian FTS 3100 FTIR spectrometer equipped with a Pike Technologies EasiDiff accessory. 2.4. Zeta potential measurements The zeta potentials were determined on a Malvern Zetasizer 3000 DTS 5300 by laser Doppler electrophoresis. 3. Results and discussion
Table 1 Applied Hamaker constants Material
A 11 ( J × 10−20 )
A 11 (kT ) at 293.2 K
Ethanol Butanol Silicon Amorphous SiO2
4.24 4.99 20.60 6.28
10.46 12.33 50.89 15.51
and n is the refractive index [13]. Equation [3] usually applies to what are normally referred to as dielectric or non-conducting materials [11] and was therefore used for calculating A 11 of 1-butanol and ethanol. The calculations of A 11 of silicon and amorphous silicon dioxide were based on the dielectric functions for a large energy range instead of the relative dielectric constants for more accurate approximation [14]. The calculated Hamaker constants for all involved materials are listed in Table 1. An expression for the Hamaker constant A 131 , i.e., for the situation of two particles suspended in a liquid, is derived by assuming that the interaction constant between the two different materials equals approximately the geometric mean of the interaction constants of the individual materials [11]. Therefore A 131 is given by [11] A 13 ≈
3.1. Theoretical approach
A 11 A 33 ,
(4)
followed by As mentioned before stable suspensions (with regard to aggregation) of SiNP in 1-butanol and ethanol were obtained by dispersing in a stirred media mill [2,3] without the use of any additives. The high stability of SiNP in 1-butanol and ethanol has been predicted theoretically and confirmed experimentally by Bleier [9]. However, only attractive forces were considered thereby and the calculated Hamaker constants differ noticeably from other literature values. In order to achieve a more detailed understanding of the stability of SiNP in 1-butanol and ethanol the total interaction energy of the SiNP was estimated according to the DLVO theory [7,10] in this work. The total interaction energy E T results from summation of the van der Waals interaction E vdW , electrostatic repulsion E El , and the Born repulsion E B E T = E vdW + E El + E B .
(1)
For calculations, which explain the stability of the SiNP with regard to the height of the formed energy barrier of the total interaction energy, the Born repulsion can be neglected. For consideration of the primary minimum of the total interaction energy the Born repulsion, approximated by a hard sphere potential at the minimal contact distance of 0.165 nm [11], was included in the calculations. The non-retarded van der Waals interaction E vdW of two solid spherical particles of radii R 1 and R 2 at a distance H apart is given by [12] E vdW = −
A
+ ln
2R 1 R 2 2( R 1 + R 2 ) H + H 2
6
+
2R 1 R 2 4R 1 R 2 + 2( R 1 + R 2 ) H + H 2
2( R 1 + R 2 ) H + H 2
,
4R 1 R 2 + 2( R 1 + R 2 ) H + H 2
(2)
where A is the Hamaker constant. For the “symmetric case” of two identical phases 1 interacting across vacuum, one can infer the Hamaker constant A 11 via [11] A 11 =
3 4
kT
ε1 − 1 ε1 + 1
2 +
3hνe (n21 − 1)2
√
16 2 (n21 + 1)3/2
,
(3)
where k is the Boltzmann constant, ε is the static dielectric constant [13], h is the Planck constant, νe is the main electronic absorption frequency in the UV typically around 3 × 1015 s−1 [11]
A 131 ≈ A 11 + A 33 − 2 A 13 .
(5)
For media 1 and 2 interacting across medium 3 the Hamaker constant A 132 can be written as [11] A 132 ≈
A 11 −
A 33
A 22 −
A 33 .
(6)
The electrostatic repulsion E El between two spherical particles can be estimated by using [8] E El =
a 32πεε0 ( R T )2
υ2
F2
γ 2 e −κ H ,
(7)
with γ = (e z/2 − 1)/(e z/2 + 1) and z = υ F ψ0 / R T , where υ is the valency, R is the gas constant, F is the Faraday constant, and ψ0 is the surface potential [8]. The surface potential ψ0 was substituted by the zeta-potential ζ determined by the means of electrophoresis, i.e., −46.6 mV for SiNP in 1-butanol and −40.0 mV for SiNP in ethanol. κ is the Debye–Hückel parameter expressed [8]
κ2 =
2F 2
εε0 R T
I,
(8)
where I is the ionic strength. The Debye–Hückel parameter κ has the dimension of a reciprocal length. The quantity 1/κ is related to the thickness of the diffuse layer surrounding the particles. Applying the formulas above the total interaction energy E T was calculated for three model systems depicted in Fig. 1: (a) two solid silicon spheres (solid sphere model), (b) two spheres with a silicon core and an amorphous silicon dioxide shell (core–shell model), and (c) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules (core–shell adsorbate model). For the calculations an overall sphere diameter x of 100 nm was assumed, which is roughly the primary particle diameter of the SiNP used for the dispersing experiments. The thickness of the shell of amorphous silicon dioxide d was estimated being 4 nm, whereas the thickness of the adsorbate layer σ was estimated being equal to the Lennard–Jones diameter of one molecule of 1-butanol/ethanol, i.e., 0.527 and 0.437 nm [15,16], respectively. The van der Waals interaction with regard to the solid sphere model was determined for two silicon spheres (radius = x/2) by a
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175
Fig. 2. Total interaction energy E T of SiNP (100 nm) in 1-butanol at I = 1 × 10−4 mol/L for the three different model systems.
E vdW (shell1 , shell2 )| H =a = E vdW (sphere1 , sphere2 )| H =a
− E vdW (sphere1 , core2 )| H =a+d − E vdW (sphere2 , core1 )| H =a+d + E vdW (core1 , core2 )| H =a+2d .
(11)
The Hamaker constants necessary to calculate the individual van der Waals interactions were determined by Eq. (6) and adapted according to the interacting materials, i.e., Si–Si, Si–SiO2 , or Si–SiO2 . The van der Waals interaction of the adsorbate layer in the core–shell adsorbate model in Fig. 1c does not need to be considered separately because the Hamaker constant of two adsorbate layers across the solvent medium equals zero. Therefore the adsorbate layer merely functions as a spacer. For the calculation of the total interaction energy of two SiNP using the core–shell adsorbate model the corresponding radii apparent in Fig. 1c were applied. The van der Waals interaction for this case can be expressed as [17,18] Fig. 1. Schematic representation of the model systems for DLVO calculations: (a) solid sphere model, (b) core–shell model, and (c) core–shell adsorbate model.
E vdW (sphere1 , sphere2 )| H =a+2σ = E vdW (shell1 , shell2 )| H =a+2σ
+ E vdW (core1 , core2 )| H =a+2d+2σ distance H apart according to Eq. (2). For the core–shell model the van der Waals interaction can be written as [17,18] E vdW (sphere1 , sphere2 )| H =a = E vdW (shell1 , shell2 )| H =a
+ E vdW (core1 , core2 )| H =a+2d + E vdW (core1 , shell2 )| H =a+d + E vdW (core2 , shell1 )| H =a+d ,
(9)
where E vdW (x, y ) is the van der Waals interaction, assuming additivity, between the geometrical objects x and y [17,18], subjected to the geometrical conditions of Fig. 1b. E vdW (core1 , core2 ) is a function, which describes the van der Waals interaction energy between the core of sphere 1 (radius = x/2 − d) and the core of sphere 2 (radius = x/2 − d) by the distance H = a + 2d apart. E vdW (core1 , shell2 ) is a function, which describes the van der Waals interaction energy between the core of sphere 1 (radius = x/2 − d) and the shell of sphere 2 (outer radius = x/2, inner radius = x/2 − d) by the distance H = a + d apart, expressed as [17,18] E vdW (core1 , shell2 )| H =a+d = E vdW (core1 , sphere2 )| H =a+d
− E vdW (core1 , core2 )| H =a+2d .
(10)
Obviously the same expression can be used for the case that indexes 1 and 2 are reversed. Substituting Eq. (10) into Eq. (9) and by rearranging one obtains the function E vdW (shell1 , shell2 ), which describes the van der Waals interaction energy between shell 1 and shell 2 by the distance H = a apart. Accordingly, one can write [17,18]
+ E vdW (core1 , shell2 )| H =a+d+2σ + E vdW (core2 , shell1 )| H =a+d+2σ .
(12)
In literature a suspension is typically considered as stable [7,8], if the total interaction energy develops an energy barrier larger than 15kT , as mentioned in the introductory part of this work. The height of the energy barrier E T can be determined by
E T = E max − E md ,
(13)
where E max is the maximum of the total interaction energy and E md is the total interaction energy at the mean separation distance of the particles in suspension (derived by considering the particle in a unit cell with respect to the applied volume fraction). The mean separation distances for a 20 wt% suspension of SiNP (100 nm) in ethanol and 1-butanol, as used for the dispersing experiments, are 83.48 and 81.96 nm, respectively. In Fig. 2 the total interaction energy E T at 20 ◦ C of SiNP (100 nm) in 1-butanol is exemplarily depicted for an ionic strength I = 1 × 10−4 mol/L for the three different model systems. Obviously an energy barrier of E T > 15kT , indicating a stable suspension, was only found for the core–shell model and the core–shell adsorbate model. Since the exact ionic strength I of the SiNP suspensions is difficult to determine, the total interaction energy was calculated for I ranging from 1 × 10−3 to 1 × 10−5 mol/L. The resulting total interaction energies for SiNP in 1-butanol at room temperature are exemplarily shown in Fig. 3. The calculations for SiNP in 1-butanol as well as in ethanol indicated a sufficiently high energy barrier of E T > 15kT , only if a core–shell model or a core–shell adsorbate model is assumed. The difference in E T between the solid sphere
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Fig. 3. Energy barrier E T of SiNP (100 nm) in 1-butanol for the three different model systems.
Fig. 4. Energy barrier E T of SiNP (100 nm) in 1-butanol as a function of the thickness of the silicon dioxide shell.
model and the core–shell models is most significant for high ionic strengths. But even for an ionic strength as low as 1 × 10−5 mol/L the core–shell models indicated an energy barriers E T > 15kT . Therefore a very small amount of ions resulting from contamination or attrition is capable of stabilizing the SiNP and one can expect to receive intrinsically stable suspensions when dispersing SiNP in 1-butanol or ethanol. Furthermore Fig. 3 indicates that the most significant gain regarding the energy barrier is obtained by assuming the presence of a 4 nm amorphous silicon dioxide shell. Hence, the variation of the thickness of the amorphous dioxide shell was also considered in this work. In Fig. 4 the energy barrier E T is exemplarily depicted for SiNP in 1-butanol at an ionic strength of 10−4 mol/L. The calculations revealed, when assuming the core–shell model a thickness of the amorphous silicon dioxide shell of 2.3 nm is expected to be sufficient in stabilizing the SiNP, while assuming the core–shell adsorbate model a thickness as small as 1.6 nm is expected to be sufficient. Assuming the core–shell adsorbate model the total interaction energy develops an energy barrier larger than 15kT for particles with a diameter larger than 80 nm. Hence, the intrinsic stability found during the dispersion of SiNP with a primary particle size of 100 nm in 1-butanol as well as ethanol is manifested by the energy barriers calculated with the core–shell adsorbate model. For SiNP smaller than 80 nm the calculated height of the energy barrier is significantly smaller than 15kT , e.g., for SiNP with a diameter of 20 nm energy barriers less than 5kT were estimated even when assuming a core–shell adsorbate model. However, dispersing experiments indicated intrinsically stable suspensions of SiNP in range of 20 nm. Therefore solely considering the height of the energy barrier explains the found intrinsic stability only for a limited size range. In Fig. 5 the total interaction energy of SiNP (20 nm) in 1-butanol with an oxide thickness of 2 nm is ex-
Fig. 5. Total interaction energy E T of SiNP (20 nm) in 1-butanol at I = 1 × 10−4 mol/L for the solid sphere model and the core–shell model. The oxide thickness for the core–shell model was set at 2 nm.
emplarily depicted for the solid sphere model and the core–shell model. The solid sphere model indicates a primary minimum of the total interaction energy of −53kT at the minimal contact distance of 0.165 nm [11], which implies favored aggregation of the particles. The core–shell model on the other hand indicates a primary minimum at around 3kT at the minimal contact distance of 0.165, which suggests that no aggregation occurs. The total interaction energy calculated by the core–shell adsorbate model is not depicted in Fig. 5, because the progression is overlapping strongly with the one calculated for the core–shell model. However, assuming the core–shell adsorbate model no minimum is formed at the distance of 0.165 nm, since the strongly attached solvent molecules at the SiNP surface function as a spacer and inhibit a close contact and subsequently aggregation of the particles. In conclusion the core–shell model as well as the core–shell adsorbate model is able to explain the intrinsic stability of SiNP in 1-butanol and ethanol, even at the lower nanometer range, if both the energy barrier and the primary minimum of the total interaction energy are considered. Furthermore the calculations indicated that the presence of an oxide shell plays the most important role with regard to the stability of the SiNP. The refractive index and consequently the Hamaker constant of the oxide are more similar to that of the solvent than the one of silicon. Therefore, the van der Waals interaction between the SiNP is reduced by the formation of the native oxide. One aspect which has not been addressed yet is the effect of multibody interactions, a topic which is discussed controversially in literature. Several authors have reported different models for calculating the total interaction energy considering multibody interactions in concentrated colloidal dispersions, with volume fractions typically larger than 30%, e.g., [19–29]. Nevertheless, these contributions indicated that for less concentrated suspensions the multibody interactions become negligible. The boundary conditions depend on the ionic strength, surface potential, and particle concentration of the suspension. However, the boundary conditions reported differ significantly. More recent results based on ab initio density functional theory, introduced by Tehver et al. [30], even dispute the effect of multibody interactions altogether. The effect of multibody interactions for the particulate systems of the present work was evaluated by calculating the total interaction energy E md at the mean separation distance of the particles in suspensions of different volume fractions. Since the exact ionic strength was difficult to determine, the evaluation was performed for a relatively broad range of ionic strength from 10−3 to 10−5 mol/L. For 20 wt% SiNP in butanol (0.08 volume fraction) E md equals to 0.07kT , which corresponds to 0.35% of the maximal total interaction energy E max at an ionic strength of 10−4 mol/L. Due to the compression of the electrical double layers the total interaction energy E md is even smaller for higher ionic strengths.
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Fig. 6. DRIFTS of SiNP dispersed for 6 h in 1-butanol.
For an ionic strength of 10−5 mol/L E md equals to 3.83kT , which corresponds to 19% of the maximal total interaction energy E max . Accordingly, one can expect that neglecting multibody interactions for the particle systems investigated within the scope of this work is reasonable, especially for higher ionic strengths. For an increasing volume fraction multibody interaction become more and more important, because the mean separation distance decreases accordingly. However, for 40 wt% SiNP in butanol (0.19 volume fraction) E md equals 0.47, 13, and 58% of the maximal interaction energy E max for an ionic strength of 10−3 , 10−4 , and 10−5 mol/L, respectively. Since for the dispersion up to 40 wt% SiNP in 1-butanol stable suspensions were obtained, the model introduced in this work is eligible for explaining the found stability, especially for higher ionic strengths, even though multibody interactions were neglected. 3.2. Experimental validation of the core–shell adsorbate model A combination of DRIFTS and HRTEM measurements was conducted to obtain experimental confirmation of the assumptions made in the DLVO calculations and consequently to evaluate, which one of the three models is the most realistic one. A more detailed analysis of the structure and surface of the SiNP is reported elsewhere [2,3]. The DRIFT spectrum of SiNP dispersed for 6 h in 1-butanol (Fig. 6) contains characteristic vibrational modes that indicate the presence of an oxide with a complex stoichiometry: several ν (Si–H) stretching and δ (Si–H) bending modes with a varying number of O neighbor atoms [31] and a broad band in the region from 1000–1100 cm−1 accounting for ν (Si–O) stretching modes of Si–O y –Si4− y complexes [32]. The band around 500 cm−1 may be assigned to the Si–O–Si out-of-plane bond-rocking motion [33]. The ν (Si–H) stretching modes result from Si–H bonds, which are presumably located on the interface between crystalline Si and the oxide and originate from the gas phase syntheses of the SiNP. The characteristic bands generated by Si–O bonds can be associated with a natively grown oxide. Since the stoichiometry of the oxide is very complex a SiO2 stoichiometry was assumed for the DLVO calculations as a valid approximation. Additionally the DRIFT spectrum in Fig. 6 contains strong and characteristic bands that indicate residual 1-butanol molecules on the SiNP surface: ν (C–H) stretching, δ (C–H) bending and ν (O–H) stretching, even though the sample was heated at 300 ◦ C for 12 h prior to analysis. In Fig. 7 the sections of DRIFTS, accounting for the region of ν (C–H) stretching, are depicted for SiNP samples heated for 30 min at the denoted temperatures. The complete disappearance of the ν (C–H) stretching mode and therefore the total removal of 1-butanol occurred only for the sample heated at 550 ◦ C, which indicates that the surface of the SiNP is mechano-chemically
177
Fig. 7. Sections of DRIFTS of SiNP samples heated at the denoted temperatures.
Fig. 8. HRTEM image of the surface of a SiNP: c-Si, SiOx , and C-film are representing the crystalline silicon bulk, the amorphous SiOx shell and the carbon film, respectively.
activated during the dispersing process and 1-butanol is strongly attached to the surface of the SiNP. Since similar results are found for the SiNP dispersed in ethanol—more than 500 ◦ C were necessary to remove ethanol completely from the surface of the SiNP. Therefore the assumption of a monolayer of strongly attached solvent molecules in the core–shell adsorbate model is realistic. The occurrence of a mechano-chemical activation of particle surfaces during wet dispersion has been observed by other authors as well [34,35]. In order to verify the appearance of an amorphous oxide shell and to estimate its thickness, the morphology of the SiNP surface was examined by high resolution transmission electron microscopy (HRTEM). The HRTEM micrograph of a SiNP surface in Fig. 8 shows an amorphous layer of 5 nm next to a crystalline silicon phase. Other HRTEM images indicated a thickness of the amorphous layer from 3 to 5 nm. Therefore the HRTEM measurements in combination with the DRIFTS measurements validate the consideration of a 4 nm thick oxide shell in the DLVO calculations. Overall the experimental data obtained by HRTEM and DRIFTS suggests that the core–shell adsorbate model is the most realistic one for calculating the total interaction energy of SiNP dispersed in 1-butanol or ethanol. 4. Conclusions Stable suspensions with regard to aggregation of silicon nanoparticles in 1-butanol and ethanol were fabricated by dispersing SiNP without the use of any additives. In order to achieve an indepth insight into the stabilizing mechanism the particle–particle interactions need to be considered. Therefore the total interaction
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energy of the silicon nanoparticles in 1-butanol and ethanol was calculated for three model systems according to the DLVO theory: (1) two solid silicon spheres, (2) two spheres with a silicon core and an amorphous silicon dioxide shell, and (3) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules. For the two core–shell models a sufficiently high energy barrier of E T > 15kT was found for SiNP with a diameter larger than 80 nm. The formation of a native oxide upon the surface of the SiNP plays the most important role in the stabilizing mechanism. For both core–shell models the calculations of E T showed, that a very small amount of ions resulting from contamination or attrition is capable of stabilizing the SiNP in 1butanol as well as in ethanol. Strongly attached solvent molecules on the SiNP surface function as spacer and bring an additional advantage in terms of stabilization. Even for particles in the lower nanometer range the core–shell models are capable of explaining the intrinsic stability of SiNP. But one has to consider both, the energy barrier and the primary minimum of the total interaction energy. Finally, in the last part of this work experimental data obtained from HRTEM and DRIFTS measurements was discussed with regard to the theoretical models. The data revealed that the core– shell adsorbate model is the most realistic one in explaining the intrinsical stability of SiNP in 1-butanol and ethanol. Although the results obtained in this work relate to the concrete system of SiNP, the theoretical approach proposed for explaining the intrinsical stability of nanoparticles in an organic solvent is of fundamental interest and can be used for other particulate systems as well. Acknowledgments Support of the Deutsche Forschungsgemeinschaft (Graduiertenkollegs 1161/1) is gratefully acknowledged. Additionally we are grateful for the generous support by Evonik Degussa GmbH. References [1] F. Stenger, S. Mende, J. Schwedes, W. Peukert, Chem. Eng. Sci. 60 (2005) 4557. [2] A. Reindl, C. Cimpean, W. Bauer, R. Comanici, A. Ebbers, W. Peukert, C. Kryschi, Colloids Surf. A Physicochem. Eng. Aspects 301 (2007) 382.
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Intrinsically stable dispersions of silicon nanoparticles A. Reindl, W. Peukert ∗ Institute of Particle Technology, Friedrich-Alexander University, Cauerstr. 4, 91058 Erlangen, Germany
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 22 January 2008 Accepted 22 May 2008 Available online 28 May 2008
Stable suspensions of silicon nanoparticles (SiNP) were fabricated by dispersion in 1-butanol as well as ethanol without the application of an additive. In order to achieve an in-depth insight into the stabilizing mechanism, the particle–particle interactions need to be considered. In this respect the total interaction energy of the silicon nanoparticles in 1-butanol and ethanol was calculated for three model systems according to the DLVO theory: (1) two solid silicon spheres, (2) two spheres with a silicon core and an amorphous silicon dioxide shell, and (3) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules. The results of the calculations are evaluated and discussed with regard to experimental data obtained by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), high resolution transmission electron microscopy (HRTEM), and zeta potential measurements. © 2008 Elsevier Inc. All rights reserved.
Keywords: Silicon nanoparticles Stabilizing Dispersing DLVO theory Core–shell
1. Introduction Nanoparticles are of growing interest in many areas of the chemical, pharmaceutical, ceramic, and microelectronic industry from the scientific as well as the technological point of view. Applications range from pigments, nanocomposites, drug delivery and ceramic materials to the fabrication of thin semi-conductive films based on various printing technologies. Therefore a high industrial demand exists on stable suspensions (with regard to aggregation) of nanoparticles in aqueous as well as non-aqueous media. Besides the direct synthesis by chemical methods, wet grinding and dispersing are suitable methods for the production of nanoparticulate systems, since a high specific energy input is accomplished [1]. However, the stability of the dispersions is strongly influenced by particle–particle interactions. Particles in the order of 1 μm and below feature a high mobility due to Brownian diffusion, which leads to a high collision frequency between the particles. Nonstabilized nanoparticles usually tend to aggregate easily, especially when dispersed in an organic medium. Therefore the particle– particle interactions need to be understood in detail in order to tailor the properties of the nanoparticulate system according to specific needs. In this case stable suspensions of silicon nanoparticles (SiNP) in an organic solvent are required for the manufacture of electronic/optoelectronic devices using printing technologies. As reported recently [2,3], intrinsically stable suspensions of SiNP in 1-butanol were obtained by dispersing in a stirred media mill
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0021-9797/$ – see front matter doi:10.1016/j.jcis.2008.05.042
©
2008 Elsevier Inc. All rights reserved.
without the application of an additive. This work focuses on determining the particle–particle interactions of SiNP in 1-butanol and ethanol to achieve an in-depth insight into the stabilizing mechanism of the particulate system. In this regard the total interaction energy of the SiNP was calculated via DLVO theory for different models including core–shell approaches. The approach of describing colloidal stability with core–shell models has been reported in literature before [4–6]. The results of the calculations of this work are evaluated and discussed with regard to experimental data obtained by diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS), high resolution transmission electron microscopy (HRTEM) and zeta potential measurements. In literature a suspension is typically considered as stable [7,8], if the total interaction energy develops an energy barrier larger than 15kT . However, this approach explains the observed stability of the SiNP only for a limited range of particle sizes. The present work shows that one has to consider not only the height of the energy barrier but also the depth of the primary minimum of the total interaction energy, to achieve a detailed understanding of the particle interactions and the associated suspension stability. 2. Experimental 2.1. Materials Ethanol (absolute) and 1-butanol (p.a.) purchased from Aldrich and used as received. Silicon nanoparticles (SiNP) with a primary particle size of approximately 100 nm were obtained from Evonik Degussa GmbH (Evonik). Suspensions of 20 wt% SiNP in 1-butanol and in ethanol (volume fraction 0.080 and 0.078, respectively)
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were dispersed for 6 h using a stirred media mill. A detailed description of the dispersing procedure is reported elsewhere [2,3]. 2.2. Transmission electron microscopy (TEM) A suspension of SiNP was placed on an ultra thin carbon film on a 400 mesh Cu-grid and then dried in air. The HRTEM images were obtained using a Philips CM 300 UltraTwin microscope at an acceleration voltage of 300 kV in the bright-field mode. 2.3. Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) The DRIFT spectra of the SiNP were recorded on a Varian FTS 3100 FTIR spectrometer equipped with a Pike Technologies EasiDiff accessory. 2.4. Zeta potential measurements The zeta potentials were determined on a Malvern Zetasizer 3000 DTS 5300 by laser Doppler electrophoresis. 3. Results and discussion
Table 1 Applied Hamaker constants Material
A 11 ( J × 10−20 )
A 11 (kT ) at 293.2 K
Ethanol Butanol Silicon Amorphous SiO2
4.24 4.99 20.60 6.28
10.46 12.33 50.89 15.51
and n is the refractive index [13]. Equation [3] usually applies to what are normally referred to as dielectric or non-conducting materials [11] and was therefore used for calculating A 11 of 1-butanol and ethanol. The calculations of A 11 of silicon and amorphous silicon dioxide were based on the dielectric functions for a large energy range instead of the relative dielectric constants for more accurate approximation [14]. The calculated Hamaker constants for all involved materials are listed in Table 1. An expression for the Hamaker constant A 131 , i.e., for the situation of two particles suspended in a liquid, is derived by assuming that the interaction constant between the two different materials equals approximately the geometric mean of the interaction constants of the individual materials [11]. Therefore A 131 is given by [11] A 13 ≈
3.1. Theoretical approach
A 11 A 33 ,
(4)
followed by As mentioned before stable suspensions (with regard to aggregation) of SiNP in 1-butanol and ethanol were obtained by dispersing in a stirred media mill [2,3] without the use of any additives. The high stability of SiNP in 1-butanol and ethanol has been predicted theoretically and confirmed experimentally by Bleier [9]. However, only attractive forces were considered thereby and the calculated Hamaker constants differ noticeably from other literature values. In order to achieve a more detailed understanding of the stability of SiNP in 1-butanol and ethanol the total interaction energy of the SiNP was estimated according to the DLVO theory [7,10] in this work. The total interaction energy E T results from summation of the van der Waals interaction E vdW , electrostatic repulsion E El , and the Born repulsion E B E T = E vdW + E El + E B .
(1)
For calculations, which explain the stability of the SiNP with regard to the height of the formed energy barrier of the total interaction energy, the Born repulsion can be neglected. For consideration of the primary minimum of the total interaction energy the Born repulsion, approximated by a hard sphere potential at the minimal contact distance of 0.165 nm [11], was included in the calculations. The non-retarded van der Waals interaction E vdW of two solid spherical particles of radii R 1 and R 2 at a distance H apart is given by [12] E vdW = −
A
+ ln
2R 1 R 2 2( R 1 + R 2 ) H + H 2
6
+
2R 1 R 2 4R 1 R 2 + 2( R 1 + R 2 ) H + H 2
2( R 1 + R 2 ) H + H 2
,
4R 1 R 2 + 2( R 1 + R 2 ) H + H 2
(2)
where A is the Hamaker constant. For the “symmetric case” of two identical phases 1 interacting across vacuum, one can infer the Hamaker constant A 11 via [11] A 11 =
3 4
kT
ε1 − 1 ε1 + 1
2 +
3hνe (n21 − 1)2
√
16 2 (n21 + 1)3/2
,
(3)
where k is the Boltzmann constant, ε is the static dielectric constant [13], h is the Planck constant, νe is the main electronic absorption frequency in the UV typically around 3 × 1015 s−1 [11]
A 131 ≈ A 11 + A 33 − 2 A 13 .
(5)
For media 1 and 2 interacting across medium 3 the Hamaker constant A 132 can be written as [11] A 132 ≈
A 11 −
A 33
A 22 −
A 33 .
(6)
The electrostatic repulsion E El between two spherical particles can be estimated by using [8] E El =
a 32πεε0 ( R T )2
υ2
F2
γ 2 e −κ H ,
(7)
with γ = (e z/2 − 1)/(e z/2 + 1) and z = υ F ψ0 / R T , where υ is the valency, R is the gas constant, F is the Faraday constant, and ψ0 is the surface potential [8]. The surface potential ψ0 was substituted by the zeta-potential ζ determined by the means of electrophoresis, i.e., −46.6 mV for SiNP in 1-butanol and −40.0 mV for SiNP in ethanol. κ is the Debye–Hückel parameter expressed [8]
κ2 =
2F 2
εε0 R T
I,
(8)
where I is the ionic strength. The Debye–Hückel parameter κ has the dimension of a reciprocal length. The quantity 1/κ is related to the thickness of the diffuse layer surrounding the particles. Applying the formulas above the total interaction energy E T was calculated for three model systems depicted in Fig. 1: (a) two solid silicon spheres (solid sphere model), (b) two spheres with a silicon core and an amorphous silicon dioxide shell (core–shell model), and (c) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules (core–shell adsorbate model). For the calculations an overall sphere diameter x of 100 nm was assumed, which is roughly the primary particle diameter of the SiNP used for the dispersing experiments. The thickness of the shell of amorphous silicon dioxide d was estimated being 4 nm, whereas the thickness of the adsorbate layer σ was estimated being equal to the Lennard–Jones diameter of one molecule of 1-butanol/ethanol, i.e., 0.527 and 0.437 nm [15,16], respectively. The van der Waals interaction with regard to the solid sphere model was determined for two silicon spheres (radius = x/2) by a
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175
Fig. 2. Total interaction energy E T of SiNP (100 nm) in 1-butanol at I = 1 × 10−4 mol/L for the three different model systems.
E vdW (shell1 , shell2 )| H =a = E vdW (sphere1 , sphere2 )| H =a
− E vdW (sphere1 , core2 )| H =a+d − E vdW (sphere2 , core1 )| H =a+d + E vdW (core1 , core2 )| H =a+2d .
(11)
The Hamaker constants necessary to calculate the individual van der Waals interactions were determined by Eq. (6) and adapted according to the interacting materials, i.e., Si–Si, Si–SiO2 , or Si–SiO2 . The van der Waals interaction of the adsorbate layer in the core–shell adsorbate model in Fig. 1c does not need to be considered separately because the Hamaker constant of two adsorbate layers across the solvent medium equals zero. Therefore the adsorbate layer merely functions as a spacer. For the calculation of the total interaction energy of two SiNP using the core–shell adsorbate model the corresponding radii apparent in Fig. 1c were applied. The van der Waals interaction for this case can be expressed as [17,18] Fig. 1. Schematic representation of the model systems for DLVO calculations: (a) solid sphere model, (b) core–shell model, and (c) core–shell adsorbate model.
E vdW (sphere1 , sphere2 )| H =a+2σ = E vdW (shell1 , shell2 )| H =a+2σ
+ E vdW (core1 , core2 )| H =a+2d+2σ distance H apart according to Eq. (2). For the core–shell model the van der Waals interaction can be written as [17,18] E vdW (sphere1 , sphere2 )| H =a = E vdW (shell1 , shell2 )| H =a
+ E vdW (core1 , core2 )| H =a+2d + E vdW (core1 , shell2 )| H =a+d + E vdW (core2 , shell1 )| H =a+d ,
(9)
where E vdW (x, y ) is the van der Waals interaction, assuming additivity, between the geometrical objects x and y [17,18], subjected to the geometrical conditions of Fig. 1b. E vdW (core1 , core2 ) is a function, which describes the van der Waals interaction energy between the core of sphere 1 (radius = x/2 − d) and the core of sphere 2 (radius = x/2 − d) by the distance H = a + 2d apart. E vdW (core1 , shell2 ) is a function, which describes the van der Waals interaction energy between the core of sphere 1 (radius = x/2 − d) and the shell of sphere 2 (outer radius = x/2, inner radius = x/2 − d) by the distance H = a + d apart, expressed as [17,18] E vdW (core1 , shell2 )| H =a+d = E vdW (core1 , sphere2 )| H =a+d
− E vdW (core1 , core2 )| H =a+2d .
(10)
Obviously the same expression can be used for the case that indexes 1 and 2 are reversed. Substituting Eq. (10) into Eq. (9) and by rearranging one obtains the function E vdW (shell1 , shell2 ), which describes the van der Waals interaction energy between shell 1 and shell 2 by the distance H = a apart. Accordingly, one can write [17,18]
+ E vdW (core1 , shell2 )| H =a+d+2σ + E vdW (core2 , shell1 )| H =a+d+2σ .
(12)
In literature a suspension is typically considered as stable [7,8], if the total interaction energy develops an energy barrier larger than 15kT , as mentioned in the introductory part of this work. The height of the energy barrier E T can be determined by
E T = E max − E md ,
(13)
where E max is the maximum of the total interaction energy and E md is the total interaction energy at the mean separation distance of the particles in suspension (derived by considering the particle in a unit cell with respect to the applied volume fraction). The mean separation distances for a 20 wt% suspension of SiNP (100 nm) in ethanol and 1-butanol, as used for the dispersing experiments, are 83.48 and 81.96 nm, respectively. In Fig. 2 the total interaction energy E T at 20 ◦ C of SiNP (100 nm) in 1-butanol is exemplarily depicted for an ionic strength I = 1 × 10−4 mol/L for the three different model systems. Obviously an energy barrier of E T > 15kT , indicating a stable suspension, was only found for the core–shell model and the core–shell adsorbate model. Since the exact ionic strength I of the SiNP suspensions is difficult to determine, the total interaction energy was calculated for I ranging from 1 × 10−3 to 1 × 10−5 mol/L. The resulting total interaction energies for SiNP in 1-butanol at room temperature are exemplarily shown in Fig. 3. The calculations for SiNP in 1-butanol as well as in ethanol indicated a sufficiently high energy barrier of E T > 15kT , only if a core–shell model or a core–shell adsorbate model is assumed. The difference in E T between the solid sphere
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Fig. 3. Energy barrier E T of SiNP (100 nm) in 1-butanol for the three different model systems.
Fig. 4. Energy barrier E T of SiNP (100 nm) in 1-butanol as a function of the thickness of the silicon dioxide shell.
model and the core–shell models is most significant for high ionic strengths. But even for an ionic strength as low as 1 × 10−5 mol/L the core–shell models indicated an energy barriers E T > 15kT . Therefore a very small amount of ions resulting from contamination or attrition is capable of stabilizing the SiNP and one can expect to receive intrinsically stable suspensions when dispersing SiNP in 1-butanol or ethanol. Furthermore Fig. 3 indicates that the most significant gain regarding the energy barrier is obtained by assuming the presence of a 4 nm amorphous silicon dioxide shell. Hence, the variation of the thickness of the amorphous dioxide shell was also considered in this work. In Fig. 4 the energy barrier E T is exemplarily depicted for SiNP in 1-butanol at an ionic strength of 10−4 mol/L. The calculations revealed, when assuming the core–shell model a thickness of the amorphous silicon dioxide shell of 2.3 nm is expected to be sufficient in stabilizing the SiNP, while assuming the core–shell adsorbate model a thickness as small as 1.6 nm is expected to be sufficient. Assuming the core–shell adsorbate model the total interaction energy develops an energy barrier larger than 15kT for particles with a diameter larger than 80 nm. Hence, the intrinsic stability found during the dispersion of SiNP with a primary particle size of 100 nm in 1-butanol as well as ethanol is manifested by the energy barriers calculated with the core–shell adsorbate model. For SiNP smaller than 80 nm the calculated height of the energy barrier is significantly smaller than 15kT , e.g., for SiNP with a diameter of 20 nm energy barriers less than 5kT were estimated even when assuming a core–shell adsorbate model. However, dispersing experiments indicated intrinsically stable suspensions of SiNP in range of 20 nm. Therefore solely considering the height of the energy barrier explains the found intrinsic stability only for a limited size range. In Fig. 5 the total interaction energy of SiNP (20 nm) in 1-butanol with an oxide thickness of 2 nm is ex-
Fig. 5. Total interaction energy E T of SiNP (20 nm) in 1-butanol at I = 1 × 10−4 mol/L for the solid sphere model and the core–shell model. The oxide thickness for the core–shell model was set at 2 nm.
emplarily depicted for the solid sphere model and the core–shell model. The solid sphere model indicates a primary minimum of the total interaction energy of −53kT at the minimal contact distance of 0.165 nm [11], which implies favored aggregation of the particles. The core–shell model on the other hand indicates a primary minimum at around 3kT at the minimal contact distance of 0.165, which suggests that no aggregation occurs. The total interaction energy calculated by the core–shell adsorbate model is not depicted in Fig. 5, because the progression is overlapping strongly with the one calculated for the core–shell model. However, assuming the core–shell adsorbate model no minimum is formed at the distance of 0.165 nm, since the strongly attached solvent molecules at the SiNP surface function as a spacer and inhibit a close contact and subsequently aggregation of the particles. In conclusion the core–shell model as well as the core–shell adsorbate model is able to explain the intrinsic stability of SiNP in 1-butanol and ethanol, even at the lower nanometer range, if both the energy barrier and the primary minimum of the total interaction energy are considered. Furthermore the calculations indicated that the presence of an oxide shell plays the most important role with regard to the stability of the SiNP. The refractive index and consequently the Hamaker constant of the oxide are more similar to that of the solvent than the one of silicon. Therefore, the van der Waals interaction between the SiNP is reduced by the formation of the native oxide. One aspect which has not been addressed yet is the effect of multibody interactions, a topic which is discussed controversially in literature. Several authors have reported different models for calculating the total interaction energy considering multibody interactions in concentrated colloidal dispersions, with volume fractions typically larger than 30%, e.g., [19–29]. Nevertheless, these contributions indicated that for less concentrated suspensions the multibody interactions become negligible. The boundary conditions depend on the ionic strength, surface potential, and particle concentration of the suspension. However, the boundary conditions reported differ significantly. More recent results based on ab initio density functional theory, introduced by Tehver et al. [30], even dispute the effect of multibody interactions altogether. The effect of multibody interactions for the particulate systems of the present work was evaluated by calculating the total interaction energy E md at the mean separation distance of the particles in suspensions of different volume fractions. Since the exact ionic strength was difficult to determine, the evaluation was performed for a relatively broad range of ionic strength from 10−3 to 10−5 mol/L. For 20 wt% SiNP in butanol (0.08 volume fraction) E md equals to 0.07kT , which corresponds to 0.35% of the maximal total interaction energy E max at an ionic strength of 10−4 mol/L. Due to the compression of the electrical double layers the total interaction energy E md is even smaller for higher ionic strengths.
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Fig. 6. DRIFTS of SiNP dispersed for 6 h in 1-butanol.
For an ionic strength of 10−5 mol/L E md equals to 3.83kT , which corresponds to 19% of the maximal total interaction energy E max . Accordingly, one can expect that neglecting multibody interactions for the particle systems investigated within the scope of this work is reasonable, especially for higher ionic strengths. For an increasing volume fraction multibody interaction become more and more important, because the mean separation distance decreases accordingly. However, for 40 wt% SiNP in butanol (0.19 volume fraction) E md equals 0.47, 13, and 58% of the maximal interaction energy E max for an ionic strength of 10−3 , 10−4 , and 10−5 mol/L, respectively. Since for the dispersion up to 40 wt% SiNP in 1-butanol stable suspensions were obtained, the model introduced in this work is eligible for explaining the found stability, especially for higher ionic strengths, even though multibody interactions were neglected. 3.2. Experimental validation of the core–shell adsorbate model A combination of DRIFTS and HRTEM measurements was conducted to obtain experimental confirmation of the assumptions made in the DLVO calculations and consequently to evaluate, which one of the three models is the most realistic one. A more detailed analysis of the structure and surface of the SiNP is reported elsewhere [2,3]. The DRIFT spectrum of SiNP dispersed for 6 h in 1-butanol (Fig. 6) contains characteristic vibrational modes that indicate the presence of an oxide with a complex stoichiometry: several ν (Si–H) stretching and δ (Si–H) bending modes with a varying number of O neighbor atoms [31] and a broad band in the region from 1000–1100 cm−1 accounting for ν (Si–O) stretching modes of Si–O y –Si4− y complexes [32]. The band around 500 cm−1 may be assigned to the Si–O–Si out-of-plane bond-rocking motion [33]. The ν (Si–H) stretching modes result from Si–H bonds, which are presumably located on the interface between crystalline Si and the oxide and originate from the gas phase syntheses of the SiNP. The characteristic bands generated by Si–O bonds can be associated with a natively grown oxide. Since the stoichiometry of the oxide is very complex a SiO2 stoichiometry was assumed for the DLVO calculations as a valid approximation. Additionally the DRIFT spectrum in Fig. 6 contains strong and characteristic bands that indicate residual 1-butanol molecules on the SiNP surface: ν (C–H) stretching, δ (C–H) bending and ν (O–H) stretching, even though the sample was heated at 300 ◦ C for 12 h prior to analysis. In Fig. 7 the sections of DRIFTS, accounting for the region of ν (C–H) stretching, are depicted for SiNP samples heated for 30 min at the denoted temperatures. The complete disappearance of the ν (C–H) stretching mode and therefore the total removal of 1-butanol occurred only for the sample heated at 550 ◦ C, which indicates that the surface of the SiNP is mechano-chemically
177
Fig. 7. Sections of DRIFTS of SiNP samples heated at the denoted temperatures.
Fig. 8. HRTEM image of the surface of a SiNP: c-Si, SiOx , and C-film are representing the crystalline silicon bulk, the amorphous SiOx shell and the carbon film, respectively.
activated during the dispersing process and 1-butanol is strongly attached to the surface of the SiNP. Since similar results are found for the SiNP dispersed in ethanol—more than 500 ◦ C were necessary to remove ethanol completely from the surface of the SiNP. Therefore the assumption of a monolayer of strongly attached solvent molecules in the core–shell adsorbate model is realistic. The occurrence of a mechano-chemical activation of particle surfaces during wet dispersion has been observed by other authors as well [34,35]. In order to verify the appearance of an amorphous oxide shell and to estimate its thickness, the morphology of the SiNP surface was examined by high resolution transmission electron microscopy (HRTEM). The HRTEM micrograph of a SiNP surface in Fig. 8 shows an amorphous layer of 5 nm next to a crystalline silicon phase. Other HRTEM images indicated a thickness of the amorphous layer from 3 to 5 nm. Therefore the HRTEM measurements in combination with the DRIFTS measurements validate the consideration of a 4 nm thick oxide shell in the DLVO calculations. Overall the experimental data obtained by HRTEM and DRIFTS suggests that the core–shell adsorbate model is the most realistic one for calculating the total interaction energy of SiNP dispersed in 1-butanol or ethanol. 4. Conclusions Stable suspensions with regard to aggregation of silicon nanoparticles in 1-butanol and ethanol were fabricated by dispersing SiNP without the use of any additives. In order to achieve an indepth insight into the stabilizing mechanism the particle–particle interactions need to be considered. Therefore the total interaction
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energy of the silicon nanoparticles in 1-butanol and ethanol was calculated for three model systems according to the DLVO theory: (1) two solid silicon spheres, (2) two spheres with a silicon core and an amorphous silicon dioxide shell, and (3) two spheres with a silicon core, an amorphous silicon dioxide shell and a monolayer of adsorbed solvent molecules. For the two core–shell models a sufficiently high energy barrier of E T > 15kT was found for SiNP with a diameter larger than 80 nm. The formation of a native oxide upon the surface of the SiNP plays the most important role in the stabilizing mechanism. For both core–shell models the calculations of E T showed, that a very small amount of ions resulting from contamination or attrition is capable of stabilizing the SiNP in 1butanol as well as in ethanol. Strongly attached solvent molecules on the SiNP surface function as spacer and bring an additional advantage in terms of stabilization. Even for particles in the lower nanometer range the core–shell models are capable of explaining the intrinsic stability of SiNP. But one has to consider both, the energy barrier and the primary minimum of the total interaction energy. Finally, in the last part of this work experimental data obtained from HRTEM and DRIFTS measurements was discussed with regard to the theoretical models. The data revealed that the core– shell adsorbate model is the most realistic one in explaining the intrinsical stability of SiNP in 1-butanol and ethanol. Although the results obtained in this work relate to the concrete system of SiNP, the theoretical approach proposed for explaining the intrinsical stability of nanoparticles in an organic solvent is of fundamental interest and can be used for other particulate systems as well. Acknowledgments Support of the Deutsche Forschungsgemeinschaft (Graduiertenkollegs 1161/1) is gratefully acknowledged. Additionally we are grateful for the generous support by Evonik Degussa GmbH. References [1] F. Stenger, S. Mende, J. Schwedes, W. Peukert, Chem. Eng. Sci. 60 (2005) 4557. [2] A. Reindl, C. Cimpean, W. Bauer, R. Comanici, A. Ebbers, W. Peukert, C. Kryschi, Colloids Surf. A Physicochem. Eng. Aspects 301 (2007) 382.
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