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The effect of particle wettability on the accuracy of determination of particle sizes by the supersaturation variation technique
Aerosol Sci Vol. 31, Suppl. 1, pp. $438-$439, 2000
Pergamon www.elsevier.com/locate/jaerosci
Poster Session I. Nucleation THE EFFECT OF PARTICLE WETTABILITY ON THE ACCURACY OF DETERMINATION OF PARTICLE SIZES BY THE SUPERSATURATION VARIATION TECHNIQUE L.A. KETKOVA, V.A. KRYLOV and O.P. LAZUKINA Institute of Chemistry of High-Purity Substances RAS, 49 Tropinin St., 603600, Nizhny Novgorod, Russia Keywords: PARTICLE CHARACTERISATION, KELV1N-EQIVALENT PARTICLE RADIUS, LIQUID ADSORPTION FILM, CRITICAL SIZE NECESSARY FOR START OF GROWTH INTRODUCTION High-purity volatile hydrides, chlorides, and organometallic compounds are widely used in many modem technologies. The presence of impurities in the form of solid particles in these substances can be the reason for low quality of the materials obtained. At present time the problem of controlling the nanometer-size particles becomes important. The problem is greatly complicated due to aggressive and explosive nature of the analyzed substances. Thus, the use of diffusion batteries and analyzers of electrical mobility should be excluded during determination of particle sizes. The method of the controlled enlargement of particles with the inert substance-enlarger, employed in condensation nuclei counters (CNC) with variable supersaturation (e.g., Dreiling and Jaenicke, 1988; Krylov et al., 1995), is of great interest to the analysis of particles in aggressive gases. One of the main problems of this method is to find the condition for condensing enlargement of particles which define the smallest particle size detectable by the CNC, and the possibility in recovery of the true particle size distribution from the Kelvin-equivalent size distribution. THEORY Usually, the critical particle size necessary for start of growth (r.) is estimated by the Kelvin equation, assuming that the conditions for condensation on the surface of a solid particle are the same as on the surface of a liquid drop (r, = rk, where rk is the Kelvin-equivalent radius). Investigation of the effect of the particle wettability on their condensation enlargement, carried out by Scheibel and Porstendorfer (1986) under the classical approaches of the macroscopic theory of heterogeneous nucleation (Fletcher, Krystanov), has a significant drawback due to disregard of the adsorption nature of an embryo (lens or film) on a solid particle surface (e.g., Rusanov and Kuni,1991). In the present paper the condition for condensation enlargement of particles is found as a result of analysis of stability of polymolecular adsorption films on the surface of a solid particle. An expression has been obtained for the work of formation of a liquid adsorption film on a spherical insoluble particle in the polymolecular adsorption-condensation region. The .additivity of the contributions of surface and capillary forces into the chemical potential of a film (Ix) was assumed. An equation has been obtained for the minimum (critical) radius of a particle with the expected spontaneous unlimited film growth on its surface at the given vapor supersaturation (or at the given rk) in the system: r, = rk ( 1 - ADz(h.,r,)/Ap.k(rk))"1- h, where h. is the thickness of the equilibrium critical film (a~/ah=0); Ap~(h,r) is the component of the chemical potential of molecules in the film connected with contribution of the long-range surface forces accounting for the effect of the solid substrate on the liquid in the film; A~(rk) is the capillary component of the chemical potential of a liquid drop with the size rk. In most cases, the enlargement of particles with size less than r., due to fluctuation thickening of the film up to the critical thickness, can be neglected.
$438
Abstracts of the 2000 European Aerosol Conference
$439
The calculations for specific systems were carried out neglecting the distortion of the surface forces' field caused by curvature of the solid surface: AjA(h,r) zA~o(h). The explicit form of A~ts~(h) is known from the isotherm of vapor adsorption on the solid plane surface.
RESULTS AND DISCUSSION The dependence of the minimum size r. of the enlarging particles upon supersaturation was studied for some known adsorption isotherms (non-retarded dispersion interaction, semi-empirical Adamson's isotherms) both in case of spreading and in case of not perfectly wettable particle material. The r./rk ratio is mainly determined by the form of the isotherm of vapor adsorption on the solid surface. The equilibrium contact angle 0 for the macrosample of the particle material can not be the main and single characteristic of solid-liquid interaction while determining sizes of the enlarging particles as it follows from the Fletcher theory. Thus, with different types of adsorption isotherms the situations can take place when an increase in the 0 values is accompanied by a decrease in the r. values. At the same time within one and the same type of the adsorption isotherm the minimum size of the enlarging particles usually increases with degradation in material wettability. The cases are possible when condensation on particles is facilitated as compared to condensation on drops of the same size (r,/rk < 1) not only at complete wetting (spreading), but at poor wetting of the particle material as well. These results are easily interpreted within the framework of the used approach, and can explain the heterogeneous condensation on small particles observed in reality at unexpected low supersaturation. In contradistinction to the results of calculation of Scheibel and Porstendorfer (1986), indicating strong dependence of the r. value upon the angle 0, our analysis leads not only to strong but also to rather weak dependence. For example, for the 1 - 100 nm particles with 0 ° < 0 < 90 °, the r,/rk ratio is < 4, whereas the analysis based on Fletcher's theory gives r,/rk <100. The weak effect of the contact angle 0 upon the condition of condensation enlargement is in agreement with the whole set of experimental data, where actually no difference was observed in the critical sizes of the particles from materials with substantially varying wettability. It should be noted that attempts to find agreement between the above-mentioned experimental data with the calculated dependence, obtained by Scheibel and Porstendorfer (1986), require assumption on a certain dependence of the contact angle upon the particle size. Establishing of this dependence still requires to take into account the adsorption nature of the film (Papyrina, 1990). An accurate calculation of the r°, for which a detailed information on the isotherm of vapor adsorption on the curved surface is necessary, can be done in the future only. Despite this fact, the approximate calculations of the present work demonstrate how much can be the r./r ratio. Thus, in the considered types of adsorption isotherms for the 1 - 10 nm particles, the value r can differ from that of the Kelvin-equivalent radius for not more than twice for the systems with I A I < 1 0 -13 erg ( A is the Hamaker constant) in case of spreading and for system with 0 < 300 in case of not perfect wetting. In most cases met in practice (IAI < 10 erg, 0 < 90°), the expected difference between r. and rk can be up to an order of magnitude. REFERENCES Dreiling, V., R. Jaenicke (1998). Measurements of aerosol size distributions with a pocket counter with variable expansion ratio. Lect. Notes Phys. 305, 194. Krylov V.A., O.P. Lazukina, N.A. Gracheva, V.V. Andrianov, L.A. Ketkova (1995). Counter of condensation nuclei to determine the suspended particles in high-purity volatile inorganic hydrides. Vysokochistye Veshchestva, N 3, 33 (in Russian). Scheibel, H.G., J. Porstendorfer (1986). Counting efficiency and detection limit of condensation nuclei counters for submicrometer aerosols, J.. Colloid Interface Sci. 109, 261. Rusanov, A.N., F.M. Kuni (1991). The case of a stable embryo in thermodynamics of heterogeneous nucleation, Transactions (Doklady) of the USSR Academy of Sciences 318, 1410. Papyrina, L.A. (1990). Wetting of slightly curved solid surfaces, Colloid Journal (Russ.) 52, 876.
Pergamon www.elsevier.com/locate/jaerosci
Poster Session I. Nucleation THE EFFECT OF PARTICLE WETTABILITY ON THE ACCURACY OF DETERMINATION OF PARTICLE SIZES BY THE SUPERSATURATION VARIATION TECHNIQUE L.A. KETKOVA, V.A. KRYLOV and O.P. LAZUKINA Institute of Chemistry of High-Purity Substances RAS, 49 Tropinin St., 603600, Nizhny Novgorod, Russia Keywords: PARTICLE CHARACTERISATION, KELV1N-EQIVALENT PARTICLE RADIUS, LIQUID ADSORPTION FILM, CRITICAL SIZE NECESSARY FOR START OF GROWTH INTRODUCTION High-purity volatile hydrides, chlorides, and organometallic compounds are widely used in many modem technologies. The presence of impurities in the form of solid particles in these substances can be the reason for low quality of the materials obtained. At present time the problem of controlling the nanometer-size particles becomes important. The problem is greatly complicated due to aggressive and explosive nature of the analyzed substances. Thus, the use of diffusion batteries and analyzers of electrical mobility should be excluded during determination of particle sizes. The method of the controlled enlargement of particles with the inert substance-enlarger, employed in condensation nuclei counters (CNC) with variable supersaturation (e.g., Dreiling and Jaenicke, 1988; Krylov et al., 1995), is of great interest to the analysis of particles in aggressive gases. One of the main problems of this method is to find the condition for condensing enlargement of particles which define the smallest particle size detectable by the CNC, and the possibility in recovery of the true particle size distribution from the Kelvin-equivalent size distribution. THEORY Usually, the critical particle size necessary for start of growth (r.) is estimated by the Kelvin equation, assuming that the conditions for condensation on the surface of a solid particle are the same as on the surface of a liquid drop (r, = rk, where rk is the Kelvin-equivalent radius). Investigation of the effect of the particle wettability on their condensation enlargement, carried out by Scheibel and Porstendorfer (1986) under the classical approaches of the macroscopic theory of heterogeneous nucleation (Fletcher, Krystanov), has a significant drawback due to disregard of the adsorption nature of an embryo (lens or film) on a solid particle surface (e.g., Rusanov and Kuni,1991). In the present paper the condition for condensation enlargement of particles is found as a result of analysis of stability of polymolecular adsorption films on the surface of a solid particle. An expression has been obtained for the work of formation of a liquid adsorption film on a spherical insoluble particle in the polymolecular adsorption-condensation region. The .additivity of the contributions of surface and capillary forces into the chemical potential of a film (Ix) was assumed. An equation has been obtained for the minimum (critical) radius of a particle with the expected spontaneous unlimited film growth on its surface at the given vapor supersaturation (or at the given rk) in the system: r, = rk ( 1 - ADz(h.,r,)/Ap.k(rk))"1- h, where h. is the thickness of the equilibrium critical film (a~/ah=0); Ap~(h,r) is the component of the chemical potential of molecules in the film connected with contribution of the long-range surface forces accounting for the effect of the solid substrate on the liquid in the film; A~(rk) is the capillary component of the chemical potential of a liquid drop with the size rk. In most cases, the enlargement of particles with size less than r., due to fluctuation thickening of the film up to the critical thickness, can be neglected.
$438
Abstracts of the 2000 European Aerosol Conference
$439
The calculations for specific systems were carried out neglecting the distortion of the surface forces' field caused by curvature of the solid surface: AjA(h,r) zA~o(h). The explicit form of A~ts~(h) is known from the isotherm of vapor adsorption on the solid plane surface.
RESULTS AND DISCUSSION The dependence of the minimum size r. of the enlarging particles upon supersaturation was studied for some known adsorption isotherms (non-retarded dispersion interaction, semi-empirical Adamson's isotherms) both in case of spreading and in case of not perfectly wettable particle material. The r./rk ratio is mainly determined by the form of the isotherm of vapor adsorption on the solid surface. The equilibrium contact angle 0 for the macrosample of the particle material can not be the main and single characteristic of solid-liquid interaction while determining sizes of the enlarging particles as it follows from the Fletcher theory. Thus, with different types of adsorption isotherms the situations can take place when an increase in the 0 values is accompanied by a decrease in the r. values. At the same time within one and the same type of the adsorption isotherm the minimum size of the enlarging particles usually increases with degradation in material wettability. The cases are possible when condensation on particles is facilitated as compared to condensation on drops of the same size (r,/rk < 1) not only at complete wetting (spreading), but at poor wetting of the particle material as well. These results are easily interpreted within the framework of the used approach, and can explain the heterogeneous condensation on small particles observed in reality at unexpected low supersaturation. In contradistinction to the results of calculation of Scheibel and Porstendorfer (1986), indicating strong dependence of the r. value upon the angle 0, our analysis leads not only to strong but also to rather weak dependence. For example, for the 1 - 100 nm particles with 0 ° < 0 < 90 °, the r,/rk ratio is < 4, whereas the analysis based on Fletcher's theory gives r,/rk <100. The weak effect of the contact angle 0 upon the condition of condensation enlargement is in agreement with the whole set of experimental data, where actually no difference was observed in the critical sizes of the particles from materials with substantially varying wettability. It should be noted that attempts to find agreement between the above-mentioned experimental data with the calculated dependence, obtained by Scheibel and Porstendorfer (1986), require assumption on a certain dependence of the contact angle upon the particle size. Establishing of this dependence still requires to take into account the adsorption nature of the film (Papyrina, 1990). An accurate calculation of the r°, for which a detailed information on the isotherm of vapor adsorption on the curved surface is necessary, can be done in the future only. Despite this fact, the approximate calculations of the present work demonstrate how much can be the r./r ratio. Thus, in the considered types of adsorption isotherms for the 1 - 10 nm particles, the value r can differ from that of the Kelvin-equivalent radius for not more than twice for the systems with I A I < 1 0 -13 erg ( A is the Hamaker constant) in case of spreading and for system with 0 < 300 in case of not perfect wetting. In most cases met in practice (IAI < 10 erg, 0 < 90°), the expected difference between r. and rk can be up to an order of magnitude. REFERENCES Dreiling, V., R. Jaenicke (1998). Measurements of aerosol size distributions with a pocket counter with variable expansion ratio. Lect. Notes Phys. 305, 194. Krylov V.A., O.P. Lazukina, N.A. Gracheva, V.V. Andrianov, L.A. Ketkova (1995). Counter of condensation nuclei to determine the suspended particles in high-purity volatile inorganic hydrides. Vysokochistye Veshchestva, N 3, 33 (in Russian). Scheibel, H.G., J. Porstendorfer (1986). Counting efficiency and detection limit of condensation nuclei counters for submicrometer aerosols, J.. Colloid Interface Sci. 109, 261. Rusanov, A.N., F.M. Kuni (1991). The case of a stable embryo in thermodynamics of heterogeneous nucleation, Transactions (Doklady) of the USSR Academy of Sciences 318, 1410. Papyrina, L.A. (1990). Wetting of slightly curved solid surfaces, Colloid Journal (Russ.) 52, 876.