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Computer experiments on nucleation processes in the lattice gas model
l~'rosol Sciem'e, 1974. Vol. 5. pp. 507 to 508. Pergamon Press. Printed in Great Britain.
CURRENT WORK ON NUCLEATION
Compiled by D. STAUFFER Institute of Theoretical Physics, University, 66 Saarbriicken 15, West Germany Brief abstracts of work which has not yet been published may be submitted to the compiler for inclusion in this section. Determination of the particle size distribution of an aerosol using a diffusion battery. By J.-P. MAIGNE; Service Technique d'Etudes de Protection et de Pollution Atmospherique, Centre d'Etudes Nucl6aires, Fontenay-auxRoses, France. The principal methods for the treatment of concentration measurements both upstream and downstream of a difl'usion battery are reviewed and discussed, the purpose of the measurements being the determination of the aerosol particle size distribution. It is then demonstrated that the resolution of the equations arising from the problem leads to the imposing of physical constraints on the distribution sought, these constraints being more and more restrictive with increasing experimental inaccuracies. An algorithm is proposed which provides an approximate solution to the system of equations, certain predetermined criteria, and the constraints imposed on the distribution being taken into account. {Thesis. University of Paris). Computer experiments on nucleation processes in the lattice gas model. By K. B~NDER, Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. Review: no abstract given. Structure of binary solution droplets: Continuum theory and Monte Carlo simulation. By D. STAUFFER; PhysikDepartment T 30, Technical University of Munich, 8046 Garching, West Germany; K. BINDER; (as above), and V. WILDPANER~Atominstitut der C)sterreichischen Hochschulen, A-1020 Vienna, Austria. To calculate the formation energy of binary mixture droplet out of the gas phase in classical "heteromolecular" nucleation theory, one has to take into account that the concentration of the solution near the droplet surface can be different from the composition in the droplet interior ("surface enrichment", Gibbs adsorption equation). This problem is solved in a simple picture where the composition varies spatially but where one has a sharp liquid-gas surface. In a material independent continuum theory, the variation of the composition is assumed to give a free energy contribution proportional to the square of the concentration gradient. This treatment of the surface enrichment gives a formation energy contribution smaller (for large droplets) by a factor 0.42 than previous theories (Neumann and D6ring; Stauffer and Kiang), which therefore overestimated the surface enrichment effect for large droplets. This continuum theory is tested by Monte Carlo methods on a particularly symmetric mixture, the magnetic spin 1/2 Ising model. Here up spins are identified with one type of molecules and down spins with the other type. Reasonable agreement with the continuum theory is found, even for parameter ranges where the assumptions of the continuum theory are no longer valid. The results show clearly a strong but smooth variation of the concentration within the droplet. They constitute to our knowledge the first computer simulations of mixture microdroplets with several molecules of both types. Calculation of dynamical critical properties from a cluster reaction theory. By K. BINDER, D. STAUFFER; (as above) and H. Mi'JLt,L:R-KRUMBHAAR;IBM Ziirich Research Laboratory, 8803 Riischlikon, Switzerland. Critical fluctuations in kinetic Ising models are interpreted in terms of cluster reactions. The basic assumption, that clusters with n spins grow at a rate proportional to nr, is tested by Monte Carlo computations in the single spin flip case. The dynamic susceptibilities associated with order parameter and energy are then calculated also for nonzero field, and are shown to fulfill dynamic scaling, The exponent (2-r)f13 of the relaxation times can be different from tile susceptibility exponent 7. A field emission investigation of adsorption and nucleation of silver on tungsten, and of interaction of the deposits with oxygen. By W. Wt~STNERand D. MENZEL; Institute for Physical Chemistry, Technical University of Munich. 8046 Garching. West Germany. The adsorption of silver on tungsten field emission tips, the formation of silver layers and crystallites, and the interaction of silver layers and crystallites with oxygen have been investigated using a field emission microscope. Good agreement with earlier work has been obtained for the nucleation of silver crystallites. Smooth silver layers many monolayers thick, which retain the symmetry of the W tip. can be produced by slow evaporation at 450°K under extreme ultrahigh vacuum. The work function changes upon adsorption of silver on tungsten agree with those found by other authors, except that careful calibration of the Ag source leads to a coverage of 6.10 t* cm z at the work function minimum, in contradiction to Jones (1965). Work function and preexponential changes suggest the formation of a non-metallic layer at low coverages, which reverts to a metallic layer at higher coverages. Interaction of oxygen with silver layers and with silver crystallites on W tips leads to a work function rise of about 0-5 eV, with an initial sticking coefficient up to 10 2 at 90~K. Exposures above 100 L cause strong rearrangement and transport of silver, even at 9 0 K . Even under these conditions, however, oxygen does not penetrate through smooth silver layers and attach itself to the tungsten surface. It is concluded that oxygen adsorption on silver at low pressures leads to rearrangement of the surface, but not to penetration into the bulk. 507
CURRENT WORK ON NUCLEATION
Compiled by D. STAUFFER Institute of Theoretical Physics, University, 66 Saarbriicken 15, West Germany Brief abstracts of work which has not yet been published may be submitted to the compiler for inclusion in this section. Determination of the particle size distribution of an aerosol using a diffusion battery. By J.-P. MAIGNE; Service Technique d'Etudes de Protection et de Pollution Atmospherique, Centre d'Etudes Nucl6aires, Fontenay-auxRoses, France. The principal methods for the treatment of concentration measurements both upstream and downstream of a difl'usion battery are reviewed and discussed, the purpose of the measurements being the determination of the aerosol particle size distribution. It is then demonstrated that the resolution of the equations arising from the problem leads to the imposing of physical constraints on the distribution sought, these constraints being more and more restrictive with increasing experimental inaccuracies. An algorithm is proposed which provides an approximate solution to the system of equations, certain predetermined criteria, and the constraints imposed on the distribution being taken into account. {Thesis. University of Paris). Computer experiments on nucleation processes in the lattice gas model. By K. B~NDER, Bell Laboratories, Murray Hill, New Jersey 07974, U.S.A. Review: no abstract given. Structure of binary solution droplets: Continuum theory and Monte Carlo simulation. By D. STAUFFER; PhysikDepartment T 30, Technical University of Munich, 8046 Garching, West Germany; K. BINDER; (as above), and V. WILDPANER~Atominstitut der C)sterreichischen Hochschulen, A-1020 Vienna, Austria. To calculate the formation energy of binary mixture droplet out of the gas phase in classical "heteromolecular" nucleation theory, one has to take into account that the concentration of the solution near the droplet surface can be different from the composition in the droplet interior ("surface enrichment", Gibbs adsorption equation). This problem is solved in a simple picture where the composition varies spatially but where one has a sharp liquid-gas surface. In a material independent continuum theory, the variation of the composition is assumed to give a free energy contribution proportional to the square of the concentration gradient. This treatment of the surface enrichment gives a formation energy contribution smaller (for large droplets) by a factor 0.42 than previous theories (Neumann and D6ring; Stauffer and Kiang), which therefore overestimated the surface enrichment effect for large droplets. This continuum theory is tested by Monte Carlo methods on a particularly symmetric mixture, the magnetic spin 1/2 Ising model. Here up spins are identified with one type of molecules and down spins with the other type. Reasonable agreement with the continuum theory is found, even for parameter ranges where the assumptions of the continuum theory are no longer valid. The results show clearly a strong but smooth variation of the concentration within the droplet. They constitute to our knowledge the first computer simulations of mixture microdroplets with several molecules of both types. Calculation of dynamical critical properties from a cluster reaction theory. By K. BINDER, D. STAUFFER; (as above) and H. Mi'JLt,L:R-KRUMBHAAR;IBM Ziirich Research Laboratory, 8803 Riischlikon, Switzerland. Critical fluctuations in kinetic Ising models are interpreted in terms of cluster reactions. The basic assumption, that clusters with n spins grow at a rate proportional to nr, is tested by Monte Carlo computations in the single spin flip case. The dynamic susceptibilities associated with order parameter and energy are then calculated also for nonzero field, and are shown to fulfill dynamic scaling, The exponent (2-r)f13 of the relaxation times can be different from tile susceptibility exponent 7. A field emission investigation of adsorption and nucleation of silver on tungsten, and of interaction of the deposits with oxygen. By W. Wt~STNERand D. MENZEL; Institute for Physical Chemistry, Technical University of Munich. 8046 Garching. West Germany. The adsorption of silver on tungsten field emission tips, the formation of silver layers and crystallites, and the interaction of silver layers and crystallites with oxygen have been investigated using a field emission microscope. Good agreement with earlier work has been obtained for the nucleation of silver crystallites. Smooth silver layers many monolayers thick, which retain the symmetry of the W tip. can be produced by slow evaporation at 450°K under extreme ultrahigh vacuum. The work function changes upon adsorption of silver on tungsten agree with those found by other authors, except that careful calibration of the Ag source leads to a coverage of 6.10 t* cm z at the work function minimum, in contradiction to Jones (1965). Work function and preexponential changes suggest the formation of a non-metallic layer at low coverages, which reverts to a metallic layer at higher coverages. Interaction of oxygen with silver layers and with silver crystallites on W tips leads to a work function rise of about 0-5 eV, with an initial sticking coefficient up to 10 2 at 90~K. Exposures above 100 L cause strong rearrangement and transport of silver, even at 9 0 K . Even under these conditions, however, oxygen does not penetrate through smooth silver layers and attach itself to the tungsten surface. It is concluded that oxygen adsorption on silver at low pressures leads to rearrangement of the surface, but not to penetration into the bulk. 507