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Monte Carlo simulation of the kinetics of heterogeneous nucleation
Aerosol Science, 1973, Vol. 4, pp. 265 to 267. Pergamon Press. Printed in Great Britain.
CURRENT WORK ON NUCLEATION C o m p i l e d b y C. S. IOAlqG a n d D . STAUFFER Physics Department, Clark College, Atlanta, Georgia, 30314 U.S.A. Brief abstracts of work which has not yet been published may be submitted to the compilers for inclusion in this section. On the validity of homogeaeous nucleation theory. By J. J. BURTON;Henry Krumb School of Mines, Columbia University, New York, New York 10027, U.S.A.
Exact thermodynamic properties of small clusters of 3-87 atoms have been computed for a simple model system. The differences between the exact results and the capillarity model are examined. The exact thermodynamic properties are used to calculate the homogeneous vapor phase nucleation rates, Jex,ot, and the results are compared with the predictions of classical nucleation theory, Jcta,.. It is found that Jexa¢t/Jc~.*, varies from 10 -2 to 10 -7 and depends strongly on temperature and supersaturation. The predicted values of Jexact are compared with existing experimental results involving a wide range of temperatures and materials. The agreement between the theory and experiment is quite good.
Melting of a small cluster of atoms. By C. L. BRIANTand J. J. BURTON; Henry Krumb School of Mines, Columbia University, New York, New York 10027, U.S.A. We have used molecular dynamics to examine the melting of a 55 atom duster. The transition from solid to liquid is first order. However, immediately prior to melting, a second order phase transition also occurs.
On the role of rotation and translation in nucleation theory. By J. J. BURTON and A. PEYTON FLEISHMAN, Henry Knmlb School of Mines, Columbia University, New York, New York 10027, U.S.A.
We have calculated the equilibrium constant for formation of iodine dimers (I2) from iodine monomers including and excluding rotation-translation contributions to partition function. The results are compared with experimental data. We conclude that rotation-translation factors are necessary and must, hence, be included in nucleation theory.
Number dependence of small-crystal thermodynamic properties--HI. By F. F. AnRAHAM, IBM Research Laboratory, San Jose, California, U.S.A. and g. N. KORTZEBORNand H. H. WANG,IBM Scientific Center, Palo Alto, California, U.S.A. Using numerical techniques, we have computed the classical excess entropy for three-dimensional octahedron crystallites and "approximately spherical" crystaUites of the fcc close packed lattice. Using these data and previously calculated entropies for various other two-dimensional and three-dimensional crystallites, a least squares analysis is performed to determine the coefficients of a function which is assumed to represent the functional dependence of the entropy on crystal size and shape. The features of the entropy function are discussed. An analysis of the replacement free energy and the total Helmholtz free energy for the various shaped clusters is presented, as well as a comparison of the exact surface free energy of the spherical clusters with the capillarity approximation.
Monte Carlo simulation of the kinetics of heterogeneous nucleation, By A. I. MICHAELS and G. M. POUND; Materials Science Department, Stanford University, Stanford, California 94305, U.S.A. and F. F. AagAHAM; IBM Research Laboratory, San Jose, California, U.S.A. 265
266
Current work on nucleation
This paper describes a computer simulation model which reproduces the random atomic processes which occur in condensation, evaporation, and surface diffusion (upon an idealized (100) crystalline substrate surface). Computer simulation experiments based on this model were carried out over a range of adatomadatom interaction energies and adsorption fluxes chosen so as to produce observable nucleation phenomena in a reasonably short computation time. The equilibrium distribution of cluster sizes and the critical cluster size were measured in a large number of cases and compared to predictions of the Walton-Rhodin atomistic nucleation theory. Very good agreement between the experimental and theoretical values was obtained. The nucleation rate was also measured for one particular set of parameters and found to agree satisfactorily with the atomistic theory prediction. Consequently, we conclude that within the limitation of the assumptions of the simulation model used, the Monte Carlo method is suitable for the simulation of the phenomena of heterogeneous nucleation. A number of suggestions are offered for the refinement and extension of this simulation method which may help to answer some of the unresolved questions of heterogeneous nucleation theory.
Molecular dynamics study of the clustering in hard parallel squares. By C. CARLIERand H. L. FRISCH; State University of New York, Albany, New York 12222, U.S.A. A molecular dynamics study of clustering in systems of 400 and 900 hard parallel squares shows that in the high density region, the distributions N(n) of clusters of size n depend only upon one dimensionless variable. Results are slightly different in the intermediate density fluid region. For all densities and values of the clustering distance parameter L, N(n) is a monotone decreasing function of n. A simple free volume theory predicts relatively well the results in the high density region. The clusters are relatively compact. From an exponential fit to the function N(n)/N(1) obtained for densities near the phase--transition region, one estimates the value of the parameters of the exponential law given by the classical theory of nuclation.
Heteromolecular nucleation theory applied to gas to particle conversion. By C. S. KIANG and D. STAUFFER; Physics Department, Clark College, Altanta, Georgia 30314, U.S.A. and V. A. Morrr~N; Atmospheric Sciences Research Center, State University of New York, Albany, New York 12222, U.S.A. and J. BRICARD; Physique des Aerosols, Facult6 des Sciences, Universit6 de Paris, France. An attempt has been made to explain gas to particle conversion with the beteromolecular nucleation theory, The theory is applied to a binary mixture of H 2 0 - H z S O , and H 2 0 - H N O a respectively in air. The resulting formation of critical sized clusters is calculated as function of relative humidity up to 99 per cent. Sulfuric acid resulting from gas phase reactions in the atmosphere has one of the lowest vapor pressures of all reaction products. Nitric acid with its relatively high vapour pressure would represent an upper limit for gas to particle conversion to occur under atmospheric conditions.
Homogeneous nudeafion in steam nozzle condensation. By D. BARSCHDORFF,W. J. DUNNING,P. P. WEGENER and B. J, C. Wu; Department of Engineering and Applied Science, Yale University, New Haven, Connecticut 06520, U.S.A.
(No abstract given; to be published in Nature.)
RecentstudiesenSO2 oxidation in the presence of liquid water. By S. BEILKE,D. LAMB and J. MILLER; Institut fur Metenrologie und Genphysik, OniversitAt, Frankfurt, West Germany. The following studies refer in a wide sense to problems of trace gas and atmospheric aerosol agglomoration on cloud droplets and rain droplets. Of particular interest is here the incorporation of atmospheric sulphur compounds like S02, H2S, and sulfate, which is an essential constituent of atmospheric aerosols. (In German.)
Condensation nuclei discriminator based on optical measurements during fog formation: A new tool for environmental research. By E. J. HART, K. H. SCHMIDT and K. N. VASUDEVAN;Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, U,S.A.
(No abstract given.)
CURRENT WORK ON NUCLEATION C o m p i l e d b y C. S. IOAlqG a n d D . STAUFFER Physics Department, Clark College, Atlanta, Georgia, 30314 U.S.A. Brief abstracts of work which has not yet been published may be submitted to the compilers for inclusion in this section. On the validity of homogeaeous nucleation theory. By J. J. BURTON;Henry Krumb School of Mines, Columbia University, New York, New York 10027, U.S.A.
Exact thermodynamic properties of small clusters of 3-87 atoms have been computed for a simple model system. The differences between the exact results and the capillarity model are examined. The exact thermodynamic properties are used to calculate the homogeneous vapor phase nucleation rates, Jex,ot, and the results are compared with the predictions of classical nucleation theory, Jcta,.. It is found that Jexa¢t/Jc~.*, varies from 10 -2 to 10 -7 and depends strongly on temperature and supersaturation. The predicted values of Jexact are compared with existing experimental results involving a wide range of temperatures and materials. The agreement between the theory and experiment is quite good.
Melting of a small cluster of atoms. By C. L. BRIANTand J. J. BURTON; Henry Krumb School of Mines, Columbia University, New York, New York 10027, U.S.A. We have used molecular dynamics to examine the melting of a 55 atom duster. The transition from solid to liquid is first order. However, immediately prior to melting, a second order phase transition also occurs.
On the role of rotation and translation in nucleation theory. By J. J. BURTON and A. PEYTON FLEISHMAN, Henry Knmlb School of Mines, Columbia University, New York, New York 10027, U.S.A.
We have calculated the equilibrium constant for formation of iodine dimers (I2) from iodine monomers including and excluding rotation-translation contributions to partition function. The results are compared with experimental data. We conclude that rotation-translation factors are necessary and must, hence, be included in nucleation theory.
Number dependence of small-crystal thermodynamic properties--HI. By F. F. AnRAHAM, IBM Research Laboratory, San Jose, California, U.S.A. and g. N. KORTZEBORNand H. H. WANG,IBM Scientific Center, Palo Alto, California, U.S.A. Using numerical techniques, we have computed the classical excess entropy for three-dimensional octahedron crystallites and "approximately spherical" crystaUites of the fcc close packed lattice. Using these data and previously calculated entropies for various other two-dimensional and three-dimensional crystallites, a least squares analysis is performed to determine the coefficients of a function which is assumed to represent the functional dependence of the entropy on crystal size and shape. The features of the entropy function are discussed. An analysis of the replacement free energy and the total Helmholtz free energy for the various shaped clusters is presented, as well as a comparison of the exact surface free energy of the spherical clusters with the capillarity approximation.
Monte Carlo simulation of the kinetics of heterogeneous nucleation, By A. I. MICHAELS and G. M. POUND; Materials Science Department, Stanford University, Stanford, California 94305, U.S.A. and F. F. AagAHAM; IBM Research Laboratory, San Jose, California, U.S.A. 265
266
Current work on nucleation
This paper describes a computer simulation model which reproduces the random atomic processes which occur in condensation, evaporation, and surface diffusion (upon an idealized (100) crystalline substrate surface). Computer simulation experiments based on this model were carried out over a range of adatomadatom interaction energies and adsorption fluxes chosen so as to produce observable nucleation phenomena in a reasonably short computation time. The equilibrium distribution of cluster sizes and the critical cluster size were measured in a large number of cases and compared to predictions of the Walton-Rhodin atomistic nucleation theory. Very good agreement between the experimental and theoretical values was obtained. The nucleation rate was also measured for one particular set of parameters and found to agree satisfactorily with the atomistic theory prediction. Consequently, we conclude that within the limitation of the assumptions of the simulation model used, the Monte Carlo method is suitable for the simulation of the phenomena of heterogeneous nucleation. A number of suggestions are offered for the refinement and extension of this simulation method which may help to answer some of the unresolved questions of heterogeneous nucleation theory.
Molecular dynamics study of the clustering in hard parallel squares. By C. CARLIERand H. L. FRISCH; State University of New York, Albany, New York 12222, U.S.A. A molecular dynamics study of clustering in systems of 400 and 900 hard parallel squares shows that in the high density region, the distributions N(n) of clusters of size n depend only upon one dimensionless variable. Results are slightly different in the intermediate density fluid region. For all densities and values of the clustering distance parameter L, N(n) is a monotone decreasing function of n. A simple free volume theory predicts relatively well the results in the high density region. The clusters are relatively compact. From an exponential fit to the function N(n)/N(1) obtained for densities near the phase--transition region, one estimates the value of the parameters of the exponential law given by the classical theory of nuclation.
Heteromolecular nucleation theory applied to gas to particle conversion. By C. S. KIANG and D. STAUFFER; Physics Department, Clark College, Altanta, Georgia 30314, U.S.A. and V. A. Morrr~N; Atmospheric Sciences Research Center, State University of New York, Albany, New York 12222, U.S.A. and J. BRICARD; Physique des Aerosols, Facult6 des Sciences, Universit6 de Paris, France. An attempt has been made to explain gas to particle conversion with the beteromolecular nucleation theory, The theory is applied to a binary mixture of H 2 0 - H z S O , and H 2 0 - H N O a respectively in air. The resulting formation of critical sized clusters is calculated as function of relative humidity up to 99 per cent. Sulfuric acid resulting from gas phase reactions in the atmosphere has one of the lowest vapor pressures of all reaction products. Nitric acid with its relatively high vapour pressure would represent an upper limit for gas to particle conversion to occur under atmospheric conditions.
Homogeneous nudeafion in steam nozzle condensation. By D. BARSCHDORFF,W. J. DUNNING,P. P. WEGENER and B. J, C. Wu; Department of Engineering and Applied Science, Yale University, New Haven, Connecticut 06520, U.S.A.
(No abstract given; to be published in Nature.)
RecentstudiesenSO2 oxidation in the presence of liquid water. By S. BEILKE,D. LAMB and J. MILLER; Institut fur Metenrologie und Genphysik, OniversitAt, Frankfurt, West Germany. The following studies refer in a wide sense to problems of trace gas and atmospheric aerosol agglomoration on cloud droplets and rain droplets. Of particular interest is here the incorporation of atmospheric sulphur compounds like S02, H2S, and sulfate, which is an essential constituent of atmospheric aerosols. (In German.)
Condensation nuclei discriminator based on optical measurements during fog formation: A new tool for environmental research. By E. J. HART, K. H. SCHMIDT and K. N. VASUDEVAN;Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, U,S.A.
(No abstract given.)