Temperature scaling of the homogenous vapor-to-liquid nucleation rate, J, is examined in a model Lennard-Jones (LJ) system. The model uses the Bennett Metropolis Monte Carlo technique to determine small cluster growth/decay rate constant ratios ßn-1|αn at four temperatures (T = 40, 50, 60, and 83.6K) below the argon Lennard-Jones critical temperature, Tc. The ßn-1|αn for clusters ranging in size from n = 2 to n = 192 LJ particles are applied to a kinetic steady-state nucleation rate formalism and nucleation rates are determined at the same four temperatures. When these rates are plotted first in the standard way vs. lnS, (where S is the ratio of ambient to coexistence vapor pressure) and then vs. the scaled supersaturation, lnS / [Tc/T-1]3/2, the values of logJ are found to collapse onto a single line. This demonstrates that the nucleation rate is a function of lnS / [Tc/T-1]3/2 -- rather than of the independent variables, S and T. A similar scaling has been observed in the experimental nucleation rate data of water and toluene. The present study is the first simulation based demonstration of vapor to liquid nucleation rate temperature scaling in a model dilute vapor system and provides insight into the \"law of mass action\" model assumptions which give rise to the scaling.
","abstract_html":"<p>Temperature scaling of the homogenous vapor-to-liquid nucleation rate, J, is examined in a model Lennard-Jones (LJ) system. The model uses the Bennett Metropolis Monte Carlo technique to determine small cluster growth/decay rate constant ratios ß<sub>n-1</sub>|α<sub>n</sub> at four temperatures (T = 40, 50, 60, and 83.6K) below the argon Lennard-Jones critical temperature, T<sub>c</sub>. The ß<sub>n-1</sub>|α<sub>n</sub> for clusters ranging in size from n = 2 to n = 192 LJ particles are applied to a kinetic steady-state nucleation rate formalism and nucleation rates are determined at the same four temperatures. When these rates are plotted first in the standard way vs. <em>lnS</em>, (where S is the ratio of ambient to coexistence vapor pressure) and then vs. the <em>scaled supersaturation</em>, <em>lnS</em> / [T<sub>c</sub>/T-1]<sup>3/2</sup>, the values of logJ are found to collapse onto a single line. This demonstrates that the nucleation rate is a function of <em>lnS</em> / [T<sub>c</sub>/T-1]<sup>3/2</sup> -- rather than of the independent variables, S and T. A similar scaling has been observed in the experimental nucleation rate data of water and toluene. The present study is the first simulation based demonstration of vapor to liquid nucleation rate temperature scaling in a model dilute vapor system and provides insight into the "law of mass action" model assumptions which give rise to the scaling.</p>","abstract_has_math":false,"creators":["Thomason, Mark Allan"],"institution":"Missouri University of Science and Technology","degree_name":"Ph. D. in Physics","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-02-10T08:00:00Z","date_published":"2016-02-10T08:00:00Z","updated_at":"2026-07-24T03:19:12Z","subjects":["Physics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsmine.mst.edu/doctoral_dissertations/2025","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Thomason, Mark Allan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-10T08:00:00Z"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation - Open Access"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D. in Physics"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Missouri University of Science and Technology"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsmine.mst.edu/doctoral_dissertations/2025"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Temperature scaling of the homogenous vapor-to-liquid nucleation rate, J, is examined in a model Lennard-Jones (LJ) system. The model uses the Bennett Metropolis Monte Carlo technique to determine small cluster growth/decay rate constant ratios ßn-1|αn at four temperatures (T = 40, 50, 60, and 83.6K) below the argon Lennard-Jones critical temperature, Tc. The ßn-1|αn for clusters ranging in size from n = 2 to n = 192 LJ particles are applied to a kinetic steady-state nucleation rate formalism and nucleation rates are determined at the same four temperatures. When these rates are plotted first in the standard way vs. lnS, (where S is the ratio of ambient to coexistence vapor pressure) and then vs. the scaled supersaturation, lnS / [Tc/T-1]3/2, the values of logJ are found to collapse onto a single line. This demonstrates that the nucleation rate is a function of lnS / [Tc/T-1]3/2 -- rather than of the independent variables, S and T. A similar scaling has been observed in the experimental nucleation rate data of water and toluene. The present study is the first simulation based demonstration of vapor to liquid nucleation rate temperature scaling in a model dilute vapor system and provides insight into the \"law of mass action\" model assumptions which give rise to the scaling.
"]},{"key":"dc:title","label":"Title","values":["A Monte Carlo study of the scaling of nucleation rates in a Lennard-Jones system"]}]}],"canonical_facts":{"dc:creator":["Thomason, Mark Allan"],"dc:date.available":["2016-02-10T08:00:00Z"],"dc:description.abstract":["Temperature scaling of the homogenous vapor-to-liquid nucleation rate, J, is examined in a model Lennard-Jones (LJ) system. The model uses the Bennett Metropolis Monte Carlo technique to determine small cluster growth/decay rate constant ratios ßn-1|αn at four temperatures (T = 40, 50, 60, and 83.6K) below the argon Lennard-Jones critical temperature, Tc. The ßn-1|αn for clusters ranging in size from n = 2 to n = 192 LJ particles are applied to a kinetic steady-state nucleation rate formalism and nucleation rates are determined at the same four temperatures. When these rates are plotted first in the standard way vs. lnS, (where S is the ratio of ambient to coexistence vapor pressure) and then vs. the scaled supersaturation, lnS / [Tc/T-1]3/2, the values of logJ are found to collapse onto a single line. This demonstrates that the nucleation rate is a function of lnS / [Tc/T-1]3/2 -- rather than of the independent variables, S and T. A similar scaling has been observed in the experimental nucleation rate data of water and toluene. The present study is the first simulation based demonstration of vapor to liquid nucleation rate temperature scaling in a model dilute vapor system and provides insight into the \"law of mass action\" model assumptions which give rise to the scaling.
"],"dc:identifier":["https://scholarsmine.mst.edu/doctoral_dissertations/2025"],"dc:subject":["Physics"],"dc:title":["A Monte Carlo study of the scaling of nucleation rates in a Lennard-Jones system"],"dc:type":["Dissertation - Open Access"],"thesis:degree_name":["Ph. D. in Physics"],"thesis:institution_name":["Missouri University of Science and Technology"]},"updated_at":"2026-07-24T03:19:12Z"}