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Title:  Stochastic Theory of Desorption Reactions (Brownian Motion) 
Author(s):  Lightfoot, Edwin James 
Department / Program:  Chemical Engineering 
Discipline:  Chemical Engineering 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Engineering, Chemical 
Abstract:  A Brownian motion model is used to study the escape of a molecule from a physisorbed state into a dense fluid. In the limit of a high dynamical friction coefficient, the Smoluchowski diffusion equation, with an annihilation boundary condition, is used to predict the concentration profile, the rate constant for desorption, and the mean time to desorption. A general asymptotic solution to the Smoluchowski equation is obtained which demonstrates that within the restrictions of the annihilation assumption the concentration profile is given by the Boltzmann distribution multiplied by a depletion factor determined exclusively by the asymptotic form of the attraction to the surface. Two methods of determining the rate constant by direct integration are givenone a variational approach and the other a pseudosteadystate approach introduced by Kramers. Both methods are used to estimate the rate constant for the escape from a piecewise parabolic potential and from a potential of the LennardJones type (r('2n)  r('n)). For both potentials the two methods give essentially identical results. Over a broad range of conditions (including a dynamical friction coefficient which rises near the surface), the mean time to escape is found to approach asymptotically a linear function of the distance between the surface and the annihilation point. Asymptotic estimates are made of both the slope and intercept of this linear function; numerical integration confirms the accuracy of these estimates. For moderate values of the dynamical friction, the FokkerPlanck phase space diffusion equation, popularized by Kramers and Chandrasekhar, is used to estimate the rate of equilibration in a LennardJones type double well (in the limit of high friction this is equivalent to the annihilation formalism used with the Smoluchowski equation). Again, the mean time to escape from a LennardJones type potential well is found to approach asymptotically a linear function of the distance from the surface to the center of the double well. The slope of this linear relationship is found to reduce to the same slope found for the Smoluchowski equation as either the friction constant or the width of the double well becomes large. The predicted dependence of the rate constant on the dynamical friction is confirmed by numerical integration of the FokkerPlanck equation. 
Issue Date:  1985 
Type:  Text 
Description:  174 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1985. 
URI:  http://hdl.handle.net/2142/69762 
Other Identifier(s):  (UMI)AAI8600255 
Date Available in IDEALS:  20141215 
Date Deposited:  1985 
This item appears in the following Collection(s)

Dissertations and Theses  Chemical and Biomolecular Engineering
Dissertations and Theses  Chemical and Biomolecular Engineering 
Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois