Browsing by Author "Chang, Wen-Yih"

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Estimation of the Moments of the Residence Time and First Passage Time from Experimentally Measurable Permeation Parameters via a New Formulation of the Transmission Matrix
(2014-08-01)
Chen, Jenn-Shing
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Yeh, Kwei-Tin
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Chang, Wen-Yih
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Baird, James K.
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應用化學系
Siegel\'s analysis on membrane transport in the Laplace domain [J. Phys. Chem. 95 (1991) 2556] in terms of transmission matrix, T(s), has been extended to a more useful formulation. This is achieved by combining uses of the matrix transport equations appropriate for void initial condition, or for saturated equilibrium, or of Dirac delta functional type and the theorem det[T(s)]=1. This formulation enables us to expand T(s) in power series of the Laplace variable, s, with the expansion coefficients as the algebraic functions of the experimentally measurable transport parameters. Utility of the formulation is illustrated in the estimation of the experimentally inaccessible time moments for the first passage or residence times. It was also applied to the percutaneous drug delivery to obtain from the experimental data. The higher moments of the time lag or time lead using a graphic method.
Green's Function and Eigenvalue Representation of Time Lag for Absorptive Permeation Across a Heterogeneous Membrane
(2017-09-01)
Chen, Jenn-Shing
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Yeh, Kwei-Tin
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Chang, Wen-Yih
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應用化學系
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Department of Applied Chemistry
The time- lag problem is treated for absorptive penetration across a heterogeneous membrane, where both the diffusivity D( x) and the partition coefficient K( x) depend on the coordinate x ( 0. x. h), with 0 and h being the coordinates of the upstream and downstream faces, respectively. A new concept of time- lag distribution is introduced, and the first ( time) moment t d1_ L and the second ( time) moment t d2_ L over this distribution are also difined and treated in the Lapalce domain in conjuction with the Green's function G( x, y), and eigenvalues associated with the time- independent diffusion equation subject to the absorbing boundary condition at both ends of the membrane. Our central results include t d1_ L = d h 0 Gdx, x_dx = X i 1.i and t d2_ L = d h 0 d h 0 Gdx, y_Gdy, x_dxdy = X i 1.i 2 + X i 1.2i, where.i is the ith eigenvalue of the aforementioned diffusion equation. The merits of these new resprentations and comparison with the treatments of Frisch or Eyring are also discussed.
Insights into the Kramers' flux-over-population rate for chemical reactions in liquid phases through the matrix transport equation
(2019-08-01)
Chen, Jenn-Shing
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Yeh, Kwei-Tin
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Chang, Wen-Yih
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應用化學系
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Department of Applied Chemistry
Kramers' equation models a chemical reaction as a Brownian particle diffusing over a potential barrier under the influence of medium viscosity. In the case of high viscosity, the equation reduces to a simpler Smoluchowski equation. In this report, we have contrived an equivalent matrix-transport equation that relates the ordered pair (activity, flux) of the output (activated complex) to that of the input (reactant). With an initial condition of the Dirac delta type placed at the location of the reactant, and a reflecting boundary condition set on the reactant state, and an absorbing boundary condition on the activated complex state, we are able to prove the equality relation between the mean first passage time, t over bar fp, for the diffusion and the inverse of the rate constant, k(-1), for the reaction counterpart. We have also derived t over bar fp= n-ary sumation i lambda i-1, where lambda(i) is the ith eigenvalue of the Smoluchowski differential operator stipulated with the above-mentioned boundary conditions. We have also deduced that, in the long time limit, the number of particles remaining inside the diffusion domain decays exponentially with a relaxation time tau=t over bar fp=k-1 just the same as the concentration of the reactant does for a first-order reaction system.