Browsing by Author "Yeh, Kwei-Tin"

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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
;
Chang, Wen-Yih
;
Baird, James K.
;
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
;
Chang, Wen-Yih
;
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
;
Yeh, Kwei-Tin
;
Chang, Wen-Yih
;
應用化學系
;
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.
IR Study of Monomer-Dimer Self-association of 2,2-Dimethyl-3-ethyl-3-pentanol in n-Octane: Determination of the Molar Absorptivities of Monomer and Dimer Bands, and Dimerization Constants Using Novel Equations
(2013-12-01)
Chen, Jenn-Shing
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Yeh, Kwei-Tin
;
Wu, Cheng-Chang
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Kao, Dah-Yu
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應用化學系
The monomer-dimer self-association equilibrium of 2,2-dimethyl-3-ethyl-3-pentanol in n-octane has been studied by IR spectroscopy at four temperatures (288, 298, 308, and 318 K). The solute was chosen to restrict the self-association between solute molecules to dimerization only, owing to steric hindrance of the bulky chains in the vicinity of the OH group. Two linear equations have been derived for the treatment of the experimental data. One of these equations was used to treat the data of the concentration dependent integrated absorbance of the monomer bands for each temperature to obtain the monomer molar absorptivity, epsilon (m), and dimerization constant, K. The other equation was used to treat the data of concentration-dependent dimer bands to obtain the dimer molar absorptivity, epsilon (d), and K. Thus, the dimerization constant was determined by two methods. Since the same thermodynamic quantity K is obtained from either the monomer bands or the dimer bands, the difference between them at a given temperature can serve as an assessment of the quality of the experiment. The standard enthalpy and entropy of dimerization were also obtained from a van't Hoff plot.
Simulation for optimization of mask error enhancement factor by design of experiments in both dry and immersion ArF lithography
(2006-08-01)
Yeh, Kwei-Tin
;
Lin, Chih-Hung
;
Hu, Ji-Ren
;
Loong, Wen-An
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應用化學系
Simulations for the optimization of the mask error enhancement factor (MEEF) by using Taguchi's design of experiment (DOE) method in both dry and immersion ArF lithography have been demonstrated here. By DOE, MEEF has been successfully reduced, and the process window hash also been enlarged. Furthermore, in immersion lithography, MEEF has been significantly reduced, and resolution is also enhanced. In this study, we determined the optimal process and optical parameters to enlarge the process window and reduce MEEFs for different types of mask by DOE.
Toward a Better Determination of Infrared Molar Absorptivities and Dimer Formation Constants in Self-association Through Hydrogen Bonding: 3-Ethyl-2-methyl-3-pentanol in Tetrachloroethylene as an Example
(2017-10-01)
Chen, Jenn-Shing
;
Yeh, Kwei-Tin
;
Kao, Dah-Yu
;
Baird, James K.
;
應用化學系
The monomer-dimer self-association of the dilute 3-ethyl-2-methyl-3-pentanol in tetrachloroethylene in the very dilute state was studied by infrared spectroscopy at several temperatures. The solute was deliberately chosen so that higher oligomers were suppressed by the steric hindrance arising from bulky groups on both sides of hydroxyl group. Two linear utility equations were derived to treat, respectively, the integrated absorbance of the monomer band, A(m), and of the dimer band, A(d), as functions of the initially prepared solute concentration, [B](0). The respective molar absorptivities were obtained by fitting these equations to the data. Unlike previous methods, the dimerization constant (K) can be obtained from either A(m) or A(d). Any discrepancy between these two values of K serves as a measure of the quality of the data. The values of K at different temperatures were employed to calculate the standard enthalpy and entropy of dimerization by using a van't Hoff plot. The dimer is predominantly in the cyclic form where both hydroxyl protons are hydrogen-bonded. This is inferred from the following observations: (1) the spectrum displays only two bands between 3300 and 3750 cm(-1); (2) the constancy of A(d)/A(m)(2) as a function of [B](0); and (3) the linearity of both plots [B](0)/A(m) vs. A(m), and [B](0)/A(d) vs. A(d)(2).