Analytical investigation of two-step adsorption kinetics on surfaces

Nagaoka, Hiroki; Imae, Toyoko

doi:10.1016/s0021-9797(03)00314-x

Cited by 18 publications

(18 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The system of ordinary differential equation (11) has to be integrated in time. Using the finite difference approximation and the explicite Euler scheme forĊ s andĊ g , We have,…”

Section: Finite Element Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic boundary conditions for a coupled convection-diffusion model with heat effects: applications in cross-contamination control

Santatriniaina¹,

Deseure²,

Nguyen³

et al. 2015

IJAMR

View full text Add to dashboard Cite

This work investigates the mass transfer of the Airborne Molecular cross Contamination (AMCs) between the Front Opening Unified Pod (FOUP) and wafer (silicon substrates) during the microelectronics devices manufacturing using dynamic boundary conditions. Such cross-contamination phenomena lead to detrimental impact on production yield in microelectronic industry and a predictive approach using modelling and computational methods is a very strong way to understand and qualify the AMCs cross contamination processes. The FOUP is made of polymeric materials and it is considered as a heterogeneous porous media, it can asorb and desorb the contaminant, thus the modelled processes are the contamination of two-component in transient flow. Coupled diffusion and convection-diffusion model with heat effects are used to define the phenomena. The present methodology is, first using the optimization methods with the numerical solution in order to define the physical constants of various materials which have been studied experimentally and separately, and the second using the finite element methods including these physical constants and relevant interface condition in order to take into account the adsorption kinetics law. Numerical methods to solve the problem are proposed. The dynamics behavior of the AMCs analysis was determined thanks to the switch of Dirichlet to Neumann condition. The mathematical model preserves the classical forms of the diffusion and convection diffusion equations and yields to consistent form of the Fick's law. The computed results are in correlation with the experimental measurements. Some numerical results are presented in this work.

show abstract

“…The system of ordinary differential equation (11) has to be integrated in time. Using the finite difference approximation and the explicite Euler scheme forĊ s andĊ g , We have,…”

Section: Finite Element Methodsmentioning

confidence: 99%

“…They are also able to absorb volatile compounds present in their atmosphere coming from the connection to an equipment or from the release of wafers post processed [1]- [4], [9]. These phenomena result a reversible and a irreversible outgassing of contaminant previously trapped in polymer [9], [10], [11].…”

Section: Introductionmentioning

confidence: 99%

Dynamic boundary conditions for a coupled convection-diffusion model with heat effects: applications in cross-contamination control

Santatriniaina¹,

Deseure²,

Nguyen³

et al. 2015

IJAMR

View full text Add to dashboard Cite

show abstract

“…At the interface of that domain a kinetics law will be established. According to Fick's first and second law, also known as the diffusion equation [9]- [10], is defined in the first part of the equation (1). Where here i: = s, g. The AMCs cross contamination is governed by diffusion time dependent process in which the rate of diffusion is a fraction of time.…”

Section: Model Settingsmentioning

confidence: 99%

“…In this process, the contaminant moves from a region of high concentration (wafer) to one of low concentration (internal surface of FOUP) [11]. According to Fick's first and second law, also known as the diffusion equation [10] also known as the diffusion equation, the flux per unit of area perpendicular to the flux direction is given by:…”

Section: Model Settingsmentioning

confidence: 99%

Coupled system of PDEs to predict the sensitivity of some materials constituents of FOUP with the AMCs cross-contamination

Santatriniaina

Deseure²,

Nguyen³

et al. 2014

International Journal of Applied Mathematical Research

View full text Add to dashboard Cite

This paper deals a predictive model using modeling and computational methods to investigate the sensitivity of some materials constituents of the FOUP with the AMCs cross contamination. Required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs were developed. Numerical optimization and finite elements formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. This mode was used to study the sensitivity of some material with the cross contamination. The behavior of the AMCs in transient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption kinetics of the contaminant on the surface (interface contaminant/polymer) was assumed. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. Many tests of contamination processes were assumed in order to study the sensitivity of the materials. Optimization methods with analytical solution were used to define physical constants for each material versus contaminant. Finite element methods including adsorption kinetic were also used and by using Henry law on the interface and the switch of Dirichlet to Neumann conditions.

show abstract

“…Thus, "desorption" means a number of processes resulting in the release of the sorbing gas from the sorbent. When speaking about the release of methane from a coal bed into an excavation, we typically mean the combination of the filtration (Crank 1975;Timofejew 1967;Pillalamarry et al 2011;Hu et al 2009;Wu et al 1998), diffusion, and sorption processes, which will further be referred to as "the sorption proper" (Harpalani and Chen 1997;Pillalamarry et al 2011;Day and Sakurovs 2008;Weniger et al 2010;CeglarskaStefańska and Zarębska 2005;Majewska et al 2009;Busch and Gensterblum 2011;Nagaoka and Imae 2003). Under laboratory conditions, in which case the investigations are carried out for small-sized grain samples, we can assume that the transportation of gas is influenced mainly by the diffusion processes.…”

Section: Introductionmentioning

confidence: 99%

Sorption Rate of Carbon Dioxide on Coal

Gawor

Skoczylas

2013

Transp Porous Med

View full text Add to dashboard Cite

Traditionally, physicochemical processes whose result is the release of methane from a coal sample-often referred to as desorption-are discussed in relation to two phenomena, i.e., the transportation of gas inward (or outward) the porous substance, and the desorption (or sorption) proper of gas from the coal surface. The complex pore structure of coal necessitated the adoption of an arbitrary division of the gas transportation into: the diffusion of gas within the pore network in grains (understood as a molecular phenomenon) and the filtration of gas through the system of fissures and large pores (understood as a phenomenon related to the fluid mechanics). The filtration-type transportation of gas through a porous medium is most typically discussed in the context of the flow of gas through coal beds, or other porous rocks. In laboratory analyses carried out on granular samples obtained from the porous material, the filtrational flow of gas among the sorbent grains and within the fissure system is so fast (as compared to the diffusion occurring inside the grains) that the decisive factor influencing the kinetics of gas release is, most often, diffusion. In the case of such observations, it is assumed that the process of the sorption proper is almost instantaneous in its nature. There are no theoretical premises that would challenge an assumption thus formed, however, it would be very interesting to carry out an experiment confirming their existence. The present paper discusses an attempt to estimate, under laboratory conditions, the kinetics of the sorption proper. It provides a description of the specially built measuring equipment, as well as the results of the performed experiments, together with their analysis. In the performed experiments, the obtained time constants of sorption were smaller than 50 ms. The lowest values did not exceed 10 ms. Since the obtained time constant values are very low-in spite of the fact that it was impossible to completely eliminate the delays connected with the transportation of molecules to the sorption sites-the authors are of the opinion that the process of sorption proper shall be assumed to be instantaneous.

show abstract

Analytical investigation of two-step adsorption kinetics on surfaces

Cited by 18 publications

References 31 publications

Dynamic boundary conditions for a coupled convection-diffusion model with heat effects: applications in cross-contamination control

Dynamic boundary conditions for a coupled convection-diffusion model with heat effects: applications in cross-contamination control

Coupled system of PDEs to predict the sensitivity of some materials constituents of FOUP with the AMCs cross-contamination

Sorption Rate of Carbon Dioxide on Coal

Contact Info

Product

Resources

About