Diffusion Influenced Adsorption Kinetics
When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir–Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the La...
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| Published in | The journal of physical chemistry. B Vol. 119; no. 34; pp. 10954 - 10961 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
American Chemical Society
27.08.2015
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1520-6106 1520-5207 1520-5207 |
| DOI | 10.1021/acs.jpcb.5b00580 |
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| Abstract | When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir–Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir–Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald–Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage. |
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| AbstractList | When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage. When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Gruenwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage. When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage. When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir–Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir–Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald–Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage. |
| Author | Seki, Kazuhiko Miura, Toshiaki |
| AuthorAffiliation | National Institute of Advanced Industrial Science and Technology (AIST) |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25969862$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1007/BF01474958 10.1016/0022-3697(57)90054-9 10.1021/jp001649t 10.1021/jp983433l 10.1021/la970923g 10.1021/ja01290a091 10.1021/ja042898o 10.1016/0927-7757(94)03061-4 10.1016/0166-6622(92)80230-Y 10.1016/S0021-9797(03)00530-7 10.1016/j.compchemeng.2009.08.004 10.1016/0095-8522(61)90043-5 10.1021/jp960377k 10.1021/la015567n 10.1016/0009-2509(83)85021-0 10.1126/science.262.5142.2010 10.1021/la00002a049 10.1137/030602666 10.1063/1.1605946 10.1016/S0167-7322(99)00124-5 10.1143/JJAP.40.6945 10.1063/1.1587126 10.1016/j.bpj.2009.05.022 10.1021/j100159a065 10.1103/PhysRevE.91.052604 10.1016/j.cis.2014.01.006 10.1103/PhysRevE.75.031804 10.1063/1.1724167 10.1021/jp0749017 10.1080/00018737800101474 10.1063/1.1287335 |
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| SubjectTerms | Adsorption chemical elements Diffusion equations Exact solutions Lower bounds Mathematical analysis Mathematical models Nonlinearity solutes Surface chemistry |
| Title | Diffusion Influenced Adsorption Kinetics |
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