Diffusion coefficient for a Brownian particle in a periodic field of force

Festa, Roberto; d’Agliano, E. Galleani

doi:10.1016/0378-4371(78)90111-5

Cited by 142 publications

(96 citation statements)

References 10 publications

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“…The range of concentrations in the smectic phase supplies a range of ordering potentials for which the theoretical predictions can be tested [37] …”

Section: Resultsmentioning

confidence: 99%

Dynamics in the smectic phase of stiff viral rods

2011

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We report on the dynamics in colloidal suspensions of stiff viral rods, called fd-Y21M. This mutant filamentous virus exhibits a persistence length 3.5 times larger than the wild-type fd-wt. Such a virus system can be used as a model system of rodlike particles for studying their self-diffusion. In this paper, the physical features, such as rod contour length and polydispersity have been determined for both viruses. The effect of viral rod flexibility on the location of the nematic-smectic phase transition has been investigated, with a focus on the underlying dynamics studied more specifically in the smectic phase. Direct visualization of the stiff fd-Y21M at the scale of a single particle has shown the mass transport between adjacent smectic layers, as found earlier for the more flexible rods. We could relate this hindered diffusion with the smectic ordering potentials for varying rod concentrations. The self-diffusion within the layers is far more pronounced for the stiff rods as compared to the more flexible fd-wt viral rod.

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“…The range of concentrations in the smectic phase supplies a range of ordering potentials for which the theoretical predictions can be tested [37] …”

Section: Resultsmentioning

confidence: 99%

Dynamics in the smectic phase of stiff viral rods

2011

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“…Finally, the indium tracer diffusion tensor D is obtained by solving the master equation for the corresponding network of sites in the long-time limit ͑see the Appendixes͒. 43 This method has been previously applied to adatom diffusion on stepped surfaces, 44 Ga diffusion on GaAs͑001͒-␤2(2 ϫ4), Ref. 45, and In diffusion on GaAs͑001͒-c(4ϫ4), Ref.…”

Section: ⑀ӷ1 ͑2͒mentioning

confidence: 99%

Anisotropic diffusion of In adatoms on pseudomorphicInxGa1−xAsfilms: First-p

et al. 2004

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In the Stranski-Krastanow growth of strained pseudomorphic films, material transport by surface diffusion plays a crucial role for the development of the three-dimensional island morphology. In an attempt to elucidate the atomistic aspects of this growth mode, we study diffusion of a single indium adatom on (1ϫ3)-and (2 ϫ3)-reconstructed subcritical In 2/3 Ga 1/3 As(001) films using first-principles total energy calculations of the corresponding adiabatic potential-energy surfaces ͑PES͒. We find that In diffusion is anisotropic, and substantially enhanced compared to the conventional GaAs͑001͒-c(4ϫ4) substrate. Special attention is also paid to the methodology of deriving the tracer diffusion coefficients of indium from knowledge of the PES, using the continuous-time random-walk formalism.

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“…It is also applicable to the case when the molecule changes channels; the time spent in perpendicular channels can be modeled by proper potential wells at the channel cross sections. Equation 18 was derived rigorously by Festa and d'Agliano 16 for the case of a periodic potential U. At low temperature, the first term in eq 18 is proportional to the maximum of the potential, while the second one is more sensitive to its minimum.…”

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confidence: 99%

“…Hence, there is no problem to estimates the parameters A and C if the exact potential is known but to calculate the latter is not a trivial work. Usually, it is easy to calculate the potential minima, which are important for description of the adsorption in zeolites 16 . The number n is usually larger than 5 and if the coefficients A and C are commensurable, it is clear that the leading term in the derivatives of  is the last one.…”

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confidence: 99%

Resonant Diffusion of Normal Alkanes in Zeolites: Effect of the Zeolite Structure and Alkane Molecule Vibrations

Tsekov

Smirniotis

1998

J. Phys. Chem. B

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Diffusion of normal alkanes in one-dimensional zeolites is theoretically studied on the basis of the stochastic equation formalism. The calculated diffusion coefficient accounts for the vibrations of the diffusing molecule and zeolite framework, molecule-zeolite interaction, and specific structure of the zeolite. It is shown that when the interaction potential is predominantly determined by the zeolite pore structure, the diffusion coefficient varies periodically with the number of carbon atoms of the alkane molecule, a phenomenon called resonant diffusion. A criterion for observable resonance is obtained from the balance between the interaction potentials of the molecule due to the atomic and pore structures of the zeolite. It shows that the diffusion is not resonant in zeolites without pore structure, such as ZSM-12. Moreover, even in zeolites with developed pore structure no resonant dependence of the diffusion constant can be detected if the pore structure energy barriers are not at least three times higher than the atomic structure energy barriers. The role of the alkane molecule vibrations is examined as well and a surprising effect of suppression of the diffusion in comparison with the case of a rigid molecule is observed. This effect is explained with the balance between the static and dynamic interaction of the molecule and zeolite.Zeolites attract scientific attention because of their remarkable catalytic and sorption properties. They are regular porous materials with pore size in the order of several Angstroms. Because of their structure, zeolites can exhibit molecular shape selectivity to certain molecules, which is very important for many applications of practical interest 1 . An important factor for the efficiency of each process utilizing zeolites is the rate of intracrystalline mass transfer of species. For instance, chemical reactions are catalyzed in zeolites at some active centers and, therefore, are frequently diffusion controlled since the reactants have to reach these active centers first.The methods to measure the mobility of molecules in zeolites are naturally divided in two groups 2 . The first group consists of measurements of some macroscopic integral response of the system. One can mention here, for instance, the classical absorption/desorption experiments. On this method the diffusion constant is calculated by comparing the experimental absorption/ desorption curves with exact solutions of the unsteady state diffusion equation for the particular shape of zeolite grains employed 3 . The experimental curves, however, are influenced not by the diffusion process only. In fact, there are at least three consequent processes, namely, transfer of

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Diffusion coefficient for a Brownian particle in a periodic field of force

Cited by 142 publications

References 10 publications

Dynamics in the smectic phase of stiff viral rods

Dynamics in the smectic phase of stiff viral rods

Anisotropic diffusion of In adatoms on pseudomorphicInxGa1−xAsfilms: First-p

Resonant Diffusion of Normal Alkanes in Zeolites: Effect of the Zeolite Structure and Alkane Molecule Vibrations

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