Transmission probabilities and particle–wall contact for Knudsen diffusion in pores of variable diameter

Albo, Simon E.; Broadbelt, Linda J.; Snurr, Randall Q.

doi:10.1016/j.ces.2007.08.041

Cited by 9 publications

(8 citation statements)

References 17 publications

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“…The track-etched polycarbonate membrane was clamped in the sample holder, with an effective section area of 0.396 cm 2 , and nitrogen gas was delivered upstream from the sample at a pressure ranging from 10 4 to 4 × 10 5 Pa. The gas flow rate (mL/min) downstream from the sample was then measured using a flowmeter (Agilent), giving access to the mean diameter of the pores by using relationships based on the Knudsen diffusion and the viscous or Hagen−Poiseuille flow. ,, …”

Section: Methodsmentioning

confidence: 99%

Growth Mechanism of Confined Polyelectrolyte Multilayers in Nanoporous Templates

et al. 2009

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We investigate the mechanism of polyelectrolyte multilayer (PEM) assembly in nanoporous templates with a view to synthesizing nanotubes or nanowires under optimal conditions. For this purpose, we focus on the effect of parameters related to the geometrical constraints (pore diameter), the size of the macromolecules (their molar mass and the ionic strength), and the interaction between the pore walls and the adsorbed chains (modulated by the ionic strength). Our results reveal the existence of two regimes in the mechanism of PEM growth: (i) the first regime is comparable to that observed on flat substrates, including the influence of ionic strength and (ii) the second regime, which is slower in terms of kinetics, results from the interconnection established between polyelectrolyte chains across the pores and leads to the formation of a dense gel. As a consequence, the diffusion of polyelectrolytes in nanopores becomes the controlling factor of PEM growth in this second regime. The dense gel, owing to its peculiar structure, enhances the formation of nanowires or of partially occluded nanotubes in some cases, depending on initial pore dimensions.

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Section: Methodsmentioning

confidence: 99%

Growth Mechanism of Confined Polyelectrolyte Multilayers in Nanoporous Templates

et al. 2009

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“…For gases, a unique nano-confinement phenomenon occurs that has been studied since the beginning of the 20th Century, and is called Knudsen diffusion [3,[256][257][258][259][260][261][262][263][264][265][266][267][268][269][270][271][272], after Martin Knudsen [273,274], who first described it as "molecular flow" (German: Molekularströmung). When the mean free path of gas molecules, , becomes larger or is of the same order of magnitude as the local channel diameter, d , the frequency of the collisions between the molecules and the walls exceeds the intermolecular collision frequency.…”

Section: General Features Of Diffusion In Mesoporous Materialsmentioning

confidence: 99%

“…Knudsen assumed that the collisions with the wall are diffuse, rather than specular; that is, upon colliding with the walls, molecules adsorb for a short time, after which energy is redistributed over their various degrees of freedom, and partially exchanged with the walls, so that, when molecules desorb back into the pore space and continue their trajectory, the angle of reflection is independent of the angle of incidence and follows a cosine distribution-similar to Lambert's law of diffuse light reflection [3,[256][257][258][259][260][261][262][263][264][265][266][267][268][269][270][271][272]. Clausing [467] later showed that the cosine distribution is a direct result of the second Law of Thermodynamics, rather than requiring roughness.…”

Section: Knudsen Diffusion In Pore Channelsmentioning

confidence: 99%

“…These results are only partially consistent with the results of Albo et al [262] In particular, entrance effects are lacking in their hitting distributions, which is an artifact of their model. Albo et al [260] have also performed Knudsen dynamics simulations in cylindrical pores with multiple sections of different diameters. Simulations performed in two-section pores have shown that the angle of transition between the different diameters has little effect on the transmission probability and the distribution of hits on the wall, except when the transition angle is very small, and the transition is extremely smooth.…”

Section: Knudsen Diffusion In Pore Channelsmentioning

confidence: 99%

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Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

et al. 2021

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Nanoporous solids are ubiquitous in chemical, energy, and environmental processes, where controlled transport of molecules through the pores plays a crucial role. They are used as sorbents, chromatographic or membrane materials for separations, and as catalysts and catalyst supports. Defined as materials where confinement effects lead to substantial deviations from bulk diffusion, nanoporous materials include crystalline microporous zeotypes and metal–organic frameworks (MOFs), and a number of semi-crystalline and amorphous mesoporous solids, as well as hierarchically structured materials, containing both nanopores and wider meso- or macropores to facilitate transport over macroscopic distances. The ranges of pore sizes, shapes, and topologies spanned by these materials represent a considerable challenge for predicting molecular diffusivities, but fundamental understanding also provides an opportunity to guide the design of new nanoporous materials to increase the performance of transport limited processes. Remarkable progress in synthesis increasingly allows these designs to be put into practice. Molecular simulation techniques have been used in conjunction with experimental measurements to examine in detail the fundamental diffusion processes within nanoporous solids, to provide insight into the free energy landscape navigated by adsorbates, and to better understand nano-confinement effects. Pore network models, discrete particle models and synthesis-mimicking atomistic models allow to tackle diffusion in mesoporous and hierarchically structured porous materials, where multiscale approaches benefit from ever cheaper parallel computing and higher resolution imaging. Here, we discuss synergistic combinations of simulation and experiment to showcase theoretical progress and computational techniques that have been successful in predicting guest diffusion and providing insights. We also outline where new fundamental developments and experimental techniques are needed to enable more accurate predictions for complex systems.

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“…In our previous work we have used Knudsen dynamics simulations without reaction to study the transmission probability and the number and distribution of hits between the particles and the wall in cylindrical pores of uniform diameter 6 and in cylindrical pores of variable diameter. 7 Here we add the possibility that particles that hit the wall will react. Other researchers have performed simulations for Knudsen diffusion but considering one particle at a time for pores of different shapes [11][12][13][14] and roughness [15][16][17] and with diffusion-limited reactions.…”

Section: Model and Simulation Detailsmentioning

confidence: 99%

Designing Nanostructured Membranes for Oxidative Dehydrogenation of Alkanes Using Kinetic Modeling

Albo¹,

Snurr²,

Broadbelt³

2008

Ind. Eng. Chem. Res.

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Continuum-level modeling and Knudsen dynamics simulations were used to investigate the oxidative dehydrogenation of ethane in nanostructured membranes. Different operational modes were investigated, including pass-through and sweep-gas modes, and pores with total and partial catalyst coverage on the walls were studied. It was determined that by adjusting the aspect ratio (L/d) of the pore in the pass-through mode it is possible to achieve high conversions and yields even for slow reactions. On the other hand, in the sweepgas mode, the velocity of the reaction limits the conversion and yield that can be achieved. It was also found that, under Knudsen diffusion, covering the wall of the pores only partially with catalyst could improve the per gram conversion obtained. However, it does not improve the selectivity achieved for a given conversion when compared to that obtained in a pore fully covered in catalyst.

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Transmission probabilities and particle–wall contact for Knudsen diffusion in pores of variable diameter

Cited by 9 publications

References 17 publications

Growth Mechanism of Confined Polyelectrolyte Multilayers in Nanoporous Templates

Growth Mechanism of Confined Polyelectrolyte Multilayers in Nanoporous Templates

Connecting theory and simulation with experiment for the study of diffusion in nanoporous solids

Designing Nanostructured Membranes for Oxidative Dehydrogenation of Alkanes Using Kinetic Modeling

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