Simulation of diffusion in 2-D heterogeneous systems: comparison with effective medium and percolation theories

Schlicht, L.; Ilgenfritz, G.

doi:10.1016/0378-4371(95)00407-6

Cited by 10 publications

(17 citation statements)

References 17 publications

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“…This was a critical step in establishing the validity of the conclusions reached in our previous articles. In fact, our results agree perfectly with a number of theories for the electrical conductivity of heterogeneous media [24], and for the diffusion coefficient of random walkers in systems with obstacles [25,26]. Therefore, once the elements to be included in the model are identified, our approximation-free mathematical approach does indeed provide extremely accurate results.…”

Section: Improved Ogston Modelssupporting

confidence: 76%

“…(1), is invalid. This is consistent with Monte Carlo simulation studies of particle diffusion in inhomogeneous systems [20,24,25], but it conflicts with the recent work of Locke and Trinh [12]. In particular, we have demonstrated that curved field lines do not validate Eq.…”

Section: Resultscontrasting

confidence: 55%

“…(6) in the limit where it reduces to D Ã C fC. However, zero-field Monte Carlo simula- tions of particle diffusion among fixed obstacles are wellknown to give results in strong disagreement with this prediction [20,24,25]. For instance, such a study, published by the very same group, showed that the diffusion coefficient does not follow a universal curve D*(C) = (C), but that it instead depends on the medium architecture [20].…”

Section: The Field Line Problemmentioning

confidence: 78%

“…In particular, we stress the fact that the geometry of the gel has a strong impact on the dependence of the mobility upon the excluded volume f(C) even in the low-obstruction limit, a result that is fully supported by Monte Carlo simulations [20,24,25]. In other words, the geometric parameter (C) = 1-f(C) is not sufficient to describe the precise effect of the geometry and topology of a sieving matrix.…”

Section: Discussionmentioning

confidence: 93%

“…For example, many groups have been studying the electrical conductivity of various systems with nonconducting domains by comparing it to the unbiased random-walk (diffusion) problem in the same system (see, e.g., [24]). The Monte Carlo diffusion coefficient thus obtained (with no field) is then assumed to be directly proportional to the electrical conductivity in the original problem (which obviously had curved field lines).…”

Section: Discussionmentioning

confidence: 99%

See 4 more Smart Citations

An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation

2001

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In this article, we examine the low-field electrophoretic migration of infinitely small analytes in dilute sieving media made of nonconducting gel fibers. Using an Ogston obstruction model, we show that the electrophoretic mobility is not affected by the presence of curved field lines. In other words, the Nernst-Einstein relation between the mobility and the diffusion coefficient is valid regardless of the electrical properties of the gel fibers. Although this finding may greatly simplify the development of obstruction models of electrophoretic sieving, it also represents a critical test for any analytical or computational approach.

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Section: Improved Ogston Modelssupporting

confidence: 76%

Section: Resultscontrasting

confidence: 55%

Section: The Field Line Problemmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 93%

Section: Discussionmentioning

confidence: 99%

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An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation

2001

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Theory of DNA electrophoresis (∼ 1999 –2002 ½)

et al. 2002

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Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.

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Role of Nanocomposite Hydrogel Morphology in the Electrophoretic Separation of Biomolecules: A Review

Simhadri

Stretz

Oyanader

et al. 2010

Ind. Eng. Chem. Res.

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Hydrogels are widely used to produce biomolecular separations in electrophoretic applications, where gel morphology and charge effects combine to produce the separation. Nanocomposite gels are poised to revolutionize this field in both improved handling characteristics and improved separations. Gel morphology and charge effects have traditionally been manipulated by varying the copolymer composition, but recent reports show that novel morphological changes can also be induced in the gel using templating methods and nanoparticle addition. To aid realization of the potential for novel electrically driven separations arising from such novel morphologies, we review here advances in materials development alongside a review of the directions in biomolecule/hydrogel electrophoretic transport modeling. Models for polyelectrolyte transport that are potentially useful for understanding novel behaviors caused by gel morphology are analyzed first. With the perspective of theoretical guidance, we then survey nanocomposite hydrogel morphologies keyed by the nanoparticle and matrix. Finally, we survey as well reports of dramatic improvements in the mechanical properties that may be the key to the early adoption of these new materials in biomolecular separation applications. For modeling, we have identified the different scales involved in biomolecular transport in these materials and provided a taxonomy of transport models that emphasize the role of gel morphology in determining both polyelectrolyte mobility and diffusion. Three aspects for future work unique to nanocomposite gel materials are described: (a) descriptions of the distribution of nanoparticles within the gels; (b) descriptions of the motion of the buffer solution that may include electroosmotic effects for nanoparticles with surface charges; (c) descriptions of the motion of the polyelectrolyte molecule inside the new gel material for a given application. These aspects will help to uncover further quantitative details about the ability of these gels to be tunable for differential mass transport of a given type of molecule. Standard gels, currently, lack a broad flexibility to increase the separation of biomolecules and, in general, are not tunable.

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Simulation of diffusion in 2-D heterogeneous systems: comparison with effective medium and percolation theories

Cited by 10 publications

References 17 publications

An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation

An exactly solvable Ogston model of gel electrophoresis: VIII. Nonconducting gel fibers, curved field lines, and the Nernst-Einstein relation

Theory of DNA electrophoresis (∼ 1999 –2002 ½)

Role of Nanocomposite Hydrogel Morphology in the Electrophoretic Separation of Biomolecules: A Review

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