Statistical theory for the equilibrium distribution of rigid molecules in inert porous networks. Exclusion chromatography

Giddings, J. Calvin; Kučera, E.; Russell, Christopher P.; Myers, Marcus N.

doi:10.1021/j100859a008

Cited by 490 publications

(338 citation statements)

References 5 publications

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“…Furthermore, Eq. [25] demonstrates that the magnitude of the equilibrium coefficient for water in the crosslinker phase, K eq , will directly affect the diffusion coefficients in crosslinked gels. Small K eq values (K eq Ӷ 1) will have no effect on the diffusion in gels, which may explain the lack of crosslinker effect on the diffusion coefficients in gels.…”

Section: Figmentioning

confidence: 99%

“…In Eq. [25] is a function of D ␤ , the diffusion coefficient in the crosslinker phase, and K eq , the permeability into the crosslinker phase:…”

Section: Volume Averaging In V T and The One-equation Modelmentioning

confidence: 99%

“…Ogston's original analysis has been applied and extended extensively within the gel electrophoresis and gel chromatography literature (19 -23). Gel structure also has been interpreted within a broader range of structures to include distributions of variously shaped pores (24,25). Richards and Temple (26) applied and extended the Ogston theory to the analysis of the structure of crosslinked polyacrylamide gels in order to account for the effects of crosslinker concentration on the microscopic structure of the gel.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

Penke

Kinsey

Gibbs

et al. 1998

Journal of Magnetic Resonance

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The structure of polyacrylamide gels was studied using proton spin-lattice relaxation and PFG diffusion methods. Polyacrylamide gels, with total polymer concentrations ranging from 0.25 to 0.35 g/ml and crosslinker concentrations from 0 to 10% by weight, were studied. The data showed no effect of the crosslinker concentration on the diffusion of water molecules. The Ogston-Morris and Mackie-Meares models fit the general trends observed for water diffusion in gels. The diffusion coefficients from the volume averaging method also fit the data, and this theory was able to account for the effects of water-gel interactions that are not accounted for in the other two theories. The averaging theory also did not require the physically unrealistic assumption, required in the other two theories, that the acrylamide fibers are of similar size to water molecules. Contrary to the diffusion data, T 1 relaxation measurements showed a significant effect of crosslinker concentration on the relaxation of water in gels. The model developed using the Bloch equations and the volume averaging method described the effects of water adsorption on the gel medium on both the diffusion coefficients and the relaxation measurements. In the proposed model the gel medium was assumed to consist of three phases (i.e., bulk water, uncrosslinked acrylamide fibers, and a bisacrylamide crosslinker phase). The effects of the crosslinker concentration were accounted for by introducing the proton partition coefficient, K eq , between the bulk water and crosslinker phase. The derived relaxation equations were successful in fitting the experimental data. The partition coefficient, K eq , decreased significantly as the crosslinker concentration increased from 5 to 10% by weight. This trend is consistent with the idea that bisacrylamide tends to form hydrophobic regions with increasing crosslinker concentration.

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Section: Figmentioning

confidence: 99%

“…In Eq. [25] is a function of D ␤ , the diffusion coefficient in the crosslinker phase, and K eq , the permeability into the crosslinker phase:…”

Section: Volume Averaging In V T and The One-equation Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

Penke

Kinsey

Gibbs

et al. 1998

Journal of Magnetic Resonance

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show abstract

“…17 fails to account. Based on geometric [34] as well as thermodynamic arguments [48], Eq. 17 has been modified in literature through the introduction of a steric term, which accounts for sieving effects that arise as a result of the finite size of the solute relative to the pore, quantified by the parameter λ i [27].…”

Section: Solute Partitioning At Electrochemical Equilibriummentioning

confidence: 99%

Fundamentals of low-pressure nanofiltration: Membrane characterization, modeling, and understanding the multi-ionic interactions in water softening

Labban

Liu

Chong

et al. 2017

Journal of Membrane Science

152

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Recently, a novel class of low-pressure nanofiltration (NF) hollow fiber membranes, particularly suited for water softening and desalination pretreatment have been fabricated in-house using layer-by-layer (LbL) deposition with chemical crosslinking. These membranes can operate at exceedingly low pressures (2 bar), while maintaining relatively high rejections of multivalent ions. In spite of their great potential, our understanding as to what makes them superior has been limited, demanding further investigation before any large-scale implementation can be realized. In this study, the Donnan-Steric Pore Model with dielectric exclusion (DSPM-DE) is applied for the first time to these membranes to describe the membrane separation performance, and to explain the observed rejection trends, including negative rejection, and their underlying multi-ionic interactions. Experiments were conducted on a spectrum of feed chemistries, ranging from uncharged solutes to single salts, salt mixtures, and artificial seawater to characterize the membrane and accurately predict its performance. Modeling results were validated with experiments, and then used to elucidate the working principles that underlie the low-pressure softening process. An approach based on sensitivity analysis shows that the membrane pore dielectric constant, followed by the pore size, are primarily responsible for the selectively high rejections of the NF membranes to multivalent ions. Surprisingly, the softening process is found to be less sensitive to changes in membrane charge density. Our findings demonstrate that the unique ability of these membranes to exclusively separate multivalent ions from the solution, while allowing monovalent ions to permeate, is key to making this low-pressure softening process realizable.

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“…For the case of uncharged solutes , 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 -5-only purely steric effects determine this ratio, which coincides with the steric partitioning coefficient. Assuming that flow through a membrane takes place along the x-axis direction, being x=0 and x=∆x the coordinates for the interfaces, and denoting by -and + the left and right sides of each interface, the membrane partition coefficient [19,20] is:…”

Section: Membrane Partition Coefficientmentioning

confidence: 99%

Pore size analysis from retention of neutral solutes through nanofiltration membranes. The contribution of concentration–polarization

et al. 2014

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Pore size distribution is one of the most important characteristics of a membrane.This can be obtained from the fitting of pore radius calculated from retention versus flux measurements for a set of solute solutions. In this work a set of non-charged similar molecules are chosen as solutes to minimize other interactions apart of those related to size. The hydrodynamic model will be used to characterize the behavior of the membrane to uncharged solutes, assuming that membrane pores are straight and cylindrical.As is known, the phenomenon of concentration polarization must be taken into account because true retention is not experimentally accessible by concentration measurements. Frequently, the film layer model is applied for the dependence of

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Statistical theory for the equilibrium distribution of rigid molecules in inert porous networks. Exclusion chromatography

Cited by 490 publications

References 5 publications

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

Proton Diffusion andT1Relaxation in Polyacrylamide Gels: A Unified Approach Using Volume Averaging

Fundamentals of low-pressure nanofiltration: Membrane characterization, modeling, and understanding the multi-ionic interactions in water softening

Pore size analysis from retention of neutral solutes through nanofiltration membranes. The contribution of concentration–polarization

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