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Enhanced migration and ionic transport through membranes
Abstract
The effect of Coulomb forces upon transport enhancement of mobile ions, in the presence of slowly migrating charged polymeric chains, is investigated in a nonequilibrium regime brought about by a semipermeable membrane and a chemical reaction. By means of a numerical solution of the Nernst-Planck-Poisson equations, we predict the size of the effect, the conditions for positive or negative enhancement, and the dependence upon all relevant parameters. The limitations of the description of migration enhancement by an effective diffusion coefficient are also established.
... The use of magnetic resonance imaging (MRI) in material science applications has become widespread over the years [1][2][3]. By looking at the image profiles obtained through properly designed experimental arrangements it is possible to assess aspects of the structure, the underlying mechanisms of transport and chemical kinetics of many interesting processes [1,2,4,5]. In particular, the possibility of monitoring these processes with spatial resolution constitutes a unique advantage of MRI over methods where only global temporal dynamics can be extracted. ...
... The second feature is a decay of the signal at the center of the image which occurs simultaneously with the reaction-front progression (see, for instance, the horizontal arrow for T = 120 min). Both features are important for the quantitative description of the gelling process [4]. To better appreciate the latter effect, Fig. 4 shows horizontally taken radial profiles of the region inside the dialysis membrane as the reaction takes place. ...
Proton-electron double-resonance imaging (PEDRI) was recently employed to monitor the process of formation of a calcium alginate hydrogel at a field of 16mT. Here, under the same experimental conditions, images obtained through this technique are compared to images obtained by conventional T(2)-weighted method. The results confirm that the image contrast obtained using PEDRI, thanks to the Overhauser effect, exhibits an improved sensitivity with respect to changes in water mobility as previously suggested in the literature. Furthermore, by increasing the echo time interval for the T(2)-weighted images, important features of the gelling dynamics obtained via PEDRI could not be reproduced.
... After adhesion, low acetylated fastidian becomes important in multiple biofilm layers. It has been shown that negative polysaccharides increase by a factor of 2.5 ionic transport through membranes, compared to that produced by apolar ones [26]. Therefore, similar faster cation transport to Xf biofilm, than that predicted by the diffusion process, can quickly sequester the cationsFig. ...
Xylella fastidiosa is the causal agent of citrus variegated chlorosis and Pierce's disease which are the major threat to the citrus and wine industries. The most accepted hypothesis for Xf diseases affirms that it is a vascular occlusion caused by bacterial biofilm, embedded in an extracellular translucent matrix that was deduced to be the exopolysaccharide fastidian. Fourier transform infrared spectroscopy analysis demonstrated that virulent cells which form biofilm on glass have low fastidian content similar to the weak virulent ones. This indicates that high amounts of fastidian are not necessary for adhesion. In this paper we propose a kinetic model for X. fastidiosa adhesion, biofilm formation, and virulence based on electrostatic attraction between bacterial surface proteins and xylem walls. Fastidian is involved in final biofilm formation and cation sequestration in dilute sap.
A new bipyridyl derivative 1 bearing rhodamine B as visible fluorophore was designed, synthesized and characterized as a fluorescent and colorimetric sensor for metal ions. Interaction with Cu2+, Zn2+, Cd2+, Hg+, and Hg2+ ions was followed by UV/Vis and emission spectroscopy. Upon addition of these metal ions, different colorimetric and fluorescent responses were observed. “Off-on-off” (Cu2+, Zn2+, and Hg2+) and “off-on” (Hg+ and Cd2+) systems were obtained. Probe 1 was explored to mimic XOR and OR logic operations for the simultaneous detection of Hg+–Cu2+ and Hg+–Zn2+ pairs, respectively. DFT calculations were also performed to gain insight into the lowest-energy gas-phase conformation of free receptor 1 as well as the atomistic details of the coordination modes of the various metal ions.
Chemosensor L showed a nonlinear fluorescence response on specific binding to Cr3+ ion in the presence of various alkali, alkaline earth, transition, and lanthanide metal ions. A luminescence band with maxima at 512 nm for L was observed (lambda(ext) = 330 nm) for a twisted intramolecular charge transfer (TICT) transition following antienergy gap law behavior. However, normal energy gap law behavior prevailed on formation of a new nonluminescent charge transfer complex, Mn+center dot L. For paramagnetic metal ions, paramagnetism induced luminescence quenching could have also contributed to this. A new switched on fluorescence response at lambda(ems) of 356 nm (lambda(ext) of 330 nm) was observed due to Franck-Condon charge transfer (FC-CT) transition only on the formation of a complex, (Cr3+)(2)center dot L. Spectral studies revealed a unique dynamic coordination behavior and migration of Cr3+ from the terpyridyl fragment to the N-NMe2 center of L as a function of the varying concentration of another ion (Zn2+) and the subtle difference in the binding affinities of the terpyridyl moiety toward Cr3+ and Zn2+. Further, spectral responses of L toward Zn2+, different concentration of Cr3+, H+ and on subsequent addition of F- as different ionic inputs could be correlated well for demonstrating various basic and combinatorial circuits.
Alternating deposition of oppositely charged polyelectrolytes on porous supports is an attractive way to synthesize selective, ultrathin ion-separation membranes. This study reports the use of Cu2+ as a template in poly(acrylic acid) (PAA)/poly(allylamine hydrochloride) (PAH) membranes to control fixed charge density and hence enhance anion-transport selectivity. Alternating deposition of PAA partially complexed with Cu2+ and PAH on porous alumina supports followed by removal of Cu2+ and deprotonation results in fixed −COO- sites in these films. Cu2+-templated PAA/PAH membranes show a 4-fold increase in Cl-/SO42- transport selectivity compared to pure PAA/PAH membranes deposited under similar conditions. Cross-linking of these templated membranes further increases Cl-/SO42- selectivity by an order of magnitude to a value of 610. Changing the top layer of cross-linked, Cu2+-templated membranes from negatively charged PAA to positively charged PAH decreases Cl-/SO42- selectivity 10-fold, indicating that Donnan repulsion from a negatively charged surface is a major factor behind selectivity. Modeling studies suggest that selectivity is due to both Donnan exclusion and diffusivity differences among ions.
Alternating deposition of oppositely charged polyelectrolytes on porous supports is an attractive way to synthesize selective, ultrathin ion-separation membranes. This study reports the use of Cu2+ as a template in poly(acrylic acid) (PAA)/poly(allylamine hydrochloride) (PAH) membranes to control fixed charge density and hence enhance anion-transport selectivity. Alternating deposition of PAA partially complexed with Cu2+ and PAH on porous alumina supports followed by removal of Cu2+ and deprotonation results in fixed −COO- sites in these films. Cu2+-templated PAA/PAH membranes show a 4-fold increase in Cl-/SO42- transport selectivity compared to pure PAA/PAH membranes deposited under similar conditions. Cross-linking of these templated membranes further increases Cl-/SO42- selectivity by an order of magnitude to a value of 610. Changing the top layer of cross-linked, Cu2+-templated membranes from negatively charged PAA to positively charged PAH decreases Cl-/SO42- selectivity 10-fold, indicating that Donnan repulsion from a negatively charged surface is a major factor behind selectivity. Modeling studies suggest that selectivity is due to both Donnan exclusion and diffusivity differences among ions.
We examine the parameters that govern the motion of the reaction front in the A+B-->C reaction-diffusion system with initially separated reactants. We claim that three different parameters determine the direction of motion of the front at different time regions. We predict the surprising possibility of two switches in the direction of motion of the front, as well as a situation of a stationary front after a single change of direction.
A Monte Carlo simulation model, which incorporates the effect of tensile forces as well as diffusion, is proposed to explain the behavior of water transport in a saturated porous gel. The algorithm is able to account for the puzzling moisture profiles, which were first observed by conventional magnetic resonance imaging and, more recently, by Overhauser imaging.
We present a general, physically motivated nonlinear and nonlocal advection equation in which the diffusion of interacting random walkers competes with a local drift arising from a kind of peer pressure. We show, using a mapping to an integrable dynamical system, that on varying a parameter the steady-state behavior undergoes a transition from the standard diffusive behavior to a localized stationary state characterized by a tailed distribution. Finally, we show that recent empirical laws on economic growth can be explained as a collective phenomenon due to peer pressure interaction.
Diffusion characteristics of nitrate through calcium-alginate gel beads were studied and compared to diffusion of glycerol, a non-charged small molecule. Compared to the theoretical effective nitrate diffusion coefficients in gel beads of different alginate concentrations, calculated by the Mackie and Meares approach, experimental nitrate diffusion through alginate of different characteristics showed significant differences. When the residence time of gel beads in calcium chloride solution was increased from 10 to 60 min, 30% more nitrate diffused from outside to inside the polymeric matrix. When alginate concentration was varied from 3 to 6%, 25% less nitrate diffused from inside to outside alginate gel beads. In addition, experimental diffusion of a non-charged heavier molecule (glycerol) occurred faster than the one for nitrate. Significantly minor diffusion (some 30%) through alginate gel beads was found for a positive ion, ammonium. In this paper such differences mentioned above are discussed to be due to the possible electrostatic interactions between the negative charge of nitrate and calcium clusters around the polymer surface. These results could have significance in the field of inorganic nitrogen bioelimination using immobilized photosynthetic cells.
In this paper, we show a numerical model designed for analysing the propagation of ionic concentrations and electrical potential in space and time in the liquid-junction and in the solution∣ion-exchangingmembrane system. In this model, diffusion and migration according to the Nernst–Planck flux equation govern the transport of ions. The electrical interaction of the species is described by the Poisson equation. These two equations and the continuity equation make a system of partial differential equations that is numerically resolved by the finite difference method. Consequently, the contact and/or boundary potential and diffusion potential are presented as a result of the physicochemical properties of the system rather than assumed a priori in order to find an analytical solution in the form of an equation. We show that the paradigmatic equations in potentiometry, such as Henderson and Nikolskii–Eisenman (N–E), are special cases in our model. Although we discuss the examples relevant to electroanalytical potentiometry and, in particular, to the field of ion-selective membrane electrodes (ISE), it is evident that the method presented here is a good tool for solving broader problems in membrane biology and electrochemistry with membranes.
The electronic Overhauser effect was employed to enhance nuclear magnetic resonance images obtained in a magnetic field of only 16 mT. Despite the weak magnetic field, the technique can reveal, in some systems, various aspects of ionic transport and kinetics apparently not observed in conventional high-field magnetic resonance imaging. We employed Overhauser imaging to monitor the spatial and temporal evolution of the gelation of sodium alginate by calcium ions. The sensitivity of the Overhauser enhancement to small changes in gel composition permits a stringent test of the underlying mechanisms of transport and chemical kinetics.
Charged polysaccharides often form hydrogels in the presence of cations. In many applications the polymer network density distribution and associated physical properties are of major practical importance. Depending on the detailed conditions, the resulting gel density may vary from fully homogeneous to strongly inhomogeneous.
We have established a simple set of coupled chemical reaction–diffusion equations to model the gelling process of calcium-induced alginate gels. The necessary algorithms for numerical solution of the resulting simultaneous parabolic differential equations have been developed both for one-dimensional models and three-ldimensional models with cylindrical or spherical symmetry. The algorithms make use of the Crank–Nicolson implicit finite difference method. The results of the numerical analyses of the gel formation can be divided into several different regimes depending on the physical and chemical parameters of the alginates and the cations. The numerical results are in good agreements with reported experimental results.
An efficient finite difference simulation procedure for the steady state and transient solution of the Nernst-Planck and Poisson equation system is presented. The procedure is general and extremely efficient, containing refinements in time and distance scaling. The implicitly-formulated non-linear equations are solved with an iterative Newton-Raphson technique. The derivation is presented in sufficient detail for the reader to directly formulate similar computer codes. Steady state solutions, transient responses, and impedance-frequency responses are presented for a number of examples from the fields of membrane electrochemistry and solid state physics.
It has been previously demonstrated that calcium alginate gels prepared by dialysis often exhibit a concentration inhomogeneity being the polymer concentration considerably lower in the center of the gel than at the edges. Inhomogeneity may be a preferred structure in microcapsules due to low porosity and higher stability so that it is interesting to evaluate the polymer gradient in spherically symmetrical small alginate beads (1.0–0.7 mm diameter) obtained in different conditions. In this paper, two complementary techniques have been used to investigate this aspect. The concentration gradient of alginate has been analyzed by measuring both the spatial distribution of calcium ions in sections of alginate gel spheres, by means of x-ray fluorescence spectroscopy, and the T2 relaxation behavior on intact gel beads using magnetic resonance microimaging. The experimentally determined gradients from three-dimensional gels provide data to reevaluate the parameter estimates in the recently reported mathematical model for alginate gel formation (A. Mikkaelsen and A. Elgsaeter, Biopolymers, 1995, Vol. 36, pp. 17–41). The model may account for the gels being less inhomogeneous when nongelling sodium or magnesium ions are added during gelation. © 2000 John Wiley & Sons, Inc. Biopoly 53: 60–71, 2000
Microorganisms in soil, especially those associated with plant roots, are surrounded by envelopes of polysaccharides. These originate from both microbes and roots and are a characteristic feature of the rhizosphere. We have shown these materials to selectively restrict the diffusion of anions by the measurement of diffusion potentials. Using xanthan gum as a model microbial polysaccharide, increasing polymer concentration or polysaccharide layer thickness or the removal of acetyl and pyruvyl groups have been shown to increase the degree of anion exclusion. The anion-exclusive behaviour of xanthan has been validated independently by direct measurements of diffused ion concentrations. Data is presented showing this phenomenon to operate in KCl, KNO3 and KH2PO4 systems. In all cases, the anion exclusion appears to be partial, restricting the diffusion of anions in the presence of a layer of 3% xanthan by 50-80%. By measurement of diffusion potentials, scleroglucan and polysaccharides produced by two soil bacteria, Azotobacter chroococcum and Enterobacter cloacae, were also shown to behave anion-exclusively. Ca-polygalacturonate, which has been used as a model root surface polymer, showed little ion-exclusive behaviour compared to polymers extracted from bulk soil and the rhizosphere and root surface of pea, which all showed high levels of anion exclusion. By chemical characterisation of all polymers under study, it was possible to link the presence of uronic acids within the gel to anion-exclusive behaviour. The results suggest that anion exclusion is a common property of microbial and soil polysaccharides. The ability of these materials to restrict the diffusion and thus the availability of nutrient anions at the microorganism or root cell surface may be of significance to the survival and growth of polysaccharide-producing organisms in soil.
The gelation of sodium alginate by calcium ions is studied by proton-electron double resonance imaging in a magnetic field of only 16 mT using a newly developed free radical. The high sensitivity of the Overhauser enhancement to small variations in water mobility permits the detection of minute changes in gel composition. Spatial inhomogeneity and temporal evolution of this, and possibly other processes involving diffusion and chemical reaction, could be accurately monitored by this technique. © 2002 American Institute of Physics.
In accordance with the theory of contact exchange, it is hypothesized that the presence of negative charge in microbial exopolysaccharides increases the rate of cation transport. These typically acidic materials may provide a fast-track for the diffusion of nutrient cations through the polymer layer for uptake at the organism cell surface. We have measured the diffusion coefficient of a model cation, Mn(2+,) through xanthan, de-acetylated xanthan, scleroglucan and chitosan using spatially resolved NMR relaxometry. The concentration of Mn(2+) in solution was measured by recording the change in the spin-spin (T(2)) relaxation time of water (1)H over time in compartments either side of a polymer layer. This approach provides a sensitive, in situ, non-invasive method of measuring the rate of diffusion of paramagnetic cations through hydrophilic polysaccharides. The negatively-charged polysaccharides, xanthan and de-acetylated xanthan, permitted a significantly faster rate (2-2.5x) of cation transport compared to the uncharged polymer, scleroglucan. The positively-charged polysaccharide chitosan reduced the rate of Mn(2+) diffusion to around half the value obtained for scleroglucan. These results suggest that the presence and nature of fixed charges on the polysaccharide molecule affects the rate of cation transport in accordance with the theory of contact exchange. The presence of negative charge on microbial exopolysaccharides may thus improve the availability of nutrient cations at the organism cell surface.