Andriy Yaroshchuk

Interpretation of Electrokinetic Measurements with Porous Films: Role of Electric Conductance and Streaming Current within Porous Structure

It is shown that in tangential electrokinetic measurements with porous films the porous structure makes contribution not only to the cell electric conductance (as demonstrated previously) but also to the observed streaming current. Both of these contributions give rise to dependences of streaming-potential and streaming-current coefficients on the channel height. However, due to the combined contribution of two phenomena, the dependence of streaming-potential coefficient on the channel height may be rather complicated and not allow for simple extrapolation. At the same time, the dependences of streaming-current coefficient and cell electric conductance on the channel height turn out linear and can be easily extrapolated to zero channel heights. This enables one to determine separately the contributions of external surface of porous film and of its porous structure to the streaming current and of the channel and porous structure to the cell electric conductance. This procedure is illustrated by the measurements of tangential electrokinetic phenomena and electric conductance with Millipore mixed-cellulose membrane filters of various average pore sizes (from 0.025 to 5 mum) in the so-called adjustable-gap cell of SurPASS electrokinetic instrument (Anton Paar GmbH). The design of this cell allows for easy and quasi-continuous variation of channel height as well as accurate determination of cell electric conductance, streaming-current coefficient, and channel height (from the cell hydraulic permeability). The quality of linear fits of experimental data has been found to be very good, and thus, the extrapolation procedures were quite reliable and accurate. Zeta-potentials could be determined of both external film and internal pore surfaces. It is demonstrated that the porous structures make considerable contributions to both streaming-current coefficient and cell electric conductance especially in the case of filters with larger pores. It is also found that, rather surprisingly, in filters with smaller pores the reduction in the filter electric conductivity turns out essentially stronger than could be expected proceeding from the filter porosity.

Fundamentals of Selective Ion Transport through Multilayer Polyelectrolyte Membranes

Membranes composed of multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films on porous alumina supports exhibit high monovalent/divalent cation selectivities. Remarkably, the diffusion dialysis K(+)/Mg(2+) selectivity is >350. However, in nanofiltration this selectivity is only 16, suggesting some convective ion transport through film imperfections. Under MgCl(2) concentration gradients across either (PSS/PAH)(4)- or (PSS/PAH)(4)PSS-coated alumina, transmembrane potentials indicate Mg(2+) transference numbers approaching 0. The low Mg(2+) transference numbers with both polycation- and polyanion-terminated films likely stem from exclusion of Mg(2+) due to its large size or hydration energy. However, these high anion/cation selectivities decrease as the solution ionic strength increases. In nanofiltration, the high asymmetry of membrane permeabilities to Mg(2+) and Cl(-) creates transmembrane diffusion potentials that lead to negative rejections (the ion concentration in the permeate is larger than in the feed) as low as -200% for trace monovalent cations such as K(+) and Cs(+). Moreover, rejection becomes more negative as the mobility of the trace cation increases. Knowledge of single-ion permeabilities is vital for predicting the performance of polyelectrolyte films in the separation and purification of mixed salts.

Coating of Nafion membranes with polyelectrolyte multilayers to achieve high monovalent/divalent cation electrodialysis selectivities.

Electrodialysis (ED) membranes typically exhibit modest selectivities between monovalent and divalent ions. This paper reports a dramatic enhancement of the monovalent/divalent cation selectivities of Nafion 115 membranes through coating with multilayer poly(4-styrenesulfonate) (PSS)/protonated poly(allylamine) (PAH) films. Remarkably, K(+)/Mg(2+) ED selectivities reach values >1000, and similar monovalent/divalent cation selectivities occur with feed solutions containing K(+) and Ca(2+). For comparison, the corresponding K(+)/Mg(2+) selectivity of bare Nafion 115 is only 1.8 ± 0.1. However, with 0.01 M KNO3 and 0.01 M Mg(NO3)2 in the source phase, as the applied current density increases from 1.27 to 2.54 mA cm(-2), the K(+)/Mg(2+) selectivities of coated membranes decrease from >1000 to 22. Water-splitting at strongly overlimiting current densities may lead to a local pH increase close to the membrane surface and alter film permeability or allow passage of Mg(OH)x species to decrease selectivity. When the source phase contains 0.1 M KNO3 and 0.1 M Mg(NO3)2, the K(+) transference number approaches unity and the K(+)/Mg(2+) selectivity is >20,000, presumably because the applied current is below the limiting value for K(+) and H(+) transport is negligible at this high K(+) concentration. The high selectivities of these membranes may enable electrodialysis applications such as purification of salts that contain divalent or trivalent ions.

Negative rejection of ions in pressure-driven membrane processes

Negative rejections of ions in pressure-driven membrane processes can be caused by several distinct mechanisms. In a number of cases, in a final count, the phenomenon is brought about by increased concentration of an ion in the membrane phase. In the case of charged membranes, the increased concentration has to be accompanied by a weakening of electric field of filtration potential, which normally retards counter-ions and prevents the increased concentrations from manifesting themselves in negative rejections. This occurs in charge-mosaic membranes due to the so-called current circulation phenomenon or in electrolyte mixtures due to the presence of more mobile counter-ions. Negative rejections can also occur for ions whose concentration is decreased in the membrane phase. This occurs in electrolyte mixtures due to the acceleration of such ions by the electric field of diffusion potential arising because of strong rejections of other mixture components. This phenomenon is most pronounced for single-charge ions in the presence of predominant amounts of ions of higher charge of the same sign. All those mechanisms are considered within the scope of a common theoretical framework. An attempt is made of a tentative classification of mechanisms of negative rejections. An overview of available literature data is provided and it is shown that in a number of cases the published information is not sufficiently detailed for a reliable identification of the mechanisms. It is concluded that the studies of negative rejections could be a valuable membrane characterization tool but they need to be more systematic and targeted to fulfil this role.

TRACER DIFFUSION IN SINTERED STAINLESS STEEL FILTERS : MEASUREMENT OF EFFECTIVE DIFFUSION COEFFICIENTS AND IMPLICATIONS FOR DIFFUSION STUDIES WITH COMPACTED CLAYS

The use of porous filters is indispensable in laboratory- and field-scale diffusion studies, where sample confinement is needed for mechanical reasons. Examples are diffusion studies with compacted swelling clays or brittle clay stones. Knowledge of the diffusion properties of these filters is important in cases where they contribute significantly to the overall diffusive resistance in the experimental setup. In the present study, measurements of effective diffusion coefficients (Db) in porous, stainless steel filter discs are reported for tritiated H2O (HTO), 22Na+, Cs+, and Sr2+ before and after use of the filters in diffusion experiments with different clay minerals. The Db values for used filters were found to be less than those of the as-received filters by ∼30–50%. The Db values measured for the diffusion of HTO, 22Na+, Cs+, and Sr2+ in unused and used stainless steel filter discs correlated fairly well with the respective molecular diffusion coefficients in bulk water. Although such correlations are inherently associated with some uncertainties, they allow reasonable estimates to be made for diffusants for which no Db values are available. For the first time, a procedure is outlined that allows an integrative assessment to be made for the impact of the uncertainties in the filter diffusion properties on the combined standard uncertainties of the diffusion parameters obtained from through-diffusion experiments. This procedure can be used in the design and optimization of through-diffusion experiments in which the diffusive resistance of the porous filters must not be ignored. Shown here, as a general rule of thumb, is that, if the effective diffusion coefficient in the porous filter is at least three times larger than that in the clay, the choice of geometrical boundary conditions is rather uncritical, as long as the thickness of the clay sample is greater than that of the porous filters.

Transport properties of long straight nano-channels in electrolyte solutions: A systematic approach

The principle of local thermodynamic equilibrium is systematically employed for obtaining various transport properties of long straight nano-channels. The concept of virtual solution is used to describe situations of non-negligible overlap of diffuse parts of electric double layers (EDLs) in nano-channels. Generic expressions for a variety of transport properties of long straight nano-channels are obtained in terms of quasi-equilibrium distribution coefficients of ions and functionals of quasi-equilibrium distribution of electrostatic potential. Further, the Poisson-Boltzmann approach is used to specify these expressions for long straight slit-like nano-channels. In the approximation of non-overlapped diffuse parts of double electric layers in nano-channels, simple analytical expressions are obtained for the apparent electrophoretic mobilities of (trace) analytes of arbitrary charge as well as for the salt reflection coefficient (osmotic pressure), salt diffusion permeability and electro-viscosity (electrokinetic energy conversion). The approximate solutions are compared with the results of rigorous solution of non-linearized Poisson-Boltzmann equation, and the accuracy of approximation is shown to be typically excellent when the nano-channel half-height exceeds ca.3 Debye screening lengths. Due to non-negligible electrostatic adsorption of ions by nano-channels, the apparent electrophoretic mobilities of counter-ionic analytes in nano-channels are smaller than in micro-channels whereas those of co-ionic analytes are larger. This dependence on the charge is useful for the separation of analytes of close electrophoretic mobilities. The osmotic pressure is shown to be positive, negative or pass through maxima as a function of applied salt-concentration difference within a fairly narrow range of ratios of nano-channel height to the Debye screening length. The diffusion permeability of charged nano-channels to single salts is demonstrated (for the first time) to be typically larger than that of neutral nano-channels of the same dimensions due to electrical facilitation of salt diffusion.

Separation of ions using polyelectrolyte-modified nanoporous track-etched membranes

Selective ion exclusion from charged nanopores in track-etched membranes allows separation of ions with different charges or mobilities. This study examines pressure-driven transport of dissolved ions through track-etched membranes modified by adsorption of poly(styrene sulfonate) (PSS)/protonated poly(allylamine) (PAH) films. For nominal 30 nm pores modified with a single layer of PSS, Br(-)/SO4(2-) selectivities are ∼3.4 with SO4(2-) rejections around 85% due to selective electrostatic exclusion of the divalent anion from the negatively charged pore. Corresponding membranes containing an adsorbed PSS/PAH bilayer are positively charged and exhibit average K(+)/Mg(2+) selectivities >10 at 8 mM ionic strength, and Mg(2+) rejections are >97.5% at ionic strengths <5 mM. The high rejection of Mg(2+) compared to SO4(2-) likely results from both a smaller pore size after deposition of the PAH layer and higher surface charge because of Mg(2+) adsorption. Simultaneous modeling of K(+) and Mg(2+) rejections using the nonlinearized Poisson-Boltzmann equation gives an average modified pore diameter of 8.4 ± 2.1 nm, which does not vary significantly with ionic strength. This diameter is smaller than that calculated from hydraulic permeabilities and estimated pore densities, suggesting that narrow regions near the pore entrance control ion transport. In addition to simple electrostatic exclusion, streaming potentials lead to differing rejections of Br(-) and acetate in PSS/PAH-modified pores, and of Li(+) and Cs(+) in PSS-modified pores. For these cases, electrical migration of ions toward the feed solution results in higher rejection of the more mobile ion.

Electrophoresis and stability of nano-colloids: History, theory and experimental examples

The paper contains an extended historical overview of research activities focused on determining interfacial potential and charge of dispersed particles from electrophoretic and coagulation dynamic measurements. Particular attention is paid to nano-suspensions for which application of Standard Electrokinetic Model (SEM) to analysis of experimental data encounters difficulties, especially, when the solutions contain more than two ions, the particle charge depends on the solution composition and zeta-potentials are high. Detailed statements of Standard Electrokinetic and DLVO Models are given in the forms that are capable of addressing electrophoresis and interaction of particles for arbitrary ratios of the particle to Debye radius, interfacial potentials and electrolyte compositions. The experimental part of the study consists of two groups of measurements conducted for Pt/C nano-suspensions, namely, the electrophoretic and coagulation dynamic studies, with various electrolyte compositions. The obtained experimental data are processed by using numerical algorithms based on the formulated models for obtaining interfacial potential and charge. While analyzing the dependencies of interfacial potential and charge on the electrolyte compositions, conclusions are made regarding the mechanisms of charge formation. It is established that the behavior of system stability is in a qualitative agreement with the results computed from the electrophoretic data. The verification of quantitative applicability of the employed models is conducted by calculating the Hamaker constant from experimental data. It is proposed how to explain the observed variations of predicted Hamaker constant and its unusually high value.

The use of trace ions for advanced characterisation of transport properties of NF membranes in electrolyte solutions: theoretical analysis

It is well known that the rejection of electrolyte mixtures by nanofiltration membranes has a number of particularities. This is suggested to be exploited to obtain additional information on the transport properties and rejection mechanisms of NF membranes from conventional filtration measurements. To avoid the ambiguity related to the possible dependence of membrane properties on the feed composition, it is proposed to use the feeds containing dominant single salts and trace ions whose concentrations are sufficiently low to be not able to influence the membrane properties. It is shown that the rejection of traces is much more sensitive to the rejection mechanisms than that of dominant salts. The shape of dependencies of their rejections on the transmembrane volume flow is qualitatively different for predominantly Donnan and non-Donnan rejection mechanisms and also essentially depends on the sign of membrane charge. That can be used for a qualitative membrane classification. A quantitative interpretation is also possible especially if several traces of different mobilities and charges are used at once.

Recent progress in the transport characterisation of nanofiltration membranes

One of the principal purposes of transport characterization is obtaining input information for a predictive modelling of membrane performance. To be able to fit the model parameters in a unique way for a given feed composition, additional measurements other than single salt rejections are needed. The recent progress in the development of corresponding experimental and theoretical approaches is outlined. These novel approaches to the transport characterization of active layers of NF membranes are presented: chronopotentiometry of membrane potential after a concentration step, pressure switch-off, and current switch-off, voltammetry of NF membranes, NF of trace ions and dominant single salts within a wide pressure range.