Predicting ion selectivity in water purification by capacitive deionization: Electric double layer models

Ion-selective water treatment is needed to address emerging problems in an energy- and cost-efficient manner. Capacitive deionization (CDI) is a membraneless water treatment technology, which relies on storing ions in charged electric double layers (EDLs) of micropores. CDI has shown remarkable selectivity, with local density approximations (LDAs) showing some success in guiding selective separations. However, many underlying processes are represented by lumped fitting parameters in LDA models, hindering further progress. Atomistic models help unravel selectivity mechanisms, but are difficult to integrate with cell-level CDI theory. Here, we review and extend LDA models for CDI, highlight a knowledge gap in connecting between LDA and atomistic models for CDI, and emphasize and build upon analogies between micropore EDLs and nanofiltration membranes.     

Monolithic stationary phases with a longitudinal gradient of porosity

The duration of the hypercrosslinking reaction has been used to control the extent of small pores formation in polymer‐based monolithic stationary phases. Segments of five columns hypercrosslinked for 30–360 min were coupled via zero‐volume unions to prepare columns with segmented porosity gradients. The steepness of the porosity gradient affected column efficiency, mass transfer resistance, and separation of both small‐molecule alkylbenzenes and high‐molar‐mass polystyrene standards. In addition, the segmented column with the steepest porosity gradient was prepared as a single column with a continuous porosity gradient. The steepness of porosity gradient in this type column was tuned. Compared to a completely hypercrosslinked column, the column with the shallower gradient produced comparable size‐exclusion separation of polystyrene standards but allowed higher column permeability. The completely hypercrosslinked column and the column with porosity gradient were successfully coupled in online two‐dimensional liquid chromatography of polymers.     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

An exactly soluble case of the triangular ising model in a magnetic field

An anisotropic triangular Ising model in which the first- and second-order parameters and the field parameters are functionally related is solved exactly by representing the distribution of the atom patterns in terms of a suitably constructed Markov process. The probabilities of patterns, defined as the probabilities generated by this process, are a mathematically tractable alternative to the classical representation of these probabilities in terms of the partition function. The interaction and field parameters of this Ising model, its magnetization, free energy, and its nearest neighbor correlation functions, are expressed in terms of the parameters of this Markov process. Special cases are worked out in detail and numerical examples are given.     

Dynamics of a Tagged Particle in the Asymmetric Exclusion Process with the Step Initial Condition

The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources.     

Why Matter Occupies so Large a Volume？

The paper represents a rigorous treatment of the underlying quantum theory, not just in words but providing the underlying technical details, as to why matter occupies so large a volume and its intimate connection with the Pauli exclusion principle, as more and more matter is put together, as well as of the contraction or shrinkage of ＂bosonic matter＂, upon collapse, for which the Panli exclusion is abolished. From the derived explicit bounds of integrals of powers of the particle number densities, explicit bounds on probabilities of the occurrences of the events just described are extracted. These probabilities lead one to infer the change of the ＂size＂ or extension of such matter, upon expansion or contraction, respectively, as their content is increased.     

Identification and quantification of polycarboxylates in detergent products using off-line size exclusion chromatography-nuclear magnetic resonance

The performance of many contemporary detergent products critically depends on polymers. Water-soluble polycarboxylates represent an important class of detergent polymers, and their quantitative assessment in detergent matrices stands as a considerable challenge. The presence of high levels of surfactants is a major complication, due to the strong tendency of surfactants to form micelles and to interact with the polymers. First, we addressed critical steps in the subsequent combined use of liquid extraction and off-line size exclusion chromatography-nuclear magnetic resonance (SEC-NMR) for identification and quantification of polycarboxylates in detergent products. Next, the different steps in the off-line SEC-NMR procedure were optimized with respect to precision and accuracy. This resulted in recoveries of more than 80% for maleic acid/acrylic acid copolymers; in detergent products a proportional bias of 30% is achieved. The method showed good precision with a relative standard deviation of within-laboratory reproducibility between 5% and 14%.     

Size exclusion chromatography – A blessing and a curse of science and technology of synthetic polymers

Size exclusion chromatography, SEC is one of the most popular methods for the separation of different kinds of macromolecules. This critical review gives concise information about macromolecules and their behavior in solution, basic understanding about principles, instrumentation, and application possibilities of SEC, and more in detail discusses drawbacks and pitfalls of the method with the emphasis on synthetic polymers. Selected practical advices are included to help enhance the quality of SEC results.     

Optimisation of ambient and high temperature asymmetric flow field-flow fractionation with dual/multi-angle light scattering and infrared/refractive index detection

Asymmetric flow field-flow fractionation (AF4) enables to analyse polymers with very high molar masses under mild conditions in comparison to size exclusion chromatography (SEC). Conventionally, membranes for AF4 are made from cellulose. Recently, a novel ceramic membrane has been developed which can withstand high temperatures above 130 °C and chlorinated organic solvents, thus making it possible to characterise semicrystalline polyolefins by HT-AF4. Two ceramic membranes and one cellulose membrane were compared with regard to their quality of molar mass separation and the loss of the polymer material through the pores. Separating polystyrene standards as model compounds at different cross-flow gradients the complex relationship between cross-flow velocity, separation efficiency, the molar mass and peak broadening could be elucidated in detail. Moreover, the dependence of signal quality and reproducibility on sample concentration and mass loading was investigated because the evaluation of the obtained fractograms substantially depends on the signal intensities. Finally, the performance of the whole system was tested at high temperature by separating PE reference materials of high molar mass.