Competitive Interactions Within Cm3+ Solvation in Binary Water/Methanol Solutions
Explore the source record for details and available documents.
Kelley, Morgan Patrick↗
SEARCH · Engineering Papers
Results for “SOLUTIONS”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Potential-pH diagrams considering complex oxide solution phases for understanding aqueous corrosion of multi-principal element alloys
The potential-pH diagram, a graphical representation of the thermodynamically predominant reaction products in aqueous corrosion, is originally proposed for the corrosion of pure metals. The original approach only leads to stoichiometric oxides and hydroxides as the oxidation products. However, numerous experiments show that non-stoichiometric oxide scales are prevalent in the aqueous corrosion of alloys. In the present study, a room temperature potential-pH diagram considering oxide solid solutions, as a generalization of the traditional potential-pH diagram with stoichiometric oxides, is constructed for an FCC single-phase multi-principal element alloy (MPEA) based on the CALculation of PHAse Diagram method. The predominant reaction products, the ions in aqueous solution, and the cation distribution in oxides are predicted. The oxide solid solution is stabilized by the mixing free energy (or mixing entropy) and the stabilizing effect becomes more significant as the temperature increases. Consequently, solid solution oxides are stable in large regions of the potential-pH diagram and the mixing free energy mostly affects the equilibrium composition of the stable oxides, while the shape of stable regions for oxides is mostly determined by the structure of the stable oxides. Agreements are found for Ni 2+ , Fe 2+ , and Mn 2+ between the atomic emission spectroelectrochemistry measurements and thermodynamic calculations, while deviations exist for Cr 3+ and Co 2+ possibly due to surface complexation with species such as Cl - and the oxide dissolution. By incorporating the solution models of oxides, the current work presents a general and more accurate way to analyze the reaction products during aqueous corrosion of MPEAs.
Materials Science↗
Solution to the sign problem in a frustrated quantum impurity model
In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weight configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonadiabatic rate constants for proton transfer and proton-coupled electron transfer reactions in solution: Effects of quadratic term in the vibronic coupling expansion
Rate constant expressions for vibronically nonadiabatic proton transfer and proton-coupled electron transfer reactions are presented and analyzed. The regimes covered include electronically adiabatic and nonadiabatic reactions, as well as high-frequency and low-frequency proton donor-acceptor vibrational modes. These rate constants differ from previous rate constants derived with the cumulant expansion approach in that the logarithmic expansion of the vibronic coupling in terms of the proton donor-acceptor distance includes a quadratic as well as a linear term. The analysis illustrates that inclusion of this quadratic term in the framework of the cumulant expansion framework may significantly impact the rate constants at high temperatures for proton transfer interfaces with soft proton donor-acceptor modes that are associated with small force constants and weak hydrogen bonds. The effects of the quadratic term may also become significant in these regimes when using the vibronic coupling expansion in conjunction with a thermal averaging procedure for calculating the rate constant. In this case, however, the expansion of the coupling can be avoided entirely by calculating the couplings explicitly for the range of proton donor-acceptor distances sampled. The effects of the quadratic term for weak hydrogen-bonding systems are less significant for more physically realistic models that prevent the sampling of unphysical short proton donor-acceptor distances. Additionally, the rigorous relation between the cumulant expansion and thermal averaging approaches is clarified. In particular, the cumulant expansion rate constant includes effects from dynamical interference between the proton donor-acceptor and solvent motions and becomes equivalent to the thermally averaged rate constant when these dynamical effects are neglected. This analysis identifies the regimes in which each rate constant expression is valid and thus will be important for future applications to proton transfer and proton-coupled electron transfer in chemical and biological processes.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Countercations Control Local Specific Bonding Interactions and Nucleation Mechanisms in Concentrated Water-in-Salt Solutions
One of the continuing challenges presented in aqueous salt solutions is to understand ion association reactions driving dynamic demixing from solvation, complexation and solute clustering. The problems understanding this phenomenon are exacerbated in the highly-concentrated water-in-salt electrolytes, where the deficiency of water leads to a dramatic retardation of solvating water and formation of extended solvent-solute clustering networks. By probing microscopic dynamics of water and prenucleation clusters using quasi-elastic neutron scattering and proton nuclear magnetic resonance spectroscopy, we observed contrasting mechanistic specifics of ion-water mobilities in highly-concentrated Na+- vs. K+-based aluminate solutions (diffusion coefficients of 0.2 vs. 2.6?10-10m2s-1 at 293 K, respectively). The magnitude of the differences is far beyond the kosmotropic (Na+) and chaotropic (K+) effects typically understood at low ionic concentrations. The distinct crystallization mechanisms observed in analogous deuterated systems further imply that different prenucleation cluster dynamics and network packing morphologies can either frustrate or promote crystallization, as described by non-classical nucleation theory.
Wang, Hsiu-Wen↗
Size-dependent error of the density functional theory ionization potential in vacuum and solution
Density functional theory is often the method of choice for modeling the energetics of large molecules and including explicit solvation effects. It is preferable to use a method that treats systems of different sizes and with different amounts of explicit solvent on equal footing. However, recent work suggests that approximate density functional theory has a size-dependent error in the computation of the ionization potential. We here investigate the lack of size-intensivity of the ionization potential computed with approximate density functionals in vacuum and solution. We show that local and semi-local approximations to exchange do not yield a constant ionization potential for an increasing number of identical isolated molecules in vacuum. Instead, as the number of molecules increases, the total energy required to ionize the system decreases. Rather surprisingly, we find that this is still the case in solution, whether using a polarizable continuum model or with explicit solvent that breaks the degeneracy of each solute, and we find that explicit solvent in the calculation can exacerbate the size-dependent delocalization error. We demonstrate that increasing the amount of exact exchange changes the character of the polarization of the solvent molecules; for small amounts of exact exchange the solvent molecules contribute a fraction of their electron density to the ionized electron, but for larger amounts of exact exchange they properly polarize in response to the cationic solute. In vacuum and explicit solvent, the ionization potential can be made size-intensive by optimally tuning a long-range corrected hybrid functional.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Local atomic environment analysis of short and long-range solute-solute interactions in a symmetric tilt grain boundary
We develop an efficient molecular-statics algorithm for predicting local solute-solute interaction effects on grain-boundary segregation. This algorithm is applied to the segregation and interaction of Ni and Cu solutes in a Σ9 (221) symmetric tilt grain boundary in Ag. It is found that the strength of interaction between two solutes directly correlates with the change of average segregation energy in the local atomic environment of a fixed grain-boundary solute. It is shown that local interaction effects at grain boundaries can be either attractive or repulsive wherein long-range attractive effects increase the propensity for solute cluster nucleation. This study underscores the atomic nature of grain-boundary solute segregation and provides a tool that could yield meaningful insight into heterogeneous solute segregation phenomena in polycrystalline alloys beyond their dilute limit.
36 MATERIALS SCIENCE↗
Ion aggregation in high salt solutions. III. Computational vibrational spectroscopy of HDO in aqueous salt solutions
The vibrational frequency, frequency fluctuation dynamics, and transition dipole moment of the O—D stretch mode of HDO molecule in aqueous solutions are strongly dependent on its local electrostatic environment and hydrogen-bond network structure. Therefore, the time-resolved vibrational spectroscopy the O—D stretch mode has been particularly used to investigate specific ion effects on water structure. Despite prolonged efforts to understand the interplay of O—D vibrational dynamics with local water hydrogen-bond network and ion aggregate structures in high salt solutions, still there exists a gap between theory and experiment due to a lack of quantitative model for accurately describing O—D stretch frequency in high salt solutions. To fill this gap, we have performed numerical simulations of Raman scattering and IR absorption spectra of the O—D stretch mode of HDO in highly concentrated NaCl and KSCN solutions and compared them with experimental results. Carrying out extensive quantum chemistry calculations on not only water clusters but also ion-water clusters, we first developed a distributed vibrational solvatochromic charge model for the O—D stretch mode in aqueous salt solutions. Furthermore, the non-Condon effect on the vibrational transition dipole moment of the O—D stretch mode was fully taken into consideration with the charge response kernel that is non-local polarizability density. From the fluctuating O—D stretch mode frequencies and transition dipole vectors obtained from the molecular dynamics simulations, the O—D stretch Raman scattering and IR absorption spectra of HDO in salt solutions could be calculated. The polarization effect on the transition dipole vector of the O—D stretch mode is shown to be important and the asymmetric line shapes of the O—D stretch Raman scattering and IR absorption spectra of HDO especially in highly concentrated NaCl and KSCN solutions are in quantitative agreement with experimental results. We anticipate that this computational approach will be of critical use in interpreting linear and nonlinear vibrational spectroscopies of HDO molecule that is considered as an excellent local probe for monitoring local electrostatic and hydrogen-bonding environment in not just salt but also other confined and crowded solutions.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Solution Irregularity Remediation for Spatial Discretization Error Estimation for S N Transport Solutions
The discrete ordinates linear Boltzmann transport equation is typically solved in its spatially discretized form, incurring spatial discretization error. Quantification of this error for purposes such as adaptive mesh refinement or error analysis requires an a posteriori estimator, which utilizes the numerical solution to the spatially discretized equation to compute an estimate. Because the quality of the numerical solution informs the error estimate, irregularities, present in the true solution for any realistic problem configuration, tend to cause the largest deviation in the error estimate vis-a-vis the true error. In this paper, an analytical partial singular characteristic tracking (pSCT) procedure for reducing the estimator’s error is implemented within our novel residual source estimator for a zeroth-order discontinuous Galerkin scheme, at the additional cost of a single inner iteration. Here, a metric-based evaluation of the pSCT scheme versus the standard residual source estimator is performed over the parameter range of a Method of Manufactured Solutions test suite. The pSCT scheme generates near-ideal accuracy in the estimate in problems where the dominant source of the estimator’s error is the solution irregularity, namely, problems where the true solution is discontinuous and problems where the true solution’s first derivative is discontinuous and the scattering ratio is low. In problems where the scattering ratio is high and the true solution is discontinuous in the first derivative, the error in the scattering source, which is not converged by the pSCT scheme, is greater than the error incurred due to the irregularity. Ultimately, a pSCT scheme is judged to be useful for error estimation in problems where the computational cost of the scheme is justified. In the presence of many irregularities, such a scheme may be intractable for general use, but in benchmarks, as an analytical tool, or in problems that have nondissipative discontinuities, the scheme may prove invaluable.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Electronic structure of aqueous solutions: Bridging the gap between theory and experiments
Predicting the electronic properties of aqueous liquids has been a long-standing challenge for quantum mechanical methods. However, it is a crucial step in understanding and predicting the key role played by aqueous solutions and electrolytes in a wide variety of emerging energy and environmental technologies, including battery and photoelectrochemical cell design. Here, we propose an efficient and accurate approach to predict the electronic properties of aqueous solutions, on the basis of the combination of first-principles methods and experimental validation using state-of-the-art spectroscopic measurements. We present results of the photoelectron spectra of a broad range of solvated ions, showing that first-principles molecular dynamics simulations and electronic structure calculations using dielectric hybrid functionals provide a quantitative description of the electronic properties of the solvent and solutes, including excitation energies. The proposed computational framework is general and applicable to other liquids, thereby offering great promise in understanding and engineering solutions and liquid electrolytes for a variety of important energy technologies.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A first principles approach for determining solute effect on electrical resistivity of Aluminum solid solution
There are no general approaches for predicting the effect of solutes on electrical resistivity changes in aluminum (Al) solid solutions. Here, we introduce a first principles-based approach for predicting temperature-dependent electrical resistivity of Al solid solutions. A combination of electronic structure methods was applied to calculate electronic scattering effects on chemical disorder and temperature induced atomic vibrations or phonons. Our calculations are validated by contrasting experimental resistivity measurements for two elements in Al solid solution: at 0.3 at. % concentration, Sn (an sp-valence solute) increases the residual resistivity by 0.2 μΩ·m, whereas Zr (a d-valence solute) causes a 2.5 μΩ·m increase. This trend may deviate for solute elements in Al that form semiconductors in pure state, like Si. Our findings provide an understanding of the role of valence electron character of solute atoms in determining electrical resistivity of Al alloys.
Samolyuk, German [ORNL] (ORCID:0000000168778255)↗
ZnxMn1-xO Solid Solutions in the Rocksalt Structure: Optical, Charge Transport, and Photoelectrochemical Properties
Theoretical predictions of ZnO:MnO solid solutions (abbreviated here as ZMO) with the rocksalt-type structure suggest improved visible light absorption and suitable band edge positions for the overall water splitting reaction, but experimental efforts to produce such phases are limited by the low solubility of Zn within this structure type. Here, we produce solid solutions of ZnxMn1-xO, with x = 0.5 and 0.3 in the metastable rocksalt phase, using high-pressure and high-temperature (HPHT) techniques. X-ray diffraction and electron microscopy methods were employed to determine the crystal structure, chemical composition, and homogeneity on the submicron scale. The solid solutions exhibit increased optical absorbance in the visible spectral range as compared to those of the parent oxides ZnO and MnO. Our theoretical calculations for ZnxMn1-xO with x = 0.5, 0.25 predict band gaps of 2.53 and 2.98 eV, respectively, with an unusually large band gap bowing. Our calculations also show small effective electron mass for these materials indicating their potential for solar energy applications. Initial photoelectrochemical tests reveal that ZMO solid solutions are suitable for water oxidation and warrant further experimental optimization.
36 MATERIALS SCIENCE↗
Structural Dynamics and Evolution of Bismuth Electrodes during Electrochemical Reduction of CO 2 in Imidazolium-Based Ionic Liquid Solutions
Real-time changes in the composition and structure of bismuth electrodes used for catalytic conversion of CO2 into CO were examined via X-ray absorption spectroscopy (including XANES and EXAFS), electrochemical quartz crystal microbalance (EQCM), and in situ X-ray reflectivity (XR). Measurements were performed with bismuth electrodes immersed in acetonitrile (MeCN) solutions containing a 1-butyl-3-methylimidazolium ([BMIM]+) ionic liquid promoter or electrochemically inactive tetrabutylammonium supporting electrolytes (TBAPF6 and TBAOTf). Altogether, these measurements show that bismuth electrodes are originally a mixture of bismuth oxides (including Bi2O3) and metallic bismuth (Bi0) and that the reduction of oxidized bismuth species to Bi0 is fully achieved under potentials at which CO2 activation takes place. Furthermore, EQCM measurements conducted during cyclic voltammetry revealed that a bismuth-coated quartz crystal exhibits significant shifts in resistance (ΔR) prior to the onset of CO2 reduction near -1.75 V vs Ag/AgCl and pronounced hysteresis in frequency (Δf) and ΔR, which suggests significant changes in roughness or viscosity at the Bi/[BMIM]+ solution interface. In situ XR performed on rhombohedral Bi (001) oriented films indicates that extensive restructuring of the bismuth film cathodes takes place upon polarization to potentials more negative than -1.6 V vs Ag/AgCl, which is characterized by a decrease of the Bi (001) Bragg peak intensity of ≥50% in [BMIM]OTf solutions in the presence and absence of CO2. Over 90% of the reflectivity is recovered during the anodic half-scan, suggesting that the structural changes are mostly reversible. In contrast, such a phenomenon is not observed for thin Bi (001) oriented films in solutions of tetrabutylammonium salts that do not promote CO2 reduction. Overall, these results highlight that Bi electrodes undergo significant potential-dependent chemical and structural transformations in the presence of [BMIM]+-based electrolytes, including the reduction of bismuth oxide to bismuth metal and changes in roughness and near-surface viscosity.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Transition between vortex rings and MAP solutions for electrically charged magnetic solutions
We consider the bifurcation and transition of axially symmetric monopole-antimonopole pair (MAP) and vortex ring solutions in the presence of electric charge for the SU(2) Yang-Mills-Higgs field theory. Here we investigate the properties of MAP/vortex ring solutions with n = 3,η = 0.65, for different Higgs field strength λ. For λ < 4.93, there is only one fundamental branch of vortex ring solution, but at the critical value of λ{sub b} = 4.93, branching happens and 2 sets of new solutions appeared. The new branch with less energy is a full MAP solution while the branch with higher energy contains MAP at the beginning and separation between poles of MAP on the z-axis reduces gradually and at another critical value of λ{sub t} = 14.852, they merge together at z = 0. Beyond this point the solutions change to the vortex ring solutions and a transitions between MAP and vortex ring solutions happens at this branch.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Cost-Benefit Analysis For Indonesia Building Sector: Whole-Building Cooling Solutions
The Net Zero World (NZW) Initiative Collaborative Work Program with the Government of Indonesia (GoI) includes technical assistance and investment mobilization facilitation to accelerate deployment of energy efficiency technologies and solutions for the building sector. A February 2023 U.S.–Indonesia Joint Workshop on Decarbonizing the Building Sector yielded a NZW Indonesia Building Decarbonization Working Group (NZW IBDWG) with four sub-working groups (SWG): SWG-A National Center, SWG-B Capacity Building, SWG-C Investment and Financing, and SWG-D Pilot Projects. Technical analysis of whole-building cooling solutions for tropical climates of Indonesia was conducted by SWG-A to quantify energy savings, carbon dioxide reductions, and comfort improvements offered by 12 passive or low-energy cooling strategies: ceiling fans with and without thermostat setbacks; cool roofs; cool walls; exterior awnings; exterior shades; interior shades; insulated roofs; insulated walls; low-e windows; solar window films; and natural ventilation. Leveraging the results from SWG-A, cost-benefit analysis (CBA) was conducted by SWG-C to assess the consumer and national costs and impacts associated with these 12 cooling solutions. The evaluation involved estimating life-cycle costs (LCC), payback period (PBP), net present values (NPV), annual electricity burden change for low-income households, and reduced national annual power-sector generation demand by 2030, 2040, 2050, and 2060. This evaluation can help guide Indonesia’s Just Energy Transition Partnership (JETP) investments in policies and programs to advance research, development, deployment, and commercial adoption (RDDCA) of efficient residential building sector cooling technologies and solutions in Indonesia. Four key energy conservation measures (ECM) have been identified to reduce air-conditioning (AC) energy demand in single-family housing in Indonesia: ceiling fan with temperature setback (to 28.1 °Celcius from 25 °C); insulated walls; insulated roof; and cool roof. This study found that low-income households with AC installations in Indonesia currently face a high energy cost burden of approximately 10%. However, by implementing a ceiling fan with temperature setback, this burden could decrease to 2.5% today and further reduce to 1.3% by the year 2060. The PBP for a ceiling fan with temperature setback is one year, indicating one of the lowest LCC and best NPV. In the planned upcoming phase of CBA, a series of building cooling improvement scenarios can be further defined, incorporating more than one ECM in combination with socio-economic factors evaluated in the initial CBA phase. Additionally, the analysis of ECM effects in multifamily housing can be expanded. This broader national analysis aims to encompass a holistic and comprehensive system-level perspective, including factors such as avoided power sector infrastructure investments, domestic job creation, domestic manufacturing job creation, and gross domestic product (GDP) growth.
29 ENERGY PLANNING, POLICY, AND ECONOMY↗
Tailoring grain growth and solid solution strengthening of single-phase CrCoNi medium-entropy alloys by solute selection
In the present study, we selected solutes to be added to the CrCoNi medium-entropy alloy (MEA) based on the mismatch of self-diffusion activation energy (SDQ) between the alloying elements and constituent elements of the matrix, and then investigated their grain growth behavior and mechanical properties. Mo and Al were selected as the solutes for investigation primarily because they have higher and lower SDQ, respectively, than those of the matrix elements; a secondary factor was their higher and lower shear modulus. Their concentrations were fixed at 3 at.% each because previous work had shown these compositions to be single-phase solid solutions with the face-centered cubic structure. Three alloys were produced by arc melting, casting, homogenizing, cold rolling and annealing at various temperatures and times to produce samples with different grain sizes. They were (a) the base alloy CrCoNi, (b) the base alloy plus 3 at.% Mo, and (c) the base alloy plus 3 at.% Al. The activation energies for grain growth of the CrCoNi, CrCoNi-3Mo and CrCoNi-3Al MEAs were found to be ~251, ~368 and ~219 kJ/mol, respectively, consistent with the notion that elements with higher SDQ (in this study Mo) retard grain growth (likely by a solute-drag effect), whereas those with lower values (Al) accelerate grain growth. The room-temperature tensile properties show that Mo increases the yield strength by ~40% but Al addition has a smaller strengthening effect consistent with their relative shear moduli. The yield strength as a function of grain size for the three singlephase MEAs follows the classical Hall-Petch relationship with much higher slopes (> 600 MPa μm -0.5 ) than traditional solid solutions. Furthermore, this work shows that the grain growth kinetics and solid solution strengthening of the CrCoNi MEA can be tuned by selecting solute elements that have appropriate diffusion and physical properties.
36 MATERIALS SCIENCE↗
A novel signal transduction protein: Combination of solute binding and tandem PAS-like sensor domains in one polypeptide chain: Periplasmic Ligand Binding Protein Dret_0059
We report the structural and biochemical characterization of a novel periplasmic ligand-binding protein, Dret_0059, from Desulfohalobium retbaense DSM 5692, an organism isolated from the Salt Lake Retba in Senegal. The structure of the protein consists of a unique combination of a periplasmic solute binding protein (SBP) domain at the N-terminal and a tandem PAS-like sensor domain at the C-terminal region. SBP domains are found ubiquitously and their best known function is in solute transport across membranes. PAS-like sensor domains are commonly found in signal transduction proteins. These domains are widely observed as parts of many protein architectures and complexes but have not been observed previously within the same polypeptide chain. In the structure of Dret_0059, a ketoleucine moiety is bound to the SBP, whereas a cytosine molecule is bound in the distal PAS-like domain of the tandem PAS-like domain. Differential scanning flourimetry support the binding of ligands observed in the crystal structure. There is significant interaction between the SBP and tandem PAS-like domains, and it is possible that the binding of one ligand could have an effect on the binding of the other. We uncovered three other proteins with this structural architecture in the non-redundant sequence data base, and predict that they too bind the same substrates. The genomic context of this protein did not offer any clues for its function. We did not find any biological process in which the two observed ligands are coupled. The protein Dret_0059 could be involved in either signal transduction or solute transport.
Wu, R.↗
An analytical solution of the solution-diffusion-electromigration equations reproduces trends in ion rejections during nanofiltration of mixed electrolytes
Here, this paper develops an analytical solution to the equations governing the solution-diffusion-electromigration transport of the ions from two salts that contain a common ion. The analytical expressions, which rely on constant ion permeances, readily enable simple spreadsheet computations of the permeate ion concentrations in nanofiltration (NF). Despite the model simplicity, calculations of ion rejections as a function of transmembrane volume fluxes, feed-solution compositions, and permeance values reproduce experimental trends, with ion permeances as the only adjustable parameters. For example, with solutions containing dissolved MA and M 2 B, when the membrane permeance to B 2– is much lower than the permeances to A – and M + , plots of A – rejection versus transmembrane volume flux show the negative minimum that is often characteristic of NF. Moreover, B 2– rejection increases with increasing MA in the feed solution, reflecting a decreasing electric field in the membrane. The analytical solution also enables spreadsheet computations of electric fields in membrane separation layers and effectively models experimental data for intrinsic rejections as a function of transmembrane volume flow. Interestingly, the model suggests that with sufficiently high permeances of A – (relative to M + ), at certain feed compositions the A – /B 2– selectivity may increase without bound as a function of volume flow. Otherwise, this selectivity does not vary greatly with feed composition and quickly reaches a limit as the volume flow increases. Despite the simplifying approximation of constant ion permeances, using only a few adjustable parameters this model readily reveals trends in NF ion rejections and may help to identify the desired ion permeances or solution compositions for specific separations.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗