Statistical mechanical theories of the electric double layer

A comparison is made of present-day statistical mechanical theories of the diffuse part of the electric double layer in aqueous 1-1 electrolyte at a charged plane interface. These theories fall into three categories: (1) the modified Poisson-Boltzmann equation (MPB) based on the Kirkwood-Loeb charging of an ion; (2) the adaption to the electric double layer of the Bogoliubov-Born-Green-Yvon (BBGY) hierarchy of integral equations; (3) the use of the Ornstein-Zernike equation (OZ) for the direct correlation functions of the pair interfacial plane wall-molecular particle, as derived by Henderson, Abraham and Barker (HAB). The HAB-OZ equation is used in conjunction with the mean spherical approximation (MSA) or hypernetted chain approximation (HNC). All the theories make use of the primitive model of the bulk electrolyte, so that inhomogeneity of the dielectric permittivity next to the plane wall is neglected. Except perhaps for a variation of the BBGY theory, which uses a closure based on electrical neutrality, all the theories predict oscillatory behaviour in potential distribution as a function of distance at the higher electrolyte concentrations. The HAB-OZ model has the defect that electrostatic imaging is not consistent with the assumptions of central forces and pair-wise additivity of ionic interactions. It is found that the MPB provides the best overall agreement with Monte Carlo calculations.     

Dependence of depletion layer thickness on polymer concentration determined by Vincent's pragmatic and Donath's electrophoretic theories

On the interface of a solid surface and a solution of nonadsorbing polymer there exists a depletion layer (DL), where the concentration of polymer segments is lower. Donath's electrophoretic theory, based on the decreased viscosity in the DL region, allows computing DL thickness from the relative (with and without polymer) electrophoretic mobility, the bulk viscosity, and the ionic strength. The aim of this work is to check experimentally Donath's nonlinear electrophoretic (NLE) theory under the most favorable conditions--liposomes in solutions of low-molecular poly(ethylene glycol) (PEG). In order to determine DL thickness, the dependence of mobility on viscosity is chosen instead on ionic strength. The value obtained from NLE theory is compared with the DL thickness calculated by Vincent's pragmatic theory. The conformation-statistical parameters are calculated on the base of viscosimetric measurements of PEG solution. The results indicate a few shortcomings of NLE theory. The main one is that DL thickness does not depend on polymer concentration, a fact that is in discrepancy with the prediction of Vincent's theory. The conclusion is that NLE theory describes well the experimental dependence of the relative mobility on the bulk viscosity, but it is inapplicable to quantitative determination of DL thickness.     

A molecular Debye-Hückel theory and its applications to electrolyte solutions

In this report, a molecular Debye-Hu?ckel theory for ionic fluids is developed. Starting from the macroscopic Maxwell equations for bulk systems, the dispersion relation leads to a generalized Debye-Hu?ckel theory which is related to the dressed ion theory in the static case. Due to the multi-pole structure of dielectric function of ionic fluids, the electric potential around a single ion has a multi-Yukawa form. Given the dielectric function, the multi-Yukawa potential can be determined from our molecular Debye-Hu?ckel theory, hence, the electrostatic contributions to thermodynamic properties of ionic fluids can be obtained. Applications to binary as well as multi-component primitive models of electrolyte solutions demonstrated the accuracy of our approach. More importantly, for electrolyte solution models with soft short-ranged interactions, it is shown that the traditional perturbation theory can be extended to ionic fluids successfully just as the perturbation theory has been successfully used for short-ranged systems.     

Comparison of the application of Debye-Huckel and specific ion interaction theories for the complexation of tungsten(VI) with ethylenediaminediacetic acid

Equilibrium of the reaction of tungsten(VI) with ethylenediaminediacetic acid (EDDA) has been investigated in aqueous solution of pH 7.5 and 25°C. All measurements have been carried out at different ionic strengths ranging from (0.1 to 1.0) mol dm⁻³ (NaClO₄). According to our results the metal to ligand ratio is 1: 1. Stability constants and stoichiometry of the complex have been determined from a combination of potentiometric and UV spectroscopic measurements. In this semi-empirical model, two parameters have been introduced in a Debye-Huckel type equation based on the Gauss—Newton nonlinear least-squares method and minimizing the sum of the squares of the errors. Comparison of the ionic strength effect on these complex formation reactions has been made using a Debye-Huckel type equation and Bronsted—Guggenheim—Scatchard specific ion interaction theory (SIT). Published in Russian in Zhurnal Neorganicheskoi Khimii, 2009, Vol. 54, No. 5, pp. 864–868. The article is published in the original     

Relationships among coarse-grained field theories of fluctuations in polymer liquids

Two closely related field-theoretic approaches have been used in previous work to construct coarse-grained theories of corrections to the random phase approximation for correlations in block copolymer melts and miscible polymer blends. The "auxiliary field" (AF) approach is based on a rigorous expression for the partition function Z of a coarse-grained model as a functional integral of an auxiliary chemical potential field. The "effective Hamiltonian" (EH) approach is instead based on an expression for Z as a functional integral of an observable order parameter field. The exact effective Hamiltonian H(eff) in the EH approach is defined as the free energy of a system with a constrained order parameter field. In practice, however, H(eff) has often been approximated by a mean-field free energy functional, yielding what we call a mean-field effective Hamiltonian (MFEH) approximation. This approximation was the starting point of both the Fredrickson-Helfand analysis of fluctuation effects in diblock copolymers and earlier work on the Ginzburg criterion in polymer blends. A more rigorous EH approach by Holyst and Vilgis used an auxiliary field representation of the exact H(eff) and allowed for Gaussian fluctuations of this field. All applications of both AF and EH approaches have thus far relied upon some form of Gaussian, or "one-loop" approximation for fluctuations of a chemical potential and/or order parameter field about a mean-field saddle-point. The one-loop EH approximation of Holyst and Vilgis and the one-loop AF theory are equivalent to one another, but not to the one-loop MFEH theory. The one-loop AF and MFEH theories are shown to yield predictions for the inverse structure factor S(-1)(q) that (in the absence of further approximations to either theory) differ by a function that is independent of the Flory-Huggins interaction parameter χ. As a result, these theories yield predictions for the peak scattering intensity that exhibit a similar χ-dependence near a spinodal. The Fredrickson-Helfand theory for the structure factor in disordered diblock copolymer melts is an asymptotic approximation to the MFEH one-loop theory that captures the dominant asymptotic behavior of very long, symmetric copolymers very near the order-disorder transition.     

Solubility of small molecule in ionic liquids: a model study on the ionic size effect

Recently, the solvent power of ionic liquid (IL) has been described based on Flory-Huggins (FH) theory assuming that the volumes of the components are the same (J. Phys. Chem. B, 2006, 110, 16205). Here, we extended the FH theory to derive the solvent power in the case of different sizes (molar volumes) of the IL's components based on "polymer-like" model. Applying this model, the effect of ionic size on the solvent power of ionic liquids has been investigated. It was found that the effect of size can be characterized by introducing the effective volume (V+ and V-) of each site of the ion, and for the equivalent ionic liquid, the larger effective volume of the ionic liquid has the larger solvent power. Our results are in excellent agreement with the experimental solubility data in various ionic liquids.     

Parallel direct implementations of second-order perturbation theories

Two algorithms are presented for parallel direct computation of energies with second-order perturbation theory. Closed-shell MP2 theory as well as the open-shell perturbation theories OPT2(2) and ZAPT2 have been implemented. The algorithms are designed for distributed memory parallel computers. The first algorithm exhibits an excellent load balance and scales well when relatively few processors are used, but a large communication overhead reduces the efficiency for larger numbers of processors. The other algorithm employs very little interprocessor communication and scales well for large systems. In both implementations the memory requirement has been reduced by allowing the two-electron integral transformation to be performed in multiple passes and by distributing the (partially) transformed integrals between processors. Results are presented for systems with up to 327 basis functions. © 1995 John Wiley & Sons, Inc.     

Complexation of tungsten(VI) with ethylenediaminetetraacetic acid and iminodiacetic acid at different ionic strengths using the Debye-Hückel and specific ion interaction theories

The equilibria in systems ethylenediaminetetraacetic acid-W^VI and iminodiacetic acid-W^VI were studied by a combination of UV-Vis spectrophotometric and potentiometric techniques at different ionic strengths ranging from 0.1 to 1.0 mol L^s-1 (NaC1O₄, 25 °C, pH = 7.5). The ionic strength effect on these complex formation reactions was studied using a Debye-Hückel-type equation and the Brønsted-Guggenheim-Scatchard specific ion interaction theory.     

Hydrogen bonds in imidazolium ionic liquids

It is critically important to understand the structural properties of ionic liquids. In this work, the structures of cations, anions, and cation-anion ion-pairs of 1,3-dialkylimidazolium based ionic liquids were optimized systematically at the B3LYP/6-31+G level of DFT theory, and their most stable geometries were obtained. It was found that there exist only one-hydrogen-bonded ion-pairs in single-atomic anion ionic liquids such as [emim]Cl and [emim]Br, while one- and two-hydrogen-bonded ion-pairs in multiple atomic anion ionic liquids such as [emim]BF(4) and [emim]PF(6) exist. Further studies showed that the cations and anions connect each other to form a hydrogen-bonded network in 1,3-dialkylimidazolium halides, which has been proven by experimental measurement. Furthermore, the correlation of melting points and the interaction energies was discussed for both the single atomic anion and multiple atomic anion ionic liquids.     

An application of the novel quantum mechanical/molecular mechanical method combined with the theory of energy representation: An ionic dissociation of a water molecule in the supercritical water

A novel quantum chemical approach recently developed has been applied to an ionic dissociation of a water molecule (2H(2)O-->H(3)O(+)+OH(-)) in ambient and supercritical water. The method is based on the quantum mechanical/molecular mechanical (QM/MM) simulations combined with the theory of energy representation (QM/MM-ER), where the energy distribution function of MM solvent molecules around a QM solute serves as a fundamental variable to determine the hydration free energy of the solute according to the rigorous framework of the theory of energy representation. The density dependence of the dissociation free energy in the supercritical water has been investigated for the density range from 0.1 to 0.6 g/cm(3) with the temperature fixed at a constant. It has been found that the product ionic species significantly stabilizes in the high density region as compared with the low density. Consequently, the dissociation free energy decreases monotonically as the density increases. The decomposition of the hydration free energy has revealed that the entropic term (-TDeltaS) strongly depends on the density of the solution and dominates the behavior of the dissociation free energy with respect to the variation of the density. The increase in the entropic term in the low density region can be attributed to the decrease in the translational degrees of freedom brought about by the aggregation of solvent water molecules around the ionic solute.     

A new approach for efficient simulation of Coulomb interactions in ionic fluids

We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cutoff distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma-->0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

Infrared spectra and theoretical calculations of KH and (KH)2 in solid hydrogen

A matrix isolation IR study of laser-ablated potassium atom reactions with H2 has been performed in solid molecular hydrogen. The KH molecule and (KH)2 cluster were identified by infrared spectra with isotopic substitution (HD and D2) and by comparison to frequencies calculated using density functional theory. In para-hydrogen, the sharp KH absorption suggests dihydrogen complex formation with the ionic KH molecule, which is also characterized by an absorption at 4095 cm(-1). The highly ionic rhombic (KH)2 molecule is formed by dimerization and trapped in solid hydrogen. Calculations at the CCSD(T) level of theory show the increasing ionic character and decreasing stability for the (MH)2 molecule series from Li to Cs.     

Controversy and complementarity in mechanistic organic chemistry. The transition state and structural theories reexamined

It is proposed that molecular phenomena may only be described within the framework of the Complementarity Principle (‘CP’), and that scientific controversy may originate in the essential incompatibility of complementary representations. Complementarity based on the temporal Uncertainty Principle leads to new insights into transition state theory, microscopic reversibility and the Curtin-Hammett Principle. An empirical application of the ‘CP’ to the structural theory leads to a revision of present concepts of ‘reaction dynamics’, with the Principle of Least Nuclear Motion (‘PLNM’) emerging as a general alternative to electronic theories of reactivity. In fact, it is argued that the ‘PLNM’ is a better basis for the Woodward-Hoffmann rules than is orbital symmetry. A more flexible approach to organic reaction mechanisms is thus indicated. Also, as the basis of the structural theory is fundamentally uncertain, and the present theory of X-ray diffraction apparently incompatible with the ‘UP’, a reinterpretation of the Bragg equation has been attempted.     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Nitromethane as solvent in capillary electrophoresis

Nitromethane has several properties that make it an interesting solvent for capillary electrophoresis especially for lipophilic analytes that are not sufficiently soluble in water: freezing and boiling points are suitable for laboratory conditions, low viscosity leads to favourable electrophoretic mobilities, or an intermediate dielectric constant enables dissolution of electrolytes. In the present work we investigate the change of electrophoretically relevant analyte properties - mobilities and pKa values - in nitromethane in dependence on the most important experimental conditions determined by the background electrolyte: the ionic strength, I, and the pH. It was found that the mobility decreases with increasing ionic strength (by, e.g. up to 30% from I = 0 to 50 mmol/L) according to theory. An appropriate pH scale is established by the aid of applying different concentration ratios of a buffer acid with known pKa and its conjugate base. The mobility of the anionic analytes (from weak neutral acids) depends on the pH with the typical sigmoidal curve in accordance with theory. The pKa of neutral acids derived from these curves is shifted by as much as 14 pK units in nitromethane compared to water. Both findings confirm the agreement of the electrophoretic behaviour of the analytes with theories of electrolyte solutions. Separation of several neutral analytes was demonstrated upon formation of charged complexes due to heteroconjugation with chloride as ionic constituent of the background electrolyte.     

Study of the phase behavior of a diblock copolymer in an ionic liquid: Outlook for use of the integral-equation theory

It is shown that the integral-equation theory may be used to study the phase behavior of a diblock copolymer in an ionic liquid with allowance made for the solvent structure. Features of microphase separation are exemplified via calculation of the mean-field spinodal temperature and order-disorder transition temperature as functions of the copolymer concentration at two different lengths of the cationic tail of the ionic liquid. The need to allow for the solvent structure during construction of the theory of the phase behavior of block copolymers in ionic liquids is substantiated.     

Dipolar solvation dynamics in room temperature ionic liquids: an effective medium calculation using dielectric relaxation data

Solvation dynamics in four imidazolium cation based room temperature ionic liquids (RTIL) have been calculated by using the recently measured dielectric relaxation data [ J. Phys. Chem. B 2008, 112, 4854 ] as an input in a molecular hydrodynamic theory developed earlier for studying solvation energy relaxation in polar solvents. Coumarin 153 (C153), 4-aminophthalimide (4-AP), and trans-4-dimethylamino-4'-cyanostilbene (DCS) have been used as probe molecules for this purpose. The medium response to a laser-excited probe molecule in an ionic liquid is approximated by that in an effective dipolar medium. The calculated decays of the solvent response function for these RTILs have been found to be biphasic and the decay time constants agree well with the available experimental and computer simulation results. Also, no probe dependence has been found for the average solvation times in these ionic liquids. In addition, dipolar solvation dynamics have been predicted for two other RTILs for which experimental results are not available yet. These predictions should be tested against experiments and/or simulation studies.     

An enthalpic approach to delineate the interactions of cations of imidazolium-based ionic liquids with molecular solvents

We present a systematic investigation on the enthalpic assessment of the interactions operating between the cation and anion of four imidazolium ionic liquids with aqueous and various nonaqueous solvents. Accurate experimental information gathered with the help of an isothermal titration calorimeter at 298.15 K has been analyzed for excess partial molar enthalpy of the ionic liquid, H(IL)(E), in terms of hydrophobic and solvation effects. The variations in the limiting excess partial molar enthalpy of the ionic liquid, H(IL)(E, ∞), have been correlated with solvent properties. We have quantified the enthalpic effects due to dissociation of ionic liquids in very dilute solutions and to clathrate formation with the increasing concentration of ionic liquid. A change in enthalpic behavior from endothermic to exothermic is observed on increasing the carbon chain length attached to the imidazolium ring. The solvent reorganization around the cationic species has been unraveled by employing the ionic liquid interaction parameters called as H(IL-IL)(E) deduced from the H(IL)(E) data. The apparent relative molar enthalpy, φ(L), derived from H(IL)(E) data has been examined in the light of the specific ion interaction theory as advanced by Pitzer with accurate results.