Volume Of Counterions Research Articles

Ion transport in polymerized ionic liquids: a comparison of polycation and polyanion systems.

The correlation among chemical structure, mesoscale structure, and ion transport in 1,2,3-triazole-based polymerized ionic liquids (polyILs) featuring comparable polycation and polyanion backbones is investigated by wide-angle X-ray scattering (WAXS), differential scanning calorimetry, and broadband dielectric spectroscopy (BDS). Above the glass transition temperature, Tg, higher ionic conductivity is observed in polycation polyILs compared to their polyanion counterparts, and ion conduction is enhanced by increasing the counterion volume in both polycation or polyanion polyILs. Below Tg, polyanions show lower activation energy associated with ion conduction. However, the validity of the Barton-Nakajima-Namikawa relation indicates that hopping conduction is the dominant charge transport mechanism in all the polyILs studied. While a significant transition from a Vogel-Fulcher-Tammann to Arrhenius type of thermal activation is observed below Tg, the decoupling index, often used to quantify the extent to which segmental dynamics and ion conduction are correlated, remains unaltered for the polyILs studied, suggesting that this index may not be a general parameter to characterize charge transport in polymerized ionic liquids. Furthermore, detailed analyses of the WAXS results indicate that both the mobile ion type and the structure of the pendant groups control mesoscale organization. These findings are discussed within the framework of recent models, which account for the subtle interplay between electrostatic and elastic forces in determining ion transport in polyILs. The findings demonstrate the intricate balance between the chemical structure and interactions in polyILs that determine ion conduction in this class of polymer electrolytes.

The size and affinity effect of counterions on self-assembly of charged block copolymers.

The effect of counterions' size and affinity on the microphase separated morphologies of neutral-charged diblock copolymers is investigated systematically using a random phase approximation (RPA) and self-consistent field theory (SCFT). The phase diagrams as a function of χAB and fA at different counterion sizes and different affinities to neutral blocks are constructed, respectively. Stability limits calculated using the RPA are in good agreement with the disorder-body-centered cubic phase boundaries from SCFT calculations. It was found that increasing the size of counterions causes the phase diagram to shift upward and leftward, which is attributed to electrostatic interactions and the intrinsic volume of counterions. The domain size of the ordered phase shows an unexpected tendency that it decreases with increasing counterions' size. The counterions' distributions in H and G phases demonstrate that it is electrostatic interaction, instead of packing frustration, that plays a leading role in such systems. For finite size counterions, with the increase in affinity between counterions and neutral blocks, the phase diagram shifts upward, indicating the improved compatibility between different blocks. Furthermore, the affinity effect between counterions and neutral blocks can be mapped into an effective Flory parameter χAB ' = χAB + 0.27χBC.

Ion size effect on counterion condensation around a spherical colloidal particle in a salt-free medium containing only counterions

A theory of counterion condensation around a spherical colloidal particle in a salt-free medium containing only counterions developed by Imai and Oosawa as reported by Busseiron Kenkyu 52:42, 1952 ibid. 59:99, 1953) and later by Ohshima (J Colloid Interface Sci 247:18, 2002) is extended to incorporate the ion size effect on the basis of the modified Poisson-Boltzmann equation using the Carnahan-Starling activity coefficient of counterions. The potential distribution depends on the particle surface charge, the particle volume fraction, and the average counterion volume fraction. It is shown that for a dilute particle suspension, the counterion condensation occurs, leading to a decrease in the particle surface potential when the following two conditions are both satisfied: (i) the scaled particle surface charge is greater than the logarithm of the inverse of the particle volume fraction and (ii) the average counterion volume fraction is much smaller than the particle volume fraction.

Engineering ionic conductivity of ionomeric membranes: influence of Van der Waals volume of counterions and temperature

Ionomeric membranes are essential constituents of many ionic devices including fuel cells, lithium-ion polymer batteries, and ionomeric polymer transducers. Understanding the dynamics of ionic conductivity of ionomeric membranes is significant in better understanding and optimizing ionic devices. In this work, effects of temperature and Van der Waals volume of Nafion counterions on ionic conductivity of Nafion ionomeric membrane are studied. Ionic conductivity of lithium (Li+), potassium (K+), and 1-Ethyl-3-methylimidazolium (EMI+) ion-exchanged Nafion membranes at temperatures varying from 30 °C–70 °C was investigated and a direct correlation between ionic conductivity and both temperature and Van der Waals volume of counter ions was observed. Ionic conductivity as a function of temperature (for all three counterions) exhibited two distinct slopes below and above ∼50 °C which is an indication of changes in activation energy and confirms previously claims of ionic decomposition of EMI-Tf ionic liquid around ∼50 °C.

Effect of counterion excluded volume on the conformational behavior of polyelectrolyte chains.

Conformational behavior of a single strongly charged polyelectrolyte chain in a dilute solution is studied by molecular dynamics simulations. The novel feature of the model is variation of the excluded volume of counterions for investigating its effect on the chain conformation, especially in low-polar media. It has been confirmed that the chain with conventional counterions collapses into a dense globule with increasing electrostatic interactions. However, if the counterions are bulky enough, they prevent the chain collapse even in media with strong electrostatic interactions. They stay bound in the vicinity of the backbone of the chain that adopts a swollen conformation. In this conformation, the scaling relation for the polymer dimensions with the chain length is the same as for neutral macromolecules in a good solvent, however the polyelectrolyte chain complexed with bulky counterions has a larger gyration radius than its uncharged analogue due to the excluded volume of the counterions contributing to the chain rigidity. Study of the counterion mobility has shown that, similar to the conventional counterions, the bulky counterions do not form stable ion pairs with ions on the polymer chain even in media with strong electrostatic interactions, but rather freely move along the chain backbone. In solutions containing mixtures of counterions with a bimodal size distribution, the conformations of linear polyelectrolytes depend considerably on the fraction of bulky counterions. Furthermore, a kind of intramolecular microphase separation can take place within a polyelectrolyte globule with the formation of a core-shell particle: the smaller counterions concentrate within the globular core while the bulkier counterions form a shell on the globule surface. The stability of the core-shell globule depends on the relative size of the counterions as well as their fractions in the solution. Thus, fine tuning of the balance between the counterion excluded volume and the electrostatic interactions opens new ways for controlling the conformational behavior of polyelectrolytes.

Polymerized Ionic Liquids: Correlation of Ionic Conductivity with Nanoscale Morphology and Counterion Volume.

The impact of the chemical structure on ion transport, nanoscale morphology, and dynamics in polymerized imidazolium-based ionic liquids is investigated by broadband dielectric spectroscopy and X-ray scattering, complemented with atomistic molecular dynamics simulations. Anion volume is found to correlate strongly with Tg-independent ionic conductivities spanning more than 3 orders of magnitude. In addition, a systematic increase in alkyl side chain length results in about one decade decrease in Tg-independent ionic conductivity correlating with an increase in the characteristic backbone-to-backbone distances found from scattering and simulations. The quantitative comparison between ion sizes, morphology, and ionic conductivity underscores the need for polymerized ionic liquids with small counterions and short alkyl side chain length in order to obtain polymer electrolytes with higher ionic conductivity.

Asymmetric electrostatic properties of an electric double layer: a generalized Poisson-Boltzmann approach taking into account non-uniform size effects and water polarization

We theoretically study electrostatic properties of electric double layer using a generalized Poisson-Boltzmann approach taking into account the orientational ordering of water dipoles and the excluded volume effect of water molecules as well as those of positive and negative ions with different sizes in electrolyte solution.Our approach enables one to predict that the number densities of water molecules, counterions and coions and the permittivity of electrolyte solution close to a charged surface, asymmetrically vary depending on both of sign and magnitude of the surface charge density and the volume of counterion. We treat several phenomena in more detail. Firstly, an increase in the volume of counterions and an increase in the surface charge density can cause the position of the minimum number density of water molecules to be farther from the charged surface. Secondly, width of the range of voltage in which the properties at the charged surface symmetrically vary decreases with increasing bulk salt concentration. In addition, we show that the excluded volume effect of water molecules and the orientational ordering of water dipoles can lead to early onset and lowering of the maximum of electric capacitance according to surface voltage. Our approach and results can be applied to describing electrostatic properties of biological membranes and electric double layer capacitor for which excluded volume effects of water molecules and ions with different sizes may be important.

An interlayer expansion model for counterion-intercalated montmorillonite from first-principles calculations

From density functional theory calculations on dry and hydrated MMT, Na-MMT, NH4+-MMT, and formamide-MMT structures at various interlayer spacings, we proposed an interlayer expansion model for the counterion-intercalated MMT systems. Complex interactions exist among the counterions, lower and upper MMT surfaces, including ionic bonding, hydrogen bonding, electrostatic attraction/repulsion, and van der Waals forces. These interactions vary with different counterions and different interlayer spacings, playing a crucial role in the energy landscape of interlayer expansion. The equilibrium spacings are related to counterion volume, and the competition between interlayer electrostatic attraction and repulsion. The expansion energy potential near the equilibrium spacings can be approximately described with a quadratic function of spacing increase. At large spacings, however, the counterions have a tendency to form relatively strong interaction with either surface, making their energy potential in MMT approach to constant values.

Influence of Counterions on Micellization of Tetramethylammonium Perfluorononanoic Carboxylate in 1-Butyl-3-methylimidazolium Ionic Liquid

The influence of counterions on micellization of perfluorononanoic carboxylate ammonium salts in water and 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim]BF(4)) solutions was investigated by surface tension and (19)F NMR measurements and freeze-fracture transmission electron microscopy (FF-TEM) observations. Changes in the counterions of the fluorocarbon surfactants have different effects on the two solvents. With the increase of counterion volume, the critical micelle concentration (cmc) value of relevant fluorinated surfactant decreases in aqueous solutions. This is because the counterions with larger size, such as (+)N(CH(3))(4), can be little hydrated, which can screen the electrostatic repulsion of the headgroups of the fluorocarbon surfactant and thus facilitate micelle formation. However, the fluorocarbon surfactants can dissolve and form micelles in [bmim]BF(4) only when they provide with largest counterion such as (+)N(CH(3))(4). This is because the counterion, (+)N(CH(3))(4), disperses the charge of the cations, which could weaken the electrostatic interaction between the ion pair of the surfactant, leading to a higher degree of counterion binding. The thermodynamic parameters estimated from the temperature dependence of the cmc values tell us that the micelle formation for tetramethylammonium perfluorononanoic carboxylate (C(8)F(17)COON(CH(3))(4), PFNT) in ionic liquids (ILs) is an entropy-driven process at low temperature but an enthalpy-driven process at high temperature. The driving force of the micellization for fluorocarbon surfactants in [bmim]BF(4) is the solvophobic effect, due to the hydrophobic and oleophobic properties of fluorocarbon chains.

Counterion volume effects in mixed electrical double layers

When a monolayer of negatively charged surfactant molecules is brought in contact with an aqueous solution containing mixtures of counterions of different size and valency, very large deviations from Poisson–Boltzmann theory (PBT) develop at a high surface charge, with the smaller counterion outcompeting the larger one (even if divalent) near the interface, leading to counterion segregation [V.L. Shapovalov, G. Brezesinski, J. Phys. Chem. B 110 (2006) 10032]. We use a modified PBT that empirically includes an extended Carnahan–Starling equation-of-state to describe hard-sphere interactions in electrical double layers containing ions of different size and charge. Model calculations are made for ion concentration profiles, free energies, surface pressures, and differential capacities. At high surface charge, volume interactions become important, leading to significant deviations from PBT. In contrast to PBT, at high surface charge, contributions to energy and pressure are no longer mainly entropic, but instead volume and electrostatic field effects now dominate. When the hydrated size of the divalent ion is used as an adjustable parameter, the theory is in good agreement with the experimental data.

Small-Angle Neutron Scattering of Ionic Perfluoropolyether Micellar Solutions: Role of Counterions and Temperature

This paper reports a small-angle neutron scattering (SANS) characterization of perfluoropolyether (PFPE) aqueous micellar solutions with lithium, sodium, cesium and diethanol ammonium salts obtained from a chlorine terminated carboxylic acid and with two perfluoroisopropoxy units in the tail (n(2)). The counterion and temperature effects on the micelle formation and micellar growth extend our previous work on ammonium and potassium salts n(2) micellar solutions. Lithium, sodium, cesium and diethanol ammonium salts are studied at 0.1 and 0.2 M surfactant concentration in the temperature interval 28-67 degrees C. SANS spectra have been analyzed by a two-shell model for the micellar form factor and a screened Coulombic plus steric repulsion potential for the structure factor in the frame of the mean spherical approximation of a multicomponent system reduced to a generalized one component macroions system (GOCM). At 28 degrees C, for all the salts, the micelles are ellipsoidal with an axial ratio that increases from 1.6 to 4.2 as the counterion volume increases. The micellar core short axis is 13 A and the shell thickness 4.0 A for the alkali micelles, and 14 and 5.1 A for the diethanol ammonium micelles. Therefore, the core short axis mainly depends on the surfactant tail length and the shell thickness on the carboxylate polar head. The bulky diethanol ammonium counterion solely influences the shell thickness. Micellar charge and average aggregation number depend on concentration, temperature and counterion. At 28 degrees C, the fractional ionization decreases vs the counterion volume (or molecular weight) increase at constant concentration for both C = 0.1 M and C = 0.2 M. The increase of the counterion volume leads also to more ellipsoidal shapes. At C = 0.2 M, at 67 degrees C, for sodium and cesium micelles the axial ratio changes significantly, leading to spherical micelles with a core radius of 15 A, lower average aggregation number, and larger fractional ionization.

Adsorption of charged particles on an oppositely charged surface: Oscillating inversion of charge

Adsorption of multivalent counterions on the charged surface of a macroion is known to lead to inversion of the macroion charge due to the strong lateral correlations of counterions. We consider a nontrivial role of the excluded volume of counterions on this effect. It is shown analytically that when the bare charge of the macroion increases, its net charge including the adsorbed counterions oscillates with the number of their layers. Charge inversion vanishes every time the top layer of counterions is completely full and becomes incompressible. These oscillations of charge inversion are confirmed by Monte Carlo simulations. Another version of this phenomenon is studied for a metallic electrode screened by multivalent counterions when the potential of the electrode is controlled instead of its charge. In this case, oscillations of the compressibility and charge inversion lead to oscillations of capacitance of this electrode with the number of adsorbed layers of multivalent counterions.

Physicochemical Consequences of Generating a Thin Layer of Ionic Liquid at Microelectrode Surface in Undiluted Redox Liquid

Very-thin layers of ionic liquids are formed at microelectrode surfaces during electrolysis of undiluted redox liquids containing only supporting electrolyte at a low concentration. The layers consist of ionic product and counterion coming from supporting electrolyte. Formation of ionic−liquid layer leads to increased viscosity, changes in activity coefficients, and thus to changes in diffusion coefficients of all species involved in the electrode process. This engenders also a specific type of convection. Exchange of one supporting electrolyte for another may change dramatically the physicochemical properties of the generated ionic layer and, in consequence, the magnitude of the electrochemical response of an undiluted substance. A computational model for predicting the phenomena mentioned above is presented. An important step in the model is extension of the concentration dependence of diffusivities to concentrations corresponding to ionic liquids. The calculations done have shown a substantial influence of counterion volume on the electrochemical behavior of undiluted redox liquids even if the counterions are present at a very-low concentration. The consequences of changing supporting electrolyte concentration are also included in the model. The theoretical predictions were compared with experimental data obtained for undiluted nitrobenzene and methanol. The model can be used for both transient and steady-state responses.

Phase transitions in lipid bilayers A theoretical model for phosphatidylethanolamine and phosphatidic acid bilayers

We present an application of an earlier model to the description of phase transitions in phosphatidylethanolamine and phosphatidic acid bilayers. For the former system we modify the model to allow for very slightly closer chain packing. This small modification alone sufficient to shift the main phase transition temperature to higher values, and to eliminate the lower transition. For the charged bilayers we incorporate electrostatic contributions into the free energy using double layer theory and we consider the excluded volume of counterions at the bilayer/water interface. Phase transition temperatures and the presence or absence of a lower transition are determined for various pH values, and the results are compared with experiment.