Density functional theory of adsorption of mixtures of charged chain particles and spherical counterions

We propose a microscopic density functional theory to describe nonuniform ionic fluids composed of chain molecules with charged "heads" and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is based on the approach of Yu and Wu [J. Chem. Phys. 117, 2368 (2002)] of adsorption of chain molecules and on theory of adsorption of electrolytes [O. Pizio, A. Patrykiejew, and S. Sokolowski, J. Chem. Phys. 121, 11957 (2004)]. As an application of the proposed formalism we investigate the structure and adsorption of fluids containing segments of different length in a slitlike pore.     

Molecular thermodynamics for swelling of a mesoscopic ionomer gel in 1 : 1 salt solutions

For a microphase-separated diblock copolymer ionic gel swollen in salt solution, a molecular-thermodynamic model is based on the self-consistent field theory in the limit of strongly segregated copolymer subchains. The geometry of microdomains is described using the Milner generic wedge construction neglecting the packing frustration. A geometry-dependent generalized analytical solution for the linearized Poisson-Boltzmann equation is obtained. This generalized solution not only reduces to those known previously for planar, cylindrical and spherical geometries, but is also applicable to saddle-like structures. Thermodynamic functions are expressed analytically for gels of lamellar, bicontinuous, cylindrical and spherical morphologies. Molecules are characterized by chain composition, length, rigidity, degree of ionization, and by effective polymer-polymer and polymer-solvent interaction parameters. The model predicts equilibrium solvent uptakes and the equilibrium microdomain spacing for gels swollen in salt solutions. Results are given for details of the gel structure: distribution of mobile ions and polymer segments, and the electric potential across microdomains. Apart from effects obtained by coupling the classical Flory-Rehner theory with Donnan equilibria, viz. increased swelling with polyelectrolyte charge and shrinking of gel upon addition of salt, the model predicts the effects of microphase morphology on swelling.     

Density-functional theory for fluid mixtures of charged chain particles and spherical counterions in contact with charged hard wall: Adsorption, double layer capacitance, and the point of zero charge

We consider a density-functional theory to describe nonuniform fluids composed of chain molecules, containing a charged segment each, and spherical counterions. The chain molecules are modeled as freely jointed chains of hard spheres, the counterions are oppositely charged spheres of the same diameter as all segments of chain molecules. The theory is applied to study the structure of adsorbed layers, the excess adsorption isotherms, the capacitance of the double layer, and the potential of the zero charge. We show that all electric properties are strongly dependent on the length of the chain molecules. Moreover, these properties are also dependent on the position of the charged segment in the chain.     

A simplified molecular-thermodynamic model of a microphase-separated ionic gel swollen in salt solution

A molecular-thermodynamic model [A.I. Victorov, C.J. Radke, J.M. Prausnitz, Mol. Phys., 2004, submitted for publication] of diblock copolymer ionic gels swollen in brine is simplified by deriving asymptotic expressions for electrostatic terms. This model derived recently from the self-consistent field theory in the limit of strong segregation gives thermodynamic functions for gels of lamellar, bicontinuous, cylindrical and spherical morphologies and details the gel structure including equilibrium microdomain spacing, distribution of mobile ions, polymer segments, and the electric potential across the microdomains. The model reflects the copolymer chain composition, length, rigidity, ionization degree and the effective polymer–polymer and polymer–solvent interactions. Several asymptotic regimes are considered that lead to simple formulae for the solvent chemical potential. Applicability of asymptotic relations is tested. Equilibrium uptakes of salt are calculated for gels of varying ionic charge over a wide range of solution salinity.     

Chain collapse by lattice simulation

Monte Carlo simulations have been performed on a self-avoiding simple cubic lattice chain with the nearest-neighbor interactions for a range of chain lengths N from 40 to 1000 segments to investigate equilibrium properties of polymer chains from an athermal to a collapsed state. Both the fraction of segments in the clusters and the number of contacts exhibit the three stage process for the chain collapse, consistent with our previous molecular dynamics simulations of a fully atomistic chain. In the collapse region corresponding to the nearest-neighbor interaction parameter larger than 0.5 for a segment-solvent pair, polymer chains are quite spherical and both ends lie nearly randomized within the sphere. The peak height of the specific heat is proportional to N(In N)^3/11, as predicted by the renormalization group theory.     

Polymer-particle mixtures: depletion and packing effects

The structure of polymers in the vicinity of spherical colloids is investigated by Monte Carlo simulations and integral equation theory. Polymers are represented by a simple bead-spring model; only repulsive Lennard-Jones interactions are taken into account. Using advanced trial moves that alter chain connectivity, depletion and packing effects are analyzed as a function of chain length and density, both at the bond and the chain level. Chain ends segregate to the colloidal surface and polymer bonds orient parallel to it. In the dilute regime, the polymer chain length governs the range of depletion and has a negligible influence on monomer packing in dense polymer melts. Polymers adopt an ellipsoidal shape, with the larger axis parallel to the surface of the particle, as they approach larger colloids. The dimensions are perturbed within the range of the depletion layer.     

Density functional theory for encapsidated polyelectrolytes: A comparison with Monte Carlo simulation

Genome packaging inside viral capsids is strongly influenced by the molecular size and the backbone structure of RNA∕DNA chains and their electrostatic affinity with the capsid proteins. Coarse-grained models are able to capture the generic features of non-specific interactions and provide a useful testing ground for theoretical developments. In this work, we use the classical density functional theory (DFT) within the framework of an extended primitive model for electrolyte solutions to investigate the self-organization of flexible and semi-flexible linear polyelectrolytes in spherical capsids that are permeable to small ions but not polymer segments. We compare the DFT predictions with Monte Carlo (MC) simulation for the density distributions of polymer segments and small ions at different backbone flexibilities and several solution conditions. In general, the agreement between DFT and MC is near quantitative except when the simulation results are noticeably influenced by the boundary effects. The numerical efficiency of the DFT calculations makes it promising as a useful tool for quantification of the structural and thermodynamic properties of viral nucleocapsids in vivo and at conditions pertinent to experiments.     

Vector length distributions and polarizabilities of effective polymer chains: a statistical segment approach

The freely orienting model of a polymer chain is generalized by considering the distribution of vector lengths and polarizabilities of the statistical segments in the chain with a constant number of skeletal bonds in each of the segments The bonds in the segments are assumed to exist in their RIS (Rotational Isomeric States) conformations. The segment is characterized, i.e., its end-to-end length and polarizability distributions are computed. Bond polarizabilities, as determined by Denbigh, have been used for polyethylene and poly(cis-isoprene), and are assumed to be independent of the environment. Two methods are used to compute the chain length distribution from the length distribution of statistical segments: (i) an exact method, using a modified version of Chandrasekhar’s approach, originally formulated for chains of segments having constant length; and (ii) an alternative approach, which considers the series expansion of the Helmholtz Free Energy of an isolated chain, making the analysis computationally more viable without significant loss in accuracy. The averages of the chain end-to-end length distributions have been computed at 373 K for poly(cis-isoprene) and at 403 and 413 K for polyethylene. Also, chain polarizability is determined from the distribution of statistical segment lengths and polarizabilities. The results are in a form that can be used to obtain stress-deformation and optical anisotropy-deformation relationships of assemblies of chains, such as crosslinked networks.     

Ion-induced nucleation of dibutyl phthalate vapors on spherical and nonspherical singly and multiply charged polyethylene glycol ions

Dibutyl phthalate vapor nucleation induced by positive polyethylene glycol (PEG) ions with controlled sizes and charges was experimentally studied. The ions were produced by electrospray ionization, classified in a high-resolution differential mobility analyzer, and studied in a nano condensation nucleus counter of the mixing type. Ionic radii of PEG varied from 0.52 to 1.56 nm, including from singly to quadruply charged ions. Some of these ions are fully stretched chains, other are spherical, and others have intermediate forms, all of them having been previously characterized by mobility and mass spectrometry studies. Activation of PEG1080(+2) requires a supersaturation almost as high as that required for small singly charged ions and higher than for PEG1080(+). This anomaly is explained by the Coulombic stretching of the ion into a long chain, where the two charged centers appear to be relatively decoupled from each other. The critical supersaturation for singly charged spherical ions falls below Thomson's (capillary) theory and even below the already low values seen previously for tetraheptyl ammonium bromide clusters. Spherical PEG4120(+2) falls close to the Thomson curve. The trends observed for slightly nonspherical PEG4120(+3) and highly nonspherical (but not quite linear) PEG4120(+4) are intermediate between those of multiply charged spheres and small singly charged ions.     

Superhydrogels of Nanotubes Capable of Capturing Heavy‐Metal Ions

Self‐assembly regulated by hydrogen bonds was successfully achieved in the system of lithocholic acid (LCA) mixed with three organic amines, ethanolamine (EA), diethanolamine (DEA), and triethanolamine (TEA), in aqueous solutions. The mixtures of DEA/LCA exhibit supergelation capability and the hydrogels consist of plenty of network nanotubes with uniform diameters of about 60 nm determined by cryogenic TEM. Interestingly, the sample with the same concentration in a system of EA and LCA is a birefringent solution, in which spherical vesicles and can be transformed into nanotubes as the amount of LCA increases. The formation of hydrogels could be driven by the delicate balance of diverse noncovalent interactions, including electrostatic interactions, hydrophobic interactions, steric effects, van der Waals forces, and mainly hydrogen bonds. The mechanism of self‐assembly from spherical bilayer vesicles into nanotubes was proposed. The dried hydrogels with nanotubes were explored to exhibit the excellent capability for capturing heavy‐metal ions, for example, Cu²⁺, Co²⁺, Ni²⁺, Pb²⁺, and Hg²⁺. The superhydrogels of nanotubes from the self‐assembly of low‐molecular‐weight gelators mainly regulated by hydrogen bonds used for the removal of heavy‐metal ions is simple, green, and high efficiency, and provide a strategic approach to removing heavy‐metal ions from industrial sewage.     

Statistics of polymer chains in orienting fields

The theory of a freely jointed polymer chain is modified by introduction of interactions between dipole chain segments and an orienting field. Such a field results either from external forces (e.g. external electric or magnetic fields) or represents interactions between dipole segments of chains (molecular mean-field). The distribution of orientations of chain segments and the free energy of a chain in such orienting fields are calculated and discussed.     

Dynamic Electrophoretic Mobility of a Soft Particle

A theory of the dynamic electrophoretic mobility of a spherical soft particle (that is, a polyelectrolyte-coated spherical particle) in an oscillating electric field is presented. In the absence of the polyelectrolyte layer a spherical soft particle becomes a spherical hard particle, while in the absence of the particle core it tends to a spherical polyelectrolyte. The present theory thus covers two extreme cases, that is, dynamic electrophoresis of hard particles and that of spherical polyelectrolytes. Simple analytic mobility expressions are derived. It is shown how the dynamic electrophoretic mobility of a soft particle depends on the volume charge density distributed in the polyelectrolyte layer, on the frictional coefficient characterizing the frictional forces exerted by the polymer segments on the liquid flow in the polyelectrolyte layer, on the particle size, and on the frequency of the applied oscillating electric field. Copyright 2001 Academic Press.     

Density functional description of adsorption in slitlike pores modified with chain molecules: a simple model for pillaredlike materials

We propose a density functional theory to describe adsorption of Lennard-Jones fluid in slitlike pores modified by chain molecules. Specifically, the chains are bonded by their ends to the opposite pore walls, so they can form pillaredlike structure. Two models are studied. In the first model, the nonterminating segments of chains can change their configuration inside the pore upon adsorption of spherical species. In the second model, the chains configuration remains fixed, so that the system is similar to a nonuniform quenched-annealed mixture. We study capillary condensation of fluid species inside such modified pores and compare the results obtained for two models.     

Thermodynamic modeling of CO2 solubility in ionic liquid with heterosegmented statistical associating fluid theory

Heterosegmented statistical associating fluid theory is used to represent the CO₂ solubility in ionic liquids. As in our previous work, ionic liquid molecule is divided into several groups representing the alkyls, cation head, and anion. The cation of ionic liquid is modeled as a chain molecule that consists of one spherical segment representing the cation head and groups of segments of different types representing different substituents (alkyls). The anion of ionic liquid is modeled as a spherical segment of different type. To account for the electrostatic/polar interaction between the cation and anion, the spherical segments representing cation head and anion each have one association site, which can only cross associate. Carbon dioxide is modeled as a molecule with three association sites, two sites of type O and one site of type C, where sites of the same type do not associate with each other. The parameters of CO₂ are obtained from the fitting of the density and the saturation vapor pressure of CO₂. For the CO₂-ionic liquid systems, cross association between site of type C in CO₂ and another association site in anion is allowed to occur to account for the Lewis acid–base interaction. The parameters for cross association interactions and the binary interaction parameters used to adjust the dispersive interactions between unlike segments are obtained from the fitting of the available CO₂ solubility in ionic liquids. The model is found to well represent the CO₂ solubility in the imidazolium ionic liquids from 283 to 415 K and up to 200 bar.     

Onsager chains: Semi-flexible polymers revisited

Using a density functional approach we derive the equations describing the equilibrium orientational distribution of a system of chains composed of elongated segments that interact with segments located on other chains through excluded volume interactions and with neighbouring segments of the same chain through a potential that determines the chain flexibility. We analytically determine the limit of stability of the low density isotropic phase as a function of the number of segments and the chain stiffness. The approach turns out to be formally equivalent to a recently proposed mean-field theory by Petschek and Terentjev. Comparison with the Khoklov-Semenov theory shows that the latter is based on an additional assumption that is not valid in an orientationally ordered phase.     

Vibrational and electronic properties of polyaza chain molecules and their metal complexes

The polyaza chain molecules exhibit a quasi planar backbone with all-trans geometry. The chelation of several metallic ions such as copper (II) and zinc (II) constrains different conformations of the chain molecules. The vibrational and electronic properties are typical of the conformation of the polyaza backbone as well as the spin spin exchange between the metallic ions through the azine bonds.     

Study on the Gas Permeability of Nickel(II) Polyurethane Complexes

Ionic polyurethanes (PUs) were prepared from hydroxyl‐terminated polybutadiene (HTPB) and 4,4′‐dicyclohexylmethane diisocyanate (H₁₂MDI) by a two‐stage method. The ionic group was introduced by adding 4,8‐diazaundecanediamide (L‐2,3,2) as the chain extender of which the tertiary amines and carbonyl groups were complexed with nickel ions. It was found that the binding of hard segments and the flexibility of soft segments had subtle effects on the gas permeability. The effects of hard segment content and the amount of nickel ion on the gas permeability and morphological properties were investigated. Fourier transform infrared (FTIR) spectroscopy was utilized to identify the segregation between hard and soft segments and structure change, which affect the transport properties. The hydrogen bonding index (HBI), frequency difference, and shift as a measure of the phase segregation and the average strength of the interpolymer hydrogen bonds were utilized to study the intermolecular interaction and transport property of the prepared PUs. The oxygen and nitrogen permeabilities of membranes were determined by using gas permeability analyzer. The results of FTIR, differential scanning calorimetry and thermogravimetric analysis measurements explain the complexation and, hence, the gas permeability.