Cylindrical cell model for the electrostatic free energy of polyelectrolyte complexes

Associative phase separation (complex coacervation) in a mixture of oppositely charged polyelectrolytes can lead to different types of (inter-)polyelectrolyte complexes (soluble micelles, macroscopic precipitation). In a previous report [Langmuir 2004, 20, 2785-2791], we presented a model for the electrostatic free energy change when (weakly charged) polyelectrolyte forms a homogeneous complex phase. The influence of ionization of the polymer on the electrostatic free energy of the complex was incorporated but the influence of complex density neglected. In the present effort, cylindrical cells are assumed around each polyelectrolyte chain in the complex, and on the basis of the Poisson-Boltzmann equation, the electrostatic free energy is calculated as a function of the complex density. After combination with Flory-Huggins mixing free energy terms and minimization of the total free energy, the equilibrium complex density is obtained, for a given ratio of polycations to polyanions in the complex. The analysis is used in an example calculation ofpolyelectrolyte film formation by alternatingly applying a polycation and a polyanion solution. The calculation suggests that the often observed exponential growth of a polyelectrolyte film when the polymer is weakly charged has a thermodynamic origin: the polyelectrolyte complex shifts repeatedly between two equilibrium states of different densities and compositions. However, when the polyelectrolytes are strongly charged the difference in the compositions between the two equilibrium states is very small, and exponential growth by an absorption mechanism is no longer possible.     

Computation of the contribution from the cavity effect to protein-ligand binding free energy

We present results of the investigation of the cavity creation/annihilation effect in view of formation of the protein-ligand (PL) complexes. The protein and ligand were considered as rigid structures. The change of the cavity creation/annihilation free energy DeltaG(cav) was calculated for three PL complexes using the thermodynamic integration procedure with the original algorithm for growing the interaction potential between the cavity and the water molecules. The thermodynamic cycle consists of two stages, annihilation of the cavity of the ligand for the unbound state and its creation at the active site of the protein (bound state). It was revealed that for all complexes under investigation, the values of DeltaG(cav) are negative and favorable for binding. The main contribution to DeltaG(cav) appears due to the annihilation of the cavity of the ligand. All computations were made using the parallel version of CAVE code, elaborated in our preceding work.     

Calculations of the electrostatic free energy contributions to the binding free energy of sulfonamides to carbonic anhydrase

The interactions between biologically important enzymes and drugs are of great interest. In order to address some aspects of these interactions we have initiated a program to investigate enzymedrug interactions. Specifically, the interactions between one of the isozymes of carbonic anhydrase and a family of drugs known as sulfonamides have been studied using computational methods. In particular the electrostatic free energy of binding of carbonic anhydrase II with acetazolamide, methazolamide,p-chlorobenzenesulfonamide,p-aminobenzenesulfonamide and three new compounds (MK1, MK2, and MK3) has been computed using finite-difference Poisson-Boltzmann (FDPB) [1] method and the semimacroscopic version [2, 3] of the protein dipole Langevin dipole (PDLD) method [4]. Both methods, FDPB and PDLD, give similar results for the electrostatic free energy of binding even though different charges and different treatments were used for the protein. The calculated electrostatic binding free energies are in reasonable agreement with the experimental data. The potential and the limitation of electrostatic models for studies of binding energies are discussed.     

The effect of interface electrostatic interaction based on acid–base theory on friction behavior

Fluorine‐containing amorphous carbon films [fluoring‐containing diamond‐like carbon (F‐DLC)] were fabricated on Si wafer by direct current plasma enhanced chemical vapor deposition (dc‐PECVD) technique using CF₄ and Ar as gas sources, confirmed by XPS and Raman analyses. The friction tests were carried out on a rotating ball‐on‐disk apparatus in high vacuum atmosphere (≤5.0 × 10^?4 Pa) at the load of 0.5 N selecting glass (mainly containing silicon–oxygen tetrahedron structure) and Al₂O₃ with the same hardness and surface roughness as the counterpart balls. The results indicate that glass/F‐DLC results in lower friction coefficient of 0.14 than that of the Al₂O₃/F‐DLC (0.20). At the same time, no wear was occurred, and the transfer layer was not formed on the counterpart ball for glass/F‐DLC, while the wear of Al₂O₃/F‐DLC is slightly larger than that of glass/F‐DLC. However, just like the glass ball, there is no formation of transfer layer on the Al₂O₃ ball surface. Furthermore, the chemical state of fluorine in the film after friction, which mainly existed in the form of the C–CF and C–F bonds, did not change compared with the F‐DLC film, while the fluorine content has changed significantly. As a result, it is assumed that interface electrostatic interaction based on acid–base theory plays an extremely important role in the process of friction. Copyright © 2017 John Wiley & Sons, Ltd.     

Dubinin"s theory and its contribution to adsorption science

Dubinin"s theory for the volume filling of micropores (TVFM), originally developed for the adsorption of single vapours by microporous solids such as activated carbons and zeolites, has gradually been extended to other areas. They include immersion calorimetry, the adsorption of water vapour and of mixtures, as well as adsorption from aqueous solutions. Recent studies in the field of adsorption from aqueous solutions, by activated carbons, suggest that the principle of temperature invariance is fulfilled and in the case of phenolic compounds a modified DRK equation can be used to predict the adsorption equilibrium over a certain range of temperatures. Computer modelling of CO₂ adsorption by carbons at 273 K leads to micropore distributions, which are in good agreement with those derived from other techniques. It also appears that the model isotherms in single slit-shaped micropores can be fitted to the Hill-de Boer isotherm, in agreement with mathematical studies of the origin of the Dubinin—Astakhov equation.     

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: a perspective of integral equation theory

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.     

A model for the free energy of adsorption on low energy surfaces.

In constructing a generalized thermodynamics for the fluid-vapor-solid equilibrium in poorly wetted systems the specific free energy of adsorption at saturation vapor pressure is a basic and elusive term. If the adsorbed phase is modeled as a two dimensional gas, systems for which a complete spectrum of data is available can serve as an empirical basis for constructing and testing adsorption-contact angle relationships. From the extension of such relationship other often inassessible terms can be estimated. Such a construct is reported here and extended to the estimation of the excess adsorption entropy at saturation vapor pressure in non-wetting systems     

Electrokinetic effect and surface free energy behavior in the adsorption process of a reactive dye onto Leacril pretreated with polyethyleneimine ion

In a previous paper, we studied the adsorption of a polyelectrolyte, polyethyleneimine ion (PEI), onto Leacril in order to increase the amount of the reactive dye Remazol Brilliant Blue R (RBBR) taken up by these fibers. We observed that this polycation changes the fibers zeta potential sign at low concentration, ca. 0.03 g/L, and thus the RBBR adsorption onto Leacril is improved when implementing the PEI treatment. The aim of this work is to study the PEI effect related to the amount of dye adsorbed by Leacril. For this purpose, we present data on streaming potential, adsorption isotherms, and surface free energy component determination as a function of the PEI concentration used in the pretreatment, as well as a function of the RBBR concentration used in the dyeing solutions. Adsorption experimental results show that the amount of RBBR taken by the fibers increases with the PEI concentration used in the pretreatment, and this effect becomes significant at higher concentrations of RBBR solution. The zeta potential increases to positive values in the range of low concentrations of dye solution when Leacril fibers have been pretreated with the polyelectrolyte. From surface free energy component determinations it is worth noting that the electron-donor component, gamma(-), decreases with the RBBR concentration in the treatment. The results we have obtained suggest that the interaction between the amine group of the PEI previously adsorbed and the reactive beta-sulfato-ethysulfonyl group of the dye can be responsible for the improvement in dye uptake.     

Molecular dynamics simulations of multilayer polyelectrolyte films: effect of electrostatic and short-range interactions

The effect of the strength of electrostatic and short-range interactions on the multilayer assembly of oppositely charged polyelectrolytes at a charged substrate was studied by molecular dynamics simulations. The multilayer buildup was achieved through sequential adsorption of charged polymers in a layer-by-layer fashion from dilute polyelectrolyte solutions. The strong electrostatic attraction between oppositely charged polyelectrolytes at each deposition step is a driving force behind the multilayer growth. Our simulations have shown that a charge reversal after each deposition step is critical for steady multilayer growth and that there is a linear increase in polymer surface coverage after the first few deposition steps. Furthermore, there is substantial intermixing between chains adsorbed during different deposition steps. We show that the polymer surface coverage and multilayer structure are each strongly influenced by the strength of electrostatic and short-range interactions.     

The influence of electrostatic forces on protein adsorption

In this paper we investigate the importance of electrostatic double layer forces on the adsorption of human serum albumin by UV-ozone modified polystyrene. Electrostatic forces were measured between oxidized polystyrene surfaces and gold-coated atomic force microscope (AFM) probes in phosphate buffered saline (PBS) solutions. The variation in surface potential with surface oxygen concentration was measured. The observed force characteristics were found to agree with the theory of electrical double layer interaction under the assumption of constant potential. Chemically patterned polystyrene surfaces with adjacent 5 microm x 5 microm polar and non-polar domains have been studied by AFM before and after human serum albumin adsorption. A topographically flat surface is observed before protein adsorption indicating that the patterning process does not physically modify the surface. Friction force imaging clearly reveals the oxidation pattern with the polar domains being characterised by a higher relative friction compared to the non-polar, untreated domains. Far-field force imaging was performed on the patterned surface using the interleave AFM mode to produce two-dimensional plots of the distribution of electrostatic double-layer forces formed when the patterned polystyrene surfaces is immersed in PBS. Imaging of protein layers adsorbed onto the chemically patterned surfaces indicates that the electrostatic double-layer force was a significant driving force in the interaction of protein with the surface.     

On the electrostatic energy of charged alkali clusters

In the framework of the jellium model an algorithm is presented to calculate the electrostatic energy of charged metal clusters of arbitrary shape. Explicit expressions are given for some special shapes.     

Fast adaptive multipole method for computation of electrostatic energy in simulations of polyelectrolyte DNA

This article presents a fast adaptive method for the computation of long-range electrostatic interactions in computer simulations of polyelectrolyte DNA. Classically, the computation of electrostatic energy involves a direct summation of all pairwise in teractions due to the charged phosphate groups in the molecule. This results in an N-body interaction problem with an asymptotic time complexity of O(N²) which is computationally very expensive and limits the number of phosphate groups that can be used in computer simulations of polyelectrolyte DNA to at most several hundred. We describe an effort to speed up computer simulations of polyelectrolyte DNA with the use of a fast adaptive hierarchical algorithm for the computation of electrostatic energy (i.e., modified Debye–Hückel energy). The asymptotic time complexity is reduced to O(N) with the implementation of the fast hierarchical algorithm on serial computers. This is achieved by grouping phosphate groups into an adaptive hierarchical data structure and computing the interactions between groups using low order multipole and Taylor series expansions expressed in Cartesian coordinates. We first examine the accuracy and speed enhancements of the fast hierarchical method in the computation of the electrostatic energy of circular DNA at zero and high salt concentrations. The fast hierarchical method is further tested in a one-step Monte Carlo (MC) simulated annealing algorithm for closed circular supercoiled DNA. In all cases, we observe order of magnitude reductions in the computation time with negligible loss of numerical accuracy in the electrostatic energy computation. © 1996 by John Wiley & Sons, Inc.     

The estimation of the hydrophobic and electrostatic contributions to the free energy change upon cationic surfactants binding to Jack bean urease

The binding of a homologous series of n-alkyltrimethyl ammonium bromides with Jack bean urease (JBU) have been studied previously. It has been suggested that both electrostatic and hydrophobic interactions are involved in the formation of surfactant-protein complexes, but there is not any quantities analyzing method for resolution of their contributions in the process. In the present study, at first, the intrinsic Gibbs free energy of binding, ΔG_b,ν, has been calculated for these systems and the trend of variation for both binding sets have been interpreted on basis of cooperativity and hydrophobicity of surfactants. Subsequently, a novel approach has been introduced for estimation of electrostatic and hydrophobic interactions in ΔG_b,ν, by considering of this fact that ΔG_b,ν is the summation of electrostatic, ΔG_b,ν(ele), and hydrophobic, ΔG_b,ν(hyd), parts and considering this fact that just ΔG_b,ν(hyd) is a function of hydrocarbon tail length of surfactant (C_n). The results represents the higher positive rule of electrostatic interactions in binding affinity of first set and inhibiting rule of this interaction in the second binding set. The predominate driving force in the second binding set is entropy statistical effect, which arises from numerous number of binding sites in this set. A binding mechanism on basis of structural changes in JBU due to its interaction with cationic surfactants has also been proposed.     

On the theory of photoadsorption kinetics of a-Se colloids: The thermal activation energy and compensation effect

In this study, a model is developed to explain in microscopic terms the results obtained from thermally activated photoadsorption experiments in a-Se colloids. The observed compensation effect can be described for two different cases. At low efficiency adsorption, the process is controlled by the potential at the boundary layer. In the high efficiency adsorption case, the process is controlled by diffusion transport.On leave from Center of Technological Education, Holon, Israel