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.     

Prion protein self-peptides modulate prion interactions and conversion

Background  

Molecular mechanisms underlying prion agent replication, converting host-encoded cellular prion protein (PrP^C) into the scrapie associated isoform (PrP^Sc), are poorly understood. Selective self-interaction between PrP molecules forms a basis underlying the observed differences of the PrP^C into PrP^Sc conversion process (agent replication). The importance of previously peptide-scanning mapped ovine PrP self-interaction domains on this conversion was investigated by studying the ability of six of these ovine PrP based peptides to modulate two processes; PrP self-interaction and conversion.     

Optimization of Viscous Mixing in a Two-Dimensional Cavity Transfer Mixer

Following up ideas put forward by J.M. Ottino and colleagues, the possibility of designing a computational tool to optimize the mixing of viscous fluids in industrial devices is studied. It is shown that an efficient method to characterize and quantify a mixing process is to apply the statistical measures introduced by Danckwerts (e.g., intensity of segregation and scale of segregation) on the coarse-grained density distribution of points in Poincaré sections and advection patterns, that can be obtained by tracking the positions of marked fluid elements numerically. This method is not computationally excessively costly and, as is demonstrated here, can be applied easily to experimental dye advection studies. The model system used is the Stokes flow in a two-dimensional cavity transfer mixer: two rectangular cavities which are periodically driven by a solid wall and by the passage of the cavities over each other. This system shares with many industrial devices the complexity that the geometry of the flow is time-dependent. These changes in the geometry of the flow impose difficulties on the techniques of calculating the fluid velocity field (a boundary element method) and the advection of marked fluid elements. Ways of overcoming these difficulties are described.     

Electrochemistry and capacitive charging of porous electrodes in asymmetric multicomponent electrolytes

We present porous electrode theory for the general situation of electrolytes containing mixtures of mobile ions of arbitrary valencies and diffusion coefficients (mobilities). We focus on electrodes composed of primary particles that are porous themselves. The predominantly bimodal distribution of pores in the electrode consists of the interparticle or macroporosity outside the particles through which the ions are transported (transport pathways), and the intraparticle or micropores inside the particles, where electrostatic double layers (EDLs) are formed. Both types of pores are filled with electrolyte (solvent plus ions). For the micropores we make use of a novel modified-Donnan (mD) approach valid for strongly overlapped double layers. The mD-model extends the standard Donnan approach in two ways: (1) by including a Stern layer in between the electrical charge and the ions in the micropores, and (2) by including a chemical attraction energy for the ions to go from the macropores into the micropores. This is the first paper where the mD-model is used to model ion transport and electrochemical reactions in a porous electrode. Furthermore we investigate the influence of the charge transfer kinetics on the chemical charge in the electrode, i.e., a contribution to the electrode charge of an origin different from that stemming from the Faradaic reaction itself, e.g. originating from carboxylic acid surface groups as found in activated carbon electrodes. We show that the chemical charge depends on the current via a shift in local pH, i.e. ??current-induced charge regulation.?? We present results of an example calculation where a divalent cation is reduced to a monovalent ion which electro-diffuses out of the electrode.     

Membrane capacitive deionization

Membrane capacitive deionization (MCDI) is an ion-removal process based on applying an electrical potential difference across an aqueous solution which flows in between oppositely placed porous electrodes, in front of which ion-exchange membranes are positioned. Due to the applied potential, ions are adsorbed in the electrodes and a product stream with a reduced salt concentration is obtained. Including the membranes in the process has two advantages: first, they block co-ions from leaving the electrodes, thereby increasing the salt removal efficiency of the process, and second, when during ion release a reversed voltage is used, counterions can be more fully flushed from the electrode region, thereby increasing the driving force for ion removal in the next cycle. Here we present pilot-plant experimental data for salt removal in MCDI as function of inlet ionic strength and flow rate. In the subsequent stage of ion release the flow rate is temporarily reduced to zero and the voltage sign reversed. This “stop-flow” operation mode results in a small and concentrated product stream. We present a theoretical process model for MCDI which describes the time-dependent electric current and effluent ion concentration, both during the deionization stage and during the subsequent stage of ion release. The process model describes the MCDI cell as a number of stirred volumes placed in-series, and includes the transport resistance of the ion-exchange membrane and of the stagnant diffusion layer in front of the membrane. Ion storage in the electrodes is described according to the equilibrium Gouy–Chapman–Stern model for the electrostatic double layer.     

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.     

Electrostatic free energy of interacting ionizable double layers

The electrostatic contribution to the interaction free energy of charge-regulating materials, similar as well as dissimilar, contains electric work as well as chemical work and can be obtained from an integration over the diffuse part of the double layer together with a summation of the surface contribution to the free energy over the two surfaces. Examples for the surface contribution are given for acid, base, zwitterionic, and amphoteric (1-pK and 2-pK) materials for a diffuse double layer and for the Stern-Gouy-Chapman model, with and without ion adsorption. For charge-regulating materials, the electrostatic contribution to the interaction free energy at contact (adhesion force of curved surfaces, or particles) is always finite and can be obtained from a simple calculation.