Field theoretic description of charge regulation interaction

In order to find the exact form of the electrostatic interaction between two proteins with dissociable charge groups in aqueous solution, we have studied a model system composed of two macroscopic surfaces with charge dissociation sites immersed in a counterion-only ionic solution. Field-theoretic representation of the grand canonical partition function is derived and evaluated within the mean-field approximation, giving the Poisson-Boltzmann theory with the Ninham-Parsegian boundary condition. Gaussian fluctuations around the mean-field are then analyzed in the lowest order correction that we calculate analytically and exactly, using the path integral representation for the partition function of a harmonic oscillator with time-dependent frequency. The first order (one loop) free energy correction gives the interaction free energy that reduces to the zero-frequency van der Waals form in the appropriate limit but in general gives rise to a mono-polar fluctuation term due to charge fluctuation at the dissociation sites. Our formulation opens up the possibility to investigate the Kirkwood-Shumaker interaction in more general contexts where their original derivation fails.Comment: 12 pages, 9 figures, submitted to EPJ

The field theoretic derivation of the contact value theorem in planar geometries and its modification by the Casimir effect

The contact value theorem for Coulomb gases in planar or film-like geometries is derived using a Hamiltonian field theoretic representation of the system. The case where the film is enclosed by a material of different dielectric constant to that of the film is shown to contain an additional Casimir-like term which is generated by fluctuations of the electric potential about its mean-field value.Comment: Link between Sine-Gordon and Coulomb gas pressures via subtraction of self interaction terms included. Discussion of results within Debye-Huckel approximation included. Added reference

Order and Chaos in some Trigonometric Series: Curious Adventures of a Statistical Mechanic

This paper tells the story how a MAPLE-assisted quest for an interesting undergraduate problem in trigonometric series led some "amateurs" to the discovery that the one-parameter family of deterministic trigonometric series \pzcS_p: t\mapsto \sum_{n\in\Nset}\sin(n^{-{p}}t), $p>1$, exhibits both order and apparent chaos, and how this has prompted some professionals to offer their expert insights. It is proved that \pzcS_p(t) = \alpha_p\rm{sign}(t)|t|^{1/{p}}+O(|t|^{1/{(p+1)}})\;\forall\;t\in\Rset, with explicitly computed constant $\alpha_p$. Experts' commentaries are reproduced stating the fluctuations of \pzcS_p(t) - \alpha_p{\rm{sign}}(t)|t|^{1/{p}} are presumably not Gaussian. Inspired by a central limit type theorem of Marc Kac, a well-motivated conjecture is formulated to the effect that the fluctuations of the $\lceil t^{1/(p+1)}\rceil$-th partial sum of \pzcS_p(t), when properly scaled, do converge in distribution to a standard Gaussian when $t\to\infty$, though --- provided that $p$ is chosen so that the frequencies \{n^{-p}\}_{n\in\Nset} are rationally linear independent; no conjecture has been forthcoming for rationally dependent \{n^{-p}\}_{n\in\Nset}. Moreover, following other experts' tip-offs, the interesting relationship of the asymptotics of \pzcS_p(t) to properties of the Riemann $\zeta$ function is exhibited using the Mellin transform.Comment: Based on the invited lecture with the same title delivered by the author on Dec.19, 2011 at the 106th Statistical Mechanics Meeting at Rutgers University in honor of Michael Fisher, Jerry Percus, and Ben Widom. (19 figures, colors online). Comments of three referees included. Conjecture 1 revised. Accepted for publication in J. Stat. Phy

Partially Annealed Disorder and Collapse of Like-Charged Macroions

Charged systems with partially annealed charge disorder are investigated using field-theoretic and replica methods. Charge disorder is assumed to be confined to macroion surfaces surrounded by a cloud of mobile neutralizing counterions in an aqueous solvent. A general formalism is developed by assuming that the disorder is partially annealed (with purely annealed and purely quenched disorder included as special cases), i.e., we assume in general that the disorder undergoes a slow dynamics relative to fast-relaxing counterions making it possible thus to study the stationary-state properties of the system using methods similar to those available in equilibrium statistical mechanics. By focusing on the specific case of two planar surfaces of equal mean surface charge and disorder variance, it is shown that partial annealing of the quenched disorder leads to renormalization of the mean surface charge density and thus a reduction of the inter-plate repulsion on the mean-field or weak-coupling level. In the strong-coupling limit, charge disorder induces a long-range attraction resulting in a continuous disorder-driven collapse transition for the two surfaces as the disorder variance exceeds a threshold value. Disorder annealing further enhances the attraction and, in the limit of low screening, leads to a global attractive instability in the system.Comment: 21 pages, 2 figure

Adsorption of mono- and multivalent cat- and anions on DNA molecules

Adsorption of monovalent and multivalent cat- and anions on a deoxyribose nucleic acid (DNA) molecule from a salt solution is investigated by computer simulation. The ions are modelled as charged hard spheres, the DNA molecule as a point charge pattern following the double-helical phosphate strands. The geometrical shape of the DNA molecules is modelled on different levels ranging from a simple cylindrical shape to structured models which include the major and minor grooves between the phosphate strands. The densities of the ions adsorbed on the phosphate strands, in the major and in the minor grooves are calculated. First, we find that the adsorption pattern on the DNA surface depends strongly on its geometrical shape: counterions adsorb preferentially along the phosphate strands for a cylindrical model shape, but in the minor groove for a geometrically structured model. Second, we find that an addition of monovalent salt ions results in an increase of the charge density in the minor groove while the total charge density of ions adsorbed in the major groove stays unchanged. The adsorbed ion densities are highly structured along the minor groove while they are almost smeared along the major groove. Furthermore, for a fixed amount of added salt, the major groove cationic charge is independent on the counterion valency. For increasing salt concentration the major groove is neutralized while the total charge adsorbed in the minor groove is constant. DNA overcharging is detected for multivalent salt. Simulations for a larger ion radii, which mimic the effect of the ion hydration, indicate an increased adsorbtion of cations in the major groove.Comment: 34 pages with 14 figure

Hydronium and hydroxide at the air–water interface with a continuum solvent model

The distribution of hydronium and hydroxide ions at the air-water interface has been a problem of much interest in recent years. Here we explore what insights can be gained from a continuum solvent model. We extend our model of ionic solvation free energies and surface interaction free energies to include hydronium and hydroxide. The hydronium cation is attracted to the air-water interface, whereas the hydroxide anion is repelled. If the cavity size parameters required by the model are adjusted to reproduce solvation energies, quantitative agreement with experimental surface tensions is achieved. To the best of our knowledge, this is the most accurate theoretical estimation of this property so far. The results indicate that even if 'water structure' is important, its effects can be captured with a relatively simple model. They also contradict the inference from electrophoresis that there is strong hydroxide enhancement at the air-water interface

Nonelectrostatic ionic forces between dissimilar surfaces: A mechanism for colloid separation

The interaction between two dissimilar surfaces across an electrolyte is re-examined. The focus is on effects of ion-specific dispersion forces missing from classical electrostatic double-layer theory. The pressure between two flat surfaces is derived by two alternate methods (midpoint and whole domain approaches). Significant differences emerge from expectations of classical theory. These are illustrated by model interactions across electrolytes of mica and oil-like surfaces. A novel consequence that emerges from inclusion of ionic dispersion forces is the possible separation of mixed colloidal suspensions at moderate (0.1 M) concentrations of divalent salt. Repulsion between the model oil and mica surfaces is found to be due to entropic repulsion driven by high adsorption of both counterions and co-ions at the mica surface. Co-ion adsorption is a consequence of electric field reversal ("charge reversal"), caused by attractive ionic dispersion interactions of the counterion to the mica surface. Charge reversal is also found with monovalent electrolyte but only at impracticably high concentrations

Application of Mechanochemistry in Ferrite Materials Technology

An overview of progress and implications of recent technological advances in mechanochemical processing of ferrites is presented. We discuss the potential for applications of mechanical activation by induced phase transformations and chemical reactions in soft and hard ferrite materials through enhancement of structural and magnetic properties