arXiv subjects

L. Blum

Publications and source records attributed to L. Blum.

8 recordsLinked to original sources

arXiv2007

Towards an analytical theory for charged hard spheres

Ion mixtures require an exclusion core to avoid collapse. The Debye Hueckel theory, where ions are point charges, is accurate only in the limit of infinite dilution. The MSA is the embedding of hard cores into DH, is valid for higher densities. In the MSA the properties of any ionic mixture can be represented by a single screening parameter $Γ$. For equal ionic size restricted model is obtained from the Debye parameter $κ$. This one parameter representation (BIMSA) is valid for complex and associating systems, such as the general n-polyelectrolytes. The BIMSA is the only theory that satisfies the infinite dilution limit of the DH theory for any chain length. The contact pair distribution function of hard ions mixture is a functional of $Γ$ and a small mean field parameter. This yields good agreement with the Monte Carlo (Bresme et al. Phys. Rev. E {\textbf 51} 289 (1995)) .

cond-mat.soft↗

arXiv2006

Structure and thermodynamics of multi-component/multi-Yukawa mixtures

New small angle scattering experiments reveal new peaks in colloidal systems (S.H. Chen et al) in the structure function S(k), in a region that was inaccessible with older instruments. We propose here general closure of the Ornstein Zernike equation, that is the sum of an arbitrary number of yukawas, and that that will go well beyond the MSA . For this closure we get for the Laplace transform of the pair correlation function . This function is easily transformed into S(k) by replacing the Laplace variable by the Fourier wariable. Although the method is general and valid for polydisperse systems, an explicit continued fraction solution is found for the monodisperse case.

cond-mat.stat-mech↗

arXiv2005

Scaling in Complex Systems: Analytical Theory of Charged Pores

In this paper we find an analytical solution of the equilibrium ion distribution for a toroidal model of a ionic channel, using the Perfect Screening Theorem (PST). The ions are charged hard spheres, and are treated using a variational Mean Spherical Approximation (VMSA) . Understanding ion channels is still a very open problem, because of the many exquisite tuning details of real life channels. It is clear that the electric field plays a major role in the channel behaviour, and for that reason there has been a lot of work on simple models that are able to provide workable theories. Recently a number of interesting papers have appeared that discuss models in which the effect of the geometry, excluded volume and non-linear behaviour is considered. We present here a 3D model of ionic channels which consists of a charged, deformable torus with a circular or elliptical cross section, which can be flat or vertical (close to a cylinder). Extensive comparisons to MC simulations were performed. The new solution opens new possibilities, such as studying flexible pores, and water phase transformations inside the pores using an approach similar to that used on flat crystal surfaces .

physics.bio-ph↗

arXiv2003

Yukawa fluids in the mean scaling approximation: III New scales

In recent work a general solution of the Ornstein Zernike equation for a general Yukawa closure for a single component fluid was found. Because of the complexity of the equations a simplifying assumption was made, namely that the main scaling matrix $\bGamma$ had to be diagonal. While in principle this is mathematically correct, it is not physical because it will violate symmetry conditions when different Yukawas are assigned to different components. In this work we show that by using the symmetry conditions the off diagonal elements of $\bGamma$ can be computed explicitly for the case of two Yukawas, and that although the solution is different than in the diagonal case, the excess entropy is formally the same as in the diagonal case. Analytical expressions for the Laplace transforms of the pair distribution functions are derived.

cond-mat.stat-mech↗

arXiv2001

Scaling for Mixtures of Hard Ions and Dipoles in the Mean Spherical Approximation

Using new scaling parameters $β_i$, we derive simple expressions for the excess thermodynamic properties of the Mean Spherical Approximation (MSA) for the ion-dipole mixture. For the MSA and its extensions we have shown that the thermodynamic excess functions are a function of a reduced set of scaling matrices ${\mathbfΓ}_χ$. We show now that for factorizable interactions like the hard ion-dipole mixture there is a further reduction to a diagonal matrices ${\mathbfβ}_χ$. The excess thermodynamic properties are simple functions of these new parameters. For the entropy we get \[ S=-{{\frac{k V}{3 π}}}({\cal F}[{\mathbfβ}_α])_{α\in {\mathbf χ}} \] where ${\cal F}$ is an algebraic functional of the scaling matrices of irreducible representations $χ$ of the closure of the Ornstein-Zernike. The new scaling parameters $β_i$, are also simply related to the chemical potentials of the components. The analysis also provides a new definition of the Born solvation energy for arbitrary concentrations of electrolytes.

cond-mat.stat-mech↗

arXiv2001

The Electrochemical Reduction of Hydrogen in the Presence of Bisulfate on Platinum(111)

A new model for the intermediate compound of the hydrogen evolution reaction (HER) is proposed, for the electrochemical reduction of hydrogen in the presence of bisulfate on platinum(111). The formation of this compound, a regular 2 dimensional honeycomb ice lattice, occurs by a first order phase transitions that involves the reorientation of water molecules. The model is analyzed using new and simple effective cluster approach which highlights the relevant transitions in system. This method is based on the cluster variation method used successfully in our previous work on the UPD of Cu onto Au(111), and permits us to explore a large region of parameter space, an essential feature to study this complex system. The theory makes full use of the properties of the diffuse layer: The water molecule is reoriented as the potential is changed. For positive potentials it forms linear chains which are responsible for the $\sqrt 3 \times \sqrt 7$ structure of the sulfate observed by STM. At negative potentials water turns so that its dipole points towards the Pt. Then it will form a regular honeycomb network of hydrogen bonded molecules, with the sulfate at the center of the hexagons. Then the bisulfate is desorbed, leaving the honeycomb HER structure behind. Our model thus provides an explanation of the well known fact that only 2/3 of the Pt atoms participate in the electroreduction of the hydrogen. The theory implies geometrical constraints to the water potential.

physics.chem-ph↗

arXiv2000

Density functional formalism in the canonical ensemble

Density functional theory, when applied to systems with $T\neq 0$, is based on the grand canonical extension of the Hohenberg-Kohn-Sham theorem due to Mermin (HKSM theorem). While a straightforward canonical ensemble generalization fails, work in nanopore systems could certainly benefit from such extension. We show that, if the asymptotic behaviour of the canonical distribution functions is taken into account, the HKSM theorem can be extended to the canonical ensemble. We generate $N$-modified correlation and distribution functions hierarchies and prove that, if they are employed, either a modified external field or the density profiles can be indistinctly used as independent variables. We also write down the $N$% -modified free energy functional and prove that its minimum is reached when the equilibrium values of the new hierarchy are used. This completes the extension of the HKSM theorem.

cond-mat.stat-mech↗

arXiv2000

Density fluctuations and entropy

A new functional for the entropy that is asymptotically correct both in the high and low density limits is proposed. The new form is [ S=S^{(id)}+S^{(ln)}+S^{(r)}+S^{(c)} ] where the new term S^{(c)} depends on the p-bodies density fluctuations $α_p$ and has the form [ S^{(c)}= {ln 2-1+\sum_{p=2}^\infty \frac{(\ln 2) ^p}{p!}α_p-[ \exp (α_2-1)-α_2]} +\hat S ], where $\hat S$ renormalizes the ring approximation S^{(r)}. This result is obtained by analyzing the functional dependence of the most general expression of the entropy: Two main results for S^{(c)} are proven: i) In the thermodynamic limit, only the functional dependence on the one body distribution function survives and ii) by summing to infinite order the leading contributions in the density a new numerical expression for the entropy is proposed with a new renormalized ring approximation included. The relationship of these results to the incompressible approximation to entropy is discussed.

cond-mat.stat-mech↗