Arbitrary Charge Distribution Research Articles

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields.

A self-consistent method is presented for the calculation of the local dielectric permittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute/liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum protein electrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for on-the-fly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with field-dependent dielectric response.

Electromagnetic momentum balance equation and the force density in material media

We present a momentum balance equation derived directly from Maxwell's equations. This equation contains a force density, which we call Maxwell's force density, which generalizes the Lorentz force density, now including total fields rather than only external fields, and arbitrary charge and current distributions. As a test for this balance equation we derive for gases the electrostatic and magnetostatic Helmholtz force densities. This deduction will be useful for advanced undergraduates and graduate students, as well as for specialists interested in the conceptual aspects of electromagnetism.

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: Exact results for spherical inclusions

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.

Debye–Hückel theory for mixtures of rigid rodlike ions and salt

Like-charged surfaces are able to attract each other if they are embedded in an electrolyte solution of multivalent rodlike ions, even if the rods are long. To reproduce this ability the Poisson-Boltzmann model has recently been extended so as to account for the rodlike structure of the mobile ions. Our model properly accounts for intraionic correlations but still neglects correlations between different rodlike ions. For sufficiently long rods, the model shows excellent agreement with Monte Carlo simulations and exhibits two minima - a depletion and a bridging minimum - in the interaction free energy. In the present work, we generalize the Poisson-Boltzmann model to systems with polydisperse rod lengths and arbitrary charge distributions along the rods, including the presence of salt. On the level of the linearized Debye-Hückel model we derive a general criterion for whether an electrolyte with given distribution of rodlike ions is able to mediate attraction between like-charged surfaces. We numerically analyze two special cases, namely the influence of salt on symmetric and asymmetric mixtures of monodisperse rodlike ions. The symmetric mixture is characterized by the presence of both negatively and positively charged (but otherwise identical) rodlike ions. For the asymmetric mixture, the system contains rodlike ions of only one type. We demonstrate that the addition of salt retains the depletion minimum but tends to eliminate the bridging minimum.

Analytical solutions for space charge fields in TPC drift volumes

At high particle rates and high multiplicities, Time Projection Chambers can suffer from field distortions due to slow moving ions that accumulate within the drift volume. These variations modify the electron trajectory along the drift path, affecting the tracking performance of the detector. In order to calculate the track distortions due to an arbitrary space charge distribution in a TPC, novel representations of the Green's function for a TPC-like geometry were worked out. This analytical approach permits accurate predictions of track distortions due to an arbitrary space charge distribution (by solving the Langevin equation) as well as the possibility to benchmark common numerical methods to calculate such space charge fields.

Theory of microphase separation in charged crosslinked polymer blends with arbitrary charge distribution

In this paper, we are interested in the phase behavior and scattering properties of charged crosslinked polymer blends in solution. The system undergoes a microphase separation, below some critical temperature. To study such a transition, use is made of the standard de Gennes theory based on an analogy with a dielectric medium. This analogy is extended to include the effects of the initial composition fluctuations in order to improve its agreement with experimental data in the small wave vector range. The excluded-volume interactions are explicitly introduced through the blob model. The charge effects on the phase behavior are examined, for any charge distribution of polyions and for any salt concentration. This completes a previous study which was concerned with the situation where only one species is charged. The early kinetics of microphase separation is discussed, and the charges contribution to the growth rate is also evaluated.

An analytical approach to space charge distortions for time projection chambers

In a time projection chamber (TPC), the possible ion feedback and also the primary ionization of high multiplicity events result in accumulation of ionic charges inside the gas volume (space charge). This charge introduces electrical field distortions and modifies the cluster trajectory along the drift path, affecting the tracking performance of the detector. In order to calculate the track distortions due to an arbitrary space charge distribution in the TPC, novel representations of the Green's function for a TPC geometry were worked out. This analytical approach finally permits accurate predictions of track distortions due to an arbitrary space charge distribution by solving the Langevin equation.

Resolving a distribution of charge into intrinsic multipole moments: A rankwise distributed multipole analysis

We present a method for the rankwise distributed multipole analysis of an arbitrary distribution of charge and its surrounding field. Using the superposition principle, the electrostatic field created by a distribution of charge can be resolved recursively into the contributions of a set of intrinsic multipole moments "tied to" their rank-specific multipole centers. The positions of the multipole centers, which are fixed with respect to the distribution of charge, are determined from a term-by-term optimization of the Taylor's expansion of the electrostatic potential with respect to the charge coordinates. We describe the recursive construction of the intrinsic multipole moments and derive the algebraic expression of the multipole centers. The resulting distributed multipole expansion provides a conceptual framework for the analysis and modeling of the electrostatic field and of its associated distribution of charge.

Nonuniform Electro-osmotic Flow on Charged Strips and Its Use in Particle Trapping

In this article, we investigate theoretically electro-osmotic flow set up by charged strips on an otherwise uncharged surface. Starting with a single-strip problem we demonstrate that for simple polynomial surface charge distributions several basic solutions can be derived in closed forms constituted by the analogous idea-flow solutions, which provide a more lucid way of revealing the flow features. These solutions reveal two types of flow topology: simple draining-in/pumping-out streaming and a pair of microvortices for symmetric and antisymmetric surface charge distributions, respectively. For an arbitrary surface charge distribution, more complicated flow structures can be found by the superposition of these basic solutions. We further extend the analysis to two uniformly charged strips and show how the flow characteristics vary with the strips' dimensions and surface zeta potentials. The far-field velocity behavior is also asymptotically identified and indicates that the hydrodynamic nature of the flow is typically long-range. An application to particle trapping with electro-osmotic vortices is also investigated theoretically for the first time. We show that in collaboration with short-range attraction effects the trapping can be facilitated by symmetric vortices with a converging stagnation point, but not by asymmetric vortices.

Anisotropy in two-dimensional arrays of collinear in-plane rotated identical particles with arbitrary charge or polarization distribution

As the size and separation between nanometric objects arranged on a two-dimensional lattice become progressively smaller, the influence of interparticle coupling increases to the point that it may dominate the system's collective behavior. In this paper, a simple method to calculate isotropic and anisotropic interaction energies of charged or polarized particles in two-dimensional arrays is developed, where anisotropy refers to changes in energy upon in-plane rotation. The calculations are performed in the framework of a multipole expansion in spherical coordinates. The role of the array symmetry with respect to the order of the expansion is deduced from the symmetry properties of the interaction. The interaction energy is calculated exactly to infinite distance by means of lattice sums; thus, no cut-off radius to nearest neighbors is introduced. Several lattice symmetries, rectangular, quadratic, and hexagonal, up to multifold rotationally symmetric quasicrystals are investigated, and the influence of local disorder is discussed.

Optical response of a metal-semiconductor field effect transistor in the presence of interface states and interfacial layer at the gate contact

A simple analytical model on the electrical characteristics of a metal-semiconductor field effect transistor under optical illumination has been proposed by considering the inherent effects of interface states and interfacial layer at the gate-channel interface. The drain current of the device under optical illumination has been studied by treating optically generated carriers within the framework of a model that concerns arbitrary charge distribution in the channel region. It has been found that for a metal of relatively higher work function acting as the gate contact of the device, the drain current increases with increasing interface state density. An expression for the threshold voltage of the device has been derived and its dependence on the interface state density has been studied. It has been found that both the channel current and threshold voltage of the device increase appreciably under illuminated condition.

Polarizable Atomic Multipole Solutes in a Generalized Kirkwood Continuum.

The generalized Born (GB) model of continuum electrostatics is an analytic approximation to the Poisson equation useful for predicting the electrostatic component of the solvation free energy for solutes ranging in size from small organic molecules to large macromolecular complexes. This work presents a new continuum electrostatics model based on Kirkwood's analytic result for the electrostatic component of the solvation free energy for a solute with arbitrary charge distribution. Unlike GB, which is limited to monopoles, our generalized Kirkwood (GK) model can treat solute electrostatics represented by any combination of permanent and induced atomic multipole moments of arbitrary degree. Here we apply the GK model to the newly developed Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field, which includes permanent atomic multipoles through the quadrupole and treats polarization via induced dipoles. A derivation of the GK gradient is presented, which enables energy minimization or molecular dynamics of an AMOEBA solute within a GK continuum. For a series of 55 proteins, GK electrostatic solvation free energies are compared to the Polarizable Multipole Poisson-Boltzmann (PMPB) model and yield a mean unsigned relative difference of 0.9%. Additionally, the reaction field of GK compares well to that of the PMPB model, as shown by a mean unsigned relative difference of 2.7% in predicting the total solvated dipole moment for each protein in this test set. The CPU time needed for GK relative to vacuum AMOEBA calculations is approximately a factor of 3, making it suitable for applications that require significant sampling of configuration space.

Calculation of coherent synchrotron radiation in toroidal waveguides by paraxial wave equation

A new technique for the simulation of coherent synchrotron radiation (CSR) and space-charge fields from a single electron bunch in straight or toroidal rectangular waveguide sections has been developed. It is based on the integration of the paraxial approximation to the wave equations, using the perturbation technique where the bending radius is large compared to the dimension of the waveguide. We have implemented an unconditionally stable integration method in the time domain with transparent boundary conditions that allows the use of a minimally sized computational domain about the bunch. This technique explicitly enforces the causality condition so that no portion of the fields can propagate faster than the speed of light, can be used with arbitrary three-dimensional charge distributions, and contains corrections for finite energy. We have also developed a method for the calculation of the transverse forces within the bunch including space-charge. This method has been developed for incorporation with a particle-in-cell code so that we may self-consistently model CSR and space-charge in combinations of bending sections with a fully dynamic electron bunch in an efficient manner. In this paper we describe the model and methods for calculation of the fields in detail and compare results to theory wherever possible.

Simulation of non-linearity in electronic image readouts

Simulation of detector operation can be a valuable tool in optimizing design before recourse to cutting metal, and, if successful, can significantly reduce the requirement for design iteration. We describe this process as applied to the reduction of spatial non-linearities in electronic charge division image readout devices. Several theoretical analyses of the non-linearities expected in such devices have been previously undertaken; however, all suffered from the inability to analyze the perimeter pattern areas where the electrode geometry does not bear simple analytical description. We present a technique whereby an arbitrary radial charge distribution may be convolved with any multiple electrode structure, which can be defined as a set of closed polygons, to calculate total charge deposited on each electrode. This technique can be used for electronic charge division image readouts to accurately determine the effect of arbitrary electrode perimeter designs; the major cause of non-linearity in these devices.

Black rings with varying charge density

We find the general five-dimensional, supersymmetric black ring solutions in M-theory based upon a circular ring, but with arbitrary, fluctuating charge distributions around the ring. The solutions have three arbitrary charge distribution functions, but their asymptotic charges and angular momenta only depend upon the total charges on the ring. The arbitrary density fluctuations thus represent "hair." By varying the charge distributions one can continuously change the entropy of these black rings; to our knowledge this is the first solution in which the entropy depends on classical moduli. We also show that there is a family of solutions, with two arbitrary functions, for which the horizon remains rotationally invariant, and yet the complete solution breaks rotational symmetry. If the horizon area is set to zero then one obtains families of supertube solutions. We find that our general solutions are governed by three harmonic functions that may be thought of as classical excitations of a string. The horizon area provides a natural Lorentz metric on these excitations, and the constancy of the rotational invariance of the horizon imposes a set of Virasoro constraints.

Alternative separation of Laplace's equation in toroidal coordinates and its application to electrostatics

The usual method of separation of variables to find a basis of solutions of Laplace's equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate θ (rather than the toroidal coordinate η or the azimuthal coordinate ψ ) . Applying these solutions to electrostatics leads to solutions, given as infinite sums over Legendre functions of the second kind, for (i) an arbitrary charge distribution on a circle, (ii) a point charge between two intersecting conducting planes, (iii) a point charge outside a conducting half plane. In the latter case, a closed expression is obtained for the potential. Also the potentials for some configurations involving charges inside a conducting torus are found in terms of Legendre functions. For each solution in the basis found by this separation, reconstructing the potential from the charge distribution (corresponding to singularities in the solutions) gives rise to integral relations involving Legendre functions.

Electroosmotic flow in microchannels with arbitrary geometry and arbitrary distribution of wall charge

General solutions are developed for direct current (DC) and alternating current (AC) electroosmotic flows in microfluidic channels with arbitrary cross-sectional geometry and arbitrary distribution of wall charge (zeta potential). The applied AC electric field can also be of arbitrary waveform. By proposing a nondimensional time scale ϖ defined as the ratio of the diffusion time of momentum across the electric double-layer thickness to the period of the applied electric field, we demonstrate analytically that the Helmholtz–Smoluchowski electroosmotic velocity is an appropriate slip condition for AC electroosmotic flows in typical microfluidic applications. With this slip condition approach, electroosmotic flows in rectangular and asymmetric trapezoidal microchannels with nonuniform wall charge, as examples, are investigated. The unknown constants in the proposed general solutions are numerically determined with a least-squares method through matching the boundary conditions. We find that the wall charge affects significantly the electroosmotic flow while the channel geometry does not. Moreover, the flow feature is characterized by another nondimensional time scale Ω defined as the ratio of the diffusion time of momentum across the channel hydraulic radius to the period of the applied electric field. The onset of phase shift between AC electroosmotic velocity and applied electric field is also examined analytically.

Rotational friction on globular proteins combining dielectric and hydrodynamic effects

Rotational friction on proteins and macromolecules is known to derive contributions from at least two distinct sources – hydrodynamic (due to viscosity) and dielectric friction (due to polar interactions). In the existing theoretical approaches, the effect of the latter is taken into account by increasing the size of the protein with the addition of a hydration layer. Here, we calculate the rotational dielectric friction on a protein ( ζ DF) by using a generalized arbitrary charge distribution model (where the charges are obtained from quantum chemical calculation) and the hydrodynamic friction with stick boundary condition, by using the sophisticated theoretical technique known as tri-axial ellipsoidal method ( ζ TR). The calculation of hydrodynamic friction is done with only the dry volume of the protein (no hydration layer). We find that the total friction thus obtained by summing up ζ DF and ζ TR, gives reasonable agreement with the experimental results, i.e., ζ exp ≈ ζ DF + ζ TR.

Spectral Element Method for the Schrödinger-Poisson System

A novel fast spectral element method (SEM) with exponential accuracy for the self-consistent solution of the Schrodinger-Poisson system has been developed for the simulation of semiconductor nanodevices. Gauss-Lobatto-Legendre polynomials were used to represent the unknown fields in the Schrodinger and Poisson equations. The model allows arbitrary potential energy and charge distributions. The predictor-corrector algorithm is applied to solve the outer loop of the self-consistent iteration. The nonlinear Poisson equation is solved by Newton's method to increase the efficiency of the system. In this paper, the spectral element method is first applied on an infinite quantum well under an external bias to solve the Schrodinger equation. Numerical results confirm the spectral accuracy of this method. The method can achieve high accuracy with a low sampling density, thus significantly lowering the computer memory and computational time compared to conventional methods.

Solvent reorganization energy of electron-transfer reactions in polar solvents.

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.