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Linear Poisson-Boltzmann equation

Davis, M. E., McCammon, J. A. Solving the finite difference linearized Poisson-Boltzmann equation A comparison of relaxation and conjugate gradients methods.. J. Comp. Chem. 10 (1989) 386-394. [Pg.195]

If there are ions in the solution, they will try to change their location according to the electrostatic potential in the system. Their distribution can be described according to Boltzmarm. Including these effects and applying some mathematics leads to the final linearized Poisson-Boltzmann equation (Eq. (43)). [Pg.365]

For small deviations from electroneutrality, the charge density at x is proportional to -(x)/kT9 where < is the difference of the electrostatic potential from its (constant) value when there is no charge density (the density of a species of charge z is proportional to 1 - zkT on linearizing the Boltzmann exponential). Then the Poisson equation [Eq. (44)] becomes the linearized Poisson-Boltzmann equation ... [Pg.85]

Here, b is the distance between the nearest unit charges along the cylinder (b = 0.34nm for the ssDNA and b = 0.17nm for the dsDNA), (+) and (—) are related to cations and anions, respectively, and a = rss for the ssDNA and a rds for the dsDNA. The expressions (5) and (6) have been obtained using the equations for the electrostatic potential derived in [64, 65], where a linearization of the Poisson-Boltzmann equation near the Donnan potential in the hexagonal DNA cell was implemented. [Pg.225]

Derive and solve the appropriate linear Poisson-Boltzmann equation for the interface between two immiscible solutions. [Pg.170]

As a final topic in this section, we briefly consider the effect of electrolyte concentration on the solvent properties. The linearized Poisson-Boltzmann equation [31,121] can be used instead of (2) and (3) when the dielectric medium... [Pg.14]

A more detailed view of the dynamies of a ehromatin chain was achieved in a recent Brownian dynamics simulation by Beard and Schlick [65]. Like in previous work, the DNA is treated as a segmented elastic chain however, the nueleosomes are modeled as flat cylinders with the DNA attached to the cylinder surface at the positions known from the crystallographic structure of the nucleosome. Moreover, the electrostatic interactions are treated in a very detailed manner the charge distribution on the nucleosome core particle is obtained from a solution to the non-linear Poisson-Boltzmann equation in the surrounding solvent, and the total electrostatic energy is computed through the Debye-Hiickel approximation over all charges on the nucleosome and the linker DNA. [Pg.414]

Combining Eqs. (2.18) and (2.19) yields the linearized Poisson-Boltzmann equation... [Pg.19]

The Poisson-Boltzmann equation. The slab model is based on a solution of the linearized Poisson-Boltzmann equation that is valid only for low electrostatic surface potentials. As... [Pg.442]

One of the simplest equations is obtained using the Debye-Hiickel approximation (for low potentials) and the superposition principle. The latter assumes that the unperturbed potential near a charged surface can be simply added to that potential due to the other (unperturbed) surface. Thus, for the example shown in the Figure 6.12, it follows that /m = 2 /d/2- This is precisely valid for Coulomb-type interactions, where the potential at any point can be calculated from the potentials produced by each fixed charge, individually. However, the Poisson-Boltzmann equation is non-linear (this has to do with the fact that in the diffuse double-layer the ions are not fixed but move because of their kinetic energy) and so this is formally not correct although it still offers a useful approximation. [Pg.114]

The above equation is known as the linearized Poisson-Boltzmann equation since the assumption of low potentials made in reaching this result from Equation (29) has allowed us make the right-hand side of the equation linear in p. This assumption is also made in the Debye-Hiickel theory and prompts us to call this model the Debye-Hiickel approximation. Equation (33) has an explicit solution. Since potential is the quantity of special interest in Equation (33), let us evaluate the potential at 25°C for a monovalent ion that satisfies the condition e p = kBT ... [Pg.510]

For studying the stability of colloidal particles in suspension (Chapter 13) or for determining the potential at the surface of particles (Chapter 12), one often needs expressions for potential distributions around small particles that have curved surfaces. Solving the Poisson-Boltzmann equation for curved geometries is not a simple matter, and one often needs elaborate numerical methods. The linearized Poisson-Boltzmann equation (i.e., the Poisson-Boltzmann equation in the Debye-Hiickel approximation) can, however, be solved for spherical electrical double layers relatively easily (see Section 12.3a), and one obtains, in place of Equation (37),... [Pg.511]

The solution of the linearized Poisson-Boltzmann equation around cylinders also requires numerical methods, although when cylindrical symmetry and the Debye-Hiickel approximation are assumed the equation can be solved. The solution, however, requires advanced mathematical techniques and we will not discuss it here. It is nevertheless useful to note the form of the solution. The potential for symmetrical electrolytes has been given by Dube (1943) and is written in terms of the charge density a as... [Pg.511]

What are the assumptions that are needed to obtain the linearized Poisson-Boltzmann (LPB) equation from the Poisson-Boltzmann equation, and under what conditions would you expect the LPB equation to be sufficiently accurate What is the relation between the Debye-Huckel approximation and the LPB equation ... [Pg.530]

Obtain the corresponding Poisson-Boltzmann equation and the linearized version based on the Debye-Hiickel approximation. [Pg.531]

Another related phenomenon to be discussed in 2.3 is known in the polymer literature as counterion condensation. This term refers to a phase transition-like switch of the type of singularity, induced by a line charge to solutions of (2.1.2), occurring at some critical value of the linear charge density. Counterion condensation as a limiting property of the solutions of the Poisson-Boltzmann equation was studied in detail in [11]—[19]. Presentation of 2.3 follows that of [17]. [Pg.24]

The question to be discussed is whether saturation of the electric field (asserted by Proposition 2.1) implies saturation of the interparticle force of interaction. Consider for definiteness repulsion between two symmetrically charged particles in a symmetric electrolyte solution. In the onedimensional case (for parallel plates) the answer is known—the force of repulsion per unit area of the plates saturates. (This follows from a direct integration of the Poisson-Boltzmann equation carried out in numerous works, primarily in the colloid stability context, e.g., [9]. Recall that again in vacuum, dielectrics, or an ionic system with a linear screening, the appropriate force grows without bound with the charging of the particles.)... [Pg.30]

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. [Pg.200]

Table I. Constants of Integration for the General Solution of the Linearized Poisson—Boltzmann Equation... Table I. Constants of Integration for the General Solution of the Linearized Poisson—Boltzmann Equation...
In many practical cases we can use the low-potential-assumption and it leads to realistic results. In addition, it is a simple equation and dependencies like the one on the salt concentration can easily be seen. In some cases, however, we have high potentials and we cannot linearize the Poisson-Boltzmann equation. Now we treat the general solution of the onedimensional Poisson-Boltzmann equation and drop the assumption of low potentials. It is convenient to solve the equation with the dimensionless potential y = ertp/kBT. Please do not mix this up with the spacial coordinate y In this section we use the symbol y for the... [Pg.46]

Plot the potential versus distance for surface potentials of 60 mV, 100 mV, and 140 mV using the solution of the linearized and the full Poisson-Boltzmann equation for an aqueous solution with 2 mM KC1. [Pg.56]

Using Poisson-Boltzmann theory we can derive a simple expression for the disjoining pressure. For the linear case (low potentials) and for a monovalent salt, the one-dimensional Poisson-Boltzmann equation (Eq. 4.9) is... [Pg.100]

Two approaches for the calculation of the double-layer contribution are explored. Hogg el of. (16) linearized the Poisson- -Boltzmann equation to compute the double-layer force between two dissimilar plane surfaces, then used Derjaguin s approximation to extend this result to the interaction of two spheres of different radii. When the radius of one sphere is infinite, their result becomes... [Pg.107]

Clint el al. (4) measured the rate of deposition of 0.43-gm-diameter polystyrene latex particles onto a rotating disk coated with a polystyrene film in Ba(N03)s solutions of three different ionic strengths. Results are reported ia Table II. Also reported in this table are the surface potentials of the disk which are needed to force agreement between predicted and observed rates. Speculations 1 and 2 again refer to approach at constant surface potential or charge, respectively, when the potential is small enough to linearize the Poisson-Boltzmann equation. However, when the... [Pg.113]


See other pages where Linear Poisson-Boltzmann equation is mentioned: [Pg.171]    [Pg.185]    [Pg.217]    [Pg.222]    [Pg.252]    [Pg.22]    [Pg.19]    [Pg.440]    [Pg.12]    [Pg.12]    [Pg.25]    [Pg.38]    [Pg.41]    [Pg.55]    [Pg.59]    [Pg.352]    [Pg.18]    [Pg.45]    [Pg.18]    [Pg.112]    [Pg.113]   
See also in sourсe #XX -- [ Pg.19 ]




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