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Electronic and Ionic Conductivities of Microtubules and Actin Filaments, Their Consequences for Cell Signaling and Applications to Bioelectronics
Published in Sergey Edward Lyshevski, Nano and Molecular Electronics Handbook, 2018
Jack A. Tuszynski, Avner Priel, J.A. Brown, Horacio F. Cantiello, John M. Dixon
The electro-conductive medium is a condensed cloud of ions surrounding the polymer and separated from it due to the thermal fluctuations in the solution. The distance beyond which thermal fluctuations are stronger than the electrostatic attractions or repulsions between charges in solution is defined as the so-called Bjerrum length, λB. With the dielectric constant of the medium denoted by ε, the Bjerrum length is given by () e24πεε0λB=kBT
Molecular Packing in Cylindrical Micelles
Published in Raoul Zana, Eric W. Kaler, Giant Micelles, 2007
To account for the influence of electrostatic interactions on micellar growth we should include their contribution, fel, in the overall free energy per amphiphile in a micelle, f. For simplicity, let us assume, as in the simple OFM, that fc is constant, and suppose further that nonelectrostatic repulsions between headgroups (e.g., those due to excluded volume and hydration forces) are adequately described by the term B/a, so that f = γa + B/a + fel (see Equation 2.13). Based on the linearized Poisson-Boltzmann theory, the electrostatic (charging) free energy per headgroup is given by fel = 2πkBTlBlD/a, and thus depends on the Bjerrum length, lB, and the Debye screening length, lD. (This result is valid for charges on a planar interface, such as that of a lipid bilayer. We ignore here the usually weak dependence of fel on surface curvature.) The Bjerrum length, Lb =e2/(4πɛ0ɛWkBT), measures the distance over which the interaction between two elementary charges e equals the thermal energy kBT (note that ɛ0 is the permittivity of free space). In an aqueous solution of dielectric constant ɛW = 80 its value is lB ≈ 7Å. The Debye length lD = (8πlBn0)-1/2 is the distance beyond which electrostatic interactions (here in a symmetric 1:1 electrolyte present with bulk concentration n0) are effectively screened. Using f = γa + B/a + 2πkBTlBlD/a, we now find a0=[(B+2πlBlDkBT)/γ](1/2)
Time-dependent electrical properties of liquid crystal cells: unravelling the origin of ion generation
Published in Liquid Crystals, 2018
Rate equations similar to (2) were already reported in several papers to describe the kinetics of image sticking in liquid crystal cells [18,19,37–41]. However, as will be shown later on in this paper, Equation (2) alone is unable to describe both ion capturing and ion releasing regimes in liquid crystals reported by different research groups [17–21]. To explain a broad variety of existing experimental results, the contamination factor should be introduced and Equation (2) should be solved together with Equation (3). As was already discussed in papers [42–44], Equations (2)–(3) can be reasonably applied to calculate the concentration of ions in liquid crystals. A relatively low concentration of mobile ions in liquid crystals (on the order of ) is a major physical factor enabling the applicability of these equations [42–44]. In short, as a result of this small concentration of ions in liquid crystals, (i) the Bjerrum length (the distance at which electrostatic energy of two charges equals their thermal energy) is shorter than the average distance between ions; and (ii) the surface coverage of alignment layers is very small [42–44] thus justifying the use of the approximation expressed by Equations (2)–(3). However, if the concentration of ions is comparable to that of typical electrolytes (on the order of and higher for 1:1 electrolyte of nearly 1 mM concentration), a more rigorous approach based on Poisson–Boltzmann equation should be considered [45–48].