scholarly journals Maxwell Equations Without a Polarization Field, Using a Paradigm from Biophysics

2020 ◽  
Author(s):  
Robert Eisenberg
Keyword(s):  
Integrated Circuits ◽  
Electric Field ◽  
Electric Fields ◽  
Operational Definition ◽  
Polarization Field ◽  
Charge Movement ◽  
Electrical Measurements ◽  
Field Dependent ◽  
Dependent Polarization ◽  
Electrodynamic Forces

Electrodynamics is usually written using polarization fields to describe changes in distribution of charge as electric fields change. This approach does not specify polarization fields uniquely from electrical measurements. Many polarization fields will produce the same electrodynamic forces and flows because only divergence of polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. To be unique, models must describe the charge distribution and how it varies. I propose a different paradigm to describe field dependent charge, i.e., the phenomenon of polarization. This operational definition of polarization has worked well in biophysics for fifty years, where a field dependent, time dependent polarization provides gating current that makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that operational definition be used to define polarization charge in general. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’. The classical polarization field need not enter into that treatment at all. When nothing is known about polarization, it is necessary to use an approximate representation with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.

scholarly journals Maxwell Equations Without a Polarization Field, Using a Paradigm from Biophysics

2020 ◽  
Author(s):  
Robert Eisenberg
Keyword(s):  
Integrated Circuits ◽  
Electric Field ◽  
Electric Fields ◽  
Operational Definition ◽  
Polarization Field ◽  
Charge Movement ◽  
Electrical Measurements ◽  
Field Dependent ◽  
Dependent Polarization ◽  
Electrodynamic Forces

Electrodynamics is usually written using polarization fields to describe changes in distribution of charge as electric fields change. This approach does not specify polarization fields uniquely from electrical measurements. Many polarization fields will produce the same electrodynamic forces and flows because only divergence of polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. To be unique, models must describe the charge distribution and how it varies. I propose a different paradigm to describe field dependent charge, i.e., the phenomenon of polarization. This operational definition of polarization has worked well in biophysics for fifty years, where a field dependent, time dependent polarization provides gating current that makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that operational definition be used to define polarization charge in general. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’. The classical polarization field need not enter into that treatment at all. When nothing is known about polarization, it is necessary to use an approximate representation with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.

scholarly journals Maxwell Equations without a Polarization Field, Using a Paradigm from Biophysics

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 172
Author(s):  
Robert S. Eisenberg
Keyword(s):  
Electric Field ◽  
Operational Definition ◽  
Local Electric Field ◽  
Time Dependent ◽  
Polarization Field ◽  
Structural Basis ◽  
Gating Current ◽  
Electrical Measurements ◽  
Induced Charge ◽  
Definition Of

When forces are applied to matter, the distribution of mass changes. Similarly, when an electric field is applied to matter with charge, the distribution of charge changes. The change in the distribution of charge (when a local electric field is applied) might in general be called the induced charge. When the change in charge is simply related to the applied local electric field, the polarization field P is widely used to describe the induced charge. This approach does not allow electrical measurements (in themselves) to determine the structure of the polarization fields. Many polarization fields will produce the same electrical forces because only the divergence of polarization enters Maxwell’s first equation, relating charge and electric forces and field. The curl of any function can be added to a polarization field P without changing the electric field at all. The divergence of the curl is always zero. Additional information is needed to specify the curl and thus the structure of the P field. When the structure of charge changes substantially with the local electric field, the induced charge is a nonlinear and time dependent function of the field and P is not a useful framework to describe either the electrical or structural basis-induced charge. In the nonlinear, time dependent case, models must describe the charge distribution and how it varies as the field changes. One class of models has been used widely in biophysics to describe field dependent charge, i.e., the phenomenon of nonlinear time dependent induced charge, called ‘gating current’ in the biophysical literature. The operational definition of gating current has worked well in biophysics for fifty years, where it has been found to makes neurons respond sensitively to voltage. Theoretical estimates of polarization computed with this definition fit experimental data. I propose that the operational definition of gating current be used to define voltage and time dependent induced charge, although other definitions may be needed as well, for example if the induced charge is fundamentally current dependent. Gating currents involve substantial changes in structure and so need to be computed from a combination of electrodynamics and mechanics because everything charged interacts with everything charged as well as most things mechanical. It may be useful to separate the classical polarization field as a component of the total induced charge, as it is in biophysics. When nothing is known about polarization, it is necessary to use an approximate representation of polarization with a dielectric constant that is a single real positive number. This approximation allows important results in some cases, e.g., design of integrated circuits in silicon semiconductors, but can be seriously misleading in other cases, e.g., ionic solutions.

scholarly journals Heterogeneous Intramolecular Electric Field as a Descriptor of Diels-Alder Reactivity

2020 ◽  
Author(s):  
Matthew Hennefarth ◽  
Anastassia N. Alexandrova
Keyword(s):  
Electric Field ◽  
Electron Density ◽  
Electric Fields ◽  
Alder Reaction ◽  
Diels Alder ◽  
Charge Movement ◽  
External Electric Fields ◽  
Topological Features ◽  
Diels Alder Reaction ◽  
Kinetics Of

<div> <div> <div> <p>External electric fields have proven to be an effective tool in catalysis, on par with pressure and temperature, affecting the thermodynamics and kinetics of a reaction. However, fields in molecules are complicated heterogeneous vector objects, and there is no universal recipe for grasping the exact features of these fields that implicate reactivity. Herein, we demonstrate that topological features of the heterogeneous electric field within the reactant state, as well as of the quantum mechanical electron density – a scalar reporter on the field experienced by the system – can be identified as rigorous descriptors of the reactivity to follow. We scrutinize specifically the Diels-Alder reaction. Its 3-D nature and the lack of a singular directionality of charge movement upon barrier crossing makes the effect of the electric field not obvious. We show that the electric field topology around the dienophile double bond, and the associated changes in the topology of the electron density in this bond are predictors of the reaction barrier. They are also the metrics by which to rationalize and predict how the external field would inhibit or enhance the reaction. The findings pave the way toward designing external fields for catalysis, as well as reading the reactivity without an explicit mechanistic interrogation, for a variety of reactions. </p> </div> </div> </div>

scholarly journals Time-Dependent Electric Field Distribution in Layered Paper-Oil Insulation

2019 ◽  
pp. 58-63 ◽  
Author(s):  
Gunnar Håkonseth ◽  
Erling Ildstad
Keyword(s):  
Electric Field ◽  
Field Distribution ◽  
Electric Fields ◽  
Current Density ◽  
Test Object ◽  
Dielectric Response ◽  
Electric Field Distribution ◽  
Time Dependent ◽  
Polarization Current ◽  
Dependent Polarization

Layered paper–oil insulation is used in several types of HVDC equipment. In order to better understand breakdown mechanisms and optimize the design, it is important to understand the electric field distribution in the insulation. In the present work, a test object with such insulation has been modeled as a series connection of oil and impregnated paper. The permittivity, conductivity, and the dielectric response function has been measured for impregnated paper and oil separately and used as parameters in a dielectric response model for the layered insulation system. A system of differential equations has been established describing the voltages across each material, i.e. across each layer of the test object. These equations have been solved considering a DC step voltage across the whole test object. Based on this, the time-dependent electric field in each material as well as the time-dependent polarization current density in the test object have been calculated. The calculated polarization current density was found to agree well with the measured polarization current density of the test object. This indicates that application of dielectric response theory gives a good estimate of the time-dependent electric field distribution in layered insulation systems. The results show that 90 % of the change from initial values to steady-state values for the electric fields has occurred within the first 35 minutes after the voltage step. This applies to the electric fields in both of the materials of the examined test object at a temperature of 323 K.

scholarly journals Electric field dependent polarization switching of tetramethylammonium bromotrichloroferrate(III) ferroelectric plastic crystals

2020 ◽  
Vol 116 (24) ◽  
pp. 242902
Author(s):  
Julian Walker ◽  
Simon Scherrer ◽  
Nora Statle Løndal ◽  
Tor Grande ◽  
Mari-Ann Einarsrud
Keyword(s):  
Electric Field ◽  
Polarization Switching ◽  
Plastic Crystals ◽  
Field Dependent ◽  
Dependent Polarization

scholarly journals Quantification of pulsed electric field for the rupture of giant vesicles with various surface charges, cholesterols and osmotic pressures

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0262555
Author(s):  
Md. Kabir Ahamed ◽  
Marzuk Ahmed ◽  
Mohammad Abu Sayem Karal
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Mole Fraction ◽  
High Frequency ◽  
Pulsed Electric Field ◽  
Surface Charges ◽  
Maximum Probability ◽  
Giant Vesicles ◽  
Biochemical Processes ◽  
Field Dependent

Electropermeabilization is a promising phenomenon that occurs when pulsed electric field with high frequency is applied to cells/vesicles. We quantify the required values of pulsed electric fields for the rupture of cell-sized giant unilamellar vesicles (GUVs) which are prepared under various surface charges, cholesterol contents and osmotic pressures. The probability of rupture and the average time of rupture are evaluated under these conditions. The electric field changes from 500 to 410 Vcm-1 by varying the anionic lipid mole fraction from 0 to 0.60 for getting the maximum probability of rupture (i.e., 1.0). In contrast, the same probability of rupture is obtained for changing the electric field from 410 to 630 Vcm-1 by varying the cholesterol mole fraction in the membranes from 0 to 0.40. These results suggest that the required electric field for the rupture decreases with the increase of surface charge density but increases with the increase of cholesterol. We also quantify the electric field for the rupture of GUVs containing anionic mole fraction of 0.40 under various osmotic pressures. In the absence of osmotic pressure, the electric field for the rupture is obtained 430 Vcm-1, whereas the field is 300 Vcm-1 in the presence of 17 mOsmL-1, indicating the instability of GUVs at higher osmotic pressures. These investigations open an avenue of possibilities for finding the electric field dependent rupture of cell-like vesicles along with the insight of biophysical and biochemical processes.

Structural Response of BaTiO3/CaTiO3 Superlattice to Applied Electric Fields

2009 ◽  
Vol 1199 ◽  
Author(s):  
Ji Young Jo ◽  
Rebecca Sichel ◽  
Ho Nyung Lee ◽  
Eric Dufresne ◽  
Paul Evans
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Structural Response ◽  
Hysteresis Curve ◽  
Electrical Measurements ◽  
Broad Distribution ◽  
Time Resolved ◽  
X Ray ◽  
Polarization Electric Field ◽  
High Electric Fields

AbstractThe structural response of a ferroelectric BaTiO3/dielectric CaTiO3 superlattice to the bipolar applied electric field was studied using time-resolved x-ray microdiffraction. Structural results were compared to the polarization-electric field hysteresis curve obtained from electrical measurements. The superlattice x-ray reflections were found to have a broad distribution of intensity in reciprocal space under applied electric fields exceeding the nominal coercive electric field. The broad distribution of the lattice constant at high electric fields is compared with a model in which the constituent layers of the superlattice have different coercive fields for the polarization switching.

BLOCH DYNAMICS IN SPATIALLY LOCAL INHOMOGENEOUS ELECTRIC FIELDS

2001 ◽  
Vol 11 (02) ◽  
pp. 425-453
Author(s):  
JOSEPH P. REYNOLDS ◽  
GERALD J. IAFRATE ◽  
JUN HE
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Nearest Neighbor ◽  
Constant Electric Field ◽  
Tight Binding ◽  
Homogeneous Field ◽  
Wannier Functions ◽  
Field Dependent ◽  
Bloch Electrons ◽  
Special Case

The influence of local inhomogeneities on the electric field dependent properties of Bloch electrons is studied. The homogeneous electric field is described through the use of the vector potential, and the instantaneous Wannier functions of the homogeneous field dependent Hamiltonian are used as bases states to depict Bloch dynamics and properties. Model examples are treated using Slater-Koster inhomogeneities and nearest-neighbor tight-binding band structure in a one dimensional, single-band analysis. Detailed analysis is presented for the special case of a constant electric field; here the influence of localization due to the presence of the electric field is shown to clearly affect the energy spectrum of the Bloch electron for a single and double impurity configuration.

scholarly journals Heterogeneous Intramolecular Electric Field as a Descriptor of Diels-Alder Reactivity

2020 ◽  
Author(s):  
Matthew Hennefarth ◽  
Anastassia N. Alexandrova
Keyword(s):  
Electric Field ◽  
Electron Density ◽  
Electric Fields ◽  
Alder Reaction ◽  
Diels Alder ◽  
Charge Movement ◽  
External Electric Fields ◽  
Topological Features ◽  
Diels Alder Reaction ◽  
Kinetics Of

<div> <div> <div> <p>External electric fields have proven to be an effective tool in catalysis, on par with pressure and temperature, affecting the thermodynamics and kinetics of a reaction. However, fields in molecules are complicated heterogeneous vector objects, and there is no universal recipe for grasping the exact features of these fields that implicate reactivity. Herein, we demonstrate that topological features of the heterogeneous electric field within the reactant state, as well as of the quantum mechanical electron density – a scalar reporter on the field experienced by the system – can be identified as rigorous descriptors of the reactivity to follow. We scrutinize specifically the Diels-Alder reaction. Its 3-D nature and the lack of a singular directionality of charge movement upon barrier crossing makes the effect of the electric field not obvious. We show that the electric field topology around the dienophile double bond, and the associated changes in the topology of the electron density in this bond are predictors of the reaction barrier. They are also the metrics by which to rationalize and predict how the external field would inhibit or enhance the reaction. The findings pave the way toward designing external fields for catalysis, as well as reading the reactivity without an explicit mechanistic interrogation, for a variety of reactions. </p> </div> </div> </div>

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