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Polarización en Membranas
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Fick's Law for Charged Particles
Equation

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The diffusion leads to the difference in concentrations dc over a distance dx generates a flow of particles j that is calculated by the so-called Fick's law :

j =- D \displaystyle\frac{ dc }{ dx }

where D is the diffusion constant.

ID:(3878, 0)


Current density
Equation

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The flow density j is understood as the current I by section S, so

j =\displaystyle\frac{ I }{ S }

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Diffusion Constant for Charged Particles
Equation

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The diffusion constant D was modeled by Einstien and depends on the absolute value of the number of charges \mid z \mid, the mobility \mu_e, the universal gas constant, T the absolute temperature and F the Faraday constant that has a value of 9.649E+4 C/mol:

D =\displaystyle\frac{ \mu_e R T }{\mid z \mid F }

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Ohm's law with Conductivity
Equation

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If a potential difference dV of a long conductor dx and section S with a resistivity \rho_e is considered you have with Ohm's law that the current is

I = \displaystyle\frac{S}{\rho_e dx}dV

so with

j=\displaystyle\frac{I}{S}

y

\kappa_e=\displaystyle\frac{1}{\rho_e}

with what

j =- \kappa \displaystyle\frac{ dV }{ dx }

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Nernst Current
Equation

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The electron current is the dQ charge that passes through a S section in a dt time. If it is assumed that electrons or ions travel at a speed v the volume of these that will pass in time dt through the section S is the same to Svdt. If, on the other hand, the ion concentration is c and its charge is q the current will be

I=\displaystyle\frac{dQ}{dt}=\displaystyle\frac{Svdtc}{dt}=Svc

that is

equation/druyd>

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Nernst Potential
Equation

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If the potential difference is integrated, the relationship of the potential difference corresponding to the limit in which the electric field is compensated with the Diffusion can be established:

V_m =-\displaystyle\frac{ R T }{ F }\ln\displaystyle\frac{ c_1 }{ c_2 }

where R is the gas constant, T the temperature, z the number of charges, F the constant Farday and the concentrations between both sides of the membrane c_1 and c_2.

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