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corroded_b
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Hi,
I'm doing MD-simulations in a capacitor-like system: 2 charged electrodes with a dense ionic liquid in between (non-diluted) with periodic boundaries in 2 dimensions (so for the electrodes I get infinite planes (xy) ,charged).
I want to get the potential [itex]U(z)[/itex] along the z-axis (witch is perpendicular to the electrodes). This is the superposition of the linear electrode pot. and the potential contribution of the ions.
So I calculate the charge density [itex]\rho(z)[/itex] and use the poisson equation [itex]\nabla^2\Psi=-\frac{\rho}{\epsilon}[/itex] to get the potential.
Now, in the http://pubs.acs.org/doi/suppl/10.1021/jp803440q/suppl_file/jp803440q_si_002.pdf" (page 3 on top) this potential (in gaussian units) is written as [itex]\Psi(z)=-\frac{4 \pi}{\epsilon^*} \int_0^z (z-z') \rho(z')dz' [/itex]. Can someone explain/proof this expression?
Thanks,
corro
I'm doing MD-simulations in a capacitor-like system: 2 charged electrodes with a dense ionic liquid in between (non-diluted) with periodic boundaries in 2 dimensions (so for the electrodes I get infinite planes (xy) ,charged).
I want to get the potential [itex]U(z)[/itex] along the z-axis (witch is perpendicular to the electrodes). This is the superposition of the linear electrode pot. and the potential contribution of the ions.
So I calculate the charge density [itex]\rho(z)[/itex] and use the poisson equation [itex]\nabla^2\Psi=-\frac{\rho}{\epsilon}[/itex] to get the potential.
Now, in the http://pubs.acs.org/doi/suppl/10.1021/jp803440q/suppl_file/jp803440q_si_002.pdf" (page 3 on top) this potential (in gaussian units) is written as [itex]\Psi(z)=-\frac{4 \pi}{\epsilon^*} \int_0^z (z-z') \rho(z')dz' [/itex]. Can someone explain/proof this expression?
Thanks,
corro
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