Electric energies of a charged sphere surrounded by electrolyte

István P. Sugár; István P. Sugár

doi:10.3934/biophy.2021012

AIMS Biophysics

2021, Volume 8, Issue 2: 157-164. doi: 10.3934/biophy.2021012

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Electric energies of a charged sphere surrounded by electrolyte

István P. Sugár ^,

Neurology Department, Icahn School of Medicine at Mount Sinai, New York, NY 10029

Received: 21 January 2021 Accepted: 21 March 2021 Published: 24 March 2021

By using the recently generalized version of Newton's Shell Theorem [6] analytical equations are derived to calculate the electric potential energy needed to build up a charged sphere, and the field and polarization energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the electrolyte's ion concentration and the radius of the charged sphere. The work needed to build up the charged sphere, E_CC (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the electrolyte ions' increasing screening effect on the charge-charge interaction. The work needed to build up the charged sphere appears as a sum of the field and polarization energy of the electrolyte. At zero ion concentration the electrolyte's field energy is equal with E_CC while the polarization energy is zero. At high electrolyte ion concentrations (C > 10mol/m³) 50% of E_CC appears as the polarization energy of the electrolyte, 25% as the electrolyte's field energy inside the sphere and 25% as the electrolyte's field energy around the sphere.
- Debye length,
- screened potential,
- electrolyte's field energy,
- charge-charge interaction energy
Citation: István P. Sugár. Electric energies of a charged sphere surrounded by electrolyte[J]. AIMS Biophysics, 2021, 8(2): 157-164. doi: 10.3934/biophy.2021012

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Abstract

By using the recently generalized version of Newton's Shell Theorem [6] analytical equations are derived to calculate the electric potential energy needed to build up a charged sphere, and the field and polarization energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the electrolyte's ion concentration and the radius of the charged sphere. The work needed to build up the charged sphere, E_CC (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the electrolyte ions' increasing screening effect on the charge-charge interaction. The work needed to build up the charged sphere appears as a sum of the field and polarization energy of the electrolyte. At zero ion concentration the electrolyte's field energy is equal with E_CC while the polarization energy is zero. At high electrolyte ion concentrations (C > 10mol/m³) 50% of E_CC appears as the polarization energy of the electrolyte, 25% as the electrolyte's field energy inside the sphere and 25% as the electrolyte's field energy around the sphere.

Acknowledgments

The author is very thankful for Chinmoy Kumar Ghose.

Conflict of interest

The author declares no conflict of interest.

References

[1]	Gabriel JL, Chong PLG (2000) Molecular modeling of archaebacterial bipolar tetraether lipid membranes. Chem Phys Lipids 105: 193-200. doi: 10.1016/S0009-3084(00)00126-2
[2]	Chong PLG (2010) Archaebacterial bipolar tetraether lipids: Physico-chemical and membrane properties. Chem Phys Lipids 163: 253-265. doi: 10.1016/j.chemphyslip.2009.12.006
[3]	Almeida PFF (2009) Thermodynamics of lipid interactions in complex bilayers. BBA-Biophys 1788: 72-85.
[4]	Sugár IP, Thompson TE, Biltonen RL (1999) Monte Carlo simulation of two-component bilayers: DMPC/DSPC mixtures. Biophys J 76: 2099-2110. doi: 10.1016/S0006-3495(99)77366-2
[5]	Newton I (1999) A New Translation. The Principia: Mathematical Principles of Natural Philosophy Berkeley: University of California Press, 590.
[6]	Sugár IP (2020) A generalization of the shell theorem. Electric potential of charged spheres and charged vesicles surrounded by electrolyte. AIMS Biophys 7: 76-89. doi: 10.3934/biophy.2020007
[7]	Griffiths DJ (2005) Introduction to Electrodynamics Cambridge University Press.
[8]	Hasted JB, Ritson DM, Collie CH (1948) Dielectric properties of aqueous ionic solutions. Parts I and II. J Chem Phys 16: 1-21. doi: 10.1063/1.1746645
[9]	Gavish N, Promislow K (2016) Dependence of the dielectric constant of electrolyte solutions on ionic concentration: a microfield approach. Phys Rev E 94: 012611. doi: 10.1103/PhysRevE.94.012611
[10]	Suslick KS (2001) Encyclopedia of physical science and technology. Sonoluminescence and Sonochemistry Massachusetts: Elsevier Science Ltd, 1-20.

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