Elektrostatske lastnosti nanostruktur v modelih celičnih membran

Drab, Mitja (author), Kralj Iglič, Veronika (mentor)

Motivirani s fizikalnimi modeli elektricne dvojne plasti v nanostrukturah smo v doktorskem delu preucili modelski sistem nabitih fermionov med dvema vzporednima razsežnima ploskvama z gostoto nasprotnega elektricnega naboja. Zanimalo nas je, ali bi omejitve zasedbenih stanj, ki jih fermionom predpisuje Fermi- Diracova statistika, v limiti nizkih temperatur vodile do nastanka difuzne elektricne plasti, ki ga pri visokih temperaturah predvideva Poisson-Boltzmannova teorija ionskih raztopin v stiku z nabito površino. Po ustaljenih postopkih statisticne termodinamike smo izpeljali izraz za Helmholtzevo prosto energijo modelskega sistema in poiskali globalno termodinamsko ravnovesje z metodo Lagrangevih multiplikatorjev. Z upoštevajnem robnih pogojev elektronevtralnosti smo numericno rešili ustrezne Euler-Lagrangeve enacbe za elektricni potencial in številsko gostoto delcev med nabitima ploskvama v realni in kompleksni domeni ter jim dolocili ustrezne približke z analiticnimi funkcijami. V limiti nizke temperature so delci tvorili difuzno dvojno plast, ki se je v limiti visoke temperature približala rezultatom znane Poisson-Boltzmannove teorije. Dolocili smo odvisnost gostote Helmholtzeve proste energije od razmika med ploskvama in ugotovili, da je v realni domeni sila med ploskvama vedno odbojna. V kompleksni veji smo dolocili fazni prostor fizikalno smiselnih rešitev in poiskali parametre sistema, pri katerih lahko pride do privlaka med enako nabitima ploskvama. Izpeljali smo izraza za diferencialno kapacitivnost sistema, ki se kvalitativno razlikujeta od Poisson-Boltzmannove napovedi, a se nahajata znotraj istega velikostnega razreda.

• Language: Slovenian
• Keywords: nanostrukture, fizikalni modeli, termodinamika, celične membrane, elektricna dvojna plast, superkondenzatorji, Fermi-Diracova distribucija
• Work type: Doctoral dissertation
• Typology: 2.08 - Doctoral Dissertation
• Organization: BF - Biotechnical Faculty
• Year: 2018
• PID: 20.500.12556/RUL-102311
• COBISS.SI-ID: 919927
• Publication date in RUL: 17.08.2018

Secondary language

• Language: English
• Title: Electrostatic properties of nanostructures in cell membrane models

Abstract

Motivated by the physical models of the electric double layer in nanostructures we investigated a model system composed of charged fermions trapped between two parallel oppositely charged planar surfaces. We inquired wether the restrictions imposed on the fermions by the Fermi-Dirac statistics would form a diffuse double layer in the limit of low temperatures, which is predicted in the high temperature limit by the acknowledged Poisson-Boltzmann theory due to entropic mixing. By standard statistical mechanics derivations we arrived at the Helmholtz free energy of the model system and found its global thermodynamic minimum by means of undetermined Lagrange multipliers. Taking into accout the boundary conditions of electroneutrality we present a rigorous numerical solution for electric potential and particle number density between the charged surfaces in the real and complex domains. We also derived approximate analytical solutions. In the low-temperature limit the particles indeed formed a diffuse double layer that approached the results obtained by the Poisson-Boltzmann theory in the hightemperature limit. We also derived the dependency of Helmholtz free energy on the separation of the charged surfaces and concluded that the force between them is always repelling in the real-solutions regime. In the domain of complex solutions we explored the phase-space of the problem and found parameters for which the force between surfaces is attractive. We further derived the expression for differential capacitance that qualititavely differs the high-temperature limit but agrees with it magnitude-wise

• Keywords: nanostructures, physics models, thermodynamics, cellular membranes, electric double layer, supercapacitors, Fermi-Dirac distribution