doktorska disertacija
Abstract
Motivirani s fizikalnimi modeli električne dvojne plasti v nanostrukturah smo v
doktorskem delu preučili modelski sistem nabitih fermionov med dvema vzporednima
razsežnima ploskvama z gostoto nasprotnega električnega naboja. Zanimalo
nas je, ali bi omejitve zasedbenih stanj, ki jih fermionom predpisuje Fermi-
Diracova statistika, v limiti nizkih temperatur vodile do nastanka difuzne električne
plasti, ki ga pri visokih temperaturah predvideva Poisson-Boltzmannova
teorija ionskih raztopin v stiku z nabito površino. Po ustaljenih postopkih statistične
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
numerično rešili ustrezne Euler-Lagrangeve enačbe za električni potencial in številsko
gostoto delcev med nabitima ploskvama v realni in kompleksni domeni ter
jim določili 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. Določili 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
določili 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.
Keywords
nanostrukture;fizikalni modeli;termodinamika;celične membrane;električna dvojna plast;superkondenzatorji;Fermi-Diracova distribucija;disertacije;
Data
Language: |
Slovenian |
Year of publishing: |
2018 |
Typology: |
2.08 - Doctoral Dissertation |
Organization: |
UL ZF - University College of Health Studies |
Publisher: |
[M. Drab] |
UDC: |
620.3:577.352(043.3)=163.6 |
COBISS: |
919927
|
Views: |
34 |
Downloads: |
6 |
Average score: |
0 (0 votes) |
Metadata: |
|
Other data
Secondary language: |
English |
Secondary title: |
Electrostatic properties of nanostructures in models of cellular membranes |
Secondary 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 from the high-temperature
limit but agrees with it magnitude-wise. |
Secondary keywords: |
nanostructures;physics models;thermodynamics;cellular membranes;electric double layer;supercapacitors;Fermi-Dirac distribution; |
Type (COBISS): |
Doctoral dissertation |
Study programme: |
0 |
Embargo end date (OpenAIRE): |
1970-01-01 |
Thesis comment: |
Univ. v Ljubljani, Biotehniška fak. |
Pages: |
VI, 68 f. |
ID: |
10951716 |