Your browser does not allow JavaScript!
JavaScript is necessary for the proper functioning of this website. Please enable JavaScript or use a modern browser.
Open Science Slovenia
Open Science
DiKUL
slv
|
eng
Search
Browse
New in RUL
About RUL
In numbers
Help
Sign in
Elektrostatske lastnosti nanostruktur v modelih celičnih membran
ID
Drab, Mitja
(
Author
),
ID
Kralj Iglič, Veronika
(
Mentor
)
More about this mentor...
PDF - Presentation file,
Download
(28,74 MB)
MD5: 221818C8FDE86E2F3081E019B052FDD7
Image galllery
Abstract
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
Views:
1844
Downloads:
478
Metadata:
Cite this work
Plain text
BibTeX
EndNote XML
EndNote/Refer
RIS
ABNT
ACM Ref
AMA
APA
Chicago 17th Author-Date
Harvard
IEEE
ISO 690
MLA
Vancouver
:
Copy citation
Share:
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
Similar documents
Similar works from RUL:
Similar works from other Slovenian collections:
Back