Vpliv velikosti ionov na razporeditev elektrolita ob nabiti steni. Primerjava Poisson-Boltzmannove teorije in simulacij Monte Carlo.

Ravnik, Vid (author), Lukšič, Miha (mentor)

Okoli nabitih površin (npr. makromolekule, biološke membrane, kovinske elektrode) se v raztopinah elektrolitov tvori električni dvosloj. V tem delu smo uporabili modificirano različico Poisson-Boltzmannove teorije (MPB), ki velikost ionov vpelje preko mrežnega modela idealnega Coulombskega plina. Študirali smo razporeditev ionov ob ravni, neskončno veliki nabiti plošči. Numerične rešitve MPB smo primerjali z rezultati kanoničnih simulacij Monte Carlo (MC), v katerih smo uporabili t.i. primitivni model raztopine +1:-1 elektrolita. Potek elektrostatskega potenciala in koncentracij ionov elektrolita blizu nabite stene je odvisen od velikosti ionov ter gostote naboja na steni. Rezultati MC in MPB metod za vrednosti koncentracije protiionov blizu nabite stene so različni. Opaženo razliko pripisujemo različnim modelom, ki jih MPB in MC metodi uporabljata za opis velikosti delcev (primitivni model elektrolita za MC ter mrežni Coulumbski plin za MPB). Pri MPB teoriji za močno nabite stene in velike delce elektrolita je koncentracija ob steni mnogo manjša v primerjavi z manjšimi delci, vendar tvori nasičen sloj v katerem je koncentracija večinoma konstantna. Pri rezultatih simulacij MC pa za podobne primere lahko opazimo drug sloj ionov, kjer se središče modelnih ionov nahaja en in pol premera stran od stene, koncentracija ionov v prvem sloju pa je neodvisna od velikosti delcev.

• Language: Slovenian
• Keywords: Električni dvosloj, Poisson-Boltzmannova teorija, kanonične simulacije Monte Carlo
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Year: 2019
• PID: 20.500.12556/RUL-109546
• COBISS.SI-ID: 1538314947
• Publication date in RUL: 05.09.2019

Secondary language

• Language: English
• Title: The effect of ion size on the electrolyte distribution near a charged wall. A Poisson-Boltzmann and Monte Carlo study.

Abstract

Charged objects, e.g. membranes, macromolecules, metal surfaces, in contact with an electrolyte solution form an electric double layer. A modified free energy functional, valid within the Poisson-Boltzmann (PB) theory, obtained using a lattice version of the ideal Coulomb gas for the electrolyte, was used to account for the size of the electrolyte ions in contact with an infinite charged wall. The modified PB equation (MPB) was solved numerically. The results were compared with Canonical Monte Carlo (MC) simulations where a primitive +1:-1 model electrolyte was used. The electrostatic potential and concentration profile near a changed wall depends upon the size of the ions and the charge density of the wall. Close to the wall the disagreement between the MPB and MC results is magnified. This is attributed to differences in the models used in simulations and theory (primitive model vs. lattice Coulombic gas). For walls with high surface charge densities and for big ions, the concentration profile of the counterions obtained via MPB plateaus near the wall as it forms a saturated layer. The results of the MC simulations for similar cases sometimes show a second layer of ions one and a half diamater away from the wall and a much higher maximum concentration than predicted by the MPB theory.

• Keywords: Electric double layer, Poisson-Boltzmann theory, canonical Monte Carlo simulation