Senčenje medionskih interakcij v nabitem adsorbentu – uporaba replika Ornstein-Zernikovih enačb

Mlakar, Tibor (author), Hribar Lee, Barbara (mentor)

V sklopu magistrskega dela smo teoretično obravnavali proces adsorpcije elektrolita v nabitem adsorbentu. Sistem (poimenovan sistem s šablono) je bil na začetku sestavljen iz treh komponent: adsorbenta, adsorbata in šablone. V fazi zamrznitve smo šabloni omogočili, da zapusti adsorbent in postane del adsorbata, ki je imel splošno razmerje nabojev ionov. Tekom celotnega procesa je sistem navzen ostal elektronevtralen, v podsistemih pa je prišlo do presežka oziroma primankljaja naboja. Nadalje smo se poslužili teorije replika Ornstein-Zernikovih enačb, s katero smo matematično ponazorili sistem kot set sklopljenih integralskih enačb. Bistvo je bila analitična obravnava omenjenega seta enačb, posledično izpeljava rigorozne renormalizacijske sheme za sistem s šablono. Z reševanjem smo generirali oblike porazdelitvenih funkcij za vse možne pare delcev. Le-te smo primerjali z rešitvami pretekle študije, kjer je bil sistem sestavljen iz adsorbenta in adsorbata. Ker sta bila oba podsistema sama po sebi elektronevtralna, so ga avtorji poimenovali elektronevtralni sistem. Imel je fiksirano razmerje nabojev adsorbata, saj je modeliral 1-1 elektrolit. Ker je bil naš sistem splošnejši (poljubno razmerje nabojev adsorbata) smo primerjavo izvedli, ko je bilo razmerje nabojev zanj ena. Izrisali smo oblike q^{ab}_{ij} krivulj glede na razdaljo od referenčnega delca. Ker nas je prav tako zanimal vpliv razmerja nabojev adsorbata na porazdelitvene funkcije sistema s šablono, smo le-te narisali še za drugačna razmerja. S pomočjo slik je bilo kvalitativno razvidno ujemanje oz. neujemanje med obema sistemoma. V skladu s pričakovanji so rešitve obeh sistemov v večini primerov zelo dobro sovpadale. Prišlo pa je tudi do nekoliko večjih razlik, ki so bile utemeljene glede na zasnovo posameznega sistema. Oblike porazdelitvenih funkcij sistema s šablono se pri različnih izbirah parametrov niso bistveno razlikovale, z izjemo nekoliko hitrejše oz. počasnejše konvergence proti ničli. S spreminjanjem razmerja nabojev adsorbata smo pokazali, da imajo krivulje analogen trend obnašanja v odvisnosti od le-tega.

• Language: Slovenian
• Keywords: replika Ornstein-Zernikova enačba, adsorpcija, renormalizacija, sistem s šablono, porazdelitvene funkcije, ionske interakcije
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Year: 2022
• PID: 20.500.12556/RUL-141446
• COBISS.SI-ID: 133083139
• Publication date in RUL: 29.09.2022

Secondary language

• Language: English
• Title: Screening of ionic interactions in a charged adsorbent - the application of Replica Ornstein-Zernike equations

Abstract

As part of the master's thesis, we theoretically discussed the process of electrolyte adsorption in a charged adsorbent. The system (called templated system) initially consisted of three components: adsorbent, adsorbate and template. During the freezing phase, the template was allowed to leave the adsorbent and become part of the adsorbate, which had a general ion charge ratio. During the entire process, the external system remained electroneutral, but the subsystems had an excess or deficit of charge. Furthermore, we used the replica Ornstein-Zernike equation theory, with which we mathematically illustrated the system as a set of coupled integral equations. The point was the analytical treatment of the mentioned set of equations, resulting in the derivation of a rigorous renormalization scheme for the templated system. By solving, we generated the shapes of the distribution functions for all possible pairs of particles. We compared them with the solutions of a previous study, where the system consisted of an adsorbent and an adsorbate. Since both subsystems were intrinsically electroneutral, the authors named it the electroneutral system. It had a fixed adsorbate charge ratio as it modeled a 1-1 electrolyte. Since our system was more general (arbitrary adsorbate charge ratio), we performed the comparison when the charge ratio for it was one. We plotted the shapes of the q^{ab}_{ij} curves depending on the distance from the reference particle. Since we were also interested in the influence of the ratio of adsorbate charges on the distribution functions of the templated system, we plotted them for other ratios. With the help of pictures, it was possible to clearly see the match or mismatch between the two systems. As expected, the solutions of both systems were very similiar in most cases. However, there were also some major differences, which were based on the design of the individual system. The shapes of the distribution functions of the templated system did not differ significantly with different choices of parameters, the exception being slightly faster or slower convergence towards zero. By changing the ratio of adsorbate charges, we showed that the curves have an analogous trend of behavior depending on it.

• Keywords: replica Ornstein-Zernike equation, adsorption, renormalization, templated system, correlation functions, ion interactions