Obravnava preprostega dvo-dimenzionalnega modela vode s teorijo integralskih enačb in termodinamično perturbacijsko teorijo

Ogrin, Peter (author), Urbič, Tomaž (mentor)

Wertheimovo teorijo integralskih enačb (IET) in termodinamično perturbacijsko teorijo prvega reda (TPT) za asocirajoče tekočine smo aplicirali na vrtnični model vode. Vrtnični model je preprost dvodimenzionalni model vode, podoben Mercedes-Benz (MB) modelu vode. Prednost vrtničnega modela je, da je zaradi njegove preprostosti računsko učinkovit, pri čemer še vedno izkazuje večino anomalnih lastnosti vode. Molekule vode so pri vrtničnem modelu modelirane kot dvodimenzionalni Lennard-Jonesovi diski z dodanim potencialom vodikove vezi, v katerem so uporabljene trilistne funkcije vrtnic. Poleg računske učinkovitosti je vrtnični model vode enostavno prilagodljiv. V tem delu smo z uporabo teorije integralskih enačb in termodinamične perturbacijske teorije preučili strukturne in termodinamične lastnosti čistega vrtničnega modela vode. Uporabljeni sta bili dve različni parametrizaciji vrtničnega modela, ena, ki posnema MB model, in druga, ki ima lastnosti podobnejše eksperimentalni vodi. Rezultate, izračunane z uporabo IET in TPT, smo primerjali z rezultati, dobljenimi z Monte Carlo (MC) simulacijami. Ujemanje med porazdelitvenimi funkcijami voda-voda, dobljenimi z IET in MC, je pri zmerni in visoki temperaturi dobro. Termodinamične lastnosti so bile računane tako pri konstantnem volumnu kot pri konstantnem tlaku. IET in TPT semi-kvantitativno napovesta energijo, entalpijo, toplotno kapaciteto pri konstantnem volumnu in konstantnem tlaku, tlak, gostoto, temperaturni razteznostni koeficient in izotermno stisljivost. Ujemanje med rezultati teorij in MC simulacij je boljše pri višjih temperaturah in nižji zasedenosti prostora. Z uporabo termodinamične perturbacijske teorije smo določili tudi ravnotežno krivuljo para-tekočina ter kritično točko vrtničnega modela vode. Preučili smo tudi solvatacijo nepolarnega topljenca v vodi, modelirani z vrtničnim modelom. Z uporabo IET smo izračunali radialne porazdelitvene funkcije topljenec-voda in topljenec-topljenec, ki se pri zmerni in visoki temperaturi dobro ujemajo s porazdelitvenimi funkcijami, dobljenimi z MC. S termodinamično perturbacijsko teorijo smo izračunali tudi energijo ter prosto energijo prenosa nepolarnega topljenca v vodo; TPT kvalitativno napove temperaturne odvisnosti teh količin.

• Language: Slovenian
• Keywords: teorija integralskih enačb, termodinamična perturbacijska teorija, model vode, termodinamika, solvatacija nepolarnega topljenca
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FKKT - Faculty of Chemistry and Chemical Technology
• Year: 2021
• PID: 20.500.12556/RUL-129645
• COBISS.SI-ID: 79007491
• Publication date in RUL: 06.09.2021

Secondary language

• Language: English
• Title: Integral equation theory and thermodynamic perturbation theory study of simple two-dimensional water model

Abstract

We applied Wertheims's integral equation theory (IET) and first order thermodynamic perturbation theory (TPT) for associative liquids to rose model of water. The model is a simple two-dimensional water model similar to Mercedes-Benz water model. The advantage of rose model is its computational efficiency, while exhibiting majority of water's anomalous properties. In rose water model molecules are modeled as two-dimensional Lennard-Jones disks with added hydrogen-bonding potential, in which 3-petal rose functions are used. Besides computational efficiency rose water model is easily adjustable. In this work integral equation theory and thermodynamic perturbation theory were used to study structural and thermodynamic properties of pure water model. Two different parametrisations of rose model were used, one that mimics MB model and other with more experimental water-like properties. The results calculated using IET and TPT were compared to results obtained from Monte Carlo (MC) simulations. Agreement between water-water radial distribution functions obtained using IET and MC is good at moderate and high temperature. Thermodynamic properties were calculated both at constant volume and at constant pressure. IET and TPT semi-quantitatively predict energy, enthalpy, heat capacity at constant volume and at constant pressure, pressure, density, thermal expansion coefficient and isothermal compressibility. Agreement between results from the theories and MC simulations is better at higher temperature and lower packing fraction of molecules. Using thermodynamic perturbation theory we calculated vapor-liquid equilibrium line and critical point of rose water model. We also studied solvation of nonpolar solute in water modeled with rose water model. Using IET we calculated solute-water and solute-solute radial distribution functions, which at moderate and high temperatures are in good agreement with distribution functions obtained from MC. Using thermodynamic perturbation theory energy and free energy of transfer for nonpolar solute in water were calculated, TPT qualitatively predicts temperature dependencies of these quantities.

• Keywords: integral equation theory, thermodynamic perturbation theory, water model, thermodynamics, solavtion of nonpolar solute