Vpeljava interakcij posredovanih preko molekul topila v Poisson-Boltzmannovo teorijo

Electrostatic interactions are omnipresent in colloidal and biological systemsfor example they take place in aqueous solutions that contain mobile salt ions. Water plays a crucial role for the energetics of such systems. The ordering of water molecules changes the polarization and thus contributes to the electrostatic properties of the system. In particular, structural correlations between solvent molecules give rise to an inhomogeneous and non-local dielectric response that contributes to the energetics and the stability of biomacromolecules. This work is concerned with including solvent structures into mean-field electrostatics. It consists of three related subjects. In the first part we introduce a solvent model of interacting Langevin dipoles and incorporate that model into the Poisson-Boltzmann (PB) theory for an aqueous solution of monovalent ions in contact with a charged surface. The interplay between the electric double layer and the orientational ordering of solvent molecules determines the spatial decay of the solvent polarization. We showed that our model can result in a sign inversion of the electrostatic potential at a charged surface. The second part applies the PB model for a solvent of interacting Langevin dipoles to a mixed anionic/zwitterionic lipid layer. In the model the headgroups have ability to polarize the water in the headgroup region. The result is a positive electrostatic potential everywhere in the system. In the last part we introduce the Poisson-Helmholtz-Boltzmann theory, which adds to the electrostatic interaction potential between two ions an additional Yukawa potential. The latter accounts for solute-mediated ion-ion interactions. We demonstrate that these interactions can give rise to ion specific effects. One of the possible applications of the theory is related to the Hofmeister series. The presented analysis focuses on two systems. The first is the system of two charged surfaces embedded in a solution of only counterions, whereas the second system is one single charged surface in contact with a symmetric 1:1 electrolyte solution.Eno od pomembnejših področij celične biologije je razumevanje elektrostatskih interakcij med biološkimi strukturami (biopolimeri, membrane, celične organele). Večina bioloških struktur vsebuje prostorsko porazdeljen naboj. Elektrostatske interakcije med biomakromolekulami potekajo v vodnih raztopinah, ki vsebujejo eno in več-valentne majhne ione. V omenjenih sistemih igra voda pomembno vlogo. Le ta je močno polarizabilna in tako senči elektrostatske interakcije. Med molekulami vode delujejo vodikove vezi, katere omogočajo tvorbo lokalnih struktur. V bližini nabitih površin in ionov pride do urejanja molekul vode. Takšno urejanje spremeni polarizacijo vode in prispeva k elektrostatskim lastnostim sistema. Strukturne korelacije med vodnimi molekulami povzročijo nehomogene in nelokalne dielektričnosti. Le te so pomembne za razumevanje stabilnosti in dinamike bioloških struktur in interakcij med njimi. Prvi cilj doktorskega dela je vpeljava solvatacijskega modela interagirajočih Langevinovih dipolov v PB teorijo točkastih ionov ob naelektreni površini. Drugi cilj doktorskega dela je obravnava zwitterionsko lipidnih plast v stiku z monovaletnimi ioni in Langevinovimi dipoli, medtem ko je tretji cilj doktorskega dela je vpeljava neelektrostatskih interakcij v PB teorijo preko dodatnega odbojnega Yukawa potenciala med ioni v raztopini