Summary_eng (Статистическое описание многочастичных эффектов в классических ион-молекулярных системах)

National Research University Higher School of EconomicsManuscript copyrightBudkov Yury AlekseevichStatistical description of the many-body eects in classicalion-molecular systemsDissertation summaryfor the purpose of obtaining academic degreeDoctor of Science in Applied Mathematics HSEMoscow 2019IntroductionRelevance of a thesis work and degree of the problem development. Up to dateion-molecular systems (such as ionic liquids, zwitterions, polyelectrolytes, dielectric polymers, etc.)are very perspective for the eld of the so-called smart materials development, that are materials,which physical-chemical properties could be controlled by the change of the dierent physical stimuli(such as temperature, pH, electric eld, etc.) within some narrow intervals.

Recently, coarse-grainedmodelling (CGM) methods have been widely used for the modelling of the equilibrium properties ofthe ion-molecular systems. CGM is based on the idea that separate atomic (molecular) groups arecombined into large particles, interactions between which are described by the eective potentials.Despite of the certain success, achieved in reduction of the computational working time while usingMD simulation with coarsening of the real structure of the molecules in comparison with theirfull-atomistic representation, modelling of the systems of a large number of particles (even with thecoarsened structure) under the conditions of the condensed phase is still a suciently computationalexpensive.

On the other side, for the modern chemical engineering it is necessary to posses suchcomputational tools, which allow one to predict behavior of the thermodynamic parameters in thefast and eective way. Methods of modern statistical physics, such as eld-theoretic methods,classical density functional theory, mean-eld theory, etc., well-proven at the description of thethermodynamic properties of simple liquids and synthetic polymers, could, in principle, take onthe role of such tools. However, for application of such approaches for the description of the ionmolecular systems at the equilibrium in the bulk and at the phase boundaries, it is necessary to takeinto account not only the universal intermolecular interactions (dispersion and excluded volumeinteractions), but also a peculiarity of the molecular structure of components, such as multipolemoments, electronic polarizability, hydrophobicity/hydrophilicity, congurational asymmetry of themolecule, etc.

Still, at the moment only rst steps have been made in that direction. It is worthnoting, that statistical methods, based on the concept of self-consistent eld, in comparison with thecoarse-grained MD simulation methods, are highly underestimated among modern physic-chemistsand material scientists because of their mathematical complexity, on the one side, and the lack ofthe accessible software for the general public users, on the other side. There is a lump of problemsdown this road waiting for solution, some of them are presented in this work.Lately in dierent electrochemical applications it has become necessary to study the inuence ofsmall impurities (co-solvents) in the electrolyte solutions on the properties of the electrical doublelayer, occurring at the metal electrode/liquid electrolyte interface.

The main question, which bothers researches is: ”How do properties of the molecules of impurities (dipole moment, polarizability,eective size, etc.) aect on the most important electrochemical characteristic dierential capacitance of the electrical double layer?” From general considerations it is clear, that presence of theelectric eld gradient, appearing due to the screening of the electrode charge by counterions, leadsto the attraction of the polar/polarizable particles of the impurity from the bulk solution to theelectrode surface, driven by dielectrophoretic force, which, in turn, leads to the increase in the localdielectric permittivity and, consequently, to the increase in dierential capacitance. To investigateraised question, it is necessary to formulate self-consisted eld theory, taking into account explicitlypresence of the co-solvent molecules in the solution with constant dipole moments and/or electronicpolarizability. On the other hand, latest experimental research of the electrical double layer properties, occurring at the ionic liquid/metal electrode interface, show that even small impurities of thepolar solvents in the bulk of ionic liquid, such as acetonitrile and water, could aect on the valueof the dierential capacitance.

As opposed to electrolyte solutions, for correct description of theelectrical double layer properties in ionic liquids with small impurities of the polar solvents, it isnecessary to consider, besides electrostatic interactions and excluded volume interactions betweenions and polar molecules, short-range specic interactions (which range is about several eectivemolecular sizes), associated, for example, with the hydrogen bonding, π − π stacking, asymmetryeect of ions, their hydrophobic/hydrophilic properties, etc.

However, until recently, there have notbeen made even any eorts in development of the phenomenological theory of the electrical doublelayer for ionic liquids, taking into account presence of the polar molecules of the impurity in the bulksolution with account for the short-range specic interactions between the mixture components.2Recent advances in experimental studies of the dierent organic compounds, such as proteins,betaines, zwitterionic liquids, etc., consisting simultaneously of the positively and negatively chargedionic groups, located at rather long distances (∼ 10 nm), oer a challenge to statistical physicsto develop analytical approaches to describe their thermodynamic properties. The fundamentaldierence of such systems from classical polar small molecules, such as water and aliphatic alcohols,is that they should not be modelled as particles, carrying point-like dipoles.

Instead, they must beconsidered as pairs of bonded oppositely charged ionic groups, located at the xed or uctuatingdistances between each other, incorporating to the theory another length scale, associated with theeective distance between ionic groups. Moreover, since in practice such systems are located inthe polar solvent (primary in water) with the addition of dierent electrolytes, it is necessary todevelop a model of the electrolyte solution with the additive of the polar particles, described as ionicpairs with uctuating distances between charged centers.

Such an ”nonlocal” theory could allowone to solve a range of the fundamental problems, existing in the polar uids theory. Firstly, suchmodel allows one to describe behavior of the point charge potential in the medium of the electrolytesolution with the addition of polar particles at the scale of their eective size. Secondly, this theorymust be devoid of the ”ultraviolet” divergences of the electrostatic free energy of the pure polaruid, happening in the existing ”local” theories.Nowadays statistical thermodynamics of the dielectric polymers, i.e.

polymers, carrying permanent dipole moments on their monomers or having suciently large polarizability (such as ionomers,polymeric ionic liquids, weak polyelectrolytes, etc.) is a poorly developed area of the polymerphysics. One of the underexplored, but, at the same time, extremely important for applicationsproblems of dielectric polymer physics is connected with the investigation of the conformationalbehavior of the weak polyelectrolytes chains in the dilute solutions. In the dilute solutions of weakpolyelectrolytes it is thermodynamically favorable for charged monomers and counterions to formsolvent-separated ionic pairs, so the letter could be considered as dipoles, freely rotating around themacromolecular backbone.

If macromolecule is in the coil conformation, then dipoles, located in average at suciently large distance between each other, suer the eective Keesom attraction. Thus,under temperature decrease polymer chain must shrink due to the Keesom attraction of monomersand, ultimately, undergo a transition from the conformation of expanded coil to the conformation ofsuciently compact globule. However, it is worth noting that mechanism of the dipole-dipole interactions for the suciently dense globule can not be restricted to the representation of the pair-wiseKeesom interaction.

Instead, one must account for the dipole correlations at the many-body level.Whereas there are models, describing mentioned collapse of macromolecule qualitatively, all of themconsider the dipole correlations as pair-wise, i.e. at the level of Keesom interaction. Thus, there is afundamental problem of the consideration of the dipole correlations of macromolecule monomers ofthe weak polyelectrolytes at the many-body level.

On the other side, when a polymer chain adoptsconformation of suciently dense globule, dipole moments on monomers can not be described aspoint-like dipolar particles, as for the case of the coil conformation. On the contrary, in that case,it is necessary to take into account presence of the ionic groups on the monomer, located at somedistance. This description, obviously, must lead to the new regimes of the conformational behaviorof the weak polyelectrolytes macromolecules relative those, predicted by previously formulated localtheories.Another important problem of statistical physics of dielectric polymers is related to the investigation of the external electric eld inuence on the conformational behavior of the dielectricmacromolecules in dilute solutions. Indeed, possibility to control the conformational state of themacromolecules in solutions by the change of the electric eld strength is very attractive for moderntechnological applications, considering relative simplicity of its technical implementation.

As is wellknown, conformations of xed in space polyelectrolytes, carrying electric charges on their monomers,are strongly sensitive to the external electric eld. However, as it was mentioned above, there is awide class of pointed above dielectric polymers, which monomers are electrically neutral, but able toobtain dipole moment in the external electric eld due to the dierent mechanisms of polarizability.Due to the chain connectivity of the polarizable monomers in exible polymer chain, application ofthe electric eld must lead to not only macroscopic polarisation of the polymer, as in the case of3liquid dielectrics, consisting of chemically unbounded polarizable particles, but also to the substantial change of its conformational condition due to the electrostriction eect. However, unlike thepolyelectrolytes, carrying electric charge on the monomers, change of the conformational state ofthe dielectric polymers in the external electric eld must be suciently weaker.