PHYSICS AND MATHEMATICS

ДИФУЗ1Я В ДИМЕТИЛ-1М1ДАЗОЛ1УМ ХЛОРИД-ТОЛУОЛ1 НА КОРОТКИХ 1НТЕРВАЛАХ

ЧАСУ

Атамась Н.

КиХвський нацюнальний унгверситет шет Тараса Шевченка, УкраХна 1нститут ф1зично'1 xiMii ПольськоХ академИ наук, Польща

д.ф.-м.н., с.н.с., Матушко I.

Кшвський нацюнальний ymiверситет iменi Тараса Шевченка, УкраХна

к. х. н., с. н.с. Таранюк Г.

Мiжнародний европейський yнiверсиmеm, УкраХна

THE DIFFUSION AT SHORT-TIME INTERVALS IN DIMETHYL-IMIDAZOLIUM CHLORIDE-

TOLUENE

Atamas N.

National Taras Shevchenko University of Kyiv, Kyiv, Ukraine Institute of Physical Chemistry of the Polish Academy of Sciences, Poland

PhD, Senior Researcher Matuschko I.

National Taras Shevchenko University of Kyiv, Kyiv, Ukraine

PhD, Senior Researcher, Taranyik G.

International European University, Ukraine DOI: 10.5281/zenodo.7014328

АНОТАЦ1Я

В робот методом МД, що реалiзовувався з використаннням модифжованого програмного пакету DL_POLY_4.09, розраховаш на проаналiзованi часовi залежносп функцп середньоквадратичного вщхи-лення для компонент юнно! рщини та толуолу при Т=400К. На основi отриманих даних побудоваш мо-дельнi уявлення для опису процеав дифузii, як1 визначають процеси релаксаци у дослвджуванш система

ABSTRACT

In the work, using the MD method, which was implemented using the modified software package DL_POLY_4.09, the MSD functions for the components of the ionic liquid dimethylimidazolium chloride and the dissolved toluene molecule at T=400K were calculated for the analyzed. On the basis of the obtained data, model representations were built to describe the processes of diffusion at small time intervals in the liquid, which determine the processes of relaxation in it.

Ключовi слова: зелеш технологи, юнт рщини, дифузiя, середньокадратичне вщхилення, релаксащя.

Keywords: green technologies, ionic liquids, diffusion, root mean square deviation, relaxation.

In connection with the need for a gradual transition to "green technologies" in the petrochemical industry, modern theoretical and practical tasks were formed, which are closely related to the extraction of aromatic hydrocarbons. A new class of solvents that are considered promising to replace organic solvents in industrial processes are ionic liquids (IL), which are liquid salts consisting of large, mostly organic, cations and a wide variety of anions. The positive properties of ionic liquids are a fairly wide range of temperatures within which they are in a liquid state, low vapor pressure, and reducibility, and there is an opportunity to create an ionic liquid as a solvent in the case of a specific extraction problem. Thanks to this, the use of IL in petrochemicals in experimental production has recently attracted increasing interest. However, there are still no reports on the processes of industrial extraction of aromatic hydrocarbons from oil using ILs, since for many of them their structural and dynamic properties have

not been finally clarified and the features of the interaction of ILs with aromatic hydrocarbons depending on the concentration and properties of aromatic hydrocarbons have not been clearly defined. Therefore, the purpose of this work is a detailed study of the micro-characteristics of the dissolution process and the dynamics of systems based on ILs using the MD method. Molecular simulations allow getting a clear idea of the processes of interaction between the components of the liquid system and the kinematic processes in it. Considering that room temperature ionic liquids (RTIL) with a room temperature melting point deserve special interest from an industrial point of view. One of the classes of RTILs is ionic liquids based on the dimethyl imidazo-lium cation (dmim+). With this in mind, the study of systems for the extraction of aromatic hydrocarbons based on IL was carried out for liquids based on this particular cation. At the same time, taking into account the ionic character of ionic liquids, the "polarity of an

aromatic hydrocarbon" should be perceived as a generalized property for extraction, which in turn depends on all intermolecular interactions and diffusion in the system. To clearly determine the mechanisms of interaction between aromatic hydrocarbons, for example, toluene, and the components of an IL at the micro level allows the study of infinitely diluted systems. The use of only one solute molecule makes it possible to exclude from consideration the interaction of solute molecules with each other. All of the above determined the purpose of the research, namely, the analysis of the influence of the properties of aromatic hydrocarbons using the example of toluene on the structural, dynamic, and energetic properties of an infinitely dilute solution of dimethyl imidazolium chloride (dmim+/Cl-) at T=400K using the MD method. At the same time, the following complex tasks were solved: to analyze and

U UL-D + UCoulomb

determine the mechanisms of local structure formation and structural and dynamic properties of systems ionic liquid (1,3-dimethyl imidazolium - chloride (dMim+/Cl-) - toluene molecule T=400K; to build model representations of diffusion mechanisms and its models for components of a liquid system based on dimethyl imidazolium - chloride (dmim+/Cl-) - toluene.

Research methods and model concepts

When researching a system based on an ionic liquid based on a dimethyl imidazolium (dmim+) cation, it was taken into account that the strongest intermolecular interaction is observed in systems containing chlorine anions. Intermolecular interaction in the dimethyl im-idazolium chloride-toluene system at T=400K was described using the effective potential of intermolecular interaction, which can be represented as the sum of the Lennard-Jones and Coulomb components [1]:

r

V 'J y

O"„

r

V 'J

+

z

qqj

riJ

(1)

where Oj, % and q are the parameters and are obtained based on model representations and from the analysis of experimental data. The parameters of the potential and for the interaction between the atoms of the solvent molecules and the atoms of the solute molecules are calculated using the Lorenz-Bartlo combination rule. In the case of studying the influence of solute molecules on the characteristics of solutions of ionic liquids based on the dmim+ cation, the values of atomic charges were used, and the parameters of the potentials are given in the work [2]. The values of the parameters for the toluene molecule are given in [3]. The molecular dynamics (MD) method was implemented using the DL_POLY _4.05 software package with a time step of 2fc and periodic boundary conditions. Atoms of molecules of cations and ions were solid, charged model systems with fixed geometry. The volume of the unit cell corresponded to the experimental values of the density of the ionic liquid at T=400K. Stabilization of the system in the NVT ensemble was carried out using the Berendsen thermostat. Close-range electrostatic interaction at short distances was achieved using point charges on each atom of the system. The long-range electrostatic interaction between particles was taken into account using Ewald summation. Calculations

were carried out according to the following scheme: stabilization of the studied system was achieved in 1*106 steps, after which 1*106 steps of calculations were carried out. All calculations were performed for a system consisting of 192 chlorine ions, 192 dimethyl imidazolium cations, and one solute molecule at a temperature of T=400 K. Radial distribution functions (RDFs) were constructed based on the obtained data, and dynamic properties of the studied systems were analyzed.

Results and their analysis

RDFs for the probability of interaction of toluene with the components of the dmim+/Cl- (Fig. 1) show that free space is formed between the hydrogen atoms of the toluene molecule and the components of the IL, the average size of which is ~ (3.5 - 4.6) A. Taking into account the fact that the toluene molecule can be represented as a ring with a diameter of ~10.15A, RDFs confirm that the dissolution of toluene in dmim+/Cl- leads to the rupture of the network of HB between the components of the IL and its significant reorganization of local structure. This, in turn, violates the percolation properties of the network of hydrogen bonds in dmim+/Cl- and leads to the compaction of the IL structure.

R (A)

Fig. 1 RDFs of the dmim+/Cl~ - toluene system at T = 400 K: (1)- Htolu - Ndmim, (2) - CH3tolu -Ndmim, (3) -

Htolu - Cl-, (4)- CH3tolu - Cl-.

The movement of particles in the studied system can be described using the diffusion equation [4]:

DV2 P(r, t) = dP(r> %

the solution of which has the form:

( . \ (

P (r, t) = 4xr1

2^r2(t})JeXP^ lx(r2(t})

3r2

(2)

(3)

here \r / - is the second spatial moment of the

function P(r, t) , which determines the mean square particle displacement (MSD). A linear time depend-

ence \r / at short time intervals indicates Brownian

particle dynamics. In this case, diffusion can be calculated as [5]:

(r2) = 6Dt, (4)

where D - is the diffusion coefficient. Fig. 2 presents the MSDs for the dmim+/Cl- _ toluene system at T=400K. The functions of dmim+ cations and Cl- anions in the studied liquid systems coincide at time intervals t<2.5ps. Given that linear growth over short time intervals corresponds to Brownian dynamics, we can consider the movement of dmim+/Cl- components at times

t < 2.5 ps to be Brownian. In this case, the motion of the IL components occurs due to ballistic collisions and the diffusion of IL components can be determined using the expression (4), where D is the value of the diffusion coefficient at short time intervals.

The change in the growth rate of the function for the system components at time intervals t >2.5 ps corresponds to the change in the micro-dynamic properties of the system. Namely, in this case, there is a transition from direct from ballistic collisions to the slowed-down averaged motion of particles in the liquid at times t >2.5 ps. The values of the functions for both Cl- and dmim+ anions have different time dependences, which indicates a change in the nature of the motion of IL components and a change in the nature of diffusion processes in this system depending on the properties of the dissolved substance. The qualitative analysis of the dynamic heterogeneities and diffusion models in the liquid can be performed by examining parameter a (Fig.2b) in log(r2(t)) ~ a log t (<r2(t)» = Cta, whose values reveal how the diffusion of particles deviates from the Brown diffusion. The obtained values of the parameter a for all components of the system under study are less than unity, which indicates a slow sub-diffuse mechanism of motion of both the IL components and the solute.

2

v

15 20 t,ps

"2.

v

1-

a = 0.5

log t

Fig. 2 Time dependence of the mean square deviation \r / for cations dmim+ (1), anions Cl- (2) and toluene (3) in the dmim+/Cl- -toluene system at T = 400K

That is, in this case, small changes dominate the dynamic properties of the system, and the movement of IL components participating in ballistic collisions slows down, which is confirmed by the results obtained for IL components. The analysis of chlorine anions, according to the data in Fig.2, shows that in this system, the local structure of the liquid is rearranged already at small times due to the rupture of the network of hydrogen bonds, and Cl- anions, in this case, can move for some time independently. IL dmim+/Cl- can be considered as a mixture of large (dmim+) and small particles (Cl-) with a mass ratio

Malrge 1Msmall = Mdmim 1 MCl = 27 , and stacteal

rearrangement in dmim+/Cl- is determined by relaxation processes at short times. The result obtained indicates the existence of at least two time intervals within which the studies are described by different model representations.

Conclusion

The structural and dynamic features of infinitely diluted liquid systems "ionic liquid - dmim+/Cl- - toluene" were investigated using the method of molecular dynamics. Based on the obtained data, a model is proposed to describe diffusion processes in the studied systems and it is shown that:

_ at times shorter than 25 ps, the movement of IL component and dissolved molecules toluene can be rep-

resented within the framework of the same model representations, namely, as a result of inelastic collisions with IL components.

_ at times longer than 25 ps dynamic inhomogene-ity in the motion of a toluene molecule in the dmim+/Cl-system is associated with a qualitative change in the dynamics of the system and a change in the mechanism of diffusion of solute molecules.

References

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3. Jorgensen W. L., Swenson C. J. Optimized intermolecular potential functions for liquid hydrocarbons // Journal of the American Chemical Society. -1984. - 106.22. - P.6638-6646.

4. Forester T.R. The DL-P0LY-4.0. Daresbury Laboratory.

http://www.scd.stfc.ac.uk/SCD/44516.aspx

5. Brilliantov N.V., Poschel T. Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog // Chaos: An Interdisciplinary Journal of Nonlinear Science. - 2005. - 15. - P. 026108. https://aip.scitation.org/doi/10.1063/1.1889266

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