Electrical Conductivity of Methylimidazolium Hexafluorophosphate

Article Cite This: J. Phys. Chem. C 2017, 121, 24434-24443

pubs.acs.org/JPCC

Electrical Conductivity of Methylimidazolium Hexafluorophosphate Ionic Liquid in the Presence of Colloidal Silver Nano Particles with Different Sizes and Temperatures Farid Taherkhani*,† and Samaneh Kiani‡ †

Department of Chemistry, Sharif University of Technology, Tehran 11365-11155, Iran Department of Management, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

‡

ABSTRACT: Colloidal nanoparticle could be used for recognition location of tumors and cancer tissue. A simulation of molecular dynamic for colloidal silver nanoparticles (Ag NPs) based on density functional theory (DFT) potential parametrization with different sizes in 1-ethyl-3-methylimidazolium hexafluorophosphate [EMim][PF6] ionic liquid was performed. Then, using Green Kubo formalism, diffusion coefficient for Ag NPs in IL and in the gas phase was calculated. We also calculated diffusion coefficients of anions and cations for pure IL and IL in the presence of different sizes of Ag NPs at different temperatures. The findings showed that the diffusion coefficient of anions and cations increases in proportion with temperature and the sizes of colloidal Ag NPs. Next, cationic transference number for pure IL and IL in the presence of Ag NPs, electrical conductivity of pure IL, and IL with different sizes of Ag NPs were calculated and compared. After that, the calculated diffusion coefficient and electrical conductivity for pure IL were compared to that of other simulation and experiment; they accorded well. Anions and cations diffusion coefficient and electrical conductivity of IL are more for colloidal Ag NPs than those of pure IL. Electrical conductivity caused by ions of IL in the presence of colloidal Ag NPs went up as the temperature and size increased. The results of simulated molecular dynamic show that the electrical conductivity mechanism for IL in the presence of colloidal Ag NPs with temperature and size of colloidal Ag NPs increases by the diffusion mechanism.

1. INTRODUCTION The property common of ionic liquids (ILs) is ionic conductivity because they contain mobile ions.1−4 An accurate prediction of the electrical conductivity of ILs can be useful in many applications. There are many proposed applications for ILs, among them we can name those of replacement of organic solvents, charge transport in energy generators, as solvents for synthesis and stabilization of metallic nanoparticles (NPs),5−11 and electrolytic medium in metals and semiconductors electrodeposition processes.12−14 ILs are suitable as solvents or inert electrolytes in electrochemical devices,15 batteries,16 fuel cells,17 double-layer capacitors, and solar cells.18−21 In ILs as the length of alkyl chain increases hydrophobicy of ILs increases,22 for synthesized colloidal NPs in IL the increase of alkyl size leads to the expansion of size distribution function and a decrease in the height of the distribution function in terms of mean size of NPs.23 For any application of an IL, the physical properties are a key feature. In particular, the transport © 2017 American Chemical Society

properties are crucial when considering the reaction kinetics in a synthetic process or ion transport in an electrochemical device. The cation diffusion coefficients for the liquid salts show a decrease in diffusion coefficient as the length of the alkyl chain increases. Increasing the length of the alkyl chain makes the movement of the cations difficult, as a result; the ILs with longer chains contribute less to the electrical conductivity.24 This fact makes EMIM cation the most appropriate IL to be used in applications where a good charge transporter is needed. Electrical conductivity of [EMIM][PF6] encapsulated in carbon nanotube in the presence of doped nitrogen decreases as the temperature increases; however, in the absence of nitrogen, it goes up.25 Received: August 14, 2017 Revised: October 20, 2017 Published: October 20, 2017 24434

DOI: 10.1021/acs.jpcc.7b08126 J. Phys. Chem. C 2017, 121, 24434−24443

Article

The Journal of Physical Chemistry C

Molecular dynamic (MD) simulations are powerful tools to understand interfacial processes at a molecular level. It is because they are able to describe the systems with atomistic details. Accurate simulations of the transport properties of ILs around metallic NPs are very challenging due to the slow dynamics, the large number of atoms, and strong Coulombic long-range interactions of these complex liquids. A number of IL-metal systems have been modeled using classical MD simulations.63−67 Vibrational properties for colloidal nanoparticle and metallic nanoparticle could be investigated by quantum dynamics and could be used for investigation of electronic population dynamics.63,68 In 2001, Hanke et al.69 developed the first force field for imidazolium-based ILs. Diffusion coefficients were calculated using the Einstein relation by linear fitting of the mean-square displacement (MSD) function. Margulis et al.70 also computed the MSD and diffusion coefficients for the ions using the Einstein relation from a simple generalized Langevin model. Bhargava and Balasubramanian71 employed the fully flexible, all-atom force field developed by Canongia Lopes et al.72 They calculated the self-diffusion coefficient and electrical conductivity of IL using MD simulations. Performed MD simulations of ILs in different force fields to calculate transport properties and electrical conductivity of ILs were obtained from the available literature.73−79 This study is an attempt to determine the effect of the Ag NPs with different sizes on the dynamic behavior and transport properties of 1-ethyl-3-methylimidazolium hexafluorophosphate [EMim][PF6] ionic liquid. In the search for highly conducting ILs, we investigated the influence of Ag NP size on the transport properties of [EMim][PF6]. The Nernst−Einstein equation is used to understand the relationship between diffusion and conductivity.

The transference numbers measure the relative ability of specific ions cations or anions to carry charge. In general, for ILs and especially for imidazolium-based ILs, the cationic transference number is greater than the anionic transference number.26 Tokuda et al. have proposed one way around this by calculating the ratio of molar conductivity to ion self-diffusion coefficient,27,28 as this may be used as quantitative evidence for ionic aggregates in ILs.29 Many applications and fundamental developments of ILs focus on their use as electrolytes in electrochemistry. The behavior of ILs as electrolytes is determined by the transport properties of their ionic constituents. Several empirical equation and relationship are widely used for clarifying the kinetics of the mobile ions in the aqueous solutions, even for that of the mobile ions in nonaqueous solutions. The intermolecular or ion−ion interaction in ionic liquid can be to discuss by means of pKa, which is qualitative value from aqueous solution. ILs which have a low pKa value compose low concentration of ionic species in the liquids, therefore such a protic ionic liquid shows low ionic conductivity. Umebayashi and co-workers stated in their article30 that Watanabe et al. proposed an ionicity parameter as a measure of the ion−ion interaction in ILs.27,31 It is generally known that the solvent physicochemical and acid− base properties vary on cation and anion species changing and ion−ion interactions in the IL. Since the main interactions in the ILs are Coulombic, the ionic structural effects on the physical properties are also discussed as a function of the effective ionic concentration in order to understand how the Coulombic forces dominate the properties. Pure ILs possess reasonably good ionic conductivities; however, strong ion pairing and aggregation10,32−34 decreases the number of charge carriers in ILs and leads to smaller than expected conductivity. Adding NPs to ILs causes the separation of the constituent ions of the IL by reducing NPs ion pairing or ion aggregation in the IL, and the number of available charge carriers and the mobility of these charge carriers are increased. Previous studies show that, compared to pure IL, the electrical conductivity of IL in the presence of Au NPs increases. They show that Au NPs can play an important role in increasing the electrical conductivity of IL.35 Considering the above properties, it is of great interest to study NPs in ILs,36−40 especially metal NPs in ILs which attract significant attention based on their novel properties.41−45 Many types of structural forces for colloidal nanoparticles within ionic liquids by using the surface force balance technique have been investigated by Perkin.46 Many researchers have been interested in studying NPs or small clusters of metal.47−52 In this paper, we chose silver NPs because of their various applications such as utility in microelectronics and electrochemical sensor.53,54 Using IL as the solvent for dispersion of colloidal particles and for the generation and stabilization of metal NPs presents such a useful way to new functional materials6,55−57 that it has been employed to build devices for energy applications. For example, colloidal silica dispersed in IL can be transformed into colloidal gels or colloidal glasses to create solid conducting electrolytes for solar cell applications.58,59 It has also potential applications in optoelectronic devices.55,60,61 Titania spheres62 and gold nanoparticles35 have also been used in gel ILs and to produce electrolyte materials.

2. COMPUTATIONAL METHOD 2.1. Molecular Dynamics Simulations. IL−IL, metal− metal (M−M), and M−IL interactions were used in this system. The potential function of the system (U) will have contributions from all of these interactions: U = UIL − IL + UM − M + UM − IL

(1)

The force field used in our simulations includes the typical short-range Lennard-Jones and the long-range Coulomb interaction terms between atoms that are not covalently bonded and an intramolecular or bonded term that includes bond stretching, r, angle bending, θ, and dihedral torsions, ψ. UIL−IL may be written as ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij + UIL − IL(rij) = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ 4πε◦rij ⎣⎝ ij ⎠ +

∑ angles

2

k θ(θ − θeq) +

∑

∑

k b(r − req)2

bonds

k ψ [1 + cos(nψ − δ)]2

dihedrals

(2)

where rij is the distance between the atoms i and j of different ions. The force field parameters were those previously suggested by Canongia Lopes et al.72 based on the AMBER and OPLS force fields.80 The equilibrium values of the bond angles θeq and the bond lengths in the [EMim]+ and [PF6]− are derived from the crystallographic X-ray structure of solid [EMim][PF6].81 There is some progress for Canongia Lopes 24435


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The Journal of Physical Chemistry C force field for getting better value for transport properties including viscosity, conductivity and diffusivity.82 The quantum Sutton-Chen (Q-SC) potential was used to describe the interatomic interaction for silver nanoclusters. The UM−M potential is given by83 N

N

N

i=1

i

j≠i

∑ Ui = ∑ ε[ 1 2 ∑ V (rij) − C

account for the polarization of the metal surface by the ions, the Drude model has been used.89 The previous study reveals that the inclusion of electronic polarizability can considerably improve the agreement between simulation and experiment for IL.90 Electrostatic forces of the point partial charges on the atomic sites of the ions and the Drude dipoles on the metal atoms have been applied to the polarization of the surface as shown in Figure 1. Ewald summation method has been applied as well to calculate the electrostatic interaction between all charged particle in MD simulation.

ρi ] (3)

where rij stands for the distance between atoms i and j, c is a positive dimensionless parameter, and ε is a parameter with the dimensions of energy. V(rij) in eq 3 is defined by ⎛ a ⎞n V (rij) = ⎜⎜ ⎟⎟ ⎝ rij ⎠

(4)

ρi in eq 3 is a local electron density defined by the following equation ⎛ a ⎞m ρi = ∑ ⎜⎜ ⎟⎟ r j ≠ i ⎝ ij ⎠

(5)

a is a length parameter, n and m are both positive integer parameters, where n > m.50,84 Lennard-Jones has also been used as an estimation for M−IL potential interaction. Interaction between metal−IL is more than IL at the air interface.85,86 Site−site potential functions of the type n−m similar to Lennard-Jones potential has been applied for potential interaction of surface metal of iron nanoparticle with IL.87 The interaction between metal and IL can be considered as a Lennard-Jones potential from fitting DFT result as a63 qiqj ⎡⎛ σ ⎞12 ⎛ σ ⎞6 ⎤ UM − IL = 4ε⎢⎜ ⎟ − ⎜ ⎟ ⎥ + ⎝r⎠ ⎦ r ⎣⎝ r ⎠

Figure 1. Cations and anions induce many image charges δ+ and δ− on the surface due to polarizability of the Ag NP surface.

(6)

Q-SC and Lennard-Jones potential parameters used in this study are presented in Tables 1 and 2, respectively. In the

Fitting atomistic potential of surface metal NP with IL with DFT method or experimental data leads to more reliable structural result for MD simulation.87 BP86 level using Slater type basis sets could be used for optimization of transition metal−carbonyl bond.91 Density function theory has been used for investigating the electronic structure and interaction between bare and hydrated first-row transition-metal ions.92 All units of energy in our calculation are kJ/mol. Picálek and Kolafa76 tested the finite-size effects using the allatom force field by Canongia-Lopes et al. for 100, 200, or 400 ion pairs of [bmim][PF6]. The results of the diffusion coefficient were not influenced by the number of the particles under their simulation conditions, and the influence of the box size on the simulation results was not significant. We used the periodic cubic box containing 128 [EMim]+ and 128 [PF6]− where nanocluster of silver was inserted in the center of the simulation box within a cutoff distance 12 Å at an equilibrium pressure of 1.0 bar. The snapshot of the Ag NP (500 atoms) solvated in the IL at temperature 350 K is shown at Figure 2. To control the temperature, the Berendsen thermostat was applied. The temperature range for all the simulations was chosen 350−470 K. The DL_POLY program version 4.0393 was used to perform all MD simulations as three steps. In the first step, pure [EMim][PF6] was equilibrated with an NPT simulation until the volume converged. This trend also was done in previous literatures94 and the berendsen thermostat was also used in 500 ps. Optimum silver nanocluster was

Table 1. Quantum Sutton−Chen Potential for Ag Atoms Ag−Ag

ε (kJ/mol)

C

m

n

α (Å)

ref

0.38063

94.948

6

11

4.0691

84

Table 2. Lennard-Jones Potential for Ag with ILa Ag Ag Ag Ag Ag Ag Ag Ag Ag Ag a

C1 C2 CR CW HA HC H1 NA P F

ε (kJ/mol)

α (Å)

3.03051 3.03051 3.12101 3.12101 2.04318 2.04318 2.04318 4.86375 5.27548 2.91334

3.0720 3.0720 3.0970 3.0970 2.5320 2.5720 2.5720 2.9470 3.1920 2.8810

From ref 63.

present study, triple-zeta valence basis set, TZVP basis set for ionic fragmentation and LanL2DZ basis set for both metal and liquid have been used to get surface potential via firefly quantum chemistry package88 for present MD simulation. To 24436


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The Journal of Physical Chemistry C t+ =

D+ (D+ + D−)

(9)

where D+ and D− are diffusion coefficients of cations and diffusion coefficients of anions, respectively. The electrical conductivity of IL which is a measure of the number of the charge carriers by ions and their mobility is calculated from the Nernst−Einstein equation96 σNE =

Ne 2 (Z+2D+ + Z −2D−) VKBT

(10)

where N denotes the number of ion pairs, e is the elementary electronic charge, V is the volume of the system, KB is the Boltzmann constant, T is the temperature in Kelvin and is the formal charge on the cation (anion). The electrical conductivity is proportional to the ionic diffusion coefficients, and the mechanism of the charge transport in the ILs is related to the diffusivity of the ions. To calculate the true electrical conductivity of the system, one should consider the collective counterpart of the MSD and the corresponding Einstein equation

Figure 2. Snapshot of the Ag NP (500 atoms) solvated in the IL at temperature 350 K, using color labeling: Ag, [EMIM], and [PF6]: green, gray, and orange, respectively.

N

σ = lim

t →∞

N

d e2 ⟨∑ ∑ ZiZj([ric(t ) − ric(0)] × [r jc(t ) − r jc(0)])⟩ dt 6VKBT i = 1 j = 1

(11)

inserted in the center of the simulation box of optimum structure of IL from step one as a initial structure for the MD simulation of step two. For the second step, the MD simulation was done in 400 ps with a time step 0.4 fs and a canonical ensemble with the Berendsen thermostat. In the third step, MD simulation with time 100 ps was performed on optimum structure from step two by using NPT ensemble with relaxation time for thermostat and barostat 0.10 and 2 fs, respectively. As a result, the simulation of colloidal Ag NP in IL was performed in a nanosecond. Simulation time is extended to the 1.5 nano second and the result shows that longer simulation time does not change the physical quantities for the present study. The Verlet leapfrog scheme95 was used for the integration of the equation of motions. The production runs for NP in the gas phase in an NVE ensemble lasting 500 ps. 2.2. Methodology. The diffusion coefficient of different sizes of Ag NPs simulated is calculated from the Green−Kubo integral formula96,97 1 ∞ D= ⟨v (⃗ t ) ·v (0) ⃗ ⟩ dt (7) 3 0

3. RESULTS AND DISCUSSION 3.1. Diffusion Coefficient of Ag NPs in Gas Phase and in IL. The diffusion coefficient of Ag NPs simulated in sizes of 108, 192, 256, 400, and 500 atoms using eq 7 in both gas phase and IL with different temperatures were calculated. The diffusion coefficients for different sizes of Ag NPs in terms of temperature in the gas phase and in IL are shown in Figures 3

∫

where v(⃗ 0) is the velocity vector of a particle at initial time and v(⃗ t) is the velocity at time t. In IL, the diffusion coefficient of ions can also be obtained from the long-time limit of the MSD using the Einstein relation98 N

Di =

1 d lim ⟨∑ |ric(t ) − ric(0)|2 ⟩ 6 t →∞ dt i = 1

(8)

Figure 3. Diffusion coefficients for different sizes of Ag NPs simulated in terms of temperature in the gas phase.

the term ∑i = 1 |ric(t ) − ric(0)|2 in the Einstein relation is regarded as mean square displacement (MSD), where rci (t) is the location of the center of mass of ion i at time t. The relative contribution of the charged species to the transfer of the total charge is defined by ionic transference number. Cationic transference number has been calculated using the following relation

and 4, respectively. The diffusion coefficient of colloidal Ag NP and Ag NP in gas phase decreases as the size of cluster increases. In addition, as it is shown, diffusion coefficient for Ag NPs in the gas phase is more than that of in IL. In addition, the effect of size on the diffusion coefficient for Ag NPs in IL is less than that in the gas phase. To show this effect, the differences in

N

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350 K

470 K

350 K

470 K

NPs of colloidal Ag in two temperatures and two sizes. Table 3 shows that the thermal sensitivity of diffusion coefficient for Ag NP for equal sizes in the gas phase is much more than that in the IL. Now the question is why is the sensitivity of diffusion coefficient for colloidal Ag NP is less than that of Ag NP in the gas phase? This is because the temperature has to overcome two energy obstacles: first, the electrostatic energy caused by the electrostatic of the induced charge on the surface of colloidal Ag NP and the ionic particles; second, the temperature has to overcome the solid vibrating frequencies for solid movement. In the gas phase, Ag NP has to overcome only one obstacle which is the solid vibrating frequencies. On the basis of both Figures 3 and 4 as well as Table 3, the diffusion coefficients for colloidal Ag NP and Ag NP decrease as the size of Ag NP increases, which is due to the decrease in the surface effect. 3.2. Cation and Anion Diffusion Coefficients for Pure IL. Previous studies show that a number of simulations have been done with regard to diffusion coefficients calculated from the functions of mean-square displacement (MSD).76,78,99,100 The findings of these studies point to the fact that, in general, the diffusion coefficient of cations and anions in IL increases as the temperature goes up.24,76,79,101 In this study, ions diffusion coefficient of IL from the linear fitting of the slope of MSD was calculated. Furthermore, the diffusion coefficient of simulated IL in the temperature of 350−500 K for pure IL was calculated. The results obtained for neat IL were compared to those found in other simulation studies.76 The diffusion coefficients for ions of IL were calculated, and comparison in the 400 K temperature is shown in Table 4. [EMim]+ cations have

8.16 4.01 4.15

17.6 11.0 6.60

9.85 5.11 4.74

23.1 13.25 9.85

Table 4. Diffusion Coefficients and Electrical Conductivity of EMimPF6 at T = 400 K

Figure 4. Diffusion coefficients for different sizes of Ag NPs simulated in terms of temperature in IL.

diffusion coefficients for size 108 and 500 atoms in the temperatures 350 and 470 K are represented in Table 3. As Table 3. Simulated Ag NP Diffusion Coefficients DN (in 10−12 m2 s−1), N is Numbers of Ag atoms at 350 and 470 K in IL D108 D500 ΔD (D108 − D500)

gas phase

shown, the discrepancy of diffusion coefficients for sizes of 108 and 500 in the two temperatures in IL is less than those in the gas phase. This can be accounted for by the fact that compared to cluster inner atoms, surface atoms in the gas phase have more freedom of movement; thus, in smaller sizes of Ag NPs having a greater ratio of surface to inner atoms, there is more diffusion coefficient. But in the IL, the surface atoms of Ag are placed in the electrical field of cations and anions present in the IL, so the effect of size on diffusion coefficient for Ag NP is less. In the IL, there is an electrostatic interaction between colloidal Ag NPs and ions of the IL which leads to less diffusion coefficients, but this interaction is absent in the gas phase. Furthermore, the induced charge which occurs on the surface of Ag NP in the IL causes an electrostatic interaction between Ag NP and IL’s ions. This, in turn, leads to the state of localization, preventing the Ag movement in the ions particles. All these will lead to the decrease of diffusion coefficients of Ag in IL. According to Figure 3, the diffusion coefficient for Ag increases as the temperature increases. As the temperature increases, the thermal energy increases for the vibration of the higher frequency of Ag which leads to an increase in the diffusion coefficients. In accordance with Figure 4, the diffusion coefficients for colloidal Ag NPs increase as the temperature increases. This rise in the temperatures raises the thermal energy of the system. The rise in the thermal energy can overcome the electrostatic attraction which exists between the colloidal Ag NP and ions in the IL. This will cause an increase of diffusion coefficient for colloidal Ag. Table 3 represents the result for diffusion coefficient of Ag NPs in the gas phase and

D+ (10−11 m2 s−1) D− (10−11 m2 s−1) σ (S m−1)

our work

simulation

6.1 3.9 5.1

5.58 ± 0.51a 3.54 ± 0.32a 1.35 ± 0.89a

Calculated using force field by Hanke et al. 102. a

69

experiment

5.57b b

from ref 76. From ref

more diffusion coefficient than [PF6]− anions. This has to do with the flat structure of [EMim]+ cations; compared with anions, these flat cations cause less friction in the transfer movements. The energy needed to overcome cations transfer movements can be provided by temperature, which, in turn, leads to an increase in diffusion coefficients for cations and anions in proportion with the temperature increase. 3.3. Cation and Anion Diffusion Coefficients for IL in the Presence of Ag NPs. The diffusion coefficients for ions of IL were calculated based on the linear slope of MSD plots. In addition, the diffusion coefficients for simulated IL in 350−500 K in the presence of Ag NPs having 108, 192, 256, 400, and 500 atoms were obtained. Figures 5 and 6 represent the size effect of Ag NPs on anions and cations’ diffusion. These figures show that the greater the size of Ag NP, the greater the diffusion of ions. Ag NPs have strong electrostatic interaction between the induced charge on the surface of Ag NP and the ions around it. Therefore, ions’ diffusion coefficient for smaller sizes of colloidal NPs is smaller than that for bigger sizes of colloidal NPs. As the temperature goes up, the thermal energy needed to transport ions increases, resulting in an increase in the diffusion coefficient of ions. The diffusion coefficient of cations is more 24438


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Figure 5. Anions diffusion coefficients for pure IL and IL in the presence of Ag NPs different sizes as a function of temperature.

Figure 7. Comparing the cations and anions diffusion coefficients in the presence of Ag NPs 108 and 500 atoms as a function of temperature.

Figure 6. Cations diffusion coefficients for pure IL and IL in the presence of Ag NPs different sizes as a function of temperature.

Figure 8. Cationic transference number versus temperature for pure IL and IL in the presence of colloidal Ag NPs.

than that of anions. To better compare the diffusion coefficient of cations and that of anions for the sample, we decided to choose the ions’ diffusion coefficient in the presence of Ag NPs with the sizes of 108 and 500 atoms. This is shown in Figure 7. 3.4. Comparing Ionic Diffusion Coefficients for Pure IL and for IL in the Presence of Ag NPs. As Figures 5 and 6 show, anions and cations of pure IL show less diffusion coefficients than Ag NPs in the present of Ag NPs. Here, the augmented electrostatic forces of the point partial charges on the atomic sites of the ions and the Drude dipoles on the metal atoms decreases the Coulombic attraction between cations and anions. Therefore, the mobility of ions will speed up in the presence of colloidal Ag NPs. All these mean that the diffusion coefficients of ions increase in comparison with pure IL. 3.5. Comparing Cationic Transference Number for Pure IL and IL in the Presence of Ag NPs. Cationic transference number has been calculated using eq 9. As Figure 8 shows, in pure IL, the cationic transference number is more than the anionic transference number (cationic transference number > 0.5) which is due to the cation planar structure and

less friction of mobility. Also, in IL in the presence of Ag NPs, the cationic transference number is more than the anionic transference number. This is because anions in the created electrostatic interaction on the surface of Ag NPs speed up the mobility of the cations, therefore the cationic transference number tends to be more than that of anions in the presence of Ag NPs. In Figure 8, cationic transference number for pure IL is more than that in the presence of Ag NPs. Also cationic transference number increases in proportion with sizes of colloidal Ag NPs. In general, due to the electrostatic interaction of ions in IL with the surface of colloidal Ag NPs, ionic transference number in IL and in the presence of colloidal Ag NPs is less than that of ions in the pure IL.

4. ELECTRICAL CONDUCTIVITY DUE TO IONIC CONTRIBUTION FOR PURE IL The electrical conductivity of IL using ionic diffusion coefficient was calculated from the Nernst−Einstein equation and from the slope of the collective MSD (eq 11). The electrical conductivity of pure IL obtained in this study was compared to 24439


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and anions. Therefore, the ions have a faster mobility. The electrical conductivity of IL in purity we calculated was in conformity with the experimental data.102 It is worth mentioning that although the effect of gold NPs on increasing the electrical conductivity of IL was previously investigated,35 there was no such data concerning the electrical conductivity of Ag NPs in [EMim][PF6] in lab conditions, so we did this theoretically.

those found in other simulation and experimental studies at 400 K (see Table 4). Besides, a comparison of calculated electrical conductivity of IL with experimental electrical conductivity is represented in Figure 9. The results gained through MD about

5. CONCLUSION This study was an attempt to examine the effect of Ag NPs with different sizes on both the diffusion coefficient and transference number as well as the electrical conductivity of IL. Using the simulation MD, the diffusion coefficient and electrical conductivity created by ionic transfer of IL were calculated. The calculations were based on different sizes of Ag NPs and temperature. The diffusion coefficient of Ag NPs in gas phase and IL was calculated through the Green Kubo equation. The thermal sensitivity of diffusion coefficient for Ag NPs with equal size in the gas phase was much more than that in the IL. Furthermore, the diffusion coefficient for ions was calculated from the slope of MSD, and the electrical conductivity caused by ionic transfer was calculated by Nernst−Einstein equation. Then we compared the results with those of pure IL experimental data. The results for simulated MD regarding the electrical conductivity of IL were in line with the experimental results. Ag NPs increased the diffusion coefficient of ions and electrical conductivity of ions in IL. The effect of NP size with the range of 108 to 500 atoms for Ag NPs was also studied. It was shown that the diffusion coefficient and the electrical conductivity of IL increased in proportion with the size of Ag NPs. The results gained from the calculation of simulated MD showed that diffusion plays an important role in the electrical conductivity of ions in the presence or absence of Ag NPs for IL.

Figure 9. Comparing the electrical conductivity as a function of temperature for pure IL, IL in the presence of colloidal Ag NPs, and experimental.102

the ion’s electrical conductivity agree with the experimental findings.102 According to the findings in Figure 9, the electrical conductivity of ions for pure IL increases as the temperature goes up. This is because temperature can greatly overcome the electrostatic attraction of cations and anions in the IL, leading to an increase of diffusion coefficient in anions and cations. The findings of MD show that the electrical conductivity of ions in pure IL takes place through the diffusion mechanism. 4.1. Electrical Conductivity due to Ion Transfer for IL in the Presence of Ag NPs. The electrical conductivity of IL in the presence of Ag NPs with different sizes was calculated through the eqs 10 and 11 mentioned before. Figure 9 shows the electrical conductivity of IL in the presence of colloidal Ag NPs with sizes of 108, 192, 256, 400, and 500 atoms. As Figure 9 shows, the electrical conductivity of IL in the presence of 108 to 500 atom size increases; in other words, as the size of NP increases so does the electrical conductivity of IL. Furthermore, an increase in the temperature will lead to an increase of electrical conductivity of ionic transfer in IL in the presence of colloidal Ag NPs. As the size of colloidal Ag NPs increases, produced charge on the Ag surface will lead to an electrostatic interaction between ions in the IL and the surface of Ag. All these mean that ions can move freely inside the IL, and the electrical conductivity created by the movements of ions increases in proportion to the size of colloidal Ag NPs. When temperature increases, the thermal energy leads to an increase in the mobility of ions inside the liquid. This means that the electrical conductivity of IL increases as well. 4.2. Comparing Electrical Conductivity due to Ion Transfer for Pure IL and IL in the Presence of Ag NPs. According to the results of simulated MD in Figure 9, the electrical conductivity caused by ions in the IL in the presence of Ag NPs is more than that of pure IL. This is because the electrostatic interaction which occurs between the induced charge of the surface of the silver and the ions in the IL somehow decreases the Coulombic attraction between cations

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Farid Taherkhani: 0000-0003-2433-4964 Notes

The authors declare no competing financial interest.

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REFERENCES

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