The Effect of Temperature on Kinetics and Diffusion Coefficients of Metallocene Derivatives in Polyol-Based Deep Eutectic Solvents

The temperature dependence of the density, dynamic viscosity and ionic conductivity of several deep eutectic solvents (DESs) containing ammonium-based salts and hydrogen bond donvnors (polyol type) are investigated. The temperature-dependent electrolyte viscosity as a function of molar conductivity is correlated by means of Walden’s rule. The oxidation of ferrocene (Fc/Fc+) and reduction of cobaltocenium (Cc+/Cc) at different temperatures are studied by cyclic voltammetry and potential-step chronoamperometry in DESs. For most DESs, chronoamperometric transients are demonstrated to fit an Arrhenius-type relation to give activation energies for the diffusion of redox couples at different temperatures. The temperature dependence of the measured conductivities of DES1 and DES2 are better correlated with the Vogel-Tamman-Fulcher equation. The kinetics of the Fc/Fc+ and Cc+/Cc electrochemical systems have been investigated over a temperature range from 298 to 338 K. The heterogeneous electron transfer rate constant is then calculated at different temperatures by means of a logarithmic analysis. The glycerol-based DES (DES5) appears suitable for further testing in electrochemical energy storage devices.


Introduction
In the probe for new types of green solvents, deep eutectic solvents (DESs) as alternative media to ionic liquids (ILs), have received recent attention [1][2][3]. DESs share many notable properties of conventional ILs such as inherent conductivity, negligible vapor pressure, wide electrochemical potential windows, high thermal stability, non-flammability and outstanding solvation potential [4][5][6]. When their constituents are chosen wisely, DESs are environmentally friendly, biodegradable, and non-toxic. In addition, DESs can be prepared simply at low cost [7][8][9]. A variety of practical industrial applications of DESs have already been reported, e.g., as solvents for electrodeposition [10][11][12], catalysts or solvents for a range of chemical and enzymatic reactions [13,14], solvents for extractions [15][16][17] and co-solvents in inorganic [18] and organic [19,20] syntheses, as well as in bio-catalysis [21][22][23]. The most common form of DESs are those composed of quaternary salts (ammonium or phosphonium) with an organic compound (such as an alcohol, acid, amine or amide) which is a hydrogen bond donor (HBD) able to form a bond with the anion of the salt. Some DESs also consist of metal halides or hydrated halides that form a complex with ammonium or phosphonium salts. DESs melt and freeze at lower temperatures than the constituting components [24][25][26][27][28][29].
Ferrocene/ferrocenium (Fc/Fc + ) or cobaltocenium/cobaltocene (Cc + /Cc) redox couplescommon metallocenes-are reversible in most non-aqueous solutions and have been investigated as candidates for internal references in various ILs [30][31][32][33][34]. Quasi-reference electrodes (QREs) with electrochemically reversible couples, such as Fc/Fc + or Cc + /Cc have also been used for the development of reference potential scales in ILs [35,36]. The electrochemical oxidation of ferrocene to the mono-cation ferrocenium, has been investigated in numerous organic solvents at different temperatures. Crooks and Bard [37] measured electrochemical parameters of the Fc/Fc + in acetonitrile at a temperature range of 298 to 573 K, including supercritical conditions. Tsierkezos [38] investigated the voltammetric behavior of the Fc/Fc + couple over a range of temperatures in eight different organic solvents. Wang et al. [39] used voltammetric data to infer diffusion coefficients of both Fc and Fc + as a function of temperature in acetonitrile systems. Despite all this, there are few reports on the diffusions and kinetics for the Fc/Fc + couple in ILs. Rogers et al. [33] examined in detail the voltammetry of the Fc/Fc + and Cc + /Cc couples over a wide range of temperatures and concentrations in several ILs. Matsumiya et al. [40] studied the temperature dependencies of the diffusion coefficients and rate kinetics of Fc/Fc + in the quaternary ammonium cation and bis(trifluoromethanesulfone) imide anion type ionic liquid using an I − /I 3− reference electrode. Weaver et al. [41] investigated the electrochemistry of ferrocene-functionalized phosphonium ILs at a temperature range of 289 to 353 K. Compton et al. [42] reported that the diffusion coefficients of Fc in a pure IL is more temperature dependent than that observed in a CO 2 -saturated IL, therefore the activation energy of diffusion of Fc in the IL was approximately halved when the liquid was saturated with CO 2 . There was concern, however, regarding the fact that the Fc/Fc + process displayed irregular electrochemical behavior in some ILs at different temperatures [42]. In fact, Guo et al. [43] reported that Fc molecules could diffuse faster even at lower temperatures if ILs were saturated with CO 2 at elevated pressures beyond approximately 3 MPa. Taylor et al. [44] determined the diffusion coefficients for Fc derivates in five ILs as a function of temperature and the data revealed a disobedience to the Stokes-Einstein equation. However, no systematic study is available on the effects of varying temperatures on the Fc/Fc + oxidation and Cc + /Cc reduction processes in DESs.
A DES performs the dual role of electrolyte and solvent and hence represents a different kind of medium for electrochemical applications. Herein, we report electrochemical data obtained by means of cyclic voltammetry and chronoamperometry using DESs based on quaternary ammonium salts and polyol hydrogen bond donors over a range of temperatures. Also the effect of temperature on the physicochemical properties of the studied DESs is examined.

Materials and Method Preparation and characterization of DESs
In this work, 6 DESs based on two ammonium salts were prepared. Choline chloride (C 5 H 14 ClNO) and N,N-diethylenethanol ammonium chloride (C 6 H 16 ClNO) as quaternary ammonium salts as well as triethylene glycol (C 6 H 14 O 4 ), glycerol (C 3 H 8 O 3 ) and ethylene glycol (C 2 H 6 O 2 ) as hydrogen bond donors were obtained from Merck Chemicals (Germany) with high purity (! 98%) and were used as-received. All starting chemicals were stored in an inert glove box (Innovative Technology, Pure LabHE, USA) purged with argon (oxygen-free). The water mass fraction of the chemicals (as per the manufacturer's guide) was <10 −3 %. Table 1 lists the DESs studied in the present work. The DESs were formed according to the preparation method described earlier [8][9][10][11]. In brief, two components were mixed in the argon-filled glove box (having oxygen and water contents lower than 1 ppm), in the proportions indicated in Table 1, at 348 K, 300 rpm agitation and atmospheric pressure until a homogeneous, colorless liquid formed. The time of the mixing process was about 3-5 h. The densities of the synthesized DESs at various temperatures were determined using a DMA 4100 Density Meter (Anton Paar, Austria) with three replicates for each reading (having an uncertainty of ± 0.00008 g•cm -3 ). The density of water (degassed and distilled) was measured at 298 K and compared with the corresponding values in density tables, to adjust the density meter for accuracy. The results exhibited a difference of ± 0.00005 g•cm -3 which showed good accuracy.
The viscosities of the DESs were obtained by averaging at least three to five measurements, using a Brookfield DV-II + Pro EXTRA instrument. The uncertainty in viscosity measurements did not exceed ±1% of the measured values in this study. The conductivities were determined using a DZS-708 Multi-parameter analyzer, which was calibrated using a 0.001 M standard solution of KCl (Merck).

Electrochemical measurements
The electrochemical experiments of all Fc and Cc + solutions were studied in a standard threecompartment glass cell, consisting of a 3 mm diameter Glassy Carbon (GC) or 20 μm diameter platinum working electrode, while Ag wire (pre-treated as described in the literature) [45] and Pt. wire were used as the quasi-reference and counter electrodes, respectively. Working electrodes were carefully polished with 0.3 μm alumina paste (Wirth Buehler) and ultrasonically rinsed in acetone. All electrochemical measurements were carried out using a computercontrolled í-Autolab potentiostat (PGSTAT302N). A Faraday cage was also employed to minimize electrochemical noise, which in turn was placed in the argon-filled glove box. The anodic and cathodic limits of each DES were arbitrarily specified as the potential at which the current density reached higher than 0.2 mA cm -2 .

Results and Discussion
Synthesis and physicochemical properties of DESs DESs prepared by mixing two different quaternary ammonium salts with different polyol HBDs (that have the ability to form a complex with the halide anions of the quaternary ammonium salts) [45] and their fundamental physicochemical properties including density, viscosity and conductivity were examined. The results are reported in Table 1.
The densities of DESs were measured over the temperature range of 298 to 368 K at atmospheric pressure. The difference in density could be attributed to a different molecular arrangement or packing of the DES. For the DESs, the density was found to decrease linearly with temperature as shown in Fig 1. Such results would be expected since, as temperature increases, substances (at constant pressure) become less dense due to thermal expansion. The density values were compared to those reported in the literature [46][47][48] and found to be in good agreement. The following equation fits the experimental data for the densities (ρ) of the DESs very well over the entire temperature range: Where T is the absolute temperature while A and B are empirical constants that depend on the type of DES. As displayed in Table 1, DES1 has a higher density than its other counter parts due to a higher intermolecular packing of the compound's denser structure. The density of ethylene glycol based DESs were found to be slightly less than those of other polyol-based counterparts.
The viscosity is a very important parameter in electrochemical studies due to its strong effect on the rate of mass transport within the solution. It significantly influences the diffusion of species, which are dissolved or dispersed in an ionic liquid. The viscosity can be influenced by various parameters such as the relative capacity to form hydrogen bonds, anionic species, size, higher alkalinity, van der Waals forces and cation size [49]. The viscosity is generally affected by the interaction of the salt with the HBD, and their ability to coordinate. Fig 2(a) indicates that, as the temperature increases from 298 to 368 K, the viscosity of the DESs decrease due to the higher mobility of ions. DESs with the glycerol HBD exhibits higher viscosities than other polyol based DESs, resulting in lower conductivities. Moreover, choline chloride based DESs [50] show lower viscosities in comparison to diethylenethanol ammonium chloride based DESs, and the value at 298 K follows the order: The temperature dependency of the viscosity (η) for the DESs and the profiles are fitted to the Arrhenius equation (Eq (2)), which describes the temperature dependence for non-associating electrolytes [51], as depicted in Fig 2( Where T is the temperature in Kelvin, η is the viscosity, E η is the activation energy, η 0 is a constant and R is the universal gas constant. The value of E η , η 0 and sums of square errors are tabulated in Table 2. The regression correlation coefficients have values higher than 0.99 showing a reasonably good fit. Fig 3(a) illustrates the temperature dependence of ionic conductivity (the most important property of electrolyte materials) for the DESs. Conductivity of DESs generally increase significantly as the temperature rises due to the ions moving faster at higher temperatures as a consequence of lower viscosities (of the neat DESs). The conductivity of the salts-ethylene glycol DESs (DES3, DES6)-show higher values in comparison to other polyol based DESs. Considering the hole theory for transport in molten salts, an Arrhenius equation (Eq (3)) was obtained for the temperature-dependence of the electrical conductivity (σ), which can be written as [52,53]: Where T is the absolute temperature, σ 0 is a constant and E σ is the activation energy for conduction. Consequently, from Eq (3), E σ , σ 0 and sums of square errors are tabulated in Table 2. ln σ except DES1 and DES2, as predicted by the Arrhenius equation. The relation between ln (σ) and 1/T are well explained by a linear model with a correlation coefficient, R 2 , of more than 0.99 which indicates that the variation of electrical conductivity with temperature follows an Arrhenius model. However, the curvature of ln(σ) as a function of (1/T) in Fig 3(b), for DES1 and DES2 exhibit non-linear trends. Hence, for these two particular DESs, the Vogel-Tamman-Fulcher (VTF) was used to determine the temperature dependence of conductivity according to the following equation [54]: Where σ 0 , T 0 and B σ are fitting parameters. In Fig 3(c), the variation of ln (σ) versus 1/(T-T 0 ) is plotted. The best fit values for σ 0 (mS cm -1 ), B σ (K) and T 0 (K) are given in Table 3. T 0 is supposed to have a close relationship with glass-transition temperature, and σ 0 and B σ are usually associated with several carrier ions and activation energies, respectively [55]. From the measured ionic conductivity σ (S m -1 ), the values of the molar conductivity Λ (m 2 S mol −1 ) were calculated using Λ = (M σ) /ρ, where M and ρ are the respective equivalent weight and density of the DES. Solvent-free ionic liquids usually can be well illustrated by correlating the molar conductivity with temperature-dependent fluidity according to the modified Walden's rule [56] using a qualitative approach [57]: Where α is the slope of the line in the Walden plot, which reflects decoupling of the ions, and C (Walden product) is a temperature-dependent constant. This scheme is specifically appropriate in ILs [57], because it is a useful measure for examining ion pairing in electrolytes, and supplies the basis for comprehending the relationship between conductivity and viscosity.

Electrochemical stability
The electrochemical stability is one of the most important characteristics to be identified for electrolytes and solvents used in electrochemical applications. Electrochemical stability is dependent on the type of electrodes, the measurement situation, and the references employed.  The arbitrary current cut-off used to define the onset of redox processes (typically between 0.1 and 1.0 mA cm −2 ) may not be strictly electrochemically determined. This difficulty is further combined in the case of ILs due to their sensitivity to air, water, and other impurities [58]. The cathodic stability of DESs is mainly determined by the potential at which the reduction of the cations (salts) takes place, while the anodic stability is measured where oxidation of the anions  (HBDs) is expected to occur. For particular applications (e.g., super-capacitors), it is the overall potential window that matters, while in other applications, the actual anodic and cathodic limits associated to some reference is the restricting factor. The limiting reduction and oxidation potentials of the DESs are analyzed by performing cyclic voltammetry using a GC working electrode and a Pt. microelectrode at ambient temperature and at a scan rate of 0.1 V s -1 , as shown in Fig 5(a) and 5(b) where the limiting current density reaches 0.2 mA cm −2 .
The potential window of studied DESs, determined from the difference in potentials, is found to be similar on the GC electrode vs. Ag/AgQRE and has a wider potential range as compared to previously tested DESs [59]. In addition, the cathodic potential on the Pt. electrode (Fig 5a) is observed to decrease for the DESs in the order of DES1 >DES2 >DES3 when using the choline chloride salt. However, for DESs made with the diethylenethanol ammonium chloride salt the cathodic potential values are similar. Such variations are not seen for the anodic potential [45].

Temperature dependence of the voltammetric data for Fc/Fc + and Cc + / Cc in DESs
Initially, in order to compare electrochemical parameters obtained in DESs as a function of temperature, it is essential to use either a reference electrode of a familiar potential against a standard reference electrode, or refer all data to a procedure whose reversible potential is presumed to be independent of the DESs. The oxidation of Fc is prevalently used to provide an internal potential scale standard in voltammetric studies [30][31][32][33]. Bond et al. have demonstrated that the reduction of Cc + provides a broadly practical reference scale in both ILs and organic solvents [60,61]. In these DESs, Fc and Cc + exhibit a reversible one-electron process.
½CoðC 5 H 5 Þ 2 þ þ e À , ½CoðC 5 H 5 Þ 2 ð 7Þ Figs 6(a) and 7(a) indicate typical cyclic voltammograms for oxidation of Fc and reduction of Cc + in DES1, respectively, which were obtained from individually prepared 10 mM solutions in the temperature range of 298-348 K. The voltammetric data of Fc and Cc + is summarized in Table 4. Fc and Cc + exhibited reversible reactions in all of the investigated DESs [45]. The anodic and cathodic peak currents had increased substantially with increasing temperature for oxidation of Fc and reduction of Cc + , respectively {Figs 6(a) and 7(a)}. The peak potential separation (ΔE p ) was found to be in the range between 0.064-0.103 V for Fc and 0.073-0.103 V for Cc + (Table 4). It was observed in all cases that ΔE p decreased with increasing temperature and this at least partly reflected the faster electron kinetics. For DESs, the ΔE p was found to be higher than the theoretical value (ΔE p = 0.059 V), attributing to the effect of either slow heterogeneous electron transfer kinetics or the enhanced impact of Ohmic drop as was previously described by other researchers [32,34,36,41]. Reversible kinetics was assumed for both Fc and Cc + following a similar presumption from work reported in the literature [38,40,62]. In addition, the half wave potential (E 1/2 ) of the redox couples (vs. Ag/AgQRE) was determined according to the following equation Significant drifts in potential were initially observed for the AgQRE wire dipped directly in DESs, including electroactive compounds. However, separation of the Ag wire immersed in DESs from the bulk solution by means of a glass frit reduced this effect. The E 1/2 data increased   proportionately with temperature. Moreover, the E 1/2 values changed significantly for different DESs at a given temperature. It was demonstrated that E 1/2 shifted toward more negative potentials for the oxidation of Fc, and to more positive potentials for the reduction of Cc + in DESs. The shift of E 1/2 could be illustrated by the donor-acceptor Lewis-type interactions as discussed elsewhere [63].

Calculation of Diffusional Activation Energies for Fc and Cc +
The diffusion coefficient, D, of both the Fc/Fc + and Cc + /Cc redox couples in DESs at different temperatures were determined through analysis of double chronoamperometric measurements conducted at Pt. microelectrodes. The technique was undertaken using a sample time of 0.01 s. After pre-treatment by holding the potential at a point corresponding to zero Faradaic current for 20 s, the potential was stepped from 0 to +0.60 V (oxidation of Fc to Fc + ) and -0.40 to -1 V (reduction of Cc + to Cc), and the current was calculated for 5 s. The potential was then stepped back to 0 (reduction of Fc + to Fc) and -0.40 V (oxidation of Cc to Cc + ), and the current response was calculated for a further 5 s. The nonlinear curve fitting function in Origin 7.0 (MicroCal Software Inc.) following the approximation made by Shoup and Szabo [64] was used to fit the first potential step experimental data. The equations used in this approximation {Eqs (9)-(11)} describing the current response to within 0.6% over the entire time range is given below: Here, r d represents the radius of the microdisk electrode, D is the diffusion coefficient, F is the Faraday constant, c is the bulk concentration of the electro-active species, n is the number of electrons transferred, and t is the time. Figs 6(b) and 7(b) show the best theoretical fit (O) to the experimental double potential step chronoamperograms (-) for the Fc/Fc + and Cc + /Cc redox couples at 293, 298, 303, 308, 313, and 318 K in DES1. The limiting currents of the first step incline regularly and the trend of the second step becomes slightly less steep as the temperature increases in both Fc and Cc + . It is reasonably established that D Fc and D Cc + improves with increasing temperature in all six DESs ( Table 5). The D of the electroactive species have been analyzed in terms of the Arrhenius exponential function of the temperature following the Eq (12).
Where D 0 is a constant corresponding to the hypothetical diffusion coefficient at infinite temperature, and E D is the diffusional activation energy of the electroactive species. Plot of lnD against 1/T resulted in a straight line, and from the slope the activation energy for diffusion, E D , was determined, as shown in Fig 8(a) and 8(b) (least-squares correlation coefficient, R 2 > 0.99 for Fc and Cc + ). The calculated E D for each sample is summarized in Table 6, which compares well with the value determined for the E η in DESs and corresponds well to that observed in the literature for ILs [33]. The activation energies increased systematically with increasing viscosity in DESs. A slight deviation for activation energies of D Cc+ is observed, which may be due to impeded diffusion of the reduced species as a result of stronger solvation by the DES.

Effect of temperature on kinetic electron transfer
The cyclic voltammetric data have been further analyzed for the evaluation of the heterogeneous electron transfer rate constant (k 0 ) of the Fc/Fc + and Cc + /Cc redox couples according to the electrochemical absolute rate relation adapted from Nicholson's method [65]. This is based on the variation of peak potential separation (ΔE p ) between the forward and the reverse scans of the cyclic voltammogram for a simple one electron transfer process [41,66,67]. It is important to note that these values are only apparent, and are susceptible to errors resulting from charging currents and ohmic polarization, which can cause an overstatement of the rate constant. The rate constants of Fc and Cc + increase with temperature, and Fig 8(a) and 8(b) display an Arrhenius relationship for the obtained k 0 values for Fc in DES1 and Cc + for DES5, respectively. Nearly identical slopes are established for D and k 0 in the Arrhenius plots for selected DESs. From these plots, the activation energy of rate constants for Fc and Cc + are determined, which are listed in Table 6.

Conclusions
The effect of temperature on the measured physicochemical and electrochemical properties of the studied DESs has been discussed in detail. The activation energies for viscosity (E η ) and conductivity (E σ ) for each DES were calculated from the slopes of the Arrhenius plots. The temperature dependence of the measured conductivities did not exhibit linear behavior in the Arrhenius equation for DES1 and DES2, but it could be well described by the VTF model. The D and k 0 values tended to increase with the rise of temperature in DESs. The applicability of the Arrhenius law was verified by examining the temperature dependencies of D and k 0 . The trends of electrochemically derived activation energy (E D ) from chronoamperometric evaluations of DESs were found to be related with E η and E σ in the order of: DES5 > DES2 > DES4 > DES1 > DES3 > DES6. In addition, ΔE p was reduced while E 1/2 values shifted towards more negative potentials for oxidation of Fc and more positive potentials for reduction of Cc + in DESs with the enhancement in temperature.