Farouq S.Mjalli*,Hasan Mousa *

1 Petroleum and Chemical Engineering Department,Sultan Qaboos University,Oman

2 Department of Chemical Engineering,Jordan University of Science and Technology,Irbid 22110,Box 3030,Jordan

1.Introduction

Deep eutectic solvents(DESs)are special types of ionic liquids formed by mixing Lewis(Bronsted)acid with anionic and/or cationic base.The resulting mixture possesses a melting point much smaller than the original components.Due to its unique properties such as low vapor pressure,high ionic conductivity etc.,DESs are used in many chemical applications such as separation of azeotropic mixtures by extraction[1],sulfur removalfrom petroleum products[2],synthesis of polymers,[3],solvent for CO2capture[4],energy storage material[5]and many other applications such as dissolution of metal oxides,drug purification of biodiesel,a solventin the catalysis processes,biotrans formation reactions,organic synthesis,electro chemistry,as a solvent in the preparation of materials such as zeolite-type materials,metalorganic frameworks(MOFs),metal oxides,nano-materials,and carbon materials[6].

The DES has unique properties such as low melting point compared to the original constituents,high solubility of metal oxides,very low vapor pressure,and non flammable.Numerous papers are available in literature in which the physical properties of DES and the effect of additives on its properties are available for example[7,8].

Viscosity,which is a measure of the fluid resistance to flow,is one of the most important physical properties of liquids in general and DES in particular.Most of the DES exhibit relatively high viscosities at room temperature(＞100 mPa·s)with very few exceptions.The hydrogen bond network between the constituents of the DES,the large ion size,the little voidage,the presence ofelectrostatic and van der Waals attraction forces are the main reasons behind the relatively high viscosity.Since DESs are used in chemical processes,it is essential to produce ones that are of low viscosity[6].One way to achieve this is by mixing with other components to reduce the viscosity of commonly used DESs.

The viscosities of eutectic mixtures are mainly affected by the temperature[9-12],the chemical nature of the DES components(the used salt and the hydrogen bond donor(HBD)),and the concentration of the HBD[13].In general,DES possesses higher viscosity than the original const ituents that affects it suse in variousengineering applications.Hence,it is essential to investigate various effects on the viscosity ofthe DESsolutions.In a recent molecular dynamic study on aqueous Reline mixtures,Mjalli and Shah[14]found a strong effect of water on the viscosity of Reline solution(a DES type-III system).They attributed the change in viscosity at water content＜5%to Urea-Urea interaction and at high water content＞25%to the hydration of urea and the increase in its diffusivity.

Addressing the variation of viscosity with liquid composition and temperature through the parameters of conventional Eyring equation,Mjalli and Naser modified Gong model reducing the parameters from 8 to 6[13].An excellent agreement between the experimental results and the modified model was obtained.The model was further tested and verified statistically through the use of the coefficient of determinate,the t-test and the average relative deviation.Fang and He[15]developed a one parameter equation describing the dependence of viscosity for binary mixture based on Eyring's absolute reaction rate theory and the Flory-Huggins equation by introducing the concept of molecular surface fraction.Their results were able to express the viscosity for numerous binary mixtures and showed improvement over the Grunberg-Nissan equation.Dai et al.[16]studied the effect of water content on the viscosity of natural deep eutectic solvents.They found that the viscosity sharply decreased at water content below 20%and no influence of water molar content on viscosity after 20%water content.Rizana et al.[17]investigated the effect of hydrogen bond donor concentration in the range 66.7%to 90%on the viscosity of tetrabuty lammonium bromide based DES.Four different HBD were tested namely ethylene glycol,1,3-propanediol,1,5-pentanediol and glycerol.Except for glycerol,the concentration of HBD strongly affected the viscosity of DES.Moreover such DES,when compared to other DESs,has the highest density and viscosity and the lowest ionic conductivity.Francisco et al.[4]found that the viscosity of the formulated DES follow Vogel and Andrade equation and in the range of temperature studied(300-360 K).The results show thatthe increase in water contentsharply reduces the viscosity of the DES and the effect diminishes as the temperature increases.Guo et al.[18]studied the viscosity of DES prepared from choline chloride and three types of HBD namely phenol,o-cresol,and 2,3-xylenol.They found that the viscosity of the prepared DES decreases as the concentration of phenol increases.The measured viscosity was found to fit Vogel-Tamman-Fulcher(VTF)equation.

To address the substantialintermolecularinteraction between water and the DES molecules,a systematic experimental study was done to measure the viscosity of water mixtures of three common choline chloride-based DESs namely reline,ethaline and glyceline.Water molar ratio in the mixtures as well as temperature were varied to explore their effect.The molecular interaction among the mixture molecules was modeled using the molecular surface fraction concept.A one parameter viscosity model was optimized and validated against the experimental data.This model takes into account the effects of mixture composition and temperature.A similar modeling approach can be applied for similar systems.

2.Modeling Mixtures Viscosity

Modeling mixtures viscosity is a topic of utmost importance,and many sources have discussed its details[19].The fundamental viscosity rate theory of Eyring[19,20],states that the liquid mixture viscosity(μmix)can be related to the excess free energy of activation(GE#),molar volume,temperature and the ideal mixture viscosity and molar volume(μid,Vid)as:

From an engineering point of view,the assumption of negligible mixture volume change relative to the much bigger volume of solution is valid.Using this assumption in Eq.(1),(i.e.by setting:Vid=Vmix)and expressing the ideal viscosity in a simple mixing rule of linear molar fractions contribution[21,22],the Eq.(1)can be written as:

Eq.(2)can be written for a binary mixture as:

To account for the nonideality portion of Eq.(3),namely the(GE#/RT)term,Grunberg and Nissan[23]used a one parameter model to account for the molecular interactions as:

and they expressed Eq.(3)as:

Despite the success of the Grunberg and Nissan viscosity model in predicting the viscosity nonideality in many mixtures,the modelsuffers from a serious limitation.For symmetric molecular size mixtures,this model shows excellent viscosity predictions.However,for asymmetric molecules,the Grunberg and Nissan model fails to explain the nonidealities in the mixture viscosity.This shortcoming is more pronounced for the case of aqueous solutions.Many modifications have been proposed for correcting this limitation[24-26].

To better express the relative number of lattice cells occupied by the two components,the mole fraction in Eq.(5)should be replaced by the molecular surface fraction,θi.Assuming a hard sphere molecular geometry,the molecular surface fraction for a particular molecule(i)can be defined as:

Fang and He[15]proposed to use a one parameter mixture viscosity model on the basis of the Eyring's absolute reaction rate theory and the Flory-Huggins equation.They further expressed the(GE#/RT)term in Eq.(3)by analogy to the thermodynamic excess free energy.This was done by expressing the Flory-Huggins equation as:

And hence,Eq.(3)became:

where(w)is a model parameter that accounts for the binary exchange energy in a lattice model which can be calculated by regressing experimental viscosity data.The model of Eq.(8)was used for successfully predicting the viscosity of 527 binary systems and total 17268 points.The Fang-He model was also used for calculating the viscosities of binary ionic liquid co-solvent mixtures in which the difference in molecular sizes of the two components is large[22].

3.Experimental Methods

3.1.Chemicals used

All DESs ingredients,choline chloride(C5H14ClNO),ethylene glycol(C2H6O2),urea(CO(NH2)2)and glycerol(C3H8O3),were obtained from Merck Chemicals with high purity(＞98%)and used for the synthesis ofDESs with out further purification.As per the manufacturer's guide,the water mass fraction of these chemicals was less than 0.0001.An Ultrapure Synergy system supplied by Millipore,USA,was used to supply deionized UV treated water.The produced water is of resistivity 18.2 MΩ·cm(at 25°C)and TOC of＜5×10-9.

3.2.DESs preparation and characterization

Prior to any DES synthesis procedure,the salt as well as the corresponding hydrogen bond donor were dried in a vacuum oven set at 353.15 K overnight in order to get rid of any moisture or volatile traces in the samples.

A certain quantity of the choline chloride and each of the three DESs hydrogen bond donors were weighed and mixed mechanically in an incubator shaker(Brunswick Scientific Model INNOVA 40R)operated at 300 r·min-1and 80 °C for a maximum of 2 h.The two components were removed from the shaker when they form into a homogenous solution with no visible solid particles.The mixing of the DES samples was done at atmospheric pressure and under tight control of moisture content and also kept in air tight vials for storage in a moisture controlled desiccator(Cole-Parmer,Model:YO-17030-28).

3.3.Viscosity measurement

Viscosities of DES systems were measured at different temperatures using a Brook field R/S plus Rheometer.The device was calibrated by a zero-calibration method.Viscosity values were measured between 298.15 K and 358.15 K at 10 K intervals.The variation in the temperature is achieved by utilizing an external water bath and circulator(Protech HC-10).The viscosity measurements were validated against a standard specimen supplied by the manufacturerat three different temperatures.The exact and measured viscosity values at temperatures 293.15,333.15 and 373.15 K were(1505,1500),(4511,4504)and(4321,4311)mPa·s,respectively.The uncertainty in the viscosity and temperature measurements are 3%-5%of measured value and±0.01 K,respectively.

4.Results and Discussion

The aqueous mixtures viscosity of three of common choline chloride-based DESs namely Reline,Ethaline and Glyceline was measured each at different molar composition(0-1 mol fraction)and temperatures(298.15-353.15 K).A total of 125 viscosity data values were collected and used for further analysis.All these measurements are reported in Table 1.

Table 1 Measured viscosity(mPa·s)data for the studied DES mixtures

Figs.1-3 show a pictorial representation of the effects of water molar fraction and mixture temperature on its viscosity for the three studied DESs.It is worth mentioning that at the lowest temperature(298.15 K),the pure Reline sample was so viscose and its viscosity could not be measured due to solidification of the sample within the viscometer spindle cavity which prevented a reliable measurement.Generally speaking,the pure DESs viscosity can be ranked in the order Reline＞Glyceline＞Ethaline.This order is maintained for all other tested temperatures.

Fig.1.Viscosity of Reline aqueous mixtures at different temperatures.Experimental values(symbol),Fang-Hi model(solid line)and Grunberg-Nissan model(dashed line)predictions.

Fig.2.Viscosity of Ethaline aqueous mixtures at different temperatures.Experimental values(symbol),Fang-Hi model(solid line)and Grunberg-Nissan model(dashed line)predictions.

It was reported,that DESs have lower excess free energy of activation()than conventional ILs[26].The viscosity of DES is related to the volumes of the salt ions and the voids according to the Eyring equation=kNAV-1where k and NAare the Boltzmann and Avogadro constants,respectively,and V is the molar volume of the liquid.It was concluded thatthe electrostatic forces,which enhance the ionic conduction,are more predominant than the van der Walls interactions,which determine the level of fluidity of the solution[27].

Fig.3.Viscosity of Glyceline aqueous mixtures at different temperatures.Experimental values(symbol),Fang-He model(solid line)and Grunberg-Nissan model(dashed line)predictions.

It is well known that water can easily in filtrate the strong hydrogen bonding pattern in the hydrogen bond donors and consequently hydrate these molecules by the formation of new hydrogen bonds[28].From the figures corresponding to the three studied DES aqueous systems,it is clear that at low water content,the viscosity of the mixtures are much higher than those at high water content.Our previous molecular dynamics study[14]revealed that the HBD-HBD hydrogen bonds increase within the low water content region(＜5 wt%),as evidenced by the increase in number of hydrogen bonds.This increase become clearer as the amount of water increases,and after a water concentration of 25%,the components of the DES become highly hydrated with water.At these concentrations,water prefers the chloride anion for complexation over the choline cation or the HBD molecules.This can be also seen in the mixtures viscosity pro files.The pure DES viscosities decrease sharply as more water is added to the mixture.At a temperature of 303.15 K and a water mass fraction of 25%,the relative decrease ofthe Reline mixture is around 92%.Atthe same temperature and water mole fraction,the relative reduction of the Ethaline and Reline aqueous solutions are 64%and 73%respectively.

Temperature is another variable that has a considerable effect on the viscosity of mixtures.The increase of temperature weakens the H-bonding interactions between the DES salt and HBD molecules resulting in enhancing the degree of fluidity of these molecules and a corresponding decrease in viscosity.Looking at the Reline mixture viscosity(Fig.1),increasing the temperature from 303.15 to 353.15 K results in a viscosity reduction of around 94.5%,88%,83%,74%and 54%corresponding to the mixtures molar ratios of 0.9,0.7,0.5,0.3 and 0.1,respectively.Similarly,within the same water molar fractions,the Ethaline and Glyceline mixtures viscosities undergo viscosity reduction within the ranges(77%-72%)and(88%-72%)respectively.From these numbers,we see that the Reline mixture was the most affected by temperature ascompared to the othertwo systems.This may be anticipated due to the stronger H-bonding in Ethaline and Glyceline DESs as compared to Reline.However,more investigation on the molecular level need to be conducted to confirm this explanation based on the pattern and number of H-bonding as well as the atom radial distribution functions within the constituents of these DESs.

The model described in Eq.(8),was used to predict the aqueous DESs mixtures viscosity as a function of mixture composition and temperature.Writing the model in terms of DES and water components(denoted by the subscripts D and w respectively),the liquid viscosity can be written as:

The model predictions were compared to the conventional Grunberg-Nissan model of Eq.(5).To check the predictive efficiency of this model,the Average Relative Deviation(ARD)was calculated as:

where:μiexp:Experimental Solubility,μipred:Predicted Solubility and i:counter representing each mixture viscosity measurement at a certain water molar ratio and mixture temperature.This indicator quantifies the mean value of relative errors between the experimental and model predicted viscosities.In addition,the standard deviation(σ),which is another important statistical parameter,is calculated as a measure for the degree of dispersion of model predictions away from the average.This gives an estimation for the goodness of fit for the used model.This indicator is estimated using the following formula:

The binary exchange energy parameter in a lattice model(w in the model of Eq.(9))for the three studied DES aqueous mixtures was estimated by consolidating the modelpredictions with the experimentalviscosity data.This is done by minimizing an objective function of the form:

The estimated model parameter as well as the two goodness of fit indicators are reported in Table 2 for the three studied DES aqueous systems.All model predictions were with excellent quality as indicated by the ARD values.The average ARD for the Reline-based mixture was 2.1%while that of Ethaline and Glyceline-based mixtures were 1.1%and 1.6%respectively.On the other hand,the Grunberg-Nissan model gave unsatisfactory results for all systems studied.The ARD values for the Reline,Ethaline and Glyceline-based systems were:11.6%,8.1%,and 12.5%.Similarly,the degree of dispersion in model predictions around the mean which is quantified by the standard deviation was 7.975,0.394 and 1.894 for the three respective systems,while the Grunberg-Nissan model attained much higher standard deviations of:9.666,2.648 and 21.315 respectively.This indicates the superiority of the Fang-He viscosity model over the conventional Grunberg-Nissan model.It is clear that the asymmetry in the geometry of molecular constituents for the studied DESs could not be handled by the Grunberg-Nissan model,which is a fact reported for other similar binary mixtures.This is very clear from the predicted viscosity pro files and especially for the case of Glyceline-water mixture shown in Fig.3.(See Table 3.)

Table 2 The fitted binary exchange energy parameter in a lattice model(w)for the three studied DES aqueous mixtures with corresponding goodness of fit indicators

Table 3 The fitted Grunberg and Nissan parameter(d)for the three studied DES aqueous mixtures with corresponding goodness of fit indicators

Deviation of viscosity from ideal behavior(which is due to intermolecular interaction forces)can be estimated from the viscosity deviation calculated as:

where Δμ is the viscosity deviation from ideality,μmandμiare the viscosity of the mixture and the individual components,xiis the mole fraction.In general,negative values of the deviation in viscosity(Δμ)indicate the existence of weak intermolecular interactions upon mixing while the positive values of Δμ are due to strong intermolecular interaction.

Fig.4.Deviation in viscosity of Reline aqueous mixtures at different temperatures modeled by the Redlich-Kister model.

Fig.5.Deviation in viscosity of Ethaline aqueous mixtures at different temperatures modeled by the Redlich-Kister model.

Fig.6.Deviation of viscosity of Glyceline aqueous mixtures at different temperatures modeled by the Redlich-Kister model.

Eq.(13)was used to calculate the variation in viscosity of the DES aqueous mixture,Figs.4-6 show these deviation for Reline,Ethaline and Glyceline respectively.All measured viscosity deviations were negative for all water mole fractions and temperatures measured.The negative deviations in viscosity,may be due to unequal DES and water molecular sizes[29].In addition these large negative Δμ values signify the weakening of H-bonding between the DES constituents due to hydration by water molecules.This behavior is very similar to many ionic liquid mixtures[30,31].In all the studied DESs,the addition of water distorts the hydrogen bond network and consequently,increase the fluidity of the solution.This distortion is in the order Reline＞Glyceline＞Ethaline.This order also corresponds to the viscosity values of these DESs.

In all studied DES-water mixtures,the highest deviation was observed at around 30 mol%water.The deviation of viscosity with mole fraction is more pronounced at lower temperature possibly due to larger temperature effect as compared to the effect of mole fraction.Figs.4-6 also show the Redlich-Kister(RK)model prediction for the viscosity deviation pro files.The fitted model parameters are given in Table 4 for each of the temperature studied.The regression coefficient was above 0.998 for all considered temperatures.The RK model was capable for effectively explaining the reduction in viscosity compared to ideal behavior for the three DES aqueous mixtures with average ARDvalues of0.1146,0.0023 and 0.0266.The very lowaverage standard deviation values of 0.065,0.0013 and 0.0138 indicating that the RK model prediction are closely clustered around the data mean,which translates to a high agreement with the experimental values.

Table 4 The fitted Redlich-Kister parameters for the three studied DES aqueous mixtures with corresponding goodness of fit indicators

5.Conclusions

Three common choline chloride-based DESs namely Reline,Ethaline and Glyceline were mixed with water at differentmolar ratios and their viscosity was measured as a function of mixture molarcomposition and temperature.

In general,at low water content,the viscosity of the mixtures were much higher than those at high water content due to the hydration effect of water on the structure of DESs.In addition,increase in temperature resulted in enhancing the degree of fluidity of the mixtures molecules and consequently decreasing the viscosity.Among the system studied,Reline mixture was the most affected by temperature.At a temperature of 303.15 K and a water mass fraction of 25%,the relative decrease ofthe Reline mixture viscosity is around 92%.Atthe same temperature and water mole fraction,the relative reduction of the Ethaline and Reline aqueous solutions are 64 and 73%respectively.This can be explained by the stronger H-bonding in Ethaline and Glyceline DESs as compared to Reline.

The average ARDforthe Reline-based mixture was 2.1%while thatof Ethaline and Glyceline-based mixtures were 1.1%and 1.6%respectively.On the other hand,the Grunberg-Nissan model gave unsatisfactory results forallsystems studied.The with ARDvalues for the Reline,Ethaline and Glyceline-based systems were:11.6%,8.1%and 12.5%.

The experimental viscosity data of the three mixtures was regressed using the one parameter Fang-He viscosity model and compared to predictions of conventional Grunberg-Nissan model.Due to the asymmetric nature of molecular sizes involved in forming these mixtures,the Grunberg-Nissan model failed to predict viscosity and especially for the case of Glyceline-based syesm where the ARD reached 12.6%.On the other hand,the Fang-He model gave very good prediction results with ARD values of 2.1%,1.1%and 1.6%for the systems Reline,Ethaline and Glyceline-based mixtures respectively.

The deviation of viscosities of these mixtures was all negative indicating the effect of unequal DES and water molecular sizes as well as the weakening of H-bonding between the DES constituents due to hydration by water molecules.The highest viscosity deviation was observed at around 30 mol%water.The RK model was capable of effectively explaining the reduction in viscosity compared to ideal behavior for the three DES aqueous mixtures.

This study highlights the importance of incorporating water in the structure of common DESs and opens the way for more investigation of these systems on the molecular scale.The variation of viscosity can be deployed for improving the performance of liquid-liquid separation and reactive process by controlling the viscosity of these mixtures involved.

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