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Dissolution Kinetics of [Hmim][BF4] Ionic Liquid Droplets in 1-Pentanol Peixi Zhu,† Thomas V. Harris,‡ Michael S. Driver,‡ Curt B. Campbell,‡ Lawrence R. Pratt,† and Kyriakos D. Papadopoulos*,† Department of Chemical and Biomolecular Engineering, Tulane UniVersity, New Orleans, Louisiana 70118, and CheVron Energy Technology Company, 100 CheVron Way, Richmond, California 94802 ReceiVed: June 4, 2009; ReVised Manuscript ReceiVed: July 29, 2009
Dissolving ionic-liquid droplets of 1-hexyl-3-methylimidazolium tetrafluoborate ([Hmim][BF4]) into surrounding 1-pentanol phase were investigated inside a glass rectangular channel microscopically at 23 ( 0.5 °C. The Epstein-Plesset mathematical model was used to fit the change of drop radius with respect to time. With solubility data of ionic liquid (IL) in 1-pentanol determined from UV-visible spectroscopy, the diffusion coefficient was determined. Measurements of conductivity and UV-visible spectroscopy at various concentrations at the same temperature were conducted in an effort to further understand the molecular aggregation/clustering behavior of the IL in 1-pentanol. Using the similarity between the solvent and the hydrophobic part of the IL, an aggregation structure was proposed. Introduction Ionic liquids (ILs) are molten salts with their melting point below 100 °C. Typically, ILs can remain liquid at room temperature and pressure. Their unique properties, such as low volatility, high solvation capacity, significant thermal stability, and their ability to catalyze reactions, render them ideal substitutes for conventional organic solvents and catalysts.1,2 The polarity and chemical properties of ILs can be tuned by varying the alkyl chain or the anion or by tailoring their molecular structure to generate task-specific ILs.3 Therefore, they can be used as solvents and catalysts for a wide range of reactions,4 while other applications include lubrication,5 electrochemical reaction,6 solvent extraction,7 gas separation,8 polymer plasticization,9 and self-assembly.10 Investigating dissolution kinetics and thus determining IL diffusivities, as well as understanding molecular interactions of ILs in alcohols, can be of great help in the design of liquid-liquid extraction and/or biphasic reaction systems. One typical example is hydroformylation with IL as the catalyst phase. Aldehyde and alcohol are the primary products in such process, and it is known that the mutual solubility of alcohols/ aldehydes in ILs rises with the increase of alcohol/aldehydes carbon number.11,12 IL issues that need to be addressed in this process stem from the fact that (i) dilution of ILs with heavy aldehydes or alcohols can reduce the phase separation properties, which hinders recycling capability; (ii) deactivation of transition metal complex may occur; and (iii) leaching of IL into the organic phase can raise product cost. Therefore, to improve IL behavior as a catalytic phase it would be necessary to understand fundamentally the interaction of ILs with alcohols. Certain aspects of liquid-phase behavior and solubility of IL/ alcohol mixtures have already been studied,13-17 and more specifically, the diffusion coefficient has also been reported for a few infinitely dilute systems.18 The Epstein-Plesset diffusion model has been previously used in conjunction with experiments for determining diffusion * To whom correspondence should be addressed. Email: kyriakos@ tulane.edu. Phone: (504) 865-5826. Fax: (504) 865-6744. † Tulane University. ‡ Chevron Energy Technology Company.
coefficients of gases in liquids.19-21 Such a model22 describes the diffusion-controlled dissolution of gas bubbles with radius r into an unsaturated liquid phase at time t without convection and hence the process is diffusion controlled. An improvement of this model was advanced by Duncan and Needham23 by taking into account the Laplace pressure inside the bubble, which lead to the rate-of-change of bubble radius
(
dr ) -DkHRT dt
2MWσ FRTr 4MWσ 1+ 3FRTr
1-f+
)
(
1 1 + r √πDt
)
(1)
where D is the diffusion coefficient of the gas species in the liquid, kH is Henry’s constant, R is the gas constant, and T is the temperature. f is defined as the ratio of initial concentration, C0, and saturated concentration, CS, f ) C0 /CS, MW is the molecular weight of gas, σ is the interfacial tension between gas and liquid, and F is the density of gas. When the radius of gas bubbles is relatively small, i.e., tens of micrometers as opposed to hundreds of micrometers, the transient term 1/πDt can be neglected due to the fact that D is large, and eq 1 can be written in a quasi-steady state form as
(
dr ) -DkHRT dt
)
2MWσ FRTr 1 4MWσ r 1+ 3FRTr
1-f+
(2)
It has also been shown that the Epstein-Plesset model is suitable for describing the dissolution of a liquid droplet in a secondary liquid phase.24 In such a case, Laplace pressure turns out to be relatively small, while 1/πDt may be comparable to 1/r. Duncan and Needham24 investigated the effect of the Laplace pressure on dissolution of aniline-in-water/water-inaniline, and negligible errors in droplet lifetimes were found for f up to 0.99. On the other hand, comparison of droplet lifetime with and without consideration of 1/πDt term shows
10.1021/jp9052693 CCC: $40.75 2009 American Chemical Society Published on Web 08/21/2009
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J. Phys. Chem. C, Vol. 113, No. 37, 2009 16459
a significant error, particularly for low f. The term kHRT can be substituted by CS/F on the basis of Henry’s law. Equation 1 can then be written as
[
dr (1 - f) 1 1 ) -DCS + dt F r √πDt
]
(3)
If the transient term is neglected in eq 3 and f is set to be 0, then a closed form of the equation can be obtained (eq 4) on the condition that r ) R0 at t ) 0:
R20 - r2 DCS ) t 2 F
(4)
Equation 4 gives the droplet radius as a function of time and the dissolution time of a droplet can be obtained by setting r ) 0, so
R20F ) td 2DCS
(5)
where td is lifetime (dissolution time) of the droplet. Therefore, the diffusion coefficient D can be obtained from data on solubility, original drop size, and dissolution time. In Duncan and Needham’s work,24 no attempt was made to determine the diffusion coefficient for the systems they studied. In our work, as will be explained later, the diffusion coefficient is determined. We used two methods of combining experimental data with the Epstein-Plesset model to determine the diffusion coefficient of 1-hexyl-3-methyimidazolium tetrafluoborate ([Hmim][BF4]) in 1-pentanol at 23 ( 0.5 °C. Comparison of our result with the well-known empirical Wilke-Chang equation, the latter predicts a greater value for the diffusion coefficient, indicating that large aggregates of IL species may take place in solution. To better understand the molecular aggregation of this IL in 1-pentanol we used UV-visible spectroscopy and measured the electrical conductivity of ILin-pentanol solution from very dilute to saturation conditions. All experiments were conducted at the temperature mentioned above. Experimental Section Materials. IL [Hmim][BF4] (97% purity) and 1-pentanol (99%) were purchased from Sigma. Prior to usage, the IL was diluted with dichloromethane to reduce viscosity and stirred with activated charcoal for 6 h to remove color. Activated charcoal was subsequently filtered out, and the IL/CH2Cl2 mixture was extracted with deionized water to remove residue ions. The IL/ CH2Cl2 was then subjected to vacuum at 70 °C for 12 h to remove residue water and CH2Cl2, and stored in a vacuum desiccator. Residue water in 1-pentanol was removed with 3 Å molecular sieve (Sigma). Microscopy in Rectangular Channels. Glass melting-point tubes (i.d. ) 0.70 mm) were purchased from Drummond. With a micropipet puller (Narishige, PB-7), they were turned into micropipets that had an i.d. of around 10 µm. Micropipet tips were ground with a microgrinder (Narishige EG-400), followed by forging with a microforge (Narishige MF-9). Because the IL is hydrophilic and tends to spread on the tip, micropipets were treated with 2% Siliclad (from Gelest) for 1 min and left in the oven at 60 °C until the tip was dried. The rectangular
Figure 1. Microscopy setup.
glass channel (5 mm × 2 mm × 70 mm, from Friedrich and Dimmock, Inc.) in Figure 1 was filled with 1-pentanol and was placed on the stage of an inverted microscope (Olympus IMT2) incorporated with a 210 frames-per-second camera (Imperx IPX-VGA-210-L). The micropipet was then filled with IL and inserted from the side of the channel. Injection of an IL droplet was achieved by using a micropipet injector (Narishige, IM200). The temperature was maintained at 23 ( 0.5 °C. After a droplet was formed, the pressure was adjusted so that the liquid inside the micropipet did not move and the droplet was held by the pipet tip. The droplet started to shrink after injection. The high-frame-rate camera mentioned above filmed the process. IL Solubility in 1-Pentanol and Electrical Conductivity of IL/1-Pentanol Mixture. Solubility measurements followed the procedure described by Chapeaux et al.25 Roughly 0.3 mL of [Hmim][BF4] and 0.5 mL of 1-pentanol was placed in a vial sealed with Teflon cap at 23 ( 0.5 °C. The mixture was stirred for 24 h to ensure phase equilibrium and stored for another 24 h for phase separation. An aliquot (0.1 mL) of the 1-pentanolrich phase was diluted with 1-pentanol in a 50 mL volumetric flask. The solubility was determined with UV-visible spectroscopy at the wavelength of 211 ( 2 nm using a Shimadzu 1700 spectrometer. Note that the Beer-Lambert linear range of [Hmim][BF4] in 1-pentanol is below 0.3 mmol/L, although solutions with higher concentration were also used for investigating IL aggregation behavior. Solution conductivity for concentrations between 0.05 and 40 mmol/L were measured with a conductivity meter (FisherScientific Traceable Bench). All measurements were performed at 23 ( 0.5 °C. Results and Discussion Study of Rate of Dissolution and Determination of Diffusion Coefficient. The dissolution behavior of the [Hmim][BF4] in 1-pentanol is shown through the snapshots of Figure 2. Several experiments were conducted with droplets that had different original radii. The evolution of three droplets’ radius with different R0 with respect to time is shown in Figure 3. As explained below, for a strictly diffusion-controlled dissolution of a drop, it would be possible to use the data of Figure 3 to
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Figure 2. Frames showing dissolution of droplet at an ambient temperature of 23 ( 0.5 °C.
Figure 4. Plot of t(dr/dt) vs (t/r). Figure 3. Evolution of three [Hmim][BF4] droplets in 1-pentanol.
obtain both the diffusion coefficient and the solubility of [Hmim][BF4] droplet in 1-pentanol. Multiplying by t both sides of eq 3 yields
√t
[
DCS √t dr 1 )+ dt F r √πD
]
(6)
Equation 6 indicates that a plot of t(dr/dt) vs (t)/(r) should produce a linear curve, where the slope S and intercept I are
S)-
DCS F
(7)
and
I)-
√DCS F√π
(8)
These two equations may then simply be solved for the two unknowns: diffusion coefficient, D, and solubility, CS. Our plot of t(dr/dt) vs (t)/(r) with R0 ) 45.32 µm in Figure 4, however, shows a few plateaus, although the linearity in some regions is maintained. The departure from linearity may be the result of imperfections inherent in the experiment, such as minute random vibrations of the microscope stage, which would
lead to faster dissolution. However, it may also indicate transformations of molecular states at the interface during dissolution process; it is possible that IL species form clusters of differing sizes at different stages of the dissolution process, resulting in an alteration of the free energy at the interface, therefore changing the rate of dissolution. In order to determine an “average” or “effective” diffusion coefficient during the IL-droplets’ dissolution process, we measured the solubility CS independently via UV-visible spectroscopy, and used eq 3 as follows. By setting ξ ) r/R0, and τ ) πDt/R02, eq 3 can be written as
(
CS 1 dξ 1 )+ dτ πF ξ √τ
)
(9)
The initial condition is ξ ) 1 at τ ) 0. Equation 9 is in dimensionless form and a numerical solution for ξ vs τ is shown in Figure 5, with CS ) 0.018 g/mL and F ) 1.149 g/mL26 at 23 ( 0.5 °C. At this point it is important to note that the dimensionless lifetime of the droplet is
τd ) τDtd /R20,
(10)
and that τd is a constant for a given system that has a fixed CS/F ratio as per eq 9. Since τd is independent of diffusion coefficient D and initial radius R0, a plot of the experimental initial radii R0 vs their corresponding td0.5 should be a straight
Dissolution Kinetics of [Hmim][BF4] Ionic Liquid Droplets
Figure 5. Dimensionless evolution of an IL droplet radius as a function of time as per eq 3. The value of τd is numerically found to be equal to 85.7.
Figure 6. Near-linear relationship of R0 vs td0.5.
line, with slope (πD/τd)1/2. Since τd is known (Figure 5), D can be easily determined. Figure 6 is a plot of R0 vs td0.5 for five different droplets showing a linear relationship between the two and revealing a diffusion coefficient D ) 1.87 × 10-10 m2/s. Noticing that not all five points fall exactly on the regressed straight line of Figure 6, in order to determine a measure of the error involved in the obtained value for D, we also evaluated D for each of the five drops of the experiments by fitting singledrop radius-vs-t experimental data to the MATLAB solution of eq 3 with f ) 0. The diffusion coefficient obtained from this method is D ) (1.87 ( 0.12) × 10-10 m2/s. The error is within 6.4%, but it should be noted that D measured by our method is an average diffusion coefficient during the dissolution process of the IL drops. In previous studies on the diffusivity of IL in water, the Wilke-Chang equation gave good agreement with experimental data when a correction factor of 1.634 was used.27 According to the original Wilke-Chang equation,
0 DAB
-12
) 7.4 × 10
(φMB)1/2T ηBVA0.6
(11)
J. Phys. Chem. C, Vol. 113, No. 37, 2009 16461
Figure 7. Conductivity measurement of the [Hmim][BF4]-1-pentanol solution at 23 ( 0.5 °C.
where MB and ηB are molecular weight and viscosity of the solute, VA is molar volume of the solvent, T is temperature, and φ is a factor equal to 1.0 for 1-pentanol. The estimated D value from the corrected Wilke-Chang equation for [Hmim][BF4] in 1-pentanol is 2.31 × 10-10 m2/s. It has previously been reported that ILs in alcohols tend to associate as aggregation states even at low concentrations,28 which may explain the lower D of our experiments when compared to the value obtained from the Wilke-Chang equation, i.e., [Hmim][BF4] may form large aggregates as it dissolves in the surrounding 1-pentanol, which would slow down the overall diffusion process. Electrical Conductivity Measurement. To understand the IL dissociation behavior, the electrical conductivity of the ILin-pentanol solution was measured over a range of concentrations below saturation (72 mmol/L). Molar conductivity, Λm, as a function of C1/2 is shown in Figure 7. Clearly, [Hmim][BF4] behaves as a weak electrolyte in 1-pentanol. We then assume that CA h C+ + A-, where C+ and A- stands for cation and anion of IL, respectively, is the only clustering equilibrium at the lowest concentrations. If R, the fraction of CA molecules dissociated, may be approximated by
R = Λm /Λ0 29,
(12)
the equilibrium ratio, assumed to be independent of concentration, can be defined by
K)
2 CΛm CR2 ) 0 0 1-R Λ (Λ - Λm)
(13)
While extrapolation of molar conductivity for infinite dilution in Figure 7 would be unreliable, a standard way of determining K is to transform eq 13 to
CΛm )
K(Λ0)2 - KΛ0 Λm
(14)
Assuming that K and Λ0 are satisfactorily constants, eq 14 indicates that a plot of CΛm vs 1/Λm should be linear over a range of low concentrations, and Figure 8 shows such a plot
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Figure 8. Plot of CΛm vs 1/Λm. The straight line is a linear fit at low concentrations.
Figure 9. UV-visible spectroscopy of [Hmim][BF4] in 1-pentanol at 23 ( 0.5 °C.
for [Hmim][BF4] in 1-pentanol. The linear fit for concentrations below 0.3 mmol/L gives Λ0 ) 7.73 µS/cm · mmol · L and K ) 0.251 mmol/L, but since CΛm vs 1/Λm is not linear over the entire measurement range, the above assumption may not be valid over that broader range and higher-order aggregates may be formed. Furthermore, we see that the normal ionic solutions’ straight line followed by a break point at the incipience of ionic clustering30 is not observed in our case and that the absolute conductivity is lower than the same IL’s aqueous solution.27 Since conductivity is affected by charge density and mobility of ions, the conductivity measurements suggest that [Hmim][BF4] may exist primarily in the form of large aggregates in 1-pentanol, particularly at high concentrations, which will lower both the ion density and mobility. UV-Visible Spectroscopy. To further investigate the aggregation behavior of [Hmim][BF4] in 1-pentanol, UV-visible spectroscopy measurements were conducted at various concentrations at 23 ( 0.5 °C (Figure 9). It is shown that at low concentrations the maximum absorption λmax occurs at 211 nm and linearity is sustained. Therefore, spectra at low concentrations (from 0.05 to 0.3 mmol/L) were used to generate a calibration curve for the determination of solubility. As concentration goes up, a red-shift of the spectrum starts to occur and the signal-to-noise ratio makes the determination of λmax difficult. Therefore, the differential method was applied and λmax
Zhu et al.
Figure 10. λmax as a function of C. Inset: Zoom-in at low concentration.
was determined as the position where the second derivative is minimum. The result in Figure 10 shows that λmax goes up with increasing concentration. Unlike in the case of IL in water,31 a critical aggregate concentration (CAC) cannot be determined from Figure 10 since no distinct break point is observed. However, like in the IL-water system, a similar trend may be identified,31 which is a much steeper slope of the curve at lower concentration. The absorption at 211 nm corresponds to the πfπ* transition of the imidazolium ring. Below 0.3 mmol/L, λmax is independent of concentration since CA h C+ + A- is the only equilibrium, and no aggregates are formed. The increase of λmax indicates the lowering of such transition energy, which is due to the formation of hydrogen bonds. The rapid increase of λmax at low concentration (C > 0.3 mmol/L) suggests that [Hmim][BF4] may start to form aggregates (e.g., dicationic aggregates, C2A+), which are internally associated with hydrogen bonding, although such hydrogen bonds are weaker compared to those between H2O and IL molecules. At such concentration, the IL is solvated by several 1-pentanol molecules. As the concentration goes up (C > 2.5 mmol/L), excess IL cations will insert to the already existing solvated ions.31 Since the polarity of solvent has great impact on aggregation behavior of ILs,28 it is likely that larger aggregates are generated, which slows down the increase of λmax. At even higher concentrations (above 10 mmol/L), a further slowing down of λmax is observed. This probably indicates that maximum aggregation size is reached, as well as the possible saturation of hydrogen bonds. By noticing that the hydrophobic part of the IL has a similar chain length as the solvent molecule, a reverse-micellar type of structure is proposed for the aggregate in Figure 11. In this structure, the IL cation is mixed with 1-pentanol, with their hydrophilic domain pointing inward and hydrophobic domain pointing outward. The saturation of such aggregates is reached (if such saturation is lower than the solubility) when IL cation and 1-pentanol are alternatively adjacent to each other (see drawing). The hydrogen bond is formed between the oxygen atom and the C-H bond that is located on the imidazolium ring. Anions either surround the cluster or are to be found in the center of the cluster, with hydrogen bonds stabilizing the aggregate. Conclusions The dissolution of IL [Hmim][BF4] droplet in 1-pentanol showed deviation from linearity in the plot of t(dr/dt) vs (t/r), which may indicate the transformation of molecular states
Dissolution Kinetics of [Hmim][BF4] Ionic Liquid Droplets
Figure 11. Possible aggregation scheme.
during the process. An “average” or “effective” diffusion coefficient was determined, which was lower than the one estimated by the Wilke-Chang equation. Electrical conductivity measurements of the solution at various concentrations showed that CA h C+ + A- is the only equilibrium at low concentrations, while aggregates may form as concentration rises. Furthermore, λmax obtained from UV-visible spectroscopy corroborated the electrical conductivity data. Hydrogen bonds must be the main binding force for the formation of aggregates and clusters. Using the fact that the IL is of similar length as the solvent molecule, an aggregation structure was proposed for high concentration, with IL and 1-pentanol alternatively adjacent to each other. Acknowledgment. Support from the Louisiana Board of Regents (Industrial Ties Research Subprogram) and Chevron Energy Technology Company is gratefully acknowledged. References and Notes (1) Welton, T. Chem. ReV. 1999, 99, 2071. (2) Dupont, J.; de Souza, R. F.; Suarez, P. A. Z. Chem. ReV. 2002, 102, 3667. (3) H. Davis, J. J. Chem. Lett. 2004, 33, 1072.
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