Article pubs.acs.org/IECR
Ethanol Clusters in Gasoline-Ethanol Blends Alexander Turanov†,‡ and Anatoly K. Khitrin*,‡ †
Zavoisky Physical-Technical Institute RAS, Sibirsky Tract, 10/7, Kazan 420029, Russia Department of Chemistry, Kent State University, Kent, Ohio 44242, United States
‡
S Supporting Information *
ABSTRACT: Formation of ethanol clusters in gasoline-ethanol fuel blends was studied by pulsed-fieldgradient NMR measurement of diffusion of ethanol molecules. The results, consistent with a simple model of clusterization, show that ethanol molecules form hydrogen-bonded clusters with concentration- and temperature-dependent average size. Association/dissociation kinetics is fast, and the measured diffusion coefficients are average values. Water molecules are attached to ethanol clusters and have the same coefficient of diffusion.
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INTRODUCTION Gasoline-ethanol blends are common motor fuels in several countries. The blend with 10% ethanol E10 is standard in the United States. Addition of bioethanol increases the octane number 1 and decreases the carbon footprint. Among disadvantages are increased fuel consumption and the drawbacks coming from the presence of water: a shorter shelf life, possible phase separation, and corrosive aggressiveness.2 Gasoline is a complex mixture of thousands of different hydrocarbons. It is virtually impossible to identify and quantify them all. At the same time, there are several molecules which have proton NMR peaks in “empty” regions of the spectrum. They can be easily identified, and their spectral intensities (concentrations) can be measured with high accuracy.3 NMR study using such probe molecules, existing in the blend or artificially added, can give valuable information about molecular organization and physical and chemical properties of the blends. In terms of solubility, “triple” gasoline-ethanol-water solutions are interesting physical systems because water is infinitely soluble in ethanol but insoluble in gasoline, while ethanol is infinitely soluble in gasoline. Only a 0.5 mass % water in the E10 blend causes fast phase separation. Therefore, the azeotrope bioethanol-water solution obtained by rectification should be dehydrated before it is mixed with gasoline. In this work, we studied formation of ethanol clusters in the fuel blends. In contrast to water, which forms a threedimensional (3D) network of hydrogen bonds, ethanol molecules with a single hydroxyl group prefer one-dimensional (1D) chains. Such chains of hydrogen bonds are present, as an example, in solid ethanol.4 Liquid ethanol, studied by X-ray diffraction, showed some presence of clusters, especially hexamers.5 Computational and IR study of ethanol dimers showed that they have a bonding energy even higher than that of water dimers (6.99 and 5.13 kcal/mol, respectively).6 When ethanol is dissolved in gasoline, we expect two factors to compete. The possibility of forming hydrogen bonds favors formation of clusters, while good solubility of ethanol in nonpolar gasoline facilitates dissociation of the ethanol clusters. © 2016 American Chemical Society
Among the few studied model systems resembling gasolineethanol blends is the ethanol-hexane binary solution explored by IR and NMR spectroscopy.7 It has been found that at low temperatures ethanol forms clusters even in dilute solutions. For the ethanol molecule, the O−H stretch frequency and chemical shift of the hydroxyl proton are sensitive to formation of hydrogen bonds. However, the average number of hydrogen bonds per molecule saturates fast at increased average size of the clusters, and it is at maximum for all cyclic clusters. In our experiments, we measured the coefficient of diffusion of ethanol molecules, the quantity more directly related to cluster size. The results can be interpreted in terms of a greatly simplified theoretical picture described in the next section.
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THEORETICAL BASIS In this section, we present a simple theory of diffusion for molecules forming weakly bonded clusters. The clusters are short-lived, and we assume that their association/dissociation kinetics is fast on a scale of the time used in diffusion measurement. In this case, the measured coefficient of diffusion D is the average over equilibrium distribution of cluster sizes. The equilibrium constants Kn, which relate the concentrations cn of the clusters with n ethanol molecules to the concentration c1 of free unimers, satisfy the Gibbs equation c K n = n n = e−ΔGn°/ RT (c1) (1) where cn is the dimensionless concentration of clusters with n ethanol molecules (molarity divided by 1 M) and ΔGn° is the standard molar Gibbs energy of formation of the cluster from individual molecules. We disregard the actual structure of the clusters by assuming that attachment of one more molecule to the cluster requires the same average Gibbs energy g°: Received: Revised: Accepted: Published: 9952
July 5, 2016 August 22, 2016 August 29, 2016 August 29, 2016 DOI: 10.1021/acs.iecr.6b02569 Ind. Eng. Chem. Res. 2016, 55, 9952−9955
Industrial & Engineering Chemistry Research ΔGn° = (n − 1)g °
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(2)
D1 n
RESULTS AND DISCUSSION
To study the effect of ethanol concentration on diffusion of ethanol molecules, we used the model system, which was prepared by adding variable amounts of anhydrous ethanol to ethanol-free gasoline. The results are shown in Figure 1 together with the theoretical fit by eq 8.
The effect of the cluster size on the diffusion coefficient Dn can be estimated using the Rouse model,8 which works well for dilute solutions of polymers.9,10 In our case, because hydrogen bonds are the major cluster-forming interactions, we expect linear structures similar to those of polymeric molecules. Then, Dn =
Article
(3)
where D1 is the diffusion coefficient of a single ethanol molecule (unimer). By introducing α = e−g °/ RT and γ = c1α
(4)
one obtains cn = c1(c1α)n − 1 = c1γ n − 1
(5)
and the average coefficient of diffusion D = D1
∑ γ n−1 ∑ nγ n − 1
= D1(1 − γ ) = D1(1 − c1α)
Figure 1. Coefficient of diffusion of ethanol in the prepared gasolineethanol blend as a function of ethanol concentration. The line is a theoretical fit by eq 8. Rhomb denotes the value for E10 sample.
(6)
By expressing c1 through the total concentration of the ethanol molecules c = ∑ ncn = c1/(1 − c1α)2
(7)
The fitting parameters are D1 = 7.2 × 10−5 cm2/s and α = 5.5. The standard molar Gibbs energy g0 of attaching one ethanol molecule to a cluster, estimated from this value of α, is g0 = −4.2 kJ/mol. D1 is the ethanol diffusion coefficient at infinite dilution when all ethanol clusters dissociate completely. We can assign this value to the diffusion coefficient of an individual ethanol molecule. The diffusion coefficient Db of the larger benzene molecule, almost unaffected by the addition of ethanol, is also shown in Figure 1 for comparison. One can notice that the diffusion coefficient of ethanol drops many times as the ethanol concentration increases. It is an unambiguous indication that ethanol molecules form clusters at higher ethanol concentrations, and that these clusters are not formed at small concentrations. By using eq 9, one can estimate from the data in Figure 1 that the average number of ethanol molecules per cluster for E10 gasoline at 25 °C is ⟨n⟩ = 2.9. A decrease in the diffusion time in the PFG NMR experiment to 5 ms did not spoil a perfect fit by the Stejskal−Tanner equation.11 This is an indication that averaging over cluster sizes (clusters dissociation/association) happens at much shorter time. The ethanol diffusion coefficient for the E10 sample at 25 °C is also shown in Figure 1 for comparison. This sample contains a small amount of water (one water molecule per 55 molecules of ethanol). The diffusion coefficient of water is very close to that of ethanol. It can be measured more accurately at decreased temperatures when the water peak is farther from the ethanol CH2 peak (see below). As an example, at 12.3 °C, the diffusion coefficients for water and ethanol are 1.79 × 10−5 and 1.91 × 10−5 cm2/s, respectively. This suggests that all water molecules are attached to the ethanol clusters, while most of ethanol clusters do not contain water. Similar to what occurs with decreased concentration, dissociation of clusters is favored by elevated temperature. Figure 2 shows the temperature dependence of the diffusion coefficients of ethanol and benzene in the E10 blend.
solving for c1 as a function of c and inserting it into eq 6, one finally obtains D = D1
1 + 4αc − 1 2αc
(8)
In the limit of small concentrations of αc ≪ 1, the clusters are fully dissociated, and D = D1. At large concentrations of αc ≫ 1, D = D1/ αc . By using eqs 5 and 6, one can obtain the following expression for the average number of molecules in a cluster: ⟨n⟩ =
∑ ncn ∑ nγ n − 1 D = = 1 ∑ cn D ∑ γ n−1
(9)
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EXPERIMENTAL SECTION The sample of regular E10 gasoline (octane number 87) was purchased on February 8, 2016 from a BP gas station in Kent, Ohio. Ethanol-free gasoline (octane number 90) was purchased on January 25, 2016 from Ravenna Oil Co. in Ravenna, Ohio. Ethanol-free gasoline contained a trace amount of ethanol (0.0015 mass %). Concentrations of ethanol and water were measured from 1H NMR spectra, as explained3 in our previous work. The spectrum and peak assignment for E10 gasoline used in this work is shown in the Supporting Information, Figure S1. The coefficients of diffusion of ethanol, water, and benzene were measured using the Stejskal−Tanner11 pulsed-fieldgradient (PFG) NMR sequence with the following parameters: diffusion time 20 and 10 ms x-gradients with maximum strength 10 G/cm. Except for the temperature-dependent measurements, all NMR experiments were done at 25 °C using an Agilent 500 MHz NMR spectrometer. Gasoline samples were placed in standard 3 mm NMR tubes filled to 4 cm. 9953
DOI: 10.1021/acs.iecr.6b02569 Ind. Eng. Chem. Res. 2016, 55, 9952−9955
Article
Industrial & Engineering Chemistry Research
Figure 2. Temperature dependence of the diffusion coefficients of ethanol (solid circles) and benzene (open circles) in the E10 gasoline blend.
Figure 4. Dependence on temperature of the chemical shifts of C6H6, −OH, H2O, −CH2−, and −CH3 in prepared gasoline-ethanol blend with a 13.2 mass % of ethanol (solid symbols), and chemical shifts of C6H6, −OH, H2O, −CH2−, and −CH3 in the E10 sample (open symbols).
Arrhenius dependences in Figure 2 can be interpreted as the following. For benzene, a molecule with fixed geometry, increased diffusion at elevated temperatures is a result of decreased viscosity of gasoline. For ethanol, in addition to the same effect of viscosity, there is an extra increase in diffusion due to dissociation of ethanol clusters. The activation energies in Figure 2 are 39 and 60 kJ/mol for benzene and ethanol, respectively. Additional proof of the cluster formation can be obtained from the chemical shift measurements. It is well-known that the NMR chemical shift of participating protons is greatly affected by the formation of hydrogen bonds.12−14 Chemical shifts for the model system at varying concentrations of ethanol are shown in Figure 3. Formation of ethanol clusters increases the
makes it possible to observe a relatively narrow peak. By assuming that the width of the resonance frequency distribution is about 1 kHz (2 ppm, compare to Figure 3), in the limit of short correlation time, we obtained that cluster lifetime is on the order of 1 μs.
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CONCLUSIONS Ethanol molecules in gasoline-ethanol fuel blends form small clusters. Average cluster size strongly depends on temperature and ethanol concentration. Association/dissociation kinetics is fast, and cluster lifetime is on the order of 1 μs. As a result, measured coefficients of diffusion are the values averaged over the equilibrium distribution of the cluster sizes. Our diffusion data can be interpreted in terms of the simple clusterization theory described in the Theoretical Basis. Very close values of the diffusion coefficients for ethanol and water suggest that water molecules are incorporated into ethanol clusters and move together with ethanol molecules.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b02569. (PDF)
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Figure 3. Chemical shifts of C6H6, −OH, H2O, −CH2−, and −CH3 in prepared gasoline-ethanol blend as a function of ethanol concentration.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. fraction of hydrogen-bonded protons in OH groups of ethanol and water. As a result, their chemical shifts increase at higher ethanol concentrations when larger clusters are formed. A similar increase at low temperatures, shown in Figure 4, can also be explained by increasing size of the ethanol clusters. We did not find a way to accurately measure the lifetime of the ethanol clusters. However, it can be roughly estimated from the width of the ethanol OH peak (7.9 Hz in the E10 sample). The major broadening mechanism for this peak is the dependence of the chemical shift of individual clusters on the cluster size in contrast to the water peak, where most of the broadening comes from the proton exchange. Fast change of the cluster size and, therefore, the ethanol OH chemical shift
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The work was supported by the ACS Petroleum Research Fund 55813-ND6. REFERENCES
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