Dehydration of Isobutanol and the Elimination of Water from Fuel

Article pubs.acs.org/JPCA

Dehydration of Isobutanol and the Elimination of Water from Fuel Alcohols Claudette M. Rosado-Reyes* and Wing Tsang National Institute of Standards and Technology, Gaithersburg, Maryland 20899, United States

Ionut M. Alecu, Shamel S. Merchant, and William H. Green Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States S Supporting Information *

ABSTRACT: Rate coefficients for the dehydration of isobutanol have been determined experimentally from comparative rate single pulse shock tube measurements and calculated via multistructural transition state theory (MS-TST). They are represented by the Arrhenius expression, k(isobutanol → isobutene + H2O)experimental = 7.2 × 1013 exp(−35300 K/T) s−1. The theoretical work leads to the high pressure rate expression, k(isobutanol → isobutene + H2O)theory = 3.5 × 1013 exp(−35400 K/T) s−1. Results are thus within a factor of 2 of each other. The experimental results cover the temperature range 1090−1240 K and pressure range 1.5−6 atm, with no discernible pressure effects. Analysis of these results, in combination with earlier single pulse shock tube work, made it possible to derive the governing factors that control the rate coefficients for alcohol dehydration in general. Alcohol dehydration rate constants depend on the location of the hydroxyl group (primary, secondary, and tertiary) and the number of available H-atoms adjacent to the OH group for water elimination. The position of the H-atoms in the hydrocarbon backbone appears to be unimportant except for highly substituted molecules. From these correlations, we have derived k(isopropanol → propene + H2O) = 7.2 × 1013 exp(−33000 K/T) s−1. Comparison of experimental determination with theoretical calculations for this dehydration, and those for ethanol show deviations of the same magnitude as for isobutanol. Systematic differences between experiments and theoretical calculations are common.

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INTRODUCTION This is the third in a series of papers on the unimolecular decomposition of butanols.1,2 Attention will be focused on the rate coefficients for the dehydration process involving isobutanol along with results of theoretical calculations, including comparisons between experiments and theory. Considering the variety of processes during combustion, theoretical calculations must be extensively used in compiling the kinetics databases. However, there is a great deal of uncertainty in the accuracy of such calculations. In the case of unimolecular decompositions, the comparative rate single pulse shock tube technique provides a means of calibrating a distinct class of theoretical calculations. At the same time we are interested in other means of estimating such rate coefficients using rate data that are now in the literature, leading to the derivation of empirical rate rules. We will show that the totality of single pulse shock tube experiments do in fact lead to rate rules for dehydration of alcohols. The paper will therefore begin with an extensive background discussion of the various elements described above. There has been a great deal of recent interest in the combustion of biofuels.3 Numerous studies have been published describing their combustion properties.4−10 A particular focus has been on the butanols. These results have been rationalized on the basis of simulations using various postulated mechanisms and associated rate expressions. The rate coefficients that are the key elements in the simulations are © 2013 American Chemical Society

largely based on analogies or rate rules. The lack of direct experimental measurements can lead to serious errors in the assignment of rate coefficients, invalidating the conclusions being drawn from the simulations. A particularly interesting aspect of alcohol decomposition is its dehydration. This unimolecular decomposition involves concerted breaking and forming of chemical bonds and, in the case of isobutanol, leads to the direct formation of isobutene and water. Of special importance are the relative contributions from bond breaking to form reactive radicals and the direct formation of stable products. In the case of isobutanol, the stable product is an olefin, isobutene, which can act as a chemical inhibitor and hence remove active radicals from the combustion system. A fundamental problem for the reactions that lead to molecular entities is that unlike the situation for bond breaking reactions, the energy barriers are unknown. In the past, the only means of obtaining such information was through experiments. Increasingly accurate and efficient computational quantum chemistry methods offer an alternative means of obtaining macromolecular information about reaction systems from statistical treatments of processes occurring at the molecular level. Steady progress in electronic structure theory has led to the development of modern computational methods Received: May 10, 2013 Revised: June 25, 2013 Published: June 27, 2013 6724

dx.doi.org/10.1021/jp4045513 | J. Phys. Chem. A 2013, 117, 6724−6736

The Journal of Physical Chemistry A

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abstractable hydrogen atoms in 1,3,5-trimethylbenzene. This can be compared with six abstractable primary, one tertiary, and two hydrogen atoms adjacent to the OH group in isobutanol. The bond dissociation energy of all these bonds is larger than that for the benzylic radical. Thus we expect >95% of radicals will react with the 1,3,5-trimethylbenzene either by abstraction or in case of hydrogen atoms by displacing a methyl radical via the reactions,

that can routinely achieve sub-kJ/mol accuracy for important quantities such as the reaction barrier height and the energy of reaction.11,12 Although the calculation of increasingly accurate potential energy surfaces remains an active area of research, another issue of paramount importance in reactions involving species with multiple torsional degrees of freedom is the calculation of accurate anharmonic partition functions for such species. In this paper we present comparisons between a wellestablished experimental procedure and various theoretical calculations. The ultimate goal is to develop a validated theory that can be used in the cases where experimental data are limited or unavailable. This work is focused on understanding the fundamental processes that occur in thermal reactions. The rate coefficients of such reactions form the elements of the kinetic databases that are used in the simulation of combustion phenomena.6,8 They can also be estimated from theoretical calculations. To obtain unambiguous experimental results, special attention must be paid to the reaction conditions so that what is measured is truly the thermal rate process of interest. The initial process in the combustion of most larger fuel molecules involves unimolecular decomposition. Although it is known that the H + O2 reaction is the controlling process in combustion, secondary processes such as unimolecular decomposition are the reactions that distinguish one fuel from another. This is of course the main thrust of modern combustion research.

H + 1,3,5‐trimethylbenzene → H 2 + 3,5‐dimethylbenzyl radical (abstraction)

(R1)

H + 1,3,5‐trimethylbenzene → meta‐xylene + CH3

(R2)

The ratio of abstraction product and m-xylene have been determined in an earlier study.15 The rate expressions for the two reactions are kR1 = 3.7 × 1011 exp( −4340 K/T ) L mol−1 s−1 kR2 = 6.7 × 1010 exp( −3260 K/T ) L mol−1 s−1

The rate expressions for the abstraction and addition channels have been determined earlier at temperatures below 1050 K, using hexamethylethane16 as the H-atom source. The present work assumes that rate coefficients for H-atom reactions can be extrapolated to temperatures as high at 1250 K. In any case, there is no conceivable mechanism that can account for the production of isobutene from the radical induced decomposition of 1,3,5-trimethylbenzene. The standard reaction used in these studies is the reverse Diels−Alder decomposition of cyclohexene,

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EXPERIMENTAL METHODOLOGY13 The single pulse shock tube is an ideal high temperature chemical reactor.14 The high temperatures are achieved gas dynamically, and reactions at the reactor wall contribute negligibly. The single pulse feature permits the analysis of all final products. The capability of detecting and quantifying all products is particularly important for studies on the decomposition of larger fuel molecules. The short residence times, the capability of carrying out studies at very low concentrations of reactants (∼0.1−1%), the availability of analytical instrumentation with the capability of detecting products at the lowest concentrations and the use of chemical inhibitors in large excesses to remove active radicals, all serve to isolate and identify individual reaction channels for study. The last point will be discussed in greater detail subsequently. This capability also permits the study of several unimolecular reactions simultaneously, which leads to the use of internal standards that serve to remove all the inherent systematic uncertainties associated with shock tube experiments. The method has been used for many years to study the unimolecular reactions for hydrocarbon fuel molecules and radicals, for the determination of generally accepted mechanisms, rate expressions, and bond dissociation energies. In this paper the method is applied to studies on the dehydration of isobutanol. The experiments were carried out in a heated single pulse shock tube with dilute concentrations of isobutanol (500 μL/L) in large excesses of 1,3,5-trimethylbenzene (135TMB, 10 000 μL/L) in argon. Mixtures were prepared by direct injection of liquid samples through a septum into a heated (100 °C) 15 L sample holding tank. The heated (100 °C) aspect of the shock tube permits the introduction of substances without condensation on surfaces. The ratio of inhibitors to target molecule is 20:1. Note that there are nine weak C−H bonds (the bond energy is weakened by benzyl resonance) that contain readily

cyclohexene → ethylene + 1,3‐butadiene

(R3)

which has a corresponding rate coefficient given by the following expression,17,18 kR3 = 1.4 × 1015 exp(− 33500 K/T ) s−1

The initial concentration of cyclohexene in the gas mixture of study is 200 μL/L. The cyclohexene standard reaction R3 is strictly molecular in nature. Its rate expression has been determined in numerous earlier studies in shock tubes as well as by other techniques. One obtains the experimental after-shock temperature from the following relationship, [1,3‐butadiene(or ethylene)] ⎞⎞ 1 −R ⎛ −1 ⎛ ln⎜⎜ ln⎜1 − = ⎟⎟⎟ T Ea ⎝ At ⎝ [cyclohexene]i ⎠⎠

where A and Ea are the rate parameters for the reverse Diels− Alder reaction, t is the residence time of 500 μs, and T is the reaction temperature. Note that with our internal standard technique uncertainties in the residence time will also cancel out.19,20 The estimated uncertainty in the rate coefficient of the temperature standard is 10%,18 and the uncertainties in the measured concentrations and residence time are similar, which cumulatively translates into a few percent (∼20 K) uncertainty in the experimental after-shock temperature. The basic procedure involves shock heating the reaction mixture with hydrogen as the driver and then sampling the mixture for GC/FID/MS analysis, utilizing two gas chromatographic columns. The first, Restek 30 m × 0.53 mm i.d. RtAlumina capillary column, is designed to be used for the analysis of the lighter or smaller organics, whereas the other, J&W Scientific 30 m × 0.53 mm i.d. DB-1 fused silica column, 6725



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deficient for a dynamical system composed of a multitude of interconnected torsional conformers, and instead, the SSRRHO partition functions are replaced by MS-T partition functions QMS‑T con‑rovib, in which the contributions of all structures are included in the partition function and compensations are made for the fact that the potential energy functions characterizing these torsional motions are periodic rather than quadratic (i.e., the harmonic-oscillator model is unphysical for torsional motions). The MS-T partition functions employed in MS-TST have been described in detail elsewhere,23 and the application of these partition functions to derive accurate thermochemistry for flexible molecules, as well as the remarkable accuracy that can be attained from integrating these partition functions with various versions of single-structural TST to calculate rate coefficients for complex reactions have been highlighted in recent studies.22,24−29 Therefore, we only briefly discuss the MS-T method for calculating partition functions here. The MST method involves using the number of conformers and their geometries, frequencies, and relative energies to reliably approximate local-harmonic partition functions and partition functions for free-internal-rotation (i.e., partition functions that correctly describe torsions in the limits of low and high temperature T, respectively). At intermediate temperatures, partition functions for hindered-internal-rotation are obtained by interpolating between the local-harmonic and free-rotor limits via a smooth interpolation function. Once the set of structures interconnected by torsional motions is obtained, the MS-T conformational rotational−vibrational partition functions are calculated via

is used to analyze the heavier compounds. All gas samples were obtained from Sigma-Aldrich and used without further purification. Gas chromatographic analysis indicated the absence of any detectable impurities.

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COMPUTATIONAL APPROACH AND THEORETICAL TREATMENT Modern computational chemistry is developing the capability of making increasingly accurate determination of the properties of molecules and transition states. This is due to the ability to treat complex systems in a realistic framework. In this article, we use multistructural transition state theory21,22 with tunneling modeled by an asymmetric Eckart potential (MS-TST/E) to investigate the isobutanol dehydration reaction between 600 and 2400 K. MS-TST is a version of conventional TST that is more suitable to the calculation of rate coefficients for complex reactions involving nonrigid species (reactants and transition states having multiple conformers (structures) that can readily interconvert among themselves). To better capture the dynamical nature of flexible reaction systems, the typical “rigid molecule” partition functions entering the conventional TST formula, calculated from the properties of a single structure (usually the lowest-energy conformation) of the reactant or the transition state via the rigid-rotor-harmonicoscillator model, are replaced in MS-TST by more physically meaningful conformationally averaged (i.e., multistructural) rotational−vibrational partition functions that account for torsional anharmonicity, denoted as MS-T23 partition functions. The TST and MS-TST thermal rate coefficients for such a process can be written as kSS ‐ TST(T ) = κ(T )σ ′

1 βh

k MS ‐ TST(T ) = κ(T )σ ′

SS ‐ RRHO, ‡ Q rovib,1 (T ) SS ‐ RRHO,R Q rovib,1 (T )

J MS ‐ T Q con = ‐ rovib

j=1

exp( −βV )‡

MS ‐ T, ‡ 1 Q con ‐ rovib(T ) exp( −βV ‡) MS ‐ T,R βh Q con ( T ) ‐ rovib

t

∑ Q jrot exp(−βUj)Q jHOZj ∏ f j ,τ τ=1

(3)

Qrot j

(1)

where is the classical rigid-rotational partition function of structure j, QHO is the usual normal-mode harmonic-oscillator j vibrational partition function calculated at structure j, Zj is a factor designed to ensure that the MS-T scheme reaches the correct high-temperature limit (within the parameters of the model), and f j,τ is a torsional anharmonicity function that, in conjunction with Zj, amends the harmonic partition function of structure j to account for the presence of the torsional motion τ. In the above expression, the distinguishable structures of a reactant or transition state are labeled by j = 1, 2, ..., J (where J is the total number of respective reactant or TS structures). Correspondingly, Uj denotes the potential energy of structure j with respect to the lowest-potential-energy reactant or TS structure, respectively. The lowest-potential-energy reactant or TS structure is always numbered as j = 1, so U1 is zero by definition. The reactant partition function is calculated using the zero-point-exclusive energy of isobutanol as the zero of energy; similarly, the partition function for the TS is calculated taking its zero-point-exclusive energy as the zero of energy. Multistructural F-Factors. It is often convenient to recast kMS‑TST in terms of kSS‑TST, and by inspecting eqs 1 and 2 it can be seen that this expression should be of the form

(2)

where k is the tunneling transmission coefficient (approximated via an asymmetric Eckart model in this article), σ′ is the ratio of the number of enantiomers of the TS to that of the reactant (i.e., the number of mirror image structures nonsuperposable via rotations and vibrationsbecause rotational symmetry numbers and vibrational symmetry numbers are included in the rotational and vibrational partition functions, respectively), β is (kBT)−1, kB is Boltzmann’s constant, h is Planck’s constant, and V‡ is the classical potential energy difference between the TS and the reactant. The difference between eq 1 and eq 2 is in the way the rotational and vibrational contributions to the partition function are calculated. In eq 1, just a single structure (SS) of the TS or the reactant is considered and it is assumed that its rotations and vibrations can be reasonably described by the rigid-rotor (RR) and harmonic-oscillator (HO) models, respectively; to emphasize this, we denote conventional TST as single-structural TST (SS-TST). Therefore, the QSS‑RRHO rovib,1 partition functions appearing in eq 1 simply correspond to the products of the classical rigid-rotor QRR 1 and harmonic-oscillator QHO for either the reactant or the TS, and the subscript “1” 1 refers to the fact that, in general, the properties of the lowestenergy conformer will be used in calculating these contributions. In eq 2, it is realized that the SS approximation is

k MS ‐ TST(T ) = F MS ‐ T(T ) kSS ‐ TST(T )

(4)

in which FMS‑T is a reaction-specific factor that adjusts the SSTST result for the presence of multiple TS and reactant structures interconnected by torsions. FMS‑T is obtained from the ratio of species-specific F-factors for the TS and the reactant, 6726



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Figure 1. Scheme of reaction mechanism for isobutanol dehydration (highlighted in red)as a result of thermal decomposition.

F MS ‐ T(T ) =

MS − T FTS (T )

FRMS − T(T )

used to obtain the MS-T partition functions used in MS-TST/ E. All internal degrees of freedom were scaled by 0.970, a previously determined35 empirical scale factor for vibrational frequencies obtained with M06-2X/MG3S. The classical energies of the lowest-energy conformers (at the M06-2X/ MG3S level of theory) of all species along the reaction coordinate were further refined via high-level single-point calculations with the CCSD(T)-F12a explicitly correlated method36,37 accompanied by the efficient jul-cc-pVTZ38 basis set. The ensuing CCSD(T)-F12a/jul-cc-pVTZ//M06-2X/ MG3S barrier height and energy of reaction, and the M062X/MG3S MS-T partition functions for isobutanol and the TS were then used to calculate thermal rate coefficients for the above reaction via MS-TST/E. The M06-2X/MG3S geometry optimizations and frequency calculations were carried out using the Gaussian39 program suite. All CCSD(T)-F12a/juc-cc-pVTZ single-point calculations were performed with the MOLPRO40 program suite. Conventional TST rate coefficients and Eckart tunneling corrections were calculated using the CANTHERM41 program. Finally, the MS-T partition functions for all species were obtained using the MSTor42,43 program.

(5)

where each species-specific F-factor corresponds to the ratio of the MS-T partition function to that of the SS-RRHO partition function for that particular species. For instance, if we denote either a reactant or TS by the subscript α, then FMS‑T at a α specific temperature is given by FαMS − T(T ) =

MS ‐ T Q con (T ) ‐ rovib, α

Q αSS ‐ RRHO(T )

(6)

Finally, it is often valuable to assess whether the correction introduced to kSS‑TST by a particular species-specific F-factor comes mostly from that species having multiple structures (the contribution of all but one being missed in the SS formalism) or arises primarily from the inadequate treatment of torsional modes by the HO model. To roughly diagnose this, we decompose the F-factors into a multistructural, local-harmonic component and a torsional component, Fα‑MS‑LH and FαT, respectively, FαMS ‐ T = FαMS ‐ LH(T ) FαT(T ) ⎛ Q MS ‐ LH (T ) ⎞⎛ Q MS ‐ T (T ) ⎞ con ‐ rovib, α ⎟⎜ con ‐ rovib, α ⎟ = ⎜⎜ SS ‐ RRHO ⎟⎜ Q MS ‐ LH (T ) ⎟ ( ) Q T ⎝ α ⎠⎝ con ‐ rovib, α ⎠

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RESULTS Experimental Section. The major products are isobutene, from isobutanol dehydration, meta-xylene, from 135TMB decomposition and propene formed from C−C bond cleavage channel of isobutanol. A trace amount of methane, ethane, and 1,3-methyl,5-ethylbenzene were also detected (Supporting Information), all indicative of the methyl radicals that must be present in the system. These results are consistent with the mechanism as outlined in Figure 1. Inherent in this mechanism is the assumption that the radical-induced decomposition of butanol is negligible, because the radical quencher 1,3,5trimethylbenzene suppresses the radical chain. This seems justified by the 20:1 1,3,5-trimethylbenzene to isobutanol ratio. As noted earlier, there are nine weakly bonded (the bond energy is weakened by benzyl resonance) abstractable hydrogen atoms in 1,3,5-trimethylbenzene (135TMB), compared with six abstractable primary, one tertiary, and two secondary hydrogen atoms adjacent to the OH group in isobutanol. The relevant reactions quenching the chain processes are the following,

(7)

where QMS‑LS con‑rovib,α is the multistructural local-harmonic partition function and is obtained by setting all of the f j,τ and Zj equal to unity in eq 3; i.e., it includes the contributions from all structures but torsions are treated in the vicinity of each local minimum as harmonic oscillators with infinitely high barriers between the structures. Computational Methods. The M06-2X30 hybrid metaGGA density functional and MG3S31 minimally augmented basis set (a high-performance combination that has been shown32−34 to give reliable geometries and frequencies for analogous reaction systems) have been used to characterize the stationary points along the potential energy surface for isobutanol dehydration needed for MS-TST/E. To ensure numerical convergence, all M06-2X/MG3S calculations employed an integration grid consisting of 99 radial shells around each atom and 974 angular points in each shell. Due to the presence of coupled torsions in this reaction system, comprehensive structure searches were carried out along the torsional degrees of freedom in these species, also using M062X/MG3S, and the optimized geometries and Hessians for all torsional conformers located for each of these species were then

H + 1,3,5‐trimethylbenzene

6727

→ H 2 + 3,5‐dimethylbenzyl radical (abstraction)

(R1)

H + 1,3,5‐trimethylbenzene → meta‐xylene + CH3

(R2)



Article

CH3 + 3,5‐dimethylbenzyl radical

isobutanol → isopropyl + hydroxymethyl (R4)

→ 2H + propene + formaldehyde

CH3 + CH3 → C2H6

(R5)

isobutanol → methyl + 1‐hydroxypropyl − 2

H + CH3 → CH4

(R6)

→ propene + hydroxyl

→ 1,3‐dimethyl‐5‐ethylbenzene

(R6a)

k(water elimination)

3,5‐dimethylbenzyl radical + H → 1,3,5‐trimethylbenzene

= k(total) × [(isobutene)/(propene + isobutene)]

(R6b)

OH + 1,3,5‐trimethylbenzene → H 2O + 3,5‐dimethylbenzyl radical

(R9)

the rate coefficients for which can be readily obtained via the relations

CH3 + 1,3,5‐trimethylbenzene → CH4 + 3,5‐dimethylbenzyl radical

(R8)

k(C−C cleavage) = k(total) × [(propene) (R6c)

/(propene + isobutene)]

2·3,5‐dimethylbenzyl radicals → no radical products

The resulting rate expressions are (R6d)

k(isobutanol → isobutene + H 2O)R7

Thus we expect less than 5% of the radicals formed will attack butanol. A quick analysis (Supporting Information) shows that the free radical attack on butanol is expected to affect the overall decomposition rate by less than 10%. On this basis, we find in Figure 2 the rate coefficients for the two light

= 1013.86 ± 0.3 exp( −35300 ± 750 K/T ) s−1 = 3.4 s−1 or

log10 kR7 = 0.54 at 1150 K

k(isobutanol → isopropyl + hydroxymethyl) + k(isobutanol → methyl + 1‐hydroxyprop‐2‐yl) = R8 + R9 = 1016.7 ± 0.3 exp( −41100 ± 750 K/T ) s−1

The estimated uncertainties are based on the experience from numerous comparative rate single pulse shock tube experiments20,44 using the internal standard technique and reflects the difficulties in making slope measurements (and the uncertainties in T mentioned earlier). They are considerably larger than the results obtained from a linear regression. The uncertainties given above include the possibility of systematic uncertainties.20,44 Over the range of pressures of 1.5−6 atm explored in this study, no pressure dependence could be observed in the data within the uncertainty of the measurement. These therefore appear to be high pressure rate expressions. This is in accord with the theoretical predictions made by Zhou et al.45 The internal standard method relies on two gas chromatographic measurements. As a result, when the reaction mechanism is unambiguous, the linear regression to the log10 k vs 1/T plot leads to very little scatter, as observed in the results given above. We give a more realistic estimate of the uncertainties from the comparative rate single pulse shock tube studies. In particular, we give an estimate of the combined uncertainty of these studies as opposed to simply the scatter of the data, necessary due to the small scatter. In more conventional shock tube studies, the scatter is sufficiently large so that a statistical treatment of the data may contribute significantly to uncertainties. Actually, an examination of replicate measurements suggests that even such scatter is smaller than the data values.46 The necessity for proper uncertainty in data estimates is due to the increasing possibility of deriving the range of possible errors in simulations. Without the latter,47 simulations can never play their expected role in technology.

Figure 2. Rate coefficients for the decomposition of isobutanol to form propene (upper points) and isobutene (lower points), at 1.5 and 6 bar of after-shock pressure.

hydrocarbon products, propene and isobutene, as a function of temperature. The maximum amount of isobutanol dehydration did not exceed 22%. These rate coefficients were derived from the relation −1 k(total) = tresidence time ⎛ ⎛ [propene] + [isobutene] ⎞⎞ ⎜ln⎜1 − ⎟⎟ ⎠⎠ [isobutanol] ⎝ ⎝ where the residence time determined by pressure sensors is about 500 μs. The residence time is defined as the time at which the temperature in the post shock remains unchanged. The total rate of isobutanol decomposition can be further decomposed into contributions from water elimination, and two C−C cleavage reactions, both leading to the formation of propene (Figure 1), isobutanol → isobutene + H 2O

(R7) 6728



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Figure 3. Graphical depictions, labels, and relative energies (kcal/mol) of the nine torsional conformers.

For the present purposes the uncertainties in our measurements arise from the rate expression of the internal standard, mechanistic artifacts, and relative measurements of concentrations. We estimate the appropriate values to be in the 10%, 5%, and 5% range, respectively. The total uncertainty can

therefore be as large as 20%, as upper bound, and only appears as the scatter of the experimental results. A convenient way of expressing results over a range of temperatures is in the Arrhenius form. From our experience with the single pulse tube technique, there is an uncertainty of 6 kJ/mol in the activation energy and a factor of 2 in the A-factor. 6729



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interconvert between these two structures via some vibration, in which case that particular vibration is clearly anharmonic and this should be addressed in the calculation of the vibrational contribution to the TS partition function and not in σ′ of eq 1 or eq 2. In this article, we have assumed that the two TS structures are interconnected by internal rotation around the forming O−H bond. This assumption is partially substantiated by observations from relaxed scans around this internal coordinate, which have revealed that the conformational barrier for this motion is small (∼8.4 kJ/mol). For comparison, we have also estimated the TS partition function by treating the vibration for interconversion as a bending motion. The MS-T method does not provide a rigorous treatment for anharmonicity due to bending motions (because MS-T was specifically designed to address torsional anharmonicity); nonetheless, the effects of anharmonicty from bending motions are approximated empirically in MS-T by treating bends as harmonic oscillators and scaling their frequencies. The differences between the partition functions obtained through this treatment and our original treatment are negligible over the temperature range presently explored, having a value of almost 2% at 600 K and increasing to nearly 8% by 2400 K (the deviations over the temperature range for our shock tube measurements is on the order of 3−4%). Similar deviations were found when our original partition functions were compared with those obtained by simply doubling the singlestructural anharmonic TS partition function. This is not entirely surprising, considering that the torsion under consideration is now constrained to have just one minimum, making it analogous to a harmonic oscillator. Thus, although the most reasonable method for accounting for the contribution from both TS enantiomers in such reactions is debatable, it is reassuring, from a quantitative standpoint, that this choice is unimportant in the present case. MS-TST/E Rate Coefficients. Equation 1 was used to calculate thermal rate coefficients for (R7) via SS-TST/E and, subsequently, eq 4 was used to obtain the final MS-TST/E rate coefficients. High-level CCSD(T)-F12a/jul-cc-pVTZ//M062X/MG3S calculations were performed on the lowestpotential-energy structure of isobutanol and the TS, T-G-, and A+, respectively, to calculate V‡ in eq 1, the classical potential energy difference between the TS and the reactant in (R7). Each of these species has an isoenergetic mirror image; however, these are accounted for in the vibrational partition function (as explained above), so σ′ is equal to 1 for (R7). In addition, calculations at the same level of theory were performed to refine the potential energy of the products for (R7), isobutene and water, to calculate the energy of reaction, ΔE (which is needed for the Eckart tunneling calculations). The quantities V‡ and ΔE were found to have values of 308.7 and 43.4 kJ/mol, respectively, at the CCSD(T)-F12a/jul-ccpVTZ//M06-2X/MG3S level of theory. For comparison, the inclusion of the zero-point energies (ZPEs) in the calculation of these properties (using the M06-2X/MG3S ZPEs scaled by 0.970) yields a barrier height of 286.2 kJ/mol and a heat of reaction at 0 K of 24.7 kJ/mol, which are quite similar to the values obtained by Zhou et al.45 using CCSD(T)/CBS//MP2/ 6-311G(d,p), of 289.1 and 20.1 kJ/mol, respectively. The SS-TST rate coefficients and Eckart tunneling corrections calculated for (R7) are given in Table 2. In addition, Table 2 also contains the F-factors for isobutanol, the TS, and for (R7) obtained by taking the appropriate ratios of the MS-T partition functions to their corresponding SS-RRHO

This is largely due to the uncertainties in the rate expression in the internal standard. The parameters in the rate expression have fundamental significance and results have been interpreted on the basis of these parameters. In the present application the interest is the rate relations. The derived rate expressions permit extrapolation to different temperatures and with certain assumptions the derivation of the rate expression of the reverse process. On the basis of assumptions on the latter, thermodynamic properties of the radicals may also be estimated. Theoretical Considerations. Structure Searches. Thorough structure searches were conducted along the torsional modes of isobutanol and the corresponding TS for water elimination from this species. Torsions involving methyl rotors are known to be nearly separable from other torsions. Therefore, for isobutanol, the structure searches focused only on the other two torsions in this molecule, and nine initial structure guesses were generated by the various combinations arising from rigidly rotating around the C−C and C−O bonds (corresponding to the axes for internal rotation in these two torsions) in intervals of 120°. This can be done manually; however, in this case we have taken advantage of the Confgen utility available in the MSTor42,43 program suite, which automatically generates the Cartesian coordinates for these initial guesses and can create Gaussian (among other) input files containing these coordinates. The initial guesses to the geometries of the torsional conformers of isobutanol were optimized with M06-2X/MG3S and are depicted (along with their relative zero-point-exclusive energies) in Figure 3. These nine structures can be grouped into four pairs of nonsuperimposable mirror image structures in which at least one of the torsions is in a gauche conformers of isobutanol. All values obtained from M06-2X/MG3S calculations.configuration, and one additional structure of Cs symmetry in which the two torsions are both in trans configurations. The torsional configuration nomenclature and angle ranges adopted in this article are given in Table 1. Table 1. Labeling Conventions for the Dihedral Angles in Figure 3 name convention

abbreviation

dihedral angle range (deg)

cis cis± gauche± anti± trans± trans

C C± G± A± T± T

0 (0, ± 45] (±45, ± 90] (±90, ± 135] (±135, ± 180) 180

The only two structures for the TS in R7 are depicted in Figure 4. These two structures are isoenergetic nonsuperimposable mirror images. There is some ambiguity regarding whether or not these two structures can be interconverted into one another through vibrations, e.g., via internal rotation around the forming O−H bond or via an H−OH bending motion in the forming water molecule. If it is assumed that vibrational interconversion cannot occur between these two structures, then the fact that the TS has two enantiomers should be accounted for in σ′ of eq 1 or eq 2, which, because the two TS structures are isoenergetic mirror images, corresponds to doubling the single-structural anharmonic partition function of one of the TS enantiomers. Alternatively, it may be more reasonable to assume that it is possible to 6730



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Figure 4. Graphical depictions, labels, and relative energies (kcal/mol) of the two torsional conformers for the TS of R1. All values obtained from M06-2X/MG3S calculations.

from nine different structures whereas only two structures make contributions to the MS-T partition function of the TS. For direct comparison with our shock tube measurements, we have fit the calculated dehydration rate coefficients to the Arrhenius expression over the temperature range 1100−1250 K and obtained

Table 2. Calculated Thermal Rate Coefficients for R7 T (K) 600 800 1000 1100 1150 1200 1250 1500 2000 2400

kSS‑TST (s−1) 2.43 6.22 4.62 1.20 4.94 1.81 6.01 7.35 3.08 6.40

× × × × × × × × × ×

−12

10 10−6 10−2 100 100 101 101 103 106 107

κEckart

FMS‑T R

FMS‑T TS

FMS‑T

3.09 1.78 1.43 1.34 1.31 1.28 1.25 1.17 1.09 1.06

11.12 11.50 11.32 11.10 10.97 10.82 10.67 9.81 8.05 6.84

2.79 2.81 2.74 2.69 2.66 2.64 2.61 2.46 2.19 2.00

0.25 0.24 0.24 0.24 0.24 0.24 0.24 0.25 0.27 0.29

kMS‑TST/E (s−1) 1.88 2.70 1.60 3.89 1.57 5.64 1.84 2.16 9.15 1.99

× × × × × × × × × ×

10−12 10−6 10−2 10−1 100 100 101 103 105 107

k MS‐TST/E = 3.5 × 1013 exp(− 35400 K/T ) s−1

These calculated rate coefficients for (R7) are in good accord with those measured in the shock tube experiments, with the measured rate coefficient being larger than the calculated rate coefficient by a factor of ∼2.2 over the temperature range considered. As can be seen from the Arrhenius plots in Figure 6, the MS-TST/E rate coefficients and those from the shock tube measurements both display very similar dependences on temperature; i.e., the computed and measured activation energies agree with each other when the uncertainties in these respective values are considered (see rate expressions above). Consequently, the bulk of the systematic discrepancy between the measured rate coefficients and those computed via MS-TST/E over the same temperature range arises from the difference between the respective pre-exponential factors derived from these two methods. It is interesting to compare the MS-TST/E thermal rate coefficients for (R7) with those recently calculated using TST/ E with one-dimensional hindered-rotor corrections by Zhou et al.45 Note that Zhou et al. do not explicitly report the thermal rate coefficient for (R7), but given that the rate coefficients they calculated at 1 atm already seem to be in the high-pressurelimiting regime, the rate coefficients computed at the highest pressure they investigated (100 atm) should be essentially converged and we will use that data in the comparison that follows. To put things on equal footing, we have used the modified Arrhenius expression of Zhou et al.45 work to evaluate rate coefficients at 1100, 1150, 1200, and 1250 K, and used these points to obtain the following Arrhenius expression over 1100−1250 K:

analogs (eqs 5 and 6). At each temperature, the combination of the F-factor for (R7) with the SS-TST/E rate coefficient, as in eq 4, yields the final MS-TST/E rate coefficient, listed in the last column of Table 2. As can be seen, the effect of the F-factor for (R7) is to effectively decrease the rate coefficient by factors in the range of 3.4−4.1 over the temperatures considered in this work. This net decrease in the rate coefficient arises from the fact that, in the present case, the MS-T partition function of the reactant is underestimated to a much larger extent by its SSRRHO counterpart than the MS-T partition function of the TS is underestimated by its corresponding SS-RRHO partition function, as can be seen from Table 2. To better understand this, the F-factors for these species are decomposed in Table 3 into a multistructural, local-harmonic component and a torsional component, F‑MS‑LH and FTα , respectively, as per eq α 7. It is clear from Table 3 that this discrepancy between the Ffactors of the reactant and TS is largely brought about by the differing amounts of multistructural effects in these two species; i.e., the reactant MS-T partition function receives contributions Table 3. F-Factors for Isobutanol and the TS for R7 T (K)

FMS R

FTR

FMS‑T R

FMS TS

FTTS

FMS‑T TS

600 800 1000 1100 1150 1200 1250 1500 2000 2400

7.03 7.20 7.31 7.35 7.36 7.38 7.39 7.45 7.52 7.55

1.58 1.60 1.55 1.51 1.49 1.47 1.44 1.32 1.07 0.90

11.12 11.50 11.32 11.10 10.97 10.82 10.67 9.81 8.05 6.84

2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00

1.40 1.40 1.37 1.35 1.33 1.32 1.30 1.23 1.10 1.00

2.79 2.81 2.74 2.69 2.66 2.64 2.61 2.46 2.19 2.00

kZhou = 2.8 × 1013 exp(− 35200 K/T ) s−1

Over this temperature range, the rate coefficients obtained by Zhou et al.45 agree well with the MS-TST/E rate coefficients, with the latter being larger than the former by a nearly constant value of 10%. Naturally, this also means that the Zhou et al.45 calculations are in good accord with our shock tube measurements, underestimating these by a factor of about 2.4 over the overlapping temperature range, which once again 6731



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Table 4. Rate Expressions and Coefficientsa for the Dehydration Reaction of Isobutanol in Databases Used for Simulating Isobutanol Combustion

comes primarily from a discrepancy between the respective preexponential factors. Though it is encouraging that the results from the two theoretical treatments are comparable, the remarkable level of agreement between the rate coefficients calculated by Zhou et al. using essentially SS-TST/E with just simple one-dimensional hindered-rotor corrections for torsions (1D-HR-TST/E) and those calculated with MS-TST/E is, at first glance, surprising given that the torsions of analogous oxygen-containing species have been recently shown to be strongly coupled.22−29,41 To better understand why there is only a 10% difference between these two results, it is important to explore the differences between the three factors entering both of these calculations the transmission coefficient, the ratio of the TS and isobutanol partition functions, and the exponential term. At the center of the temperature range considered, 1175 K, using the two aforementioned zero-point-inclusive barrier heights we find that the exponential term entering our TST calculations is 35% larger than that entering Zhou et al.’s45 calculations. At this temperature, tunneling is not very important, and the similar reaction energetics and treatments of tunneling employed in both of these studies would suggest that the transmission coefficients should be very similar (although this may not necessarily be true if the imaginary frequency corresponding to motion along the reaction coordinate in the TS is drastically different at the MP2/6-311G(d,p) level of theory than at the M06-2X/MG3S level of theory), so the partition function ratio of Zhou et al.45 must be ∼23% higher than the one from the MS-T calculations to lead to the observed overall difference of just 10%. Furthermore, because the TS for this particular reaction is composed of only separable torsions, this 23% difference is the result of the 1D-HR model underestimating the anharmonic partition function of isobutanol, which is expected because a 1D-HR treatment would miss the contributions from torsional conformations of isobutanol that can only be generated through the coupling of torsions. Overall, a 23% difference in the isobutanol partition function calculated by the two torsional models is not unreasonable, but clearly, this discrepancy could be much more significant if the species under consideration had more than just the two coupled torsions available in isobutanol.

isobutanol → isobutene + H2O [primary-OH, tert-H] ref

A-factor, s−1

n

Ea/R, K

log10 k [1150 K]

Moss Grana6 Sarathy,9 Yasunaga5

2 × 106 5 × 1013 4.5 × 1013

2.12 0 0

31 200 33 000 32 700

1.01 1.24 1.30

8

a

k = ATn exp(−Ea/RT), where T is in K.

This is consistent with our earlier observation that although the ignition delay is most sensitive to the H + O2 reaction, the nature of the fuel clearly is of importance because it releases Hatoms into the system. The relationship between molecular geometries and computed thermal rate coefficients is being closely analyzed. Zhou et al.45 recently explored various important reaction channels in the thermal decomposition of isobutanol as a function of temperature and pressure using the one-dimensional master equation method. The stationary points used in their analyses were characterized using MP2/6-311G(d,p) theory for geometries and frequencies and high-level coupled cluster theory extrapolated to the complete basis set limit (CBS) for energies, i.e., CCSD(T)/CBS//MP2/6-311G(d,p). For the water elimination channel, Zhou et al.45 employed conventional transition state theory with Eckart tunneling and one-dimensional hindered-rotor corrections to obtain microcanonical rate coefficients. Interestingly, their calculations indicated that, at the temperatures considered in the present work, the rate coefficients for water elimination from isobutanol should not exhibit a dependence on pressure over the range 1− 100 atm, suggesting that the rate coefficients measured under our present experimental conditions should be in their highpressure limit (i.e., thermal rate coefficients). In addition to testing this claim experimentally, in this work, we also more thoroughly explore the effects of torsional anharmonicity on the computed thermal rate coefficients by using a multidimensional torsional model to account for the potential couplings between the torsional modes in isobutanol and the transition state for water elimination. Table 5 summarizes pertinent data from recent and earlier single pulse shock tube data on the decomposition of large alcohols. Although there are systematic trends, the rate coefficients may not be particularly revealing because the spread of results are not far from our estimated experimental uncertainties. The rate coefficients (log10 k) at a particular temperature at the midpoint of the range covered yield more informative results in terms of the correlations and rate rules for predictions. It is clear that, normalized for H-atoms, the dehydration processes particularly for the primary and secondary alcohols are strikingly similar to each other. Particularly significant are the k values for dehydration of 2butanol because the results are derived from the same starting molecule. Clearly, the position of the H-atom (primary or secondary) does not make any difference with respect to the dehydration rate coefficient. It is not until tert-butyl alcohol that one sees any really significant change in the rate coefficients. Note that the results for ethanol and tert-butanol come from a direct study. Therefore, the difference in rate coefficients of a factor slightly less than 2 is clearly meaningful. In contrast to the situation for the 1- and 2-butanol, β substitution in tertiary systems does

■

DISCUSSION The mechanism for isobutanol decomposition can be found in Figure 1. It is an integral part of the more general combustion mechanism. Except for the tertiary alcohols48,49 there have been no kinetic studies on the elementary reactions involved in isobutanol unimolecular decomposition via dehydration or, for that matter, for most of the reactions involving the larger alcohols. It is therefore of interest to examine the values of the rate coefficients that are used in the simulations and assess the quality of these estimates. Table 4 contains data on the estimated rate coefficients for the dehydration of isobutanol used in these mechanisms. It can be seen that there is a scatter of a factor of 2 in the estimated rate coefficients. This is undoubtedly due to the different assumptions made in assigning rate coefficients for this process. When making estimates and assigning rate coefficients to chemical processes where experimental data is lacking, one should take into consideration chemical properties of fuel molecules such as molecular structure that influences important combustion properties. An important observation is that the ignition delays are different for each of the butanol isomers.6,8 6732



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Table 5. Summary of Rate Coefficients (1150 K) for the Dehydration of Various Alcohols (Primary, Secondary, or Tertiary Alcohols)a ref Herzler et al.50 Rosado-Reyes and Tsang1 Rosado-Reyes and Tsang2 Rosado-Reyes and Tsang2 Rosado-Reyes and Tsang2 Rosado-Reyes and Tsang2 Tsang49 Lewis et al.48 Tsang49 Tsang49

reaction

type of OH (no. of H, position)

log10 A-factor [s−1]

Ea/R [K]

log10 k [s−1, 1150 K, per H]

ethanol → ethylene + H2O 1-butanol → 1-butene + H2O

primary (3,p) primary (2,s)

13.6 14.0

32 900 34 800

70 54

2-butanol → 1-butene + H2O

secondary (3,p)

13.5

33 000

56

2-butanol → cis-2-butene + H2O

secondary (1,s)

13.5

33 800

73

2-butanol → trans-2-butene + H2O

secondary (1,s)

13.2

33 400

58

2-butanol → cis,trans-2-butene + H2O sum

secondary (2,s)

3,3-dimethylbutan-2-ol → 3,3-dimethylbut-1-ene + H2O tert-butanol → isobutene + H2O 2,3-dimethylbutan-2-ol → 2,3-dimethylbutene-1 + H2O 2,3-dimethylbutanol-2 → 2,3-dimethylbut-1-ene + H2O

secondary (3,p)

14.0

34 200

61

tertiary (9,p) tertiary (1,t)

14.5 13.7

33 300 32 700

97 1.35

tertiary (6,p)

14.2

32 300

1.22

62

a Rate coefficients for ethanol and tert-butanol decomposition are changed slightly to reflect the use of different values for the rate coefficients of the internal standard reaction, cyclohexene decomposition. The alcohol identifier includes the number of H atoms available for water elimination and their position (p = primary, s = secondary, or t = tertiary) in the alcohol.

influence the rate coefficient for dehydration. The accuracy of all these values rely on determination of multiple products from a single molecule, as is the case for all substituted tertiary alcohols. Overall, these values indicate the importance of the number of available H-atoms and the overall magnitude is in fact not that much different than the contribution from the position of the OH group. The present study will therefore add to our knowledge of rate coefficients for the dehydration of a primary alcohol. Particularly interesting is that the hydrogen atom being removed is now in a tertiary position. Note that in the case of the tertiary alcohol this leads to a somewhat larger rate constant. From Figure 5, it appears that the numbers in the literature are based solely on the existing values for elimination derived

from the tertiary alcohols, where account was taken of the available number of hydrogens for water elimination but not of the tertiary position of the OH group. It now appears that these two combined (number of hydrogen atoms and OH group position) are different for the primary and secondary alcohols. However, there is concordance in the data between the rate coefficients for isobutanol and 1-butanol dehydration to isobutene (log10 k = 0.54) and 1-butene (log10 k = 0.56), respectively, at 1150 K (Table 5). Our experimental rate coefficient for the dehydration of isobutanol is roughly a factor of 2 larger than our theoretical value throughout the temperature range considered. We estimate that our measured rate coefficients have an uncertainty of about 20%. In addition, coupled cluster calculations such as the ones used to calculate the energetics in this study are expected to have an uncertainty of about 4 kcal/mol for such quantities, and reducing the barrier height by this amount would increase the calculated rate coefficients by factors of 1.58 and 1.50 at 1100 and 1250 K, respectively, further narrowing the gap between the experimental and theoretical results. Uncertainties of a similar magnitude are likely for the partition functions, so an overall uncertainty of a factor of 2−3 for the rate coefficients calculated via MS-TST is entirely realistic. As will be seen below, theoretical underestimations by similar amounts seem to be endemic for dehydration reactions in general. For isobutanol dehydration it can be seen that there are discrepancies between our calculated and experimental determinations of about a factor of 2, as seen in Figure 5. This may be a more realistic measure for larger compounds. Comparisons with available literature values can be seen in Figure 6. It is also possible to compare the experimental values with theoretical calculations. Park et al.51 and Sivaramakrishnan et al.52 have published high level calculations on the dehydration of ethanol. Bui et al.53 have published similar calculations for isopropanol. They find

Figure 5. Rate coefficients for the dehydration of isobutanol. Experimental and calculated data are from the present work. The dotted line is from calculations of Zhou et al.45 Moss et al.,8 Sarathy et al.,9 and Grana et al.6 provide the estimated values used in combustion models. Error bars are given as the standard σ uncertainty derived from the statistical fit.

kPark et al.(ethanol → ethene + H 2O) = 7 × 1013 exp( −34200 K/T ) s−1 6733



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An interesting observation from the comparison of experimental results and theoretical calculations is the fact that the discrepancy between them is fairly consistent. Theoretical estimates of rate coefficients are all smaller by about a factor of 2 than the corresponding experimentally measured value. The exact significance of this observation is unclear. Torsional anharmonicity effects are expected to be less significant in the dehydration reactions of smaller alcohols because the species involved have less torsions, and so fewer torsional couplings. In such cases, simple 1D-HR treatments may be justifiable and in some cases, when significant error cancellation is expected, even treating these modes as harmonic oscillators may not result in substantial overall error in the calculated rate coefficient, because ultimately, the accuracy of the rate coefficient will be largely dictated by the accuracy of the computed barrier height. An important issue addressed in this article has been to demonstrate that it is now also possible attain similar levels of accuracy for the kinetics of larger systems (containing more torsions) by employing somewhat more complex but still practical calculations. The present results are an important demonstration of the use of the comparative rate single pulse shock tube technique to determine very precise rate coefficients. The present results are reminiscent of physical organic chemical studies near room temperature in solution. Because the present results are in the gas phase where theory is much less ambiguous, this type of result should lead to an extremely accurate picture of the key determinants responsible for chemical reactivity. Thus labeling studies, for example those involving isotope effects, can be carried in great detail and accuracy and should provide crucial tests of theory.

Figure 6. Rate coefficients for ethanol (solid line) and isopropanol (dashed line) dehydration. Light lines correspond to theoretical calculations, dark lines to single pulse shock tube experiments, and dark dash lines to estimates from experiments. The values for isopropanol are shifted up by 0.5 log units for legibility.

k Sivaramakrishnan et al.(ethanol → ethene + H 2O) = 3.8 × 1020(T )−2.06 exp(− 35000 K/T ) s−1

kBui et al.(isopropanol → propene + H 2O)

■

= 2 × 106T 2.12 exp( −30700 K/T ) s−1

SUMMARY We have carried out experimental and theoretical work on the dehydration of isobutanol. The rate expressions, experimental and theoretical, that we have obtained are within a factor of 2 of each other, placing these results in agreement with each other when their uncertainty margins are considered. Thus, in the absence of experimental data, modern theory can be a powerful tool for predictions. The combination of the present experimental results with earlier single pulse shock tube work indicate that the controlling factors for fuel alcohol dehydration are the number of available hydrogens for water elimination and, to a surprisingly small extent, the position of the OH group (primary, secondary, or tertiary). On a per hydrogen atom basis, the overall range of values between the fastest and the slowest rate coefficient is less than an order of magnitude. In the absence of β substitution, the total difference in rate coefficients between primary and tertiary alcohols is only a factor of 2 apart from one another. Small, but systematic, differences between experiments and theoretical calculations are observed.

Because there have not been any single pulse shock tube studies on isopropanol dehydration, the present results can be used as a basis for an estimate. The rate data in Table 5 suggest that the rate expression for the yields of 1-butene from 2-butanol dehydration is half that of isopropanol. Our results then lead to the following estimate, k(isopropanol → propene + H 2O) = 1014 exp( −32900 K/T ) s−1

where we have taken into account the six available hydrogens for water elimination. As seen in Figure 6, the agreement is better than a factor of 2. Note also from Table 5 and the present study on isobutanol that the work of Herzler et al.50 leads to rate coefficients that are a factor of ∼1.5 larger than those for the other primary alcohols. The comparison that is being made here between rate coefficients is a very severe test of the theory. The quantities extracted from the experiments are rate constants. Entropic and energy factors are treated independently from each other in the calculations. As noted earlier, the calculated rate coefficients will have additive contributions from the uncertainties in the two factors. Of course, rate rules derived experimentally are strictly empirical and unless rationalized by theory may not be as extensible as may be hoped. We note that the ratio of rate coefficients from the isopropanol and isobutanol calculations are the same as those derived from the shock tube results. In any case, the present exercise does set some limits on the possible uncertainty limits from values derived from theory.

■

ASSOCIATED CONTENT

S Supporting Information *

Examples of gas chromatograms of postshock mixtures and tabulated raw measured data. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. 6734



Article

Notes

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The authors declare no competing financial interest.

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Dehydration of Isobutanol and the Elimination of Water from Fuel

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