Supporting Information

Acid Strength and Solvation in Catalysis by MFI Zeolites and Effects of the Identity, Concentration and Location of Framework Heteroatoms

Andrew J. Jones, Robert T. Carr, Stacey I. Zones, Enrique Iglesia

S.1. Sample information

The Si, Al, Ga, Fe, B and Na contents of MFI samples were measured by inductively-

coupled plasma optical emission spectroscopy (ICP-OES; Galbraith Laboratories) and are shown

in Table S.1.

Table S.1. Zeolite sample information

aDetermined from elemental analysis (ICP-OES; Galbraith Laboratories).

S.2. Determination of Al coordination from 27Al MAS NMR spectroscopy

The coordination of Al atoms in hydrated zeolite samples were determined from the

integrated areas of 27Al magic angle spinning (MAS) NMR lines centered at 55 ppm (tetrahedral)

and 0 ppm (octahedral), referenced to aqueous 1.0 M Al(NO3)3 (Figure S.1). Spectra were

collected on a Bruker Avance 500 MHz spectrometer using a wide-bore 11.7 Tesla magnet at

130.35 MHz (Caltech Solid-State NMR Facility). Samples were hydrated in a desiccator (1.0 M

KCl for >48 h) and sealed within 4 mm ZrO2 rotors; their spectra were measured at ambient

Zeolite Provenance Si/Ta Na/Ta

H-[Al]-MFI-1 Zeolyst 16.6 0.004H-[Al]-MFI-2 This work 22.8 0.04H-[Al]-MFI-3 Zeolyst 29.2 < 0.08H-[Al]-MFI-4 Zeolyst 43.8 < 0.08H-[Al]-MFI-5 This work 51.9 -H-[Al]-MFI-6 This work 117.6 -H-[Ga]-MFI This work 108.7 0.0001H-[Fe]-MFI This work 61.1 0.0004H-[B]-MFI This work 75.3 0.0003

temperature using a 4 mm cross-polarization (CP) MAS probe, strong proton decoupling, and a

13 kHz spinning rate (512 scans, 0.5 μs pulses, 6 s delay).

Fig. S.1. 27Al MAS NMR spectra of H-[Al]-MFI-1 (thick line), H-[Al]-MFI-3 (thin line) and H-[Al]-MFI-4 (dotted

line) referenced to aqueous 1.0 M Al(NO3)3.

S.3. Density functional theory cluster models

Converged cluster models of Al-MFI with 5, 8, 11, 20, 27, 38 and 51 T-atoms are shown

in Figure S.2.

Fig. S.2. Al-MFI cluster models containing 5, 8, 11, 20, 27, 38 and 51 T-atoms; cluster geometries converged at the

ωB97X-D/6-31G(d,p) level of theory. Atom colorings are as follows: H in gray, Si in blue, O in orange and Al in

green.

S.4. Basis set size influence

The influence of the size of the basis set used to calculated DPE values with density

functional theory is examined here as a function of the number of T-atoms in the cluster model

(Figure S.3). As the cluster size increases the difference in DPE values calculated with the larger

(6-311++G(3df,3pd)) and smaller (6-31G(d,p)) basis sets decreases from 41 to 25 kJ mol-1 from

the 5T to 20T clusters, respectively. Extrapolation to infinite cluster size suggests that

differences in DPE between the two basis sets approach 19 kJ mol-1.

Fig. S.3. Difference in DPE values calculated with 6-31G(d,p) and 6-311++G(3df,3pd) basis sets as a function of the

inverse of the number of T-atoms in the cluster. Dotted line represents a linear regression of the data.

S.5. Bader charge analysis

The Bader charge [S1] of atoms in neutral and deprotonated 38T clusters optimized at the

ωB97X-D/6-31G(d,p) level of theory are shown in Table S.2. We find that the charge associated

with each atom, as determined from the Bader analysis, does not change by more than 5 % and is

generally much smaller than this.

Table S.2. Atomic Bader charges [S1] of atoms in the neutral (HZ) and deprotonated (Z-) 38T optimized clusters calculated at the ωB97X-D/6-31G(d,p) level.

Position in HZAtom X Y Z Charge (HZ) Charge (Z-) % DifferenceO -3.378 -10.031 2.664 7.96 7.95 -0.06%H 9.884 -7.845 7.888 1.96 1.96 0.06%H 9.858 3.544 6.678 1.96 1.96 0.09%O 2.364 -0.079 4.095 7.91 7.91 0.00%H 4.371 -11.089 5.837 1.95 1.95 -0.02%Si -2.775 -9.590 -0.316 0.11 0.11 -1.07%Si -7.176 -8.671 -4.065 0.11 0.11 1.60%O -5.263 -8.499 -1.695 7.94 7.95 0.07%O -8.488 -5.958 -4.301 7.96 7.96 0.02%H -8.852 -10.764 -3.460 1.96 1.95 -0.04%O -5.709 -9.316 -6.599 7.98 7.97 -0.06%H 0.248 -12.246 -5.944 1.96 1.96 -0.13%H -1.901 -12.033 -1.228 1.96 1.96 0.02%H 13.956 3.223 4.816 1.95 1.96 0.33%Si -0.438 3.291 10.277 0.11 0.11 -0.53%Si 4.444 6.199 12.009 0.12 0.12 -0.08%O 1.861 4.812 11.386 7.99 7.98 -0.08%Si 6.187 -1.675 10.844 0.12 0.12 1.88%H 7.961 0.381 10.411 1.96 1.96 -0.23%H 6.527 5.364 10.422 1.96 1.96 -0.01%H -1.498 1.814 12.340 1.95 1.95 0.08%O -3.689 -6.760 6.500 7.97 7.97 -0.02%Si -1.186 -6.010 8.106 0.11 0.12 5.03%Si 1.647 -0.959 6.887 0.11 0.11 -2.11%H 7.600 -4.032 10.765 1.96 1.96 -0.41%H 0.808 -7.900 7.996 1.96 1.96 0.19%O -0.226 -3.370 6.864 7.97 7.96 -0.10%O 4.051 -1.735 8.618 7.97 7.97 0.03%H 5.001 -1.433 13.312 1.96 1.97 0.76%H -2.037 -5.740 10.706 1.96 1.96 -0.05%H 5.047 5.699 14.645 1.96 1.96 0.13%O 0.266 1.512 7.966 7.95 7.95 0.06%

Si 5.203 2.184 -2.813 0.11 0.11 0.99%Si 9.919 4.982 -0.839 0.11 0.11 -1.00%O 7.465 4.161 -2.492 7.95 7.94 -0.04%H 5.784 -12.912 2.058 1.96 1.96 0.27%H 12.713 -9.051 4.736 1.95 1.95 0.12%Si 10.318 -7.772 5.174 0.12 0.11 -4.05%Si 5.461 -10.522 3.377 0.12 0.12 1.21%O 8.135 -9.032 3.442 7.98 7.98 -0.06%Si 11.267 2.794 4.438 0.11 0.11 0.26%Si 9.898 -2.623 2.778 0.11 0.11 -0.54%Al 4.095 -1.753 1.961 0.09 0.09 0.56%O 11.282 -0.233 4.057 7.98 7.95 -0.42%O 11.157 -4.990 4.193 7.95 7.97 0.24%O 6.925 -2.671 3.157 7.92 7.92 0.00%O 10.521 -2.596 -0.244 7.97 7.96 -0.05%O 12.367 3.854 -2.219 7.96 7.96 -0.01%O 9.757 4.111 2.067 7.96 7.96 -0.04%O 4.340 1.259 0.080 7.74 7.92 2.28%O -0.567 -7.520 -0.738 7.95 7.95 -0.02%Si 2.374 -6.892 -0.110 0.11 0.11 0.09%O 4.109 -7.672 -2.541 7.94 7.96 0.15%O 2.543 -3.903 0.200 7.92 7.92 -0.02%O 3.298 -8.624 2.234 7.97 7.97 0.02%Si -5.081 -9.019 5.006 0.11 0.11 -0.62%Si -10.742 -7.787 4.165 0.12 0.11 -1.21%O -11.478 -5.218 2.723 7.97 7.97 0.02%H -11.619 -10.079 2.924 1.96 1.96 0.06%O -7.713 -7.889 4.061 7.98 7.96 -0.19%H -11.907 -7.592 6.647 1.96 1.96 0.07%H -5.330 -11.183 6.684 1.95 1.95 0.04%Si 0.714 -10.634 -8.123 0.11 0.11 -0.35%Si -4.807 -9.349 -9.468 0.12 0.11 -0.52%O -1.751 -9.491 -9.518 7.95 7.96 0.04%H -5.375 -7.212 -11.103 1.96 1.95 -0.06%H -5.727 -11.647 -10.664 1.96 1.96 0.17%H 2.001 -12.062 -10.089 1.96 1.96 0.10%H 16.868 2.504 -2.013 1.95 1.96 0.26%H 14.865 2.881 -6.119 1.96 1.96 0.00%H 7.833 -1.358 -8.799 1.95 1.95 0.13%Si 14.576 2.139 -3.488 0.11 0.12 2.97%Si 12.044 -3.067 -2.841 0.11 0.11 -0.90%Si 4.709 -7.380 -5.535 0.11 0.11 0.09%Si 7.323 -2.275 -6.258 0.11 0.11 -0.62%

O 14.051 -0.853 -3.374 7.95 7.96 0.07%H 13.520 -5.371 -3.113 1.95 1.96 0.52%O 5.298 -4.527 -6.479 7.96 7.95 -0.07%O 9.995 -3.214 -5.133 7.96 7.96 -0.06%O 6.088 -0.236 -4.319 7.96 7.95 -0.09%O 2.361 -8.185 -7.293 7.96 7.97 0.10%H 6.843 -9.105 -5.708 1.95 1.96 0.12%O -11.949 -3.293 -1.784 7.95 7.95 0.01%O -5.754 10.939 -0.621 7.96 7.96 0.00%Si -11.022 -4.299 -4.447 0.12 0.12 0.61%H -12.979 -5.676 -5.801 1.96 1.96 -0.01%Si -6.960 4.183 -9.591 0.11 0.11 0.88%Si -9.574 -0.922 -8.869 0.12 0.12 1.47%H -9.094 5.908 -9.419 1.96 1.96 0.13%H -11.925 -0.207 -10.103 1.96 1.96 -0.06%O -4.546 4.931 -7.828 7.96 7.95 -0.14%O -7.666 1.420 -8.546 7.96 7.97 0.04%O -10.358 -1.778 -6.035 7.95 7.96 0.11%H -8.248 -2.869 -10.287 1.96 1.96 0.02%H -5.049 8.046 12.159 1.96 1.96 0.18%H -9.852 10.871 7.787 1.96 1.96 0.02%Si -8.723 8.864 6.285 0.11 0.11 0.18%Si -4.059 7.791 9.606 0.12 0.12 1.21%O -6.155 7.807 7.419 7.96 7.96 0.00%O -2.594 5.155 9.213 7.95 7.98 0.33%H 4.092 8.901 11.638 1.96 1.96 0.20%H -2.384 9.902 9.060 1.96 1.95 -0.59%O -8.282 9.870 3.432 7.95 7.96 0.04%Si -7.014 12.175 1.868 0.12 0.11 -0.69%H -5.051 13.526 3.241 1.96 1.96 0.03%H -9.042 13.925 1.247 1.96 1.96 0.00%Si -3.115 7.445 -6.965 0.11 0.11 -0.36%Si 2.556 6.152 -5.659 0.11 0.11 0.63%Si 9.968 10.297 -2.913 0.12 0.12 -0.78%Si 4.447 11.506 -4.128 0.11 0.12 1.05%O -0.406 6.710 -5.810 7.95 7.95 0.08%O 2.781 3.551 -4.014 7.95 7.96 0.07%O 9.885 8.007 -0.871 7.95 7.95 0.01%O 7.333 11.847 -3.133 7.97 7.96 -0.07%O 3.908 8.468 -4.185 7.97 7.96 -0.06%O -4.732 8.886 -4.842 7.96 7.95 -0.04%H 2.907 12.828 -2.274 1.95 1.95 0.08%H 4.277 12.809 -6.543 1.96 1.96 0.20%

Si -4.726 11.608 -3.413 0.12 0.12 0.94%H -2.281 12.839 -3.153 1.96 1.96 0.14%H -6.432 13.278 -4.777 1.96 1.96 0.06%Si -13.320 -3.730 0.856 0.12 0.11 -2.57%H -15.750 -4.990 0.593 1.95 1.96 0.20%O -10.647 6.516 6.163 7.95 7.95 -0.02%Si -13.590 5.826 5.708 0.12 0.12 0.17%Si -15.259 0.487 4.251 0.11 0.12 0.61%H -14.797 7.321 3.742 1.96 1.96 0.20%H -14.911 6.178 8.093 1.96 1.96 -0.13%O -13.812 -0.930 1.951 7.95 7.95 0.04%O -13.526 2.871 4.985 7.96 7.96 -0.01%H -17.710 1.227 3.248 1.96 1.96 0.07%H -15.524 -1.066 6.504 1.96 1.96 -0.09%H 11.729 12.061 -1.755 1.95 1.95 0.17%H -6.117 3.999 -12.202 1.96 1.96 0.04%H 3.740 5.868 -8.124 1.95 1.95 -0.01%H 10.972 9.762 -5.416 1.96 1.96 0.28%O -2.729 9.302 -9.342 7.99 7.97 -0.20%H -0.493 9.205 -13.623 1.97 1.96 -0.06%Si -1.195 10.834 -11.522 0.12 0.12 -0.68%H 1.040 12.104 -10.546 1.96 1.97 0.23%H -2.994 12.705 -12.431 1.95 1.96 0.41%H 3.307 2.384 1.100 0.27 N/A N/A

S.6. Comparison of direct and sequential dehydration routes

Rate expressions for the direct and sequential routes, derived from their elementary steps

and appropriate assumptions, have been shown previously [S2]. In this section we compare these

derived rate expressions under the low pressure regimes, which favor H-bonded CH3OH

monomers as the most abundant intermediates (see the text).

A simplified schematic of direct and sequential routes is shown in Scheme S.1. Both

routes involve the adsorption of CH3OH to form H-bonded CH3OH monomers (Step 1, Scheme

S.1). In direct routes these monomers undergo subsequent reaction with CH3OH to form

protonated CH3OH dimers (Step D2), which rearrange (Step D3) and react to eliminate water in

a kinetically relevant step (Step D4). Assuming protons are occupied by monomers and

protonated dimers this leads to the rate equation (S1) [S2]:

(S1)

where kDME,d is the rate constant for the formation of DME from rotated dimers (Step D4), KR is

the equilibrium constant for the rotation of protonated CH3OH dimers and KD is the equilibrium

constant for the adsorption of CH3OH to monomers to form protonated dimers. Note that to

compare with the text, kDME = kDME,dKR.

Sequential routes involve the monomolecular dehydration of monomers (Step S2) to form

methoxides, which undergo reaction with CH3OH to form methoxide-CH3OH pairs (Step S3).

These pairs react to form DME and regenerate the proton (Step S4). If we assume that steps S2

and S4 are kinetically relevant and protons occupied by methoxides and monomers, as was done

previously [S2], we arrive at the rate equation (S2) [S2]:

(S2)

where kDME,s is the rate constant for the formation of DME from methoxide-CH3OH pairs (Step

S4), kelim is the rate constant for the elimination of H2O (Step S2) and KP is the equilibrium

constant for the adsorption of CH3OH adjacent to methoxides (Step S3).

Low CH3OH pressures favor the formation of H-bonded CH3OH monomers as observed

in the infrared (see the text). The predominate occupation of protons by monomers leads to the

following rate equations for direct (S3) and sequential routes (S4):

(S3)

(S4)

In direct routes, monomer occupation leads to first order dependencies of turnover rates on

CH3OH pressure. Sequential routes, however, lead to zero-order dependencies on CH3OH

because the kinetically relevant step involves the monomolecular reaction of monomers to form

methoxides. Turnover rates that increase linearly with CH3OH pressure (see text) while protons

are occupied predominately by monomers, therefore provides strong evidence that dehydration

proceeds through direct routes.

Scheme S.1. Comparison of the steps involved in the dehydration of CH3OH to dimethyl ether through direct (left)

and sequential (right) routes.

S.7. Free energy difference of measured CH3OH dehydration rate constants on Al-MFI

The first-order and zero-order CH3OH dehydration rate constants (kfirst and kzero,

respectively) are related to the free energies of the DME formation transition state and their

respective reactive intermediates (Scheme 1) through transition state theory formalisms [S3]

(S5):

(S5)

where kB is the Boltzmann constant (1.38 x 10-23 J K-1), h is Planck’s constant (6.63 x 10-34 J s), R

is the ideal gas constant (8.314 J mol-1 K-1), T is the temperature (K) and ΔGǂ is the free energy

differences between the transition state and reactive intermediates (J mol-1). The ratio of rate

constants on two samples is therefore related to their difference in activation free energy barriers

(ΔGǂ) by the equation:

(S6)

which, upon rearrangement becomes,

(S7)

The 3-fold difference in the values of kfirst on Al-MFI samples with different H+ densities (Section

3.5), therefore, corresponds (S7) to a 4 kJ mol-1 difference in activation free energy barriers at

433 K.

References

[S1] W. Tang, E. Sanville, and G. Henkelman, J. Phys.-Condes. Matter 21 (2009).[S2] R.T. Carr, M. Neurock, and E. Iglesia, J. Catal. 278 (2011) 78-93.[S3] J.A. Dumesic, D.F. Rudd, L.M. Aparicio, J.E. Rekoske, A.A. Treviño, The Microkinetics of Heterogeneous Catalysis, ACS Publishing: Washington, DC, 1993, p. 35.