Monosaccharide and Disaccharide Isomerization over Lewis Acid Sites in Hydrophobic and Hydrophilic Molecular Sieves
SUPPORTING INFORMATION
Rajamani Gounder and Mark E. Davis*
Chemical Engineering, California Institute of Technology, Pasadena, California91125, United States
*Corresponding author. E-mail:
S.1. X-ray diffractograms of zeolite samples
Powder X-ray diffraction patterns of the samples used in this study are shown in Fig. S.1.
Figure S.1.Powder X-ray diffraction patterns of Ti-Beta-F, Sn-Beta, Ti-Beta-OH and TiO2-SiO2(bottom to top).
S.2. Single-component vapor-phaseadsorption isotherms of zeolite samples
N2(77 K), H2O (293 K) and CH3OH(293 K) adsorption isotherms are shown for Ti-Beta-F (Fig. S.2), Ti-Beta-OH (Fig. S.3) and Sn-Beta-F (Fig. S.4). Corresponding micropore uptakes shown in Table 1 (main text).
Figure S.2.N2 (77 K) (), H2O (293 K) () and CH3OH () adsorption isotherms for Ti-Beta-F.
Figure S.3.N2 (77 K) (), H2O (293 K) () and CH3OH () adsorption isotherms for Ti-Beta-OH.
Figure S.4.N2 (77 K) (), H2O (293 K) () and CH3OH () adsorption isotherms for Sn-Beta-F.
S.3. Deactivation studies of Ti-Beta-F during reactions of glucose in liquid water
The deactivation of Ti-Beta-F during conversion of a 1% (w/w) aqueous glucose solutionat 373 K (1:50 Ti:glucose ratio) was assessed by first measuring the evolution of fructose and sorbose products as a function of batch reaction time for two hours (Figs. 5a and 5b). The catalytic solids were then isolated from the reaction mixture by centrifugation; they retained a yellow discoloration that reflected the presence of adsorbed sugars or sugar decomposition products. The reaction of a fresh glucose reactant solution with the spent Ti-Beta-F catalyst led to initial fructose and sorbose formation rates that werelower by factors of ~2.5 (Figs. S.5a and S.5b), indicating that partial deactivation of Ti-Beta-F occurred during the first reaction cycle and, in part, contributed to the approach of monosaccharide product concentrations to steady-state values at long reaction times.
Figure S.5. Aqueous-phase (a) fructose and (b) sorbose concentrations as a function of reaction time during the first () and second () reaction cycles of a 1% (w/w) aqueous glucose solution with Ti-Beta-F (1:50 glucose:Ti molar ratio, 373 K).
S.4. Derivation of batch reactor concentration profiles for glucose and lactose isomerization
S.4.1. Concentration profiles in a batch reactor for a reversible first-order reaction
Here, we provide an abridged derivation of the concentration profiles in an ideal, constant volume, batch stirred tank reactor for the following reversible reaction:
(S.1)
where KRis the equilibrium constant for the stoichiometric reaction. The mole balances for A and B (Eq. (S.1)) in a constant volume, stirred batch tank reactor can be expressed in terms of their concentrations (cA(l), cB(l)) according to:
(S.2)
where rnet is the net rate (per metal site) of the reaction shown in Eq. (S.1), M is the total number of metal sites in the reactor, and V is the reactor volume. The assumption that the forward and reverse rates are first-order in cA(l) and cB(l), respectively, leads to the following expression for the net rate of reaction:
(S.3)
where kfand kr are the effective first-order forward and reverse rate constants for the reaction (Eq. (S.1)). These two effective rate constants are related by the equilibrium constant for the stoichiometric reaction (Eq. (S.1)):
(S.4)
At any point in time, the following relationship must hold between the concentrations of A and B:
(S.5)
where cA0(l) is the initial concentration of A in the reactor.
Combining Eqs. (S.2)-(S.5) leads to the following expression:
(S.6)
Rearrangement and separation of variables enables Eq. (S.6) to be integrated with respect to time, with the appropriate limits, to give the following expression for cB(l)(t):
(S.7)
where is the concentration of B at equilibrium and is given by:
(S.8)
In Eq. (S.7), is an effective first-order time constant given by:
(S.9)
Combining Eqs. (S.5), (S.7) and (S.8) gives the following expression for CA(l)(t):
(S.10)
where is the concentration of A at equilibrium.The net rate of reaction at time t can be evaluated from the derivative of Eq. (S.7) with respect to time (according to Eq. (S.2)) and the initial rate of reaction can be determined by evaluating this expression at t = 0.
S.4.2. Concentration profiles for parallel glucose-fructose and glucose-sorbose isomerization
The conversion of glucose (G) to fructose (F) and sorbose (S) in parallel reactions is reflected in the following:
(S.11)
(S.12)
The full solution of the concentration profiles requires solving a system of coupled differential equations, but for illustrative purposes we simply provide the following expressions, which describe their functional dependence on reaction time:
(S.13)
(S.14)
The concentration of glucose is given by:
(S.15)
The glucose conversion (X) and fructose-to-sorbose ratios are given by:
(S.16)
(S.17)
The experimental data are modeled accurately by Eqs. (S.13) and Eqs. (S.14), evident in the parity plots shown in Figures S.6a and S.6b of measured fructose and sorbose concentrations (Fig. 2a and 2b of the main text) from reaction of a 1% (w/w) aqueous glucose solution with Ti-Beta-F (1:50 glucose:Ti molar ratio, 373 K), plotted against the predicted fructose and sorbose concentrations using Eqs. (S.13) and Eqs. (S.14).
We note that the functional dependence of the fructose and sorbose concentrations on reaction time given in Eqs. (S.13) and (S.14), respectively, is the same as expected for reaction with a first-order deactivation process, evidence for which is provided for glucose isomerization on Ti-Beta-F in liquid water in Section S.3. Effective rate constants for glucose isomerization change as a function of batch reaction time because of the reversibility of isomerization steps and because of first-order deactivation processes. As a result, the values of forward rate constants are not determined from interpretation of fitted parameters in Eqs. (S.13) and (S.14). Instead,they are estimated by extrapolation of concentration profiles to zero reaction time to determine initial turnover rates, which are subsequently normalized by initial liquid-phase glucose concentration. This method gives identical values, within experimental error, to those estimated from differential batch reactors (<5% conversion) as well as from the dependence of initial turnover rates on liquid-phase glucose concentration (Section 3.2, main text of the manuscript).
Figure S.6.Measured (a) fructose and (b) sorbose concentrations from reaction of a 1% (w/w) aqueous glucose solution with Ti-Beta-F (1:50 glucose:Ti molar ratio, 373 K) against values predicted using Eqs. (S.13) and (S.14).
S.4.3. Concentration profiles for lactose isomerization to lactulose
The conversion of lactose (L) to lactulose (L’) is reflected in the following:
(S.18)
A derivation similar to that presented in Section S.4.1 gives the following expressions for the concentrations of lactose and lactulose:
(S.19)
(S.20)
where
(S.21)
Experimentallymeasured disaccharideconcentrations are modeled accurately by Eqs. (S.19) and Eqs. (S.20). A parity plot is shown in Figure S.7 of measured lactulose concentrations (Fig. 6 of the main text) from reaction of a 1% (w/w) aqueous lactose solution with Sn-Beta-F (1:20Sn:lactose molar ratio, 373 K), plotted against the predicted lactulose concentrations using Eq. (S.20).
Figure S.7.Measured lactulose concentrations from reaction of a 1% (w/w) aqueous lactose solution with Sn-Beta-F (1:20 glucose:Ti molar ratio, 373 K) against values predicted using Eq. (S.20).
S.5. 13C NMR spectra of products formed from reaction of glucose-13C-C1 with TiO2-SiO2 in methanol
The 13CNMR spectrum of the total reactor contents (without fractionation of individual products) after reaction of glucose-13C-C1 with TiO2-SiO2 in methanol is shown in Fig. S.8. 13C resonances appeared for the C1 position in unreacted glucose reactants ( = 95.8 and 92.0 ppm) and for the C2 position in mannose products ( = 71.1 and 70.5 ppm), consistent with glucose-mannose epimerization by an intramolecular C2-C1 shift of C3 carbon centers known as the Bilik reaction. A resonance at = 76.6 ppm is also present in Fig. S.8, but in trace amounts (<3% of total 13C content; <7% of product 13C content); this resonance currently remains unassigned, but does not appear in 13C NMR spectra for hexose sugars (glucose, fructose, mannose or sorbose) observed from glucose reactions with other solid Lewis acids.
Figure S.8.13C NMR spectrum of the total reactor contents obtained after reaction of a 1% (w/w) glucose-13C-C1 solution in methanol with TiO2-SiO2 at 373K for 4h.
S.6. Glucose isomerization rate constants on Ti-Beta-F samples of varying Si/Ti ratio
Glucose-fructose and glucose-sorbose isomerization rate constants (per total Ti; 373 K) on Ti-Beta-F samples of varying Si/Ti ratio (66-207) in liquid water and methanol are shown in Figs. S.9a and S.9b, respectively. Across all Ti-Beta-F samples, rate constants for glucose-fructose isomerization were within factors of ~1.7 and ~1.8 in water and methanol, respectively, and for glucose-sorbose isomerization were within factors of ~1.6 and ~1.3 in water and methanol, respectively.Strong intrazeolitic mass transfer limitations would lead to a systematic increase in isomerization rate constants (per total Ti) with decreasing Ti/Si ratio, as appears for glucose-sorbose isomerization in methanol (Fig. S.9b); yet, the lack of a similar dependence on Ti/Si ratio for parallel glucose-fructose isomerization (Fig. S.9b)suggest that intrazeolitic glucose diffusion does not influence isomerization turnover rates, and that small rate constant differences (within factors of ~1.3-1.8) may reflect active site heterogeneities among samples.
Figure S.9.Dependence of measured first-order glucose-fructose () and glucose-sorbose () isomerization rate constants (373 K) on Ti/Si atomic ratio for different Ti-Beta-F samples in (a) water and (b) methanol solvent.
S.7. Derivation of mechanism-based rate expressions for glucose isomerization and lactose isomerization on Lewis acid zeolites
S.7.1. Glucose-fructose and glucose-sorbose isomerization in parallel via different adsorbed glucose precursors
A reaction sequence for the formation of fructoseand sorbosein parallel reactions of glucose, mediated by different adsorbed glucose precursors, is given in Scheme S.1. In this reaction scheme, G, F and S represent glucose, fructose and sorbose in the liquid-phase, represents a Lewis acid site, G’ and G’’ represent the different bound glucose precursors respectively leading to fructose and sorbose, and F and S respectively refer to bound fructose and sorbose.The sequential adsorption of two solvent molecules (B) onto a Lewis site forms bound intermediates represented byBand 2B (Scheme S.1).
Scheme S.1.Plausible reaction mechanism for glucose-fructose isomerization (Steps 1a, 2a, 3a) and glucose-sorboseisomerization (Steps 1b, 2b, 3b) on a Lewis acid site (). Quasi-equilibrated adsorption (Steps 1a, 1b) of glucose from the liquid phase (G) to active sites to form bound precursors (G’ and G’’) that isomerize to fructose (F) and sorbose (S), respectively, in kinetically-relevant and reversible steps (Steps 2a, 2b), followed by quasi-equilibrated desorption of fructose and sorbose into the liquid phase (F, S). Quasi-equilibrated sequential adsorption of two solvent (B) molecules at Lewis acid sites shown in Steps 4 and 5.
In Scheme S.1, glucose isomerization to fructose and to sorbose occur in sequences a and b, respectively. Net rates of isomerizationto fructose (risom,F) and to sorbose (risom,S) are given by:
(S.22)
(S.23)
Reaction rates for the elementary steps in Eqs. (S.22) and (S.23) are given by the law of mass action, and are proportional to rate constants and reactant thermodynamic activities, allowing net rates to be written as:
(S.24)
(S.25)
Eqs. (S.24) and (S.25) can be rewritten as:
(S.26)
(S.27)
or:
(S.28)
(S.29)
where 2aand 2b are the approach-to-equilibrium terms for Steps 2a and 2b (Scheme S.1), respectively.
The assumption of quasi-equilibrium on Steps 1a, 1b, 3a, 3b, 4 and 5 (Scheme S.1) give the following equilibrium expressions relating the thermodynamic activities (ai) of reactant and product species:
(S.30)
(S.31)
(S.32)
(S.33)
(S.34)
(S.35)
Combining Eqs. (S.28)-(S.31) allows the isomerization rates to be expressed as:
(S.36)
(S.37)
The activities of each species appearing in Eqs. (S.36) and (S.37) can be written as the product of their activity coefficients (i) and concentrations (ci):
(S.38)
(S.39)
The concentration of total Lewis acid sites () is related to the concentration of unoccupied sites () and those of sites containing the bound adsorbates in Scheme S.1according to the following site balance:
(S.40)
Combining Eqs. (S.30)-(S.35) and (S.40) allows the Lewis acid site balance to be written as:
(S.41)
Factoring out the term in the right-hand side of Eq. (S.41) leads to the following equation
(S.42)
in which the argument in parentheses represents the fractional coverage (i) of each bound intermediate:
(S.43)
and is located in the denominator of the isomerization rate expressions before assumption of the most abundant surface intermediate.
The assumption that the Lewis acid site with two bound solvent molecules is the most abundant surface intermediate allows Eq. (S.41) to be reduced to:
(S.44)
Substitution of Eq. (S.44) into Eqs. (S.38) and (S.39) give expressions for the isomerization turnover rates (per total Lewis site):
(S.45)
(S.46)
The assumption that only a fraction of all Lewis sites (xisom,F) are able to mediate glucose-fructose isomerization or bind glucose in the configuration required for isomerization to fructose (G’), and that a separate fraction (xisom,S) are able to mediate glucose-sorbose isomerization orbind glucose in theconfiguration required for isomerization to sorbose (G’’), is reflected in the following relations:
(S.47)
(S.48)
The rate equations given in Eqs. (S.45) and (S.46) are rigorously correct only if, in the left-hand side of the equations, isomerization rates (risom,F, risom,S) are normalized by the number of sites able to catalyze their respective reactions. Thus, isomerization rates per total Lewis sites are rigorously expressed only after incorporation of the relations in Eqs. (S.47) and Eqs. (S.48), respectively:
(S.49)
(S.50)
Eqs. (S.49) and (S.50) can be rearranged to give:
(S.51)
(S.52)
or:
(S.53)
(S.54)
where kisom,S and kisom,S are measured first-order glucose-fructose and glucose-sorbose isomerization rate constants given by:
(S.55)
(S.56)
The rate and equilibrium constants that appear in Eqs. (S.55) and (S.56), expressed in terms of free energy differences between transition states, reactants and products for the steps in Scheme S.1:
(S.57)
(S.58)
(S.59)
(S.60)
(S.61)
(S.62)
Combining Eqs. (S.55), (S.57), (S.59), (S.61) and (S.62) give the following expression for the product of rate and equilibrium constants that appear in the measured glucose-fructose isomerization rate constant (Eq. (S.55)):
(S.63)
Thus, measuredglucose-fructose isomerization rate constants depend on the free energy of between one bound isomerization transition state and two solvent molecules in the liquid phase, relative to two bound solvent molecules and one glucose molecule in the liquid phase (Scheme 2, main text), according to the following relation:
(S.64)
with an effective equilibrium constant given by K1ak2aK4-1K5-1.
Combining Eqs. (S.56), (S.58), (S.60), (S.61) and (S.62) give the following expression for the product of rate and equilibrium constants that appear in the measured glucose-sorbose isomerization rate constant (Eq. (S.56)):
(S.65)
Thus, measured glucose-sorbose isomerization rate constants depend on the free energy of between one bound isomerization transition state and two solvent molecules in the liquid phase, relative to two bound solvent molecules and one glucose molecule in the liquid phase, according to the following relation:
(S.66)
with an effective equilibrium constant given by K1bk2bK4-1K5-1.
Separation of the zeolite-dependent and zeolite-independent terms in Eqs. (S.63) and(S.65) gives:
(S.67)
(S.68)
S.7.2. Lactose isomerization to lactuloseon Lewis acid sites
A plausible reaction mechanism for the isomerization of lactose (L) to lactulose (L’), whichinvolves the isomerization of a glucose moiety within a galactose-glucose sugar dimer, on Lewis acid centers (*) coordinated tetrahedrally within pure-silica zeolite frameworks (e.g., Sn-Beta, Ti-Beta)is shown in Scheme S.2. This mechanism, based on that for glucose isomerization (Scheme S.1), involves the adsorption of lactose from the liquid phase (L(l)) onto Lewis acid centers (L*) (Step 1), subsequent isomerization to form lactulose bound to Lewis acid centers (L’*) (Step 2), and desorption into the aqueous phase (L’(l)) (Step 3) to complete the catalytic cycle (Scheme 5). Scheme 5 also includes steps for the sequential adsorption of two water (B) molecules at Lewis acid centers (Steps 4 and 5). The assumption of quasi-equilibrated lactose and lactulose adsorption (Steps 1 and 3) and water adsorption (Steps 4 and 5), together with two bound water molecules (2B*) as the MASI, by extension of the assumptions made for glucose isomerization, can be used to derive an expression for the lactose isomerization turnover rate (per LA) with the following functional form (analogous to the derivation for glucose isomerization presented in Section S.7.1):
(S.69)
Scheme S.2.Plausible reaction mechanism for lactose isomerization (Steps 1-3) on a Lewis acid site (*), based on the mechanism of glucose isomerization (Scheme S.1). Quasi-equilibrated adsorption (Step 1) of lactose from the liquid phase (L(l)) to active sites to form bound precursors (L*) that isomerize to lactulose (L’*) in the kinetically-relevant and reversible step (Step 2), followed by quasi-equilibrated desorption of lactulose into the liquid phase (L’(l)). Quasi-equilibrated sequential adsorption of two solvent (B(l)) molecules at Lewis acid sites shown in Steps 4 and 5.