Monosaccharide and disaccharide isomerization over Lewis acid sites in hydrophobic and hydrophilic molecular sieves

Journal of Catalysis 308 (2013) 176–188

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Monosaccharide and disaccharide isomerization over Lewis acid sites in hydrophobic and hydrophilic molecular sieves Rajamani Gounder, Mark E. Davis ⇑ Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, United States

a r t i c l e

i n f o

Article history: Received 28 February 2013 Revised 20 May 2013 Accepted 19 June 2013 Available online 20 July 2013 Keywords: Sugar Isomerization Hydrophilic Hydrophobic Lewis Acid Zeolites

a b s t r a c t Lewis acid sites isolated within low-defect, hydrophobic molecular sieves (Sn-Beta-F, Ti-Beta-F) catalyze monosaccharide (glucose–fructose) and disaccharide (lactose–lactulose) aldose–ketose isomerization reactions in liquid water at initial turnover rates (per total metal atom; 373 K) that are, respectively, 10–30 and 103–104 factors higher than sites isolated within highly defective, hydrophilic molecular sieves (Ti-Beta-OH) or amorphous co-precipitated oxides (TiO2–SiO2). Glucose-H2/glucose-D2 kinetic isotope effects of 2 (at 373 K) for intramolecular C2–C1 hydride shift isomerization to fructose indicate that glucose transport to active sites within Ti-Beta-F or Ti-Beta-OH does not limit turnover rates in liquid water or methanol, in spite of dramatic differences in the volumetric occupation of hydrophobic and hydrophilic void spaces by physisorbed solvent molecules. Glucose isomerization turnover rates (per total Ti; 373 K) in liquid water are first-order in aqueous glucose concentration (at least up to 1.5% (w/ w)). The mechanistic interpretation of measured first-order isomerization rate constants indicates that they reflect free energies of kinetically relevant isomerization transition states relative to two bound solvent molecules, which adsorb competitively with sugars at Lewis acid sites and are the most abundant surface intermediates during steady-state catalysis. The lower isomerization rate constants on Ti centers in highly defective environments, in part, reflect stronger coordination of solvent molecules to Ti centers via additional hydrogen bonding interactions with proximal surface hydroxyl groups. The direct measurement of glucose isomerization rate constants in the liquid phase provides a rigorous and quantitative description of the catalytic differences prevalent among Lewis acidic silica-based solids with hydrophobic or hydrophilic properties, and their interpretation using a mechanism-based rate equation provides further clarity into the inhibition of catalytic turnovers at Lewis acid sites by solvent coordination. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Lewis acidic metal (M) centers, such as tetravalent Sn4+ or Ti4+ heteroatoms isolated within crystalline or amorphous silica-based frameworks, can coordinate with and polarize electronegative oxygen atoms in carbonyl functional groups and render carbonyl carbon atoms more susceptible to nucleophilic attack [1,2]. Lewis acid centers can also coordinate with oxygen atoms in alkoxides, formed upon alcohol deprotonation by hydroxyl groups on ‘‘open’’ M sites ((HO)–M–(OSi)3), which increases the nucleophilicity of substituents located at the alkoxide carbon atom [1]. Intermolecular Meerwein–Ponndorf–Verley aldehyde or ketone reduction and Oppenauer alcohol oxidation (MPVO) reaction cycles involve the nucleophilic addition of an alkoxide hydride species to the carbonyl carbon of a different molecule bound to the same M center [1,3,4]. Intramolecular MPVO cycles also involve nucleophilic at-

⇑ Corresponding author. E-mail address: [email protected] (M.E. Davis). 0021-9517/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcat.2013.06.016

tack of carbonyl carbons by electronegative H or C atoms attached to alkoxide carbons and typically involve the bidentate coordination of carbonyl and alcohol groups within a polyfunctional molecule (e.g., monosaccharides, disaccharides) to a single M center. Intramolecular MPVO cycles mediate a class of stereospecific rearrangements of hexose sugars, including: (i) glucose–fructose isomerization via C2–C1 hydride shift (Sn-Beta [5]; Ti-Beta [6]; Mg2+- or Mn2+-based D-xylose isomerase metalloenzymes [7,8]), (ii) glucose–mannose epimerization via C2–C1 carbon shift of C3 centers (Sn-Beta [9]; homogeneous Ni2+ complexes [10,11]), and (iii) glucose–sorbose isomerization via C5–C1 hydride shift (Ti-Beta [6]). Intramolecular MPVO cycles also mediate aldose–ketose isomerizations of pentose [12], tetrose [13], and triose [14] sugars on heterogeneous and homogeneous Sn-based Lewis acids. Catalytic turnovers on Lewis acid sites are inhibited by coordination of solvent molecules with Lewis basic character, such as water [15,16] or the two-phase water–organic mixtures [17–19] used typically in sugar and biomass utilization routes [2,20]. Irreversible structural changes brought forth by multiple M–O bond hydrolysis events in liquid water tend to deactivate homogeneous

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Lewis acidic complexes [21], but such structural changes are mitigated in heterogeneous solids that enforce multiple-point coordination of M atoms by oxygen atoms in extended oxide frameworks. The competitive binding of molecular water onto Lewis acid sites leads to reversible catalytic inhibition of homogeneous salts (e.g., CrCl3 [22]) and of heterogeneous solids, evident in the highly exothermic adsorption enthalpies (ca. 100 to 200 kJ mol1) at Lewis sites in c-Al2O3 [23,24] and in rutile forms of TiO2 and SnO2 [25–27]. Calorimetric studies of water adsorption at Lewis acidic Ti4+ centers isolated within low-defect (hydrophobic) and highly defective (hydrophilic) beta zeolites have measured water adsorption heats of ca. 45 and 52 kJ mol1, respectively; these adsorption heats were invariant with coverage (from 0.1 to 2.0 H2O per Ti) and with framework Ti density (0.68–1.38 Ti per unit cell) [28]. Molecular dynamics simulations (300 K, 0.05 GPa) also indicate that water can adsorb locally at a single hydrophilic silanol group defect isolated within hydrophobic SiO2 (cristobalite) surfaces [29]. Taken together, these experimental and theoretical studies provide evidence that molecular water can bind at hydrophilic Lewis sites, irrespective of the surrounding environment hydrophobicity, and that such binding becomes stronger upon concurrent hydrogen bonding interactions with proximal silanol groups, which are more prevalent on defective surfaces than on low-defect surfaces. The reversible catalytic inhibition of Lewis acid centers by coordinated water, which binds more weakly at Lewis centers isolated in hydrophobic surroundings, seems connected phenomenologically to the prevalence of intramolecular MPVO cycle-mediated sugar isomerization and epimerization catalysis on enzymatic, homogeneous, and heterogeneous catalytic ensembles that confine Lewis acid sites within hydrophobic pockets. D-xylose isomerase metalloenzyme active sites, which mediate glucose–fructose isomerization via intramolecular C2–C1 hydride shift in liquid water [7,8,30], confine Mg2+ or Mn2+ centers within pockets lined with hydrophobic aromatic substituents on tryptophan and phenylalanine amino acid residues [7]. These hydrophobic residues have been proposed to facilitate glucose binding [7,8] and exclude extraneous water molecules from metalloenzyme pockets during ringopening and isomerization [30]. Homogeneous Lewis acidic Ni2+ complexes with pendant N,N-dimethy1-N0 -alkyl ethylenediamine ligands catalyze glucose–mannose epimerization via intramolecular C2–C1 carbon shift in liquid water, at rates that increase with N0 -alkyl chain length and with concomitantly more hydrophobic environments around Ni2+ centers [10,11]. The mechanistic role of these ligands, which for N0 P 10 led to formation of metallomicelle aggregates, was proposed to mitigate the inhibition of glucose binding caused by water coordination to Ni2+ centers [10,11]. Heterogeneous silicates containing Lewis acidic Sn4+ [16] and Ti4+ [16,31] centers isolated within hydrophobic molecular sieves mediate sugar isomerization via intramolecular C2–C1 hydride shift in liquid water under conditions for which Ti4+ centers isolated within hydrophilic silicates are essentially unreactive [31]. The presence of Lewis acid centers and hydrophobic surroundings in catalytic ensembles that mediate intramolecular glucose rearrangements appears to be archetypal features of homogeneous, heterogeneous, and biological catalysts. Yet, in spite of the marked catalytic differences between hydrophobic and hydrophilic Lewis acidic molecular sieves in liquid water, the mechanistic underpinnings of how channel environments that confine active Lewis acid sites influence glucose isomerization turnover rates in condensed media remains unclear. Here, we examine the kinetic consequences of isolating Lewis acidic metal centers within hydrophobic or hydrophilic silicabased solids for the isomerization of hexose monosaccharides (glucose) and disaccharides (lactose; a galactose–glucose dimer) in liquid water and methanol. We focus primarily on titanosilicates

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because they can be synthesized with a greater range of hydrophobic and hydrophilic properties than stannosilicates, via known protocols for non-alkali-assisted crystallization in F [28] and OH [32] media of low-defect (Ti-Beta-F) and highly defective (TiBeta-OH) structures, respectively, and for co-precipitation of mononuclear Si- and Ti-alkoxide precursors to form highly defective amorphous mixed oxides (TiO2–SiO2) [33]. We use batch reactor kinetic studies to determine initial glucose isomerization turnover rates (per total M) and measured first-order rate constants that reflect events of kinetic origin and are not corrupted by mass transfer artifacts. We interpret measured first-order rate constants using mechanism-based rate equations to show how they reflect free energies of kinetically relevant isomerization transition states relative to two solvent molecules bound to Lewis sites, which provides an explanation for the marked effects of hydrophobic or hydrophilic surroundings on measured isomerization turnover rates. 2. Experimental methods 2.1. Synthesis of catalyst samples Procedures to synthesize Ti-Beta-OH [32] (Si/Ti = 39) and SnBeta-F [34] (Si/Sn = 86) were adapted from previously reported protocols. The TiO2–SiO2 co-precipitate (type III, No. 2) was obtained from W. R. Grace (Si/Ti = 56). Tin (IV) oxide (SnO2) was obtained from Sigma–Aldrich (325 mesh, 99.9% (w/w)). Ti-Beta-F was synthesized over a range of Si/Ti ratios by preparing a solution of 3.43 g of tetraethylammonium fluoride hydrate (Alfa Aesar, 97% (w/w) purity) in 6.62 g of water, followed by the addition of 7.01 g of tetraethylorthosilicate (Sigma–Aldrich, 98% (w/w)) and 0.075–1.80 g of titanium (IV) isopropoxide (Sigma–Aldrich, 99.999% (w/w)). The mixture was stirred until the tetraethylorthosilicate and titanium (IV) isopropoxide were completely hydrolyzed. The gel was then allowed to reach the targeted H2O/ SiO2 ratio by complete evaporation of ethanol and isopropanol and partial evaporation of water. The final molar composition of the gel was 1 SiO2/0.0075–0.02 TiO2/0.55 TEAF/7.47 H2O. Si-Beta was mixed into this gel as seed material (8 wt% of SiO2 in gel). The final gel was transferred to a Teflon-lined stainless steel autoclave and heated at 413 K in a static oven for 14 days. The solids were recovered by filtration, washed extensively with water, and dried at 373 K overnight, prior to calcination in flowing air (1.67 cm3 s1, Air Liquide, breathing grade) at 853 K (0.0167 K s1) for 10 h to remove the organic content occluded in the crystalline material. TiO2 deposited on amorphous SiO2 (TiO2/SiO2) was prepared by mixing 1.98 g of fumed silica (Sigma–Aldrich, 0.2–0.3 mm average particle size) in 39.5 g of dichloromethane (EMD Chemicals, 99.9% (w/w)), followed by addition of 0.8 g of a 1.0 M solution of TiCl4 in CH2Cl2 (Sigma–Aldrich). The mixture was stirred overnight for 12 h at ambient temperature. The solids were recovered, washed, dried, and calcined according to the procedure for Ti-Beta-F. TiO2 deposited on Si-Beta (TiO2/Si-Beta) was prepared by mixing 0.25 g of Si-Beta in 2.9 g of dichloromethane (EMD Chemicals, 99.9% (w/w)), followed by addition of 0.14 g of a 1.0 M solution of TiCl4 in CH2Cl2 (Sigma–Aldrich). The mixture was stirred overnight for 12 h at ambient temperature, followed by washing, drying, and calcination of the recovered solids according to the procedure for Ti-Beta-F. 2.2. Characterization of catalytic solids Atomic Si, Ti, and Sn contents were measured using a JEOL 8200 electron microprobe operated in a focused beam mode at 15 kV

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and 25 nA, with a 40 lm spot size. The crystal structures of all samples were determined from powder X-ray diffraction (XRD) patterns collected using a Rigaku Miniflex II diffractometer and Cu Ka radiation. N2 (77 K) and H2O (293 K) adsorption isotherms were obtained using a Quantachrome Autosorb iQ automated gas sorption analyzer. Catalytic solids (typically 0.03–0.04 g) were pelleted and sieved to retain 150–600 lm particles, and then degassed at 353 K (0.167 K s1) for 1 h, 393 K (0.167 K s1) for 3 h and 623 K (0.167 K s1) for 8 h, prior to recording dry sample weight. Procedures for estimating N2 and H2O micropore uptakes are reported elsewhere [31]. Infrared (IR) spectra were collected with a Nicolet Nexus 470 Fourier-transform spectrometer equipped with a Hg–Cd–Te (MCT) detector. Each spectrum was recorded by averaging 64 scans at 2 cm1 resolution in the 4000–400 cm1 range. Catalytic solids were pressed into self-supporting waters (5–15 mg cm2) that were sealed within a quartz vacuum cell equipped with KBr windows. Catalyst wafers were treated in flowing air (1.67 cm3 s1, Air Liquide, breathing grade) at 773 K (at 0.0167 K s1) and holding for 12 h, evacuated at 773 K for >2 h (<0.01 Pa dynamic vacuum; oil diffusion pump) and cooled to 303 K in vacuum. The quartz IR cell was isolated from the vacuum pump, while a quartz ampoule containing CD3CN (Sigma–Aldrich, 99.8% D-atom) was purified by freeze (77 K), pump, thaw cycles (3). The catalyst wafer was then exposed to successive doses of CD3CN at 303 K without intervening evacuation and infrared spectra were collected after each dose had been equilibrated. After saturation of all Lewis acid sites and silanol groups, the IR cell was evacuated at 303 K to remove gas-phase and physisorbed CD3CN. All reported spectra were normalized by areas for overtone and combination bands of Si–O–Si silicate framework vibrations (1750–2100 cm1). 2.3. Kinetic studies of glucose and lactose isomerization Reactions with D-glucose (Sigma–Aldrich, P99%) and a-lactose monohydrate (Sigma–Aldrich, P99%) were conducted in 10-mL thick-walled glass batch reactors (VWR) sealed with crimp tops (PTFE/silicone septum, Agilent), with temperature control provided by an oil bath placed on top of a digital stirring hotplate (Fisher Scientific). Reactions with D-glucose were typically carried out at a 1:50 metal/glucose molar ratio, while reactions with lactose were typically carried out at a 1:20 metal/lactose molar ratio. These reactions involved contacting 4.0–6.0 g of a 0.5–1.5% (w/w) glucose solution in water or in methanol, or of a 1% (w/w) lactose solution in water, with the appropriate amount of catalyst in a stirred glass reactor. Isotopic studies were performed using a 1% (w/w) aqueous D-glucose-D2 solution prepared using D-glucose-D2 supplied by Cambridge Isotope Laboratories (P98%). Reactors were placed in the oil bath and small aliquots (50–100 lL) were extracted at specific time intervals via syringe (Hamilton, 700 series), filtered with 0.2 lm PTFE syringe filter (National Scientific), and mixed with 1% (w/w) aqueous D-mannitol (Sigma–Aldrich, P98%) solutions used as an internal standard for quantification. The total aliquot volume extracted from the reactor via syringe during the course of reaction constituted <10% of the initial liquid charge by volume. Reaction aliquots were analyzed by an Agilent 1200 high-performance liquid chromatograph (HPLC) equipped with an evaporative light scattering (ELS) detector (Agilent 380 LC). Glucose, fructose, sorbose, mannose, and mannitol fractions (and lactose, lactulose, and mannitol fractions) were separated with a Hi-Plex Ca column (7.7  300 mm, 8 lm particle size, Agilent) held at 353 K, using water as the mobile phase (0.01 mL s1). This separation method with water as the mobile phase does not completely resolve mannose and sorbose products, which can be separated using a 70/30 (v/v) acetonitrile/water mobile phase and signifi-

cantly longer (5) separation times [6]. Compositional analysis of product mixtures from reactions of glucose with Ti-Beta-F, TiBeta-OH, and TiO2-SiO2 by separation using 70/30 (v/v) acetonitrile/water as the mobile phase, together with 13C NMR spectra collected of the combined mannose and sorbose fraction isolated using water as the mobile phase, indicated that Ti-Beta-F and TiBeta-OH formed sorbose nearly exclusively (sorbose/mannose molar ratios >11) and that TiO2–SiO2 solely formed mannose (sorbose was undetectable in HPLC chromatograms and corresponding 13C resonances were absent in 13C NMR spectra). Thus, the kinetic data reported here were determined by HPLC separation using water as the mobile phase, with product formation rates of sorbose on TiBeta-F and Ti-Beta-OH derived from combined sorbose–mannose peak areas (>92 mol% sorbose, <8 mol% mannose).

3. Results and discussion 3.1. Synthesis and characterization of hydrophobic and hydrophilic Snand Ti-silicates Characterization data of all samples used in this study are given in Table 1. X-ray diffraction patterns (Fig. S.1, Supporting Information) and N2 adsorption isotherms at 77 K (Fig. S.2-S.4, Supporting Information) of Sn-Beta and Ti-Beta crystallized in fluoride media (Sn-Beta-F, Ti-Beta-F) and of Ti-Beta crystallized in hydroxide media (Ti-Beta-OH) were consistent with the beta topology. Zeolites crystallized in fluoride media (10 lm) are much larger in size (by 102–103 X) than those that crystallized in hydroxide media (10–100 nm) [35], evident in the much higher signal-to-noise XRD patterns for Ti-Beta-F than for Ti-Beta-OH (Fig. S.1, Supporting Information) [31,35]. Nanocrystalline Ti-Beta-OH domains aggregate into larger secondary structures [35] (10 lm aggregates detectable by SEM imaging [31]), reflected also in the significant intercrystalline condensation of N2, H2O, and CH3OH after micropore filling (Fig. S.3, Supporting Information) [31,35]. Single-component vapor-phase adsorption isotherms (Figs. S.2S.4, Supporting Information) indicate that H2O uptakes (at P/ P0 = 0.2; 293 K) are significantly lower than the total N2 micropore volume (77 K) of low-defect Ti-Beta-F zeolites (by 100; Table 1) [31]. In contrast, H2O uptakes are similar to the micropore volume of defective Ti-Beta-OH or to the area available for N2 binding on defective TiO2-SiO2 surfaces (within 3, Table 1) [31]. The much lower H2O uptakes on Ti-Beta-F, relative to N2 uptakes on Ti-Beta-F (by 100; Table 1) or to H2O uptakes on Ti-Beta-OH (by 30; Table 1), reflect the hydrophobic nature of essentially defect-free Beta channels (0.7 nm in diameter) whose surfaces are comprised of primarily non-polar Si–O–Si bonds [36,37]. This behavior is also consistent with molecular dynamics simulations that indicate that extended water structures resembling those found in bulk solution are unable to form between hydrophobic surfaces separated by less than 0.8 nm at ambient temperatures and pressures [38], and with experimental studies that indicate elevated pressures (57 MPa) are required for complete water intrusion in essentially defect-free channels of Si-Beta at ambient temperatures [39]. The low, but detectable, H2O uptakes on Ti-Beta-F at low H2O reduced pressures (Fig. S.2, Supporting Information) reflects the adsorption of molecular water at hydrophilic framework Ti heteroatoms [28,31] or defect sites [29,36], which occurs even if such sites are isolated within hydrophobic surroundings. The sole presence of Lewis acidic framework M4+ centers on SnBeta-F [5] and Ti-Beta-F [6], and not any base sites associated with extraframework MOx species [9], was evident in the lack of H/D scrambling in glucose reactants deuterated at the C2 position (glucose-D2) and in the formation of fructose with the D-label retained at the C1 position. IR spectra collected after saturation of Sn-Beta-F

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R. Gounder, M.E. Davis / Journal of Catalysis 308 (2013) 176–188 Table 1 Site and structural characterization of the samples used in this study. Sample Sn-Beta-F Ti-Beta-F Ti-Beta-OH TiO2–SiO2 TiO2/SiO2 TiO2/Si-Beta SnO2

Si/M 87 107 38 56 57 21 –

Vads (N2) (cm3 g1) a

0.22 0.21a 0.21a 0.076b – – –

Vads (H2O) (cm3 g1) c

0.0093 0.0024c 0.076c 0.024c – – –

Vads (CH3OH) (cm3 g1) a

0.18 0.20a 0.18a – – – –

Vads (H2O)/Vads (N2)

Lewis site IR band aread

0.044 0.011 0.35 0.32 – – –

0.014 0.0048 0.068 0.0035 0.0002 n.d.* –

a

N2 and CH3OH volumes at end of micropore filling transition (77 K). Data reported originally in Ref. [31]. N2 volume at P/P0 = 0.001 (77 K). Data reported originally in Ref. [31]. c H2O volumes at P/P0 = 0.2 (293 K). Data reported originally in Ref. [31]. d After adsorption of CD3CN and evacuation at 298 K; areas for bands centered at 2306 cm1 and 2316 cm1, relative to overtone and combination bands for Si–O–Si vibrations (2100–1750 cm1). * n.d.: not detected. b

and Ti-Beta-F with CD3CN and subsequent evacuation at 298 K (Fig. 1) showed bands at 2308–2316 cm1 (areas given in Table 1), consistent with C„N stretching vibrations in CD3CN bound to Lewis acidic Ti and Sn centers [40,41], and at 2276 cm1 (Fig. 1) for CD3CN adsorption on silanol groups [40,41]. IR bands at 2306 cm1 also appeared after saturation of Ti-Beta-OH and TiO2–SiO2 with CD3CN (Fig. 1; Table 1), but not after saturation of samples prepared deliberately with extraframework TiO2 deposited on Si-Beta (TiO2/Si-Beta) or on amorphous SiO2 (TiO2/SiO2) supports (Fig. 1). The TiO2-containing samples instead only showed bands at 2276 cm1 for CD3CN adsorption onto silanol groups [40,41], and at 2265 cm1 (unassigned) as reported previously for extraframework SnO2 particles [41]. These IR data indicate that Lewis acid centers are also present on hydrophilic Ti-Beta-OH and TiO2-SiO2 samples, as in the case of hydrophobic Ti-Beta-F and SnBeta-F zeolites [5,31]. 3.2. First-order glucose isomerization rate constants on titanosilicates in water and methanol The reaction of a 1% (w/w) aqueous glucose solution with TiBeta-F (1:50 glucose/Ti molar ratio, 373 K) led to the concomitant

Fig. 1. Infrared spectra of (a) Sn-Beta-F, (b) Ti-Beta-F (3), (c) Ti-Beta-OH, (d) TiO2– SiO2, (e) TiO 2/SiO2, and (f) TiO2/Si-Beta (top to bottom) after saturation with CD3CN and subsequent evacuation at 298 K. IR band areas for CD3CN bound to Lewis acid sites (2306 and 2316 cm1) given in Table 1. Spectra normalized to intensities of overtone and combination bands for Si–O–Si vibrations (1750–2100 cm1).

formation of fructose and sorbose; aqueous-phase glucose, sorbose and fructose concentrations, together with glucose conversion and fructose-to-sorbose molar ratios, are shown as a function of reaction time in Fig. 2a and b. Monosaccharide concentrations approached steady-state values with increasing reaction time (Fig. 2a, b) because of the equilibration of batch reactor contents and the irreversible deactivation of some catalytic sites (additional details given in Section S.3, Supporting Information). Fructose and sorbose were formed at non-zero initial rates and at molar ratios (2.5; Fig. 2b) that depended weakly on glucose conversion (0– 28%; Fig. 2a), reflecting their formation as primary products of parallel glucose isomerization reactions. The dashed curves in Fig. 2a and b represent best fits of monosaccharide concentrations, glucose conversion, and product molar ratios to those expected from the following functional dependences of liquid-phase fructose (cF(l)) and sorbose (cS(l)) concentrations on reaction time (derivation in Section S.4, Supporting Information):

cFðlÞ ðtÞ ¼ cFðlÞ;ss ð1  et=s1 Þ

ð1Þ

cSðlÞ ðtÞ ¼ cSðlÞ;ss ð1  et=s2 Þ

ð2Þ

In Eqs. (1) and (2), cF(l),ss and cS(l),ss are concentrations of fructose and sorbose at steady state, and s1 and s2 are time constants that reflect the dynamics of approach to this steady state. The functional forms of Eqs. (1) and (2) are consistent with those expected from reversible isomerization reactions that are proportional to liquid-phase monosaccharide concentrations in an ideal, stirred, constant volume batch reactor and from irreversible isomerization reactions with first-order deactivation processes (Section S.4, Supporting Information). The reaction profiles (Fig. 2a and b) shown for Ti-Beta-F are representative of all conditions examined in this study for low-defect or highly defective Ti-Beta samples, which catalyze glucose–fructose isomerization and glucose–sorbose isomerization via distinct intramolecular hydride shifts between C2–C1 and C5–C1 centers, respectively [6]. Lewis acidic Ti centers in TiO2–SiO2 also mediate glucose isomerization to fructose, but in parallel catalyze epimerization to mannose via Lewis-acid-mediated intramolecular C3 carbon shift from C2–C1 centers, also known as the Bilik reaction [42,43] (13C NMR spectra of products formed with glucose-13C– C1 reactants in Fig. S.8; Section S.5, Supporting Information). The underlying phenomena that cause different reactions to prevail on Ti centers confined within Beta zeolites and located at amorphous silica surfaces currently remain under investigation; as a result, comparisons among titanosilicate samples are limited here to glucose–fructose isomerization rates (risom,F) or to total glucose isomerization rates (risom,tot), given by the sum of isomerization and epimerization product formation rates.

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Fig. 2. (a) Aqueous-phase glucose () concentrations and conversion (d), and (b) aqueous-phase fructose (N) and sorbose concentrations (j) and fructose/sorbose molar ratios (d) during reaction of a 1% (w/w) aqueous glucose solution with Ti-Beta-F (1:50 glucose/Ti molar ratio, 373 K). Dashed curves represent fits of the experimental data to Eqs. (1) and (2) for fructose and sorbose concentrations, respectively (equations for glucose concentration, conversion and fructose/sorbose molar ratio in Section S.5, Supporting Information).

Initial turnover rates on Ti-Beta-F (373 K; per total Ti) for glucose–fructose isomerization (risom,F) and glucose–sorbose isomerization (risom,S) showed a first-order dependence on initial aqueous-phase glucose concentration, when varied from 0.5 to 1.5% (w/w) (Fig. 3), consistent with the following rate expressions:

r isom;F ¼ kisom;F  cGðlÞ

ð3Þ

r isom;S ¼ kisom;S  cGðlÞ

ð4Þ

In Eqs. (3) and (4), kisom,F and kisom,S are measured first-order rate constants for glucose–fructose isomerization and glucose–sorbose

Fig. 3. Dependence of initial glucose–fructose isomerization (N) and glucose– sorbose isomerization (j) turnover rates (per total Ti) on Ti-Beta-F on the initial aqueous-phase glucose concentration (data points correspond to 0.5%, 0.75%, 1.0%, and 1.5% (w/w)).

isomerization, respectively. Values of kisom,F and kisom,S are 2.0 (±0.2)  105 and 7.9 (±1.4)  106 mol [(mol Ti)s ((mol glucose) m3)]1, respectively (Table 2), when determined from leastsquares regression of the data shown in Fig. 3 to Eqs. (3) and (4). These kisom,F and kisom,S values are identical, within experimental error, to the forward isomerization rate constants estimated from initial turnover rates (per total Ti), determined by fitting monosaccharide concentration profiles (Fig. 2b) to Eqs. (1) and (2) and evaluating their time derivative at zero reaction time (kisom,5 ; kisom,S = 7.8 (±1.4)  106 mol [(mol Ti)s((mol F = 1.8 (±0.2)  10 glucose) m3)]1). These values are also identical to the isomerization rate constants measured during differential glucose conversion (kisom,F = 1.9 (±0.4)  105; kisom,S = 7.1 (±1.4)  106 mol [(mol Ti)s((mol glucose) m3)]1). Rate constants estimated by all three methods were identical, but with larger uncertainties when estimated from differential batch reactor data; as a result, the rate constants reported here were determined from initial turnover rates, estimated by fitting monosaccharide concentration profiles to Eqs. (1) and (2) and evaluating their time derivative at zero reaction time, normalized by the initial liquid-phase glucose concentration. The evolution of fructose concentrations during the reaction of a 1% (w/w) aqueous glucose solution with Ti-Beta-F, Ti-Beta-OH, and TiO2–SiO2 is shown in Fig. 4. Values of kisom,F in liquid water are an order-of-magnitude higher on low-defect, hydrophobic TiBeta-F than on highly defective, hydrophilic Ti-Beta-OH (by 9; Table 2) and TiO2–SiO2 (by 28; Table 2), consistent with undetectable glucose conversion on Ti-Beta-OH under reaction conditions that lead to differential conversion on Ti-Beta-F in liquid water [31] and reminiscent of the order-of-magnitude lower conversion with hydrophilic TiO2–SiO2 than with hydrophobic TS-1 (titanium silicalite-1; Ti-MFI) during 1-hexene epoxidation and n-octane oxidation in aqueous H2O2 [44]. Table 2 also summarizes measured first-order rate constants for each glucose isomerization (kisom,F, kisom,S) and epimerization (kepim,M) path (per Ti; 373 K), together with total glucose isomerization rate constants (kisom,tot) determined from the sum of isomerization and epimerization product formation rates, for all samples and solvents. Values of kisom,F were also an order-of-magnitude higher on Ti-Beta-F than

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Table 2 Measured first-order rate constants (per total Ti; 373 K) for glucose–fructose isomerization (kisom,F), glucose–sorbose isomerization (kisom,S), glucose–mannose epimerization (kepim,M) and their sum (kisom,tot) in water and methanol solvent on Ti-Beta-F, Ti-Beta-OH and TiO2–SiO2. Rate constant ratios of Ti-Beta-F, relative to Ti-Beta-OH and TiO2–SiO2, are also shown. Sample

Measured first-order rate constant (/106 mol (mol Tis((mol glucose) m3))1) H2O Solvent

Ti-Beta-F Ti-Beta-OH TiO2–SiO2 Ti-Beta-F/ Ti-Beta-OH Ti-Beta-F/ TiO2–SiO2 a

CH3OH Solvent

kisom,F

kisom,S

kepim,M

kisom,tot

kisom,F

kisom,S

kepim,M

kisom,tot

18 2.3 0.91

7.6 0.68 –

– – <0.11a

26 3.0 0.91

9.1 0.67 <0.30a

31 2.0 –

– – 2.8

40 2.6 2.8

7.8

11

–

8.6

16

14

–

15

20

–

–

28

11

–

–

14

Products were not detected; rates represent detection limits.

Fig. 4. Aqueous-phase fructose concentrations during reaction of a 1% (w/w) aqueous glucose solution with Ti-Beta-F (d), Ti-Beta-OH (j), and TiO2–SiO2 (N) (equivalent glucose/Ti molar ratios, 373 K). Dashed curves represent best fits of the experimental data to Eq. (1).

on Ti-Beta-OH and TiO2–SiO2 in liquid methanol (by 15 and 14, respectively; Table 2), suggesting that water and methanol solvents influence relative isomerization rates between hydrophobic and hydrophilic titanosilicates to a similar extent. Prior to mechanistic interpretation of kisom,F values (Table 2), we first provide evidence and analysis to show that measured isomerization rates are not influenced by intracrystalline mass transport artifacts.

3.3. Assessment and exclusion of intracrystalline mass transport artifacts Measured glucose isomerization turnover rates would show apparent first-order dependences on liquid-phase glucose concentration if limited by first-order kinetic processes, or by diffusion of glucose reactants from external fluid phases to intrazeolitic Ti active sites. Quantum chemical calculations of glucose–fructose isomerization reaction coordinates on isolated Lewis acidic Sn and Ti sites in silica clusters [45] indicate that C–H bond scissoring (1500 cm1) is the reaction coordinate vibrational frequency for intramolecular C2–C1 hydride shift glucose–fructose isomerization. As a result, glucose deuterated at the C2 position (glucoseD2) would lead to a kinetic isotope effect (KIE) of 2.1 (at 373 K) if turnover rates were limited by intramolecular C2–C1 hydride

shift steps, but a KIE of 1.5 (at 373 K) if limited by intrazeolitic glucose diffusion (derivation in Appendix A). Reactions of glucose-D2 in liquid water with Ti-Beta-F, whose micropores do not fill with water (Fig. S.2, Supporting Information; Table 2), led to glucose reactant disappearance rates (383 K), which predominantly reflect rates of isomerization to fructose, that were a factor of 2 lower than those for unlabeled glucose reactants [45]. Reactions with Ti-Beta-F in liquid methanol, which fills all available micropore space in Ti-Beta-F at sub-saturation pressures (P/P0  0.4; Fig. S.2, Supporting Information), also led to similar glucose-H2/glucose-D2 KIE values (2.0 ± 0.2 at 373 K [6]). These KIE values indicate that elementary steps for glucose diffusion, adsorption, and ring-opening at Ti sites do not limit rates of glucose–fructose isomerization cycles prior to kinetically relevant intramolecular C2–C1 hydride shift. These quasi-equilibrated diffusion, adsorption, and ring-opening steps are also required in glucose–sorbose isomerization cycles [6], whose turnover rates are limited by kinetically relevant C5–C1 hydride shift that lead to KIE values of 2.3 (373 K) with fully deuterated glucose reactants [6]. Moreover, kisom,F and kisom,S values did not vary systematically with Ti content on Ti-Beta-F samples (Si/Ti = 66–207), suggesting that the small variation in kisom values among these samples (within factors of 1.3–1.8 at 373 K; Figs. S9a and S9b, Section S.7, Supporting Information) reflects inhomogeneties in active Ti site structures or distributions. The observed glucose-H2/glucose-D2 KIE values and the weak dependence of isomerization rate constants (per total Ti) on framework Ti density, taken together, provide evidence that measured isomerization turnover rates in liquid water and methanol are not limited by glucose diffusion to active Ti centers confined within low-defect channels of Ti-Beta-F. Physisorbed water clusters and extended water structures are present within hydrophilic channels of Ti-Beta-OH, but not within hydrophobic channels of Ti-Beta-F, and may pose additional barriers for reactant diffusion to active sites in Ti-Beta-OH. Liquid-phase concentrations of fructose and sorbose formed from reactions of glucose-H2 and glucose-D2 with Ti-Beta-OH in liquid water (373 K) are shown in Fig. 5a and b (data in liquid methanol not shown), and the corresponding measured first-order rate constants are shown in Table 3. Values of kisom,F (per total Ti, 373 K) were lower with glucose-D2 reactants by factors of 1.9 and 2.0 in water and methanol, respectively (Table 3), as expected for kinetically relevant intramolecular C2–C1 H-shift; glucose-H2/glucoseD2 KIE values for glucose–sorbose isomerization on Ti-Beta-OH in water and methanol were 1 (Table 3), because glucose C2–D bonds are not broken during intramolecular C5–C1 hydride shift steps [6]. Values of kisom,tot in liquid water were also higher by a factor of 3 (Table 2) on Ti centers located within hydrophilic TiBeta-OH pores (0.7 nm in diameter) than on those located at

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Fig. 5. Aqueous-phase concentrations of (a) fructose and (b) sorbose from reaction of a 1% (w/w) aqueous glucose (N) or glucose-D2 (d) solution with Ti-Beta-OH (1:50 glucose/Ti molar ratio, 373 K). Dashed curves represent fits of the experimental data to Eqs. (1) and (2) for fructose and sorbose concentrations, respectively.

Table 3 Measured first-order rate constants (per total Ti; 373 K) and H/D kinetic isotope effects (KIE) for glucose–fructose isomerization (kisom,F) and glucose–sorbose isomerization (kisom,S) in water and methanol on Ti-Beta-OH using glucose-H2 and glucose-D2 reactants. Reactant

Measured first-order rate constant (/106 mol (mol Tis((mol glucose) m3))1) H2O solvent

Glucose-H2 Glucose-D2 H/D KIE

CH3OH solvent

kisom,F

kisom,S

kisom,F

kisom,S

2.3 1.2 1.9

0.68 0.75 0.9

6.4 3.2 2.0

1.9 1.9 1.0

hydrophilic surfaces of amorphous TiO2–SiO2 (10 nm in diameter), for which rates of reactant diffusion to active sites are not expected to limit turnover rates. Thus, glucose diffusion to active Ti centers in Ti-Beta-OH does not limit measured isomerization turnover rates in liquid water or methanol. We conclude from these data that intracrystalline mass transport does not limit the turnover rates on all titanosilicate samples and reaction conditions (373 K) used in this study. The kinetic relevance of intramolecular hydride shift steps requires that glucose diffusion, adsorption, and ring-opening steps be quasi-equilibrated. Glucose diffusion occurs much faster than hydride shift isomerization within low-defect Ti-Beta-F channels in both liquid water and methanol solvents, in spite of dramatic differences in the volumetric occupation of hydrophobic void spaces by water and methanol during conditions relevant for glucose isomerization catalysis. Glucose transport within the hydrophobic and hydrophilic channels of Ti-Beta-F and Ti-Beta-OH, respectively, is also kinetically irrelevant in liquid water, in spite of significant differences in their intrazeolitic water content during catalysis in liquid water. As a result, the order-of-magnitude differences in measured first-order isomerization rate constants between Ti-Beta-F and TiBeta-OH or TiO2–SiO2 (Table 2) must reflect differences of kinetic origin, and the effects of hydrophobic or hydrophilic surroundings on relevant kinetic processes, as we interpret next using a plausible reaction mechanism. 3.4. Mechanistic interpretation of glucose isomerization rate constants A plausible mechanistic sequence for parallel glucose (G) isomerization to fructose (F) and sorbose (S) on Lewis acidic Ti centers () is shown in Scheme 1. Reactions of glucose with Lewis acid zeo-

lites first involve quasi-equilibrated adsorption from external fluid phases (G(l)) onto Lewis acid sites. The adsorption of glucose within hydrophobic channels from aqueous solution occurs without its hydration shell [31] and with some enthalpic losses, because glucose hydrogen bonding interactions with water molecules (DHsol = 141 ± 6 kJ mol1 [46]) are replaced only in part by van

Scheme 1. Plausible reaction mechanism for glucose isomerization to fructose (Steps 1a, 2a, 3a) and isomerization to sorbose (Steps 1b, 2b, 3b) on a Lewis acid site (). Quasi-equilibrated adsorption (Steps 1a, 1b) of glucose from the liquid phase (G(l)) to active sites to form bound precursors ((G)O1–O2, (G)O1–O5) that isomerize to fructose (F) and sorbose (S), respectively, in kinetically relevant and reversible steps (Steps 2a, b), followed by quasi-equilibrated desorption of fructose and sorbose into the liquid phase (F(l), S(l)). Quasi-equilibrated sequential adsorption of two solvent molecules with Lewis basic character (B(l)) at Lewis acid sites (Steps 4 and 5).

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der Waals interactions with zeolitic framework oxygens (DHads = 108 kJ mol1 [46]), and with large entropy gains upon hydration shell disassembly (DSads = +90 ± 30 J mol K1 [46]) that provide the thermodynamic driving force for adsorption. Glucose undergoes subsequent Lewis-acid catalyzed ring-opening [45] to form adsorbed precursors for isomerization to fructose ((G)O1–O2; Step 1a), which bind to Lewis sites via glucose O1 and O2 atoms [45], or isomerization to sorbose ((G)O1–O5; Step 1b), which bind via glucose O1 and O5 atoms [6]. Ring-opened glucose chains isomerize in intramolecular hydride shift steps (Steps 2a, 2b) that are kinetically relevant, as inferred from observed H/D KIE values with glucose-D2 reactants (Table 2; Section 3.3) [45]. The bound openchain fructose (F) or sorbose (S) intermediates formed in Steps 2a and 2b, respectively (Scheme 1), undergo quasi-equilibrated ring closing and desorption (Steps 3a, Step 3b) into the liquid phase (F(l), S(l)) to complete the catalytic cycle (Scheme 1). Scheme 1 also includes quasi-equilibrated steps for the sequential coordination of two solvent molecules with Lewis basic character (B(l); e.g., H2O, CH3OH) at Lewis acid centers (B and 2B, Steps 4 and 5, Scheme 1); these solvent molecules complete octahedral coordination environments around metal centers substituted in tetrahedral locations of silica frameworks [45] and inhibit the coordination of reactants at such centers. In what follows, we focus on the mechanistic interpretation of glucose–fructose isomerization turnover rates and rate constants because the treatment is analogous for glucose–sorbose isomerization. The sequence of elementary steps shown in Scheme 1 accurately describes glucose reaction profiles on Ti-Beta zeolites in liquid water (Fig. 2a and b). First-order kinetic dependences of isomerization turnover rates on glucose concentration (Fig. 3; Eqs. (3) and (4)) require dilute sugar coverages on Lewis acid sites, indicating that sites are predominantly unoccupied () or occupied with one (B) or two solvent (2B) molecules during catalysis. 119Sn MAS NMR spectra of Sn-Beta-F zeolites exposed to ambient conditions show resonances for framework Sn in octahedral coordination (ca. 685 to 700 ppm); upon dehydration, these resonances disappear and new resonances appear concomitantly for framework Sn in tetrahedral coordination (ca. 425 to 445 ppm) [9,45]. These findings indicate that two H2O molecules are adsorbed at each framework Sn center, even when these heteroatoms are confined within the hydrophobic channels of low-defect zeolite beta and are consistent with stoichiometric H2O uptakes (ca. 2 per Ti center) at low H2O pressures in both hydrophobic Ti-Beta-F and hydrophilic Ti-Beta-OH zeolites [28]. The

mechanistic assumptions that two bound solvent molecules are most abundant surface intermediates (MASI) during steady-state catalysis in liquid water and that intramolecular hydride shift isomerization steps (Step 2a, Scheme 1) are kinetically relevant lead to glucose–fructose isomerization turnover rates (risom,F; per total Lewis acid site) given by (derivation of rate expression in Appendix B):

risom;F ¼

cGðlÞ

!

c2B K 1a

c

2 2 BðlÞ c BðlÞ

K4K5

 xisom;F k2a cGðlÞ ð1  g2a Þ

ð5Þ

In this equation, ci terms are activity coefficients for species i (Scheme 1), cB(l) and cG(l) are the liquid-phase solvent and glucose concentrations, respectively, K1a is the equilibrium constant relating liquid-phase glucose to open-chain precursors to fructose that are bound at Lewis sties (Scheme 1), k2a is the isomerization rate constant (Scheme 1), K4 and K5 are the equilibrium constants for solvent adsorption at Lewis sites (Scheme 1), xisom,F is the fraction of total Lewis sites that catalyze isomerization, and g2a is the approach-to-equilibrium for isomerization steps (Step 2a, Scheme 1). The mechanism-based glucose–fructose isomerization rate expression (Eq. (5)) is first-order in glucose concentration, with measured first-order isomerization rate constants (kisom,F) given by:

kisom;F ¼

cGðlÞ c2BðlÞ c2BðlÞ

!

 K 1a k2a c2B xisom;F K4K5

ð6Þ

Differences in kisom,F values among titanosilicates (Table 2) cannot reflect differences in the liquid-phase activity coefficient and concentration terms in Eq. (6) (cG(l), cB(l), cB(l)), because they are independent of catalyst identity. The order-of-magnitude rate constant differences between hydrophobic and hydrophilic titanosilicates (Table 2) may reflect differences in the fraction of total metal sites able to catalyze isomerization reactions (xisom,F); yet, order-of-magnitude differences in these fractions seem unlikely, because values of kisom,F and kisom,S (per total Ti) in water and methanol varied by less than 1.3–1.8 on Ti-Beta-F zeolites with varying Si/Ti ratio (Figs. S.9a and S.9b, Section S.7, Supporting Information). Thus, channel environments predominantly influence kisom,F values via the activity coefficient of solvent molecules bound to active sites (c2B⁄) or via the product of rate and equilib1 rium constants (K 1a k2a K 1 4 K 5 ) that are linked inextricably in measured first-order isomerization rate constants (Eq. (6)).

Scheme 2. Gibbs free energy versus reaction coordinate diagram for glucose–fructose isomerization in water on open Ti sites (one –OH group and three –OSi bonds), corresponding to the reaction mechanism in Scheme 1 (Steps 1a, 2a, 4 and 5). First-order glucose–fructose isomerization rate constants (kisom,F) reflect Gibbs free energy differences (DGisom,F) between bound intramolecular C2–C1 hydride transfer transition states and two bound water molecules.

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The rate and equilibrium constants that appear in measured isomerization rate constants (Eq. (6)), which depend on free energy differences between the specific transition states, reactants and products depicted in Scheme 2, can be expressed as (detailed derivation in Section S.8, Supporting Information):

K 1a k2a kB T ðððDGz2a þ2DGBðlÞ ÞðDGGðlÞ þDG2B ÞÞ=RTÞ kB T ðDGisom;F =RTÞ e e ¼ ¼ h h K4K5

ð7Þ

Scheme 2 and Eq. (7) show explicitly that measured isomerization rate constants reflect free energies of bound isomerization transition states (DGz2a ) and two solvent molecules in external fluid phases (2DGBðlÞ ), relative to those of two bound solvent molecules (DG2B ) and one glucose molecule in the liquid phase (2DGðlÞ ). The free energy difference that influences measured rate constants (DGisom,F, Eq. (7)) is insensitive to the chemical identities of any reactive intermediates formed in quasi-equilibrated steps en route to the kinetically relevant isomerization transition state from Lewis acid sites saturated with solvent molecules. Eq. (7) can be further rearranged into zeolite-independent (first set of parentheses) and zeolite-dependent terms (second set of parentheses):

  K 1a k2a kB T ðð2DGBðlÞ DGGðlÞ Þ=RTÞ  ððDGz2a DG  Þ=RTÞ  2B e e ¼ h K4K5

ð8Þ

Combining Eqs. (6) and (8) and canceling catalyst-independent terms shows explicitly that the ratio of first-order isomerization rate constants on two different titanosilicates (A and B) is influenced by the environments surrounding Ti centers via free energy differences between bound isomerization transition states and two bound solvent molecules:

ðkisom;F ÞA ðc2B xisom;F ÞA  ðððDGz2a DG2B Þ ðDGz2a DG2B Þ Þ=RTÞ  A B ¼ e ðkisom;F ÞB ðc2B xisom;F ÞB

ð9Þ

Isomerization rate constants in liquid water were higher on TiBeta-F than on Ti-Beta-OH and TiO2–SiO2 by factors of 9 and 20, respectively (Table 2), indicating that low-defect silica surfaces stabilize isomerization transition states and/or destabilize water molecules bound at Ti sites preferentially, compared to highly defective surfaces (via Eq. (9)). Calorimetric measurements of H2O adsorption at stoichiometric Ti coverage indicate that water binds more strongly to Ti centers within defective Ti-Beta-OH (qads  52 kJ mol1) than within defect-free Ti-Beta-F (qads  45 kJ mol1) [28]; such differences in binding energies (7 kJ mol1) resemble in magnitude the free energy differences required for a factor of 10 difference in measured isomerization rate constants at 373 K (7 kJ mol1; via Eq. (9)). We also cannot exclude the possibility that transition states are stabilized differently within hydrophobic and hydrophilic environments, because kisom,F values are sensitive only to free energy differences between transition states and bound solvent molecules. We note that hydrophobic enzyme pockets that exclude bulk water stabilize charged and polar transition states more effectively than pockets that do not, because the fixed and induced dipoles in amino acid residues, which help stabilize charged transition states, cannot be polarized as strongly when they also interact with randomly oriented dipoles present in bulk water [47]. Initial isomerization and epimerization rate constants were also an order-of-magnitude higher on Ti-Beta-F than on Ti-Beta-OH in methanol solvent (factors of 16 and 14 at 373 K, respectively, Table 2), suggesting that water and methanol molecules similarly influence the relative reactivity (per total Ti) of Ti centers in essentially defect-free and highly defective solids. Calorimetric studies indicate that polar molecules (e.g., water, toluene) bind more strongly at Ti centers in Ti-Beta-OH than in Ti-Beta-F, but that non-polar molecules (e.g., n-hexane) bind at both centers with similar adsorption heats [28]. Thus, it seems plausible that metha-

nol also binds more strongly at tetrahedral Ti centers in defective than in defect-free silicate environments. The exposure of TS-1 and Ti-Beta to methanol also causes detectable Ti-O bond lengthening in X-ray absorption spectra (Ti K-edge EXAFS) [48] and appearance of Raman bands for Ti–O–CH3 groups (600 cm1) [49], which may reflect methanol dissociative adsorption to form Ti–OCH3 groups. Thus, the exact structure of bound methanol or moieties derived from methanol during steady-state catalysis remains unclear, precluding further insight into the origin of rate constant differences among titanosilicates in methanol solvent. 3.5. Lactose–lactulose isomerization mediated by hydrophobic Lewis acid zeolites The data provided above show that glucose isomerization turnover rates are higher on Lewis acid sites confined within hydrophobic channels (Ti-Beta-F) than within hydrophilic channels (Ti-BetaOH) or surfaces (TiO2–SiO2). Molecular dynamics simulations indicate that hydrophobic environments are present between pure-silica surfaces only when separated by less than 0.8 nm [38], which are length scales characteristic of molecular sieves with 14-MR structures or smaller. Yet, constrained void spaces also influence reactivity via coupled reaction-transport phenomena [50] and via control of access to active sites using molecular size and shape as criteria; as a result, glucose (0.8 nm in kinetic diameter) isomerization occurs with Sn-Beta (0.70 nm in diameter) and Sn-MCM41 (>1.5 nm in diameter) but not with Sn-MFI (0.55 nm diameter 10-MR apertures) [16]. Hydrophobic Lewis acid zeolites with the beta topology would also react larger disaccharide reactants containing glycosidic bonds that confer rotational flexibility to monomeric subunits, such as isomaltose and isomaltulose (a (1–6)), maltose (a (1–4)), cellobiose (b (1–4)), and leucrose (a (1–5)) disaccharides, but not sucrose, which contains relatively rigid a (1–2) glycosidic bonds [51,52]. Lactose is a disaccharide of galactose and glucose linked via a flexible b (1–4) glycosidic bond (Scheme 3) and is a precursor for derivative sugars, sugar acids, and sugar alcohols used widely in the food and pharmaceutical industries [53]. One predominant route for lactose conversion involves isomerization of the glucose subunit to fructose to form lactulose [53–55], a disaccharide comprised of galactose and fructose linked via a b (1–4) glycosidic bond (Scheme 3). Lactose isomerization to lactulose is practiced industrially in homogeneous alkaline media [54], which mediates glucose–fructose isomerization via base-catalyzed enolate formation, but lactulose yields (ca. 20% in NaOH, 353–373 K) and selectivities are limited by lactose degradation side reactions [56–58] that become more prevalent with increasing temperature and pH [54]. Supra-equilibrium lactulose yields (ca. 80%) have been achieved by shifting chemical equilibrium upon addition of stoichiometric excesses of borate and aluminate salts that form complexes selectively with lactulose products [58–60]. Ion-exchange resins (alkaline sepiolite [61]) and enzymes (b-galactosidases [54]), but not solid Lewis acids, to our knowledge, have also been reported to catalyze lactose isomerization. We hypothesized that beta zeolites with framework Sn and Ti centers should catalyze lactose–lactulose isomerization, in light of the ability of their void spaces to adsorb disaccharides with b (1–4) glycosidic bonds [51,52] and of Lewis acid centers confined within these voids to mediate glucose–fructose isomerization [16]. Reactions of a 1% (w/w) aqueous lactose solution with Sn-BetaF (1:20 lactose/Sn molar ratio, 373 K) in liquid water indeed led to the selective (76–93%) formation of lactulose (Table 4). No other products were detected in the aqueous phase and carbon balances closed to >96% (Table 4), suggesting that only minor amounts of disaccharides or byproducts were retained on catalytic solids. Lactose conversions remained below detection limits in the absence of

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Scheme 3. The isomerization of lactose (b-D-galactopyranosyl (1–4)-D-glucopyranose) to lactulose (b-D-galactopyranosyl (1–4)-D-fructofuranose) involves isomerization of the glucose subunit of lactose to fructose.

Table 4 Lactose conversion (X), selectivity to lactulose (Sisom), carbon balances, net isomerization rates (risom,net), approach-to-equilibrium (g), and the number of turnovers as a function of reaction time during reaction of a 1% (w/w) aqueous lactose solution with Sn-Beta-F at 373 K (lactose/Sn = 20). Time (min)

X

Sisom

Carbon Balance

risom,net (373 K) (/103(mol lactulose) ((mol Sn)  s)1)

g

Number of turnovers ((mol lactulose) (mol Sn)1)

0 15 30 45 90

0 0.085 0.14 0.14 0.18

0 0.82 0.81 0.93 0.76

1.0 0.98 0.97 0.99 0.96

2.4 1.1 0.53 0.25 0.026

0 0.47 0.79 0.89 1.0

0 1.4 2.3 2.6 2.8

Table 5 Initial lactose isomerization turnover rates (per total metal; 373 K) on Sn- and Ti-containing solids and the initial isomerization turnover rate ratios on each catalyst relative to SnBeta-F.

a

Catalyst

Initial isomerization turnover rate (373 K) (/103 (mol lactulose) (mol metal  s)1)

risom,init (X)/risom,init (Sn-Beta-F)

Sn-Beta-F Ti-Beta-F SnO2 Sn-Beta-F (as-made) Ti-Beta-OH

2.4 0.038 0.013 <0.0004a <0.0002a

1 0.016 0.0049 <0.0002 <0.0001

Lactose isomerization was not detected; rates represent detection limits.

catalyst and on as-made Sn-Beta-F prior to calcination (Table 5), which contains tetraethylammonium cations occluded within its void spaces, indicating that Sn centers located at external surfaces of Sn-Beta-F crystallites did not contribute to measured isomerization turnover rates. These data indicate that, in liquid water, lactose isomerization turnovers occur on Lewis acidic framework Sn sites located within the hydrophobic channels of Sn-Beta-F, as demonstrated previously for glucose isomerization to fructose [16]. Aqueous-phase lactose and lactulose concentrations, together with lactose-to-lactulose molar ratios, are shown as a function of reaction time in Fig. 6 for the reaction of a 1% (w/w) aqueous lactose solution with Sn-Beta-F (1:20 lactose/Sn molar ratio, 373 K). The reaction time dependences of lactose (cL(l)) and lactulose (cL0 (l)) concentrations were consistent with those expected of a reversible, first-order reaction in a batch reactor (detailed derivation in Section S.4, Supporting Information):

cLðlÞ ðtÞ ¼ cLðlÞ;eq  ðcLðlÞ;eq  cL0ðlÞ Þet=s3

ð10Þ

cL0ðlÞ ðtÞ ¼ cL0ðlÞ;eq ð1  et=s3 Þ

ð11Þ

where cL(l),eq and cL0 (l),eq are the concentrations of lactose and lactulose at equilibrium, cL0(l) is the initial lactose concentration, and s3 is a time constant that describes the dynamics of approach to this equilibrium (details in Section S.4, Supporting Information). Leastsquares regression of the experimental data to Eqs. (10) and (11), shown as dashed curves in Fig. 6, gave a value of 0.0024 ± 0.0004 mol lactulose (mol Sn  s)1 for the initial turnover rate and 0.19 ± 0.02 for the equilibrium constant. Although thermo-

chemical data for lactose and lactulose in liquid water at 373 K were unavailable, the value of 0.19 ± 0.02 for the equilibrium constant at 373 K determined from fitting Eqs. (10) and (11) to the data in Fig. 6 shows reasonable agreement with the value of 0.25 observed with NaOH (353–373 K) [56–58], in light of the supra-equilibrium conversions typically observed in basic media because of product degradation. This agreement suggests that lactulose-to-lactose molar ratios increased with conversion asymptotically to a value of 0.19 as lactose–lactulose equilibrium became established (Fig. 6). Net isomerization rates are given by the time derivative of Eq. (11); these values are listed in Table 4 for each data point on Sn-Beta-F, together with approach-to-equilibrium values. After 15 min, Sn-Beta-F (1:20 lactose/Sn molar ratio, 373 K) converted a 1% (w/w) aqueous lactose solution nearly halfway to equilibrium and by 90 min had equilibrated this mixture and had turned over (per total Sn) nearly three times (Table 4). Initial lactose isomerization turnover rates (per total metal atom) with a 1% (w/w) aqueous lactose solution on different catalytic solids are shown in Table 5, together with initial rate ratios relative to that on Sn-Beta-F. Initial turnover rates on Sn-Beta-F were higher by 60 than on Ti-Beta-F Table 5 [5], while rates were below detection limits on Ti-Beta-OH. Bulk SnO2 also isomerized lactose to lactulose, but at rates (per total Sn) that were two orders-of-magnitude lower than Sn-Beta-F (200, Table 5), likely via base-mediated proton abstraction and reversible enolization [9]. These findings indicate that lactose isomerization occurs at >102–104 higher rates on Lewis acid sites in hydrophobic than in hydrophilic void spaces, and provide yet another example for the higher aqueous-phase aldose–ketose isomerization reactivity of

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Fig. 6. Lactose () and lactulose (N) concentrations and lactose/lactulose molar ratios (d) as a function of time during reaction of a 1% (w/w) aqueous lactose solution with Sn-Beta-F at 373 K (lactose:Sn = 20). Dashed curves represent best fits to Eqs. (10) and (11) for lactose and lactulose concentrations, respectively.

Lewis acid sites confined within hydrophobic than in hydrophilic environments.

vent on Ti-Beta-OH and TiO2–SiO2 than on Ti-Beta-F, but possible methanol dissociation to form bound methoxy groups at Ti sites precludes further mechanistic interpretation of these data. This report provides the first rigorous quantification of sugar isomerization reactivity on Lewis acidic molecular sieves in the form of measured first-order isomerization rate constants, the mechanistic interpretation of which provides further clarity into Lewis acid site inhibition via competitive adsorption of solvent molecules with Lewis basic character. The higher rates for sugar isomerization in liquid water on low-defect titanosilicates than on their highly defective, hydrophilic counterparts are reminiscent of the relative hydrocarbon oxidation rates on these solids in aqueous H2O2. Hydrophobic Sn-Beta-F and Ti-Beta-F zeolites also catalyze disaccharide (lactose–lactulose) isomerization at >102–104 higher turnover rates (per total M) than hydrophilic Ti-Beta-OH. Hydrophobic pockets that confine Lewis acid sites are a structural motif leading to turnover rate enhancements among heterogeneous (Sn4+- and Ti4+-silica-based molecular sieves), homogeneous (Ni2+ ethylenediamine complexes) and enzymatic (Mg2+- and Mn2+-based D-xylose isomerase) catalysts that mediate sugar isomerization and epimerization in liquid media. We anticipate that establishing further connections between the structural and physicochemical properties of molecular sieves, and how these properties influence the kinetic and thermodynamic parameters that are relevant catalytically, will provide additional guidance for the synthesis and design of heterogeneous Lewis acids for applications in sugar and biomass conversion in condensed media. Acknowledgments

4. Conclusions Initial turnover rates (per total Ti; 373 K) for glucose–fructose isomerization in liquid water are higher on hydrophobic, low-defect Ti-Beta-F zeolites than on hydrophilic, highly defective TiBeta-OH zeolites (by factors of 8–9) and amorphous TiO2–SiO2 (by factors of 20–30). Initial isomerization turnover rates depended linearly on initial liquid-phase glucose concentration (0.5–1.5% (w/w) in water), but were not limited by diffusion of glucose to intrazeolitic Ti sites. These transport artifacts were excluded by observed glucose-H2/glucose-D2 kinetic isotope effects of 2 (373 K) for glucose–fructose isomerization in liquid water and methanol on Ti-Beta-F and on Ti-Beta-OH, by the weak dependence of isomerization rate constants with varying framework Ti density in Ti-Beta-F, and by the similar rate constants on hydrophilic, crystalline Ti-Beta-OH and amorphous TiO2–SiO2. Glucose isomerization turnovers were not limited by intrazeolitic reactant diffusion, irrespective of whether or not intrazeolitic void spaces were filled with solvent molecules, indicating that the higher initial turnover rates on hydrophobic than on hydrophilic titanosilicates reflect differences of kinetic origin. Glucose isomerization turnovers occur on Lewis acid sites covered with two water molecules during steady-state catalysis in liquid water, consistent with independent spectroscopic and calorimetric studies of water adsorption on hydrophobic molecular sieves and with the first-order dependence of turnover rates on liquid-phase glucose concentration. Measured first-order glucose– fructose isomerization rate constants depend on free energy differences between kinetically relevant isomerization transition states and two water molecules bound at active Lewis sites. The orderof-magnitude lower rate constants on defective Ti-Beta-OH or TiO2–SiO2 than on low-defect Ti-Beta-F in liquid water, in part, reflect the stronger binding of water solvent molecules at Ti centers in defective environments because of hydrogen bonding interactions with proximal silanol groups. The stronger binding of polar molecules at Ti sites in defective surfaces would also be consistent with the order-of-magnitude lower rate constants in methanol sol-

This work was financially supported as part of the Catalysis Center for Energy Innovation, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001004. We thank Ricardo Bermejo-Deval for synthesis of the Ti-Beta-OH sample, Carly Bond for experimental assistance, and Joshua Pacheco, Yashodhan Bhawe and Marat Orazov for helpful technical discussions. Appendix A. Derivation of H/D kinetic isotope effect (KIE) for glucose–fructose isomerization The H/D kinetic isotope effect (KIE) for glucose–fructose isomerization expected for glucose reactants deuterated at the C2 position (glucose-D2) is given by the following expression [45], derived using transition state theory:

ZPE ZPE  0:13hcm  kisom;F;H2 H H D kT ¼e ¼ e kT kisom;F;D2

ðA:1Þ

In Eq. (A.1), kisom,F,H2 and kisom,F,D2 are the isomerization rate constants for unlabeled glucose and glucose-D2, respectively, ZPEH and ZPED are the zero point energies for C–H and C–D bonds, respectively, h is Planck’s constant (6.63  1034 m2 kg s1), c is the speed of light in vacuum (2.998  108 m s1), k is Boltzmann’s constant (1.38  1023 m2 kg s2 K1), T is the temperature (373 K), and mH is the C–H bond scissoring vibrational frequency (1500 cm1). Substitution of these values into Eq. (A.1) shows that observed H/ D KIE values with glucose and glucose-D2 reactants would be 2.1 (at 373 K) if glucose–fructose isomerization rates were limited by kinetically relevant C2–C1 intramolecular hydride shift steps. Reaction rates that depend on coupled intrazeolitic transport and reaction phenomena, in the limit of severe intrazeolitic diffusion limitations and of much smaller barriers for diffusion than reaction, would cause observed rate constants to be proportional to the square root of isomerization rate constants [62]. Observed

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H/D KIE values, in turn, would be proportional to the ratio of kisom,F values for glucose and glucose-D2 reactants:

   0:5 kisom;F;H2 kisom;F;H2 ¼ kisom;F;D2 obs kisom;F;D2

ðA:2Þ

Thus, observed H/D KIE values with glucose and glucose-D2 reactants would be 1.5 (at 373 K) if isomerization turnovers were limited by intraparticle reactant mass transfer.

Here, we provide an abridged derivation the rate expression for glucose–fructose isomerization (Eq. (5)) from the sequence of elementary steps shown in the reaction mechanism for parallel glucose–fructose and glucose–sorbose isomerization (Scheme 1); a complete derivation the rate expression for glucose–fructose isomerization and for glucose–sorbose isomerization is given in Section S.7 of the Supporting Information. The kinetically relevant step in the glucose–fructose isomerization sequence (Steps 1a, 2a, 3a of Scheme 1) is Lewis acid-mediated intramolecular C2–C1 hydride transfer (Step 2a), based on the observed H/D KIE (2 at 373–383 K) on Ti-Beta-F [45] and Ti-Beta-OH (Table 3) when using glucose-D2 reactants (Section 3.3). The kinetic relevance of Steps 2a and 2b in Scheme 1 requires that all other steps be quasiequilibrated. Thus, we have chosen to depict Steps 1, 3, 4, and 5 as they appear in Scheme 1 for reasons of clarity, even though they may represent a combination of more than one elementary step; for example, the adsorption of glucose from extrazeolite phases to within zeolite channels, the intrazeolitic diffusion of glucose reactants to Lewis acid active sites, and the ring-opening of glucose at Lewis acid sites to form bound open-chain sugars [45], are represented in a single quasi-equilibrated step (Steps 1a or 1b, Scheme 1). These mechanistic assumptions can be used to derive the following expressions for glucose–fructose isomerization turnover rates (per total metal site):

r isom;F ¼

D

! cGðlÞ ð1  g2a Þ

ðA:3Þ

in which cG(l) is the activity coefficient of glucose in the liquid phase, cG(l) is the liquid-phase glucose concentration, K1a is the equilibrium constant for glucose adsorption to form the adsorbed precursor for isomerization to fructose (Scheme 1), k2a is the forward rate constant for isomerization to fructose (Scheme 1), and g2a is the approach-to-equilibrium term for glucose–fructose isomerization (Step 2a, Scheme 1). The denominator term (D) in Eq. (A.3) is given by:

D ¼ 1 þ hðG ÞO1O2 þ hðG ÞO1O5 þ hF  þ hS þ hB þ h2B

ðA:4Þ

in which the hi terms represent the fractional coverage of each bound intermediate i (in Scheme 1) on Lewis sites, and the unity term represents that of an unoccupied Lewis acid site. Solvent molecules adsorb competitively with sugars onto Lewis acid sites and the assumption that two bound water molecules are the most abundant surface intermediates (MASI) during catalysis in liquid water allows Eq. (A.4) to be rewritten as:

D  h2B

risom;F ¼

cGðlÞ c2BðlÞ c2BðlÞ

!

c2B K 1a K4K5

 xisom;F k2a cGðlÞ ð1  g2a Þ

ðA:8Þ

where ci terms are activity coefficients for species i and cB(l) is the solvent concentration in the liquid phase.

Appendix B. Abridged derivation of glucose isomerization turnover rate expression

k2a K 1a cGðlÞ

where K4 and K5 are the equilibrium constants for solvent adsorption at Lewis sites (Scheme 1). Combining Eqs. (A.4)–(A.7), and after accounting for the fact that only a fraction of total metal atoms may be able to catalyze isomerization reactions (xisom), allows the isomerization rate equation (per total Lewis acid site) to be written as:

ðA:5Þ

The quasi-equilibrium assumptions on Steps 4 and 5 (Scheme 1) give the following relations:

K4 ¼

aB aB a

ðA:6Þ

K5 ¼

a2B aB aB

ðA:7Þ

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