Catalytically directed specific carbon-carbon bond formation is at the forefront of modern organic synthesis1,2 and broadly involves acid-base and metalation catalysis3,4,5,6,7,8,9. Alkylation processes have been broadly employed in chemical and fuel productions as the prevailing C–C bond-forming technologies10, using Lewis or Brønsted acidic catalysts including mineral acids and acidic oxides such as aluminum oxide and zeolites11,12,13,14,15,16,17.

Acid-catalyzed alkylation of aromatic compounds using unsaturated aliphatic hydrocarbons commonly proceeds via electrophilic substitution on aryl carbons by secondary or tertiary carbocations18. The carbocation mechanism yields very little primary carbon alkylated products because a primary carbocation rapidly rearranges to more stable secondary carbocations. Therefore, alkylation with long chain α-alkenes or primary alcohols typically produces a mixture of multiple branched alkyl products on an aryl ring through the formation Caryl–Calkyl bond in which the Calkyl may be a secondary or tertiary carbon of the alkyl chain but the primary carbons are not favored. Therefore, selectively making superlinear α-alkylated aromatics without using pre-functionalized substrates has been a persistent challenge in chemistry14. In addition, the aryl ring of alkylated products is often more kinetically reactive than the starting aromatic substrates, due to the electron-donating effect of alkyl groups. Therefore, monoalkylation is often not possible in high yield19.

Phenolics are commodity chemicals. Recent works show that phenol can be produced from guaiacol, a pyrolysis product of lignocellulosic biomass20,21,22,23. About 540,000 tons of higher alkylphenols are synthesized worldwide per year24. Linear alkyl phenolics are important chemicals as intermediates in the agrochemical and surfactant industries24. Moreover, higher alkylphenols are monomers for various phenolic resins production25. Typical acid-catalyzed electrophilic substitution on phenol yields a mixture of ortho- and para-substituted phenol derivatives, with branched alkyls dictated by the characteristic distribution of more stable carbocation intermediates26. Fatty alcohols derived from animal fats and plant oils are abundantly available primary alcohols of linear alkyl chains27,28,29. Direct α-C alkylation producing pure superlinear alkyl phenol with high selectivity using metal-free inexpensive heterogeneous catalysts would be a highly desirable strategy to break the limitation of existing processes, but remains technically elusive thus far.

The current route for the preparation of superlinear alkyl aromatics involves a Friedel–Crafts acylation followed by a Clemmensen reduction, which is not yet viable for large-scale processes15,18. To achieve site-selective ortho-alkylation of phenols, a strategy of modifying the hydroxyl group with a directing group is widely utilized26,30. However, the directing group must be pre-synthesized and then removed afterward31,32,33,34. Alkylation of phenol by a noble metal catalyst, e.g. Pd/C, in the presence of BuOLi base in a solvent was reported to produce ortho-selective α-carbon substitution35. And noble metal complex was also reported to be an alternative catalyst36. Base metal oxides can catalyze some specific alkylation reactions, for example, methylation of phenol to o-cresol with methanol in industry37,38,39,40. Further studies found that on the base sites, methanol was transformed to formaldehyde and reacted with adsorbed phenolate species to generate salicylic alcohol via hydroxymethylation at the primary stage41. Selective alkylation of phenol with 1-propanol was reported to produce 2-n-propylphenol over a CeO2-MgO at 475 °C, and the mechanism was speculated via a radical process42. Like other refractory metal oxides such as Al2O3 and SiO2, TiO2 can be prepared by specific method to bear strong Lewis or Brønsted-acid sites43,44 to catalyze the Friedel-Crafts alkylation of phenolics and arenes43,44,45,46.

In this work, we report that catalyzed by anatase TiO2, alkylation reactions of phenols with alcohols exhibit high selectivity to α-C alkylation products (α-C means the α-carbon in alcohol). According to the experimental results and computational studies, alcohol is activated at oxygen vacancies of the TiO2-A surface to produce an alkyl group, which interacts with the Ti atom in the form of Ti=C– bond. The subsequent α-C alkylation to aromatic C–H bond is simulated by DFT calculations and verified by deuterium exchanged substrate experiment.


Catalytic performances

Figure 1 shows the overall conversion rate of phenol and the yield of each product at 300 °C using H-ZSM-5, γ-Al2O3, rutile titania (TiO2-R), P25 TiO2 and anatase titania (TiO2-A) to catalyze the model reaction, alkylation of phenol with 1-propanol. The catalytic performances of the two typical solid acid catalysts, H-ZSM-5 and γ-Al2O3, are consistent with the typical electrophilic mechanism as reported47,48. Apart from low 2-n-propylphenol yield, 2-isopropylphenol was formed as the dominant product. Propyl phenyl ether was generated from the intermolecular dehydration reaction of phenol with 1-propanol. Several isopropyl polyalkylation products are identified by GC-MS and calculated by NMR spectra with the internal standard method. Polyalkylation is common in acid-catalyzed alkylation because of the electron-donating effect of alkyl groups. On the other hand, 1-propanol was mostly consumed on the two solid acid catalysts (67.2% on H-ZSM-5 and 77.6% on γ-Al2O3), producing propylene and propyl ether by dehydration process (Supplementary Table 1, entries 1 and 2). Among several TiO2 catalysts, rutile TiO2 (TiO2-R) was not active to catalyze the reaction and P25 TiO2, which is a mix of TiO2-R and TiO2-A, showed a low conversion rate. However, TiO2-A is clearly distinguished over the known acid-type catalysts. The phenol conversion rate reached 86.1%, with 74.9% 2-n-propylphenol yield and only 2.6% 2-isopropylphenol, corresponding to an 89.2% selectivity of n-propyl products on TiO2-A. Meanwhile, the consumption of 1-propanol (27.1%) and yield of by-product propylene (3.6%) on TiO2-A was significantly less than that on H-ZSM-5 and γ-Al2O3, indicating the efficient utilization of alcohol as alkylation reactant (Supplementary Table 1, entry 3).

Fig. 1: Product yields in the alkylation of phenol with 1-propanol over different oxide catalysts.
figure 1

Reaction conditions: catalyst 0.2 g, phenol 2.5 mmol, 1-propanol 10 mmol, toluene 25 mL, 300 °C, 16 h, N2 atmosphere.

We further verified this distinctively appealing catalytic nature of TiO2-A with several alcohols and substituted phenols (Fig. 2). When phenol was used to react with 1-dodecanol, a lower conversion (67.0%) was obtained compared to 1-propanol under the same condition, but a high selectivity (78.2%) to superlinear alkylation product still dominated. The conversion of 1-dodecanol was 20.8%, with a small amount of 1-dodecene (2.7%) as by-product (Supplementary Table 1, entry 4). In addition, secondary alcohols, such as 2-propanol and 2-dodecanol, were also evaluated for alkylation of phenol (Fig. 2, entries 3 and 4). The TiO2-A catalyst exhibited similar reactivity to the corresponding primary alcohols, and more importantly, maintained the selectivity of α-C alkylation. The reactions of 3-methylphenol and 3-chlorophenol as substituted phenols with 1-propanol were also investigated (Fig. 2, entries 5 and 6). The two reactions both generated ortho-substituted n-propyl products with more than 80% selectivity. It is worth noting that the conversions of these two phenols showed no obvious difference (94.3% and 90.7%, respectively), although the methyl group and chlorine group have opposite electronic effects as substituent groups. These results clearly indicate that the main alkylation mechanism on TiO2-A surface is distinguishably different from the Friedel-Crafts alkylation. Phenols with additional substituents were further tested by reacting with 1-propanol (Supplementary Fig. 2, entries 1–6), and high conversions of phenols (more than 84%) and selectivity to ortho-substituted n-propyl products (more than 80%) were obtained. In addition, naphthols as alternative substrates also showed similar alkylation selectivity in high conversions (Supplementary Fig. 2, entries 7–10). These results demonstrate that the TiO2-A catalyzed selective α-C alkylation reaction applies to a broad scope of substrates.

Fig. 2: The α-C alkylation of phenols with alcohols catalyzed by TiO2-A.
figure 2

Reaction conditions: TiO2-A 0.2 g, phenol 2.5 mmol, alcohol 10 mmol, toluene 25 mL, 300 °C, 16 h, N2 atmosphere.

The universality of the reaction was also studied by the model reaction between phenol with 1-propanol. The conversion of phenol slightly varied in different solvent systems, while 2-n-propylphenol was invariably the main product (Supplementary Fig. 1a). When the reaction time was extended from 4 h to 16 h at 300 °C, the ortho-substituted n-propyl product selectivity gradually increased with time (Supplementary Fig. 1b), indicating that the formation of 2-n-propylphenol on TiO2-A prevailed as the dominantly main catalytic mechanism and the sites that catalyze side reactions and 1-propanol consumption were suppressed. With the feeding ratio between phenol and 1-propanol varying from 1:1 to 1:4, product selectivity had no obvious changes while conversions of phenol gradually increased (Supplementary Fig. 1c) as a relatively high concentration of 1-propanol favorably drives the reaction equilibrium to the product.

Characterization of TiO2-A

To study the TiO2-A catalyst for its unique capability of forming α-C alkylation, we performed characterizations of TiO2-A before and after the reaction. Figure 3a–c shows the TEM images of TiO2-A and used TiO2-A. The TiO2-A is composed of irregular nanoparticles with a diameter of about 10 nm. The observed interplanar spacing is 0.35 nm, corresponding to the (101) crystal plane of anatase TiO2. The microstructure has no obvious change after the reaction. Figure 3d shows the XRD spectra of TiO2-A before and after the reaction. These two spectra are both consistent with the anatase TiO2 pattern (PDF #21-1272). X-ray photoelectron spectra of the catalyst (Supplementary Fig. 4) show that the valence state of Ti is +4, and the valence state of O can be divided into two parts, lattice oxygen and hydroxyl oxygen on the surface. In addition, the specific surface area of catalyst is 146 m2/g and 141 m2/g after reaction. The TiO2-A catalyst composed of nanoparticles maintained its original structure after the reaction. Its structure stability was maintained with multiple reuse tests. After three-times reuse of the TiO2-A, the phenol conversion and product yields remained no obvious changes (Supplementary Fig. 3a). It is interesting to note that the used TiO2-A had a better mass balance than the fresh TiO2-A. This may be due to the adsorption of phenol on the fresh TiO2-A surface at the termination of the first reaction test and the surface has already reached saturated phenol adsorption in subsequent reuses of the TiO2-A catalyst.

Fig. 3: Characterization of catalyst.
figure 3

a and b TEM images of TiO2-A; c TEM image of used TiO2-A; d X-ray diffractograms of TiO2-A and used TiO2-A.

Mechanism study

To study the reaction pathways, control experiments were carried out as illustrated in Fig. 4a. Since a trace amount of propylene and n-propyl ether was detected in the reaction, it is necessary to confirm whether they are intermediates or just by-products. No product was detected when 1-dodecene was used as the alkylation agent. With n-propyl ether, the yield and selectivity were not consistent with the results of using 1-propanol as reactant. In addition, we did not observe the high selectivity of n-propylphenol from Claisen rearrangement reaction of phenyl propyl ether on TiO2-A, either. Therefore, we can rule out the possibility of alcohol firstly transforming into alkene or ether, or Claisen rearrangement reaction as a dominant process in the alkylation reaction.

Fig. 4: Mechanism study.
figure 4

a Control experiments; b NH3-TPD profiles of TiO2-A and Alc-TiO2-A; c Product yields in the alkylation of phenol with 1-propanol over TiO2-A and Alc-TiO2-A; d Product yields in the alkylation of phenol with 1-propanol over TiO2-A and Ni/TiO2-A; e Alkylation of phenol-d6 with 1-propanol. Reaction conditions in c and d: catalyst 0.2 g, phenol 5 mmol, 1-propanol 10 mmol, toluene 25 mL, 300 °C, 4 h, N2 atmosphere. Ni loading of Ni/TiO2-A is 0.5 wt%.

The TiO2-A was pretreated with 1-propanol to assess the influence of weak acidity by forming Alc-TiO2-A (see the SI for details). Temperature-programmed desorption of NH3 (NH3-TPD) showed a significantly decreased amount of NH3 adsorbed on Alc-TiO2-A than on TiO2-A, indicating a weaker acidity after the pretreatment (Fig. 4b). From the catalytic alkylation results, we found no significant change in the yield of 2-n-propylphenol, but the yield of isomerized product decreased (Fig. 4c). The result suggests that the production of isomerized product is due to the inherent acidity of TiO2-A, while the α-C alkylation products may be attributed to other catalytic active sites. The Alc-TiO2-A was further employed for the alkylation of phenol with 1-dodecanol, resulting in increased selectivity (87.1%) to superlinear α-C alkylation product at high phenol conversion (84.5%) as compared to TiO2-A. The performance maintained after three-times reuse without additional treatment (Supplementary Fig. 3b), making it a superior catalyst for industrial process.

The role of oxygen vacancy on the TiO2-A surface was studied to obtain preliminary insights on the catalytic sites for selective α-C alkylation. Our recent work showed that the surface of TiO2-A can be partially reduced to generate oxygen vacancies by pretreating a TiO2-A containing a very small amount of a transition metal (e.g. Au, Ag or Ni) under hydrogen at 400 °C20,21,22,23. Using Ni/TiO2-A with 0.5 wt% Ni loading as the catalyst, phenol conversion was increased along with an increase of only α-C alkylation selectivity compared to fresh TiO2-A (Fig. 4d). The result indicates that the oxygen vacancies on TiO2-A surface were likely responsible for the generation of α-C alkylation products.

To probe the catalytic mechanism, experiment with deuterium substituted phenol as the substrate was carried out (Fig. 4e). After alkylation of phenol-d6 with 1-propanol under standard conditions for 16 h, 2-n-propylphenol was separated by column chromatography. The 2H NMR spectrum showed deuterium signal at the α-position in the n-propyl group (Supplementary Fig. 5a). Combined with 1H NMR spectroscopic analysis of the product (Supplementary Fig. 5b), the percentage of deuterium on the α-position in n-propyl was determined in 45%. The result suggests that 90% of the isolated 2-n-propylphenol products had a deuterium atom and a hydrogen atom at the α-position of the n-propyl group. No deuterium signal was detected at the β-position and γ-position, which ruled out the possibility of H-D exchange at α-position. Therefore, we hypothesize that the deuterium atom at the ortho position of benzene ring may migrate from the aromatic C to the α-C of n-propyl group in the mechanism of alkylation during 1-propanol alkylation of phenol. The result clearly confirms that the mechanism of alkylation on TiO2-A is fundamentally different from that of the known dominant electrophilic substitution reaction.

Computational study

DFT calculations were carried out to help elucidate the α-C alkylation mechanism using 1-propanol as the representative. We firstly studied the distribution and diffusion of the oxygen vacancies that are indicated by experimental evidence to be crucial for the reactivity. It is known that on bare surface of TiO2-A (101), the oxygen vacancy is more stable at subsurface than at surface sites49,50,51, and it has been reproduced by our calculation. In addition, we find that with molecular or dissociated 1-propanol (or water) adsorbed, the oxygen vacancy is more stable at surface than at subsurface sites (by 0.26 eV for the molecular state and 0.42 eV for the C–H dissociated state, Supplementary Fig. 7). The barrier for vacancy diffusion is also quite small (0.29 eV in the case of 1-propanol adsorption), indicating that the substrate adsorption induces the diffusion of the vacancy from the subsurface to surface. Similar adsorption induced diffusion has also been observed for carboxylic acid group52. We propose this is because the vacancy on surface produces four coordinated Ti atom which is more unsaturated and can be favorably coordinated by substrates.

Based on the experimental and calculated results, we propose a reaction mechanism for the α-C alkylation featured by the titanium alkylidene intermediate (Ti=C bond). As shown in the blue curve in Fig. 5, firstly the Cα−H activation reaches chdiss with the barrier of 1.88 eV. Then the isomerization of chdiss to a more stable isomer chdiss_a in which the hydroxyl group coordinates to the five coordinated Ti in [10\(\bar{1}\)] direction resulted from the surface vacancy. The Ti=C bond (ti=c_a) is readily formed through the reduction of the C−O bond by the electron polarons generated by the oxygen vacancy. The rate-determining step for the Ti=C bond formation is the C–H activation step (1.88 eV), which is slightly more difficult than the C–O breaking step (1.65 eV). Alternatively, chdiss can isomerize to chdiss_b in which the hydroxyl group coordinates to the surface five coordinated Ti in [010] direction, followed by a similar C–O addition to reach ti=c_b (red curve in Fig. 5). Our calculation shows this pathway has a much higher barrier than the ti=c_a pathway, but the barrier can be reduced by introducing additional surface vacancies. Our mechanism also agrees with the n-propylphenol selectivity observed experimentally, since the yield of 2-isopropylphenol undergoes the Ti=Cβ intermediated ti=c_c which requires two strongly endothermic C–H activation, and is much more unstable than the Ti=Cα intermediated ti=c_a which only needs one C–H activation step (purple curve in Fig. 5).

Fig. 5: The reaction path to generate Ti=C bond.
figure 5

Blue curve: formation of Ti=Cα assisted by Ti5c generated by the surface vacancy; Red curve: formation of Ti=Cα assisted by surface Ti5c; Purple curve: formation of Ti=Cβ. Black, blue, red and white spheres stand for C, H, O and Ti atoms, respectively.

Figure 6 (blue curve) shows the pathway for nucleophilic α-C alkylation of phenol at the ortho position by Ti=C bond. The dissociated state of phenol adsorbed adjacently to the titanium alkylidene. It undergoes the C–C bond formation to reach ccform, followed by hydrogen of the ortho-C migrates to the bridging oxygen (hmig), then migrates back to the propyl group to form the dissociated state of 2-n-propylphenol (hback). Finally, the adsorbed state of 2-n-propylphenol (product) is generated by proton transfer. All steps are fairly easy, with barriers of only 0.3 eV to 0.54 eV. We also studied the alkylation at the meta position (purple curve in Fig. 6). In line with the experimental results, we found its C–C bond formation is less facile than that at ortho position. The transition state (cc1-ts) is less stable by 0.32 eV and the key intermediate (cc1form) is less stable by 0.48 eV. Structural analysis shows that when the alkylidene and phenol co-adsorbed on the surface, the meta-C is much higher than the C(=Ti), while the ortho-C is only slightly higher. Therefore, the formation of the C–C bond at ortho-C needs less distortion and is easier. Finally, our mechanism matches the isotope experiments where the percentage of deuterium on the α-position in n-propyl was 45% when using phenol-d6 as a probe for the alkylation, since one hydrogen of the α-position in n-propyl indeed comes from the hydrogen of phenol at ortho position. Certainly, there are more hydrogens on neighbor bridging oxygen (come from propanol), however, the hydrogen transfer between surface bridging oxygens (red curve in Fig. 6, barrier 0.73 eV from hmig) is more difficult than the proton transfer to form the product (0.43 eV from hmig), thus has little influence on the deuterium experiments. The desorption of the 2-n-propylphenol, together with H2O forming (by adsorbed H and OH) and desorption, results in the bare surface with oxygen vacancy on the surface. The original catalyst TiO2-A (101) surface is then regenerated by the diffusion of the oxygen vacancy from the surface to the subsurface.

Fig. 6: The reaction path for the nucleophilic α-C alkylation of phenol by Ti=C bond.
figure 6

Blue curve: alkylation at ortho position; Purple curve: alkylation at meta position; Red curve: hydrogen diffusion along surface bridging oxygen. Black, blue, red and white spheres stand for C, H, O and Ti atoms, respectively.

In short, we propose that the reaction proceeds via the key titanium alkylidene intermediate formed by C–H activation and C–O breaking of propanol, followed by the α-C alkylation of phenol and the proton transfer from phenyl to propyl through surface bridging oxygen (Fig. 7, and Supplementary Fig. 8 for details). The calculated rate-determining barrier, 1.88 eV, matches the experimental value 1.92 eV very well (Supplementary Fig. 6). Our mechanism also agrees with other experimental observations such as high selectivity to n-propylphenol, high selectivity to ortho alkylation, and the results of deuterium labeling experiment. Furthermore, our mechanism highlights the impact of oxygen vacancy since it offers low-coordinated Ti for better coordination of the substrate, and more importantly, yields electron polarons which reduce the C–O bond. It also shows that the titanium alkylidene, previously reported in a homogenous system and stabilized by sterically bulky ligands53,54, can be generated on alcohol-adsorbed TiO2-A surface in situ, and show remarkable reactivities.

Fig. 7: Schematic overview of the mechanism for nucleophilic α-C alkylation on TiO2-A.
figure 7

The alcohol adsorption induces the diffusion of oxygen vacancy from subsurface to surface on TiO2-A. It undergoes C–H activation and C–O dissociation to form Ti=Cα intermediate. Then nucleophilic α-C alkylation reacts at the ortho position of phenol, followed by the proton transfer through surface bridging oxygen. Finally, the oxygen vacancy is regenerated by product desorption.

In conclusion, we find that pure TiO2-A alone catalyzes the nucleophilic alkylation of phenols with alcohols to produce α-C alkylation products. The catalyst exhibits excellent selectivity and stability, making it sustainable and scalable for the direct synthesis of linear alkylphenols. The formation of Ti=C– bond with the α-carbon of the alkyl group at oxygen vacancies is reported for the first time on a metal-free TiO2-A surface. Insights on the active site and α-C alkylation mechanism are demonstrated for the selective C–C bond formation.


Chemicals and catalysts

Rutile TiO2 (20 nm, 99.9%, labeled TiO2-R), P25 TiO2 (20 nm, 99.9%), γ-Al2O3 (20 nm, 99.9%), and all organic chemicals were purchased from Aladdin Industrial Co. Ltd without further purifications. Commercial H-ZSM-5 with a nSiO2/nAl2O3 ratio of 25 was purchased from Nankai University Catalyst Co. Ltd.

Anatase TiO2 (labeled TiO2-A) was prepared by the sol-gel method. 20 mL tetra butyl titanate was dissolved in 100 mL of ethanol to form solution A. 20 mL water, 20 mL ethanol, and 12 mL acetic acid were mixed to form solution B. Under vigorous magnetic stirring, solution B was added to solution A dropwise and kept stirring for 12 hours. The gel was placed for another 12 hours and washed with ultrapure water and separated by centrifugation. The sample was dried overnight at 110 °C after washing it five times. Finally, it was heated to 400 °C at a rate of 2 °C/min in a muffle furnace and kept for 4 h to obtain TiO2-A.

Ni-loaded anatase TiO2 (labeled Ni/TiO2-A) was prepared by an incipient wetness impregnation method with an aqueous solution of Ni(NO3)2. The sample was dried overnight at 120 °C, and then heated to 400 °C at a rate of 10 °C/ min and kept at 400 °C for 4 h. The calcined sample was further kept at 400 °C for 1 h in 10 vol% H2/Ar and then cooled to room temperature under N2 atmosphere.


Transmission electron micrographs (TEM) were obtained on a JEM-2100 microscope operated at 200 kV. The samples were suspended in ethanol and a few drops of the suspension were dried to the TEM grid for TEM measurement. X-ray diffractograms of the samples were obtained on a PANalytical XPert Powder X-ray diffractometer with a Cu Kα radiation. The measurement was operated at 40 kV and scanning 2θ from 5° to 80° with a step of 0.013°. The signal was collected by a pixel 1D detector, and the data were analyzed by comparison with reference patterns in the database (PDF2-2004). X-ray photoelectron spectra (XPS) were recorded on a Thermo Scientific K-Alpha equipped with a monochromatic Al Kα X-ray radiation source ( = 1486.6 eV). The C 1s peak was used as the reference at 284.8 eV. The specific surface area was measured on a Micromeritics ASAP 2020 physical adsorption analyzer. The measurement was operated with the Brunauer-Emmett-Teller (BET) method using N2 adsorption at 77.3 K. The sample was degassed at 200 °C for 5 h before the measurement. NH3 temperature-programmed desorption (NH3-TPD) was performed on a Micromeritics AutoChem II 2920 chemisorption analyzer. The catalyst (150 mg) was refreshed for 60 min under an argon (Ar) atmosphere at 400 °C, cooled to 100 °C, and then saturated for 60 min with 10 vol% NH3/He. After that, the catalyst was flushed in a He flow for 60 min at 100 °C. Finally, the NH3-TPD was executed by heating the catalysts in He (10 °C/min) from 100 to 400 °C. The desorbed NH3 was detected with a thermal conductivity detector (TCD). NMR was performed on a Bruker AVANCE III 400 spectrometer instrument in deuterated chloroform (CDCl3). Chemical shifts are reported in parts per million (ppm) downfield from TMS.

Catalytic evaluation

Alkylation reactions were carried out in a 50 mL stainless steel batch reactor, from Beijing Century Senlong Experimental Apparatus Co. Ltd. The reactor was equipped with a mechanical stirrer, a thermocouple, a pressure gauge, and a programmable controller. In a typical run, 5 mmol of phenol, 10 mmol of 1-propanol, 25 mL of toluene, and 0.2 g of catalyst were loaded into the reactor. The reactor was purged with N2 for 10 min to remove the air and get to a pressure of 1 MPa. The reactor was then heated to 300 °C and kept for a specified reaction time while the content was stirred at a rate of 500 rpm. After the reaction, 40.2 mg of n-hexadecane as an internal standard and 25 mL of ethanol were added into the reactor. The reaction products were identified by GC-MS (Agilent 7890A-5975C, HP-5MS) and quantified by GC (Agilent 7890 A) with a flame ionization detector (FID) using an HP-5 column (30 m × 0.32 mm × 0.25 μm).

The conversion of phenol, selectivity of phenolic compounds and product yield are calculated by Eqs. 1, 2 and 3, respectively. In these equations, ninitial phenol and nfinal phenol are the molar amount of phenol before and after reaction. nproduct i is the molar amount of aromatic product i in the reaction mixture.

$${{{{{\rm{conversion}}}}}}\left(\%\right)=\frac{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{phenol}}}}}}}-{n}_{{{{{{\rm{final}}}}}}\,{{{{{\rm{phenol}}}}}}}}{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{phenol}}}}}}}}\times 100\%$$
$${{{{{\rm{selectivity}}}}}}\left(\%\right)=\frac{{n}_{{{{{{\rm{product}}}}}}\,i}}{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{phenol}}}}}}}-{n}_{{{{{{\rm{final}}}}}}\,{{{{{\rm{phenol}}}}}}}}\times 100\%$$
$${{{{{\rm{yield}}}}}}\,\left(\%\right)=\frac{{n}_{{{{{{\rm{product}}}}}}i}}{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{phenol}}}}}}}}\times 100\%$$

We also studied the molar mass balance of alcohols. The conversion of alcohol and product yield are calculated by Eq. 4 and Eq. 5. In these equations, ninitial alcohol and nfinal alcohol are the molar amount of alcohol before and after reaction. nproduct i is the molar amount of mono alkyl group in product i after the reaction.

$${{{{{\rm{conversion}}}}}}\left(\%\right)=\frac{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{alcohol}}}}}}}-{n}_{{{{{{\rm{final}}}}}}\,{{{{{\rm{alcohol}}}}}}}}{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{alcohol}}}}}}}}\times 100\%$$
$${{{{{\rm{yield}}}}}}\left(\%\right)=\frac{{n}_{{{{{{\rm{product}}}}}}\,i}}{{n}_{{{{{{\rm{initial}}}}}}\,{{{{{\rm{alcohol}}}}}}}}\times 100\%$$

Computational details

All calculations were performed with PBE functional55 using the Vienna ab initio simulation package code56 and plane augmented wave potential57. The wave function was expanded by the plane wave, with a kinetic cut-off of 400 eV and density cut-off of 650 eV. An efficient force reversed method58 was used to locate the transition state (TS). Our surface model was cut out of a six-layer slab anatase TiO2 crystal to expose the (101) surface. The periodically repeated slabs on the surface were decoupled by 15 Å vacuum gaps. A Monkhorst−Pack grid59 of single k-points was used for the 5 × 2 surface unit cell. The vdW-dispersion energy was corrected by DFT-D3 method of Grimme et al.60.