Synthesis of 1 , 3-Diols from Isobutene and HCHO via Prins Condensation-Hydrolysis Using CeO 2 Catalysts : Effects of Crystal Plane and Oxygen Vacancy

We herein report the synthesis of 3-methyl-1,3-butanediol from isobutene and HCHO in water via a Prins condensation-hydrolysis reaction over CeO2, which is a water-tolerant Lewis acid catalyst. The CeO2 exhibits significant catalytic activity for the reaction, giving 95% HCHO conversion and 84% 3-methyl-1,3-butanediol selectivity at 150 ◦C for 4 h. The crystal planes of CeO2 have a significant effect on the catalytic activity for the Prins reaction. The (110) plane shows the highest catalytic activity among the crystal planes investigated (the (100), (110), and (111) planes), due to its higher concentration of Lewis acid sites, which is in line with the concentration of oxygen vacancies. Detailed characterizations, including NH3-TPD, pyridine-adsorbed FT-IR spectroscopy, and Raman spectroscopy, revealed that the concentration of Lewis acid sites is proportional to the concentration of oxygen vacancies. This study indicates that the Lewis acidity induced by oxygen vacancy can be modulated by selective synthesis of CeO2 with different morphologies, and that the Lewis acidity and oxygen vacancy play an important role in Prins condensation and hydrolysis reaction.

Our previous work indicates that CeO 2 is a water-tolerant Lewis acid catalyst [23,24].It has been proved that the coordinatively unsaturated Ce cations on CeO 2 surface act as the Lewis acid sites [25][26][27][28].According to experimental data and theory calculations [24,[29][30][31][32], the concentration of surface coordinatively unsaturated Ce cations is associated with the population of oxygen vacancies over CeO 2 .Additionally, the formation energy of oxygen vacancies varies greatly among different CeO 2 surfaces.For the three low-index surfaces of CeO 2 ((111), (110), and (100)), the formation energies of oxygen vacancy follow the order of (110) < (100) < (111) [33], which implies that the order of oxygen vacancy formation is (110) > (100) > (111).Therefore, selective synthesis of CeO 2 with different crystal planes would modulate the concentration of oxygen vacancies.Furthermore, the Lewis acidity of CeO 2 catalyst may be manipulated by morphology control.
In this study, 3-methyl-1,3-butanediol will be synthesized from isobutene and formaldehyde using CeO 2 catalysts via Prins condensation-hydrolysis reaction in water.CeO 2 with different morphologies (rod, octahedron, and cube) will be tested for the Prins condensation-hydrolysis reaction, and the effect of crystal planes ((111), (110), and (100)) and oxygen vacancy will also be investigated.NH 3 -TPD, pyridine adsorption IR, and Raman spectroscopy were used to characterize the acid properties and defect structures of these CeO 2 catalysts.Based on these experiments, the structure-property-activity relationship will be established.

Results and Discussion
CeO 2 has been proved a highly active and water-tolerant catalyst for the synthesis of 1,3-butanediol from propylene and HCHO via Prins condensation-hydrolysis in water [24].This work encouraged us to apply the CeO 2 catalyst for isobutene-formaldehyde condensation in water to synthesize 3-methyl-1,3-butanediol, which is an important higher-molecule alkanediol for the polymer industries; its synthesis is obviously difficult, but scientifically interesting.Our synthetic route includes the Prins condensation of isobutene with HCHO to 4,4-dimethyl-1,3-dioxane (3), and then hydrolysis of 3 to 3-methyl-1,3-butanediol (4) (Scheme 1).
condensation and hydrolysis reaction).Alternatively, a single-stage 3-methyl-1,3-butanediol synthesis from isobutene and HCHO in water is one interesting route to be investigated, and a watertolerant acid catalyst is critical.
Our previous work indicates that CeO2 is a water-tolerant Lewis acid catalyst [23,24].It has been proved that the coordinatively unsaturated Ce cations on CeO2 surface act as the Lewis acid sites [25][26][27][28].According to experimental data and theory calculations [24,[29][30][31][32], the concentration of surface coordinatively unsaturated Ce cations is associated with the population of oxygen vacancies over CeO2.Additionally, the formation energy of oxygen vacancies varies greatly among different CeO2 surfaces.For the three low-index surfaces of CeO2 ((111), (110), and (100)), the formation energies of oxygen vacancy follow the order of (110) < (100) < (111) [33], which implies that the order of oxygen vacancy formation is (110) > (100) > (111).Therefore, selective synthesis of CeO2 with different crystal planes would modulate the concentration of oxygen vacancies.Furthermore, the Lewis acidity of CeO2 catalyst may be manipulated by morphology control.
In this study, 3-methyl-1,3-butanediol will be synthesized from isobutene and formaldehyde using CeO2 catalysts via Prins condensation-hydrolysis reaction in water.CeO2 with different morphologies (rod, octahedron, and cube) will be tested for the Prins condensation-hydrolysis reaction, and the effect of crystal planes ((111), (110), and (100)) and oxygen vacancy will also be investigated.NH3-TPD, pyridine adsorption IR, and Raman spectroscopy were used to characterize the acid properties and defect structures of these CeO2 catalysts.Based on these experiments, the structure-property-activity relationship will be established.

Results and Discussion
CeO2 has been proved a highly active and water-tolerant catalyst for the synthesis of 1,3butanediol from propylene and HCHO via Prins condensation-hydrolysis in water [24].This work encouraged us to apply the CeO2 catalyst for isobutene-formaldehyde condensation in water to synthesize 3-methyl-1,3-butanediol, which is an important higher-molecule alkanediol for the polymer industries; its synthesis is obviously difficult, but scientifically interesting.Our synthetic route includes the Prins condensation of isobutene with HCHO to 4,4-dimethyl-1,3-dioxane (3), and then hydrolysis of 3 to 3-methyl-1,3-butanediol (4) (Scheme 1).
Scheme 1. Prins condensation-hydrolysis of isobutene with HCHO in water.
The hydrolysis of 3 to 4 seems to be the rate-determining step in the Prins condensation-hydrolysis reaction under our reaction conditions, and the high temperature (>130 • C) favors the hydrolysis of 4,4-dimethyl-1,3-dioxane (3) to target product (4) (Scheme 1).These results show that the best yield (80%) of target product 4 can be achieved at 150 • C among the reaction temperature range investigated.
Inorganics 2017, 5, x FOR PEER REVIEW 3 of 11 selectivity of the target product, 3-methyl-1,3-butanediol (4), has the opposite behavior.The hydrolysis of 3 to 4 seems to be the rate-determining step in the Prins condensation-hydrolysis reaction under our reaction conditions, and the high temperature (>130 °C) favors the hydrolysis of 4,4-dimethyl-1,3-dioxane (3) to target product (4) (Scheme 1).These results show that the best yield (80%) of target product 4 can be achieved at 150 °C among the reaction temperature range investigated.

Time-On-Stream Profile
Prins condensation-hydrolysis of isobutene with formaldehyde (FA) in water was conducted at 150 °C over pristine CeO2 to explore the optimal reaction time (Figure 2).The FA conversion rapidly increases to 95% after 4 h under the reaction conditions, and then levels off at ca. 95% with reaction times increased to 8 h.The highest selectivity of the target product 3-methyl-1,3-butanediol (4) is 84% during the time-on-stream investigated.Further increasing the reaction time, the selectivity of 4 seems to decrease slightly; simultaneously, the selectivities of 3 and others increase slightly.This behavior indicates the Prins condensation-hydrolysis reaction reaches equilibrium.The total selectivities of 3 and 4 are over 95% throughout the course of the reaction, and slightly decrease along with the increase in reaction time, indicating that side reactions may occur after long reaction times at such high temperature (150 °C).These results indicate that pristine CeO2 is a highly effective catalyst for the Prins condensation-hydrolysis reaction, and the best catalytic activity (95% FA conversion and 84% 3-methyl-1,3-butanediol selectivity) can be obtained at 150 °C for 4 h.

Time-On-Stream Profile
Prins condensation-hydrolysis of isobutene with formaldehyde (FA) in water was conducted at 150 • C over pristine CeO 2 to explore the optimal reaction time (Figure 2).The FA conversion rapidly increases to 95% after 4 h under the reaction conditions, and then levels off at ca. 95% with reaction times increased to 8 h.The highest selectivity of the target product 3-methyl-1,3-butanediol (4) is 84% during the time-on-stream investigated.Further increasing the reaction time, the selectivity of 4 seems to decrease slightly; simultaneously, the selectivities of 3 and others increase slightly.This behavior indicates the Prins condensation-hydrolysis reaction reaches equilibrium.The total selectivities of 3 and 4 are over 95% throughout the course of the reaction, and slightly decrease along with the increase in reaction time, indicating that side reactions may occur after long reaction times at such high temperature (150 • C).These results indicate that pristine CeO 2 is a highly effective catalyst for the Prins condensation-hydrolysis reaction, and the best catalytic activity (95% FA conversion and 84% 3-methyl-1,3-butanediol selectivity) can be obtained at 150 • C for 4 h.

Time-On-Stream Profile
Prins condensation-hydrolysis of isobutene with formaldehyde (FA) in water was conducted at 150 °C over pristine CeO2 to explore the optimal reaction time (Figure 2).The FA conversion rapidly increases to 95% after 4 h under the reaction conditions, and then levels off at ca. 95% with reaction times increased to 8 h.The highest selectivity of the target product 3-methyl-1,3-butanediol (4) is 84% during the time-on-stream investigated.Further increasing the reaction time, the selectivity of 4 seems to decrease slightly; simultaneously, the selectivities of 3 and others increase slightly.This behavior indicates the Prins condensation-hydrolysis reaction reaches equilibrium.The total selectivities of 3 and 4 are over 95% throughout the course of the reaction, and slightly decrease along with the increase in reaction time, indicating that side reactions may occur after long reaction times at such high temperature (150 °C).These results indicate that pristine CeO2 is a highly effective catalyst for the Prins condensation-hydrolysis reaction, and the best catalytic activity (95% FA conversion and 84% 3-methyl-1,3-butanediol selectivity) can be obtained at 150 °C for 4 h.

Effect of Crystalline Plane
It has been reported that the exposed crystalline planes of CeO 2 (the (100), ( 110) and (111) crystalline planes) possess different surface concentrations of oxygen vacancies because of the difference in the formation energy of oxygen vacancies [29,35].We successfully prepared CeO 2 with different morphologies via the previously reported methods [23,24,36,37], and confirmed their morphology by XRD (Figure S1) and HRTEM (Figure S2).The average sizes of CeO 2 with different morphologies were determined by TEM (Figure S2).The CeO 2 -rods are about 7.4 nm in diameter and 69 nm in length, and the average sizes of CeO 2 octahedron and CeO 2 -cube are 118 and 61 nm, respectively.Our studies [24,38,39] and others [33,40] have also proved that the nanorods, nanocubes, and nanooctahedrons of CeO 2 selectively expose (110) and ( 100), (100), and (111) planes, respectively (Table 1).The theoretical exposed crystalline planes and their ratio are shown in Table 1, as obtained from the literature [37].We tested the catalytic activities of CeO 2 with the three different morphologies in the Prins condensation-hydrolysis reaction, and the results are shown in Table 1.In order to distinguish the difference in catalytic performance of these three CeO 2 catalysts, relatively low reaction temperature (100 • C) was selected due to the similar catalytic activity of CeO 2 under harsh reaction conditions (such as 150 • C for 2 h) (Table S1).Under 100 • C for 4 h, 32% FA conversion and 87% 3-methyl-1,3-butanediol (4) selectivity were obtained for CeO 2 -rod, meanwhile only 8% and 1% FA conversion were achieved for CeO 2 -cube and CeO 2 -octahedron with similar product distributions, respectively.For comparison, the catalytic activities of pristine CeO 2 (13% FA conversion and 91% 3-methyl-1,3-butanediol selectivity) were also listed in entry 4, Table 1.The order of catalytic activity is in line with the sequence of specific surface area (S BET ), which indicates that the S BET is another key parameter for the catalytic performance over CeO 2 .These results also indicate the CeO 2 -rod is the best catalyst for the reaction among these catalysts.According to the exposed crystalline planes, we can conclude the (110) plane is the most active crystalline plane for this reaction.
As the complex crystal planes over the pristine CeO 2 surface, the well-defined CeO 2 with different morphologies were selected as models in this study to make clear the correlation between the catalytic performance and their physicochemical properties.NH 3 -TPD, pyridine adsorption IR, and Raman spectroscopy were used to characterize the acid properties and oxygen-defect structures, respectively.NH 3 -TPD technique was used to investigate the acid strength of CeO 2 with different morphologies (Figure 3).All three CeO 2 samples have two broader NH 3 -desorption peaks in the range from 50 to 600 • C in the desorption profiles.The high desorption peak around 110-156 • C can be ascribed to the weak acid sites, and the weak desorption peak centered at 340-420 • C is related to the medium acid sites on the CeO 2 surface.It can be found that these three samples mainly possess weak acid sites, along with a small number of medium ones.The two strongest peaks, at around 145 • C and 340 • C, which are ascribed to NH 3 adsorbed on weak acid sites and medium acid sites, respectively, were observed for CeO 2 -rod.Two types of acid sites at low temperature around 110 • C and 156 • C and a weak peak around 420 • C were observed for CeO 2 -octahedron.Additionally, two weak peaks around 122 • C and 360 • C were detected for CeO 2 -cube.Furthermore, the peak areas, which reflect the acidity, vary with the CeO 2 morphologies, and the CeO 2 -rod catalyst shows the highest acidity among the three morphologies.These results also imply that the predominant factor responded for the different catalytic performance between the three catalysts may be the concentration of the acid sites.
Inorganics 2017, 5, x FOR PEER REVIEW 5 of 11 weak peaks around 122 °C and 360 °C were detected for CeO2-cube.Furthermore, the peak areas, which reflect the acidity, vary with the CeO2 morphologies, and the CeO2-rod catalyst shows the highest acidity among the three morphologies.These results also imply that the predominant factor responded for the different catalytic performance between the three catalysts may be the concentration of the acid sites.Pyridine-adsorption IR is an effective characterization for measuring the concentration of the acid sites and distinguishing the acid type of solid catalysts [41][42][43].From the pyridine adsorption IR spectra of CeO2 with different morphologies (Figure 4), it can be seen that no characteristic band attributed to Brönsted acid sites, which usually appear around 1540 cm −1 [42], are observed on these samples.Strong bands around 1440 and 1595 cm −1 are observed, which are the characteristic bands of the coordinatively bound pyridine on Lewis acid sites [43].The surface concentration of Lewis acid sites can be calculated based on the integrated band area at 1440 cm −1 and Formula (1) [44], and the CeO2-rod presents the highest concentration of Lewis acid sites (188 μmol•g −1 ), which is about threefold higher than that of CeO2-octahedron (64 μmol•g −1 ), and fivefold higher than that of CeO2cube (39 μmol•g −1 ).Additionally, the concentration of Lewis acid sites over CeO2-rod is 3.5 times higher than that of pristine CeO2 (54 μmol•g −1 ) [24,25].We plot the concentration of Lewis acid sites and the catalytic performance versus the catalyst morphologies showed in Figure 5.It can be found that the CeO2-rod obtains the best catalytic activity because of its higher Lewis acidity.
It should be noted that some bands around 1622, 1573, 1485, and 1465 cm −1 were observed, which can be ascribed to the pyridine adsorbed on Lewis acid sites; these results indicate that the CeO2 surface is predominately covered by Lewis acid sites.This result is in agreement with the previous study that only Lewis acid sites exist for CeO2 [45,46] and metal-doped CeO2 surfaces [25].However, these complex bands imply the different Lewis acid sites for CeO2 with different morphologies.The bands around 1573 and 1485 cm −1 for CeO2-rod and CeO2-octahedron surfaces are weak, and the influence on the concentration of Lewis acid sites may be neglected.However, the effect of 1622 and 1465 cm −1 on the concentration of Lewis acid sites should be considered, because these bands are obvious on the octahedron and cube, respectively.Furthermore, the peak area of 1465 cm −1 is larger than that of the 1622 cm −1 peak; this result may indicate that the concentration of Lewis acid sites over CeO2-cube is larger than that of CeO2-octahedron.This may be another reason for the opposite trend of HCHO conversion over CeO2-cube and octahedron when the conversion is correlated with the Lewis acid site concentration.Unfortunately, no consensus has been reached on the assignments of these bands, and the calculated formula has not yet been established.In the literature, the band at 1623 cm −1 could be assigned to the 8a mode for pyridine adsorbed on more acidic sites [47], but others have proposed that it is more likely to be due to the (1 + 6a) combination mode of pyridine [48].The assignment of the 1465 cm −1 band is more complex.There are four assignments based on the literature [49].Thus, more work is needed to assign and quantify these bands.Pyridine-adsorption IR is an effective characterization for measuring the concentration of the acid sites and distinguishing the acid type of solid catalysts [41][42][43].From the pyridine adsorption IR spectra of CeO 2 with different morphologies (Figure 4), it can be seen that no characteristic band attributed to Brönsted acid sites, which usually appear around 1540 cm −1 [42], are observed on these samples.Strong bands around 1440 and 1595 cm −1 are observed, which are the characteristic bands of the coordinatively bound pyridine on Lewis acid sites [43].The surface concentration of Lewis acid sites can be calculated based on the integrated band area at 1440 cm −1 and Formula (1) [44], and the CeO 2 -rod presents the highest concentration of Lewis acid sites (188 µmol•g −1 ), which is about threefold higher than that of CeO 2 -octahedron (64 µmol•g −1 ), and fivefold higher than that of CeO 2 -cube (39 µmol•g −1 ).Additionally, the concentration of Lewis acid sites over CeO 2 -rod is 3.5 times higher than that of pristine CeO 2 (54 µmol•g −1 ) [24,25].We plot the concentration of Lewis acid sites and the catalytic performance versus the catalyst morphologies showed in Figure 5.It can be found that the CeO 2 -rod obtains the best catalytic activity because of its higher Lewis acidity.It is well known that the structure determines the performance.The above results spur us on to in-depth investigations of the CeO2 structures with different morphologies.The surface oxygen of a perfect CeO2-rod, which exposes the (110) and (100) crystalline planes, is 9.5 × 10 19 atom per gram, which is three-times (2.9 × 10 19 ) and seven-times (1.4 × 10 19 ) the values for a perfect cube and Combined with the catalytic performances, Lewis acid site concentration, and oxygen vacancy concentration (Figure 5), we found an increase in FA conversion when changing the shape of CeO2.The CeO2-rod shows the best FA conversion because of its having the highest concentration of Lewis acid sites and oxygen vacancies among the three morphologies investigated.
It must be noted that the conversion trend does not seem to correlate with the concentration of Lewis acid sites and the number of oxygen vacancies for octahedrons and cubes.This may be caused by the following two factors: (1) the different specific surface area (SA) between the CeO2-cube and octahedron (the SA of CeO2-cube is 21 m 2 •g −1 , which is 2.3-times higher than that of CeO2-octahedron, see Table 1); (2) the different particle sizes between CeO2-cube and octahedron (the particle size of CeO2-cube is about 61 nm, which is about 2-times larger than that of CeO2-octahedron (~118 nm), see Figure S2).The smaller and higher SA of CeO2-cube could be attributed to the higher catalytic performance than that of CeO2-octahedron.

Preparation of the CeO2 Catalysts
Pristine CeO2 were prepared by a traditional precipitation process described in the literature [23,24].In a typical experiment, Ce(NO3)3•6H2O (5.0 g) was dissolved in Millipore-purified water (18 mΩ•cm, 100 mL), and then the solution was adjusted to a pH of 11.0 by the addition of NH3•H2O under stirring at room temperature.The obtained precipitate was filtered, washed with deionized water, and then dried at 120 °C for 12 h.The obtained solid was calcined at 500 °C under the flow of air (50 mL•min −1 ) for 4 h.
CeO2 samples with different morphologies were prepared by hydrothermal methodology reported by our and other groups previously [23,24,36,37].
Preparation of CeO2-rod and cube.Typically, 5.209 g of Ce(NO3)3•6H2O and a desired amount of NaOH (57.6-60 g) were dissolved in 20 mL and 210 mL of Millipore-purified water in a Teflon bottle, respectively.Then, the Ce(NO3)3 solution was added into the solution of NaOH under stirring at room temperature for 30 min, and a homogeneous milky slurry was formed.After the bottle was placed into a stainless steel vessel autoclave and sealed, the autoclave was heated to the desired temperature (100-180 °C) in an oven for 24 h.After the hydrothermal treatment, the solution above It should be noted that some bands around 1622, 1573, 1485, and 1465 cm −1 were observed, which can be ascribed to the pyridine adsorbed on Lewis acid sites; these results indicate that the CeO 2 surface is predominately covered by Lewis acid sites.This result is in agreement with the previous study that only Lewis acid sites exist for CeO 2 [45,46] and metal-doped CeO 2 surfaces [25].However, these complex bands imply the different Lewis acid sites for CeO 2 with different morphologies.The bands around 1573 and 1485 cm −1 for CeO 2 -rod and CeO 2 -octahedron surfaces are weak, and the influence on the concentration of Lewis acid sites may be neglected.However, the effect of 1622 and 1465 cm −1 on the concentration of Lewis acid sites should be considered, because these bands are obvious on the octahedron and cube, respectively.Furthermore, the peak area of 1465 cm −1 is larger than that of the 1622 cm −1 peak; this result may indicate that the concentration of Lewis acid sites over CeO 2 -cube is larger than that of CeO 2 -octahedron.This may be another reason for the opposite trend of HCHO conversion over CeO 2 -cube and octahedron when the conversion is correlated with the Lewis acid site concentration.Unfortunately, no consensus has been reached on the assignments of these bands, and the calculated formula has not yet been established.In the literature, the band at 1623 cm −1 could be assigned to the 8a mode for pyridine adsorbed on more acidic sites [47], but others have proposed that it is more likely to be due to the (1 + 6a) combination mode of pyridine [48].The assignment of the 1465 cm −1 band is more complex.There are four assignments based on the literature [49].Thus, more work is needed to assign and quantify these bands.
It is well known that the structure determines the performance.The above results spur us on to in-depth investigations of the CeO 2 structures with different morphologies.The surface oxygen of a perfect CeO 2 -rod, which exposes the (110) and (100) crystalline planes, is 9.5 × 10 19 atom per gram, which is three-times (2.9 × 10 19 ) and seven-times (1.4 × 10 19 ) the values for a perfect cube and octahedron, respectively [23], implying the probability that oxygen vacancy formation for CeO 2 -rod is higher than that for cube and octahedron.DFT calculations have proven that the formation energies of oxygen vacancies for different CeO 2 surfaces follow the order of (110) < (100) < (111) [33], meaning that the order of intrinsic oxygen vacancy formation follows (110) > (100) > (111).Raman spectroscopy is a powerful technique for detecting the defect structures over metal oxides; here, we used it to determine the practical concentration of observed oxygen vacancies over the three CeO 2 catalysts.Figure S3 shows the visible (532 nm) Raman spectra of the CeO 2 samples with different morphologies, providing the information of several surface layers over CeO 2 .A strong band around 462 cm −1 and a weak band around 595 cm −1 were observed in all three samples.The former can be ascribed to the F 2g vibrational mode of CeO 2 , which possesses a fluorite-type structure [50].The CeO 2 -rod gives a much broader 462 cm −1 peak than that of CeO 2 -octahedron and CeO 2 -cube, which is an inhomogeneous strain broadening caused by the differences in particle size between these three samples.This is a size-dependent phenomenon observed on CeO 2 nanoparticles [51].This is consistent with TEM measurement, where CeO 2 -rod has the smallest size among these three morphologies (7.4 nm × 69 nm for CeO 2 -rod, 118 nm for CeO 2 -octahedron, and 61 nm for CeO 2 -cube) (Figure S2).Interestingly, the HCHO conversion trend over these three morphologies is line with the particle size of these catalysts, indicating that the particle size may also affect the catalytic performance for the Prins reaction.The weak band around 595 cm −1 is related to intrinsic oxygen vacancy sites [52].The oxygen vacancies detected by Raman spectroscopy are primarily those on several surface layers of the CeO 2 .The ratio of the integrated peak areas (A 595 /A 462 ) was used to quantify the relative concentrations of oxygen vacancy [53].The relative oxygen vacancy concentration of CeO 2 samples are shown in Table 1 and Figure S3.A plot of the oxygen vacancy concentration (measured by Raman spectra) and Lewis acid site concentration (measured by pyridine adsorption IR) against the catalyst morphologies was drawn (Figure 5).It can be found that the more oxygen vacancies, the more Lewis acid sites, and the CeO 2 -rod shows the highest concentration of oxygen vacancies and Lewis acid sites among the three morphologies.
Combined with the catalytic performances, Lewis acid site concentration, and oxygen vacancy concentration (Figure 5), we found an increase in FA conversion when changing the shape of CeO 2 .The CeO 2 -rod shows the best FA conversion because of its having the highest concentration of Lewis acid sites and oxygen vacancies among the three morphologies investigated.
It must be noted that the conversion trend does not seem to correlate with the concentration of Lewis acid sites and the number of oxygen vacancies for octahedrons and cubes.This may be caused by the following two factors: (1) the different specific surface area (S A ) between the CeO 2 -cube and octahedron (the S A of CeO 2 -cube is 21 m 2 •g −1 , which is 2.3-times higher than that of CeO 2 -octahedron, see Table 1); (2) the different particle sizes between CeO 2 -cube and octahedron (the particle size of CeO 2 -cube is about 61 nm, which is about 2-times larger than that of CeO 2 -octahedron (~118 nm), see Figure S2).The smaller and higher S A of CeO 2 -cube could be attributed to the higher catalytic performance than that of CeO 2 -octahedron.

Preparation of the CeO 2 Catalysts
Pristine CeO 2 were prepared by a traditional precipitation process described in the literature [23,24].In a typical experiment, Ce(NO 3 ) 3 •6H 2 O (5.0 g) was dissolved in Millipore-purified water (18 mΩ•cm, 100 mL), and then the solution was adjusted to a pH of 11.0 by the addition of NH 3 •H 2 O under stirring at room temperature.The obtained precipitate was filtered, washed with deionized water, and then dried at 120 • C for 12 h.The obtained solid was calcined at 500 • C under the flow of air (50 mL•min −1 ) for 4 h.
CeO 2 samples with different morphologies were prepared by hydrothermal methodology reported by our and other groups previously [23,24,36,37].
Preparation of CeO 2 -rod and cube.Typically, 5.209 g of Ce(NO 3 ) 3 •6H 2 O and a desired amount of NaOH (57.6-60 g) were dissolved in 20 mL and 210 mL of Millipore-purified water in a Teflon bottle, respectively.Then, the Ce(NO 3 ) 3 solution was added into the solution of NaOH under stirring at room temperature for 30 min, and a homogeneous milky slurry was formed.After the bottle was placed into a stainless steel vessel autoclave and sealed, the autoclave was heated to the desired temperature (100-180 • C) in an oven for 24 h.After the hydrothermal treatment, the solution above the precipitate was removed by centrifugation, and washed with deionized water and ethanol.Finally, the obtained sample was dried at 60 • C in an oven for 12 h.
Preparation of CeO 2 -octahedron.Typically, 0.023 g of Na 3 PO 4 •12H 2 O was added into the solution of Ce(NO 3 ) 3 (2.618g in 240 mL of Millipore-purified water) under stirring at room temperature for 30 min in a Teflon bottle.Subsequently, the Teflon bottle was transferred into a stainless steel autoclave, and then placed in an oven at a temperature range of 170 • C for 12 h.After the hydrothermal treatment, the solution above the precipitate was removed by centrifugation, and washed with deionized water and ethanol.Finally, the obtained sample was dried at 60 • C in an oven for 12 h.

Prins Condensation-Hydrolysis Reaction
Aqueous formaldehyde (FA) (38 wt % HCHO, 0.21 mL, 3.0 mmol of HCHO), CeO 2 (50 mg), H 2 O (1.5 mL), and a magnetic stir bar were loaded into a 15 ml Teflon-lined autoclave reactor.Quantified isobutene (99.99%) was charged into the reactor from a cylinder via weighting the reactor before and after the charging and then sealed.The sealed reactor was heated to the desired reaction temperature via a mantle.The 3-methyl-1,3-butanediol, 4,4-dimethyl-1,3-dioxane, etc., were analyzed by gas chromatography-mass spectrometry (GC-MS) using an Agilent 7890A/5975C (Santa Clara, CA, USA) instrument equipped with an HP-5MS column.The formaldehyde solution was analyzed by a GC (Tianmei, Shanghai, China) equipped with a packed column (GDX-401) and a TCD detector.An external standard was used to quantify the formaldehyde conversion.

Acidity Characterization by NH 3 Temperature-Programmed Desorption (NH 3 -TPD)
The NH 3 -TPD profiles of CeO 2 with different morphologies were recorded in a U-type quartz tube combined with an on-line mass spectrometer (MS, GSD320 Thermostar, Shanghai, China).In a typical experiment, about 40 mg of CeO 2 sample was placed in the tube and pretreated at 210 • C for 60 min under an argon flow (30 mL•min −1 ), then cooling to 30 • C; several pulses of NH 3 were injected until no change in the NH 3 concentration was detected by the on-line MS.After that, the CeO 2 sample was flushed with argon for 60 min.Finally, the NH 3 desorption was conducted via increasing the oven temperature from 30 to 600 • C in the rate of 10 • C•min −1 .On-line MS recorded the gas effluents during the NH 3 desorption process.

Acidity Characterization by Pyridine Adsorption IR Spectroscopy
The acid type and concentration were determined by pyridine-adsorption IR spectra, which was conducted on a Bruker 70 IR spectrometer.A self-supporting sample disk of about 13 mm diameter (around 30 mg) was made by pressing in a mould, then the sample disk was placed into a homemade IR cell attached to a closed glass-circulation system.The disk was pretreated under a flow of argon (10 mL•min −1 ) at 350 • C for 30 min, and then vacuumed for 30 min.After the temperature had cooled to 30 • C and the sample chamber had been evacuated to <10 −3 mbar, a reference spectrum was recorded.After that, pyridine adsorption over sample disk was conducted via exposure to pyridine vapor.When the sample disk adsorbed pyridine was vacuumed at 150 • C for 30 min and cooled to 30 • C, the IR spectrum was recorded.The concentration of Lewis acid sites were calculated based on the integrated absorbance of the L band (1440 cm −1 ) and the following formula [44]: where C is the concentration of Lewis acid sites (mmol (g of catalyst) −1 ), IA is the integrated absorbance of the L band (cm −1 ), R is the radius of the catalyst disk (cm), and W is the mass of the sample disk (mg).

Conclusions
We demonstrate that CeO 2 is a highly effective catalyst for the synthesis of 1,3-diols from isobutene and HCHO via Prins condensation-hydrolysis reaction in water.95% HCHO conversion and 84% 3-methyl-1,3-butanediol selectivity were obtained over the pristine CeO 2 catalyst under 150 • C for 4 h.The crystal planes of CeO 2 have a significant effect on the catalytic activities for the condensation-hydrolysis reaction.The (110) plane over CeO 2 -rod surface is the most active crystalline plane for the reaction because of its having the richest intrinsic oxygen vacancies and highest Lewis acidity among the three low-index crystal planes investigated (the (100), (110), and (111) planes).Furthermore, the concentration of Lewis acid sites is proportional to the concentration of relative oxygen vacancies, indicating the strong contact between oxygen vacancies and Lewis acid sites.This study also implies that the Lewis acidity induced by oxygen vacancy can be modulate by the selective synthesis of CeO 2 with different crystal planes.S1: Prins condensation-hydrolysis of isobutene with HCHO in water over CeO 2 with different morphologies.

Figure 5 .
Figure 5.The relationship between the conversion of FA and the concentration of Lewis acid sites (unit: mmol/g) or the concentration of oxygen vacancies versus the CeO 2 with different morphologies.

Table 1 .
Prins condensation-hydrolysis of isobutene with FA in water over CeO 2 with different morphologies1.