A Ru catalyst, with a metal loading of 3 wt%, was prepared by impregnation with excess solution on a commercial activated carbon (C) (NORIT, ground, and sieved to 60 - 100 mesh) according to reference [18] .

Textural properties of the support, pore volume (V_P), and specific surface area (S_BET) were established by N₂ physisorption at 77 K using a Micromeritics ASAP 2020 equipment.

The size distribution of metallic particles was determined by transmission electron microscopy (TEM) with a JEOL 100 CX II microscope. The mean particle size (d_TEM) was calculated using Equation (1):

d TEM = ∑ i n i d i 3 ∑ i n i d i 2 (1)

where d_i is the diameter of particle and n_i is the number of particles with size d_i.

The reducibility of the catalyst was studied by Temperature-Programmed Reduction (TPR) experiments using a laboratory-constructed equipment and X-ray photoelectron spectroscopy (XPS) analysis were performed on a Specs Multi-technique system (SPECS) equipped with a dual Mg/Al X-ray source and a PHOIBOS 150 hemispherical analyzer operating in the Fixed Analyzer Transmission (FAT) mode. Both characterizations were conducted following previously published protocols [18] .

The tests were carried out in a high-pressure reactor, using 0.25 g of catalyst and 50 mL of water as solvent. The reaction time was 7 h. The stirring speed, the temperature, the pressure, and the initial glucose concentration were varied between 250 - 700 rpm, 343 - 383 K, 0.5 - 2 MPa, and 0.033 - 0.133 M, respectively. The variables were modified one at a time, keeping the others constant in each test.

The reaction samples were analyzed offline by liquid chromatography in a UHPLC chromatograph equipped with a RI-detector (operating at 313 K). Separation of the components was achieved by a Phenomenex Rezex RCM Ca⁺² Monosaccharide (300 × 7.8 mm) column operated at 353 K. Elution was performed at 0.6 mL/min flow rate of mobile phase (milli-Q-water).

The conversion of glucose (Glu) was calculated using the following expression:

x ( % ) Glu = C Glu 0 − C Glu t C Glu 0 ⋅ 100 (2)

Analytical criteria were verified to determine the absence of diffusional limitations and the experimental results were interpreted by kinetic modeling using heterogeneous models of Langmuir-Hinshelwood-Hougen-Watson (LHHW).

The activated carbon used as support had a pore volume of 0.53 cm³∙g⁻¹ and a S_BET of 1000 m²∙g⁻¹ measured by N₂ physisorption. The 3 wt% Ru/C catalyst has been deeply characterized, as previously published [18] . In order to better explain the kinetic results, the main characteristics of the catalyst are gathered in Table 1.

Briefly, it can be said that TEM analysis showed the presence of small and

a. D Ru = 0.91 d TEM [19] .

uniform-sized particles that are widely dispersed, and Ru is in the metallic form as was confirmed by XPS and TPR analysis.

Analytical criteria were used to compare the initial reaction rate with the maximum transport rates in the physical stages. In the case of liquid-phase hydrogenation reactions, the diffusion of reagents and/or products in the gas-liquid interface, the liquid-solid interface, and internal diffusion in the particles must be evaluated.

The reaction conditions used to determine the initial reaction rate were 363 K, 1.25 MPa of H₂ pressure, and a stirring speed of 625 rpm, using 0.25 g of 3 wt% Ru/C catalyst and 0.90 g of glucose as substrate. From the conversion vs. time curve, the initial reaction rate was calculated at 10% conversion.

Agitation of the reaction mixture in a slurry reactor is important not only to keep the catalyst particles uniformly suspended, but also to facilitate the transport of the gaseous reactant through the gas-liquid interface and the dissolved reagent in the liquid medium towards the surface of the catalyst, there being a

relation between the increase of the stirring speed and the increase of the mass transfer coefficient.

In order to ensure the absence of mass transfer limitations in the gas-liquid interface, experiments were carried out varying the stirring speed between 250 and 700 rpm at 363 K and 1.25 MPa of H₂ pressure, with 0.25 g of Ru/C catalyst and 0.90 g of glucose as substrate. Figure 2 shows the initial reaction rates (r_i) for each stirring speed, calculated from the slopes of the conversion vs. time curves (at 10% conversion). With stirring speeds lower than approximately 600 rpm, (r_i) decreases, indicating the presence of limitations to the transfer of hydrogen at the gas-liquid interface. For this reason, a speed of 625 rpm was adopted for subsequent tests.

The influence of temperature on the catalytic activity at 1.25 MPa H₂ and 0.1 M of glucose was investigated (Figure 3), varying its value from 343 K to 383 K.

Below 353 K, the reaction rate decreases significantly, and only 80% glucose conversion is reached at 343 K after 7 h of reaction. Above 373 K, it is observed that the time necessary to achieve complete conversion is reduced to 5 h. However,

in the total time studied (7 h), at 363 K, 99% conversion is achieved. Thus, although time is longer, high conversion is achieved in milder condition. In all the cases, the selectivity was 100% to sorbitol, proving that consecutive or parallel reactions such as isomerizations do not occur (see Figure 1).

The apparent activation energy (Ea) was determined by linear regression using an Arrhenius type function. A value of 30.8 kJ/mol was obtained. This value is similar to those reported in literature [17] . Thus, kinetic data using different ruthenium catalysts and various experimental conditions have been reported. In this sense, an activation energy of 32.9 kJ/mol and first-order kinetics with respect to glucose concentration has been reported by Mishra et al. [23] over Ru/HY zeolite. Crezee et al. [24] reported an activation energy of 55 kJ/mol at 4 MPa of H₂ and 0.75 g/L of 5% Ru/C. Similar values have also been reported in studies carried out with other monosaccharides. Li et al. [25] reported that the apparent activation energy (Ea) of maltose hydrogenation using a Ru-P catalyst was 27 kJ/mol (6.45 kcal/mol) and for Ru-B was 32 kJ/mol (7.65 kcal/mol), using a maltose solution of 40% w/v, 363 K, 2 MPa pressure and stirring at 1200 rpm.

The effect of partial pressure of hydrogen (at 363 K and 0.1 M glucose) is presented in Figure 4.

It is observed that in every case an almost total conversion was obtained, increasing r i with the increase of pressure. The variation of the pressure does not produce changes in the selectivity, obtaining sorbitol as the only product.

The reaction order with respect to hydrogen was calculated by considering for r i a power law rate equation:

r i = k ⋅ ( C glu ) n ⋅ ( P H 2 ) m (7)

The linear regression of data obtained shows a reaction order with respect to the H₂ of 0.586. This value was in reasonable agreement with that reported by Zhang et al. of 0.66 over silica-supported Pt nanoparticles [6] and also with that informed by Tukac of 0.65 [26] . This latter value was obtained in the catalytic hydrogenation of glucose, using a 40 wt% aqueous solution of D-glucose and a

kieselgur-supported nickel catalysts (12% NiO, 2% Cr₂O₃). The temperature range was 388 to 433 K and pressure range of 0.5 - 10 MPa [19] .

The results of the variation of the initial glucose concentration (at 363 K and 1.25 MPa) are given in Figure 5.

Although the final conversion reached after 7 h of reaction decreases, the activity of the catalyst increases with increasing glucose concentration. The reaction order with respect to glucose was determined by linear regression from the data with Equation (8) and a value of 0.406 was obtained. In the literature, it has been reported that glucose concentration presents a relatively complex influence upon the hydrogenation rate. Guo et al. [27] studying a Ru-B amorphous catalyst, observed that increasing glucose concentration the initial rate increased linearly up to 40 wt% and then presented a plateau at higher glucose concentration. This kinetic behavior could be explained by the adsorption strength of glucose and hydrogen on the catalyst. The glucose molecule adsorbs strongly on the catalyst reaching saturated adsorption even at low concentration. Only when the glucose concentration was very low in the liquid phase, and in consequence, the surface adsorption was unsaturated, the hydrogenation rate grew up with the glucose concentration.

The catalytic hydrogenation of D-glucose is generally described by means of Langmuir-Hinshelwood kinetics with a change from first-order dependency in D-glucose at low concentrations to zero-order behavior at high concentrations [8] .

Based on the above-discussed results, the following hypotheses for the formulation of the LHHW models were considered:

1) The superficial hydrogenation reaction is irreversible (total conversion of glucose to sorbitol was obtained in the experiments performed).

2) Hydrogen concentration in the liquid phase is constant, due to the constant pressure of hydrogen throughout the test, the high volume of solvent and the

efficient mixing.

Three general models were proposed: a first model of the Eley-Rideal type, with only glucose adsorption on the solid catalyst; a second model with adsorption of molecular hydrogen in addition to glucose adsorption and a third model considering the dissociative adsorption of hydrogen. Both models, 2 and 3, considered the competitive adsorption of H₂ and glucose. By assuming different rate limiting steps (r.l.s.), (H₂ adsorption, glucose adsorption or surface chemical reaction) and the possibility or not of sorbitol (the reaction product) adsorption, 19 different LHHW sub models were analyzed.

The equations were solved numerically using the algorithm of Runge-Kutta-Merson with the data obtained at 363 K. The estimation of model parameters was performed by non-linear regression, using a Levenberg-Marquardt algorithm that minimizes the objective function:

S = ∑ i = 1 n ( C i , t * − C i , t * CALC ) 2 (8)

Table 3 presents the proposed LHHW models, with the estimated parameters

and the correlation coefficients (r). The discrimination between the models was determined, after discarding those with parameters without physical sense, according to the highest r value and using the model selection criterion (MSC), according to the following equation:

MSC = ln ( ∑ i = 1 n ( C i * − C ¯ * ) 2 ∑ i = 1 n ( C i * − C i * CALC ) 2 ) − 2 p n e (9)

The most significant model is the one that leads to the highest MSC value.

Models 2c, 2d, 2f, 3b, 3c, 3d and 3f, have some of their estimated parameters with negative and/or imaginary values, which made them lack of physical sense for the kinetic and equilibrium constants. Because of that, these models are rejected.

In addition, those models that consider that sorbitol is not adsorbed, or that the desorption of this product is the rate limiting step (1b, 1d, 1e, 2b, 2g, 3g) have a poor fit. The adsorption of sorbitol cannot be neglected, however its desorption does not constitute a limitation in the reaction rate (0 << 100 in the models with the best fit).

The best model among the ones here proposed to interpret the aqueous phase hydrogenation of glucose with 3 wt% Ru/C catalyst (Model 3a) considers that both reagents, glucose and H₂ are adsorbed on the catalyst (competitive adsorption) to give sorbitol, which is then desorbed. The H₂ adsorption is dissociative and the rate limiting step is the surface chemical reaction. Equations (i)-(iv) show the elementary steps describing this process, where (iii) is the r.l.s.:

Glu + ∗ ↔ Glu ∗ (i)

H 2 + 2 ∗ ↔ 2 H ∗ (ii)

Glu ∗ + H ∗ ↔ Sorb ∗ + ∗ (iii)

Sorb ∗ ↔ Sorb + ∗ (iv)

In Figure 6, the experimental results for the conversion of glucose as a function of time with the optimal conditions are presented in symbols, while the values

estimated by this model are represented in solid lines. As can be seen, a good agreement between the experimental and predicted data is obtained, which validates the kinetic model.

Figure 7 shows the model fit of the other conditions evaluated. Along with this, the distribution of residuals as a function of time is also shown and followed an acceptable random trend, being consistent with the random error hypothesis included in the regression and giving additional support to the adequacy of the model.

Subsequently, the dependence of the kinetic and equilibrium constants with temperature was established using the following expressions:

k d = k 0 e ( − E a R T ) (10)

K A = e ( − Δ H A R T + Δ S A R ) (11)

K B = e ( − Δ H B R T + Δ S B R ) (12)

K C = e ( − Δ H C R T + Δ S C R ) (13)

And the model 3a was adjusted with the data obtained for 343 - 383 K. The results are shown in Table 4, while the fit obtained for the different temperatures evaluated can be observed in Figure 8.

The D-glucose adsorption enthalpy H_A presents a positive value. This is indicating that the adsorption constant of D-glucose increases with temperature. This is not thermodynamically consistent with adsorption phenomena. However, this behavior has been described by other authors in terms of the mechanism of D-glucose adsorption [24] .

From the kinetic studies carried out, and considering the reaction mechanism proposed by model 3a, Figure 9 represents a surface of ruthenium atoms supported on carbon on which hydrogen is adsorbed dissociatively and glucose does so through its hemiacetal group, leading to the formation of sorbitol, following the elementary steps described from (i) to (iv).