Phenomenological approaches for quantitative temperature-programmed reduction (TPR) and desorption (TPD) analysis

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Abstract

Temperature-programmed reduction (TPR) and temperature-programmed desorption (TPD) are techniques widely used for catalyst characterization, providing information about active sites. However, results from these experiments are usually interpreted with the aid of empirical models, based on the representation of reduction or desorption profiles as summations of empirical reference curves. In this context, phenomenological approaches can present several advantages over this traditional empirical approach, as in this case the extracted information can be based on theoretical models that allows for a deeper understanding of the catalyst properties. For this reason, in the present work, empirical and phenomenological modelling approaches are evaluated for the quantitative analysis of H2-TPR and NH3-TPD profiles, obtained from the characterization of Ni/SiO2 and Al2O3 alumina catalysts, respectively, and results from both approaches are thoroughly compared and discussed for the first time. Our results, obtained from the fitting of both modelling approaches to the whole experimental profile by using nonlinear regression, indicate that the phenomenological modelling approach can be considered better and should therefore be preferred, as it allows for significantly more accurate quantification and correct discrimination of distinct active sites, in addition to simultaneously enabling the determination of reduction or desorption kinetics parameters.

Introduction

Thermoanalytical techniques are often associated with transient characterization methods that are designed to monitor certain sample properties as functions of time, usually accompanied by the simultaneous increase of temperature [1], [2], [3], allowing the acquisition of significant amount of information about the analyzed material properties in a short period of time. These thermonalytical techniques have been widely applied in several fields, like the investigation of the thermal stability and thermal and mechanical properties of polymers [4] and the characterization of heterogenous catalysts [5], [6], [7], [8].

In the field of heterogenous catalysis, monitoring of some specific catalyst properties, such as the number of acidic, basic or metallic active sites, may constitute a step of paramount importance for development of optimized catalysts, which can allow the maximization of the yields of products of interest. In addition, the characterization of these (and possibly other) properties can also be fundamental for development of mathematical kinetic models required for the design, control and optimization of industrial reactors [9].

In this context, temperature-programmed (TP) techniques play a unique role, as they may allow for characterization of catalyst properties and assessment of the physico-chemical interactions that take place between the catalyst surface and the reactive species [2], [10]. Among the many available TP techniques, Temperature-Programmed Reduction (TPR), Temperature-Programmed Desorption (TPD), Temperature-Programmed Oxidation (TPO) and Temperature-Programmed Surface Reaction (TPSR) are of particular importance. Whereas the evaluation of bulk oxygen mobility in catalysts (such as nanostructured ceria [11] and other metal catalysts [12], [13], [14]) can be performed through standard TPR analyses, which normally make use of gaseous H2 streams as the reducing agent, the characterization of acid, basic and metallic sites can frequently be carried out through TPD analyses, which make use of probe molecules (such as NH3, CO2 and H2) that can adsorb onto and subsequently desorb from catalyst sites located on the catalyst surfaces [7], [15], [16]. Moreover, the evaluation of the extent of coke deposition on the catalyst surfaces can be evaluated through TPO analyses, which usually make use of O2 streams as oxidizing agents [17], [18], whereas interactions between the catalyst surfaces and the reactive species can be evaluated through TPSR analyses [1].

Nevertheless, despite the intensive and ample use of TP techniques for characterization of heterogeneous catalysts, the proper interpretation of the obtained thermograms still constitutes a challenge, as measured thermograms may depend not only on the catalyst properties, but also on the experimental conditions employed in the TP runs, such as the catalyst mass, gas flow rate, feed concentration of the reacting/probe molecule and temperature program [19], [20], [21].

The quantification of the number of reducible metallic species, acid, basic or metallic sites usually involves the calculation of the integral over time (or temperature) of intensities of the monitored TP signal during the thermoanalytical experiment, as the number of sites of a particular nature is expected to be proportional to the amount of consumed reducing agent, in the case of TPR analyses, or desorbed probe molecules, in the case of TPD analyses [21], [22]. However, when two or more peaks are present in the TP thermogram, there may be an indication that the catalyst can contain sites with distinct characteristics, with more than one type of reducible species or active site (acid, basic or metallic) [10]. Since TPR and TPD experiments lead to transient responses, peaks related to distinct active species can be partially or highly overlapped, making the determination of the number of different types of catalyst sites and their relative quantities difficult or unfeasible [10], [12], [15]. Hopefully, in some cases it may be possible to separate the overlapped peaks through manipulation of the experimental TP conditions, although it is not always obvious how operation conditions should be changed to achieve this result. As a consequence, it may be necessary to perform additional experiments for efficient peak resolution, rendering the experimental procedure more expensive and time consuming [21].

A strategy that has been frequently used in the literature to resolve overlapping peaks in a thermogram is deconvolution (although a more appropriate term should be "curve decomposition", since "deconvolution" is a term used to describe a set of more complex and well-defined mathematical procedures [23]), which assumes that the obtained multimodal thermogram can be represented as the sum of simpler unimodal curves, after adjustment of some suitable parameters. Functions that are employed very frequently in deconvolution procedures resemble probability distribution functions like the Gaussian curve, which is unimodal, bi-parametric and symmetrical around its point of maximum. Nevertheless, any family of curves, in principle, could be considered in the decomposition procedure [24]. After curve fitting, the point of maximum, the peak width and the area beneath the individual curves can be calculated for each element of the sum. Usually, the number of curves needed to provide the appropriate fitting for the experimental thermogram is assumed to be equal to the number of distinct active species, whereas the relative area generated by each individual curve is regarded to provide a measure of the relative importance (quantity) of that site. As a matter of fact, curve deconvolution (or decomposition) has been widely used for TPD and TPR quantitative analyses [25], [26], [27], [28], [29], [30]. Given the simplicity of the proposed empirical numerical approach, the use of deconvolution procedures seems appealing, despite the complete lack of phenomenological basis to support the use of the vast majority of available statistical functions to describe either the reduction or the desorption processes. Besides, it must be emphasized that there is no formal guarantee that the number of adjusted Gaussian curves, used to fit the TP thermogram, can indeed correspond to the actual number of distinct active species present in the catalyst.

An interesting alternative to the deconvolution procedure consists in modelling TP experiments with some sort of phenomenological approach. For instance, mass balance equations coupled with adsorption/desorption rate equations can be used to model the gas-phase concentration of the probe molecule in TPD analysis, allowing the determination of the number of types of active species and their relative quantities [15], [31], [32]. Similarly, mass balance equations can be coupled with reduction reaction rate equations in order to model the gas-phase concentration of the reducing agent in TPR experiments, allowing the quantification of the number of distinct reducible active sites and their relative amounts [14], [33], [34]. Moreover, besides allowing the quantitative characterization of the active species, the use of a phenomenological approach can also provide additional information about the kinetic rate parameters involved in the reduction or desorption reactions, such as the specific kinetic rate constants and the activation energies [31], [32], which can constitute a very significant advantageous aspect of this type of mathematical representation of TP experiments.

Phenomenological approaches can also allow for specific model improvements, for instance, selection of appropriate desorption or reduction reaction rates or consideration of activation energy as a function of surface coverage and simultaneous estimation of the parameters of this function in order to achieve a better description of the experimental data [35]. Moreover, advanced experimental and chemical modelling techniques can be readily applied, such as DFT coupled microkinetic modelling [36], modelling CO-TPD profile with mean-field techniques and kinetic Monte Carlo allowing for the observation of lateral interactions among probe molecules [37] and coupled NH3 temperature-programmed desorption with thermogravimetry for acid sites quantification in zeolites [38].

In this context, numerical methods have been proposed to perform quantitative kinetic analyses of thermograms, involving the definition of the points of maximum of modes of thermograms collected at different heating rates [39], [40], [41], [42]. However, although the use of these methods can seem appealing, as they require the fitting of simple straight-lines to provide the relative amounts and main characteristics of the individual catalyst sites, they present the drawback of reducing the entire thermogram profile to a small set of points while completely disregarding the full shape of the thermogram. For these reasons, numerical approaches that take into account the complete thermogram information should be preferred, as they can allow more meaningful characterization of the active species and the kinetics of desorption or reduction processes [12], [14].

Based on the previous paragraphs, the present study evaluates—for the first time—the use of phenomenological mathematical approaches for the quantitative characterization of heterogeneous catalysts using TPR and TPD experiments when compared to empirical deconvolution methods of analysis. To do this, we use the reducible characteristics of a Ni/SiO2 catalyst, as assessed by H2-TPR, and the acid features of an Al2O3 alumina catalyst, as evaluated by NH3-TPD experiments, and fit both modelling approaches to the experimental profiles by using nonlinear regression. In both cases, results from both analysis approaches are thoroughly compared and discussed. Our results indicate that the phenomenological modelling approach can be considered better and should therefore be preferred, as it allows for more accurate quantification and correct discrimination of distinct active sites, in addition to simultaneously enabling the determination of reduction or desorption kinetics parameters.

Section snippets

H2-TPR experimental procedure

All experimental TPR profiles were compiled from [13], [43], [44]. Nickel supported on silica catalyst (Ni/SiO2) was prepared through the well-known deposition-precipitation method, as described elsewhere [13], [43], [44]. The silica used as support consisted of a diatomaceous earth, with 1% of alumina, a specific surface area of 42 m2/g and pore volume of 1.1 cm3/g [13]. A slurry containing silica and nickel nitrate solution, which was used as active precursor, was kept at 90 °C under agitation,

H2-TPR quantitative data analysis

The reduction profile of the TPR analysis of the Ni/SiO2 catalyst is presented in Fig. 1. Two well-defined H2 consumption peaks were observed around 20 and 35 min (close to 500 and 600 °C, respectively), which can be attributed to more and less accessible nickel atoms that present weaker and stronger interactions with the support, respectively [58], [59]. A third peak with lower intensity was also observed around 50 min (around 650 °C) and can be attributed to nickel species that present even

Conclusions

Although temperature-programmed (TP) techniques have been widely used for the characterization of heterogeneous catalysts for decades, the quantitative analysis of TP data remains mostly limited to empirical modelling techniques, particularly in TPR and TPD experiments. Thus, the present work has evaluated the use of phenomenological modelling approaches for quantitative analysis of TP experiments when compared to results obtained by empirical deconvolution procedures.

For TPR, the

Conflict of interest

The authors declare that they have no conflict of interest.

Acknowledgement

The study was financed in part by Conselho Nacional de Desenvolvimento Científico e Tecnológico – Brasil (CNPq) and by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES)Finance Code 001.

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