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Systematic Review

A Review for the Design and Optimization of Catalysts: The Use of Statistics as a Powerful Tool for Literature Analysis

by
Tatiana Martinez
1,
Laura Stephania Lavado Romero
1,
D. Estefania Rodriguez
2 and
Jahaziel Amaya
1,*
1
Grupo de Investigación Fundamental y Aplicada en Materiales (GIFAM), Facultad de Ciencias, Universidad Antonio Nariño, Circunvalar Campus, Carrera 1a Este #47A15, Bogota 110231, Colombia
2
Departamento de Química, Facultad de Ciencias, Universidad Nacional de Colombia, Bogota 111321, Colombia
*
Author to whom correspondence should be addressed.
Chemistry 2025, 7(3), 74; https://doi.org/10.3390/chemistry7030074
Submission received: 21 December 2024 / Revised: 2 February 2025 / Accepted: 7 February 2025 / Published: 1 May 2025
(This article belongs to the Section Catalysis)

Abstract

In this study, a statistical analysis of results reported in the literature was conducted through a 2n experimental design on the synthesis of bifunctional catalysts used in the production of lighter fuels, aiming for optimization while considering factors such as support (bentonite and vermiculite), acidity modifier (zirconium and cerium), metal (tungsten and molybdenum), metal content (5% and 10%), promoter (nickel and cobalt), and heteropolyacids (tungstophosphoric acid and molybdophosphoric acid), identifying their influence on textural properties and catalytic performance. Regarding the textural properties, vermiculite proved to be the most favorable support due to its high porosity. It was also established that the implemented metals impart positive characteristics to the catalysts due to their various properties; however, incorporating large amounts led to an adverse effect by clogging the pores. Catalytic performance was analyzed in isomerization and cracking reactions, which were enhanced by the use of cerium due to the presence of Brønsted acid sites and molybdenum for its stability. In this way, the statistical analysis conducted in this study was crucial for identifying the influence of key factors on the textural properties and catalytic performance of bifunctional catalysts. Using a 2n experimental design allowed for a systematic evaluation of variables reported in the literature, such as support, acidity modifiers, metals, metal content, promoters, and heteropolyacids.

1. Introduction

Currently, climate change stands as one of the most pressing issues, as it triggers a progressive global transformation centered in the energy sector worldwide [1,2]. As is well known, oil remains the most important source of liquid fuels, which has intensified the search for alternatives that not only increase the efficiency of existing refining mechanisms but also optimally utilize all available resources to ensure a balance between energy demand and environmental sustainability [3,4].
Bifunctional catalysts stand out for their ability to directly promote catalytic processes through cascade reactions. This feature has positioned them as a prominent option in oil refining processes [5], particularly those that require selectivity in hydrogenation and cracking reactions [6,7,8]. These catalysts aim to achieve a balance between acidic and metallic sites, which cooperate to carry out processes with high selectivity and thermal stability, among other key characteristics [9,10].
To achieve the desired balance between acidic and metallic sites in bifunctional catalysts, syntheses with various components have been carried out [11,12,13]. For hydrogenation reactions, noble metals have been widely used; however, in recent years, their use has decreased due to their high cost and low availability [14,15]. In response to this limitation, cost-effective and environmentally friendly alternatives have emerged, such as bimetallic systems with transition metals, including Ni/Mo, Ni/W, Co/Mo, and Co/W, as well as heteropolyacid (HPA) compounds. These alternatives have demonstrated effectiveness in refining processes, as evidenced by various studies [16,17,18,19,20,21].
On the other hand, the acidic characteristics of these catalysts play a crucial role, primarily influenced by the type of support used, as the textural properties provide the catalyst with the main features for interaction with substrates [22,23]. Over time, a variety of supports have been applied. Among them, notable examples include zeolites [22,24,25,26,27], alumina–silica [28,29], Beta-zeolite [30], and clay minerals [31,32,33]. The latter have emerged as a promising alternative to conventional acidic supports due to their abundance, sustainability, and ability to modulate acidity, yielding positive results in recent research [34,35,36]. In addition to the inherent acidity of the support, some catalysts have incorporated a new component designed to modulate or enhance this acidity [37,38,39]. To this end, metals with suitable characteristics for enhancing acidity have been used due to their low pKa values and high Z2/r ratios. The charge-to-radius ratio (Z/r2) is a key parameter in understanding the acid properties of catalytic materials, particularly in acid catalysis. Here, Z represents the charge of an ion, typically in terms of its valence, and r is its ionic radius. A high Z/r2 ratio indicates a higher polarizing power, meaning the ion can more effectively distort the electron clouds of surrounding atoms or molecules. This polarization enhances the formation of acidic sites on the catalyst surface, both Brønsted acid sites (which donate protons, H+) and Lewis acid sites (which accept electron pairs). Additionally, ions with high Z/r2 values often promote the formation of oxygen vacancies in metal oxide-based catalysts, which act as active sites for protonation, further increasing the catalyst’s acidity. As a result, such ions lead to a higher density of acid sites on the catalyst surface, improving its catalytic efficiency in acid-driven reactions like isomerization, cracking, and other processes. Thus, the Z/r2 ratio is crucial in determining the material’s catalytic performance by influencing its ability to generate and stabilize active acidic sites. These characteristics result in high acidity, allowing the prediction that its presence in metal oxides should lead to an increase in acidity [40]. Zr and Ce have stood out, as their incorporation significantly contributes to the catalytic performance of natural supports, being key elements in optimizing the catalytic activity of these systems [38,41].
Considering this, the specialized literature provides numerous studies and publications addressing the synthesis, characterization, and application of bifunctional catalysts that employ various combinations of metals and supports [18,42,43,44,45]. The diversity of available options allows researchers and scientists to explore and compare different combinations of metals and supports in order to optimize catalytic activity, selectivity, and stability of catalytic systems. This fosters critical analysis and continuous improvement in the synthesis of catalysts with applications in refining processes and the production of fuels.
In this context, there is growing interest in understanding how to improve material selection in the synthesis of bifunctional catalysts to make significant advancements in the development of fuels. To maximize experimental outcomes, the implementation of a literature-based approach using statistics is proposed, as it is currently seen as a viable and essential tool. Its application allows for highlighting, validating, and complementing these results in a distinct manner. Despite its implementation in various contexts, no statistical analysis has yet been conducted that provides a meaningful contrast between the factors involved in the synthesis of bifunctional catalysts for the development of more fuels. With this in mind, a detailed statistical analysis is conducted using published literature reports to evaluate the impact of different factors on the measured responses through an experimental design. This approach aims to analyze the results and understand the relationship and significance of the experimental data reported. The factors considered in this study include the support, acidity modifier, promoter, metal, metal content, and HPAs. Their influence is evaluated through responses related to both textural properties and catalytic activity

2. Materials and Methods

2.1. Systematic Review

To analyze the relationship between factors and relevant responses in the catalytic activity of bifunctional catalysts, a rigorous methodology based on the PRISMA framework was employed, which included the stages of identification, screening, eligibility, and inclusion. The PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) methodology is designed to ensure a thorough and transparent process for conducting systematic reviews. In the identification stage, an extensive literature search was conducted using Boolean operators to gather relevant studies. The initial search queries used were (“bifunctional catalysts” AND “decane”) and (“bifunctional catalysts” AND “clay minerals”). Figure 1 shows the flow diagram for the systematic reviews conducted in this study, focusing on integrating analyzed variables into the proposed experimental design. The data from selected papers were analyzed using a 2n experimental design, involving factors such as support, acidity modifier, promoter, metal, and metal quantity. The evaluated factors included surface area, pore size, isomerization, cracking percentage, and T50. A comprehensive PRISMA 2020 Checklist has been included in the Supplementary Material, created based on a methodology that follows the PRISMA framework for systematic reviews. This process involves stages such as identification, screening, eligibility assessment, and inclusion. The methodology was applied to analyze the relationship between factors and responses in the catalytic activity of bifunctional catalysts. An extensive literature search using Boolean operators was conducted with queries like (“bifunctional catalysts” AND “decane”) and (“bifunctional catalysts” AND “clay minerals”) to gather relevant studies, ensuring transparency, thoroughness, and reproducibility in the review process.
In the screening phase, articles were carefully reviewed to eliminate irrelevant studies based on predefined criteria. This step ensured that only those papers most closely aligned with the research objectives were retained for further review. The eligibility stage involved evaluating the remaining studies for their methodological quality and relevance to the specific catalytic systems under investigation. Finally, in the inclusion stage, the studies that met all the criteria were selected for in-depth analysis, contributing to a robust dataset for exploring the catalytic activity of bifunctional catalysts. This systematic approach allowed for a comprehensive understanding of the topic, ensuring that the findings were grounded in high-quality, relevant literature.
The search was then refined by adding the term “HPA” to identify studies with similar reaction conditions that included the incorporation of HPAs as a metallic factor. These searches were limited to studies published since 2013 where the experimental conditions were the same, which allowed for adequate comparison in statistical analysis, and the results were sufficiently robust to be able to perform a statistical analysis using reports published exclusively in English and available in databases such as Elsevier, Springer, and RSC. Given the significance of using clay minerals as a support and the hydroconversion of n-decane as a model molecule, a search was conducted using the Scopus database to identify authors and countries associated with these topics. The aim of this search was to enrich the discussion of the results to be analyzed in this study. This investigation revealed a close connection with other research conducted by various authors, whose quantitative findings could not be directly incorporated into this work due to the absence of critical factors in our analysis [33]. Despite this, these studies were still highly valuable in enriching the discussion, as detailed in the following sections.

2.2. Experimental Design

The quantitative results obtained from the selected papers were distributed and applied using the statistical method of 2n experimental design [46]. The first design, composed of 5 factors and 2 levels for each, differentiated as values −1 and 1, included the following: support (bentonite (−1) and vermiculite (1)), acidity modifier (Zr (−1) and Ce (1)), promoter (Ni (−1) and Co (1)), metal (Mo (−1) and W (1)), and metal quantity (5% and 10%). The 6 experimental factors to be evaluated were as follows: BET surface area, pore size (micropore and mesopore), % isomerization, % cracking, and temperature of 50% conversion (T50). To perform this analysis, the data were taken from [32,42].
The 2n experimental design, based on data obtained from the literature [32,42], consisted of 32 interactions, allowing for a systematic and comprehensive evaluation of the factors influencing catalytic performance. By leveraging published experimental results, this approach integrates diverse studies to create a robust dataset for statistical analysis. This enables the identification of significant interactions and relationships between key variables such as support, acidity modifiers, promoters, metals, and metal content. The use of literature-derived data not only maximizes the value of existing research but also provides a unique opportunity to analyze trends and validate findings across multiple studies, offering deeper insights into the optimization of catalytic performance in bifunctional catalysts.
Subsequently, a second 2n experimental design was carried out, involving only 4 of the factors, with 2 levels each: support (bentonite (−1) and vermiculite (1)), acidity modifier (Zr (−1) and Ce (1)), promoter (Ni (−1) and Co (1)), and metal (HPMo (−1) and HPW (1)). The following two experimental factors were evaluated: BET surface area and T50. This 2n experimental design consisted of 16 interactions. To perform this analysis, the data were taken from [47,48,49].
The 2n experimental design, based on data obtained from the literature [47,48,49], consisted of 16 interactions, enabling a systematic and in-depth evaluation of the factors influencing catalytic performance. By utilizing published experimental data, this approach consolidates and analyzes results from various studies, creating a unified and robust framework for statistical analysis. This method highlights significant interactions among key parameters, such as support, acidity modifiers, promoters, metals, metal content, and heteropolyacids, providing valuable insights into their combined effects on catalytic activity. The integration of literature-based data ensures that existing research is maximized, offering a novel perspective for optimizing bifunctional catalysts in fuel production.
In this study, two main groups of responses were analyzed: surface area characterization and catalytic performance. This proposes an analysis of the main effects and surface properties in response, with the aim of alternatively interpreting the results previously reported in different studies.

3. Results and Discussion

3.1. Bifunctional Catalysts with Bimetallic Systems

A bifunctional catalyst plays a crucial role in the petroleum industry, particularly in reactions such as isomerization and cracking, where both acidic and metallic functionalities are required [16,44,50,51,52,53].
These catalysts typically consist of two types of active sites: acidic sites (both Brønsted and Lewis acids) and metallic sites (often involving metal or metal oxide components). In the case of isomerization, the acidic sites on the catalyst activate hydrocarbons, enabling the rearrangement of molecular structures to form branched isomers, which are more valuable for fuel production due to their improved combustion characteristics. Simultaneously, the metallic sites facilitate the hydrogenation or dehydrogenation of certain hydrocarbons, helping to maintain the desired product selectivity and prevent the formation of undesirable by-products. Similarly, in cracking reactions, bifunctional catalysts enable the breaking of large hydrocarbon molecules into smaller, more valuable products like gasoline and diesel. The acidic sites are responsible for cleaving carbon–carbon bonds, while the metallic sites support the activation of hydrogen molecules, aiding in the removal of sulfur and other impurities from the cracked products [16,44,50,51,52,53].
These dual functionalities make bifunctional catalysts particularly efficient, as they allow for seamless integration of both acid-catalyzed and metallic processes, enhancing reaction rates, selectivity, and overall catalyst life. The use of bifunctional catalysts in the petroleum industry, especially in processes like isomerization and cracking, leads to higher yields of desired products and contributes to the optimization of refining processes, making them a key component in modern catalytic technology [16,44,50,51,52,53].
This widespread implementation is supported by extensive research and discussions in the scientific literature, which provide a solid foundation for further evaluation and analysis. In this study, data derived from previously published sources—widely cited and validated within the field—were carefully analyzed under comparable conditions to ensure consistency and reliability [32,42]. These data encompass critical factors influencing catalyst behavior, including the support material, the type and quantity of metal, the acidity modifier, and the promoter, all of which play significant roles in determining catalytic efficiency.
To gain a deeper understanding, the results for the bifunctional catalysts were categorized into two primary response parameters: surface area and catalytic performance. The surface area serves as a measure of the textural properties that influence reactant accessibility, while catalytic performance directly reflects the material’s activity and selectivity in relevant reactions such as isomerization and cracking. By carefully curating and analyzing data from established literature sources such as [32,42], this study provides a unified and rigorous statistical assessment of these key factors.

3.1.1. Textural Properties in Bimetallic Systems

It has been demonstrated that textural properties, such as physical parameters, give the catalyst its primary characteristics for interacting with substrates [54]. A high surface area leads to an increase in free pores for the deposition of active acidic sites [55]. In this way, these properties depend on each of the factors involved in the synthesis of the catalyst.
Figure 2 shows the influence of each factor on the BET responses and pore size formation. The support type stands out as the most relevant factor for the textural characteristics (Figure 2a,c) as it exerts a predominant influence on the chemisorption property of the catalyst [56]; this characteristic shows a positive correlation with both the BET surface area and the formation of mesopores (Figure 2a,c), which is confirmed in (Figure 2b,d). A larger surface area has a higher potential for the formation of new active sites, with vermiculite being predominant on the response surface. The potential of this modified clay has previously been demonstrated in various catalytic processes [57,58,59]. The negative influence of this factor on the formation of micropores (Figure 2e,f) is mainly attributed to the mesoporous nature of clay materials [57,58].
The second most relevant factor in BET and mesopore formation is the metal content (Figure 2a,c). However, the metallic content has a negative effect (Figure 2b,d), as an increase in the metal content leads to pore blockage due to the formation of metal aggregates, which results in a reduction in the porosity of the support. It is noteworthy that a lower metal content correlates with a higher surface area [32,60]. This statement is supported by Figure 2a–f, where a negative influence of the added metal content (Mo or W) is evidenced. Specifically, it has been observed that the maximum value of 10% metal concentration leads to a decrease in both the surface area and the formation of mesopores.
Although it might be expected that the BET surface area of the support decreases with increasing metal loading (since metal incorporation typically leads to a decrease in surface area), the results show that this relationship is not always linear. For instance, at 5% metal loading, an increase in BET surface area was observed, which contradicts the usual trend. However, at 10% metal loading, the trend reversed, and the BET area decreased. This suggests that metal incorporation does not always lead to a reduction in surface area. Instead, factors like metal dispersion, interactions with the support, and the distribution of the metal within the material play key roles. These findings highlight the complexity of the relationship between metal loading and surface area, emphasizing the need to consider various factors when evaluating these systems.
On the other hand, Zr is presented as a positively influential factor in BET and the formation of micropores (Figure 2a,b,e,f), primarily due to the particle size, which is larger in Ce [61,62].
Finally, the promoter is addressed as a factor that negatively influences the BET response. Two metals are identified as promoters, Ni and Co, with Ni exerting the predominant influence. This is related to greater interaction between Ni and the metal, favoring the production of aggregates with smaller particle sizes and benefiting the formation of a more extensive surface area [63].
This way, the application of statistical analysis to literature-derived data has proven to be essential in uncovering the nuanced effects of promoters on catalyst properties, particularly in the case of Ni and Co. Through a rigorous statistical approach, it became evident that Ni plays a predominant role in influencing the BET surface area response by interacting strongly with the metal [63]. This interaction leads to the formation of smaller metal aggregates, which in turn enhances the surface area, offering more active sites for catalysis. The statistical analysis allowed for a deeper understanding of these complex relationships by systematically evaluating data from various studies under consistent conditions, highlighting trends and interactions that might have otherwise been overlooked. By integrating and analyzing the existing literature, this approach provided objective insights into the multifaceted role of promoters in catalyst design, showcasing the importance of statistical tools in validating and refining our understanding of catalytic systems. This method not only reinforced previous findings but also revealed new patterns that are critical for optimizing bifunctional catalysts in fuel production.
On the other hand, interactions between factors are of great relevance, as they can generate either potential or adverse effects, as shown in Figure 3. In the case of BET, two significant interactions associated with the amount of metal stand out. In the first interaction, which is consistent with their independent influences, a maximum point is observed in the relationship between vermiculite and a low metal amount (Figure 3a). In the second influential interaction, the incorporated metal is related to its amount, showing a maximum point with Mo at a low concentration (Figure 3b). This demonstrates the direct relationship of incorporating a low amount of metal to achieve a high surface area.
With respect to pore size formation, several influential interactions are observed. Specifically, in the process of mesopore formation, the importance of the acidity modifier Zr stands out. Although in the previous section it was shown that Zr does not generate any effect independently, in this case, when interacting with vermiculite and a low metal amount, optimal mesopore formation is achieved (Figure 3c,d).
Regarding micropore formation, several factors show relevance in their interaction. Particle size is of particular interest in the development of these pores. First, vermiculite in combination with the acidity modifier Ce shows significance. Ce, due to its larger particle size, causes obstruction in the area, thus promoting the formation of micropores. Additionally, the interaction between W as a metal, in a higher quantity, induces the same beneficial effect in micropore generation (Figure 3e,f).
The application of statistical analysis to literature-based data has provided valuable insights into the factors influencing micropore formation in bifunctional catalysts. Notably, the interaction between vermiculite and the acidity modifier Ce was found to be significant, with Ce, due to its larger particle size, contributing to the obstruction of pore areas, which in turn promotes the formation of micropores. Furthermore, the analysis revealed that a higher quantity of W as a metal also plays a crucial role in enhancing micropore generation. The statistical approach enabled a detailed exploration of these interactions, highlighting the combined effects of particle size, metal content, and acidity modifier on textural properties. By leveraging the literature data, this study emphasizes how statistical methods can uncover subtle but important correlations, allowing for a deeper understanding of the complex mechanisms that govern catalyst structure and performance.

3.1.2. Catalytic Activity of Bimetallic Systems

Isomerization and cracking reactions have become promising alternatives to produce lighter fuels. These processes are considered economically viable and efficient for such transformations [5,13,54,64]. These reactions occur in typical metal–acid reactions of bifunctional catalysts, where a proper balance of both acidic and metallic sites is necessary [65]. The isomerization reaction has been reported to be favored by moderate acidity [7,66,67], while strong acidity promotes the cracking reaction [31,68,69]. This is attributed to the formation of more Bronsted acid sites, generated by the bonds formed between Si, O, and Al in the acidic support used [68,70].
Figure 4 presents the factors involved in the isomerization and cracking reactions, as well as the temperature required for 50% conversion (T50). The acidic properties of the catalyst are enhanced by incorporating metals such as Zr and Ce [31,68,71]. In Figure 4a, a negative effect on the isomerization reaction is observed due to the acid modifier, with Ce being more favorable than Zr. This preference is attributed to Ce’s properties, such as its ability to increase particle dispersion on the support, thereby enhancing activity levels [72]. In this way, cerium plays a critical role in bifunctional catalysis, acting as a bridge between acidic and redox functions, thus enhancing the efficiency and selectivity of catalysts. Specifically, cerium can form Brønsted acid sites, especially when present in compounds like ceria (CeO2) or incorporated into mixed oxide matrices or zeolites. First, cerium enhances Brønsted acidity by modifying the electronic environment of adjacent acidic sites, such as hydroxyl groups, through its redox behavior (Ce3+/Ce4+) and its ability to stabilize acidic protons. This modification occurs due to cerium’s ability to cycle between its +3 and +4 oxidation states, which influences the electron density and facilitates proton transfer. Second, in cerium-containing zeolites or oxides, Ce4+ can induce structural distortions or vacancies that increase the density of hydroxyl groups, further contributing to Brønsted acid site formation. The interaction between Ce4+ and hydroxyl groups leads to the formation of stronger Brønsted acid sites, as illustrated by the following reaction: Ce4+ + –OH → Stronger acid site (Brønsted, H+). This behavior highlights the versatility of cerium in promoting both redox- and acid-catalyzed reactions within catalytic systems [61,62].
However, it has been demonstrated that an exponential increase in acidity reduces isomerization reactions while favoring cracking reactions due to a rise in secondary reactions [7,31,67]. This observation is supported by comparing Figure 4b and Figure 7a,b, where the influence of the acid modifier is evident, albeit less pronounced.
In this way, the cracking reaction is mainly influenced by the type of metal used (Figure 4c,d) [60]. It is favored with the use of Mo, as Mo demonstrates a higher distribution across the catalyst’s surface, leading to an increased number of acidic sites [32]. In addition, various characteristics of Mo, such as hydrothermal stability and high-quality oxidation–reduction properties, have been reported, making it a promising metal [73,74].
For T50, the only factor that is relevant independently is the metal (Figure 4f). However, in this case, an optimal presence of Mo is observed (Figure 4e), which could be related to the superior solubility of Mo compared to W, resulting in cases with lower conversion temperatures [75].
These results highlight the importance of carefully selecting acidity modifiers and metals in the design of efficient catalysts. The presence of Ce as an acidity modifier and Mo as a metal seem to be particularly beneficial for isomerization and cracking reactions, respectively. Therefore, an appropriate balance of the two aforementioned factors is suggested for optimal catalytic performance.
The statistical analysis applied to the literature data underscores the critical role of carefully selecting both acidity modifiers and metals in the design of efficient bifunctional catalysts. The results reveal that the presence of Ce as an acidity modifier and Mo as a metal significantly enhances catalytic performance, with Ce proving particularly effective for isomerization reactions and Mo being more beneficial for cracking reactions. This highlights the necessity of achieving an appropriate balance between these two factors to optimize catalytic activity. By applying statistical methods to the existing literature, this study not only validates the importance of these components but also emphasizes how precise adjustments in catalyst composition can lead to improved efficiency in catalytic processes. The findings demonstrate how statistical analysis can provide a clearer understanding of the interplay between different factors and guide the development of more effective catalysts.
On the other hand, the interactions between factors exert a significant impact on the cracking reaction, as illustrated in Figure 5. The support combined with the promoter exhibits influence, resulting in an optimal point in the B-Co relationship (Figure 5a). This is attributed to the microporosity of the support and the acidity of Co, which stands out due to its charge density compared to Ni [42], further emphasizing the importance of excess acidity for cracking. Additionally, the acidity modifier combined with the metal contributes to establishing a balance between acidic and metallic sites. In this case, an optimization is observed in the Ce-Mo relationship, which is attributed to the previously mentioned properties (Figure 5b).
Understanding these relationships and identifying the optimal points on the response surfaces are essential for the development and optimization of catalysts with desired properties. These findings contribute to advancing the understanding of catalytic processes and provide valuable insights for future research and industrial applications.
The statistical analysis of the literature-derived data revealed the importance of understanding the relationships between various catalyst components and their impact on performance. Identifying the optimal points on the response surfaces is crucial for developing and optimizing catalysts with the desired properties. These findings not only enhance our understanding of catalytic processes but also provide valuable insights into how specific factors, such as acidity modifiers and metals, interact to influence catalyst efficiency. By leveraging these insights, future research can build on these findings to refine catalyst design, ultimately leading to more efficient and effective industrial applications. The application of statistical methods to the literature data plays a key role in uncovering these critical relationships, guiding both scientific progress and practical innovations in catalyst development.

3.1.3. Optimization of Bimetallic Systems

The careful selection of appropriate elements and compositions can maximize the catalytic performance and textural properties of a catalyst. It is evident that the interaction between the support, acidity modifiers, and metals plays a crucial role in optimizing catalytic responses. For instance, the formation of micropores is influenced by the choice of support and acidity modifier, while the isomerization reaction largely depends on the type of metal used.
Moreover, factors such as the porosity of the support and the particle sizes of the metal have a significant impact, as these elements individually favor different catalytic responses. However, the comprehensive design of a bifunctional catalyst requires a balanced approach, as the trend in optimal factors may be opposite depending on the desired textural and catalytic properties [42].
On the other hand, the inclusion of promoters such as Ni and the modulation of acidity with elements like Zr or Ce demonstrate a direct influence on catalytic performance, particularly in reactions such as isomerization and cracking. These results highlight the importance of carefully controlling the metallic ratios and the nature of the acidity modifiers to achieve an effective catalyst design [32].
Catalysts based on vermiculite modified with Ce and loaded with Mo (5%), along with Ni as a promoter, offer optimal performance across a variety of reactions. The selection of the acidity modifier and the metal content has a direct impact on catalytic activity. Moreover, the support and its modification play a fundamental role in generating mesopores and micropores, tailoring the textural and chemical properties of the catalyst according to the intended reaction [31,42]. In this regard, Table 1 summarizes the key parameters determined during the optimization of the evaluated catalysts. These parameters are crucial for the optimal design of bifunctional catalysts with bimetallic systems, specifically in relation to their surface area properties and catalytic performance. When metallic salts were used, the results indicated that the most effective support material was vermiculite. This can be attributed to its high surface area and its acidic properties, which promote and enhance catalytic reactions. In addition to the support material, the best acid promoter identified was cerium (Ce), which was associated with its strong acidic characteristics and its ability to increase the overall acidity of the catalytic system, thereby improving performance. In terms of the metals used, molybdenum (Mo) at a 5% concentration was found to be the most effective metal, contributing significantly to the catalytic activity. The choice of molybdenum is consistent with its known ability to facilitate important catalytic processes. Finally, the best promoter identified in this system was nickel (Ni), which further optimized the catalytic reactions. These findings highlight the intricate relationship between support materials, acid promoters, and metal components in the design of efficient bifunctional catalysts, providing valuable insights into how specific factors contribute to the overall performance of the catalytic system.

3.2. Heteropolyacids (HPAs)

Heteropolyacids are inorganic acids notable for their significantly higher acid strength compared to typical solid acids [76]. They are typically composed of a p-block element, a metal, and oxygen [77]. In recent decades, HPAs have garnered significant attention in the industry, particularly in the petroleum sector, due to their low toxicity, high acidity, and strong oxidative capacity. The data used in this analysis were obtained from previously reported results [47,78], which highlight the advantages of implementing HPAs as the metal component in bifunctional catalysts. The selected data correspond to surface area responses, such as BET, and catalytic performance through T50. These literature-derived data were subjected to statistical analysis to evaluate their impact on the textural properties and catalytic activity of the catalysts. The insights gained from this analysis provide a deeper understanding of how HPAs influence catalytic performance and contribute to optimizing catalyst design [47].

3.2.1. Textural Properties with the Incorporation of HPAs

As mentioned earlier, the incorporation of HPAs has become a promising topic in catalysis [79]. It is known that in the solid state, they exhibit a stronger acidity than other conventional acids [80], such as oxides and zeolites [81]. HPAs possess highly useful properties, including their stability, defined structure, proton mobility, and tunable acidity, making them a promising alternative [82]. Therefore, the incorporation of Keggin-type HPAs is carried out due to their properties and extensive research [47,82]. In Figure 6, a graphical representation of the BET response in catalysts after the incorporation of HPMo (phosphomolybdic acid, H3PMo12O40) and HPW (phosphotungstic acid, H3PW12O40) as the metallic component is presented. It shows a high influence of the introduced metal, with HPMo being the optimal choice for this type of catalyst, as evidenced in the Pareto chart (Figure 6a) and the main effects (Figure 6b). This can be attributed both to its stability as a component and to the stability that can be generated by its dispersion on the surface [63,83]. However, the charge level is a crucial factor for the desired properties, as mentioned in bimetallic catalysts [84,85]. Whereby, optimizing the BET surface area and porosity of catalysts is of utmost importance in catalysis because these factors play a direct and critical role in determining the overall performance, efficiency, and stability of catalytic systems. In this way, increasing the surface area, as measured by BET analysis, offers a greater number of accessible sites for reactants to interact with the catalyst. This increased surface area ensures that active sites are more readily available for adsorption, which enhances the catalyst’s efficiency by allowing more reactions to be processed simultaneously. Furthermore, the porosity of a catalyst—referring to the size, distribution, and connectivity of its pores—greatly influences the diffusion of reactants and products throughout the catalyst structure. A well-optimized porous structure facilitates the movement of molecules within the catalyst, ensuring that reactants can reach the active sites more effectively. It also prevents issues such as the agglomeration and sintering of active metals, which can occur under high-temperature reaction conditions [86]. The combination of a high surface area and an ideal porosity distribution not only improves catalytic performance but also helps to extend the catalyst’s lifespan, making it more durable and resistant to deactivation over time. Consequently, optimizing these parameters is essential for maintaining high catalytic activity and ensuring the long-term stability of the system [87].
On the other hand, the effects generated by the different factors (support, acidity modifier, and promoter) in each of the responses are crucial in the synthesis of new catalysts. Together, these factors interact in a complex and synergistic manner, resulting in a wide range of possible catalytic compositions with unique properties and behaviors. Therefore, understanding and optimizing these effects is essential for effectively designing and synthesizing new catalysts.
The application of statistical analysis to the literature-derived data is essential for uncovering the complex interactions between various factors—such as the support, acidity modifier, and promoter—in the synthesis of new catalysts. By systematically analyzing these factors, the statistical approach reveals how they interact in a synergistic manner, leading to a diverse range of catalytic compositions with unique properties and behaviors. Without this analytical framework, the subtle yet crucial effects of these interactions might remain overlooked. Through the statistical evaluation of existing data, we can better understand how these factors influence catalytic performance, which is critical for designing and synthesizing new catalysts with optimized properties. This approach not only enhances our ability to predict catalyst behavior but also provides a data-driven pathway for the targeted development of more efficient catalytic systems.

3.2.2. Catalytic Performance with the Incorporation of HPAs

The catalytic performance is also influenced by the incorporation of HPAs due to the evident acidic characteristic of these compounds, as well as their high stability and selectivity [19,83]. A key feature that can provide insight into the impact on catalytic performance with the incorporation of these catalysts is the conversion temperature, as evidenced in previous studies [88,89]. In Figure 7, the influence of HPMo and HPW on T50 in these catalysts is presented, where it is important to note that lower T50 values result in better performance in hydroconversion. Therefore, the results for this factor are analyzed in reverse. The Pareto diagram (Figure 7a) shows the negative influence of both the support and the metal, thereby proposing vermiculite and HPMo as the optimal factors, respectively. The support is important for the acidity it provides, and primarily for its porous structure, which contributes to improving the metal dispersion [89]. HPMo has a smaller size compared to HPW, which favors the reaction performance due to less pore blocking on the support, despite the formation of large molecular aggregates on the surface [90,91] (Figure 7b).
The statistical analysis of the literature data highlights the positive influence of the support–metal synergy on catalytic performance (Figure 7a). This synergy arises from the formation of new acid sites, which facilitate key reactions such as hydrogenation and dehydrogenation, driven by the metallic component incorporated into the support. The metals not only enhance the catalytic activity but also contribute to the stability of the catalyst, as demonstrated in previous studies [32,53,90]. By applying statistical methods to evaluate these interactions, the response surface plot in Figure 8 was generated, illustrating the optimal performance point for T50 at the HPMo ratio, which indicates the ratio between V and HPMo in the catalytic system; this ratio describes how much vermiculite is used in relation to HPMo in a composite material. This statistical approach allows for a deeper understanding of the support–metal relationship and its direct impact on the efficiency and longevity of the catalyst, offering crucial insights for the design of high-performance catalysts.
Considering the influence of the factors presented in the design of catalysts with the incorporation of HPAs, Table 2 presents the key factors that are critical for the optimal design of bifunctional catalysts, providing a clear overview of the conditions that lead to the best catalytic performance. The results demonstrate that the most effective configuration is achieved when the same factors are repeated in the catalyst formulation: vermiculite as the support material, cerium (Ce) as the acid promoter, and a combination of molybdenum (HPMo) and nickel (Ni) as the metal components. These specific components collectively create an ideal configuration that optimizes both the textural properties—such as surface area and porosity—and the catalytic properties of the material. The selection of vermiculite is particularly important due to its high surface area and favorable acidic characteristics, which provide an excellent base for supporting the active metal species. Cerium (Ce) is chosen for its strong acidic properties, which enhance the catalyst’s activity by promoting the necessary reaction pathways. Molybdenum (HPMo) and nickel (Ni), when used together, not only contribute to the catalytic efficiency but also help in stabilizing the catalytic system, preventing deactivation under reaction conditions. By repeating these same factors, the system maintains a consistent and well-balanced interaction between the metal, support, and promoter, ensuring maximum performance. These findings underscore the importance of selecting and optimizing specific factors to achieve the desired catalytic outcomes.
Heteropolyacids, such as HPMo, stand out for their high catalytic activity, especially in oxidation and hydroconversion processes [47]. When used as the active metal, the system explores the ability to generate additional acidic sites and increase selectivity in specific reactions; its combination with Ce and vermiculite improves the dispersion of HPMo on the support, enhancing its catalytic efficiency. In addition, the use of Ni as a promoter highlights the interest in enhancing the bifunctionality of the catalyst, combining acidic functions (Ce, HPMo) with metallic functions (Ni) to achieve optimal performance [42]. This indicates a strategy designed to balance the textural and catalytic properties of the material.
The synergy between the support, the acidity modifier, and the promoting metal appears to be responsible for the optimal responses reported, such as the high surface area (BET), efficient conversion at moderate temperatures (T50), and overall catalytic performance (optimal).
The assertion that the synergy between the support and the metal is important is strongly supported by experimental evidence demonstrating that the interaction between these components enhances both catalytic activity and stability. Better catalytic performance was observed when using HPA-type precursors, which is evident in Figure 8, where lower T50 temperatures were reported. This indicates that the catalyst achieves 50% conversion at significantly lower temperatures when HPA-type precursors are employed. In contrast, when metal salts are used, as shown in Figure 4f, the T50 temperatures are notably higher, reflecting a less efficient catalytic process. This comparative analysis highlights the significant role that the support–metal interaction plays in optimizing the catalytic activity, as the nature of the precursor directly influences the temperature at which the catalyst operates most effectively. The experimental results clearly demonstrate that when the synergy between the metal and support is carefully tuned, better catalytic performance can be achieved, leading to enhanced efficiency and stability in the reaction process.
Optimization in these systems is achieved more efficiently due to the characteristics of the factors, which clearly favor the reactions being carried out. However, it is always crucial to select the appropriate factor based on the primary needs of the catalyst design, considering the inherent properties of each level.

4. Conclusions

The design of a catalyst is crucial for understanding how different factors interact with each other. This can be achieved through statistical analysis and careful experimentation. In this sense, the statistical analysis allowed the identification of the most relevant factors both in the textural properties—V support and low metal content—and in the catalytic performance—Ce as an acidity modifier, Mo, and HPMo as the metallic function. It also enabled the determination of their individual and combined effects on catalytic activity and textural properties. Additionally, it revealed non-intuitive and complex relationships that might be overlooked using traditional approaches.
Additionally, statistical analysis helps identify potential bottlenecks or limitations in the design of new material, revealing undesirable interactions between factors such as B-10% in textural properties and Zr-W in the cracking reaction, which could reduce efficiency or long-term stability. This allows for targeted improvements in the design to overcome these limitations and ensure optimal catalyst performance.
These findings highlight the importance of carefully considering the factors and their interrelationships when designing and developing catalysts. Understanding these interactions through statistical analysis allows for the optimization of catalytic activity and improves the efficiency of industrial processes related to isomerization and cracking of substances.
Through the conducted study, it is hoped that the methodology and findings will expand to future research, aiming to foster advancements in various material combinations.
The methodology and findings from this study are expected to serve as a foundation for future research, encouraging the exploration of new material combinations and their applications in catalyst design. By systematically applying the approach used in this work, future studies can build on these results, refining and expanding the understanding of how different components interact to optimize catalytic performance. The insights gained not only offer valuable direction for the development of more efficient catalysts but also pave the way for innovations in various fields where catalyst performance is critical, such as energy production, environmental sustainability, and chemical manufacturing. As the methodology evolves and is applied to new systems, it is anticipated that it will lead to the discovery of novel material combinations that offer even greater performance and sustainability benefits. Ultimately, this research sets the stage for continuous improvements and breakthroughs in catalyst development.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/chemistry7030074/s1, The PRISMA 2020 Checklist information.

Author Contributions

Conceptualization, T.M. and J.A.; data curation, T.M.; formal analysis, T.M. and J.A.; funding acquisition, J.A.; investigation, T.M. and J.A.; methodology, T.M.; project administration, J.A.; software, T.M. and J.A.; supervision, J.A.; validation, J.A.; visualization, T.M.; writing—original draft, T.M.; writing—review and editing, T.M., L.S.L.R. and D.E.R. All authors have read and agreed to the published version of the manuscript.

Funding

Vice-Rectorate of Science, Technology, and Research (VCTI), Antonio Nariño University, Bogotá, D.C., Colombia, Internal Call 2023 “Science, Technology, Innovation, and Creation Projects” [Project 2023203].

Data Availability Statement

Data are available upon request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. PRISMA 2020 flow diagram for new systematic reviews which included searches of databases and registers only.
Figure 1. PRISMA 2020 flow diagram for new systematic reviews which included searches of databases and registers only.
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Figure 2. (a) Standardized Pareto chart showing the importance of factors based on BET; (b) main effects for BET; (c) standardized Pareto chart illustrating the importance of factors based on mesopore formation; (d) main effects of mesopores; (e) standardized Pareto chart illustrating the importance of factors based on micropore formation; and (f) main effects of micropores.
Figure 2. (a) Standardized Pareto chart showing the importance of factors based on BET; (b) main effects for BET; (c) standardized Pareto chart illustrating the importance of factors based on mesopore formation; (d) main effects of mesopores; (e) standardized Pareto chart illustrating the importance of factors based on micropore formation; and (f) main effects of micropores.
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Figure 3. (a) Response surface plot for BET versus support and metal amount; (b) response surface plot for BET versus metal and metal amount; (c) response surface plot for micropores versus support and acidity modifier; (d) response surface plot for micropores versus acidity modifier and metal amount; (e) response surface plot for mesopores versus support and acidity modifier; and (f) response surface plot for mesopores versus metal and metal amount.
Figure 3. (a) Response surface plot for BET versus support and metal amount; (b) response surface plot for BET versus metal and metal amount; (c) response surface plot for micropores versus support and acidity modifier; (d) response surface plot for micropores versus acidity modifier and metal amount; (e) response surface plot for mesopores versus support and acidity modifier; and (f) response surface plot for mesopores versus metal and metal amount.
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Figure 4. (a) Standardized Pareto chart recording the importance of factors according to the % of isomerization; (b) main effects for the % of isomerization; (c) standardized Pareto chart illustrating the importance of factors according to the % of cracking; (d) main effects for the % of cracking; (e) standardized Pareto chart illustrating the importance of factors according to T50; and (f) main effects of T50.
Figure 4. (a) Standardized Pareto chart recording the importance of factors according to the % of isomerization; (b) main effects for the % of isomerization; (c) standardized Pareto chart illustrating the importance of factors according to the % of cracking; (d) main effects for the % of cracking; (e) standardized Pareto chart illustrating the importance of factors according to T50; and (f) main effects of T50.
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Figure 5. (a) Response surface plot for % cracking versus the support and the promoter and (b) response surface plot for % cracking versus the metal and the acidity modifier.
Figure 5. (a) Response surface plot for % cracking versus the support and the promoter and (b) response surface plot for % cracking versus the metal and the acidity modifier.
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Figure 6. (a) Standardized Pareto chart showing the importance of factors according to BET with the incorporation of HPAs and (b) the main effects for BET with the incorporation of HPAs.
Figure 6. (a) Standardized Pareto chart showing the importance of factors according to BET with the incorporation of HPAs and (b) the main effects for BET with the incorporation of HPAs.
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Figure 7. (a) Standardized Pareto chart showing the importance of factors according to T50 with the incorporation of HPAs and (b) the main effects for T50 with the incorporation of HPAs.
Figure 7. (a) Standardized Pareto chart showing the importance of factors according to T50 with the incorporation of HPAs and (b) the main effects for T50 with the incorporation of HPAs.
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Figure 8. Response surface plot for T50 versus the support and metal.
Figure 8. Response surface plot for T50 versus the support and metal.
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Table 1. Factors for the optimal design of bifunctional catalysts with bimetallic systems based on their surface area properties and catalytic performance.
Table 1. Factors for the optimal design of bifunctional catalysts with bimetallic systems based on their surface area properties and catalytic performance.
ResponseSupportAcidity ModifierMetalMetal QuantityPromoter
BETVermiculiteZrMo5%Ni
MesoporesVermiculiteCeMo5%Ni
MicroporesBentoniteZrMo5%Ni
IsomerizationVermiculiteCeW5%Ni
CrackingVermiculiteCeMo10%Ni
T50VermiculiteCeMo5%Ni
OptimalVermiculiteCeMo5%Ni
Table 2. Factors for the optimal design of bifunctional catalysts with HPA incorporation based on their surface area properties and catalytic performance.
Table 2. Factors for the optimal design of bifunctional catalysts with HPA incorporation based on their surface area properties and catalytic performance.
ResponseSupportAcidity ModifierMetalPromoter
BETVermiculiteCeHPMoNi
T50VermiculiteCeHPMoNi
OptimalVermiculiteCeHPMoNi
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Martinez, T.; Romero, L.S.L.; Rodriguez, D.E.; Amaya, J. A Review for the Design and Optimization of Catalysts: The Use of Statistics as a Powerful Tool for Literature Analysis. Chemistry 2025, 7, 74. https://doi.org/10.3390/chemistry7030074

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Martinez T, Romero LSL, Rodriguez DE, Amaya J. A Review for the Design and Optimization of Catalysts: The Use of Statistics as a Powerful Tool for Literature Analysis. Chemistry. 2025; 7(3):74. https://doi.org/10.3390/chemistry7030074

Chicago/Turabian Style

Martinez, Tatiana, Laura Stephania Lavado Romero, D. Estefania Rodriguez, and Jahaziel Amaya. 2025. "A Review for the Design and Optimization of Catalysts: The Use of Statistics as a Powerful Tool for Literature Analysis" Chemistry 7, no. 3: 74. https://doi.org/10.3390/chemistry7030074

APA Style

Martinez, T., Romero, L. S. L., Rodriguez, D. E., & Amaya, J. (2025). A Review for the Design and Optimization of Catalysts: The Use of Statistics as a Powerful Tool for Literature Analysis. Chemistry, 7(3), 74. https://doi.org/10.3390/chemistry7030074

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