Chemical Engineering Communications ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/gcec20 Debunking the impact of crystallite/particle size in cobalt-based Fischer-Tropsch synthesis Joshua Gorimbo, Roick Chikati, Phathutshedzo Khangale, Isaac N. Beas, Liberty L. Mguni & Diankanua Nkazi To cite this article: Joshua Gorimbo, Roick Chikati, Phathutshedzo Khangale, Isaac N. Beas, Liberty L. Mguni & Diankanua Nkazi (2024) Debunking the impact of crystallite/particle size in cobalt-based Fischer-Tropsch synthesis, Chemical Engineering Communications, 211:8, 1262-1287, DOI: 10.1080/00986445.2024.2341263 To link to this article: https://doi.org/10.1080/00986445.2024.2341263 © 2024 The Author(s). Published with license by Taylor & Francis Group, LLC Published online: 06 May 2024. Submit your article to this journal Article views: 730 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=gcec20 https://www.tandfonline.com/journals/gcec20?src=pdf https://www.tandfonline.com/action/showCitFormats?doi=10.1080/00986445.2024.2341263 https://doi.org/10.1080/00986445.2024.2341263 https://www.tandfonline.com/action/authorSubmission?journalCode=gcec20&show=instructions&src=pdf https://www.tandfonline.com/action/authorSubmission?journalCode=gcec20&show=instructions&src=pdf https://www.tandfonline.com/doi/mlt/10.1080/00986445.2024.2341263?src=pdf https://www.tandfonline.com/doi/mlt/10.1080/00986445.2024.2341263?src=pdf http://crossmark.crossref.org/dialog/?doi=10.1080/00986445.2024.2341263&domain=pdf&date_stamp=06%20May%202024 http://crossmark.crossref.org/dialog/?doi=10.1080/00986445.2024.2341263&domain=pdf&date_stamp=06%20May%202024 https://www.tandfonline.com/action/journalInformation?journalCode=gcec20 REVIEW ARTICLE Debunking the impact of crystallite/particle size in cobalt-based Fischer-Tropsch synthesis Joshua Gorimboa, Roick Chikatib, Phathutshedzo Khangalea, Isaac N. Beasc, Liberty L. Mgunia, and Diankanua Nkazib aInstitute for the Development of Energy for African Sustainability (IDEAS), College of Science, Engineering and Technology, University of South Africa (UNISA), Johannesburg, South AfricabDepartment of Chemical and Metallurgical Engineering, University of the Witwatersrand, Johannesburg, South Africa; cDepartment of Natural Resources & materials, Botswana Institute for Technology Research and Innovation Gaborone, Botswana, South Africa ABSTRACT This review examines the relationship between the crystallite size of cobalt and the distribu- tion of products produced by Fischer-Tropsch synthesis (FTS). The ideal range for the average cobalt crystallite diameter is between 6 and 8 nm. Deviating from this range, whether by increasing or decreasing the crystallite size, influences the carbon monoxide (CO) turnover fre- quency and the selectivity of CH4, C2-C4, and C5þ. To ensure the development of a consistent catalyst, careful monitoring and adjustment of the morphology, particle size, and metal load- ing on the support particles are essential. For experimental repeatability during FTS applica- tions, it would be ideal if catalyst particles had crystallites of a uniform size. Methods for crystallite characterization and catalyst synthesis were also addressed in detail. The diameter of the cobalt crystallite appears to be a crucial parameter that influences cobalt oxidation, the thermodynamics of cobalt reduction and oxidation are reported. Conducting a Design of Experiment (DOE) with Design Experts on available literature led to determining optimal con- ditions for enhancing the primary target product of FTS—C5þ selectivity. KEYWORDS C5þ selectivity; cobalt oxidation; cobalt reduction; crystallite size Fischer- Tropsch synthesis (FTS); design of experiments Introduction Fischer-Tropsch Synthesis (FTS) is a catalytic pro- cess transforming syngas (carbon monoxide and hydrogen) into valuable hydrocarbons (Deugd et al. 2001). Transition metals like cobalt, iron, or ruthenium serve as catalysts in this reaction. With a growing emphasis on sustainable energy solu- tions globally, FTS plays a significant role in gen- erating clean and renewable hydrocarbons, helping reduce reliance on conventional fossil fuels and addressing environmental concerns (Hu et al. 2012). The Fischer-Tropsch reaction scheme involves a series of reaction steps where syngas react over a suitable catalyst to yield hydrocar- bons. The generalized reaction can be represented as shown in Equation (1). There has been a prolif- eration of studies on the effect of the size of cobalt crystallite in FTS catalytic systems when tailoring product distribution by controlling both particle and crystallite size (Bezemer et al. 2006; Herranz et al. 2009; Rane et al. 2012; Fischer et al. 2014; Fu et al. 2014; Yang et al. 2016; Fang et al. 2020). Different synthesis methods have been employed to yield the required cobalt crystallite size or a specific cobalt diameter on the surface of different supports. For instance, various 10%Co/ITQ-2 zeo- lites model catalysts were synthesized by combin- ing reverse micellar and surface-silylated ITQ-2 delaminated zeolite to yield a Co0 crystallite size distribution in the 5–11 nm range (Prieto et al. 2009). In another study, cobalt crystallite ranging from 2.6 to 16 nm was prepared, using incipient wetness impregnation, by controlling the cobalt loading from 1 to 22 wt% and varying the cobalt precursor used (Co(NO3)2xH2O or Co(CH3CO2)2� 4 H2O) or the solvent used (H2O or EtOH) CONTACT Liberty L. Mguni leemguni@gmail.com; Joshua Gorimbo joshuagorimbo@gmail.com Institute for the Development of Energy for African Sustainability (IDEAS), College of Science, Engineering and Technology, University of South Africa (UNISA), Johannesburg, South Africa. � 2024 The Author(s). Published with license by Taylor & Francis Group, LLC This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. CHEMICAL ENGINEERING COMMUNICATIONS 2024, VOL. 211, NO. 8, 1262–1287 https://doi.org/10.1080/00986445.2024.2341263 http://crossmark.crossref.org/dialog/?doi=10.1080/00986445.2024.2341263&domain=pdf&date_stamp=2024-05-24 http://creativecommons.org/licenses/by-nc-nd/4.0/ http://www.tandfonline.com https://doi.org/10.1080/00986445.2024.2341263 (J. Den Breejen et al. 2009). Borg et al. (2008) pre- pared cobalt catalysts with crystallite sizes of 3 to 18 nm using one-step incipient wetness impregna- tion of alumina supports (c and a-Al2O3), with a variety of cobalt nitrate solutions-such as water, ethylene glycol, diethylene glycol, or their combi- nations. The general observation in all these experiments is the intricacies of preparing a cata- lyst with crystallites of a certain size. 2nH2 þ nCO! −CnH2n −þnH2O (1) where n represents the number of carbon atoms in the hydrocarbon product. The literature shows that different crystallite sizes of the supported cobalt catalyst behave differ- ently during reduction and the Fischer-Tropsch (FT) reaction. Smaller cobalt crystallites (less than 6 nm) are more difficult to reduce than larger crys- tallites (20–70 nm) (Jacobs et al. 2007a). During the FT reaction, cobalt crystallites with a spherical shape and diameter less than 4.4 nm oxidize easily when PH2O/PH2 < 1.5, according to van Steen et al. (2005). This suggests that controlling the size of the crystallite is important. The pore size of the support governs the diameter of the Co3O4 cobalt crystallite, with small crystallites forming in nar- row support pores and large crystallites forming in wide pores (Borg et al. 2007). The effect of support particle size is equally essential in FTS, as it affects reactant conversion selectivity. The smaller the support particle size, the larger the specific surface area of the support. Soykal et al. (2012) conducted experiments to evalu- ate the effect of the support particle sizes of Co/ CeO2 catalysts in ethanol steam reforming. When comparing two support particles of different sizes (mm range and nm range), they observed that par- ticles in the nm range show better ethanol reform- ing activity and deliver a higher ethylene yield. The benefit of being highly resistant to coking was observed with catalysts supported on particles in the nm range, whereas larger ceria particles in the mm range were prone to coke formation. Researchers use a wide range of support par- ticle sizes in FTS systems. For instance, in a study by Tsubaki et al. (2001), they employed silica gel particles ranging from 74 to ±590 mm, with sup- port particles smaller than 149 mm. Den Breejen et al. (2009) utilized carbon nanofibers with a fraction size of 90–150 mm. Fu et al. (2014) opted for carbon nanotubes (CNT) with a particle size of 180 − 425 mm. Saib et al. (2002) used silica with a particle size ranging from 212 to 250 mm. Rane et al. (2012) used utilized alumina with a size range of 53–90 mm mixed with silicon car- bide particles sized 75–150 mm. Because of these variations in particle size, further studies are needed to determine the statistical significance of such wide variations in support size. This analysis will face the challenge of metal- support interaction with different supports, each support having distinct surface properties, acidity levels, and metal-support interactions. Moreover, we also recognize the multifaceted interplay between cobalt particle size and support size. The correlation between these two parameters adds another layer of complexity to the analysis. Table 1 gives examples that demonstrate the effect of cobalt crystallite size on FTS reaction. The choice of support size in FTS systems at industrial scale is a crucial aspect that is also dependent on the type of reaction system employed, whether it’s a fixed-bed, Continuous Stirred-Tank Reactor (CSTR), or microchannel system, plays a pivotal role in determining the optimal support particle size. In fixed-bed sys- tems, larger support particles might be preferred to minimize pressure drop but these large pellet diameters lead to greater diffusion limitations. Brunner et al. (2015b) also showed that the cata- lyst shape affected the amount of catalyst required to achieve a specified conversion. The typical pellet size range is 1 to 4 mm (Pratt 2012; Brunner et al. 2015b; Stameni�c et al. 2018). On the other hand, in CSTRs or microchannel sys- tems, where heat and mass transfer limitations can be more pronounced, using smaller support particles can be advantageous. The smaller par- ticles facilitate improved heat and mass transfer, ensuring efficient contact between the reactants and the catalyst surface (Ratchananusorn 2007). The particle size of catalysts remains a crucial factor in catalysis, even when these particles are aggregated into pellets. Various effects arise from the particle sizes that make up the pellets in catalysis, influencing key aspects of catalyst per- formance. The surface area of catalysts is signifi- cantly impacted by particle size, with smaller CHEMICAL ENGINEERING COMMUNICATIONS 1263 Ta bl e 1. E ffe ct o f co ba lt cr ys ta lli te s iz e on d iff er en t su pp or ts in F TS . Su pp or t ty pe Re ac tio n co nd iti on s, pr es su re , t em pe ra tu re , S V Co ba lt (C o) cr ys ta lli te s iz e Ch ar ac te ris at io n m et ho d us ed t o m ea su re cr ys ta lli te s iz e Ef fe ct s in F TS Re fe re nc es Si lic a 23 9. 83 � C, H 2/ CO ¼ 2) . 1 ba r 1. 4– 10 .5 nm TE M Th e w at er v ap ou r ea si ly o xi di se s Sm al le r Co p ar tic le s (1 .4 – 2. 5 nm ) du rin g FT S. A 1. 4- 2. 5 nm p ar tic le s iz e re su lts in lo w er T O F an d hi gh er se le ct iv ity t o CH 4 La rg er C o pa rt ic le s in t he 3 .5 –1 0. 5 nm r an ge s ho w n o ox id at io n du rin g FT S. A 3. 5- 10 .5 p ar tic le s iz e do es n ot a ffe ct T O F an d CH 4 se le ct iv ity . (Z . J . W an g et a l. 20 12 ) Si lic a 25 0 � C, H 2/ CO ¼ 2: 1) 5 ba r 3- 11 nm TE M Th e m ax im um a ct iv ity d is pl ay ed f or C o pa rt ic le s of 1 0– 11 nm in s iz e. CO 2 hy dr og en at io n in cr ea se s w ith a n in cr ea se in C o cr ys ta lli te si ze f ro m 3 t o 11 nm . C5 þ m ax im um e xt en t at 1 1 nm . (M el ae t et a l. 20 14 ) Al um in a 21 0o C, H 2/ CO ¼ 2. 1 20 ba r PS ¼ 53 –9 0 l m 2– 14 nm XR D , H 2- ch em is or pt io n W he n Co p ar tic le s iz e in cr ea se s, C 5þ se le ct iv ity is m ax im is ed at a c ry st al lit e si ze o f 8– 9 nm . W ith la rg er p ar tic le s, se le ct iv ity t o C 5 þ de cr ea se s be fo re a pp ro ac hi ng a c on st an t va lu e. (R an e et a l. 20 12 b) Al um in a 19 0 � C, H 2/ CO ¼ 2, 9. 9 ba r PS ¼ 15 0– 20 0 l m 2. 3- 11 .7 nm XR D , T EM Th e se le ct iv ity o f CH 4 va rie s in ve rs el y w ith a d ec re as e in cr ys ta lli te s iz e an d C 5 þ se le ct iv ity . (F is ch er e t al . 2 01 3) Al um in a 21 0o C, 2 0 ba r, an d H 2/ CO ¼ 2. 1 PS ¼ 53 a nd 9 0 l m 3 to 1 8 nm XR D , T EM , X PS 7– 8 nm C o pa rt ic le s yi el de d m ax im um C 5þ se le ct iv ity . C 5 þ se le ct iv ity is c on st an t fo r a cr ys ta lli te s iz e la rg er t ha n 9– 10 nm . (B or g et a l. 20 08 b) Si lic a de la m in at ed IT Q -2 z eo lit e. 22 0o C, H 2/ CO ¼ 2 20 ba r PS ¼ 0. 25 –0 .4 2 m m 5. 6– 14 1 nm XR D , H 2- ch em is or pt io n an d (H R) TE M Th e ac tiv at io n en er gi es C o 3 O 4 re du ct io n to C oO a nd C o cr ys ta lli te s iz e de pe nd en t, fo r pa rt ic le s ra ng in g fr om 5 .6 to 14 1 nm . (P rie to e t al . 2 00 9c ) Ca rb on n an of ib er s 21 0, 2 20 a nd 2 50 o C, H 2/ CO ¼ 2) .1 a nd 3 5 ba r PS ¼ 0. 5- 1. 0 m m an d 15 0- 21 2 l m 2. 6- 27 nm (T EM ), EX AF S, X PS an d H 2 ch em is or pt io n FT S is n ot in flu en ce d by C o cr ys ta lli te s iz e > 6 nm a t 1 ba r an d > 8 nm a t 35 ba r. Bo th T O F an d C 5 þ se le ct iv ity d ec re as ed w he n th e cr ys ta lli te si ze w as d ec re as ed f ro m 1 6 to 2 .6 nm . (G . L ee nd er t Be ze m er et a l. 20 06 ) Ca rb on n an of ib er 22 0 � C, H 2/ CO ¼ 2) .1 an d 35 ba r PS ¼ 90 -1 50 l m 2. 6- 16 nm TE M , H 2- ch em is or pt io n Co p ar tic le s < 6 nm r es ul t in d ec re as ed T O F an d in cr ea se d CH 4 se le ct iv ity . (J . P . D en B re ej en et a l. 20 09 ) Ac tiv at ed c ar bo n an d on C N Ts 23 0o C, H 2/ CO ¼ 2, 2 0 ba r PS ¼ 18 0 − 42 5 l m 2. 5 – 20 .3 XR D , T EM Co c ry st al lit e up t o 7 nm d is pl ay ed h ig he r TO F an d C 5 þ se le ct iv ity . N o ef fe ct w as o bs er ve d fo r a Co c ry st al lit e si ze g re at er t ha n 7 nm o n TO F an d C 5 þ se le ct iv ity . (F u et a l. 20 14 b) In fo rm at io n no t gi ve n. P S ¼ pa rt ic le s iz e. 1264 J. GORIMBO ET AL. particles generally providing a larger surface area per unit mass. This heightened surface area enhances catalytic activity by exposing more active sites for reactions to occur (Garc�ıa-S�anchez and Baldovino-Medrano, 2023). Even when assembled into pellets, the overall surface area is influenced by the arrangement and packing of particles within the pellet. Particle size also affects diffusion rates within the catalyst pellet. Smaller particles may mitigate diffusion limitations, facilitating easier access of reactants to active sites. However, the packing arrangement in the pellet can alter diffusion pathways, influencing overall diffusion rates (Thiele, 1939; Mitchell et al. 2013). The catalytic activity is closely linked to the size of active sites on the catalyst surface. Smaller particles may expose a higher proportion of active sites, poten- tially leading to increased catalytic activity (Zhou et al. 2010; Garc�ıa-S�anchez and Baldovino- Medrano, 2023). The arrangement of particles within the pellet, however, can impact the acces- sibility of these active sites to reactants. In some instances, smaller particles may result in higher mass transfer limitations due to increased fluid flow resistance. The assembly of these particles into pellets affects the porosity and permeability of the catalyst bed, influencing mass transfer lim- itations (Satterfield et al. 1969; Yang et al. 2010). The size of catalyst particles can influence the selectivity of catalytic reactions. Different particle sizes expose varying crystal facets or surface structures, impacting the selectivity for specific reaction pathways (Wang and Lu 2020). The particle sizes constituting catalyst pellets in catalysis have multifaceted effects on overall catalyst performance. Achieving the desired cata- lytic performance involves a delicate balance between maximizing active surface area, ensuring efficient mass transfer, and maintaining stability within the catalyst bed. The design and optimiza- tion of catalysts take into account these factors to meet specific catalytic requirements. The morphology and metal loading on support particles are other critical parameters for design- ing and developing catalysts for the FTS. The FTS process converts synthesis gas into liquid fuels and chemicals. These parameters play a cru- cial role in determining the activity, selectivity, stability, and lifetime of the catalysts. They also significantly impact the product distribution and quality of the FTS outcomes. Therefore, the opti- mization of these parameters is essential for the successful implementation of the FTS process (Parker et al. 2019). The morphology of the catalyst refers to the shape and structure of the metal particles and the support. The morphology can influence the sur- face area, the dispersion, the coordination num- ber, the electronic structure, and the exposure of different facets of the metal particles, which in turn affect the adsorption, activation, and dissoci- ation of the reactants, the chain growth and ter- mination of the products, and the rate and extent of the secondary reactions, such as cracking, iso- merization, hydrogenation, and water-gas shift (Modekwe et al. 2021). The metal loading on the support refers to the amount or the weight per- centage of the metal on the support. The metal loading can influence the dispersion, the reduci- bility, the stability, and the lifetime of the cata- lyst. Generally, higher metal loading leads to higher dispersion and reducibility, but lower sta- bility and lifetime. Lower metal loading leads to lower dispersion and reducibility, but higher sta- bility and lifetime. Therefore, carefully monitor- ing and adjusting the morphology, particle size, and metal loading on support particles for con- sistent catalyst development is crucial for achiev- ing the desired FTS outcomes, such as high yield and quality of liquid fuels, low yield of methane and carbon dioxide, and optimal catalyst per- formance and durability. Finally, the thermodynamics of cobalt catalyst reduction in FTS holds significant importance for several reasons. Firstly, the reduction process is a crucial step in activating the cobalt catalyst, transforming it from oxidized states to metallic cobalt. This activated state is what is active in FTS. The specific thermodynamic conditions dur- ing reduction, including temperature and pres- sure, impact the efficiency of the catalyst activation. Understanding and optimizing these conditions are vital for achieving the desired catalytic activity which then directs a certain product selectivity and stability of the cobalt cata- lyst. Therefore, a detailed understanding of the thermodynamics of cobalt catalyst reduction is CHEMICAL ENGINEERING COMMUNICATIONS 1265 instrumental in designing and improving catalytic systems for efficient and economically viable Fischer-Tropsch processes. In summary, understanding the impact of morphology, catalyst loading, crystallite and par- ticle size in cobalt-based Fisher-Tropsch synthesis is crucial for optimizing catalytic performance. It allows for the tailoring of catalysts to enhance specific reaction pathways, ultimately improving product selectivity. By investigating size-depend- ent phenomena, researchers can gain insight into the intricate interplay between surface area, active sites, and catalytic activity, paving the way for more efficient and sustainable processes. Ma and Dalai (2021) recently reported a review on the effect of structure and particle size with an emphasis on TOF for Co, Fe and Ru. The current work reviewed the effect of crystallite size on car- bon monoxide (CO) turnover frequency and selectivity of CH4, C2-C4 and C5þ. This research aims to understand the effect of cobalt crystallite size on performance and selectiv- ity in the FTS process, which converts synthesis gas (CO and H2) into liquid fuels and chemicals. The size of the cobalt crystallites is a significant factor affecting the catalyst’s activity, stability, and selectivity, along with the rate and extent of sec- ondary reactions such as cracking, isomerization, hydrogenation, and water-gas shift. By compre- hending how the size of cobalt crystallites influen- ces product distribution, the study offers insights for future catalyst design and the development of more efficient and selective catalysts for FTS. This, in turn, can improve the economic and environ- mental viability of the process. The work further looked at the thermodynamics of cobalt catalyst reduction and characterization techniques for determining crystallite size. Understanding the thermodynamics of cobalt catalyst reduction is crucial for optimizing catalyst activation, improv- ing energy efficiency in FTS and contributing to the fundamental understanding of the process. Influence of cobalt particle size in FTS Several catalyst preparation methods are used for FTS reactions. The different catalysts are made up of active components (usually transition met- als), which are deposited on inert supports, such as titania, silica, alumina, and carbon. These sup- ports improve certain properties, such as the sta- bility of the active component and its dispersion. Precipitation and deposition impregnation are the main methods used to prepare the catalyst (Bianchi et al. 2001), though other methods exist, specifically for the FTS reaction (Bianchi et al. 2001; Tsubaki et al. 2001; Brunner et al. 2015a; Deraz 2018). The chosen synthesis method and cobalt loading affects catalyst morphology, i.e., crystallite size, pore size distribution, pore vol- ume, surface area and promoter distribution (Deraz 2018), which eventually affects product distribution (Zhai et al. 2013; Ghogia et al. 2021). A review done by Deraz (2018) on the compara- tive jurisprudence of catalyst preparation meth- ods focused on impregnation and precipitation methods and clarified the advantages and disad- vantages of each technique. The goals of a study should define the selection of the catalyst prepar- ation method. The impregnation method is often chosen because of its simplicity: the procedure is quicker and cheaper than some other methods and the catalyst properties and configuration can be tailored. Figure 1 presents the effect of cobalt crystallite size on methane selectivity. The figure suggests that CH4 selectivity is favorable for a cobalt crys- tallite size less than 6 nm and there is a negligible effect on larger crystallite sizes. The methane selectivity shown in Figure 1 differs in magni- tude, but more importantly, the significant aspect is the pattern displayed and the flattening of the curve after approximately 8 nm. The tabulated lit- erature results (Table 1) show that crystallite size affects catalyst activity and product selectivity. Larger cobalt particles (>7 nm) favor higher TOF and C5þ selectivity. For cobalt crystallites �7 nm, CH4 selectivity is suppressed (Fu et al. 2014). In a study carried out by Wang et al. (2012) using steady-state isotopic transient kinetic measure- ments, it was reported that reduced TOF for Co crystallite <6 nm is attributable to lower intrinsic activity at the small terraces and to the blocking of edge/corner sites (to a significant extent). The proclivity of small Co crystallite (<6 nm) to favor high production of CH4 under FTS conditions is mainly due to higher coverage of the surface by hydrogen (Den Breejen et al. 2009). It should be 1266 J. GORIMBO ET AL. noted that turnover rates in FTS are not affected by Co crystallite dispersion and the type of sup- port used over the accessible dispersion range under typical FTS conditions (Iglesia 1997a). The activity of the FTS catalyst and its selectiv- ity to desirable C5þ hydrocarbons are important production design criteria to consider. Figure 2 shows the relationship between cobalt crystallite size and C5þ selectivity. Borg et al. (2008) con- ducted a series of studies on Co supported on c-Al2O3 and observed that C5þ selectivity increases sharply with an increase in crystallite size up to about 7 nm (Figure 2), with the opti- mum crystallite size being about 8 nm. The figure also shows a negligible increase in selectivity for crystallites larger than 9–10 nm (Borg et al. 2008). A correlation between CH4 and C5þ selectivity can be deduced from the available literature. Thus, a minimum CH4 selectivity and maximum C5þ selectivity are recorded with larger cobalt crystallites, while the opposite is true for smaller sizes. A similar pattern is observed during FTS in a packed bed: when indigenous water accumu- lates, C5þ selectivity increases, whereas CH4 selectivity decreases (Iglesia 1997a). A study done by Bezemer et al. (2006) supports the view that turnover frequency (TOF) and CH4 selectivity remain unchanged for catalysts with a cobalt crys- tallite size greater than 6.0 nm, while a crystallite size of less than 6 nm results in variations in both selectivity and activity. It can, therefore be con- cluded that the ideal cobalt crystallite size should be greater than 6 nm. A study done by Bezemer et al. (2006) revealed that the TOF for hydrogen- ation of CO was not affected by a cobalt crystallite size greater than 6 nm at 1 bar and greater than 8 nm at 35 bar. Several researchers agree that TOF, a surface-specific activity, decreases with a decrease in cobalt crystallite size from about 1 to 7 nm (Den Breejen et al. 2009; Fu et al. 2014). Factors like the type of support used and metal dispersion have been reported to not have an effect on the turnover rate; hence, the activity of Figure 1. The increase in cobalt crystallite size on CH4 selectivity: 220 �C, H2/CO ¼ 2, 1 bar (Bezemer et al. 2006); 210 �C, H2/CO ¼ 2, 1 bar (Den Breejen et al. 2009); 220 �C, H2/CO ¼ 2, 1 bar (Mart�ınez et al. 2003); 239 �C, H2/CO ¼ 2, 1 bar H2/CO ¼ 2, P¼ 2O bar, 210 �C (Zeng et al. 2013); 220 �C, H2/CO ¼ 2, 20 bars (Prieto et al. 2009); 240 �C, H2/CO ¼ 2, P¼ 2O bar (Wang et al. 2021) [data used to generate this graph was obtained from the references given]. Figure 2. Depiction of the relationship between C5þ selectivity and cobalt crystallite size. Source: Reproduced from (Borg et al. 2008) with permission from [Elsevier]. Copyright [2008]. CHEMICAL ENGINEERING COMMUNICATIONS 1267 the catalyst ought to be proportionate to the num- ber of active sites (Mart�ınez et al. 2003). Co3O4 crystallite size is influenced significantly by the pore size of the support. A larger pore favors the formation of larger Co3O4 crystallites. A study by Song and Li (2006) indicated that cat- alysts with a 6–10 nm pore size produce a moder- ate Co3O4 crystallite diameter, consequently yielding the required selectivity. In a study done by Liu et al. (2007), increasing the pore size of the FTS catalyst from 2.9 to 12.6 nm had a posi- tive impact: catalytic activity, C5þ, C12–C18, and C18þ selectivity increased, and an antagonistic effect on CH4 selectivity was observed. The higher a values obtained in a study by Rytter et al. (2018) were attributed to larger pore size and larger cobalt crystallites, which positively affect CO activation. Therefore, pore size is gen- erally a selectivity director. The pore size of the support may control the size of the Co3O4 cobalt crystallite, as smaller crystallites form in narrow pores, whereas larger crystallites form in larger pores (Borg et al. 2007). The data used to construct Figures 3 to 5 were extracted from various literature sources (Saib et al. 2002; Mart�ınez et al. 2003; Song and Li 2006; Lira et al. 2008; Witoon et al. 2011). These sources provided the experimental conditions, catalyst type, catalyst analysis results and product distribution in terms of C1, C2-C4, and C5 select- ivity. FT data for DOE was based on prior research on cobalt-impregnated silica support structures done by a group of academics, as reported in the available literature. Using the response surface approach, the effects of numer- ous independent and dependent variables were investigated. Design–Expert 13 was used to gen- erate the 3-D plots. In terms of the data given, smaller cobalt crystallites of less than 12 nm proved to be more selective to methane. Increasing the crystallite size resulted in a decrease in methane selectivity. This observation concurs with the details provided in Table 1. Increasing pressure has a negligible effect on the conditions given. C2–C4 selectivity decreases as crystallite size increases from 3 nm to about 15.8 nm, then grad- ually increases until it reaches 26 nm, see Figure 4. Smaller crystallites of 3 to 7.6 and larger crystallites of 21.4 to 26 are more selective to C2- C4 hydrocarbons. The data for this plot was extracted from various sources (Saib et al. 2002; Mart�ınez et al. 2003; Song and Li 2006; Lira et al. 2008; Witoon et al. 2011). The effect of pressure and crystallite size pro- duced a dome-shaped distribution, contrary to Figure 3. Three-dimensional (3-D) plot showing the effect of crystallite size and pressure on C1 selectivity (%). the 3-D plot was generated using design-expert 13. The red circles are data points above the predicted values, respectively. Figure 4. 3-D plot showing the effect of crystallite size and pressure on C2–C4 selectivity (%). The 3-D plot was generated using Design-Expert 13. The red and pink circles are data points above and below the predicted values, respectively. 1268 J. GORIMBO ET AL. the pattern observed for C2-C4 selectivity (on a carbon basis). Increasing pressure increased C5þ to about 16 bar, then gradually decreasing until it reached 20 bar. C5þ selectivity increased with an increase in crystallite size until 15.2 nm; it then decreased until it reached 26 nm. Analysis of the literature yielded Figures 3 to 5 (Saib et al. 2002; Mart�ınez et al. 2003; Song and Li 2006; Lira et al. 2008; Witoon et al. 2011). Cobalt crystallite size appears to be an important factor that influences product distribution. This novel approach pro- vides insight into selectivity being dependent on pressure and crystallite size in cobalt-cata- lyzed FTS. In summary, maintaining the cobalt crystallite diameter within the specified range is crucial for optimizing FTS outcomes. This range ensures an optimal balance between catalytic activity, select- ivity toward desired hydrocarbons, and resistance to deactivation mechanisms (to be discussed in the following section). Deviations from this range may lead to undesirable changes in CO turnover frequency and hydrocarbon selectivity, affecting the overall efficiency and performance of the Fischer-Tropsch synthesis process. Moreover, using unnecessarily large particle sizes also has these disadvantages (1) reduced active surface area since active sites for catalytic reactions are typically located on the surface of the catalyst; (2) diffusion limitations since large particles may tend to block the pores of the support material, and (3) large particles have a cost implication. Proneness of cobalt catalyst to oxidation Cobalt catalyst oxidation has been studied exten- sively as a deactivation mode in FTS (Van Berge et al. 2000; Lira et al. 2008; Rytter and Holmen 2015; C. Kliewer et al. 2019; Choudhury et al. 2020; Okoye-Chine et al. 2023). The literature analysis suggests that, in general, the catalytic properties of small cobalt crystallite differ from that of larger ones in terms of activity, selectivity and deactivation. Table 1 shows that smaller Co particles are easily oxidized by the indigenous water vapor during FTS. A study done by Wang et al. (2012) concluded that with smaller Co crys- tallite (1.4–2.5 nm), the cobalt metal was easily oxidized by the indigenous water vapor, which led to reduced TOF and increased CH4 selectiv- ity. Wang et al. (2012) also observed that larger Co crystallites of 3.5–10.5 nm are immune to oxi- dation during FTS and do not affect TOF and CH4 selectivity. Thermodynamic analysis done by van Steen et al. (2005) showed that cobalt crystallites with a spherical shape and measuring < 4.4 nm in diam- eter are prone to oxidation during FTS (PH2O/ PH2 < 1.5, T¼ 493 K). The same qualitative observation was recorded by Iglesia (1997a), who reported rapid deactivation by oxidation during FTS of cobalt metal crystallite with a diameter of less than 5–6 nm. A high PH2O/PH2 ratio is needed to re-oxidize bulk cobalt metal, but these ratios are not encountered under normal FTS conditions (Iglesia 1997b; Hilmen et al. 1999; van Steen et al. 2005). High PH2O/PH2 ratios are pos- sible at high per-pass conversions but the ranges of PH2O/PH2 ratios that may cause oxidation are not experienced in normal FT. The ratios of PH2O/PH2 experienced in normal FTS and PH2O/ PH2 ratios required for oxidation are 3 and 123, respectively (van Steen et al. 2005). The thermo- dynamic feasibility of oxidizing small cobalt crys- tallites or forming an oxide shell may occur under conditions where the oxidation of bulk metallic cobalt is not feasible. This phenomenon is associated with the influence of surface energy on the overall process, which is lower for bulk Figure 5. 3-D plot showing the effect of crystallite size and pressure on C5þ selectivity (%). The 3-D plot was generated using Design-Expert 13. CHEMICAL ENGINEERING COMMUNICATIONS 1269 metal oxides compared to their corresponding bulk metals. Consequently, it is anticipated that nanosized crystals exhibit lower oxidation resist- ance compared to bulk crystalline materials. Cobalt crystallite size significantly affects acti- vation energy in stepwise reduction: Co3O4 ! CoO ! Co0 [8] (Prieto et al. 2009). Thermodynamically, the oxidation of CoO by water during FTS is not favored as evidenced by a positive change in free energy (DG), indicating a non-spontaneous reaction, this is due to the weak reduction ability of Co0 and the relatively feeble oxidizing potential of water. However, observations indicate that under a very low PH2/ PH2O ratio, where the partial pressure of hydro- gen (PH2) is much lower than the partial pressure of water vapor (PH2O) in the gas phase, oxidation occurs (Van Berge et al. 2000). These conditions create circumstances in which the chemical potential of hydrogen is low, and the chemical potential of water is high. As a result, the oxida- tion of CoO by water moves toward equilibrium, despite being thermodynamically unfavorable. Cobalt oxidation by H2O and CO2 is governed by the PH2/PH2O and PCO/PCO2 ratios in the reactor. Cobalt oxidation follows Equation (2) below. Co sð Þ þ 1 2 O2 gð Þ⇔ CoO sð Þ (2) From Equation (2), the minimum oxygen par- tial pressure required to effect oxidation can be given by Equation (3): Log PO2 − log KðTÞ (3) For the oxidation of carbon monoxide (CO), it would be (Equation (4)): CO gð Þ þ 1 2 O2 gð Þ⇔ CO2 gð Þ (4) The O2 partial pressure can be given by Equation (5): Log PO2 ¼ 2log PCO2=PCOð Þ − log Kco (5) Equation (6) can be used for the oxidation of hydrogen: H2 gð Þ þ 1 2 O2 gð Þ⇔ H2O gð Þ (6) The oxygen partial pressure can be given by Equation (7): Log PO2 ¼ 2log PH2=PH2Oð Þ þ log KH2 (7) The oxygen partial pressure corresponds to PH2/PH2O and PCO2/PCO ratios under certain con- ditions. The plot of O2 partial pressure versus temperature with different partial pressures of H2, H2O, CO and CO2 can be used to predict the stability of varying cobalt phases. The parameters in Table 2 indicate that all the given reactions are thermodynamically feasible in the temperature ranges given. According to the three equations, the oxygen partial pressure can be related to PH2/PH2O and PCO2/PCO in the reactor at any point during the reaction. From the theoretical calculations of the thermodynamic properties, the oxidation of cobalt catalysts at dif- ferent PH2/PH2O and PCO2/PCO ratios were plot- ted—see Figure 6 (The PH2/PH2O, PCO2/PCO ratios correspond to a particular partial pressure of O2.). The thermodynamic calculations for Co0 oxidation to Co3O4 are not presented, as they are approximately four orders of magnitude higher than for Co0 to CoO. The theoretical calculations show that it is impossible to oxidize a Co-based catalyst under normal FT conditions, as the H2O/H2 ratios are usually less than 10. This concurs with van Steen et al. (2005) calculations.This observation does not agree with many FT practitioners, who recorded catalyst oxidation after characterizing the spent catalyst. For our theoretical calculations to agree with the experimental data, the effects of crystallite size (that changes the surface energy of particles) on thermodynamic properties must be considered. (Here, crystallite size refers to the size of the cobalt metal clusters on the support surface.) Table 2. Variation of thermodynamic parameters from 100 to 400 �C. Thermodynamic parameters (range 100–400oC) Equation Log (Keq) DH (kJ) DG (kJ) Co(s) þ 1 2 O2(g) ¼ CoO(s) 58.34 to 28.94 −473.83 to -468.00 −416.70 to -372.85 H2(g) þ 1 2 O2(g) ¼ H2O(g) 63.04 to 32.64 −485.13 to -490.55 −450.33 to -420.54 CO(g) þ 1 2 O2(g) ¼ CO2(g) 70.18 to 34.80 −566.70 to -567.05 −501.30 to -448.40 1270 J. GORIMBO ET AL. As per Table 1, activity and selectivity can change with changes in crystallite size. Oxidation of cobalt only happens with substantial PH2O/PH2 ratios, and these ratios are not encountered under normal FTS conditions as stated earlier. The lit- erature analysis done by Van de Loosdrecht et al. [39] revealed that, with FTS, PH2 ranges from 6.5 to 9.2 bar, and a PH2O between 4.6 and 7.6 bar, which corresponds to a PH2O/PH2 ratio between 0.5 and 1.2. Cobalt particles of less than 4–5 nm are oxidized if the H2O/H2 ratio is 1–1.5 (van Steen et al. 2005). Schanke et al. (1995) observed no oxidation on 15 and 25 nm particles at a PH2O/ PH2 of 0.33. Hilmen et al. (1999) experimented with 10 and 16 nm particles using a PH2O/PH2 ratio of 10 and observed no Co oxidation. Bian et al. (2003) studied larger Co-crystallites (10 and 29 nm) using a high PH2O/PH2 of 6.11 and observed no oxidation. A cobalt particle smaller than 4 nm oxidized at a PH2O/PH2 ratio of 0.74 (Iglesia 1997a). A study done by Jacobs et al. (2003) on a 6 nm Co particle showed that a PH2O/ PH2 ratio of 0.56 resulted in no oxidation, whereas a PH2O/PH2 of 0.60 resulted in oxidation. Therefore, cobalt oxidation of crystallites less than 6 nm can be avoided by ensuring the correct com- bination of reactor partial pressures of PH2O and PH2. A study done by Lu (2011) on FT product dis- tribution (using 10%C0/TiO2) resulted in differ- ent PH2O/PH2 ratios when using a continuously stirred tank reactor (CSTR) and tubular fixed-bed reactor (TFBR) at H2/CO ¼ 2 and 20 bar and dif- ferent pressure levels. In the same study, it was shown that the PH2O/PH2 ratio increases with temperature. With a TFBR, the ratios are signifi- cantly higher than with a CSTR. When using a CSTR, the proportions are comparatively lower and tend to approach an asymptote as the tem- perature increases toward 240 �C. The distribu- tion of FT products is influenced by several parameters, including the type of reactor employed thus affecting the PH2O/PH2 ratio. The impact of temperature on the FT product distri- bution may vary between the Fixed Bed Reactor (FBR) and the Continuous Stirred Tank Reactor (CSTR) due to the inherent characteristics of these reactors. The Anderson-Schulz-Flory (ASF) model suggests that the distribution of FT prod- ucts conforms to a geometric distribution, with a chain growth probability factor (a) that declines with an increase in temperature. As a result, higher temperatures tend to promote the forma- tion of lighter hydrocarbons, such as methane and ethane, while lower temperatures favor the production of heavier hydrocarbons, such as waxes and diesel. The model for the ASF synthe- sis serves as an elementary representation of the FT synthesis. It omits the secondary reactions that occur within the reactor, such as cracking, isomerization, hydrogenation, and water-gas shift. These reactions can significantly impact the FT product distribution, causing it to differ from the ideal ASF distribution. For instance, the process Figure 6. Theoretical study of the effect of PH2O/PH2 and PCO2/PCO on cobalt catalyst oxidation. CHEMICAL ENGINEERING COMMUNICATIONS 1271 of cracking can break down long-chain hydrocar- bons into shorter ones, isomerization can alter the structure of the hydrocarbons from linear to branched, hydrogenation can decrease the olefin content, and water-gas shift can consume CO and H2O while producing CO2 and H2. The extent of secondary reactions in chemical reactors is influenced by the reactor type and operating conditions. FBRs experience tempera- ture variations influenced by factors such as heat transfer, reaction kinetics, and reactant concen- tration. This enhances the rate of secondary reac- tions, such as cracking and isomerization, leading to a more diverse and complex distribution of products. Conversely, in CSTRs, catalyst particles are well-mixed, resulting in a more uniform tem- perature. As a result, secondary reactions occur at a lower rate, yielding a more predictable and consistent product distribution. The CSTR exhib- its little variation in pH2O/PH2 with an increase in reaction temperature, and this could be attrib- uted to the fact that the CSTR has a lower rate of secondary reactions than the FBR, making it less sensitive to temperature changes. The effect of cobalt–support interaction In studying the effect of cobalt crystallite, Bezemer et al. (2006) opined that these types of experiments are better carried out using inert materials such as graphitic or carbon-based sup- ports. Oxidic supports, silica and alumina tend to form mixed oxides that are not reduceable - such as cobalt aluminate or cobalt silicate - which may affect the observations (Van Berge et al. 2000; Li et al. 2002; Wolf et al. 2021). The strength of cobalt–support interaction has been found to increase in the order SiO2 < Al2O3 < TiO2 (Jacobs et al. 2007; James and Maity 2016; Kliewer et al. 2019; Petersen et al. 2019; Yan et al. 2021). Deductions from the literature indi- cate that strong Co–support interaction of Al2O3, and particularly TiO2, results in increased disper- sion and there is a tendency to form cobalt alu- minates and titanates, respectively. This affects the density of the Co0 surface sites. Comparatively speaking, the interaction of cobalt on silica support is weaker, which is ideal for complete cobalt oxide reducibility. However, there is a problem with the agglomeration of cobalt crystallites during catalyst preparation, which also happens at high temperatures during calcination (Mart�ınez et al. 2003). This sintering leads to low Co crystallite dispersion. Crystallite size measurement techniques The characterization of crystallites involves a range of techniques for determining their size, morphology, and structure. Among the most commonly used methods, X-ray diffraction (XRD) allows for the analysis of crystal structure and the determination of lattice parameters, as well as peak broadening, which can provide indi- cations of crystallite size. Transmission electron microscopy (TEM), on the other hand, provides high-resolution imaging of individual crystallites, revealing information about their shape, size, and defects. Scanning electron microscopy (SEM) is a useful method for obtaining surface morpho- logical information. In addition, techniques such as atomic force microscopy (AFM) and dynamic light scattering (DLS) can be employed to study the size and shape of crystallites. Transmission electron microscopy (TEM), X- ray diffraction (XRD) and H2-chemisorption are often employed to measure crystallite size before running FTS. These analytical techniques often show consistency with crystallite sizes (Miller et al. 1993; Schanke et al. 1995; Jacobs et al. 2003; Bezemer et al. 2006; Den Breejen et al. 2009; Saib et al. 2010) with X-ray absorption studies giving results that are within the experi- mental error. Powder XRD has been reported to measure millions of crystals and provide the pre- cise size distribution of nanomaterials (Chauhan and Chauhan 2014). The terms particle size and crystallite size are often used interchangeably to mean the same thing, but these refer to two dis- tinct properties of a material. Particles comprise of several small crystallites, and nanomaterial properties depend and comprise several small crystallites, and nanomaterial properties depend on crystallite size, not particle size (Chauhan and Chauhan 2014). Due to the principle of measurement, crystal- lite size calculated with XRD is always smaller than when using the chemisorption method. This 1272 J. GORIMBO ET AL. is expected because the XRD measurements also record dislocations in the crystal structure that are not registered by chemisorption (Geyer et al. 2012). The crystallite size given by TEM analysis agrees with the size derived from XRD (Rozita et al. 2010). Usually, in a minimal particle size regime (nanometer scale), there is close agree- ment between the TEM and XRD measurements. However, for larger particle size regimes, TEM tends to provide a comparatively larger average particle size than XRD. The discrepancy is attrib- uted to the size that is determined by XRD corre- lating with the average of the smallest undistorted regions in the material. In contrast, TEM measurements relate to scanned areas sepa- rated by more-or-less sharp contours in the micrograph (Rozita et al. 2010). Characterization of cobalt crystallite size In FTS, precision catalyst development with defined crystallite size is an area of interest that researchers continue to look at. From the previ- ous sections, it is clear that knowledge of the crystallite size distribution is crucial for interpret- ing the experimental results of FTS. Various syn- thetic pathways have been adopted for the preparation of catalysts with good uniform dis- persion and controlled crystallite size. Examples include incipient wetness impregnation (Xiong et al. 2005; Song and Li 2006; Lira et al. 2008; Fu et al. 2014; Gavrilovi�c et al. 2018; Rytter et al. 2018); the sol-gel technique (Okabe et al. 2004; Liu et al. 2010; Bykova et al. 2012; Sukkathanyawat et al. 2015); the chemical depos- ition method (Kazemnejad et al. 2019); the pre- cipitation method (Li et al. 2017); and the impregnation method (Bian et al. 2003). A review by Ghogia et al. (2021) provides an overview of these methods along with a detailed description of each. Different characterization techniques are used to measure crystallite size accurately. The techniques include TEM, XRD and H2-chemi- sorption as stated earlier. Each technique has cer- tain advantages and disadvantages, as there are limitations, given that they are prone to oper- ational and other fundamental uncertainties. So, it is recommended that more than one technique is used to verify the agreement of the data. Agreement of the data, which is determined using various methods, proves the absence of sig- nificant errors in the methods used for each sup- ported metal catalyst. After analyzing various experiments conducted to determine crystallite sizes using the XRD Scherrer formula and TEM, it was concluded that both methods yield similar crystallite size values, especially for sizes smaller than 60 nm (Vorokh 2018). Thus, a combination of at least two methods is needed to determine catalyst crystallite size accurately. TEM application in determining crystallite size TEM has been applied to image crystallite size directly on the supported catalyst. However, for accuracy and reproducibility, there is a need for accurate crystallite size distribution analysis. TEM has the advantage of the real-space visualization of nanoparticles. Nevertheless, to ensure accurate results, the operator must still select the correct magnification and have reasonable choices regarding the type of imaging (bright vs dark field), method of analysis, and a manual or auto- mated method (Pyrz and Buttrey 2008). These choices have an impact on resolution, the con- trast between the background and the particles, the particle population in each image, the effi- ciency of the analysis and proper background- particle boundary determination (Pyrz and Buttrey 2008). It is important to note that images visualized at coarse magnifications clearly show all the particles in that given area, but the reli- ability of the quantification was severely limited, as high magnification imaging results in sampling fewer particles. This limitation contributes to errors or bias in determining the crystallite size of a given sample. Therefore, the statistical sig- nificance of the crystallite size determination will be compromised if the particle population is not captured and it is not representative of the par- ticle population. Therefore, all variables should be considered, in order to measure particle size distribution with statistical significance and accuracy. TEM limitations Generally, measuring the crystallite diameter on the supported catalyst and understanding the CHEMICAL ENGINEERING COMMUNICATIONS 1273 distribution using TEM can be a challenging exercise. To obtain statistically meaningful data from TEM, many points should be analyzed, many particles should be analyzed and many crystallites should be measured. Other challenges with TEM image analysis are the presence of crystallites as clusters at different heights; crystal- lites that are sometimes embedded in support material; crystallites that overlap; and an uneven background. In order to address these issues, Gontard et al. (2011) invented an image-process- ing algorithm to assist in measuring crystallite size and their distribution using TEM images. The algorithm reportedly allows crystallites to be detected and characterized with greater accuracy than when using other conventional methods. In another study, Fisker et al. (2000) developed an automated image analysis technique built on a deformable ellipse model to accurately and robustly estimate crystallite size distribution from thousands of crystallites. This method has also proved to be very useful. Figure 7 shows synthesized uniform-sized cobalt crystallites on mesoporous SiO2 supports. The num- ber of crystallites varies per given area at the same magnification. There is a correlation between crystallite size and selectivity, so the ability to tune the crystallite size controls the selectivity of the products. However, a correlation between shape and product selectivity is not mentioned in the available literature. Another, disadvantage of TEM is some- times a lack of contrast between crystallites and the support, and it is difficult to see tiny particles of 0.5 nm (Mustard and Bartholomew 1981). In prin- ciple, TEM can measure the size of a discrete par- ticle, which can be used to determine the average particle size. However, different points or locations need to be imaged to avoid bias and the pictures studied should be representative of the whole sample. X-ray diffraction (XRD) XRD is another technique that is often used to measure the mean size of crystallites by applying the Scherrer equation to XRD data. The history of applying the Scherrer equation in determining crystallite size is documented in articles written by Alexander and Klug (1950), and Langford and Wilson (1978). The Scherrer equation is the most commonly used modus operandi in FT reported in the literature for extracting crystallite size Figure 7. Images obtained from TEM and a reduced catalyst’s corresponding cobalt crystallite size distribution. Crystallite size decreases from a> b> c, and metallic cobalt crystallites are dispersed almost homogeneously with a narrow size distribution. The figure was modified with permission from (Cheng et al. 2018). 1274 J. GORIMBO ET AL. information from XRD data. The Scherrer Equation was formulated in 1918 to compute the diameter of crystallite. It is given in Equation (8). L ¼ Kk b:cosh (8) Where L is the average crystallite size (crystallite diameter in nanometer (nm)); K is the crystallite shape-related constant, normally taken as 0.9 (depending on the shape of the crystallite); k is the wavelength of the X-ray, usually in nm; b is the Full Width at Half Maximum (FWHM) at 2h in radians (b ¼ value of FWHM X p/180), and b varies inversely with crystallite diameter (L); h is the Bragg angle for the peak at 2h (in degrees); h ¼ (2h/2) FWHM, and h can be expressed in radians or degrees, since the value of Cosh corresponds to the same value (Monshi et al. 2012). Uncertainties in calculating crystallite size The accuracy of the familiar Scherrer Equation is limited by the uncertainties in K (the crystallite shape factor) and b (the pure diffraction broaden- ing) (Alexander and Klug 1950). In reality, crystal- lites are not usually uniformly perfect but have irregular shapes. However, the Scherrer Equation assumes a regular shape for all samples. Although crystallite shape is usually irregular, shapes are often approximated as spheres, triangular prism, cubes, tetrahedrons and octahedrons, and in some cases include shapes that do not have cubic sym- metry (Lele and Anantharaman 1962; Wilson 1969; Lou€er et al. 1972). Special cases of non-cubic symmetry crystallite shapes that have been consid- ered are parallelepipeds such as needles and plates (Langford and Wilson 1978). The K value depends on the determined width, crystallite shape and distribution of the size. The values often used for K (the shape factor) are 0.94 for crystallites that are spherical and 0.89 for other shapes. These values can be approximated to be 1 after rounding off. K varies from 0.62 to 2.08. A detailed discussion of K is given by Langford and Wilson (1978). The literature survey shows that, when using the Scherrer Equation, the estimates are usually that crystallites are spherical; however, prior analysis using other methods (TEM, SEM, and AFM) to determine the average crystallite shape can assist in determining the most accurate value of K. The accuracy of Equation (8) (the Scherrer crystallite size equation) is restricted partly by the uncertainty regarding the b value, which varies inversely with crystallite size (Alexander and Klug 1950). FWHM is defined as the diffraction peak width, in radians, at a height halfway between the base and the maxima of the peak (Muniz et al. 2016). FWHM of the broadened line has been criticized for giving unreliable crys- tallite size values. Therefore, it was proposed that the integral breadth be used together with the Scherrer equation to reduce errors in determining crystallite size (Bushroa et al. 2012). Moreover, the line shape of an XRD pattern is affected by the uneven distribution of crystallite and the wide distribution of size (Bushroa et al. 2012). The Scherrer formula has a lower limit of applic- ability, which has been established. It has been shown that the error when using the Scherrer formula non-linearly increases with a crystallite size of less than 4 nm (Vorokh 2018). In another study, XRD was reported to be insensitive to low metal loading and small particles (<3 nm) (Mustard and Bartholomew 1981). Crystallite definition Here, the phrases crystallite size and particle size, and the word size are synonymous with the diameter of the crystallite, with the diameter being defined as the length of a straight line tra- versing through the middle of the mass of the crystallite and ending at the crystallite boundary (Green 1927; Heywood 2010). For non-uniform crystallite that cannot be completely defined by a single mean value, a mathematical shape factor for defining the geometric shape can be applied if accuracy is important (Hatch 1933). Several defi- nitions of particle size exist in the literature, but the most appropriate is governed by the system being examined and the analysis technique employed (Matyi et al. 1987). For instance, XRD is sensitive to the crystallite size on the surface or inside any given particle. However, the phrase crystallite size seems more accurate, since indi- vidual particles can be made up of many crystalli- tes or domains with a non-identical orientation. This distinction is significant if the diameter measured from diffraction broadening is juxta- posed with that obtained using other methods. CHEMICAL ENGINEERING COMMUNICATIONS 1275 Figure 8 shows that an increase in the size of par- ticles tends to result in the narrowing of the peaks to resemble a coarse crystalline material. Smaller particles less than 1.5 nm tend to produce broad peaks synonymous with amorphous substances (Vorokh 2018). This phenomenon is observed even if the particles or crystallites are not the same shape and size. The peak width varies with particle or crystallite size, and a narrow peak corresponds with a bigger crystallite diameter. When the peaks are broader, there is a limit to the smallest nanoparticles that can be measured by XRD, (<3 nm) (Mustard and Bartholomew 1981). H2 chemisorption Many catalyst characterization studies have used H2 chemisorption as a crystallite size measuring technique (Bezemer et al. 2006; Den Breejen et al. 2009; Prieto et al. 2009; Rane et al. 2012). H2 chemisorption measurements relate the con- sumption of H2 gas molecules to the available surface area of the supported metal crystallites. The relationship that exists between H2 con- sumption and the exposed surface area is gov- erned by the chemisorption stoichiometry of the hydrogen-to-metal atom. This technique is useful for small particles when the size is difficult to estimate through electron microscopy or XRD (Almithn and Hibbitts 2018). The approximation of active crystallite size calculation is a geomet- rical assumption that is based on the shape of the crystallite having a regular geometry, with the ideal geometry being a sphere (Webb 2003). This analysis makes use of an expression of grain geometry. Using the approximated regular geometry, the size (being the diameter) can then be computed in terms of volume and area (Webb 2003). The diameter computed is the average diameter of the active crystallite onto which hydrogen adsorption occurred. The significant economic advantages of using H2 chemisorption in measuring particle size are that it is less expensive than TEM and XRD techniques, is fairly accurate, and measures particles of all sizes. However, it has disadvantages, as it is easily affected by contamination, there is metal sup- port interaction and adsorption stoichiometry could vary with dispersion or metal loading (Mustard and Bartholomew 1981). The H2 chemisorption method also has other inherent difficulties that hinder its effective application, for example, in order for meas- urement by H2 chemisorption to make sense, the probe gas should be adsorbed on the surface of the metal as a monolayer and gas desorption should be complete (Matyi et al. 1987). Cobalt crystallite size determined by TEM, H2 chemisorption and XRD The crystallite sizes of cobalt-based catalysts are tabulated in Table 3. Various authors employed different preparation methods for the catalysts, Figure 8. Diffraction curves of model particles with a cubic shape and a cubic unit cell structure. Particle size measure- ments are given in nm (Vorokh 2018). 1276 J. GORIMBO ET AL. and distinct analytical techniques (TEM, H2 chemisorption, and XRD) were utilized to deter- mine the crystallite size. In comparing and com- puting differences obtained by using two or more methods for crystallite size determination, a stat- istical approach was employed to check for varia- tions when specific techniques were applied. One-way ANOVA followed by post-hoc Bonferroni correction was used to analyze the results obtained from the literature. Table 4 summarizes the one-way ANOVA results that compare different analysis methods used to determine crystallite size. A post-hoc Bonferroni correction test was performed to enable a comparison of the different techniques, and the results are tabulated. As shown in all the ANOVA tables, the P values are greater than 0.05 and F is less than Fcritical, which provides strong evidence that the techniques yield almost similar measurements. A one-way ANOVA, followed by a post-hoc Bonferroni correction test, indicated that any of the techniques (TEM, XRD and H2 chemisorp- tion) can be used to determine crystallite size with P(T<¼t) two-tail values that are greater than an alpha value of 0.05, even after applying the Bonferroni test (all are above 0.01666667). Any of the techniques discussed can be adopted to give measurements that are of statistical sig- nificance, as there are no differences within groups or any combination of techniques. Cobalt catalyst reduction Temperature-programmed reduction (TPR) is a technique applied in FT catalysis, with a catalyst precursor undergoing monitored reduction while the temperature is increased linearly with time. TPR studies of catalysts are a crucial step in FT technology as they produce the active catalyst. The method has been used extensively to study supported and unsupported catalysts, to extract qualitative information such as the oxidation state of the reducible species present (Jacobs et al. 2007; Jozwiak et al. 2007; Bao et al. 2009; Gorimbo 2018). The technique is highly sensi- tive to the presence of species in a reducible form and discussions on the sensitivity of the TPR profiles (peak shape, maximum tempera- ture, resolution of reduction steps, etc.) have been published (Bosch et al. 1984; Malet and Table 3. Cobalt crystallite size determined by TEM, H2 chemisorption and XRD. Crystallite determination method (measurements in nm) ReferencesCo- based catalyst TEM H2 chemisorption XRD Co/SiO2-20 26 19.8 – (A. M. Saib et al. 2002) Co/SiO2-40 3 5.9 – Co/SiO2-60 6.7 6 – Co/SiO2-100 6.9 7.3 – Co/SiO2-150 8.3 10.6 – Co-silica ID – 19.9 23.5 (Zhang et al. 2006) Co-acetic acid – 14.2 16.1 Co-ethanol – 19 22.3 Co-1-propanol – 15.6 18.2 Co-1-butanol – 14.9 16.5 30% Co/SiO2 183 141 125 (Prieto et al. 2009c) 10% Co/ITQ(1) 12.8 10.4 12.5 10% Co/ITQ(2) 8.2 8.9 9.9 10% Co/ITQ(3) – 7.3 9.1 10% Co/ITQ(4) 6.3 5.6 6.8 10% Co/ITQ(5) – – 5.9 Cat-12 h 11.4 10.6 12.8 (Cheng et al. 2018) Cat-8h 9.1 8.9 11 Cat-4h 7.2 7.3 8.9 Cat-1M 14.3 12.3 13.1 HDP11 30 25 (G. Leendert Bezemer et al. 2006) HDP9 14 12.5 IWN13 7.5 8.5 IEN4 3.6 4.4 IWA1 3.7 6.1 5Co/M 3 – 5 (Li et al. 2006) 10Co/M 4.5 – 11 15Co/M 6.5 – 14 CHEMICAL ENGINEERING COMMUNICATIONS 1277 Caballero 1988; Fierro et al. 1994; Christel et al. 1997; Giordano et al. 2000). The TPR technique has been used as a success- ful fingerprint method for characterizing FT cata- lysts - mainly cobalt and iron. This section focuses on the cobalt-based catalyst in FTS only. Several factors that influence the TPR profile have been studied, and sample weight, hydrogen concentration, carrier flow rate, total hydrogen consumption, and heating rate tend to have a greater degree of influence (Bosch et al. 1984). The conditions reported in the literature differ Table 4. Analysis of variance (ANOVA): single factor. Summary Groups Count Sum Average Variance TEM vs H2 Chemisorption 18 72.1 4.00555556 92.5923203 TEM vs XRD 11 82.7 7.51818182 285.787636 XRD vs H2 Chemisorption 14 41.8 2.98571429 14.6551648 ANOVA Source of variation SS df MS F P-value F crit Between groups 136.483561 2 68.2417803 0.59052311 0.55879474 3.23172699 Within groups 4622.46295 40 115.561574 Total 4758.94651 42 t-Test: Two-sample assuming equal variance TEM vs H2 chemisorption TEM vs XRD Mean 4.00555556 7.51818182 Variance 92.5923203 285.787636 Observations 18 11 Pooled variance 164.146141 Hypothesized mean Difference 0 df 27 t Stat −0.7163911 P(T<¼t) one-tail 0.2399505 t Critical one-tail 1.70328845 P(T<¼t) two-tail 0.47990099 0.01666667 FALSE t Critical two-tail 2.05183052 t-Test: Two-sample assuming equal variance TEM vs H2 chemisorption XRD vs H2 chemisorption Mean 4.00555556 2.98571429 Variance 92.5923203 14.6551648 Observations 18 14 Pooled variance 58.8195529 Hypothesized mean Difference 0 df 30 t Stat 0.37316165 P(T<¼t) one-tail 0.355826 t Critical one-tail 1.69726089 P(T<¼t) two-tail 0.711652 0.01666667 False FALSE t Critical two-tail 2.04227246 t-Test: two-sample assuming equal variance TEM vs XRD XRD vs H2 chemisorption Mean 7.51818182 2.98571429 Variance 285.787636 14.6551648 Observations 11 14 Pooled variance 132.538848 Hypothesized mean Difference 0 df 23 t Stat 0.97713251 P(T<¼t) one-tail 0.16933498 t Critical one-tail 1.71387153 P(T<¼t) two-tail 0.33866996 0.01666667 FALSE t Critical two-tail 2.06865761 Bonferroni post hoc test. 1278 J. GORIMBO ET AL. widely; as a result, it is challenging to compare TPR profiles obtained by different researchers (Figure 9). TPR with hydrogen is a commonly used tech- nique for characterizing catalysts in FTS reac- tions. An in-depth understanding of the accurate reduction pathway of the FTS catalyst is an important piece of information. In the case of the cobalt-based catalyst, Co3O4 undergoes reduction to Co in two steps, with CoO being the inter- mediate species regardless of support type (SiO2, TiO2, and Al2O3) (Xiong et al. 2005; Jacobs et al. 2007; Kliewer et al. 2019). Using hydrogen (H2) as the reduction gas yields two different reduc- tion regions, as shown in Figure 9. Various reducing agents have been used in FTS, including hydrogen, CO and syngas (Gorimbo 2016). In the case of hydrogen, the degree of reduc- tion is determined by monitoring H2, consumption while increasing the sample temperature at a con- stant rate. As a result, the reduction profiles are obtained at different temperatures. An elevated tem- perature is sometimes necessary for reduction, such as when strong metal-support interaction is experi- enced (Jacobs et al. 2007). The stoichiometry of Equation (9) suggests that 1 mole of Co3O4 yields 4 moles of H2O dur- ing reduction. H2–reduction : Co3O4 þ 4H2 ! 3Co þ 4H2O, DH ¼ −57:1 kJ=mol; DG ¼ −140:4 kJ=mol (9) Co3O4 reduction to CoO consumes 1 mole of hydrogen and then reduces to metallic Co using 1 mole of H2 - see Figure 10. First peak : Co3O4 þ H2 ! 3CoO þ H2O, DH ¼ −3:93 kJ=mol; DG ¼ −14:4 kJ=mol (10) Second peak : CoO þ H2 ! Co þ H2O, DH ¼ −12:0 kJ=mol; DG ¼ −43:2 kJ=mol (11) Thermodynamics of Co-based catalysts reduction Gibbs free energy and enthalpy of the reaction system at specific temperature and pressure levels have been used to plot the mass balance-attain- able region of the FT system (Gorimbo et al. 2020), while standard energies are provided in Equations 9–11. Gibbs free energy gives the work potential of the given scenario, while enthalpy presents the minimum reaction energy require- ments of the system. So, þDH values indicate that work and energy should be supplied to the reaction system, whereas -DH values indicate that work and energy are released by the system. Pressure deviations are not considered significant in terms of enthalpy and Gibbs free energy at the temperature levels studied. DH0 ¼ DH0 0 þ R ðT T0 DC0 R dT (12) Where DH0 and DH0 0 are heat of formation of the components at temperature T and reference temperature T0. The heat capacity term at tem- perature T is given by Equation (13). DC0 P R ¼ Aþ BT þ CT2 þ DT−2 (13) Where A, B, C, and D are heat transfer coeffi- cients. Integrating Equations (11) and (12) to get DH0 at temperature T gives Equation (13), where Ʈ ¼ Ʈ To DH� ¼ DHo � þ R� DA�To� Ʈ–1ð Þ þ DB 2 �To 2 � Ʈ2–1 � � � þ DC 3 �To 3 � Ʈ3–1 � � þ DD To � �Ʈ–1 Ʈ � # (14) DG at various temperatures can be calculated using Equation (14). (15) (Smith et al. 2018). Figure 9. The pattern represents the TCD signal resulting from Co3O4 reduction in hydrogen for a cobalt-based catalyst (Gorimbo et al. 2020). CHEMICAL ENGINEERING COMMUNICATIONS 1279 DG � T ¼ DH � o– T To DH � o– DG � o � � þ R ðT T: DCp� R dT–RT ðT T: DCp� R dT T (15) where Ð T T: DCp� R dT ¼ DA�To�ðƮ - 1Þ þ DB 2 � DB 2 � To 2 �ðƮ2 - 1Þþ D 3 �To 3 �ðƮ3 - 1Þ þ DD To � Ʈ–1 Ʈ � � and Ð T T: DCp� R dT T ¼ DA�lnƮþ DBToþ½ DCTo 2þ � DD Ʈ2To 2 Þ Ʈþ1 2 � �i �ðƮ− 1Þ (Gorimbo et al. 2020) applied the Attainable Region (AR) approach to cobalt catalyst reduc- tion thermodynamics using the above equations and depicted the reduction pathway, as shown in Figure 10. The method entails setting up ideal conditions for Co reduction and focusing on determining minimal G at varying temperatures. Figure 10, supported by Figure 9 and TAR space diagrams, shows that the reduction of Co3O4 often happens through two reaction stages. Peak 1 is assigned to direct reduction of Co3O4 to Co and Co3O4 to intermediate CoO. Then peak 2 is assigned to the reduction of Co3O4 to Co or CoO to Co (Jacobs et al. 2007). Pore size effect on crystallite sizes Several catalysts used in FTS are porous, with pores grouped as macropores, mesopores and micropores (Haber 1991). The surface area, pore volume and pore diameter determined using the Brunauer, Emmett and Teller (BET) theory, influ- ences catalyst activity and product selectivity. These parameters govern reactant diffusion. Porosity relates to the volume percentage occu- pied by the pores, and the pore-size distribution refers to the pore volume distribution with refer- ence to pore size. Porosity is a key factor in con- trolling the diffusion of reactants from the pore mouth through the catalyst pores to the immedi- ate vicinity of the internal catalytic surface and the desorption of the products from the surface (Haber 1991). The metal crystallite size and the extent of reduction were shown to increase linearly with an increase in the support pore diameter (Iglesia 1997a). Iglesia (1997a) also observed that the metal crystallites form clusters on the surface of the support and that increasing the support pore diameter resulted in an increase in the size of the clusters (Iglesia 1997a). If cobalt crystallites formed are bigger than the average pore diameter of the support, they will probably be situated on the external surface of the support. A general observation is that cobalt crystallite distribution on the support is not even, i.e. clusters of vari- ous-sized crystallites can be observed on the sup- port (Saib et al. 2002). Xie et al. (2012) used carbon nanotubes (CNT) and reported an important phenomenon: Co catalyst crystallites inside CNT reduced more eas- ily than those outside CNT; with crystallites inside the CNT, smaller Co crystallites reduced better than bigger crystallites. Xie et al. (2012) observed that FT catalytic activity was higher for Co crystallite inside the CNT than outside it. Figure 10. The prototypical G-H attainable region of the Co reduction system (vertices A, B and C) shows the G-H AR boundary vertices (Gorimbo et al. 2020). 1280 J. GORIMBO ET AL. Larger pores correspond to the formation of larger Co3O4 crystallite with decreased dispersion. Different pore sizes exhibited by supports result in varying CO adsorption properties. Supports with a pore size in the range of 6–10 nm have been shown to result in better FT activity and more selectivity to the desired C5þ. This observa- tion is attributed to moderate crystallite size and CO adsorption on the catalyst (Song and Li 2006). Effect of promoters on crystallite size In FT, promoters are chemical additives that enhance the physical, chemical and catalytic properties of the catalyst. In a study done by Jacobs et al. (2002) reduction temperature was significantly reduced by incorporating small amounts of Ru and Pt during the synthesis of a cobalt-based catalyst. Adding Mn has been shown to enhance metal cluster dispersion, which results in a smaller average size of cobalt crystallite (Sukkathanyawat et al. 2015). Mn also influences FTS product distribution by promoting the for- mation of long-chain hydrocarbon on a cobalt- supported catalyst (Sukkathanyawat et al. 2015). Morales et al. (2007) reported that MnO species cause positive structural and electronic modifica- tion of the catalyst, resulting in improved FT catalytic performance. Morales et al. (2007) also observed that the water gas shift (WGS) reaction was catalyzed by MnO, which adjusts the H2/CO ratio and alters overall FT catalytic performance. Alkali metals are also useful as FT catalyst chem- ical promoters, as they affect activity and selectiv- ity. Performance evaluation of the Co/Al2O3 catalysts promoted Li, Na, K, Rb and Cs resulted in enhanced C5þ selectivity (Gholami et al. 2021). Generally, the literature provides definitive evi- dence that promoters facilitate Co reducibility at a lower reduction temperature than non-pro- moted catalysts. Several detailed reviews and work on the effect of promoters are available (Shimura et al. 2015; Yang et al. 2022). Concluding remarks The literature analysis indicates that the catalytic properties of small cobalt particles (<6nm) differ from those of larger ones (>6nm) in FT synthe- sis. Oxidation of cobalt particles less than 6 nm in diameter can be minimized by correctly adjusting the hydrogen and water partial pressure in the FT reactor. The crystallite diameter of cobalt particle size appears to be a parameter of influence in controlling speciation by oxidation of the cobalt catalyst. From the literature sur- veyed, the general conclusion is that cobalt crys- tallite size significantly affects product selectivity. Cobalt crystallite with a size of <6–8 nm tends to favor the formation of methane and reduce C5þ selectivity. C5þ products are the most sought- after product nowadays; hence its increased selectivity is ideal. H2 adsorption is the most convenient, accurate and generally applicable technique for estimating the average crystallite size of several FT catalysts. However, TEM is a precise technique for measur- ing the average crystallite size and the distribution of the size of the metal catalysts in FT. XRD is widely used in FT to determine crystallite size, although it is generally insensitive to small metal particles that are <3 nm. It is apparent that no single method fully characterizes crystallite size and distribution in supported metal catalysts in the absence of inherent theoretical shortcomings, uncertainty in the experimental approach and ambiguity in the interpretation of results. Therefore, it is ideal to use multiple techniques whenever possible to validate the readings obtained. There are still challenges in precisely control- ling the crystallite size at the nanoscale this demands advanced synthesis methods to ensure easy synthesis, uniformity and reproducibility. Another challenge is attributing FT activity to ini- tial crystallite size. Therefore there is a need to capture and comprehend dynamic changes in crystallite size during different stages of FT reac- tion, this requires sophisticated in-situ character- ization techniques. The interaction between cobalt crystallites and catalyst supports adds complexity. Optimizing this interplay to enhance stability and catalytic activity is an ongoing challenge. Demonstrating the impact of particle or crys- tallite size at the laboratory scale is just the beginning. The translation of these findings to industrial-scale reactors presents additional CHEMICAL ENGINEERING COMMUNICATIONS 1281 challenges due to limitations in heat and mass transfer, reactor design considerations, and potential catalyst deactivation effects. Therefore, it is crucial to understand the scalability of par- ticle size effects for practical implementation. Perspectives: 1. Debunking the impact of particle and crystallite size in cobalt-based Fisher-Tropsch synthesis presents a crucial opportunity to deepen our fundamental understanding of the underlying mechanisms governing catalytic reactions. This understanding can greatly aid in designing more efficient and selective catalysts for indus- trial applications. By acquiring knowledge of the underlying processes that govern catalytic reactions, it becomes possible to optimize and improve the performance of catalysts for spe- cific applications. Therefore, this study repre- sents an important step toward the development of more effective and efficient catalytic processes, which can help to drive industrial innovation and progress. 2. The study of particle and crystallite size impact on catalyst optimization is crucial for identify- ing the optimal catalyst sizes that maximize desired product selectivity or improve activity. This knowledge is invaluable in the develop- ment of more efficient and cost-effective cobalt-based Fischer-Tropsch catalysts. By uti- lizing the insights gained from this study, it is possible to guide the development of optimized catalysts that will lead to higher product yields, lower costs, and increased sustainability. 3. Process intensification is a crucial aspect of chemical engineering, and understanding the role of particle/crystallite size can significantly aid in developing strategies for process intensi- fication. By designing catalysts with tailored properties, it may be possible to achieve higher conversion and selectivity within smaller reactor volumes, especially if smaller particles exhibit higher activity. Therefore, particle/crys- tallite size should be a key consideration in the design of catalysts and reactors to achieve opti- mal process intensification. 4. The stability of a catalyst plays a crucial role in industrial and academic settings. The impact of particle/crystallite size on catalyst stability is a subject of significant research, as it provides valuable insights into potential deactivation mechanisms. Investigating this impact enables the identification of ways to enhance catalyst longevity by mitigating particle sintering, main- taining active site accessibility, or improving resistance to catalyst poisons. These insights can help design more robust catalysts and con- tribute to the development of efficient and sus- tainable chemical processes. 5. Catalyst design and engineering: Insights gained from studying particle/crystallite size effects can contribute to more rational catalyst design and engineering. Optimizing particle sizes, surface structures, and interactions can lead to enhanced catalytic performance and overall process efficiency. 6. Finally, the integration of cutting-edge techni- ques such as in-situ microscopy and spectros- copy offers a promising perspective for unraveling real-time changes in crystallite size during Fischer-Tropsch reactions. The perspectives presented in this study high- light the potential for gaining fundamental know- ledge, optimizing catalysts, improving process intensification, enhancing catalyst stability, and enabling rational catalyst design and engineering. Therefore, it is essential to consider these per- spectives when exploring cobalt-based Fisher- Tropsch synthesis and its potential applications. Acknowledgements The author would like to acknowledge the University of South Africa (UNISA), Institute of Development of Energy for African Sustainability (IDEAs), and National Research Fund (NRF) for funding. Disclosure statement The authors declare no conflict of interest. 1282 J. GORIMBO ET AL. References Alexander L, Klug HP. 1950. Determination of crystallite size with the x-ray spectrometer. J Appl Phys. 21(2):137– 142. doi:10.1063/1.1699612. Almithn AS, Hibbitts DD. 2018. Supra-monolayer coverages on small metal clusters and their effects on H2 chemi- sorption particle size estimates. AIChE J. 64(8):3109– 3120. doi:10.1002/aic.16110. Bao A, Liew K, Li J. 2009. Fischer–Tropsch synthesis on CaO-promoted Co/Al2O3 catalysts. J Mol Catal. Chem. 304(1–2):47–51. doi:10.1016/j.molcata.2009.01.022. Bezemer GL, Bitter JH, Kuipers HP, Oosterbeek H, Holewijn JE, Xu X, Kapteijn F, Van Dillen AJ, de Jong KP. 2006. Cobalt particle size effects in the Fischer − Tropsch reaction studied with carbon nanofiber supported catalysts. J Am Chem Soc. 128(12):3956–3964. doi:10.1021/ja058282w. Bian G-Z, Fujishita N, Mochizuki T, Ning W-S, Yamada M. 2003. Investigations on the structural changes of two Co/ SiO2 catalysts by performing Fischer–Tropsch synthesis. Appl Catal Gen. 252(2):251–260. doi:10.1016/S0926- 860X(03)00470-8. Bianchi CL, Martini F, Moggi P. 2001. Co/SiO2 sol–gel cata- lysts for Fischer–Tropsch synthesis. Catal Lett. 76(1/2): 65–69. doi:10.1023/A:1016712507527. Borg Ø, Dietzel PD, Spjelkavik AI, Tveten EZ, Walmsley JC, Diplas S, Eri S, Holmen A, Rytter E. 2008. Fischer– Tropsch synthesis: cobalt particle size and support effects on intrinsic activity and product distribution. J Catal. 259(2):161–164. doi:10.1016/j.jcat.2008.08.017. Borg O, Eri S, Blekkan E, Storsater S, Wigum H, Rytter E, Holmen A. 2007. Fischer–Tropsch synthesis over c-alu- mina-supported cobalt catalysts: effect of support variables. J Catal. 248(1):89–100., doi:10.1016/j.jcat.2007.03.008. Bosch H, Kip BJ, Van Ommen JG, Gellings PJ. 1984. Factors influencing the temperature-programmed reduction pro- files of vanadium pentoxide. J Chem Soc, Faraday Trans 1. 80(9):2479–2488. doi:10.1039/f19848002479. Brunner KM, Huang B, Woodfield BF, Hecker WC. 2015a. Iron fischer-tropsch catalysts prepared by solvent-defi- cient precipitation (SDP): effects of washing, promoter addition step, and drying temperature. Catalysts. 5(3): 1352–1374. doi:10.3390/catal5031352. Brunner KM, Perez HD, Peguin RP, Duncan JC, Harrison LD, Bartholomew CH, Hecker WC. 2015b. Effects of par- ticle size and shape on the performance of a trickle fixed- bed recycle reactor for Fischer–Tropsch synthesis. Ind Eng Chem Res. 54(11):2902–2909. doi:10.1021/ie503174v. Bushroa AR, Rahbari RG, Masjuki HH, Muhamad MR. 2012. Approximation of crystallite size and microstrain via XRD line broadening analysis in TiSiN thin films. Vacuum. 86(8):1107–1112. doi:10.1016/j.vacuum.2011.10.011. Bykova M, Ermakov DY, Kaichev V, Bulavchenko O, Saraev A, Lebedev MY, Yakovlev V. 2012. Ni-based sol–gel cata- lysts as promising systems for crude bio-oil upgrading: guaiacol hydrodeoxygenation study. Appl Catal B Environ. 113-114:296–307. doi:10.1016/j.apcatb.2011.11.051. Chauhan A, Chauhan P. 2014. Powder XRD technique and its applications in science and technology. J Anal Bioanal Tech. 5(6):1–5. doi:10.4172/2155-9872.1000212. Cheng Q, Tian Y, Lyu S, Zhao N, Ma K, Ding T, Jiang Z, Wang L, Zhang J, Zheng L, et al. 2018. Confined small- sized cobalt catalysts stimulate carbon-chain growth reversely by modifying ASF law of Fischer–Tropsch synthesis. Nat Commun. 9(1):3250., doi:10.1038/ s41467-018-05755-8. Choudhury H, Cheng X, Afzal S, Prakash A, Tatarchuk B, Elbashir N. 2020. Understanding the deactivation process of a microfibrous entrapped cobalt catalyst in supercrit- ical fluid Fischer-Tropsch synthesis. Catal Today. 343: 112–124. doi:10.1016/j.cattod.2019.01.031. Christel L, Pierre A, Abel DA-MR. 1997. Temperature pro- grammed reduction studies of nickel manganite spinels. Thermochim Acta. 306(1-2):51–59. doi:10.1016/S0040- 6031(97)00299-2. Den Breejen JP, Radstake PB, Bezemer GL, Bitter JH, Frøseth V, Holmen A, De Jong KP. 2009. On the origin of the cobalt particle size effects in Fischer-Tropsch catalysis. J Am Chem Soc. 131(20):7197–7203. doi:10. 1021/ja901006x. Deraz N. 2018. The comparative jurisprudence of catalysts preparation methods: I. Precipitation and Impregnation Methods. J Ind Env Chem. 2:19–21. Deugd RMD, Ypma SM, Kapteijn F, Meeuse FM, Moulijn JA, Verheijen PJT. 2001. Model-based optimiza- tion of the periodic operation of the Fischer-Tropsch synthesis��This work is part of Delft Interdisciplinary Research Centre “Mastering the Molecules in Manufacturing. In: Froment, GF, Waugh, KC, editor. Reaction kinetics and the development and operation of catalytic processes, studies in surface science and cataly- sis, p. 255–262. doi:10.1016/S0167-2991(01)81970-4. Fang X, Liu B, Cao K, Yang P, Zhao Q, Jiang F, Xu Y, Chen R, Liu X. 2020. Particle-size-dependent methane selectivity evolution in Cobalt-based Fischer–Tropsch synthesis. ACS Catal. 10(4):2799–2816. doi:10.1021/acsca- tal.9b05371. Fierro G, Lojacono M, Inversi M, Porta P, Lavecchia R, Cioci F. 1994. A study of anomalous temperature-pro- grammed reduction profiles of Cu2O, CuO, and CuO- ZnO catalysts. J Catal. 148(2):709–721. doi:10.1006/jcat. 1994.1257. Fischer N, Clapham B, Feltes T, van Steen E, Claeys M. 2014. Size-dependent phase transformation of catalytically active nanoparticles captured in situ. Angew Chem. 126(5):1366–1369. doi:10.1002/ange.201306899. Fischer N, Van Steen E, Claeys M. 2013. Structure sensitiv- ity of the Fischer-Tropsch activity and selectivity on alu- mina supported cobalt catalysts. J Catal. 299:67–80. doi: 10.1016/j.jcat.2012.11.013. Fisker R, Carstensen JM, Hansen MF, Bødker F, Mørup S. 2000. Estimation of nanoparticle size distributions by CHEMICAL ENGINEERING COMMUNICATIONS 1283 https://doi.org/10.1063/1.1699612 https://doi.org/10.1002/aic.16110 https://doi.org/10.1016/j.molcata.2009.01.022 https://doi.org/10.1021/ja058282w https://doi.org/10.1016/S0926-860X(03)00470-8 https://doi.org/10.1016/S0926-860X(03)00470-8 https://doi.org/10.1023/A:1016712507527 https://doi.org/10.1016/j.jcat.2008.08.017 https://doi.org/10.1016/j.jcat.2007.03.008 https://doi.org/10.1039/f19848002479 https://doi.org/10.3390/catal5031352 https://doi.org/10.1021/ie503174v https://doi.org/10.1016/j.vacuum.2011.10.011 https://doi.org/10.1016/j.apcatb.2011.11.051 https://doi.org/10.4172/2155-9872.1000212 https://doi.org/10.1038/s41467-018-05755-8 https://doi.org/10.1038/s41467-018-05755-8 https://doi.org/10.1016/j.cattod.2019.01.031 https://doi.org/10.1016/S0040-6031(97)00299-2 https://doi.org/10.1016/S0040-6031(97)00299-2 https://doi.org/10.1021/ja901006x https://doi.org/10.1021/ja901006x https://doi.org/10.1016/S0167-2991(01)81970-4 https://doi.org/10.1021/acscatal.9b05371 https://doi.org/10.1021/acscatal.9b05371 https://doi.org/10.1006/jcat.1994.1257 https://doi.org/10.1006/jcat.1994.1257 https://doi.org/10.1002/ange.201306899 https://doi.org/10.1016/j.jcat.2012.11.013 image analysis. J Nanoparticle Res. 2(3):267–277. doi:10. 1023/A:1010023316775. Fu T, Lv J, Li Z. 2014. Effect of carbon porosity and cobalt particle size on the catalytic performance of carbon sup- ported cobalt fischer-tropsch catalysts. Ind Eng Chem Res. 53(4):1342–1350. doi:10.1021/ie402128y. Garc�ıa-S�anchez JT, Baldovino-Medrano VG. 2023. Elements of the Manufacture and Properties of Technical Catalysts. Ind Eng Chem Res. 62(20):7769–7838. doi:10.1021/acs. iecr.3c00369. Gavrilovi�c L, Brandin J, Holmen A, Venvik HJ, Myrstad R, Blekkan EA. 2018. Fischer-Tropsch synthesis— Investigation of the deactivation of a Co catalyst by exposure to aerosol particles of potassium salt. Appl Catal B Environ. 230:203–209. doi:10.1016/j.apcatb.2018. 02.048. Geyer R, Hunold J, Keck M, Kraak P, Pachulski A, Sch€odel R. 2012. Methods for determining the metal crystallite size of Ni supported catalysts. Chem Ing Tech. 84(1-2): 160–164. doi:10.1002/cite.201100101. Ghogia AC, Nzihou A, Serp P, Soulantica K, Pham Minh D. 2021. Cobalt catalysts on carbon-based materials for Fischer-Tropsch synthesis: a review. Appl Catal Gen. 609: 117906. doi:10.1016/j.apcata.2020.117906. Gholami Z, Ti�sler Z, Rub�a�s V. 2021. Recent advances in Fischer-Tropsch synthesis using cobalt-based catalysts: a review on supports, promoters, and reactors. Catal Rev Sci Eng. 63(3):512–595. doi:10.1080/01614940.2020. 1762367. Giordano F, Trovarelli A, de Leitenburg C, Giona M. 2000. A model for the temperature-programmed reduction of low and high surface area ceria. J Catal. 193(2):273–282. doi:10.1006/jcat.2000.2900. Gontard LC, Ozkaya D, Dunin-Borkowski RE. 2011. A simple algorithm for measuring particle size distributions on an uneven background from TEM images. Ultramicroscopy. 111(2):101–106. doi:10.1016/j.ultramic.2010.10.011. Gorimbo J. 2016. An experimental and thermodynamic study of iron catalyst activation and deactivation during Fischer Tropsch synthesis. University of the Witwatersrand. Gorimbo J. 2018. Use of stability diagrams to predict cata- lyst speciation during Fischer Tropsch reduction stage: a mini-review. Catal Sci Technol. 8(8):2022–2029. doi:10. 1039/C8CY00228B. Gorimbo J, Muvhiiwa R, Llane E, Hildebrandt D. 2020. Cobalt catalyst reduction thermodynamics in Fischer Tropsch: an attainable region approach. Reactions. 1(2): 115–129. doi:10.3390/reactions1020010. Green H. 1927. The effect of non-uniformity and particulate shape on "average particle’ size. J Frankl. Inst. 204(6): 713–729. doi:10.1016/S0016-0032(27)92037-7. Haber J. 1991. Manual on catalyst characterization. Pure Appl Chem. 63(9):1227–1246. doi:10.1351/pac199163091227. Hatch T. 1933. Determination of “average particle size” from the screen-analysis of non-uniform particulate sub- stances. J Frankl Inst. 215(1):27–37. doi:10.1016/S0016- 0032(33)90137-4. Herranz T, Deng X, Cabot A, Guo J, Salmeron M. 2009. Influence of the cobalt particle size in the CO hydrogen- ation reaction studied by in situ X-ray absorption spec- troscopy. J Phys Chem B. 113(31):10721–10727. doi:10. 1021/jp901602s. Heywood H. 2010. Numerical definitions of particle size and shape. J Chem Technol Biotechnol. 56(7):149–154. doi:10.1002/jctb.5000560702. Hilmen A, Schanke D, Hanssen K, Holmen A. 1999. Study of the effect of water on alumina supported cobalt Fischer–Tropsch catalysts. Appl Catal Gen. 186(1-2):169– 188. doi:10.1016/S0926-860X(99)00171-4. Hu J, Yu F, Lu Y. 2012. Application of Fischer–Tropsch synthesis in biomass to liquid conversion. Catalysts. 2(2): 303–326. doi:10.3390/catal2020303. Iglesia E. 1997a. Fischer-Tropsch synthesis on cobalt cata- lysts: structural requirements and reaction pathways. Stud Surf Sci Catal. 107:153–162. Iglesia E. 1997b. Design, synthesis, and use of cobalt-based Fischer-Tropsch synthesis catalysts. Appl Catal Gen. 161(1-2):59–78. doi:10.1016/S0926-860X(97)00186-5. Jacobs G, Das TK, Patterson PM, Li J, Sanchez L, Davis BH. 2003. Fischer–Tropsch synthesis XAFS: XAFS studies of the effect of water on a Pt-promoted Co/Al2O3 cata- lyst. Appl Catal Gen. 247(2):335–343. doi:10.1016/S0926- 860X(03)00107-8. Jacobs G, Das TK, Zhang Y, Li J, Racoillet G, Davis BH. 2002. Fischer-Tropsch synthesis: support, loading, and promoter effects on the reducibility of cobalt catalysts. Appl Catal Gen. 233(1–2):263–281. doi:10.1016/S0926- 860X(02)00195-3. Jacobs G, Ji Y, Davis BH, Cronauer D, Kropf AJ, Marshall CL. 2007. Fischer–Tropsch synthesis: temperature pro- grammed EXAFS/XANES investigation of the influence of support type, cobalt loading, and noble metal pro- moter addition to the reduction behavior of cobalt oxide particles. Appl Catal Gen. 333(2):177–191. doi:10.1016/j. apcata.2007.07.027. James OO, Maity S. 2016. Temperature programme reduc- tion (TPR) studies of cobalt phases in-alumina supported cobalt catalysts. J Pet Technol Altern Fuels. 7:1–12. Jozwiak W, Kaczmarek E, Maniecki T, Ignaczak W, Maniukiewicz W. 2007. Reduction behavior of iron oxides in hydrogen and carbon monoxide atmospheres. Appl Catal Gen. 326(1):17–27. doi:10.1016/j.apcata.2007. 03.021. Kazemnejad I, Feizbakhsh A, Niazi A, Tavasoli A. 2019. Highly dispersed cobalt Fischer–Tropsch synthesis cata- lysts supported on c-Al2 O3, CNTs, and graphene nano- sheet using chemical vapor deposition. Int J Ind Chem. 10(4):321–333. doi:10.1007/s40090-019-00195-9. Kliewer C, Soled S, Kiss G. 2019. Morphological transfor- mations during Fischer-Tropsch synthesis on a titania- supported cobalt catalyst. Catal Today. 323:233–256. doi: 10.1016/j.cattod.2018.05.021. Langford JL, Wilson JC. 1978. Scherrer after sixty years: a survey and some new results in the determination of 1284 J. GORIMBO ET AL. https://doi.org/10.1023/A:1010023316775 https://doi.org/10.1023/A:1010023316775 https://doi.org/10.1021/ie402128y https://doi.org/10.1021/acs.iecr.3c00369 https://doi.org/10.1021/acs.iecr.3c00369 https://doi.org/10.1016/j.apcatb.2018.02.048 https://doi.org/10.1016/j.apcatb.2018.02.048 https://doi.org/10.1002/cite.201100101 https://doi.org/10.1016/j.apcata.2020.117906 https://doi.org/10.1080/01614940.2020.1762367 https://doi.org/10.1080/01614940.2020.1762367 https://doi.org/10.1006/jcat.2000.2900 https://doi.org/10.1016/j.ultramic.2010.10.011 https://doi.org/10.1039/C8CY00228B https://doi.org/10.1039/C8CY00228B https://doi.org/10.3390/reactions1020010 https://doi.org/10.1016/S0016-0032(27)92037-7 https://doi.org/10.1351/pac199163091227 https://doi.org/10.1016/S0016-0032(33)90137-4 https://doi.org/10.1016/S0016-0032(33)90137-4 https://doi.org/10.1021/jp901602s https://doi.org/10.1021/jp901602s https://doi.org/10.1002/jctb.5000560702 https://doi.org/10.1016/S0926-860X(99)00171-4 https://doi.org/10.3390/catal2020303 https://doi.org/10.1016/S0926-860X(97)00186-5 https://doi.org/10.1016/S0926-860X(03)00107-8 https://doi.org/10.1016/S0926-860X(03)00107-8 https://doi.org/10.1016/S0926-860X(02)00195-3 https://doi.org/10.1016/S0926-860X(02)00195-3 https://doi.org/10.1016/j.apcata.2007.07.027 https://doi.org/10.1016/j.apcata.2007.07.027 https://doi.org/10.1016/j.apcata.2007.03.021 https://doi.org/10.1016/j.apcata.2007.03.021 https://doi.org/10.1007/s40090-019-00195-9 https://doi.org/10.1016/j.cattod.2018.05.021 crystallite size. J Appl Crystallogr. 11(2):102–113. doi:10. 1061/9780784479896.140. Lele S, Anantharaman TR. 1962. Influence of crystallite shape on particle size broadening of Debye-Scherrer reflections, in. Proc Indian Acad Sci. 64(5):261–274. doi: 10.1007/BF03047543. Li J, Jacobs G, Das T, Zhang Y, Davis B. 2002. Fischer– Tropsch synthesis: effect of water on the catalytic proper- ties of a Co/SiO2 catalyst. Appl Catal Gen. 236(1-2):67– 76. doi:10.1016/S0926-860X(02)00276-4. Li Q, Kartikowati CW, Horie S, Ogi T, Iwaki T, Okuyama K. 2017. Correlation between particle size/domain struc- ture and magnetic properties of highly crystalline Fe3O4 nanoparticles. Sci Rep. 7(1):9894. doi:10.1038/s41598-017- 09897-5. Lira E, L�opez CM, Oropeza F, Bartolini M, Alvarez J, Goldwasser M, Linares FL, Lamonier J-F, Zurita, MJP. 2008. HMS mesoporous silica as cobalt support for the Fischer–Tropsch Synthesis: pretreatment, cobalt loading and particle size effects. J Mol Catal Chem. 281(1-2):146– 153. doi:10.1016/j.molcata.2007.11.014. Liu Y, Fang K, Chen J, Sun Y. 2007. Effect of pore size on the performance of mesoporous zirconia-supported cobalt Fischer–Tropsch catalysts. Green Chem. 9(6):611–615. doi:10.1039/B614266D. Liu K, Suo H, Zhang C, Xu J, Yang Y, Xiang H, Li Y. 2010. An active Fischer–Tropsch synthesis FeMo/SiO2 catalyst prepared by a modified sol–gel technique. Catal Commun. 12(2):137–141. doi:10.1016/j.catcom.2010.09. 007. Li H, Wang S, Ling F, Li J. 2006. Studies on MCM-48 sup- ported cobalt catalyst for Fischer-Tropsch synthesis. J Mol Catal Chem. 244(1-2):33–40. doi:10.1016/j.molcata. 2005.08.050. Lou€er D, Weigel D, Langford JI. 1972. Etude des profils de raies de diffraction des rayons X d’une poudre d’hydrox- yde de nickel. J Appl Crystallogr. 5(5):353–359. doi:10. 1107/S0021889872009756. Lu X. 2011. Fischer-Tropsch synthesis: towards understand- ing. Univ. Witwatersrand. Ma W, Dalai AK. 2021. Effects of structure and particle size of iron, cobalt and ruthenium catalysts on Fischer– Tropsch Synthesis. Reactions. 2(1):62–77. doi:10.3390/ reactions2010006. Malet P, Caballero A. 1988. The selection of experimental conditions in temperature-programmed reduction experi- ments. J Chem Soc Faraday Trans 1. 84(7):2369–2375. doi:10.1039/f19888402369. Mart�ınez A, L�opez C, M�arquez F, D�ıaz I. 2003. Fischer– Tropsch synthesis of hydrocarbons over mesoporous Co/ SBA-15 catalysts: the influence of metal loading, cobalt precursor, and promoters. J Catal. 220(2):486–499. doi:10. 1016/S0021-9517(03)00289-6. Matyi R, Schwartz L, Butt J. 1987. Particle size, particle size distribution, and related measurements of supported metal catalysts. Catal Rev Sci Eng. 29(1):41–99. doi:10. 1080/01614948708067547. Matyi RJ, Schwartz LH, Butt JB. 1987. Particle size, particle size distribution, and related measurements of supported metal catalysts. Catal Rev. 29(1):41–99. doi:10.1080/ 01614948708067547. Melaet G, Lindeman AE, Somorjai GA. 201