Core–Shell catalyst particles for tandem catalysis: An experimental/numerical approach towards optimal design

chemical processes and increase their efficiency. On the other hand, the design of efficient, optimal and targeted tailored tandem catalysts is yet so challenging as the optimal catalyst loading is difficult to assess a priori. In this article, we present a concise route towards the design of optimal core–shell tandem catalyst particles on the example of coupled RWGS and FTS reactions for any specific spherical morphology. The route features five consecutive steps including: tandem system identification, catalyst synthesis, i.e. mono-and tandem-functional, catalyst characterization and initial performance test, kinetic modeling with parameter estimation if necessary, and optimal design of catalysts. The initial step features thermodynamic equilibrium calculations for RWGS and FTS showing a common operational window. Then, Pt and Co are selected as active metals and the formulation of the tandem catalyst is designed. For the second step, the synthesis route for the tandem catalyst Pt,CeO 2 @SiO 2 -Co, and the mono-functional catalysts, Pt@SiO 2 and CeO 2 @SiO 2 -Co are presented. For the third step, all catalysts were tested for CO 2 hydrogenation as an exemplary tandem process. A reduced transport model from literature was adjusted for RWGS and FTS reactions with kinetic expression from literature to enable numerical optimization. The kinetic parameters are estimated based on the performance tests of the mono-functional reference materials, i.e. Pt@SiO 2 for RWGS and CeO 2 @SiO 2 -Co for FTS. The model is validated by cross comparison to the data from the tandem reaction setup. In the fifth step, the model was used for the numerical optimization of the catalyst loading on core and shell leading to the identification of the optimal design, resulting in a significant increase of C2+ Yield.


Introduction
Tandem and multi-component reactions involve combining multiple consecutive reactions into a single reactor [1,2].This offers various advantages compared to the traditional sequential reactions, including the elimination of process steps like separation, purification, and intermediate transfer which leads to cost savings and a more ecofriendly process [3,4].The tandem approach has been used extensively in organic synthesis and recently in chemical processes such as CO and CO 2 hydrogenation and alcohol oxidation [5][6][7][8][9] Nominal operating point in this field, one-pot catalytic processes still have no common application due to the complexity of identifying and controlling active phases in multi-site catalysts [11,12].One strategy to simplify the intricate interactions between active phases in multi-site catalysts to systematically comprehend tandem processes, is employing core-shell structures that provide a series of well-optimized isolated active sites.
The core-shell structures can guarantee the close distance between the active sites [13].Furthermore, the compatibility of two active phases can be optimized by controlling the structural properties, including the shape, quantity, and size of active metals, as well as the specific distance between them, the pore size distribution, and the porosity of the shell [14,15].Although, using a shell may block fraction of the active surface of the core, covering and encapsulating the nanoparticles (NPs) serves as a protective measure against issues such as aggregation, leaching, and sintering.Additionally, a high porous shell can provide efficient mass transfer within the core-shell catalyst [16][17][18].The synthesis of bimetallic core-shell NPs with controllable structure is challenging and demands the development of precise model systems in the planning of multi-step synthesis.Su et al. [19] proposed a four-step method to synthesize 85 nm CeO 2 -Pt@SiO 2 core-shell structures.The process included hydrothermal synthesis of CeO 2 using high molecular weight PVP as a capping ligand, pre-synthesis of Pt NPs as the initial active metal on the core, hydrothermal deposition of Pt NPs on the CeO 2 , and sol-gel synthesis of the silica shell.Despite the successful development of a well-defined catalyst, challenges in scaling up can persist due to the demanding conditions imposed by the use of high molecular weight PVP and the small size of nanoparticles, particularly in steps 1 and 3 of their proposed synthesis method.Building on this method, Xie et al. [20] extended the network by integrating homogeneous cobalt NPs onto the shell through two additional synthesis steps, resulting multi active phases catalyst within a total of six synthesis steps.This structure functioned as a tandem catalyst for CO 2 hydrogenation, achieving approximately 10% and 40% selectivity towards C 2 + in hydrocarbon distribution at 350 °C and 250 °C, respectively.In a recent study, Gioria et al. [21] introduced a distinctive morphology for the Pt-SiO 2 @SiO 2 -Co catalyst, simplifying the rational synthesis method into five steps.This involved replacing CeO 2 NPs with SiO 2 in the core and performing an in-situ synthesis of Pt NPs on the core instead of using pre-synthesized Pt.The resulting structure comprised a 199 nm silica core covered by a 50 nm-thick mesoporous silica shell, exhibiting a 14% selectivity toward C 2 + and 86% methane in total hydrocarbon distribution in CO 2 hydrogenation.
In both studies, CO 2 hydrogenation followed the carbon monoxide intermediate pathway through two sequential reactions.Initially, CO 2 is transformed into CO via RWGS (Reverse Water Gas Shift) occurring on the core.Subsequently, as produced CO diffuses through the porous shell and reacts on its surface, hydrocarbons are generated via the FTS (Fischer-Tropsch Synthesis).Pt NPs which are well known as an active phase for RWGS at low temperatures are located on the core and Co NPs which activate both CO and CO 2 are located on the Shell [22][23][24].While well-designed tandem catalysts have been employed above, their performance in tandem systems is currently restricted, exhibiting 60% selectivity for CO and predominantly yielding methane in hydrocarbon products.The optimum performance of such systems concerning catalyst structure remains unclear.
The core of the rational catalyst design for a tandem process lies in understanding the relation between catalyst structure, properties, and performance.What constitutes an efficient strategy for optimizing the tandem catalyst's structure?The conventional approach involves the energy-and time-intensive process of experimentally determining the optimal ratio of various parameters such as shell thickness, porosity, and the ratio of active metal, through a multi-step core-shell synthesis and performance tests.In this article, we propose a new, 5 steps protocol to design an optimal core-shell catalyst design considering the structural-performance relationship.The aim is not to present the best performing core-shell structure catalyst for one certain reaction network but line out a blueprint for the proper design of any of such systems within its limits.The initial step entails investigating of a tandem reaction through thermodynamic simulation.Subsequently, the approach involves the following steps: designing a controllable coreshell structure, conducting characterization and systematic catalytic performance tests including both mono-tandem function catalysts, formulating and validating a mathematical model for the system and applying the validated model for numerical optimization of the catalyst's properties.The final step of synthesizing the catalyst again for optimized catalyst properties was not part of the study.
To show the possibility of a CO 2 hydrogenation tandem process through sequential RWGS and FTS reactions, as well as to create a comparable model catalyst with previous reports, Pt NPs and Co NPs were chosen to facilitate RWGS and FTS reactions, respectively.A general and rational synthesis method based on the microemulsion approach is introduced for creating a unique multi-core@shell structure.This structure features a well-defined architecture of Pt and Co active metals within a mesoporous silica shell, ensuring the rather constant values of each individual active metal for mono-tandem function catalysts.Importantly, given the precious nature of Pt, the model catalysts have been designed using a significantly lower proportion of Pt compared to Co. Successfully, the optimal catalyst formulation regarding the active metals loading is achieved through numerical optimization based on the approach outlined.

Synthesis of the nanoparticles 2.2.1. Synthesis of oleic acid-capped CeO 2 NPs
CeO 2 NPs have been prepared through a shape and size-controlled rational approach in one-pot hydrothermal method described in [25] with some modifications.Initially, 24.41 mmol of Ce(NO 3 ) 3 .6H 2 O were dissolved in 15 mL of deionized water.Then, an aqueous solution of cerium along with 15 mL of toluene, 632 µL of oleic acid, and 150 µL of tert-butylamine were respectively added to a 50 mL teflon chamber without stirring.The autoclave reactor was heated to 180 °C and remained for 24 h.After reaction, possible impurities were removed by centrifuging the product at 4000 rpm for 15 min.Oleic acid-capped CeO 2 NPs were precipitated by adding 40 mL ethanol to the obtained brown organic phase and separated by centrifugation at 4000 rpm for 15 min.The purified CeO 2 NPs can be dispersed in any non-polar solvents and used as an organic phase for micro-emulsion synthesis.Here, CeO 2 NPs were rapidly dispersed in 1 mL of chloroform using 2 min sonication and applied in the following step of the synthesis.

Synthesis of PVP and TTAB-capped Pt NPs
PVP and TTAB-capped Pt NPs were synthesized through the alcohol reduction method proposed by Tsung et al. [26], with some modification.Briefly, 0.0219 mmol of K 2 PtCl 4 were dissolved in 4 mL ethylene glycol using sonication.The Pt(II) solution was injected into a schlenk flask containing 0.109 mmol of TTAB and 0.196 mmol of PVP (  = 29 000) dissolved in 10 mL ethylene glycol under argon protection.The alcoholic solution was stirred at 250 rpm for 15 min at ambient temperature.The reaction temperature was then increased to 175 °C and the reaction continued for 30 min at this condition.The formation of Pt NPs was indicated by a black color of the mixture above 120 °C.After natural cool down, 60 mL of acetone were added to precipitate the PVP and TTAB-capped Pt NPs.The pre-synthesized NPs were collected by centrifugation at 6000 rpm for 5 min, and then immediately dispersed in 1 mL chloroform for the subsequent synthesis step.

Synthesis of oleic acid-capped Co NPs
The mono-dispersed Co NPs were obtained from the thermal decomposition of cobalt carbonyl under inert conditions [21].290 µL of oleic acid were dissolved in 30 mL of o-dichlorobenzene in a three-neck flask equipped with a condenser and heated up to 170 °C.Subsequently, 2.93 mmol of Co 2 (CO) 8 dissolved in 6 mL of o-dichlorobenzene was quickly injected into the flask, causing a dark-reddish color of the solution and instantly releasing CO due to the thermal decomposition of cobalt carbonyl.The reaction was continued for 20 min, and cooled to the ambient temperature naturally.Eventually, the Co NPs were precipitated using 2-propanol, recovered by centrifugation at 9000 rpm for 30 min, and redispersed in 60 mL hexane.

Synthesis of CeO 2 @SiO 2 as inert core-shell catalyst
To synthesize a mesoporous silica shell, an oil-in-water microemulsion technique, inspired from magnetic core-shell NPs [27], was applied.To prepare the water-surfactant phase, 1.09 mmol of CTAB were dissolved in 20 mL deionized water.Then, 1 mL chloroform as organic phase, containing the stabilized pre-synthesized core, was gradually added into the aqueous solution and vigorously mixed for 20 min until a milky homogeneous oil/water solution was achieved.This solution was then heated up to 60 °C for 20 min to facilitate the evaporation and removal of chloroform.Subsequently, the resulting mixture was diluted using 80 mL of deionized water, followed by sequential additions of 6 mL of ammonia solution, 1 mL of TEOS, and 10 mL of ethyl acetate for shell formation.The solution was sonicated for 30 s and the reaction was slowly stirred for 6 h at 40 °C.Afterward, the product was separated from the light yellow suspension with centrifugation at 4000 rpm for 15 min and washed five times using deionized water and ethanol.To remove CTAB, the product was mixed with 200 mL of 10 mg mL −1 ammonium nitrate solution for 6 h at ambient temperature.Finally, CeO 2 @SiO 2 NPs were washed several times with ethanol and deionized water.

Synthesis of Pt@SiO 2 as RWGS core-shell catalyst
Pt@SiO 2 core-shell NPs were obtained using the synthesis method described in Section 2.2.4.Pre-synthesized Pt NPs dissolved in 1 mL chloroform were mixed with 20 mL aqueous solution of 1.09 mmol CTAB under a stirring rate of 550 rpm for 20 min.The homogeneous light gray micro-emulsion was heated up to 60 °C for 20 min.Upon the removing of chloroform, 80 mL of deionized water, 6 mL of ammonia solution, 1 mL of TEOS, and 10 mL of ethyl acetate were added followed by sonication for 30 s.The reaction solution was stirred slowly at 40 °C for 6 h, and the product was isolated from the gray reaction suspension with centrifugation at 4000 rpm for 15 min.After being washed multiple times with ethanol and deionized water, CTAB was removed by mixing the resultant products with 200 mL ethanol containing 10 mg mL −1 of NH 4 NO 3 for 6 h, and it was subjected to a final washing step.

Synthesis of CeO 2 @SiO 2 -Co as FTS core-shell catalyst
In this study, FTS core-shell catalyst was designed by utilizing the CeO 2 @SiO 2 as an inert support and oleic acid-capped Co NPs as the active phase.The deposition of Co NPs onto the silica surface was carried out by preparing a dispersion of CeO 2 @SiO 2 in hexane, followed by the addition of the desired quantity of Co NPs to the support.The mixture was vortexed for 15 min, and the solvent was evaporated and removed from the structure at ambient temperature.In the final step, the resulting dried catalyst was calcined at 350 °C for a duration of 2 h with a heating rate of 5 °C min −1 for removing any residual organic components.

Synthesis of Pt,CeO 2 @SiO 2 -Co as tandem catalyst
Pt,CeO 2 @SiO 2 -Co tandem catalyst was synthesized using a multistep synthesis method.Initially, one batch of pre-synthesized Pt and CeO 2 NPs were prepared according to the method described in 2.2.1 and 2.2.2 sections.Next, Pt and CeO 2 NPs were separately dispersed in 500 µL of chloroform and added to 20 mL aqueous solution containing 1.09 mmol of CTAB.The solution was vigorously stirred to obtain homogeneous chloroform in water micro-emulsion solution.After the removal of chloroform at 60 °C, the solution was diluted with 80 mL of deionized water, 6 mL of ammonia solution, 1 mL of TEOS, and 10 mL of ethyl acetate.The resulting mixture was sonicated for 30 s and the shell synthesis was carried out at 40 °C for 6 h.The coreshell NPs were obtained by centrifugation and washed multiple times with deionized water and ethanol.To remove CTAB from the structure, the product was mixed with 10 mg mL −1 ammonium nitrate in 200 mL ethanol.After separating core-shell NPs, a final washing step was performed using deionized water and ethanol.The dried sample, named Pt,CeO 2 @SiO 2 , was dispersed in hexane for the next synthesis step.To apply Co NPs as second active metal, onto the core-shell structure, a wetness impregnation was performed.A desired amount of Co NPs in hexane was added to the Pt,CeO 2 @SiO 2 suspension and mixed for 15 min using a vortex.Hexane was then evaporated and removed from the structure at ambient temperature.Finally, the catalyst was calcined at 350 °C for 2 h with a heating rate of 5 °C min −1 .

Characterizations
The morphology, elemental distribution, size, and geometry of the pre-synthesized as well as core-shell NPs were investigated by transmission electron microscopy (TEM) and high-resolution scanning electron microscopy (STEM).The TEM analysis was conducted using a conventional TECNAI G 2 20 S-TWIN with LaB6 emitter from FEI/TFS company operated at 200 kV.STEM imaging was performed with a probe cscorrected JEM-ARM300F2 cold FEG from JEOL Ltd., Japan, operated at 300 kV.Also, the STEM images were recorded with a camera length of 8 cm, which corresponded to a high-angle annular dark field (HAADF) detection angle of 68-280 mrad.The microscope implemented in the mapping investigation was equipped with a dual SDD EDX system from JEOL Ltd., with an energy resolution of 134 eV and an angle of 2 × 2 sr.
Etching X-ray photoelectron spectroscopy (XPS) was performed to evaluate the composition of materials and the chemical state of the corresponding elements on the surface and inside the core-shell NPs.The measurements were performed using a ThermoScientific K-Alpha + X-ray Photoelectron Spectrometer.All samples were analyzed using a microfocused, monochromated Al K X-ray source (1486.68eV; 400 micrometer spot size).The elemental spectra were fitted with an asymmetric voigt profile after the subtraction of a Shirley background using Avantage software.Due to the absence of an internal reference level and the difficulty in determining the sample work function, we utilized the C-C peak of the C1 spectra for adventitious carbon at 284.8 eV as a reference point [28].All the spectra were adjusted in correspondence with the C-C component position at each level of etching.
Powder X-ray diffraction (XRD) was performed to study the crystalline phase of core-shell NPs using a Bruker D8 Advance diffractometer in reflection geometry.Before the test, NPs were ground on a silica sample holder, and a Cu Kα anode ( = 1.54178Å) with a current of 40 mA and a voltage of 40 kV was utilized for the collection of data.
To determine the surface area, pore size, and pore volume of core-shell NPs nitrogen sorption measurements were performed using QuadraSorb SI device Quantachrome Instruments, Boynton Beach, FL, USA, at a cryogenic temperature of 77 K.The NPs were dried and degassed at 200 °C for 12 h prior to the analysis.Brunauer-Emmett-Teller (BET) methods were applied to calculate the surface areas over a pressure range of 0.05-0.1 = p/p 0 using the N 2 adsorption isotherms and the linear fit was obtained using 5 points in the pressure range of 0.04-0.25.Furthermore, the surface area obtained was calculated using the BETSI tool for comparison and obtaining more precise results.To calculate the pore size distributions, Non-Local Density Functional Theory (NLDFT) in equilibrium mode on carbon was utilized for N 2 sorption data collected at 77 K. CO 2 sorption isotherms were recorded using the same device at room temperature.
The elemental weight loading (wt%) was quantified through the inductively coupled plasma (ICP) measurement using a Horiba Scientific ICP Ultima 2 device (Horiba, Kyoto, Japan).To prepare the samples for ICP, they were dispersed in 2 mL of HF and 5 mL of HNO 3 and heated at 200 °C for 5 h using an autoclave reactor.This digestion process was carried out to destroy the samples into their constituent elements for further analysis.

Catalytic performance test
The catalytic performance tests were conducted in five tubular parallel reactors.Four reactors were loaded in order with Pt@SiO 2 (RWGS) in R1, Pt,CeO 2 @SiO 2 -Co (tandem) in R2, CeO 2 @SiO 2 -Co (FTS) in R3, and CeO 2 @SiO 2 (inert) in R4 while the fifth reactor was dedicated to bypass measurement, Fig. S.1 [29].Catalyst particles with the sieve fraction of 100-200 µm diluted with davisil at the same size range were used for the catalytic testing.The properties of catalysts loaded in four reactors are presented in Table 1.Each reactor has a length of 64.5 cm, an inner diameter of 9.4 mm, and an effective diameter of 6.4 mm, and a reactor head containing inlet connections for the feed and a hull for placing the thermocouple with an outer diameter of 3 mm.The electric furnace was used to supply the heat and the temperature was monitored at three local points along the length of the reactor while the catalyst bed was positioned in the isothermal zone.The flows of the feed stream, including N 2 , Ar, H 2 , and CO 2 , were regulated using individual mass flow controllers (MFCs) for each component.
Prior to the reaction, all catalysts were in situ reduced by 50% of H 2 and 50% N 2 flow with GHSV of 30 000 nmL g −1 h −1 , at 350 °C and atmospheric pressure for 2 h.Then, the gas composition and temperature switched to the experimental design which is summarized in Table S.1 [29], and the pressure of 10 bar was built up according to each operation condition.The reactions were performed for the duration of 12 h under each operational condition, and data was recorded using an online gas chromatograph (GC, Agilent 7890B) at 3 h intervals.The exit gas stream was diluted with N 2 and led through a multi-position valve to the GC for analysis.To prevent condensation of the effluent, the outlet stream was transferred with heated lines at 180 °C to the GC.Helium was used as the GC carrier gas, while Ar served as the internal standard during all the experiments.The GC was equipped with a thermal conductivity detector (TCD) and a flame-ionized detector (FID) for the quantification of non-carbon and carbon base components, respectively.To separate, H 2 , N 2 , and Ar, an HP-Plot 5A column (30 m × 0.53 mm × 50 µm) was utilized, and carbon-containing components were separated using an HP-Plot Q column (30 m × 0.53 mm × 40 µm) from Agilent with a Polyarc ® reactor placed prior to FID.

Modeling
As building a valid model is crucial for the 5th step of the proposed design protocol, the modeling methodology is briefly lined out here.For modeling the catalyst performance, the fast computing model for coreshell tandem catalyst particles proposed in [30] is used and adjusted for the present system of RWGS and FTS.The model is based on first principles conservation laws for mass and energy and calculates the concentration profiles of all involved gas phase species as well as the temperature profile within  core-shell catalyst particles in a reactor.The diffusive fluxes within the particle are modeled with Knudsen diffusion.All physical properties of the catalyst, like void fraction, the amount of active metal or pore diameter are direct input parameter to the model.For a detailed description of the model please be referred to the original literature source.For model formulation, MOSAICModeling [31,32] is used.The generated code is then exported and solved in MATLAB ® , where the nonlinear solver fsolve with the trust-region-dogleg algorithm is used.The kinetics for RWGS on the N. Bashiri et al.

Table 2
Transport parameters for simulation study.
5 core were taken from [33] and for FTS on the shell the kinetics from [34] were applied up to a chain length of C4 resulting in 16  As conversion of CO 2 on the CeO 2 @SiO 2 -Co catalyst in reactor 3 could be observed contrary to the inert one in reactor 4, it was concluded that the Co was active for RWGS by itself.Therefore, the kinetics from [33] were also used to account for RWGS on the shell, assuming the same mechanism but using different pre-exponential factors for core and shell.Moreover, as no production of alcohols was observed in the experiments, their production rates were set to 0 in the model.The catalyst structure used in this study differs from the original sources of the kinetic expressions in terms of structure and support.Nevertheless, the kinetics from [33] was developed on a system most similar to the one used in this study.The catalyst used in [34] used the same active metal supported on a different compound (i.e.active carbon).
On the other hand, the proposed kinetics were the most detailed ones utilizing at least the same active metal.In order to adapt the kinetic expressions to the system used here, the pre-exponential parameters of the kinetic expressions were estimated again based on the monofunctional catalytic performance experiments described in Section 2.4.This approach implies the assumption that the tandem system can be described by superpositioning the mono-functional reaction rates.
As the model requires a number  of core-shell catalyst particles to be provided as well as a catalyst loading  and a porosity  these numbers were calculated from a nonlinear equation system added to the model described in [30]. 3 (3) The overall catalyst mass  overall , the pore volume  P and the weight percentage of the active metals  were taken from the characterization results.The transport propoerties are listed in Table 2.

Parameter estimation
The pre-exponential parameter of the RWGS on the Pt-core was estimated based on the experimental results of the mono functional catalyst Pt@SiO 2 .The pre-exponential parameters for the FTS and RWGS on the Co-shell were estimated based on the experimental results of the mono-functional catalyst CeO 2 @SiO 2 -Co.The results of the tandem catalyst Pt,CeO 2 @SiO 2 -Co can therefore be used as cross validation as their information is not utilized during the parameter estimation.Experiment numbers 1 & 2 from Table S.1 were omitted as steady state was not reached.For the parameter estimation, an optimization problem is formulated: subject to: (, ) = 0 (7) to find the best set of parameters  minimizing the deviation of measured molar fraction  exp.
(mean of 4 measurements on the same set-point) and simulated molar fraction  sim. of all  components in the objective function  .The nonlinear constraints  include the coreshell model described in Section 2.5.The deviation is weighted by the measured value to normalize the contribution of all measurements, as they are of different order of magnitude.For the Pt-core CO, CO 2 , and H 2 concentrations were used, and for the Co-shell CO, CO 2 , CH 4 , C 2 H 6 and H 2 were considered.As no C 3 H 8 was detected in the catalytic performance test of the mono-functional CeO 2 @SiO 2 -Co catalyst, this specie was not included in the parameter estimation.
For the estimation, a bootstrapping approach [35] was chosen with a total of 300 dice rolls for each estimation and the standard deviation for the concentrations from the experiments was used to weigh the objective function.The parameter estimation was carried out in MATLAB ® via the lsqnonlin function.The estimated results and the initial values from the original literature sources are displayed in Table 3.All parameters except for k 7,0 could be identified as the std.deviation indicates.The parameter k 7,0 is the pre-exponential factor for the generation of alkanes.

Numerical optimization
For the optimization of the catalyst design several decision variables could be chosen, such as catalyst loading, porosity or shell thickness.Here, catalyst loading was chosen as it could be aimed for very precisely in the synthesis.MOSAICmodeling [36] was used to generate code for AMPL [37], where the optimization algorithm ipopt [38] is utilized.The optimization problem is stated as follows: subject to: (, ) = 0 (9) with  being the objective function to minimize (i.e.maximize the Yield of C 2+ components  C 2+ ),  being the catalyst loading,  being the core-shell model representing the nonlinear constraints, and  the unknowns from the core-shell model i.e., concentrations, temperature, etc.The mass fraction of the inert support  inert is bounded to a certain minimum threshold of (a) 95% and (b) 90%.This threshold might vary from case to case but needs to be specified as otherwise the mathematical model would converge to a point where the catalyst particle consists of 100% active material and no inert material, such as support.Another approach would be to use cost functions for the reaction products and the catalyst material, which is beyond the scope of this article.

Characterization of core-shell catalysts
A general and rational synthesis method based on the microemulsion approach is introduced for creating a unique multi-core-shell structure with a well-defined architecture of Pt and Co as active metals.Fig. 1 illustrates the stepwise synthesis of multi-core-shell catalysts.For the RWGS catalyst, Pt@SiO 2 , the process involves two main synthesis steps: (1) the synthesis of TTAB and PVP-capped Pt NPs and (2) the subsequent formation of the silica shell.The FTS, CeO 2 @SiO 2 -Co, and tandem, Pt,CeO 2 @SiO 2 -Co, catalysts, on the other hand, follow four distinct steps: (1) the synthesis of the oleic acid capped-ceria and TTAB and PVP-capped Pt NPs as core, (2) the shell formation, (3) the synthesis of oleic acid-capped Co NPs, and (4) the deposition of Co NPs onto the silica surface.Pt NPs serve as the active metal in the core for both the RWGS and tandem catalysts, while CeO 2 NPs is employed as  Step 2. shell formation using O/W microemulsion method leading to Pt@SiO 2 , RWGS catalyst, and CeO 2 @SiO 2 , inert catalyst, and Pt,CeO 2 @SiO 2 , core for tandem catalyst; Steps 3 and 4. synthesis of Co NPs and subsequent impregnation on to Pt,CeO 2 @SiO 2 and CeO 2 @SiO 2 resulting in CeO 2 @SiO 2 -Co, FTS catalyst, and Pt,CeO 2 @SiO 2 -Co, tandem catalyst.
the inert core in the tandem and FTS catalysts.The developed catalyst model addresses critical aspects of a tandem system, including the sequential arrangement of active metals enabled by the redispersion capability of pre-synthesized Pt and Co NPs in organic solvent.Additionally, proximity is achieved through the close distance between two active phases, approximately 75 nm apart, and compatibility is ensured by the ability to control the quantity of active metals situated on both the core and shell under the equilibrium conditions of synthesis.
To create an oil-in-water microemulsion system, initially, the core should be able to redisperse in an organic solvent, also good dispersibility is essential for further synthesis steps [39].Here, oleic acid-capped CeO 2 NPs and PVP and TTAB-capped Pt NPs were easily redispersed in chloroform and used as an oil phase that solubilizes the oil domain into the nonpolar tail region of the surfactant to yield stable microstructure.The CeO 2 nuclei that were generated in water transferred into the toluene solution by using oleic acid as a stabilizing agent in the organic-inorganic interface, and polyhedral CeO 2 NPs with the size of 6.07 ± 0. The average diameter of core-shell NPs and the distance between the external surface of the core and the surface of the shell are shown in Table 1.Also, this distance, named , varies with particle radius since the core NPs occupy a specific region within the nanoparticles.In particular, Pt,CeO 2 @SiO 2 -Co NPs exhibit a relatively larger diameter than , measuring approximately 205 nm and 69, respectively.This size discrepancy can be attributed to the unique composition of Pt and Ce as the core material, distinguishing it from other samples which feature only a single metal oxide in the core.found to be uniformly distributed throughout the entire particle, i.e., a core-shell structure.On the basis of the EDS line profile of the NPs across the marked X and Y axes, in Fig. 2i-j, the detected intensity of Pt and Ce atoms increases from the particle's surface toward its core and proves that Pt and Ce NPs were mostly located as the core.Additionally, there is a correlated increase in the intensity of Si and O signals as the Co signal diminishes from the particle's surface toward the core.The element profiles are well in accordance with the etching XPS results, Fig. 3a.Fig. 3a depicts the variations obtained in the Pt4f and Co2p spectra throughout the eleven levels of the etching process.The spectra of Ce3d, Si2p, and O1s are also shown in Fig. S.3.The Pt4f spectra are rendered undetectable at the surface, whereas the intensity of Pt increases with the etching level, providing evidence for the presence of Pt within the core.Conversely, the Co2p spectra exhibit a decremental trend with increasing etch levels, which the surface spectra displaying the highest intensity.Fig. 3c displays the fitting of the Pt4f spectrum corresponding to the 11th step of etching.The fitting of Pt4f was performed with three doublets in which the binding energy (BE) values of the Pt4f 7∕2 peaks are at 71.81, 72.94, and 74.37 eV, accompanied by corresponding doublets for Pt4f 5∕2 with a difference of 3.30 eV (+0.2 −0.1) [40][41][42].It has been proposed that the peaks at 72.94 eV and 74.37 eV are associated with Pt oxidation states.This suggests the formation of PtO  during the shell formation in the presence of ammonia and the subsequent calcination process.Because the oxidation state of Pt in Pt 3 O 4 is lower than in PtO 2 and higher than in PtO, an intermediate BE is expected for Pt 3 O 4 that is challenging to differentiate from PtO 2 [43].However, -PtO 2 has been identified as a thermodynamically stable structure on the Pt (111) surface under atmospheric oxygen pressure and low temperatures, while Pt 3 O 4 is the stable oxide between 597-701 • C [44].Consequently, we attributed the two doublets at 72.94 eV and 74.37 eV to PtO and PtO 2 species within the oxides present in our sample.The BE at 71.81 eV coincides with the 71.9 eV (±0.1) peak observed for metallic Pt and Pt bound to chemisorbed oxygen, as reported in Refs.[26,45], consistent with XRDs results.Fig. 3b illustrates the Co2p spectra fittings for both the surface and the 11th step of etching.An slight increase in intensity on the low binding energy side of the 2p 3∕2 peak, along with increment in the intensity of satellite features of 2p 3∕2 during the etching, suggests alterations in the oxidation state of cobalt.For the high-resolution XPS spectra of 2p 3∕2 , the surface exhibits five peaks, while the 11th etched level displays four peaks.The fitting of the spectra for Co 2+ (780.7),Co 3+ (779.3), and Co + (0 >  > 2) and the corresponding satellites are shown in blue, purple, and orange, respectively [46].Notably, the satellite peak centered at 789.8 eV is attributed to the shake-up excitation of Co 3+ , while the peaks at 782.7 eV and 786.3 eV correspond to the satellite peaks of Co 2+ .Analyzing the surface spectra fitting reveals the presence of Co 2+ and Co 3+ , indicating the phase of Co 3 O 4 on the surface layer of cobalt.These fitting parameters align with those previously reported by Biesinger et al. [47].The lower BE of Co 3+ compared to Co 2+ is attributed to the final relaxation state and Madelung potential.At the 11th level of etching, the shifts in lower BE and the appearance of a peak centered at 778 eV suggest the existence of reduced Co species.This observation combined with the disappearance of the Co 3+ satellite implies that some Co 3 O 4 overlayers may have been sputtered from the surface or possibly underwent direct reduction through exposure to argon ions.In addition to consideration of the BE values, satellite structures, and spin/orbit splitting, the interval between Co2p 3∕2 and Co2p 1∕2 is also used to determine the Co oxidation state species [48,49].The energy level difference of 15 eV indicates that Co 3+ is dominant, while the BE separation of 16.0 eV indicates an oxidation state of Co 2+ .Overall, the predominant cobalt species on the surface layer is Co 3 O 4 , whereas, with etching, it shifts to CoO.For reference, the curve fitting parameters are provided in Table S.3.
X-ray diffraction (XRD) analysis was conducted to investigate the lattice structure of the NPs, and the results are shown in Fig. 3d.The broad diffraction peak observed at a 2θ ranging from 15 to 30 degrees is attributed to the amorphous silica structure, indicating the successful formation of amorphous silica during the shell synthesis process for all core-shell NPs.The distinctive peaks corresponding to the crystalline phase of cubic CeO 2 are clearly detectable in the inert, FTS, and tandem catalysts, all incorporating ceria in the core.For RWGS catalyst, peaks observed at 36.89 and 46.39 degrees align well with the (111) and (200) crystallographic planes of Pt.The peak detected at 36.45 degrees in both tandem and FTS catalysts corresponds to Co 3 O 4 , indicating that these samples share the same crystalline cobalt structure.Evidently, the tandem catalyst incorporates the active metals present in both FTS and RWGS catalysts at identical crystalline phases.
BET surface area was determined through N 2 sorption isotherm and BETSI (Table S   , shows that catalysts have likely mesoporous structure and the distribution shifts toward larger pore size for FTS and tandem catalysts.The mean pore diameter measured 1.6 nm for RWGS, while it increased to 2.9 nm and 3.7 nm for FTS and tandem catalysts, respectively.This shift may be attributed to the potential blocking of smaller pores by Co NPs.Pore size and pore volume data are subsequently utilized in the calculations for determining the size of nanoparticles in the modeling section.
The investigation of CO 2 sorption revealed substantial uptakes even at room temperature for the RWGS, FTS, and tandem catalysts, Fig. S.9.The CO 2 sorption isotherms exhibited uptake values of 48, 18.5, and 21.5 cm 3 g −1 for the RWGS, FTS, and tandem catalysts, respectively.The higher CO 2 sorption observed in the RWGS catalyst suggests a stronger affinity of Pt for CO 2 sorption compared to Co, despite Co being more accessible and comprising almost ten times the weight percentage of Pt.However, the tandem catalyst exhibits lower sorption compared to the RWGS catalyst and higher sorption compared to the FTS catalyst.This observation underscores the accessibility of Pt NPs within the core, even in the presence of a silica shell and Cobalt coverage.It is important to note that a portion of the Pt NPs is hindered due to pore blockage.
The multi-metallic core-shell NPs were precisely synthesized to achieve the comparable weight percent of active metals among the catalysts.The Pt content in Pt@SiO 2 and Pt,CeO 2 @SiO 2 -Co are measured as 0.54 and 0.50 wt.%, while the Co amount in CeO 2 @SiO 2 -Co and Pt,CeO 2 @SiO 2 -Co are 4.72 wt.% and 3.86, respectively, cf.Table 1 [29].Furthermore, the concentration of CeO 2 which acted as the inert core was found to be much lower than the other elements.

Catalytic test results and model comparison
Fig. 4 displays the carbon dioxide conversion over time on stream for inert, RWGS, FTS, and tandem catalysts under various operation conditions [29].This plot highlights the increase in X.CO 2 % for tandem catalyst compared to single-phase catalysts, providing evidence for the accessibility and activity of both active phases.CeO 2 @SiO 2 which is considered as an inert catalyst showed activity of less than 1%.This low level of activity in comparison to other catalysts supports the assumption of its inert role.The results illustrate the greater stability of the Pt@SiO 2 compared to Pt,CeO 2 @SiO 2 -Co and CeO 2 @SiO 2 -Co, which indicates the protection function of the shell in sintering of NPs.The  observed decrease in activity for both tandem and FTS catalysts during the initial 20 h of the reaction can be attributed to the sintering of Co-NPs on the shell [21].For all catalysts, the experimental X.CO 2 % are less than X.CO 2 % at thermodynamic equilibrium condition, Fig. S.14.
In Fig. 5, the results of the outgoing concentrations (molar fractions in %) from simulation and experiment for Pt,CeO 2 @SiO 2 -Co (tandem) are compared by means of parity plots.For a comparison in actual molar fractions please be referred to Fig. S.10.The dashed lines indicate a deviation of ±20%.The simulation was carried out with the estimated parameters of reactors 1 and 3 (cf.Table 3) and the design parameters according to Table 1.The concentrations of the educts CO 2 and H 2 at the reactor outlet are predicted very well by the model as Figs.5(a) and 5(b) indicate.For the products CO and C 2 H 6 , the prediction is also good (cf.Figs.5(c) and 5(e)), although the deviation increases towards lower overall values.The measured concentration of C 3 H 8 is very low (≤1 − 3%, near the detection limit) and the deviation seen in Fig. 5(f) can be explained with the gap of information from the monofunctional catalyst as stated in Section 2.6.The predictions of CH 4 tend to show a larger deviation between experiment and simulation as Fig. 5(d) indicates.From Table 3 it can be seen, that the standard deviation of the kinetic parameter k 7,1,0 , which is responsible for the generation of C 2+ alkanes, is large compared to the absolute value.Therefore, this parameter could not be estimated sufficiently with the experimental data at hand.The reason for that might be, that the adaptation from the original formulation reported in [34] was not successful, which might be due to either measurement error or a major impact of the support material on the reaction mechanism.Moreover, the assumption of super-positioning mono-functional kinetics to the tandem system cannot be validated by now.Nevertheless, Figs.S.10e and S.10f show qualitatively good agreement between simulation and experiment of the tandem system, which led to the conclusion that the modeling approach is suitable for the optimization.Generally, the product distribution is towards methane in hydrocarbon distribution.13.RWGS catalyst demonstrates remarkably high selectivity for CO under different operation conditions.On the other hand, lower selectivity towards CO is observed for FTS and tandem catalysts, confirming that the FTS reactions also take place on the catalyst shell.It can be seen that higher C 2+ selectivity is obtained for the tandem catalyst in comparison to both RWGS and FTS catalysts.Moreover, low GHSV and high temperature are in favor of C 2+ production.

Optimization of catalyst loading
Table 4 presents the results for the optimization of catalyst based on active metals loading on core and shell for experimental point No. 1 conditions (cf.Table S.1).By the optimization, the Yield for C 2+ components was increased by (a) ≈38.5% and (b) ≈134.6%.In Fig. 6, the simulation results for all experimental conditions are depicted for the optimal and the experimental catalyst loading conditions.It can be seen, that for all reactor conditions, a significant increase in the Yield of C 2+ components is achieved.In Table S.5, we have categorized the production of light hydrocarbon through CO 2 hydrogenation using core-shell structures in three general routes.Considering the 8.6 times higher amount of platinum in CeO 2 -Pt@mSiO 2 -Co [20] and three times higher amount of cobalt in SiO 2 -Pt@m-SiO 2 -Co [21] this system remains within the expected range of yield.Table 4 shows, that with increasing overall amount of active metal loading, the catalyst formulation used in this study gets closer to the ones reported in literature.It is crucial to consider the smaller distance between active metals located on the core and shell, i.e. the thickness of the shell, and other morphological differences in their designs that influence the Yield.Although the proposed synthesis approach is feasible in respect to controlling the ratio between the active phases it is important to mention the total yield of C 2+ is less in such a tandem system in comparison to the methanol route as in [50].

Conclusion
In this article, we present a concise 5 step route for the design of optimal core-shell catalyst particles for tandem catalysis on the example of RWGS and FTS reactions.After initial thermodynamic calculations, the synthesis and the experimental characterization of the catalyst particles are shown.The catalyst particles are tested on their performance, individually and under tandem conditions in a parallel reactor setup to ensure consistent reaction conditions.Next to the N. Bashiri et al. experimental investigation, a fast computing modeling approach [30] is adapted to the reaction system by using kinetics from literature.The kinetic parameters are estimated based on the mono-functional catalyst particle performance results and validated against the tandem catalyst configuration.The tuned model was then used for the numerical optimization of the catalyst design, i.e. catalyst loading for the maximization of C 2+ Yield.It was shown that the catalyst performance could be increased significantly.The proposed method can be used as a blueprint for the design of optimal core-shell catalyst particles when promising candidates for the individual reactions are found and shall be combined for tandem catalysis.It is worth noting that the presented catalyst is generally probably not the best catalyst for the selected task as overall a maximum C 2+ Yield of 0.61% is achieved.Nevertheless, only with the presented method its true potential could be assessed and evaluated and the same holds for other core-shell systems, as otherwise the degree of freedom for choosing the catalyst loading could not be eliminated from the performance tests.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
10 nm have been formed through the oriented aggregation mechanism, Fig. S.2b.Mono disperse nanopolyhedra Pt NPs with the size of 3.11 ± 0.59 nm were obtained using one-pot polyol synthesis in which ethylene glycol was used as the reducing agent, PVP was used as the stabilizer and reducing agent, and TTAB as the capping agent, Fig. S.2a.The oleic and non-polar phases of Pt and Ce NPs undergo a phase transfer to the aqueous phase through a CTAB amphiphilic molecule [39].Notably, Pt and Ce NPs are distributed in the core without aggregation or forming larger particles.Subsequently, a silica shell is coated onto Pt and Ce NPs through the hydrolysis and condensation of TEOS in the Stöber process, resulting in the formation of a mesoporous structure achieved by removing all templates, stabilizers, and surfactant molecules.Referring to the TEM images, Fig. S.2c-g, the formation of a well-defined core-shell structure consisting of multicore NPs surrounded by a mesoporous silica shell is confirmed, also the presence of Co NPs distributed on the surface for tandem and FTS catalysts is revealed.

Fig. 2
shows STEM images of Pt,CeO 2 @SiO 2 -Co NPs.In the composition mode of secondary electron and backscattered electron image, Co NPs display a distinct bright contrast and are uniformly distributed on the surface of the silica shell.The EDS map suggests that Pt and Ce are concentrated in the center of the NPs, Simultaneously, Si and O are
.4, Fig. S.6-Fig.S.8).The catalysts present a combination of type IV and type II isotherms with a type H4 hysteresis loop.RWGS catalyst occupies the surface area of 611 m 2 g −1 , whereas

FTS
and tandem catalysts have surface areas of 298 and 219 m 2 g −1 , respectively.This clearly illustrates a reduction in the specific surface area of the core-shell structure after the deposition of Co NPs on the outer shell layer, Fig. S.4.Pore size distribution, Fig. S.5

N
.Bashiri et al.

Fig. 4 .
Fig. 4. CO 2 Conversion over time on stream for inert, RWGS, FTS, and tandem catalysts under various operation conditions.
Experimental selectivity for CO, methane, and light hydrocarbons are plotted in Fig. S.11-Fig.S.
Fig. S.15 shows methane as the main product in hydrocarbon distributions.It is to note that in this study, C 2+ mainly consists of ethane.
. Highlighting CO 2 as

Table 1
Catalyst properties in each reactor.

Table 3
Kinetic parameter values.

Table 4
Results for catalyst loading and Yield of C 2+ components from numerical optimization of tandem catalyst.