Oxidation of sugar mixtures on gold nanoparticle extrudates

1. The UNIVERSITY OF VALLADOLID SCHOOL OF INDUSTRIAL ENGINEERINGS Master in chemical Engineering MASTER THESIS Oxidation of sugar mixtures on gold nanoparticle extrudates Author: HERRERO MANZANO, MARIA Supervisor: GARCIA SERNA, JUAN , SALMI, TAPIO ÅBO AKADEMI Valladolid, Julio 2020. TFM REALIZADO EN PROGRAMA DE INTERCAMBIO TÍTULO: Oxidation of sugar mixtures on gold nanoparticle extrudates ALUMNO: María Herrero Manzano FECHA: Fecha de la defensa en la universidad de destino CENTRO: ÅBO AKADEMI UNIVERSITY TUTOR: Tapio Salmi, Juan García Serna INDEX 1. INTRODUCTION ................................................................................................................... 1 1.1. THEORETICAL BASIS ..................................................................................................... 2 1.1.1. Glucose and arabinose ......................................................................................... 2 1.1.2. Reaction mechanism of sugar oxidation .................................................................. 4 1.1.3. Catalyst ................................................................................................................. 6 2. OBJECTIVES ......................................................................................................................... 7 3. PLAN .................................................................................................................................... 7 4. EXPERIMENTAL SECTION .................................................................................................... 8 4.1. Catalyst ........................................................................................................................ 8 4.1.1. Laboratory prepared catalyst ............................................................................... 8 4.1.2. Extrusion efforts ................................................................................................... 8 4.1.3. Commercial catalyst ............................................................................................. 9 4.1.4. Characterization ................................................................................................... 9 4.1.4.1. Particle size ................................................................................................... 9 4.1.4.2. TEM ............................................................................................................... 9 4.1.4.3. ICP ................................................................................................................. 9 4.2. Sugar mixture oxidation ............................................................................................ 10 4.2.1. Experimental setup ............................................................................................ 10 4.2.2. Kinetic experiments. ........................................................................................... 11 5. RESULTS AND DISCUSSION ............................................................................................... 12 5.1. Sugar oxidation .......................................................................................................... 12 5.1.1. Powder catalyst .................................................................................................. 13 5.1.1.1. Diffusion phenomena ................................................................................. 13 5.1.2. Catalyst extrudates ............................................................................................. 14 5.1.2.1. Catalyst deactivation ................................................................................... 14 5.1.2.2. Molar ratio of sugars ................................................................................... 16 5.1.3. Carbon catalyst ................................................................................................... 19 5.2. Catalyst characterization ........................................................................................... 20 5.2.1. TEM ..................................................................................................................... 20 6. MODELING OF SIMULTANEOUS KINETIC AND DIFFUSION EFFECTS ................................. 22 6.1. Kinetic model ............................................................................................................. 24 6.2. Diffusion and reaction in porous catalyst particles ................................................... 31 6.3. Diffusion coefficients in the liquid phase .................................................................. 34 6.4. Mass transfer in the liquid bulk phase ...................................................................... 35 7. CONCLUSION AND FUTURE PERSPECTIVES ...................................................................... 36 8. REFERENCES ...................................................................................................................... 37 APPENDIX I: MALVERN PLOTS DISTRIBUTION .......................................................................... 41 APPENDIX II: CHANGES IN ACID SUGARS RESIDENCE TIMES ON THE HPLC ............................ 42 APPENDIX III: KINETIC MODELING ............................................................................................ 44 APPENDIX IV: CALIBRATION CURVES ....................................................................................... 50 FIGURE INDEX Figure 1:Family of DAldoses. .................................................................................................... 2 Figure 2 : Glucose Isomerization. ............................................................................................... 3 Figure 3: Cyclic forms of glucose. ............................................................................................... 4 Figure 4: Cyclic forms of arabinose. ........................................................................................... 4 Figure 5: Glucose oxidation [17]. ............................................................................................... 5 Figure 6: Arabinose oxidation [18]. ............................................................................................ 5 Figure 7: Reactor Set up. .......................................................................................................... 11 Figure 8: Glucose consumption at different catalyst sizes. ..................................................... 13 Figure 9: Arabinose consumption at different catalyst sizes. .................................................. 13 Figure 10: 1st use of the catalyst on sugar oxidation ............................................................... 15 Figure 11: 2nd use of the catalyst on sugar oxidation ............................................................... 15 Figure 12: 3rd use of the catalyst on sugar oxidation ............................................................... 15 Figure 13: Glucose consumption at 3 times used. ................................................................... 16 Figure 14: 1G:1A molar ratio. ................................................................................................... 17 Figure 15: 2G:1A molar ratio. ................................................................................................... 17 Figure 16: 1G:2A molar ratio. ................................................................................................... 17 Figure 17: Mass balance checking for glucose in a 1:1 molar ratio experiment...................... 18 Figure 18: Mass balance checking for Arabinose in a 1:1 molar ratio experiment. ................ 18 Figure 19: Mass balance checking for glucose in a 2:1 molar ratio experiment...................... 18 Figure 20: Mass balance checking for Arabinose in a 2:1 molar ratio experiment. ................ 18 Figure 21: Mass balance checking for glucose in a 1:2 molar ratio experiment...................... 19 Figure 22: Mass balance checking for Arabinose in a 1:2 molar ratio experiment. ................ 19 Figure 23: Oxidation reaction with N-C mesoporous catalyst. ................................................ 20 Figure 24: TEM image for fresh catalyst sample. ..................................................................... 21 Figure 25: TEM images for a spent catalyst sample. ................................................................ 21 Figure 26: Particle size distribution at a spent catalyst. .......................................................... 22 Figure 27: Oxygen requirements for glucose. .......................................................................... 23 Figure 28: Oxygen requirements for arabinose. ..................................................................... 23 Figure 29: First order kinetic comparison glucose. .................................................................. 26 Figure 30: First order kinetics comparison arabinose. ............................................................. 26 Figure 31: Kinetic model of experiment 1:1 molar ratio using constant volume approximation. .................................................................................................................................................. 27 Figure 32: Kinetic model of experiment 1:1 molar ratio using linear dependence volume approximation. ......................................................................................................................... 28 Figure 33:Kinetic model of experiment 1:1 molar ratio using real data volume. .................... 29 Figure 34: Fitting of 1:1 molar ratio oxidation of glucose and arabinose over nano gold particles at 70oC ...................................................................................................................................... 30 Figure 35:Fitting of 2:1 molar ratio oxidation of glucose and arabinose over nano gold particles at 70oC ...................................................................................................................................... 30 Figure 36: Fitting of 1:2 molar ratio oxidation of glucose and arabinose ................................ 30 Figure 37: Predicted behaviour of the oxidation of arabinose and glucose to the correspondent sugar acids at 70oC. .................................................................................................................. 31 LIST OF SYMBOLS Glu Glucose 𝜃i Coverage at the catalyst surface Ara Arabinose 𝜀p Particle porosity GluO Gluconic acid 𝜌p Particle density GluRO Glucoronic acid s Shape factor AraO Arabinonic acid R Gas constant Fruc Fructose D Molecular diffusion coefficient Rib Ribulose Dei Efective diffusion coefficient Ci Concentration inside the particle X Association factor C’i Concentration in the bulk phase M Molar mass Pi Partial pressure 𝑉  Molar volume Ni Amount of substance µ Viscosity ri Reaction rate 𝜏 Tortuosity K Kinetic constant KEYWORDS Oxidation of sugars, biomass valorization, heterogeneous catalysis, gold catalyst ABSTRACT The current work was carried out at the Laboratory of Industrial Chemistry and Reaction Engineering, Department of Chemical Engineering at Åbo Akademi University (Turku/Åbo, Finland) in collaboration with University of Valladolid within the framework of Erasmus mobility. The supervisors were Academy Professor Tapio Salmi and Professor Dmitry Murzin from the host university and Professor Juan García Serna from the home university. The project was focused on the valorization of biomass from forest-based feedstock. The aim was the catalytic oxidation of sugar mixtures on gold nanoparticles supported on alumina. The sugars, originating from biomass hydrolysis, can be valorized by oxidation of a hydroxyl group to a carboxyl group, giving the corresponding sugar acid. These sugar acids are useful for the alimentary, pharmaceutical and construction industry as additives. Nowadays, alternative feedstock and more sustainable technologies are continuously under development and research, avoiding the use of oil feedstock in future. Green chemistry and green process technology are the areas of chemical engineering focusing on the design of products and processes, which minimize the environmental impact. Biorefinery belongs to this concept concerning the biomass conversion starting with non-petroleum feedstock and developing more sustainable processes. During this work, several experiments were conducted in a laboratory-scale semi-batch reactor at 70oC, pH 8 and atmospheric pressure. The system was equipped with a titrator, which automatically added sodium hydroxide into the reaction mixture to maintain a constant alkaline pH. The oxidation of two C5 and C6 sugars, arabinose and glucose, on gold nanoparticles were studied in this project. One of the novelties of this oxidation process is the application of SpinChemTm technology, which allows the use of immobilized catalyst and high turbulence to suppress external mass transfer limitations around the catalyst particles and giving the opportunity to study the reaction in a middle step between discontinuous and continuous processes. Liquid-phase samples were withdrawn from the reaction mixture during the experiments and the samples were analyzed by high-performance liquid chromatography (HPLC). A catalyst synthesized in the laboratory and a commercial one were used in the kinetic experiments. Both catalysts were characterized with transmission electron microscopy (TEM), scanning electron microscopy (SEM), nitrogen physisorption and particle size analysis. Catalyst deactivation was observed in successive experiments with recycled catalyst extrudates. It was confirmed by ICP-MS that the reason for the deactivation was leaching. Moreover, the kinetic results revealed strong internal mass transfer limitation in the pores of the catalyst extrudates. A mathematical model was derived for the reaction kinetics and the parameters in the model were estimated by non-linear regression analysis. Further studies are needed to completely understand the chemistry of the system and to implement continuous reactor technology. Even new catalyst without gold content could be screened. SPANISH ABSTRACT - RESUMEN El presente trabajo fue realizado en el laboratorio de química industrial e ingeniería de la reacción en Åbo Akademi University (Turku, Finlandia) con la colaboración de la Universidad de Valladolid (Valladolid, España) en posesión de una beca de movilidad Erasmus. El trabajo fue supervisado por Tapio Salmi, Dmitry Murzin y Juan García Serna. El proyecto enfocado en la revalorización de la biomasa proveniente de residuos forestales tiene como objetivo el estudio de la reacción de oxidación de azucares sobre un catalizador con nano partículas de oro. Los azucares, provenientes de la hidrólisis de la biomasa, pueden ser revalorizados mediante la fijación de un átomo de oxígeno en un grupo hidroxilo originando un grupo carboxilo en la molécula. Los azúcares ácidos obtenidos son compuestos de valor añadido usados en la industria farmacéutica, alimentaria y de la construcción como aditivos. El creciente desarrollo de nuestra sociedad ha obligado a la industria a buscar nuevas fuentes de materias primas, alternativas al petróleo y más sostenibles. Es por ello que la investigación está orientada al progreso de procesos eficientes y sostenibles, procesos que favorezcan el desarrollo sostenible como la teoría “Green chemistry”. Dentro de esta teoría encontramos conceptos como el aplicado en este proyecto, el concepto de biorrefinería. El concepto de biorrefinería hace referencia al conjunto de procesos y tecnologías que convierten la biomasa en energía y productos de valor añadido. Durante el desarrollo de este proyecto se llevaron a cabo experimentos en un reactor semibatch a 70oC, pH 8 y presión atmosférica equipado con un sistema de adicción automática de hidróxido sódico que permitía controlar de una forma precisa el pH. La reacción de oxidación de dos azúcares básicos C5 y C6 (arabinosa y glucosa respectivamente) gracias a la presencia de nanopartículas de oro sobre alúmina que actuaban como catalizador. El sistema disponía de una tecnología nueva conocida como SpinChemTM que permite tener inmovilizado el catalizador dentro de una red que favorece el flujo de fluido desde la parte inferior de la cesta a las paredes exteriores de ella. El dispositivo funciona a su vez como agitador, proporcionando un buen mezclado que permite depreciar las limitaciones de transferencia de materia externa. Este dispositivo es un paso intermedio entre el reactor discontinuo y continuo, dando una idea de cómo sería la reacción teniendo en cuenta la difusión de los reactivos y los productos en la superficie del catalizador. Las muestras fueron tomadas manualmente y analizadas en una columna de cromatografía líquida de alta eficacia. Se sintetizó un catalizador y se testó un catalizador comercial, ambos fueron caracterizados usando métodos de análisis como TEM, SEM, N2 physisorption y Malvern análisis. Se observó una clara desactivación del catalizador aparentemente debido a la lixiviación sufrida por la pérdida de oro en la fase líquida. Además de un alto efecto de la transferencia de materia interna. Futuros estudios son necesarios para la completa comprensión de este sistema y su desarrollo en un reactor continuo. Igualmente, una nueva propuesta de catalizador, sin contenido en oro, surgió durante el desarrollo del proyecto, la cual necesita ser estudiada en profundidad. ACKNOWLEDGMENT I would like to express my special gratitude to my professors Tapio Salmi and Juan García Serna as well as professor Dmitry Murzin for allowing me to carry out this project on the topic oxidation of sugar mixtures which helped me a lot in developing research skills and professional knowledge. I sincerely thank my friends, family members and old college mates who provided me the help I needed to carry out this labour, taking advantage of the knowledge and hard skills for making my project as best as I can. I am very fortunate for all the help given by the laboratory manager docent Kari Eränen in practical matters during my experimental work as well as docent Narendra Kumar and associate professor Päivi Mäki-Arvela, for supporting me during TEM analysis. I am very grateful for all the help people at the Laboratory of Industrial Chemistry and Reaction Engineering gave me. Especially, I would like to thank Sebastian who tutored me in the first steps of the work, Zuzana for the patience she dedicated to me elaborating the extrudate catalyst, Adriana who helped me a lot during the development of the project and everybody who has directly or indirectly collaborated with me in this task. Oxidation of sugar mixtures over gold-nano particles extrudates 7 2. OBJECTIVES The aim of this work is to determine the oxidation kinetics of selected sugar mixtures, specifically, glucose and arabinose to obtain added-value compounds such as arabinonic acid or gluconic acid. Previous studies have been conducted in batch reactors using different kinds of powder catalysts, but in future we shall move forward to understand how gold catalysts will work in a continuous reactor. A continuous process has several advantages compared with batch and semi-batch processes. For a continuous process, automation is easier and cleaning of the reactor system is needed, usually, just once per year. Continuous reactors are very suited for large-scale production because production stops are not needed between the batches. Moreover, the reaction product obtained from a continuous process is more uniform than from a discontinuous process. To achieve this goal, a novel mixing technology known as SpinchemTM was used in this work. This new technology allows the use of immobilized catalyst extrudates in a batch reactor to get similar results to those which might be obtained with a continuous reactor. Moreover, the Spinchem device enhances mass transfer, suppressing external mass transfer limitations and improving the contact between the liquid and gas phases [25]. Before changing to a continuous process, the catalyst which will be used for the continuous process should be selected. Thus the activity, selectivity and durability of the immobilized catalyst will be screened to predict the potential of a continuous reactor technology in order to shift to continuous operation in a future work. 3. PLAN Previous work carried out at the Laboratory of Industrial Chemistry and Reaction Engineering at Åbo Akademi was focused on the kinetic modelling of sugar oxidation [26], performing the reaction with a finely dispersed powder catalyst to minimize mass transfer limitations to reveal the intrinsic kinetics on the catalyst surface. The current work is devoted to catalyst extrudates to study the interaction of intrinsic kinetics and mass transfer effects. The catalyst was used in the same shape as it would have been used in a continuous reactor. The data were analysed to understand the liquid and gas internal mass transfer coupled to the oxidation kinetics on the catalyst surface. 8 4. EXPERIMENTAL SECTION 4.1. Catalyst 4.1.1. Laboratory prepared catalyst Gold was deposited on alumina via the precipitation-deposition method using hydrogen tetrachloroaurate(ııı) hydrate (99.9%-Au) (49% Au) (chloroauric acid) (Alfa Aesar and ABCR GmbH) as the precursor. It is the most common way to prepare alumina supported gold catalysts. Temperature, pH, precursor concentration, alumina pre-treatment, calcination and washing, are important parameters to control the features of the catalyst. Some of them, such as pH have a strong influence on the gold loading, the dispersion of gold nanoparticles and the cluster size [27]. The catalyst preparation process was performed at 70oC, increasing the pH gradually until it reached pH 8 because the precipitation of Au is related to the existence of neutral species. Once the desired pH was achieved, the reaction was continued at constant temperature and pH for three hours. After completing the reaction, the catalyst was washed with distilled water and filtered to remove chlorine species. Finally, the material was dried out overnight at 100oC and the calcination was continued for six hours at maximum 300oC. 4.1.2. Extrusion efforts In order to use the Spinchem device for kinetic experiments, the powder catalyst should be transformed into extrudates. The first attempt was to use fresh alumina to analyse the extrusion results with this material which had not been tried before for this kind of equipment. After a sieving pre-treatment, the slurry was shaped with fresh alumina, water, and some organic compounds of high molecular weight working as a glue, following by drying and calcination steps before performing the extrusion. Several slurry mixtures were screened and different percentages of Bindzil binder (colloidal silica Bindzil-50/80 (50% SiO2 in water, Akzo Nobel) added. The proportion of these components is extremely important for the extrusion, otherwise, the slurry can be too dry or too wet for the extrusion. The obtained extrudates can lose the catalytic activity if the amount of Bindzil is too high, but a low percentage of it can result on weak extrudates which cannot have enough strength to be used in a reactor. After diverse experiments along a month, using different composition for the slurry, even 50% Bindzil, the results were unsuccessful. Oxidation of sugar mixtures over gold-nano particles extrudates 9 4.1.3. Commercial catalyst We also tested gold (1%) on aluminum oxide extrudates (AUROlite™ Au/Al2O3) in kinetic experiments. These dark purple extrudates might have been useful for catalytic oxidation. They have a size of 1.2mm x 5mm and the gold nanoparticles are around 2-3 nm, which is an optimal cluster size for many applications. These extrudates were supplied by Strem Chemicals, a manufacturing company specialized in high purity chemicals for scientific research and development. Actually most of the catalyst extrudes were broken and did not keep the original measurements. From a measurement test of some of the fresh extrudates the average diameter was 1 mm and the average length between 2 and 4 mm, presenting some exceptions in which the extrudates were up to 8 mm long. 4.1.4. Characterization 4.1.4.1. Particle size The macroscopic particle size distribution of a solid catalyst is an important physical property, understanding how it affects the overall reaction rate and mass transfer in the particles. Malvern analysis is a laser diffraction equipment used for evaluating the particle size of a solid sample. The particle size distribution was analysed by an equipment provided by Malvern Instruments Ltd. 4.1.4.2. TEM Transmission electron microscopy (TEM) gives the distributions of metal nanoparticles on catalyst support. TEM was performed with a suspension of the gold catalyst on ethanol. A beam of electrons is conducted to a catalyst sample, which is suspended on a grid giving a nanoscale image of the catalyst. This method provides high resolution images from which the amount and the size distribution of the nanoparticles on the support can be determined. 4.1.4.3. ICP Inductively coupled plasma mass spectrometry (ICP-MS) is used to analyse the amounts of metals in liquid and solid samples. This technique was applied to determine the precise amount of gold in our catalysts. The sample of the solid catalyst was dissolved completely in an acid mixture consisting of nitric acid and hydrochloric acid. The fresh catalyst was analysed giving a total loading of 1.3% of gold content. 10 4.2. Sugar mixture oxidation 4.2.1. Experimental setup The experimental work was carried out in an isothermal laboratory-scale semi-batch reactor fully equipped. The reactor set-up is shown in Figure 7. At first glance, it is a transparent glass reactor with 250 ml of capacity. The temperature was controlled by a heating/cooling jacket using distilled water. The temperature and pH were measured by an automatic system controlled by a 907 Titrando device. This device, delivered by Metrohm, adds automatically the base or acid to control the pH during the experiment. As the reaction products are acids, addition of an alkaline solution is needed for the control pH. For the experiments described in this project, sodium hydroxide solutions with concentrations from 0.2 M to 1.0 M were used, depending on the reaction time of each experiment. Stirring was performed by a propeller head made from stainless steel under which it is located the Spinchem device. The catalyst and plastic spheres to avoid breaking the catalyst during the reaction time were placed inside this device. This new technology combines the benefits of batch and continuous processes because the catalyst is immobilized in the pellet shape but operated in a batch reactor. The results give an idea about how the catalyst might work in a continuous system. Moreover, the Spinchem supresses external mass transfer limitations in the liquid phase, because high turbulence prevails around the particles. The sugar solution was filled at the reactor while the oxygen-nitrogen mixture flow was continuously added by a Brooks 5850S mass flow control device. The reactor had a safety gas outlet which maintained the total pressure constant at 1 atm and the reactor was combined with a cooling system connected to a water line. In this way, completely isothermal conditions were preserved. Oxidation of sugar mixtures over gold-nano particles extrudates 11 4.2.2. Kinetic experiments. Different procedures were applied because both powder and extrudate catalysts were used, but the general idea was the same. The sugar mixture solution of L-arabinose (Sigma-Aldrich, ≥99%) and anhydrous D-glucose (Fluka, ≥98%) was prepared in a 150 ml beaker and heated until the desired reaction temperature (70oC) was reached. The mixture was added to the reactor under an inert atmosphere previously created by flushing with argon. The powder O2 Ar Gas outlet Electrode ACID BASE Sample Products outlet Water inlet Water outlet Figure 7: Reactor Set up. 12 catalyst was added to the reactor before the solution when the reactor was at inert atmosphere and appropriate temperature while extrudates were placed in the Spinchem basket. The Spinchem device was filled with 1 g of the catalyst and 1 mm diameter plastic balls which immobilized the catalyst particles and prevented breaks. The pre-heated reactor was kept at 73oC when the sugar solution was added to the reactor. Under a well-controlled pH and temperature, the solution remained inside the reactor until the pH and temperature were constant. At this moment, a mixture of 5 ml/min of oxygen and 35 ml/min of argon was fed into the reactor vessel. The stirring speed was kept between 9001000 rpm to reduce the mass transfer limitations. The pH was controlled with Titrando equipment which added NaOH automatically. The concentration of the NaOH solution was different depending whether the reaction was performed with catalyst powder or extrudates. The extrudate catalyst showed very low rates in comparison with the powder catalyst mainly because of internal mass transfer limitations. Thus, a small droplet of NaOH generates a big impact on the reaction while the reaction rates are low. Consequently, 1M NaOH was used for the powder catalyst and 0.2 M NaOH for the extrudates. The sampling was done by using a syringe and withdrawing a sample of around 1 mL from the reaction mixture. In both cases, for powder catalysts and extrudates, a 0.45 μm PVDF filter was used to remove any catalyst from the samples. 5. RESULTS AND DISCUSSION 5.1. Sugar oxidation The experiments were performed both with the catalyst powder and the extrudates. The powder catalyst was used to understand the reaction and test the activity of the catalyst. Moreover, the diffusion phenomena should show lower rates with an increasing catalyst particle size. Therefore, some experiments with crushed catalysts were conducted to analyse the dependence between the reaction rate and the particle size. Secondly, the investigation was focused on the oxidation study in the presence of diffusion limitations. Experimental parameters such as temperature and pH have been researched previously concluding that the optimal operation point is at 70oC, pH 8 and oxygen partial pressure 0.125 atm. The amount of commercial catalyst available was limited so the deactivation experiments were carried out preferentially, followed by the experiments with different initial molar ratios of the sugars. One of the characteristics of the project is the Oxidation of sugar mixtures over gold-nano particles extrudates 13 oxidation of sugar mixtures wherefore knowing the preferential oxidation pathway is an important issue. 5.1.1. Powder catalyst 5.1.1.1. Diffusion phenomena To investigate the existence of diffusion limitations inside the catalyst pores, various experiments using different catalyst particle sizes were compared. The experiments were carried out under identical conditions: 70oC, pH 8, 1:1 sugar mass ratio, 0.125 oxygen partial pressure, and higher than 900 rpm stirring speed. The particle size of the catalyst was measured by Malvern analysis. Four experiments are compared in this section: - The reaction by powder catalyst. The particle size of the powder is below 65 µm. - The reaction by crushed catalyst small size. 90 % of the particles are above 371 µm. - The reaction by crushed catalyst big size. 90 % of the particles are above 732 µm. - The reaction by extrudates, using the Spinchem rotating basket reactor. Figure 8: Glucose consumption at different catalyst sizes. Figure 9: Arabinose consumption at different catalyst sizes. Both plots in Figures 8 and 9 show a clear decreasing rate with an increasing particle size, which suggests the existence of mass transfer limitation phenomena; this limitation might be mainly caused by internal mass transfer. External mass transfer limitations are negligible due to the high stirring speed. Thus, it can be assumed that the oxidation is limited by internal mass transfer in the pores of the catalyst extrudate. The results from de Malvern Analysis of each crushed catalyst can be found in Appendix I. 0100 200 300 0.00 0.01 0.02 0.03 0.04 0.05 0.06 powder Small Big Spinchem Glucose (mol/L) time (min) 0100 200 300 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 powder small Big Spinchem Arabinose (mol/L) Time (min) 14 5.1.2. Catalyst extrudates As the results showed a clear internal mass transfer limitation, the reaction times were studied at first place to adequate the system for the reaction with the extrudates. The reaction times were increased from three hours (around 100% conversion) with the powder catalyst to more than three days with the extrudates. Consequently, the Titrando system was adjusted, using a lower concentration of the NaOH solution. Some molar concentrations of NaOH were tried, concluding 0.2 M of NaOH provided a stable control of the pH along the reaction, instead of 1.0 M, which was used for the powder form of the catalyst. The limited amount of catalyst available (10 g of catalyst) and the time limitation due long reaction times implied that certain experiments are given priority over others. Firstly, it was crucial to analyse the possibility of reusing the catalyst doing deactivation experiments. Secondly, the main study should be focused on the oxidation of the sugar mixtures, trying to understand which is the preferential pathway of oxidation. 5.1.2.1. Catalyst deactivation To measure the catalyst deactivation, three different experiments using the same recycled particles inside the Spinchem device were carried out. The reaction was performed at 70oC, pH 8, oxygen partial pressure 0.125 atm, stirring speed exceeding 900 rpm, 1:1 molar ratio of arabinose-to-glucose and 1 g of catalyst. Between the experiments, the system was washed several times with deionized water keeping on the heater and the stirrer to ensure proper cleaning. After each experiment, the reactor was filled with argon to maintain an inert atmosphere. Oxidation of sugar mixtures over gold-nano particles extrudates 15 Figure 10: 1st use of the catalyst on sugar oxidation Figure 11: 2nd use of the catalyst on sugar oxidation Figure 12: 3rd use of the catalyst on sugar oxidation Figures 10-12 confirm a clear catalyst deactivation in each experiment. Not only the rate but also the selectivity of the reaction changed from cycle to cycle. While in the first use, the main products were arabinonic acid and gluconic acid, in the following ones the amount of glucoronic acid produced is increased. Figure 13 shows the comparison of the glucose consumption in every experiment. Some studies reports that leaching of gold is important a pH 7, thus it will be necessary to carry out further research to solve this issue [28]. 010 20 30 40 50 60 0.00 0.02 0.04 0.06 0.08 Glucose Arabinose Arabinonic Acid Gluconic Acid Glucose (mol/L) time (hours) 010 20 30 40 50 60 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Glucose Arabinose Arabinonic Acid Gluconic Acid Glucoronic Acid Glucose (mol/L) time (hours) 010 20 30 40 50 60 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 Glucose Arabinose Arabinonic Acid Gluconic Acid Glucoronic Acid Glucose (mol/L) time (hours) 16 Figure 13: Glucose consumption at 3 times used. The deactivation can be studied with some catalyst characterization methods. To check the possible leaching of gold into the liquid phase, three samples; fresh catalyst, once used catalyst and triple used catalyst were analysed with ICP-MS. The results are shown here: Sample Wt% Fresh 0.86 Spent 1 0.82 Spent 3 0.75 The results suggest that the gold content is dissolved into the aqueous phase, the catalyst is deactivated. Leaching of catalyst is an irreversible phenomenon leading to the disappearance of active sites from the surfaces of heterogeneous catalysts operating in liquid phase. Many new processes in biorefineries use this kind of catalysts, which makes the issue very crucial [29]. 5.1.2.2. Molar ratio of sugars The experiments with different initial molar ratios were conducted in order to check which sugar is preferentially oxidized arabinose or glucose. The reference conditions were the 1:1 molar ratio glucose-to-arabinose at pH 8, 70oC, stirring speed <900 rpm and 1 g of catalyst. Two additional experiments were performed changing the molar ratio glucose-to-arabinose to 2:1 and 1:2 under similar conditions. The results are displayed in Figures 14-16. 010 20 30 40 50 60 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 1 time 2 time 3 time Glucose concentration (mol/L) time (hours) Oxidation of sugar mixtures over gold-nano particles extrudates 23 𝐶O2 =55.56 PO2 exp(3.71814+5596.17 𝑇−1049668 𝑇2)−PO2 =1.03∗10−4𝑚𝑜𝑙/𝑑𝑚3 Ec. 1 Something to be kept in the mind is that the system is not pure water, it is at pH 8 and has dissolved sodium and hydroxide ions. The dissolved electrolyte salt usually decreases the solubility of oxygen, and henry’s constant for the pure solvent can be corrected using the salting-out factor of the electrolyte dissolved using the following equation: ln𝐻 𝐻0=∑(ℎi+ℎG)𝑐i The oxygen flow in the experiments was 5 mL/min and inside the reactor, the system remained under constant conditions at 70oC and 1 atm and the maximum liquid volume never exceeded 250 mL, which was the most restrictive situation. Under these conditions, the oxygen flow was fed at 1.77*10-4 mol/min and assuming the maximun volume of 250 ml which is not reached in any case the flux would be 7.11*10-4 mol/(L·min) Figure 27: Oxygen requirements for glucose. Figure 28: Oxygen requirements for arabinose. The slopes displayed in Figures 27-28 show the amount of oxygen needed per volume and time for each component. The addition of the slopes represents the total oxygen flow requirement. The total slope has a value of 1.65*10-4 mol/(L·min). 010 20 30 40 50 0.00 0.02 0.04 0.06 0.08 Glucose (mol/L) Time (hours) Glucose slope 010 20 30 40 50 60 0.00 0.02 0.04 0.06 0.08 Arabinose (mol/L) Time (hours) Arabinose Slope 24 Comparing the experimental data of the oxygen feed, 7.11*10-4 mol/(L·min) to the initial rate 1.65*10-4 mol/(L·min), it can be concluded that the oxygen feed flow guarantees the saturation of oxygen in the liquid phase. 6.1. Kinetic model A simplified kinetic model is needed where just the main reactions are considered. The model is based on the following stoichiometry, 𝐺𝑙𝑢𝑐 + 12 ⁄ 𝑂2 → 𝐺𝑙𝑢𝑐𝑂 R. 1 𝐴𝑟𝑎 + 12 ⁄ 𝑂2 → 𝐴𝑟𝑎𝑂 R. 2 𝐺𝑙𝑢𝑐 + 12 ⁄ 𝑂2 → 𝐺𝑙𝑢𝑐𝑅𝑂 R. 3 𝐺𝑙𝑢𝑐 → 𝐹𝑟𝑢𝑐 R. 4 𝐴𝑟𝑎 → 𝑅𝑖𝑏 R. 5 Moreover, in the derivation of the rate equations, the adsorption of the compounds on the catalyst surface are taken into account. The following reactions describe the adsorption of the reactants, 𝐺𝑙𝑢𝑐 + ∗ ↔ 𝐺𝑙𝑢𝑐∗ R. 6 𝐴𝑟𝑎 + ∗ ↔ 𝐴𝑟𝑎∗ R. 7 𝑂2 + ∗ ↔ 𝑂2∗ R. 8 In this model the main reaction from the sugar to the corresponding sugar acid (R.1 and R.2) is considered. Also the formation of the by-product from the glucose, glucuronic acid (R.3) for which a very low kinetic constant was observed, is included in the model, i.e. the isomerization of glucose and arabinose to fructose and ribulose (R.5 and R.6). Molecular adsorption of oxygen is presumed and the adsorption steps are assumed to be in quasi-equilibria, while the surface reaction steps are considered to be rate limiting. Based on these hypotheses, the mass balances of the components are summarized below, 𝑑𝑁gluc 𝑑𝑡 = 𝑟gluc = −(𝑅1+ 𝑅3+ 𝑅4) 𝑚𝑐𝑎𝑡 Ec. 4 𝑑𝑁Ara 𝑑𝑡 = 𝑟Ara = −(𝑅2+ 𝑅5) 𝑚𝑐𝑎𝑡 Ec. 5 Oxidation of sugar mixtures over gold-nano particles extrudates 25 𝑑𝑁glucO 𝑑𝑡 =𝑟glucO = 𝑅1 𝑚𝑐𝑎𝑡 Ec. 6 𝑑𝑁AraO 𝑑𝑡 =𝑟AraO = 𝑅2 𝑚𝑐𝑎𝑡 Ec. 7 𝑑𝑁glucRO 𝑑𝑡 =𝑟GlucRO = 𝑅3 𝑚𝑐𝑎𝑡 Ec. 8 𝑑𝑁fruc 𝑑𝑡 =𝑟fruc = 𝑅4 𝑚𝑐𝑎𝑡 Ec. 9 𝑑𝑁rib 𝑑𝑡 =𝑟rib = 𝑅5 𝑚𝑐𝑎𝑡 Ec. 10 𝑟O2 = −(𝑅1+ 𝑅2+ 𝑅3) 𝑚𝑐𝑎𝑡 Ec. 11 The surface reaction kinetics is given by the expressions 𝑅1 = 𝑘1𝜃Gluc𝜃O2 Ec. 12 𝑅2 = 𝑘2𝜃Ara𝜃O2 Ec. 13 𝑅3 = 𝑘3𝜃Gluc𝜃O2 Ec. 14 𝑅4 = 𝑘4𝜃Gluc Ec. 15 𝑅5 =𝑘5𝜃Ara Ec. 16 In the mathematical modelling, the ordinary differential equations (4) - (10) were solved using the amounts of substance (molar amounts) instead of concentrations due to the volume change during the reaction. The main reason for the volume change is the addition of NaOH into the reaction mixture for the pH adjustment. The total mass balance of the active sites on the catalyst should be one while the coverage of each compound on the catalyst surface is proportional to the concentration of the compound inside the pores, according to the ideal adsorption theory of Langmuir, 𝜃i = 𝑘iCi𝜃v Ec. 17 ∑θi = 1 Ec. 18 From this ideal adsorption theory and the presumption of rate limiting steps, the rate equations can be expressed as 𝑅1 = 𝑘1CGluc𝐶O2 (1+𝐾Glu𝐶Gluc+𝐾AraCAra+𝐾OCO2)2 Ec. 19 26 𝑅2 = 𝑘2𝐶Ara𝐶O2 (1+𝐾Glu𝐶Gluc+𝐾Ara𝐶Ara+𝐾O𝐶O2)2 Ec. 20 𝑅3 = 𝑘3𝐶Gluc𝐶O2 (1+𝐾Glu𝐶Gluc+𝐾Ara𝐶Ara+𝐾O𝐶O2)2 Ec. 21 𝑅4 = 𝑘4𝐶Gluc 1+𝐾Glu𝐶Gluc+𝐾Ara𝐶Ara+𝐾O𝐶O2 Ec. 22 𝑅5 = 𝑘5𝐶Ara 1+𝐾Glu𝐶Gluc+𝐾Ara𝐶Ara+𝐾O𝐶O2 Ec. 23 A preliminary approach to the experimentally observed kinetics is to prepare a first order test plot of the experimental data. The results of this preliminary analysis are displayed in Figures 29-30. The test plot is based on the normalized logarithmic concentrations versus the reaction time. If the plot is linear, the system follows first-order kinetics with respect to the sugar concentration. Figure 29: First order kinetic comparison glucose. Figure 30: First order kinetics comparison arabinose. The clear deviation upwards from the logarithmic plots confirms that the effective reaction order with respect of the sugar concentration is less than one. This is in agreement with the mechanistic rate equations (19) - (23) and from the chemical viewpoint, because this deviation from first order kinetics can be explained by adsorption of the sugar molecules on the catalyst surface. As the reaction progresses, the sugar concentration decreases and the effective reaction order approaches one [32]. 0500 1000 1500 2000 2500 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 time (min) -ln(Glu / Gluo) 0500 1000 1500 2000 2500 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 time (min) -ln(Ara / Arao) Oxidation of sugar mixtures over gold-nano particles extrudates 27 To test the reliability of the kinetic model proposed, it was solved numerically with Matlab. The estimation of the apparent kinetic constants without taking into account the mass transfer limitations inside the catalyst pores will give an idea about the accuracy of the preliminary approach. The optimization problem was solved by the minimization of the objective function 𝑄 =∑∑(𝐶exp𝑖,𝑗 −𝐶est𝑖,𝑗)2 𝑚 𝑗=1 𝑛 𝑖=1 Ec. 24 Keeping in mind that the volume was continuously increasing due to the adding of sodium hydroxide during the experiment, three different approaches were applied for just one experiment in order to compare the best fit: constant liquid volume, linear dependence on time and interpolation of the real data of the NaOH addition. Figure 31: Kinetic model of experiment 1:1 molar ratio using constant volume approximation. The modelling approach using a constant liquid volume (initial volume 0.150L) had a higher deviation due to the increasing of the volume during the reaction time, which decreases the concentrations of the reactants and products. This effect was not taken into account in the kinetic modelling so the curves stay above the experimental data, with an increasing discrepancy with time. 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 050220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO 28 Figure 32: Kinetic model of experiment 1:1 molar ratio using linear dependence volume approximation. Using the linear approximation of the volume over time, the fit improved to some extent. However, as the evolution of the volume over time is not even similar to a straight line, the kinetic curve takes a shape that does not correspond to the experimental data. The dependence between volume and time presents a clear exponential trend, which can be solved analytically obtaining an exponential relationship For first order model 𝑉 (𝑡)= 𝑉∞(1−𝑒)−𝜏/𝑡 Ec. 25 or for this system specifically 𝑉 (𝑡)= (𝐶oGlu−𝐶Glu(𝑡)+𝐶oAra−𝐶Ara(𝑡) 𝐶oGlu−𝐶Glu∞+𝐶oAra−𝐶Ara∞ )𝑉∞ Ec. 26 It should be kept in mind that the equations presented above are approximations, but not exact ones. 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 050220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO Oxidation of sugar mixtures over gold-nano particles extrudates 29 Figure 33:Kinetic model of experiment 1:1 molar ratio using real data volume. An interpolation from the real volume data from the experiment gives the best accuracy for the modelling as can be seen from Figure 33. There is still some deviation at the end of the experiment, which can be explained by the formation of oligomers, which are not taken into account in this modelling effort. The kinetic constants obtained for the experiment using this approximation of the volume are the following ones: K1 278.1802 m3/(gAu s) K5 0.0001 m3/(gAu s) K2 693.8352 m3/(gAu s) KO 178.1196 m3/(gAu s) K3 15.0206 m3/(gAu s) KGlu 108.0938 m3/(gAu s) K4 0.6671 m3/(gAu s) KAra 851.0752 m3/(gAu s) For the complete kinetic model, a selected set of experiments will be used. 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 050220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO 30 Figure 34: Fitting of 1:1 molar ratio oxidation of glucose and arabinose over nano gold particles at 70oC Figure 35:Fitting of 2:1 molar ratio oxidation of glucose and arabinose over nano gold particles at 70oC Figure 36: Fitting of 1:2 molar ratio oxidation of glucose and arabinose over nano gold particles at 70oC Giving the following rate constants and performing the reaction as it is shown in the plot: K1 224.1257 m3/(gAu s) K5 7.3496 m3/(gAu s) K2 717.6418 m3/(gAu s) KO 162.5694 m3/(gAu s) K3 4.1670 m3/(gAu s) KGlu 29.3569 m3/(gAu s) K4 0.6075 m3/(gAu s) KAra 1610.1107 m3/(gAu s) 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 050220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 170220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO 0500 1000 1500 2000 2500 3000 3500 4000 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 200220 time (min) concentration (mol/L) Glucose Ara + Fruc GluO + Rib AraO Oxidation of sugar mixtures over gold-nano particles extrudates 31 Figure 37: Predicted behaviour of the oxidation of arabinose and glucose to the correspondent sugar acids at 70oC. The mathematical model describes the general behaviour of the oxidation of arabinose and glucose mixture on the gold catalyst extrudates. The model could be refined, improving the current method of analysis, by measuring the concentrations of each component. Giving a more accurate information of the amount of oligomers present in the solution and avoiding the overlapping of substances during their analysis might be the next step. 6.2. Diffusion and reaction in porous catalyst particles The mass balance for a component (i) inside a porous catalyst with radius (r) depends on the diffusion flux (Ni) and the reaction rate (ri) of each component. It can be written as [33] 𝜀p𝑑𝐶i 𝑑𝑡 =−𝑑(𝑁i𝑟𝑠) 𝑟𝑠𝑑𝑟 +𝑟i𝜌p Ec. 27 The general shape factor (s) is a dimensionless number which defines the ratio between the reaction rate and the intensity of the mass transport inside the particle [34]. It is a function of the outer surface area and the volume of the particle; 𝑠+ 1 = (𝐴P 𝑉P)𝑅 Ec. 28 0500 1000 1500 2000 2500 3000 3500 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 mol of compound time (min) Glucose Oxygen Arabinose GluO AraO GluRO 32 For a cylindrical catalyst particle with the radius (R) and the length (L) the surface area is AP = 2 πR2+ 2 πRL and the volume is VP = πR2L. 𝑠=2 (𝑅 𝐿)+1 Ec. 29 For a long cylinder in which the length is much higher than the radius, the ratio R/L is tiny, thus s can be approached to 1. The extended description of the diffusion is based on the molecular diffusion and Knudsen diffusion theories. The MaxwellStefan approach provides a general set of equations for describing mass transfer [35].The detailed concept can be found in many textbooks of chemical engineering e.g. [36–38]. Knudsen diffusion prevails when the gas density is low and the pores are small, but Knudsen diffusion is not observed in liquids solutions [33]. From the studies presented by Salmi and Wärnå [39] where is showed the comparison of different diffusion methods, it can be concluded that a simplified method using the individual effective diffusion coefficients as a function of the local concentration of each component inside the pore is very accurate. The simplest description of the diffusion is Fick's law, where the flux is assumed to be proportional to the concentration gradient, 𝑁i=−𝐷ei𝑑𝐶i 𝑑𝑟 Ec. 30 Replacing in the equation Ec.27 gives 𝜀p𝑑𝐶i 𝑑𝑡 =𝑑(𝐷e𝑖𝑑𝐶i 𝑑𝑟𝑟𝑠) 𝑟𝑠𝑑𝑟 +𝑟i𝜌p Ec. 31 Assuming that the effective diffusion coefficient (Dei) is constant for each local concentration, the equation obtains a differentiated form 𝜀p𝑑𝐶i 𝑑𝑡 =𝐷ei(𝑑2𝐶i 𝑑𝑟2+𝑠 𝑟𝑑𝐶i 𝑑𝑟)+𝑟i𝜌p Ec. 32 A dimensionless coordinate is introduced instead of the particle radius giving the following equation 𝜀p𝑑𝐶i 𝑑𝑡 =𝐷ei 𝑅2(𝑑2𝐶i 𝑑𝑥2+𝑠 𝑥𝑑𝐶i 𝑑𝑥)+𝑟i𝜌p Ec. 33 The boundary conditions as well as initial conditions allow the equations to be solved by robust numerical methods. 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Åbo Akademi - Åbo Akademi University https://www.doria.fi/handle/10024/176540 (accessed June 4, 2020). Oxidation of sugar mixtures over gold-nano particles extrudates 41 APPENDIX I: MALVERN PLOTS DISTRIBUTION  Small crushed catalyst RESULTS Dv 10 Dv 50 Dv 90 69.1 175 371  Big crushed catalyst RESULTS Dv 10 Dv 50 Dv 90 167 383 732 42 APPENDIX II: CHANGES IN ACID SUGARS RESIDENCE TIMES ON THE HPLC Time : 22,4 0,00375 g/ml Time : 22,7 0,00625 g/ml Time : 23,0 0,0083 g/ml Time : 23,5 0,0125g/ml Oxidation of sugar mixtures over gold-nano particles extrudates 43 During the analysis, it was observe a change in the residence time of the sugar acids, both of them, gluconic acid and arabinonic acid. to discard that this movement was due to the overlapping of different peaks coming from different compounds, the calibration was performed using only arabinonic acid. AS it is showed in the pictures, the calibration goes from 22.4 to 23.5. 44 APPENDIX III: KINETIC MODELING clc, clear, close all; load DATA.mat; %% Data T = 343.15; % Temperatura en K RR = 8.314 ; % constante de los gases ideales J(kg/m2s2)/molK % inicial Co = 0.103 ; % mol/m3 maximun of oxygen dissolve in water % initial concentratio of each experiemnte [Glu Ara] C1_ini = [70.84, 72.94]; C2_ini = [96.075, 48.923]; C3_ini = [46.20, 95.62]; V =0.000150 ; % m3 mcat = 1; % g dens = mcat*0.01/V; % g Au/m3 %% Datos cineticos K1 = 224.125716910677 ; %Glu+O2 -> GlucO" mol m3 min g Au K2 = 717.641833218709 ; %Ara+O2 -> AraO" K3 = 4.16704999525874 ; %Glu+O2 -> GluRO" K4 = 0.607497321734236 ; %Glu+O2 -> Fruct" K5 = 7.34964377963257e-05 ; %Glu+O2 -> Ribu" KO = 162.569443708546; KGlu = 29.3569327599385 ; KAra = 1610.11072226474; %% Theoritical curve Ks = [ K1, K2, K3, K4, K5, KO, KGlu, KAra]; % N es el numeor de moles concetracion*V % Experiment 1 N1_ini = zeros(8,1); N1_ini(1)= C1_ini(1)*V; N1_ini(2)= Co*V; N1_ini(3)= C1_ini(2)*V; % Experiment 2 N2_ini = zeros(8,1); N2_ini(1)= C2_ini(1)*V; N2_ini(2)= Co*V; N2_ini(3)= C2_ini(2)*V; % Experiment 3 N3_ini = zeros(8,1); N3_ini(1)= C3_ini(1)*V; N3_ini(2)= Co*V; N3_ini(3)= C3_ini(2)*V; t_int = [0,3500]; %(min) equation = @(t,N)odefit(t,N,Ks,dens,V,Co); [t,N1] = ode15s(equation,t_int,N1_ini); figure(1) for i = 1:8 plot(t, N1/V/1000); hold on end Oxidation of sugar mixtures over gold-nano particles extrudates 45 ylabel('mol of compound'); xlabel('time (min)'); legend('Glucose','Oxygen','Arabinose','GluO','AraO','GluRO') %% fitting Rx =-1*eye(8); b = zeros(8,1); Kss = fmincon(@fcoste,Ks,Rx,b) equation = @(t,N)odefit(t,N,Kss,dens,V,Co); [tt1,Ni1] = ode15s(equation,DATA050220(:,1),N1_ini); [tt2,Ni2] = ode15s(equation,DATA170220(:,1),N2_ini); [tt3,Ni3] = ode15s(equation,DATA200220(:,1),N3_ini); for i=1:25 V1=150; A1(i,:) = Ni1(i,:)/V1*1000; end GluO_Rib = A1(:,8)+A1(:,4); Ara_Fruc = A1(:,7)+A1(:,3); Matrix = zeros(25,5); Matrix(:,1) = A1(:,1); Matrix(:,2) = Ara_Fruc; Matrix(:,3) = A1(:,5); Matrix(:,4) = GluO_Rib; Matrix(:,5) = A1(:,6); for i=1:18 V2(i)= (interp1(VOL170220(:,1),VOL170220(:,2),tt2(i)))-1*i; A2(i,:) = Ni2(i,:)/V2(i)*1000; end GluO_Rib2 = A2(:,8)+A2(:,4); Ara_Fruc2 = A2(:,7)+A2(:,3); Matrix2 = zeros(18,5); Matrix2(:,1) = A2(:,1); Matrix2(:,2) = Ara_Fruc2; Matrix2(:,3) = A2(:,5); Matrix2(:,4) = GluO_Rib2; Matrix2(:,5) = A2(:,6); for i=1:18 V3(i)= (interp1(VOL200220(:,1),VOL200220(:,2),tt3(i)))-1*i; A3(i,:) = Ni3(i,:)/V3(i)*1000; end GluO_Rib3 = A3(:,8)+A3(:,4); Ara_Fruc3 = A3(:,7)+A3(:,3); Matrix3 = zeros(18,4); Matrix3(:,1) = A3(:,1); Matrix3(:,2) = Ara_Fruc3; Matrix3(:,3) = A3(:,5); Matrix3(:,4) = GluO_Rib3; figure (3) hold on plot(DATA050220(:,1),DATA050220(:,2),'ob','MarkerSize',3) plot(DATA050220(:,1),DATA050220(:,3),'or','MarkerSize',3) plot(DATA050220(:,1),DATA050220(:,4),'om','MarkerSize',3) 46 plot(DATA050220(:,1),DATA050220(:,5),'oc','MarkerSize',3) plot(tt1, Matrix(:,1),'b'); plot(tt1, Matrix(:,2),'r'); plot(tt1, Matrix(:,3),'m'); plot(tt1, Matrix(:,4),'c'); hold off title('050220') xlabel('time (min)'); ylabel('concentration (mol/L)'); legend('Glucose','Ara + Fruc','GluO + Rib','AraO') figure (4) hold on plot(DATA170220(:,1),DATA170220(:,2),'ob','MarkerSize',3) plot(DATA170220(:,1),DATA170220(:,3),'or','MarkerSize',3) plot(DATA170220(:,1),DATA170220(:,4),'om','MarkerSize',3) plot(DATA170220(:,1),DATA170220(:,5),'oc','MarkerSize',3) plot(DATA170220(:,1),DATA170220(:,6),'og','MarkerSize',3) plot(tt2, Matrix2(:,1),'b'); plot(tt2, Matrix2(:,2),'r'); plot(tt2, Matrix2(:,3),'m'); plot(tt2, Matrix2(:,4),'c'); plot(tt2, Matrix2(:,5),'g'); hold off title('170220') xlabel('time (min)'); ylabel('concentration (mol/L)'); legend('Glucose','Ara + Fruc','GluO + Rib','AraO') figure (5) hold on plot(DATA200220(:,1),DATA200220(:,2),'ob','MarkerSize',3) plot(DATA200220(:,1),DATA200220(:,3),'or','MarkerSize',3) plot(DATA200220(:,1),DATA200220(:,4),'om','MarkerSize',3) plot(DATA200220(:,1),DATA200220(:,5),'oc','MarkerSize',3) plot(tt3, Matrix3(:,1),'b'); plot(tt3, Matrix3(:,2),'r'); plot(tt3, Matrix3(:,3),'m'); plot(tt3, Matrix3(:,4),'c'); hold off title('200220') xlabel('time (min)'); ylabel('concentration (mol/L)'); legend('Glucose','Ara + Fruc','GluO + Rib','AraO') Oxidation of sugar mixtures over gold-nano particles extrudates 47 ODEFIT function dN = odefit(t,N,Ks,dens,V,Co) K1 = Ks(1); K2 = Ks(2); K3 = Ks(3); K4 = Ks(4); K5 = Ks(5); KO = Ks(6); KGlu = Ks(7); KAra = Ks(8); dN =zeros(8,1); N(2)= Co; %Concentraciones xGlu = N(1)/V; xo = N(2)/V; xAra = N(3)/V; xGluO = N(4)/V; xAraO = N(5)/V; xGluRO = N(6)/V; xFruc = N(7)/V; xRib = N(8)/V; r1 = K1*xGlu*xo/(1+KGlu*xGlu+KAra*xAra+KO*xo)^2; r2 = K2*xAra*xo/(1+KGlu*xGlu+KAra*xAra+KO*xo)^2; r3 = K3*xGlu*xo/(1+KGlu*xGlu+KAra*xAra+KO*xo)^2; r4 = K4*xGlu/(1+KGlu*xGlu+KAra*xAra+KO*xo); r5 = K5*xAra/(1+KGlu*xGlu+KAra*xAra+KO*xo); rGlu = -(r1+r3+r4); ro = -(r1+r2+r3); rAra = -(r2+r5); rGluO = r1; rAraO = r2; rGluRO = r3; rFruc = r4; rRib = r5; dN(1) = rGlu*(dens*V); dN(2) = 0; dN(3) = rAra*(dens*V); dN(4) = rGluO*(dens*V); dN(5) = rAraO*(dens*V); dN(6) = rGluRO*(dens*V); dN(7) = rFruc*(dens*V); dN(8) = rRib*(dens*V); end 48 FCOST function Diff = fcoste(Ks) load('DATA.mat') % DATA V =0.000150 ; % m3 mcat = 1; % g dens = mcat*0.01/V; % g Au/m3 Co = 0.103 ; % mol/m3 % initial concentration of each experiemnte [Glu Ara] mol/m3 C1_ini = [70.84, 72.94]; C2_ini = [96.075, 48.923]; C3_ini = [46.20, 95.62]; % Experiment 1 N1_ini = zeros(8,1); %mol N1_ini(1)= C1_ini(1)*V; N1_ini(2)= Co*V; N1_ini(3)= C1_ini(2)*V; % Experiment 2 N2_ini = zeros(8,1); N2_ini(1)= C2_ini(1)*V; N2_ini(2)= Co*V; N2_ini(3)= C2_ini(2)*V; % Experiment 3 N3_ini = zeros(8,1); N3_ini(1)= C3_ini(1)*V; N3_ini(2)= Co*V; N3_ini(3)= C3_ini(2)*V; %Resolucion de ODE equation2 = @(t,N)odefit(t,N,Ks,dens,V,Co); [tt1,Ni1] = ode15s(equation2,DATA050220(:,1),N1_ini); [tt2,Ni2] = ode15s(equation2,DATA170220(:,1),N2_ini); [tt3,Ni3] = ode15s(equation2,DATA200220(:,1),N3_ini); for i=1:25 V1(i)= (interp1(VOL050220(:,1),VOL050220(:,2),tt1(i)))-1*i; % mL A1(i,:) = Ni1(i,:)/V1(i)*1000; %mol/L end GluO_Rib = A1(:,8)+A1(:,4); Ara_Fruc = A1(:,7)+A1(:,3); Matrix = zeros(25,5); Matrix(:,1) = A1(:,1); Matrix(:,2) = Ara_Fruc; Matrix(:,3) = A1(:,5); Matrix(:,4) = GluO_Rib; Matrix(:,5) = A1(:,6); % for i=1:18 V2(i)= (interp1(VOL170220(:,1),VOL170220(:,2),tt2(i)))-1*i; A2(i,:) = Ni2(i,:)/V2(i)*1000; end