Modeling the Chemical Decomposition of Sodium Carbonate Peroxyhydrate

M. Brundu*, V. Guida Procter & Gamble Italia *Corresponding author: [email protected]

Abstract: Sodium Carbonate Peroxyhydrate The decomposition is apparently very simple, (SPC - Na2CO3*1.5H2O2) undergoes chemical but the mechanism hasn’t been understood yet. decomposition and physical degradation during One important limitation to its investigation is the shelf life. that water is a product of reaction but may also We used the Chemical Engineering Module interact with unconverted SPC and sodium of COMSOL Multiphysics to develop a lumped carbonate; it is demonstrated that the kinetic model of the chemical decomposition of decomposition is faster when the material is SPC that involves five different species, three exposed to high relative humidity (RH). solid state and two homogeneous reactions. Our Furthermore, the study is particularly difficult at innovative approach for the description of the conditions of interest for dry laundry complex solid phase reactions consists in the detergents. Indeed, between 30°C and 40°C the introduction of the appropriate solid state kinetic equilibrium of the system water-Sodium models in the modeling tool. These describe the Carbonate shows a region where different variation of the reaction rate with conversion and hydrates may exist and small variations of the allow the introduction of complex phenomena experimental conditions lead to phase such as reagent and product diffusion, particle transformations, water pick up/release and shrinkage, crystal granulation and growth. consequent hydration/dehydration of the solid We complemented the work with [3]. Furthermore, water is produced during the experimental studies for the estimation of the decomposition but it may also arrive to the kinetic parameters. The model is able to system from the environment. Therefore, it is reproduce the decomposition of SPC over the very difficult to interpret the experimental data shelf life and simulate the switch between the and make predictions on the behavior of the different mechanisms. The results are in good system. agreement with the experimental data. The literature shows mainly experimental studies of the system, but modeling exercises are Keywords: Percarbonate, Decomposition, scarce. Galway [1] investigated the Kinetics, Chemical engineering. decomposition of SPC and fitted the kinetic data with existing solid state kinetic models. Lunghi 1. Introduction et al [5] fitted the kinetic data produced with calorimetric experiments to get the activation The challenge with the use of Sodium energy of the whole process. Comprehensive Carbonate Peroxyhydrate (Na2CO3*1.5H2O2 - models that fully characterize the decomposition SPC) as a bleach source in dry detergent have not been developed yet. formulations, is its lower stability in comparison The case study presented in this work deals with other materials, and the risk of quality with the chemical decomposition of pure SPC, losses of the product over the shelf life. The and is a part of a wider analysis aiming at the issue can be solved with the understanding and simulation of the decomposition of a dry laundry modeling of the decomposition mechanism of detergent inside a pack. The full model, still the powder. under development, involves the moisture The global process driving the diffusion through the pack [4], moisture decomposition of SPC is usually summarized by: adsorption in the product and the chemical decomposition.

In this reaction SPC releases hydrogen peroxide that easily decomposes to give water and oxygen.

2. Experimental investigation that we called catalytic and non catalytic. Catalysis enhances the decomposition The experimental investigation consisted in originating stability issues; indeed, the material the characterization of SPC by isothermal fully decomposes in 55 days while conversion is calorimetric measurements (TAM Air – TA 20% for non catalytic systems. Experimental instruments), iodometric titration and the evidence showed that the product of reaction was equilibrium relative humidity of the sample. Sodium Carbonate Monohydrated either for the Further analyses were carried out to complement catalytic, or the non catalytic process. the results and support the calorimetric data. At the end of the experiment non catalytic The thermostat of the TAM unit was set to samples were very dry, still a free flowing 60°C; the sample size was 12g; the material used powder. On the contrary, samples showing the was Oxyper S-142, a commercial sodium catalytic behavior appeared wet; the powder was percarbonate provided by Solvay. Sample weight packed and caked. Starting from this and oxygen content were measured before and consideration, and complementing the analysis after the experiment. Different experiments had with data regarding the initial content of free different durations in order to correlate the heat water of the different samples, we are able to flow of the sample to conversion; in particular, conclude that the difference between the two duration ranged between few and 55 days. mechanisms is in the content of free water, The decomposition causes high gas release whether produced, exchanged with external or with consequent pressure increase in closed initially present in the system. systems. In order to prevent the phenomenon we From the experimental result we could used a needle to punch the cap of the ampoules. postulate the reaction mechanism to be used to For comparison we also run some experiment model the decomposition. without punching the cap. We developed a correlation between heat 3. Use of COMSOL Multiphysics developed and activity loss of the material and, by means of the total heat developed from start The innovative application of COMSOL of reaction to total decomposition, we translated Multiphysics in this context is the use of the the heat flow curve Vs time in Conversion Vs chemical reaction engineering module to develop time. In the below are reported examples of the a lumped kinetic model of the decomposition of conversion profile at 60°C for two different a bed of particles. Indeed, we developed a time replicates of the same material. dependent study of the constant volume batch As shown in Figure 1 we observed that the reactor involving five different species: Sodium decomposition of pure SPC coming from the Carbonate Peroxyhydrate (SPC), Anhydrous same material and lot shows different pathways (CSA) and Monohydrate (CSM) Sodium Carbonate, Water (W) and Hydrogen peroxide (HP); and involving three solid state and two 1,0 homogeneous reactions. Modeling this kind of systems is usually complicated because of the 0,8 changes at particle scale and the phenomena 0,6 occurring in the solid state. Nevertheless, we approached the description of such complexity

0,4 trying to avoid the development of a complicated Conversion 0,2 3D model. The versatility of COMSOL allowed the introduction of the appropriate solid state 0,0 reaction kinetic models able to describe the 0 10 20 30 40 50 60 variation of the reaction rate with conversion. Time [Days] Thus, the tool helped us to keep the computational simplicity, and at the same time Figure 1. Examples of solid conversion profiles of introduce complex phenomena such as reagent samples showing the catalytic (Red) and non catalytic and product diffusion, particle shrinkage, crystal (Blue) behavior. granulation and growth.

Model equations for this module are very simple and can be summarized as:

Where:

Where:

Density of component Thus we assume that:

Reaction rate for component

Reaction rate for reaction

3.1 Model assumptions

Experimentally we found good agreement The model for the isothermal system assumes between the Avrami-Evrofe’ev model for concentrated parameters, constant volume, and nucleation and growth limitation in solid state negligible vaporization of hydrogen peroxide. reactions and the kinetic data referred to the wet Furthermore, we assume the homogeneousness system. We decided to use the same equation to of the system. calculate the dependence of the wet SPC The system we consider is open and the decomposition on conversion for reaction 2. relative humidity (RH) of the air surrounding the Nevertheless, this would not be enough to solid should be time dependent; nevertheless, we simulate the switch between the dry and wet use RH as an operating parameter and its mechanism. For this reason we provided the influence is verified in a sensitivity analysis. expression of the reaction rate with an

exponential term on the concentration of water in 3.2 Reaction kinetics model the solid.

Thus, we assume: The model assumes that Sodium

Percarbonate decomposes to give water, oxygen

and sodium carbonate according to the set of consecutive and competitive reactions listed Hydrogen peroxide decomposition has been below: extensively studied in the past. For the affinity to the system under investigation, we refer to a 1) kinetic study carried out by Galway [1-2]. In his

work he modeled the decomposition of H2O2 in a st 2) saturated solution of sodium carbonate with a 1 order reaction rate. Thus, we assume:

3) We also assume:

4) Water evaporation is one of the key steps in our process. We calculate the evaporative flux as: 5)

Where: Experimentally we found good agreement between the Jander’s model for a 3D diffusion limited process and the kinetic data referred to dry systems, for this reason we decided to use The Water Vapor Sorption isotherm of the the equation to calculate the dependence of the sample was iused to establish a correlation dry SPC decomposition on conversion for between eRH and the water content of the solid reaction 1. and introduced in the software. According to the model developed by Jander:

3.3 Numerical method 1,0

The time dependent study was solved with 0,8 MUMPS, one of the direct methods provided by 0,6 the software. The stop condition on the content of SPC in the powder was required to avoid 0,4

computational errors. We run the program in a Conversion 0,2 Hp PROBOOK 6460b machine, with an Intel® Core™i5 processor running at 2.50GHz and 0,0 4GB RAM 0 10 20 30 40 50 60 Solution of the equations is fast, calculation Time [Days] time is about 3 seconds for a simulation of 55 days of reaction. Figure 2. Comparison between conversion calculated 4. Results and discussion by the model (black) and the experimental result (blue) for the non catalytic system The model was used to reproduce the behavior observed during the experimental investigation and understand the influence of the 1,0

balance of water in the decomposition. 0,8 To estimate the initial conditions we considered that the solid has an initial diffusive 0,6 layer constituted by Boron Silicate (coating) and 0,4

Sodium Carbonate (coming from SPC already Conversion converted). The main importance of coating is to 0,2 form a diffusive layer surrounding the particle. 0,0 Its presence can be considered in the model by 0 10 20 30 40 50 60 the introduction of an initial conversion different from zero. Time [Days] Thus, we assumed that the solid is initially constituted by Sodium Percarbonate, Sodium Figure 3. Comparison between conversion calculated carbonate monohydrated and Water. We by the model (black) and the experimental result (red) calculated the initial conversion and the initial for the catalytic system concentration of SPC from stoichiometric calculations on the global reaction: Default plots are the concentration profiles of each species involved in the process, that, together with the reaction rate have been very We measured the initial water content typical for useful to understand the contribution of the our system and assumed the initial concentration single reaction to the global decomposition. of CSM as Nevertheless, we used conversion for calibration purposes.

The initial concentration of the other In Figure 2 and Figure 3 is shown the components was set to zero. comparison between the output of the model and In a first step the kinetic parameters were the experimental results observed during the long estimated separately for each reaction, some of term analysis on a real SPC system. Modeling them measured directly,some retrieved in the results for the catalytic and non catalytic process Literature as explained in the previous are obtained with the same initial conditions and paragraph. the same set of parameters, but with a different As to improve the fitting with experimental evaporation rate. results we carried out a large sweep on the most Results are in qualitative agreement. important parameters; the final set was chosen Quantitatively, final conversion is slightly over from the solution that that best fitted with real estimated for the non catalytic system. In data. catalytic systems the model is able to capture the

Table 1. Influence of the mass transfer coefficient and the initial eRH of the material on the decomposition behavior of the sample.

K5 [mol/m3s] 5e-6 8.3e-6 1.17e-5 1.5e-5

55

57

eRH0

59

61

first part of the experiment but time to total decomposition, and drives reaction to follow one conversion is underestimated. mechanism or the other. Given the external The qualitative agreement of the results conditions, small variations of the initial eRH indicates that our kinetic model is able to may originate stability issues. describe SPC decomposition. In order to have a more complete picture of 5. Conclusions the influence of the content of free water, either initial or accumulated, we run a sensitivity This work deals with the chemical analysis on the initial eRH and the rate of decomposition of Sodium Carbonate evaporation on a wide range. In this paper we Peroxyhydrate. In particular, we investigated the present the selection of the results that are system by means of calorimetric and analytical relevant for discussion. Figures below report the methods and complemented the study with the conversion of the system over time for a development of a mathematical model of the 0 variation of the eRH in the range 55-61 and k5 process in COMSOL Multiphysics. During the in the range: 5e-6-1.5e-5 mol/m3s. experimental investigation we identified two We see both, either the catalytic, or the non overall decomposition paths of SPC catalytic path depending on a combination of the decomposition depending on the balance of initial eRH and the sealing of the system to water generation and water consumption. moisture exchange. The variation of the initial Furthermore, we proposed a reaction network eRH from 55% to 57%, and from 57% to for the decomposition and developed a 59%fosters the catalytic pathway when k5 is mathematical model by means of the chemical respectively 8.3e-6 and 1.17e-5 mol/m3s. reaction engineering module of COMSOL Results confirm that the combination of the multiphysics that is valid at 60°C. initial content of free water and the ability of the Based on the model above, we are able to system to consume water produced affects the quantitatively predict SPC decomposition

behavior and, based on slight variability of the Superscripts initial water content, and on the goodness of Initial moisture sealing of the system, we can simulate Equilibrium the switch between the two mechanisms Maximum value derived from observed experimentally. stoichiometry

6. References Subscripts Hydrogen peroxide 1. Galway A. K., Hood W. J., Thermal Water Decomposition of Sodium Carbonate Sodium Carbonate anhydrous Perhydratein the Presence of Liquid Water, J. Sodium Carbonate mono Chem. SOC., Faraday Trans. I,, 78, 2815-2827 Hydrated (1982) Sodium percarbonate 2. Galwey A. K., Thermal decomposition of Solid phase sodium carbonate perhydrate in the solid state, Gas phase The journal of physicalchemistry, 83, 14 (1979) Liquid phase 3. Gronvold F. And Meisingset K. K., Thermodynamic properties and phase transitions of salt hydrates between 270 and 400K, J. Chem. Thermodynamics, 15, 881-889 (1983) 4. Guida V., Scelsi L., Zonfrilli F., Humidity mass transfer analysis in packed powder detergents, Proceedings of the 2012 COMSOL Conference Milan, (2012) 5. Lunghi A., Cattaneo M., Cardillo P., 1996, Stabilità termica del percarbonato di sodio, La rivista dei Combustibili, 50, 229 (1996)

7. Nomenclature

Initial activity

Density of component

Initial solid density

Reaction rate

Molecular weight

Initial water activity Constant of reaction

Reaction rate

Number of species

Heat of reaction

Greek letters

Stoichiometric coefficient

Conversion as