Kinetic Study on the Preparation of Aluminum Fluoride Based on Fluosilicic Acid


 Reasonable mathematical derivation and mechanism model in the process of producing aluminum fluoride by fluosilicic acid is the key to the industrial treatment of fluorine resources in the tail gas of phosphate ore. In this work, aluminum fluoride was generated directly by fluosilicic acid to extract fluorine from the tail gas of phosphate rock. The uncreated-core model dominated by interfacial reaction and the uncreated-core model dominated by internal diffusion-reaction were then respectively utilized to describe the reaction kinetics of the generation of aluminum fluoride. The result showed that the uncreated-core model was dominated by interface reaction and internal diffusion, the apparent reaction order n = 1, and the activation energy Ea = 30.8632 kJ . mol–1. Product characterization and kinetic analysis were employed to deduce the reaction mechanism of preparing aluminum fluoride. The theoretical basis for the low-cost recycling of fluorine resources in the tail gas of industrial phosphate ore was provided in this work.


INTRODUCTION
The recovery and reuse of fl uorine in the tail gas of phosphate ore are one of the key technologies to realize environmentally friendly phosphorus chemical industry 1, 2 . As a typical product, aluminum fl uoride is widely used in the electrolytic aluminum industry 3, 4 . The production methods of aluminum fl uoride mainly included three kinds of fl uorite as the main raw material: wet method, dry method, non-water method and fl uosilicic acid as the main raw material: ammonia method, direct method, monohydrate method 5, 6, 7 . At present, with the decrease of fl uorite reserves, the production of aluminum fl uoride from fl uorite as the main raw material was no longer advantageous in terms of cost and production 8 . Among the three methods using fl uosilicic acid as the main raw material, the direct reaction method has gained the favor of industry for the low cost and simple operation process 6 . As the main raw material of wetprocess phosphoric acid in China's phosphorus chemical industry, phosphate ores containing 3-5% fl uorine have attracted extensive attention in the fl uorine chemical industry. In the process of wet-process phosphoric acid, fl uorine was mainly spilled out in the form of fl uorinecontaining gas and was transferred to fl uosilicic acid by water absorption 9, 10 . Therefore, the effective recovery of fl uorine from the tail gas of wet process phosphoric acid was a problem concerned by industry. In addition, there were phase transition and contamination problems in the direct method using fl uosilicic acid as a fl uorine source, the purity and bulk density of aluminum fl uoride was a major challenge 11, 12 .
Fluosilicic acid was used to react directly with aluminum hydroxide in the process of producing aluminum fl uoride by the direct method. However, this reaction was a three-step reaction rather than a one-step reaction.
Step 1: Fluosilicic acid neutralized aluminum hydroxide to produce aluminum fl uosilicic acid and water.
Step 2: Aluminum fl uosilicate acid was hydrolyzed to produce aluminum fl uoride, silicon dioxide and hydrogen fl uoride.
Step 3: In the second step, the product hydrogen fl uoride and unreacted aluminum hydroxide undergo acid-base neutralization reaction to produce aluminum fl uoride and water. The reaction equations were as follows 13 : Previous studies 14, 15, 16 on the direct preparation of aluminum fl uoride by fl uosilicic acid have focused on improving the stability of silica precipitation to facilitate the rapid separation of silica before the crystallization of aluminum fl uoride to improve the purity of products. For instance, Bab yat. M et al. 17 took the fi ltration rate of silicon dioxide as the index and studied the effects of fl uosilicic acid concentration, temperature, the addition of aluminum hydroxide, stirring speed and reaction time. Meanwhile, combined with scanning electron microscopy, the mechanism hypothesis of the direct preparation of aluminum fl uoride by fl uosilicic acid was proposed. Researchers found that silica adsorbed on the surface of aluminum hydroxide and formed clusters. Krysztafkiewicz A. et al. 12 improved the purity of the product by adding washing steps after the initial fi ltration of silica and aluminum fl uoride. Researchers found that placing the fi ltered silica in water at 80 degrees Celsius for secondary washing, or in hydrochloric acid at a 20 percent mass concentration, produced good results for both.
However, there were few reports on the reaction kinetics and mechanism of aluminum fl uoride prepared by direct method 18 . The direct method was a liquid-solid reaction, and its macroscopic reaction rate was not only infl uenced by the interface reaction, but also by the process of external and internal diffusion 19, 20 . In this work, based on the shooting of scanning electron microscope, a reasonable mathematical model was provided to deduce the reaction process, and the mechanism of the direct method for the preparation of aluminum fl uoride was revealed by combining the reaction kinetics and experimental data. This work not only provided a theoretical basis for the realization of low-cost recovery of fl uorine Polish Journal of Chemical Technology, 23, 3, 10-16, 10.2478/pjct-2021-0024 resources in the tail gas treatment of phosphate rock but also provided theoretical guidance for the effective separation of silica and aluminum fl uoride. Meanwhile, this experiment predicted the infl uence of different process conditions on the experimental results and tested the applicability of the process in actual production.

Materials and analysis
In this study, chemical pure grade fl uosilicic acid was used as raw material due to the mechanism study. Fluosilicic acid was used as a reactant produced by Chengdu Kelong Chemical Co., Ltd (China; CP grade; Mass concentration: 34.69%). Aluminium hydroxide was used as a reactant produced by Chengdu Jinshan Chemical Co., Ltd (China; AR grade). Deionized water was used in all experiments. The other provided reagents included sodium hydroxide, potassium hydroxide, nitric acid, hydrochloric acid, potassium chloride, phenolphthalein and anhydrous ethanol were of the analytical grades.
The content of silica in the sample was determined by potassium fluosilicate volumetric method 21 . The mass concentration of the fl uosilicic acid solution was determined by the potassium fl uosilicic acid method 22 . The fi eld emission scanning electron microscope (JSM--7500F, Japan Electron Optics Laboratory Co., Ltd.) was used to observe the morphology and microstructure of the samples.

Equipment and Procedure.
The experimental process was shown in Figure 1. The fl uosilicic acid solution was diluted by deionized water to a certain concentration and preheated in a reactor of the one-liter volume. The temperature in the reactor was controlled by an electronic constant temperature water bath pot (601, JiangSu Jinyi Instrument Technology Co., Ltd.), and the real-time temperature display in the reaction was read by a mercury thermometer. The diameter of PTFE agitator was 60.0 mm. The quantitative aluminum hydroxide was added to the reaction kettle with a certain drop acceleration (0.216 g/s). After the reactant has been added, the stirring speed was set to 400 rpm by a digital display electric mixer and the reaction began. During the reaction process, a small amount of reaction liquid was taken out with 10 mL plastic dropper every 5 minutes, and the reaction liquid was quickly fi ltered by the vacuum fi lter extractor. The fi lter residue was placed in the electric oven at 80 o C and dried until the mass was constant. After drying, remove the fi lter residue and put it into the atmospheric dryer to analyze the silica content in the fi lter residue. The total reaction time was set to 30 minutes. After the reaction, the reaction liquid was rapidly fi ltered. The filtrate was put into the electronic constant temperature water bath pot to be evaporated and crystallized. After fi ltration, the fi lter residue was placed in the electric oven at 80 o C and dried until the mass was constant.
The experimental conditions adopted in this work were described in Table 1.

RESULTS AND DISCUSSION
Characteristic analysis of the product.
The Eqs.
(1)-(3) of fl uosilicic acid and aluminum hydroxide showed that the reaction was a heterogeneous liquid-solid reaction. SEM characterization of products at different periods during the reaction process was shown in Figure 2. It could be seen that the morphology of the aluminum hydroxide was a mainly dense fl ake, while the morphology of the silicon dioxide was mainly fi ne particles. With the increase of reaction time, the agglomeration of the silica became more obvious. Aluminum hydroxide was the main matrix of silica dispersion. Babyat. M et al. 17 also observed this phenomenon and speculated that the mechanism model of this reaction could be explained by the uncreated-core model of the reaction. Aluminum hydroxide was considered to have insuffi cient internal voids for external fl uids to easily diffuse into aluminum hydroxide, thus the uncreated--core model was superior to the homogeneous model.
From the SEM diagram, we can also observe the formation of product clusters. Silica microspheres were formed on the aluminum hydroxide fl ake surface in a reaction time of only 5 minutes. This indicated that fl uorosilicic acid was diffused to aluminum hydroxide surface to produce aluminum fl uorosilicic acid, aluminum fl uorosilicic acid quickly hydrolyzed to silicon dioxide. After the reaction time of 10 minutes, silica microspheres gathered to form clusters, and the clusters attached to the surface of aluminum hydroxide gradually grew larger with the increase of time, which can be understood as the growth of silica product layer attached to the surface of aluminum hydroxide. The cluster structure may be caused (9) Eq. (8) and Eq. (9) were the rate equations for the intrinsic reaction, where k 1 , k 2 , q and m were temperature-dependent functions.

Macroscopic reaction kinetics
Considering that aluminum hydroxide was a dense fl ake reactant, the uncreated-core model was adopted in this work. According to the uncreated-core model of kinetic theory, the reaction process of aluminum hydroxide and fl uosilicic acid was composed of the following steps. (1) Fluosilicic acid diffused from the solution body through the liquid membrane to the reactant surface. (2) Fluosilicic acid diffused from the silica product layer on the outer surface of aluminum hydroxide to the unreacted aluminum hydroxide surface layer. (3) Fluosilicic acid was neutralized and hydrolyzed on the surface of unreacted aluminum hydroxide. (4) The liquid product aluminum fl uoride diffused with water through the silica product layer to the outer surface of the reaction material. (5) The liquid product aluminum fl uoride diffused with water through the liquid fi lm from the outer surface of the reaction to the solution body. This process can be divided into external diffusion control, internal diffusion control and interfacial reaction-diffusion control. Since the concentration of fl uosilicic acid in this experiment changes obviously, the classical simplifi ed formula was not adopted. Due to the high mixing speed in this experiment, external diffusion control was not considered in this work. Aluminum hydroxide was assumed to be a granular reactant of equivalent diameter, formulas controlled by interfacial reaction and by internal diffusion would be derived below.
In the process of interface reaction control, the concentration of fl uosilicic acid in the surface layer of unreacted aluminum hydroxide was equal to the concentration of the main body in the solution. The macroscopic reaction by the intense agitation that caused silica microspheres to aggregate in the aqueous medium.

Intrinsic reaction kinetics
According to the Eqs. (1)-(3), the reaction is a consecutive reaction. k 1 , k 2 and k 3 are defi ned as the reaction rate constants of Eq. (1), Eq. (2) and Eq. (3), respectively. Considering that Eq. (1) and Eq. (3) were part of the acid-base neutralization reaction, the reaction rate was higher than that of Eq. (2). Thus, Eq. (2) was inferred to be the rate control step of the reaction. That is, the total reaction rate depended on the hydrolysis rate of aluminum fl uosilicate. Assumed that both Eq. (1) and Eq. (2) were fi rst-order reactions, the following Eqs.  In the process of internal diffusion control, the diffusion rate of the reactant fl uosilicic acid through the silica product layer was the total speed of the macroscopic reaction process. According to fi ck diffusion law, the diffusion rate of fl uosilicic acid through the silica product layer was as Eq. (19) follows: (19) D e was defi ned as the diffusion coeffi cient of fl uosilicic acid through the silica product layer in Eq. (19).
Eq. (20) can be obtained from material balance: (20) The boundary condition of Eq. (20) was: was defi ned as the concentration of fl uosilicic acid on the particle surface.
Solution R c was defi ned as the equivalent radius of unreacted aluminum hydroxide in the Eq. (10), and K s was defi ned as follows: The stoichiometric relationship between aluminum hydroxide and fl uosilicic acid can be obtained as follows: (11) ρ was defi ned as the density of aluminum hydroxide, M was defi ned as the relative molecular mass of aluminum hydroxide in the Eq. (11). (12) The boundary condition of Eq. (11) was: R s was defi ned as the outer surface equivalent radius of the particle containing the reactant aluminum hydroxide and silicon dioxide product layer. Solution to the system of Eq. (6) and Eq. (12): (13) α was defi ned as follows: The boundary condition of Eq. (14) was: t fi nish was defi ned as the reaction time of the complete reaction. (15) (16) From the mechanism described earlier, k 1 is much larger than k 2 .
Eq. (18) was the macroscopical reaction kinetics equation controlled by the interface reaction of fl uosilicic acid and aluminum hydroxide. was defi ned as the amount of aluminum hydroxide, was defi ned as the relative molecular mass of silicon dioxide and was defi ned as the relative molecular mass of aluminum hydroxide in Eq. (27).  L was defi ned as the density of the liquid and m L was defi ned as the mass of liquid in Eq. (28).
According to the evaluation, the fitting degree controlled by internal diffusion and the fi tting degree controlled by interface reaction was very close to 1. The relevant fi tting degrees were marked in Fig. 5 and Figure 6. It can be inferred that the reaction between fl uosilicic acid and aluminum hydroxide was controlled by internal diffusion and interfacial reaction. When the reaction started, the reaction was mainly controlled by the interface reaction due to the product layer silica did not accumulate. When the thickness of silica in the product layer accumulated to a certain thickness, the internal diffusion resistance of fl uosilicic acid increased, and the reaction changed from interfacial reaction control to internal diffusion control.

Experimental data fi tting
From the above formula derivation, if the reaction is controlled by interfacial reaction, the plot of with time is an exponential decay 1 relationship. Similarly, if the reaction is controlled by internal diffusion, the plot of with time is an exponential decay 1 relationship. In this work, we adopted Eq. (18) and Eq. (26) to evaluate the contribution of interfacial reaction and internal diffusion to the reaction.
It can be observed from Figure 3 that with the rise of temperature, the overall trend of mass concentration of silica increased at the same time, which can be explained by the increase of temperature and the increase of reaction rate. Considering that the above equations were based on the concentration of fl uosilicic acid, the mass concentration of silica was converted into the concentration of fl uosilicic acid according to the following Eq. (27) and Eq. (28). As can be seen from Figure 4, with the rise of temperature, the overall trend of the concentration of fl uosilicic acid decreased in the same time.    8), it can be inferred that m≈0 which conformed to the previous assumption that k 1 >> k 2 , and the apparent reaction rate constant at various temperatures can be obtained based on this fi gure. It was also proved that the apparent reaction order of this reaction was 1 from Figure 7.
As shown in Figure 8, the linear fi tting degree of this curve can be observed from the arienius curve of the reaction between aluminum hydroxide and fl uosilicic acid as 0.98332, and the apparent activation energy E a can be obtained as 30.8623 kJ/mol.
(3) This dynamic mechanism directly explained that silica products contained aluminum hydroxide impurities, and internal diffusion and interfacial reaction were the control steps of this reaction. It could be considered to improve the purity of silica by improving the effect of internal diffusion and interfacial reaction. This work has certain guiding signifi cance to the direct method of aluminum fl uoride by using fl uosilicic acid. -initial molality of fl uosilicic acid in solution, mol/L; R c -equivalent radius of unreacted aluminum hydroxide, m; ρ -density of aluminum hydroxide, g/L; M -relative molecular mass of aluminum hydroxide, g/mol; R s -outer surface equivalent radius of the particle containing the reactant aluminum hydroxide and silicon dioxide product layer, m; α -reaction conversion rate; t fi nish -reaction time of the complete reaction, s; D e -diffusion coeffi cient of fl uosilicic acid through silica product layer;

ACKNOWLEDGMENTS
-molarity of fl uosilicic acid on the particle surface, mol/L; -amount of aluminum hydroxide, mol; -relative molecular mass of silicon dioxide, g/mol; -relative molecular mass of aluminum hydroxide, g/mol; -density of liquid, g/L; m L -mass of liquid, g.

CONCLUSIONS
The kinetic mechanism of the reaction between aluminum hydroxide and fl uosilicic acid was analyzed by measuring the yield of silica at different temperatures, and the following conclusions were drawn: (1) The kinetic results showed that the uncreated-core model was suitable for the reaction of fl uosilicic acid with aluminum hydroxide, which was controlled by internal diffusion and interfacial reaction. The kinetic parameters of the reaction, the apparent reaction series n = 1, the apparent activation energy E a = 30.8623 kJ/mol.
(2) In view of the obvious changes in the concentration of fl uosilicic acid, the kinetic equation different from the traditional uncreated-core model was adopted. Combining with the SEM diagram of the reaction product of fl uosilicic acid and aluminum hydroxide, the reaction process of fl uosilicic acid and aluminum hydroxide conformed to the uncreated-core model composed of three steps: diffusion, interfacial reaction and internal diffusion.