KINETIC STUDY OF THE SOLID-STATE REACTION BETWEEN PHTHALIC ANHYDRIDE AND SULFATHIAZOLE JORGE TOMAS] ENRIQUE PEREIRA, AND JORGE RONCO Departamento de Tecnologfa Quimica, Facultad de Ciencias Exactas, Universidad Nacional de L a Plata, L a Plata, Argentina
The addition reaction between compacted powders of phthalic anhydride and sulfathiazole was studied. Both reactants were ground to 100 Tyler mesh, mixed in 1 to-1 molar ratio, and compacted at a pressure of 15 kg. per sq. cm. Conversion was measured after heating at 1 00",1 1 0",and 1 2 0 " C. for 10,20, 30, and 60 minutes, Two rates were observed. After an initial boundary process, the reaction rate changes to a constant value, not greatly affected by temperature. A sintering phenomenon that appears simultaneously with the chemical reaction and modifies its kinetics was measured in phthalic anhydride pellets by a dilatometric technique. Viscous flow during sintering would explain some apparent anomalous behavior in the experimental results. An apparent diffusion coefficient for phthalic anhydride in phthalylsulfathiazole was obtained.
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ASY
chemical processes take place in the solid state.
M The kinetics and reaction mechanisms of such processes
represent a broad field where, in spite of much work, much remains to be learned. Several basic general facts are typical of every heterogeneous boundary reaction: transfer of reactants to the boundary and transfer of energy to or from the interphase. I n solid reactions, the reactants are not thoroughly mixed a t the atomic level. Therefore, they must diffuse or penetrate into each other in order to react and continue reacting within the solid phase. In such a case, the space coordinates become a controlling element. A full description of the process taking place requires the development of relationships between time and reaction rate, or time and concentration, including a t least one space coordinate. This applies also to heterogeneous reactions in general. The approach is very difficult because other characteristics are involved, representing space and history, by which the reactants reach the reaction site. Undoubtedly, a solid-state reaction cannot be defined only as a function of the usual thermodynamic parameters. I t needs other terms that are not always defined, are not under control, or are not reliable. A broad generalization of the subject will be possible only if based on two groups of expressions: basic concepts of reactions, thermodynamically expressed, and boundary conditions of the reaction. The simplest solid reaction is an addition-type reaction: AfB-AB which can involve elements or compounds. The total, partial, or null miscibility between reactants and products will result in the formation of one or more solid phases while the reaction is taking place. This paper discusses an addition-type reaction chosen for the sake of simplicity. Only a few organic solid reaction examples have been found in the literature (Gluzman, 1957; Gluzman and Milner, 1961). The reaction between phthalic anhydride and sulfathiazole leads to the formation of phthalylsulfathiazole, a compound of pharmaceutical and technological importance. 120
I&EC P R O C E S S D E S I G N A N D D E V E L O P M E N T
This reaction normally takes place in the liquid phase (pro panone) a t low temperatures, with the general inconvenience of processes that involve handling a volatile solvent (operative danger, recovery, etc.). The reaction between the same reactants in the @id state resulted in the same end product, with similar yields, a t a temperature approaching 90" C. I t is easy to foresee the advantages of the solid-solid synthesis. However, the initial conditions of the reactants demand a thorough knowledge of the variables involved. This paper studies fundamentally the influence of the physical mechanism of mass transport and transfer on the total process kinetics. Kinetic Study
The over-all rate of a solid-solid reaction is influenced by: The possibility of contact between reacting phases (space and time coincidence), depending on the geometry of the system. Boundary process, with exclusive characteristics for the system involved, including mass transfer and sintering mechanism, chemical reaction, and nucleation followed by crystal growth. Diffusion through a reaction product layer (normally the controlling step of the reaction). The whole scheme of the behavior of a reactant, for such a reaction system, could be totally modified by the previous history of the reactant phases. This cannot be always represented in classical thermodynamic parameters. Therefore, the kinetics are represented here only as a function of the particular characteristics of the reactants involved. Physical Mechanisms
Sintering Mechanisms. After the initial reaction in the contacting points or areas, the progress of a chemical reaction between solid phases depends on the characteristics and behavior of the layer formed. In spite of the fluid phase that eventually appears, a great number of reactions in the solid phase have been kinetically
8 , min Figure 1.
Conversion as a function of time and temperature
interpreted by the parabolic growth law of the product layer, which assumes a fast surface interaction followed by a slower step: diffusional control of reactants. This scheme could be modified using nonspherical particles and volumetric changes in the reaction system. Moreover, organic reactants of heavy molecular weight, with nonelectrostatic crystal bonding, could produce, a t the time the surface reaction process occurs, mass flow phenomena, which are typical of systems formed by small solid particles. Together with diffusional transport through the product layer, the simultaneous sintering phenomena would contribute in the presence of a more active substance, because of mechanisms different from diffusion. Sintering mechanisms, appearing simultaneously with the chemical reaction, modify its kinetics. Diffusion Mechanisms. The chemical reaction kinetics involving only the solid phases is normally represented by the growth rate of the layer formed by the reaction products. Such growth is frequently represented by the parabolic law where, after a fast reaction due to initial contact of reactant surfaces, further progress is determined by mechanisms of reactant transport through the product barrier. Normally, the latter mechanisms are extremely slow and have a high activation energy. The growth rate keeps increasing but reaches a maximum only asymtotically. In crystalline solids, such mechanisms are represented by diffusion processes involving elemental particle movement a t corners, on surfaces, or within the crystalline network. The driving force is normally related to the chemical potential difference of the particles diffusing within a phase or through the contacting interface. The unit transport rate is expressed in such cases by a factor D ,the diffusion coefficient, which is related to the ion and system characteristics, movement mechanism, temperature, etc. I n some cases, especially in powder phase systems, elemental particles do not contribute to mass transport. Transport is represented here by mass flow and its mechanisms, plastic or viscous. I n such cases, the force that accounts for transport is associated with the particle surface energy. The system tends
to become dense because of coalescence of the particles. The transport rate cannot be specifically expressed, as in the case of elemental particle diffusion. However, it could be worthwhile to use an apparent diffusion coefficient, Dap, that represents such a rate, including every mechanism contributing to mass transport, whatever they are. Serin and Ellickson (1941) modified the classical Jander equation and obtained a mathematical expression for the solid powder reaction kinetics with diffusional control: x = 1
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(6/r2)
(l/n2) exp(-n2.n2.Dpe/r2) n
that makes it possible to calculate the apparent diffusion coefficient, Dap. Experimental
Kinetic Study. I n studying the reaction between phthalic anhydride and sulfathiazole in the solid state, the first factor taken into account, of the many variables influencing the system, was the study of conversion as a function of time and temperature, keeping particle size, compactibility, and mass ratio constant. Influence of Time and Temperature. Both reactants were ground to 100 Tyler mesh, mixed in a 1 to 1 (molar ratio), and compacted in a metal die of 11-mm. diameter, a t a pressure of 1 5 kg. per sq. cm. The working temperatures were loo', l l O o , and 120' C., and the conversion was measured a t 10, 20. 30, and 60 minutes. The reaction system was a thermostat oil bath (temperature kept constant within 0.1" C.), the reaction taking place in small tubes. The pellets were surrounded by an inert substance in order to get better thermal conductivity. After each reaction time, the tubes were quenched with ice, and the conversion was analytically determined by a colorimetric method (measurement of free sulfathiazole). The data were not reproducible for conversion a t a reaction time interval smaller than 10 minutes. Values were statistically calculated with a 95% confidence limit (Figure 1 ) . Two different rates are observed in the curves. After the first initial boundary process, the rate changes to a constant VOL. 8
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Figure 4. flow
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0,
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Figure 3. Fractional shrinkage as a function of time and temperature
value, that represents a slow process, not greatly affected by temperature. I t is difficult to explain why in a solid particle reacting system, a relatively high conversion could have been attained in short time intervals. This fact can be interpreted only by considering some further active surface contribution, different from the former particle contacting area, and thought to be due to some physical mechanism of mass transport that proceeds simultaneously with the reaction itself, during the reactant thermal processing. Unfortunately, the fragility of the reacting crystalline medium did not allow establishing the specific active area. This value would have led us to a specific rate of boundary reaction, a more important parameter much easier to generalize. Physical Mechanisms
Sintering Mechanisms. I n order to measure the longitudinal changes of the reacting pellets a linear dilatometer was built, that operates between 90"and 130' C., with a f 0.5' C. tolerance, fitted with a micrometer with reading to 0.005 mm. The solid reaction between phthalic anhydride and sulfathiazole takes place between 30" and 120" C. (at higher tempera122
l & E C PROCESS D E S I G N A N D DEVELOPMENT
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i - i
Relationships for viscous
ture, the first reactant melts). As in this range the phthalic anhydride showed coalescence and densification, only this reactant was analyzed by dilatometry. Solid particles were obtained by grinding the crystals and sieving; three fractions were separated : 60-80 Tyler mesh, (250 to 177 microns), 100-120 Tyler mesh (149 to 125 microns), and >120 Tyler (less than 125 microns), and samples 1 cm. in height and 1 cm. in diameter were compacted a t 100 kg. per sq. cm. in a cylindrical die. The samples reached the dilatometer temperature within 10 seconds. The fractional shrinkage (3A L/L,) as a function of time (e), a t constant temperature, for the three solid fractions, is shown in Figure 2. Figure 3 shows the same relationships, for the 100- to 120-mesh fraction, a t 90', 95', and 100' C. The initial ratio between the fractionary shrinkage and the time is close to 1. This ratio had been indicated by Kingery (1959 a, b), for densification of solid particles in the presence of a liquid phase. This author considers such systems in two steps: 2n initial reordering process in which particles undergo transition from viscous to plastic flow, due to a decrease in the pore sizes of the system. The capillary pressure should be the driving force bringing the solid particles near. Obviously, this scheme cannot be thoroughly applied to our system, but the lineal function indicated above agrees closely with Kingery's assumptions. Kingery also considers that the second step of the process involves solubilization (welding) of contact points, and a corresponding densification, with particles approaching each other. For the first stage of our process y 2 / r is plotted against time, wherey is the radius of the neck between two particles, obtained from the equation: y = r(2AL/L,)1/2 (Kingery, 1959c), and r is the original radius of the particles. With the experimental values utilized in Figure 3, the relationships established by Frenkel (1945) and Kuczynski (1949) for viscous flow are obtained (Figure 4). I n the case of solid particles
p 2 / ~= 3y8/2,u where y is the surface energy of the material, and ,u is the viscosity. Therefore, the slope of the straight line is given by the angular coefficient 3y/2p that, if in agreement with experimental data for y and p, would indicate the right selection of the mechanism.
e
9 , min Figure 5.
Rate of densification process
The rate of the densification process in this first stage must be influenced by the particle size, as the driving force for the process obeys the same ratio. Figure 5 shows this relation, giving a n inverse function between sintering rate, AL/L, 0, and solid particle diameter, Y . Once the spheroidization and reordering of the compacting elements have taken place, the system continues to become denser by another process, or by the same process but a t a slower rate. When there are particles having bonding and welding points, these points will grow in diameter by contribution of material from their neighborhood. This contribution could hardly account for the remarkable change of mechanism from the original viscous flow. T h e rate change must be due to the decreasing driving force (curvature of the bonding points by growth of contacting necks), that will take the system into a plastic flow. This assumption would be confirmed by the continuity of the inverse relation between the shrinkage rate of the compact and the original particle size.
The former assumptions could be checked if the total process could be split into stages. According to Figure 3, a t temperatures near 90’ C., the system operates by spheroidization of its particles, within the first 60 minutes. The rate change of the densification process could be due to a stronger action of another mechanism. For the experimental study, the material was processed in an oven for 60 minutes and then observed microscopically. The crystal acute corners, places with higher surface energy, had rounded edges. Pellets of 1.254-cm. diameter and 0.9-cm. length were made with such material and pressed to 100 kg. per sq. cm. Dilatometric analysis a t 90’ C. showed behavior similar to the original material in the over-all reaction (Figures 2 and 3). Figure 6 shows a slope of 0.6 (the original material slope was 0.5 under similar conditions). Further experiments with materials kept in a n oven for 48 hours a t 90’ C. showed no changes in dilatometric analysis as a function of time. I t can be concluded that the sintering proceeded in two stages. During the first stage, particles tended to become spherical, the driving force coming from the large surface energy of the system. The system showed shrinkage a t a rate which was a lineal function of time. Apparently, the flow was viscous. Thereafter, the system became dense, with simultaneous contraction and lower rate. I n this case, the driving force should come from the existing pores and neck curving. This mechanism produced continuity of the first stage (surface interaction) of the reaction inside the compacted powders of phthalic anhydride and sulfathiazole by contributing new reacting masses. After sintering was completed, the control of material flow, through the product layer, predominated. Diffusion Mechanisms, Experimental values from the figures represented partially in Figure 1 have been considered for calculation of DaP for the chemical reaction stage or diffusional control zone.
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f r , r/mm Figure 6.
Fractional shrinkage as a function of time, second stage VOL. 8
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Assuming that the reactant particles are perfect spheres and including in coefficient D of the Serin and Ellickson equation every physical mechanism considered above, it is possible to obtain a D,, for our system. For a time of 3600 seconds and temperatures of looo, l l O o , and 120’ C., the values obtained from D,, x 10’0 (sq.cm. per second) are 0.27, 0.41, and 1.5, respectively. The values are similar to the one obtained by Arrowsmith and Smith (1966), during diffusion of phthalic anhydride in cylindrical sulfathiazole pellets, working a t 108.5’ C., with a time of 400 hours and a compaction pressure of 50,900 p.s.i.g.
Nomenclature
apparent diffusion coefficient, sq. cm./sec. original length, mm. final length, mm. original length initial radius of solid reactant B, cm. initial sulfathiazole conversion, mole yo radius of neck between two particles, mm. surface energy, dynes/cm. viscosity coefficient, g./mm. sec. time, min. or sec. sintering rate, mm./min.
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literature Cited
Conclusions
The reaction layer growth curve of fine powders of phthalic anhydride and sulfathiazole, between 80’ and 105’ C., shows a behavior following the parabolic law. According to the macromolecular characteristic of the reactants and its organic nature, a different behavior could have been expected because there is no possibility of ionic or elemental diffusion and the reaction should stop, once the initial contacting surface of reactants is used up. However, the existence of sintering mechanisms among the particles of one of the reactants (phthalic anhydride) has been found. This would explain the apparent abnormality of the experimental results, considering that such mechanisms, by contributinq to further contact among reactants, would slow the reaction.
Arrowsmith, R. J., Smith, J. M., Ind. En,
