The kinetics of the formation and growth of monodispersed sulfur hydrosols.

Abstract An investigation has been made of the kinetics of the formation and growth of monodispersed sulfur sols prepared by the action of dilute HCl (0.00075-0.006 M) on Na2S2O3 (0.0005-0.003 M). The study has been divided into three parts. I. The Homogeneous Reaction. The formation of molecularly dispersed sulfur begins as soon as the reactants are mixed. Ultraviolet absorption measurements with a Beckman quartz spectrophotometer at λ = 3000 A show that the concentration of dissolved sulfur reaches a constant value representing a limiting state of supersaturation, after which further formation of sulfur leads to condensation. Within the limits of experimental error the concentration of sulfur at the time, tB when the phase change occurs is unaffected by changing the concentrations of the reactants or by adding small amounts of salts. Furthermore, this time is reproducible and varies with the rate of formation of sulfur. It depends also upon the degree of supersaturation of sulfur, the solubility of sulfur in the medium, the nature of the nucleation process that occurs at the phase transition, and the wavelength of light used to detect the initiation of scattering. Since these variables were eliminated by using the same solvent and wavelength for all experiments, tB is a valid measure of the rate of the homogeneous reaction. The effect of changing the concentrations of the reactants showed that the rate of formation of sulfur is proportional to (T) 3 2 (H) 1 2 , where (T) and (H) are the total molar concentrations of thiosulfate and hydrogen ion. The fractional order and the shape of the curves for optical density as a function of time indicate an autocatalytic reaction, probably of the chain type. The reaction exhibits a positive Bronsted primary salt effect —e.g., the addition of lanthanum salts produces a marked acceleration. The rate-controlling step is, therefore, a reaction between negatively charged ionic species, either (S2O3= + HS2O3−) or (2HS2O3−). II. The Condensation Stage. This stage begins with the formation of nuclei capable of further growth, less than 2 min. before the appearance of colloidal sulfur is detected experimentally. The existence of a limiting state of supersaturation is in accord with the accepted theory for phase transitions. The degree of supersaturation that must be reached before condensation occurs is dependent to a critical extent on the rate of nucleus formation. Although, when the Tyndall beam first appears, the scattered light is bluish, its intensity is not proportional to γ 6 λ 4 and Rayleigh's limiting law (for γ λ 10 ) cannot be applied to the determination of the sizes of particles because their radii are already 1 3 the wavelength of light. Attempts to detect the scattering at smaller radii failed because the number of particles is so small (106/cm.3). The particle number which is necessary to give perceptible scattering in this region is so large that rapid coagulation would occur according to Smoluchowski's law. Values of the radius were determined by applying the Mie theory to measurements of optical density as a function of time at λ = 4000 and 8000 A. At these wavelengths sulfur is transparent and has refractive indices for which calculated values of the scattering area coefficient K3 = 2.3 log (I0/I)/πγ2nl as a function of α = 2πγ/λ′ are available. In the range α = 1.2–3.0 the variation of Ks with α can be expressed by empirical linear relationships, thus permitting the determination of radii from 0.07 to 0.30μ. Since the variation of γ2 with time is non-linear, a steady state in the diffusion process by which dissolved sulfur is deposited on the surfaces of the particles is not set up in the early stage of growth. III. The Heterogeneous Stage. The overall rate of the chemical changes that occur during the growth of a sol has been found by titrations with iodine and alkali to be proportional to (T)2(H). The variation with time of the number and radii of the particles in suspension was determined by an application of the Mie theory to transmittance measurements. The occurrence of a maximum in the number vs. time curves is explained by ascribing increases in number to the formation of molecularly dispersed sulfur at a greater rate than it can diffuse to the growing particles already present. Decreases in number result from coagulation and settling. From the asymptotic linear variation of γ2 with time it is suggested that a steady state has been reached in which the rate of diffusion of dissolved sulfur to the particle surfaces remains constant. The monodispersity of a sol is strongly influenced by the rate of sulfur formation. Polydispersity in the early stages of particle growth is caused by the continued formation of new particles while older ones are growing, and by coagulation, and is, therefore, favored by high reactant concentrations. The deterioration of a monodispersed sol on aging is largely due to the settling out of the particles. An overestimate of the total amount of colloidal sulfur in these systems has been made by correcting the particle number for decreases due to coagulation and settling, and by assuming that growth continues on all particles whether they are in suspension or not. In spite of this, the difference between the amount of sulfite found and the estimated total colloidal sulfur is too great to be interpreted as the quantity of dissolved sulfur present. This indicates that the pentathionate which is the product of a side reaction takes up sulfur to give higher polythionates.