REVERSIBLE AOOREOATIONS OF COLLOIDAL PARTICLES
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The solution of this equation is not practical in form, and it must be either approximated or handled as a two-step process:-a monomolecular seed generation defined by
- dsl _ dt
= klS
followed by a bimolecular growth of these seeds, defined by
3. The precipitation may be represented empirically by means of the apparent velocity constants presented in table 4. The reaction rate constants observed in gelatin medium are within one-tenth of the observed values in water medium, suggesting an identical mechanism for both cases. REFERESCES
(1) BOLAM,T. R., (2) (3) (4) (5) (6) (7) (8) (9)
AND COWORKERS: Trans. Faraday SOC.22, 151, 162 (1926); 29, 864 (1933). CAMPBELL, A. N., AND CAMPBELL, J. R.: Trans. Faraday soc. 33, 307 (1937). DESAI,B. N . , AND KABAR,G. M.: Trans. Faraday SOC.28, 449 (1932). FRIEDMAN, L., AND SHEARER, W.: J . Am. Chem. SOC.61, 1749 (1939). KHANOLKAR, R. R., AND DESAI,B. N.:Proc. Indian Acad. Sci. 4A,468 (1936). SVEDBERQ, T H E :The Ultracentrifuge. OxfordUniversity Press, New York (1940). VANHOOK,A.: J. Phys. Chem. 42, 1191, 1201 (1938); Kolloid-2.87, 125 (1939). VAN HOOK,A.: J. Phys. Chem. 44, 751 (1940). VANHOOK, A.: J. Phys. Chem. 46, 422 (1941).
REVERSIBLE AGGREGATIONS OF COLLOIDAL PARTICLES. I
EXPERIMENTS ON THIXOTROPIC IRONOXIDESOLS' CENTRIFUQAL WILFRIED HELLER
School of Chemistry, University of Minnesota, Minneapolis, Minnesota Received November 19, 1940
Two hypotheses have been proposed to explain the thixotropic sol-gel transformation. On the one hand, there is the hypothesis initiated by H. Zocher (26), namely, that thixotropic gels contain an elastic con-
' The experiments described in this paper were carried out, during 1936, in the Laboratoire des Recherches Physiques of the Sorbonne a t Paris. They were made possible by the generous hospitality accorded t o the author by Professor .4im6 Cotton, head of that institution. The author also feels indebted to Professor H. Freundlich for valuable discussions on the subject treated in this paper.
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WILFRIED HELLER
centrated gel phase, distributed as a net-like structure in a dilute sol phase. The distribution is supposed to be fine enough to give a solid aspect to the Thole system. On the other hand, there is Hauser’s hypothesis (9), recently somewhat modified by Goodeve (8), that all particles participate in the gel formation without separation of the system into two phases of differing colloid concentration. In our own work, which, so far, has been published only in scattered preliminary communications, we have tried to arrive a t a more precise knowledge of the mechanism of the thixotropic sol-gel transformation by means of appropriate experiments on the kinetics of this process. A preliminary outline of this theory has already been presented (11). According to it, reversible aggregates are built up in thixotropic sols (they can be destroyed reversibly by shaking). The primary particles contained in the aggregates are supposed not to be in close touch, but to assume equilibrium distances (16). The reversible aggregates are regarded as able to associate themselves to an aggregate structure. The kinetics of the sol-gel transformation and the character of the gel obtained are considered to depend upon the kinetics of three processes involved: the rate of formation of the aggregate nuclei, the rate of their growth, and the rate of association of the aggregates. If, in systems of low colloid concentration, very many nuclei develop, the result will be a quasi-homogeneous gel. As the number of nuclei decreases, the heterogeneous character of the gel will become more and more apparent and the alternation of the concentrated aggregate phase,-that is, the gel structure,-and the dilute sol phase may even become macroscopically visible. This theory was designed for and applied to systems with low and moderate colloid concentrations. As we proceed to higher colloid concentrations, a point will be reached where the equilibrium distances of the aggregated particles become equal to the average distances of the particles in the unaggregated state, that is, there will then be no separation of the system into two phases. The gel will be homogeneous and it will, so to say, represent a single reversible aggregate. This second type of sol-gel transformation will be likely to proceed almost instantaneously following shaking; only slight translatory displacements of the particles and, in the case of non-spherical particles, their rotation into a favorable position are necessary to lead from the non-aggregated to an aggregated state. I n our opinion, this is the peculiar type of thixotropy found by Freundlich and Juliusburger in suspensions of gypsum (3) and studied more extensively by Pryce-Jones on various other concentrated SUSpensions (23). Pryce-Jones called these systems “false body” systems. It seems to be more appropriate, however, to distinguish between a “rapid” thixotropy in these systems and the common “slow” thixotropy discussed above. This paper, which begins a presentation of our own results on thixotropy,
REVERSIBLE AGGREGATIOXS OF COLLOIDAL PARTICLES
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syneresis, and tactoid formation, covers the experimental proof of the existence of reversible aggregates in thixotropic systems of low and moderate colloid concentrations, as derived from centrifugal experiments. I. THEORETICAL CONSIDERATIONS
The settling of spherical particles in a centrifugal field is governed by a relation differing from the Stokes equation only in so far as the gravitational constant, g, is replaced by the acceleration, g’, in a system subjected to a centrifugal force, F ,
where = the speed of settling, r = the radius of the particles, cl = the density of the particles, d‘ = the density of the dispersive medium, and 7 = the viscosity. The magnitude of g’ depends on the angular speed of the centrifuge, w , and the distance, R , of the rotating mass from the axis of the centrifuge: g’ = w ~ R . First, considering a monodisperse system containing particies of R eak electrostatic charge, the settling of the particles must lead to the appearance of a boundary which separates the lower part of the samples from the upper, which has been largely emptied of particles. The speed with v hich this “upper” boundary, m,, moves don-nwards is continuously decreasing, owing to a n increasing tendency to back-diffusion as the concentration of the particles in the lower part increases. When the force P , resulting from this tendency, becomes equal to F , m,, becomes stationary and the so-called sedimentation equilibrium is reached. Basing his work on the rate of displacement of the boundary m,, and on the sedimentation equilibrium, Svedberg (25) developed his m ell-known ultracentifugal method for the determination of the radius of small colloidal particles in dilute suspmsions. I n this paper (secondary) n e are considering rather concentrated systems with comparatively large particles which have already settled if g’ < 20009. The diffusivity of sufficiently large particles is small enough to guarantee a temporary validity of the following equation: = ktp
