ABSTRACTS

A NEW METHOD FOR MEASURING DIFFUSION IN LIQUIDS

For the diffusion of highly dilute solutions it has been possible theoretically to derive Fick’s law for nonelectrolytes and for electrolytes in the case of their complete dissociation. For concentrated solutions Fick’s law is inapplicable, since in them one cannot neglect the interaction of the dissolved particles with one another and with the particles of the solvent, which leads to hydration, association, etc. We have in the given case a very complex dependence of the diffusion flux on the concentration gradient, for which Fick’s law is only a first approximation; consequently the coefficient of Fick’s equation, usually called the diffusion coefficient, is a function of the concentration. The problem of investigating diffusion, which until now has not been posed broadly enough, is to describe the law of diffusion for various substances and to study the dependence of the diffusion coefficient on concentration. All methods of measuring diffusion known up to now have not made it possible to approach the solution of this problem, since their use already presupposes the applicability of Fick’s law to the phenomenon of diffusion and reduces to determining the coefficient of Fick’s equation. In 1926 W. Ffort proposed a micromethod for investigating diffusion, in which the diffusion process is followed for colored liquids in layers separated from one another by microscopic distances. This method was used by him, Ulman, Pestler, Tikhlehorn, and others to study the dependence of the diffusion coefficient on concentration. At the end of 1932 R. Zuber developed a similar method for uncolored liquids and used its principle for the construction of a very perfect apparatus, making it possible to study the diffusion process with great simplicity and convenience over a short time in layers of various concentrations. The method of measuring diffusion for uncolored liquids is based, like W. Ffort’s method, on following the upward movement in a diffusion chamber of a specified concentration, but for uncolored liquids the upward movement is observed of the boundary angle of total internal reflection, whose dependence on concentration must be determined beforehand. The arrangement of R. Zuber’s apparatus and its appearance are given in Figs. 1 and 2. A monochromatic parallel beam of rays falls from the collimator \(R_0\) onto the prism \(P_r\); at the angles of exit of the rays from prism \(B\) the diffusion chamber \(A\) is attached. At different horizontal levels of the chamber, in which the diffusion process is taking place, either total internal reflection will occur at face \(B\), or the rays will penetrate from the prism into the chamber. In the microscope, into which the rays emerging from the chamber enter, the bright and dark parts of the field will be visible (Fig. 3), separated by a curved line that moves upward as the diffusion process proceeds. The point \(S\) of this line lies at that horizontal level of the chamber where, for the given angle of incidence of the rays emerging from the collimator on the face of prism \(C\), the concentration in the chamber is such that light falls on the face of prism \(B\) at

* Rudolf Zuber, Untersuchungen über Diffusion in Flüssigkeiten. II. Über einen Mikrodiffusionsapparat für ungefärbte Flüssigkeiten (Aus dem Physikalischen Institut der deutschen Universität in Prag), Z. Physik, 79, 5/6, 280, 1932.

at the angle of total internal reflection. The upward movement of this point \(S\) is measured as a function of time. The diffusion chamber is constructed as follows (Fig. 4). On face \(B\) of prism \(P\), two object glasses \(D_1\) and \(D_2\), each 1 mm thick, are cemented one above the other. Face \(A\) of the prism is turned toward the observer’s eye and is covered with a ground glass \(E\). A cover glass \(F\) is cemented over the object glasses \(D_1\) and \(D_2\) and onto the edge of the ground glass \(E\). The prism with the chamber thus obtained is mounted on a plane-parallel glass plate. The dimensions of the chamber are \(1\ \mathrm{mm}\times 7\ \mathrm{mm}\times 5\ \mathrm{mm}\). Between the object glasses \(D_1\) and \(D_2\) there enters a movable plate. Before the experiment begins, the chamber is filled up to the movable plate with solution and, above it, with solvent. When the plate is withdrawn, diffusion begins. The diffusion chamber with the prism is placed on table \(T_2\), rotating relative to table \(T_1\) (Fig. 2), which is fixed on the stand of a horizontally mounted microscope. To rotate table \(T_2\) and the prism relative to the rays of the collimator, a special device is used, set in motion by the micrometer screw \(M_1\). If the chamber is filled with a solution of the given concentration of the substance under study, then there exists such an angle of incidence of the rays on face \(C\) of the prism at which the ray emerging from the prism glides along face \(B\), and the vertical line dividing the field of view of the microscope into a bright and a dark part coincides with the image of face \(B\) of the prism. Before observing diffusion, the curve of the dependence of the concentrations of the solutions of the substance under study on the readings on the drum of the micrometer screw \(M_1\) is determined, in those of its positions in which the rays fall on face \(B\) at the angle of total internal reflection. Then the chamber is filled with the solution under study up to the movable plate and, above it, with solvent.

Fig. 1.

Fig. 2.

The stopwatch is started at the moment the plate is withdrawn. For various readings on the drum of the micrometer screw \(M_1\) (various assigned concentrations), readings are taken on the eyepiece micrometer, at which the movable thread coincides with the image

the lower edge of the unextended plate of the chamber. In 30–40 min it is possible to make 5–6 series of such readings at the same positions of the micrometer screw of the microscope. Thus, for different concentrations one obtains a series of measurements of the distance \(x\) of the levels in the chamber, where the given concentration has, from the initial interface of the solution and the solvent, at various instants of time—\(t\). Study of the dependence of \(x\) on \(t\) made it possible to approach the solution of the problem posed above. For a number of electrolytes and nonelectrolytes the applicability of Boltzmann’s law to the diffusion process was established, and the dependence of their diffusion coefficients on concentration was studied. The use of R. Tsuber’s apparatus for layering material in this direction may be of great significance for the further development of the kinetic theory of solutions and for establishing, on its basis, the law of diffusion of various substances, when the presence of forces of interaction between particles of the dissolved substance with one another and with particles of the solvent according to Bjerknes, Debye, and Hückel is taken into account. Attempts in this direction have already been made and have yielded favorable results.

Fig. 3.

Fig. 4.

Z. Volkova