Diffusion, thermodiffusion, and thermal diffusion of polystyrene in solution

Abstract

Diffusion coefficients D and Ludwig‐Soret coefficients D′/D of polystyrene in toluene were determined in a convection‐free thermodiffusion cell of 1 to 4 mm. height, 100 mm. length, and at a temperature differences of 0.1 to 0.3°C. The cell had two chambers, thus allowing observation of the concentration gradient alone by optical elimination of the temperature gradient. Philpot‐Svensson and Gouy optical methods were used. Both equilibration from homogeneous concentration to Ludwig‐Soret equilibrium and from this back to homogeneous concentration lead to D and D′/D. The last method, operating with ΔT = 0 gave more exact results. It was possible to measure very low diffusion coefficients (below 10−7 cm.2sec.−1). For sharp fractions the agreement with the free diffusion is good. For broader samples the thermodiffusional D is smaller than D of free diffusion. This difference is in accordance with the different averaging of the two methods. Up to ΔT = 0.3°C. no variation of D′/D with temperature was found. The Ludwig‐Soret coefficients increase with increasing molecular weight M and decreasing concentration. The thermal diffusion coefficient D′ is nearly independent of M and shows only a very slight decline with concentration. The results of our experiments are discussed together with the work of other authors using different techniques.

Molecular diffusion in polymer solutions

“…Data for the solvents methyl ethyl ketone, toluene, and THF, taken primarily using narrow polystyrene fractions, are included in Figure 5. Lines drawn through the points representing the toluene data of Meyerhoff and Nachtigall (1962) and the methyl ethyl ketone data of King et al (1973b) and of Tsvetkov and Klenin (1958) would be in reasonable agreement with the shapes of the theoretical curves. Furthermore, as is discussed in detail elsewhere (Vrentas and Duda, 1976a), the values of B which fit these diffusivity data are in reasonably good agreement with values of this parameter determined from unrelated experiments, especially when the slow change of D o / ( D o ) e with B for good solvents is considered.…”

“…As the concentration of the polymer in dilute solution is increased, the individual polymer chains begin to interact hydrodynamically with each other (but do not overlap and entangle), and both increases and decreases of the mutual diffusion coefficient with concentration have been reported (Meyerhoff and Nachtigall, 1962; al., 1973a, b ) . The nature of the variation of D with concentration is dependent on the interaction between hydrodynamic, thermod namic, and volumetric effects point for the analysis of the concentration dependence for such systems is an equation which relates k D to these competing influences:…”

“…The toluene data of Meyerhoff and Nachtigall (1962) are satisfactorily represented by a curve with a value of B of about 2 x 1 0 -2 7 cm? which is in excellent agreement with the value 2.19 x 10-27 cm3 derived by Yamakawa (1971) from light scattering data.…”

Measurement of the Soret, diffusion, and thermal diffusion coefficients of three binary organic benchmark mixtures and of ethanol–water mixtures using a beam deflection technique

“…As explicitly stated in the publication of the benchmark results, the "techniques employed by the participating laboratories cover all standard techniques for measuring the Soret coefficient with one exception, the diffusion cell experiments" [9]. Diffusion cells with a vertical temperature gradient between two parallel horizontal metal plates and optical detection were already used by Meyerhoff and Nachtigall, who employed a Schlieren technique [19,20]. Later, Giglio and Vendramini [21,22], Kolodner et al [23], Zhang et al [24,25], and Piazza et al [26] utilized the deflection of a laser beam by the refractive index gradient within the cell for detection.…”

Study of the thermal diffusion behavior of simple binary mixtures

“…A thermal diffusion cell is a traditional experimental method for measuring the Soret coefficient [48,178,95,102,60]. …”