The entropy factor in liquid diffusion
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here D0 is the frequency factor, Q is the activation energy, R is the gas constant, and T is the absolute temperature. In the following, it is shown that consideration of the entropy term contained in the frequency factor renders the hole theory for liquid diffusion improbable. However, the “fluctuation” theory remains a possibility. The mechanism of liquid diffusion is little understood and many theories have been developed in an attempt to explain the process.[1,2] Perhaps the greatest difficulty in developing an accurate model for liquid diffusion arises from the sparcity of reliable data. The majority of liquid diffusion data has been obtained using the capillary-reservoir technique, and it is now known that convective flow in the reservoir across the open end of the capillary causes “lid driven” flow in the capillary, resulting in artificially high liquid diffusion coefficients.[3] However, reliable and consistent data do exist for solvent self-diffusion in liquid Sn. Six independent investigations that avoided the capillary-reservoir technique and used either the long capillary or shear cell techniques have been reported. These are shown in Figure 1 and are compared with the phenomenological prediction of Cahoon.[4] Further, two of these investigations, those of Soedervall et al.[9] and Itami et al.[10] were performed in microgravity, where any convective contributions to the diffusion coefficient should be minimal. Figure 1 shows good agreement among all the investigations as well as with the phenomenological prediction.[4] If a thermally activated process for liquid diffusion is assumed (and this is by no means certain), then the diffusion coefficient is given by the Arrhenius equation (Eq. [1]). For the data in Figure 1, the best-fit linear regression (solid line in Figure 1) gives D0 ⫽ 3.5 ⫾ 0.6 ⫻ 10⫺8 m2/s and Q ⫽ 12,100 ⫾ 370 J/mole, where the error limits are estimates of standard deviation. The good agreement among the data in Figure 1, the closeness to the phenomenological prediction, and the relatively low error limits for D0 and Q all indicate that the data in Figure 1 accurately represent solvent self-diffusion in liquid Sn. The frequency factor for diffusion is given by D0 ⫽ gfa2ve⌬S/R
tures, g ⫽ Z/6, where Z is the number of nearest neighbors. The correlation factor for diffusion in pure metals is also a function of Z [11] and is shown in Figure 2. It has recently been shown that the coordination number for liquid Sn is Z ⫽ 6.7,[12] which gives g ⫽ 1.12. If it is assumed that the jump distance, a, is the nearest neighbor distance given by the position of the first peak of the radial distribution function, a ⫽ 3.16 ⫻ 10⫺10 m,[13] f ⫽ 0.684 (Figure 2), and v is given by v ⫽ kTmp /h ⫽ 1.05 ⫻ 1013 s⫺1, where Tmp is the melting temperature of Sn, then the frequency factor is given by D0 ⫽ 8.0323 ⫻ 10⫺7 e⌬S/ R. Using the value for D0 given previously, e⌬S/ R ⫽ 0.0436, which yields ⌬S ⫽ ⫺26.04 J mole⫺1 K⫺1. This negative value for ⌬S creates a problem. The hole theory for liquid diffusion postulates the
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