Evidence is presented that many-body interactions in fluids have important consequences at the liquid-vapor critical point. In particular, three-body interactions in lattice-gas models are shown to lead to revised scaling variables and to a singularity in the coexistence-curve diameter with an amplitude proportional to the molecular polarizability. This is confirmed in experiments reported here. A companion van der Waals theory explains several other observed correlations between nonuniversal critical amplitudes.
Evidence is presented that the pair-potential model of fluids is insufficient in the critical region. In particular, data on the critical properties of Ne, N2, C~H4, C2H6, and SF6 are shown to exhibit welldefined trends in the variation of certain nonuniversal critical amplitudes with the critical temperature T, . Both the slope of the coexistence-curve diameter far from the critical point, and the deviations from linear behavior which appear closer to T" increase systematically with T"and are directly correlated with the molecular polarizability.These trends are explained on the basis of the increasing importance of three-body dispersion (Axilrod-Teller) forces in the more polarizable systems, and a simple mean-field theory is developed which accounts for the observed correlations. The possibility of incorporating the effects of three-body interactions into an effective pair potential is explored within the context of perturbation theory in the grand canonical ensemble, and it is shown that such an interaction is explicitly a function of fugacity. In the critical region, this is equivalent to a thermal scaling field which depends on the bare chemical potential of the system, and ultimately leads to a breakdown in the classical law of the rectilinear diameter. The magnitude of this field mixing, and hence of the diameter anomaly, scales with the product of the particle polarizability and the critical number density, in agreement with experiment.
Five stacked parallel plates forming four capacitors were used to measure the density at four clifferent heights for nitrogen and neon near their critical points. Measurements were made on fluid samples with an average density very close to the critical value in a temperature range -5&10~t~1&10 where t is the reduced temperature ( T -T, )/T, . These measurements allow simultaneous determinations of (1) the coexistence curve, (2) isothermal compressibility both in one-phase ( T~T, ) and the two-phase region ( T~T, ), and (3) the density as a function of chemical potcnt1al of thcsc fluids. For data outside thc gravltatlonaLLy rounded rcg1011, power-law analyses ln eluding correction to scaling terms were used. Data in the gravitationally rounded region were analyzed with thc use of the restricted cubic model. Consistent results in T, (on the order of 0.2 mK) and the leading amplitudes were found between data in these two regions. In addition to the leading exponent P and y we also determined from our data the correction to scaling exponent 6 and three universal amplitude ratios. Bur values for these quantities are in good agreement with theoretical predictions.
The first observation of the predicted anomaly in the static dielectric constant of a pure fluid near its critical point is reported. This anomaly, not observed to date in nonpolar fluids, is now seen in CO, a polar fluid. The anomalous increase in the dielectric constant, 6e/e ? reaches l x 10~3 for fluid with density very close to the critical value. The functional form of the anomaly is consistent with current theoretical predictions.
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