Light scattering and sum rules of three coexisting phases for quasiternary solutions near the tricritical point

The upper critical temperatures ( T U ) and the lower critical temperatures ( T L ) were precisely determined for 11 quasiternary solutions of water + n -decane and + n -undecane + t e r t -butanol with various mass ratios of n -decane to n -undecane. Measurements of angular dependence of the scattered light intensity for each of the three liquid coexisting phases and each of the 11 solutions at the middle temperatures T m = ( T U + T L ) / 2 are reported. From the light scatting data, the zero-angle scattering intensities I 0 and the correlation lengths ξ at T m in each of the phases were calculated and used to test the Griffiths sum rules. It was found that ( Δ T ) 2 / 3 (where Δ T = T U − T L ) is a good thermodynamic field to measure the distance from the tricritical point, and the second sum is converged to zero with a proportionality to ( Δ T ) 2 / 3 as the system approaches the tricritical point, which is in agreement with what the classical asymptotic theory predicted. However the first sums are neither zero nor constant, they are significantly curved and unambiguously diverged as strongly as does an individual susceptibility, which evidences that the amplitude ratios are nonclassical.