Critical Opalescence of Polystyrene Solutions

Equations of DirichletL-functions and the intervals of their Eulerian products according to prime numbers

“…Sanchez, however, did note an intriguing exception from this rule, stating: "The most serious disagreement between experimental and predicted values of the M W indices happens to be the most important one, the (n) index associated with the correlation length ξ. The experimental value (n) obtained from light scattering (LS) measurements [3,4] is significantly larger than predicted values. .…”

“…This technique has advantages over LS, because it permits the observation of the intermolecular correlations not only in the critical region of phase demixing (ξ R g ) but also in the mean-field domain when the range of the monomer-monomer correlations becomes smaller than the size of the polymer coils (ξ < R g ). This allows us to explore the crossover in the M W -scaling of ξ 0 between the critical region of phase demixing and the mean-field Θ domain and to revisit the classical experiments of Debye and co-workers [3].…”

“…and the first studies of ξ 0 vs. M W in polymer solutions were carried out by Debye, Coll, Woermann, and Chu [3] who obtained n = 0.285. As described above, the LS measurements are in striking contradiction with the value of (n) deduced from the sum rules for b i (n = 0.197, Sanchez [1]) as well as with the scaling arguments (n = 0.185, de Gennes [5]) and the Landau-Ginzburg-Wilson (LGW) model (n = 0.172, Stepanow [6]).…”

“…As described above, the LS measurements are in striking contradiction with the value of (n) deduced from the sum rules for b i (n = 0.197, Sanchez [1]) as well as with the scaling arguments (n = 0.185, de Gennes [5]) and the Landau-Ginzburg-Wilson (LGW) model (n = 0.172, Stepanow [6]). The origins of the significant discrepancy between the LS result [3] and the theoretical predictions have remained an enigma for nearly 40 years. In this letter we attempt to resolve this issue and study, for the first time, the M W -scaling of the amplitude ξ 0 by small-angle neutron scattering (SANS).…”

“…The molecular weight of PS M W = 115000 was nearly identical to one of the samples studied in [3] (M W = 118000) and one of the solutions was prepared at exactly the same concentration (φ Debye = 0.056) as in Debye's experiment. If φ = φ C , the O-Z fits yield the "apparent" ξ 0 and ν in the limit of small τ = (T − T S )/T S , where T S is the temperature of the spinodal (of course T S ≡ T C at φ = φ C ).…”