Critical behavior in a polymer blend

Applicability of the Generalized Stokes-Einstein Equation of Mode-Coupling Theory to Near-Critical Polyelectrolyte Complex Solutions

We examine whether the mode-coupling theory of Kawasaki and Ferrell (KF) [Kawasaki, K. Kinetic Equations and Time Correlation Functions of Critical Fluctuations. Ann. Phys. 1970, 61 (1), 1-56; Ferrell, R. A. Decoupled-Mode Dynamical Scaling Theory of the Binary-Liquid Phase Transition. Phys. Rev. Lett. 1970, 24 (21), 1169-1172] can describe dynamic light scattering (DLS) measurements of the dynamic structure factor of near-critical polyelectrolyte complex (PC) solutions that have been previously shown to exhibit a theoretically unanticipated lower critical solution temperature type phase behavior, i.e., phase separation upon heating, and a conventional pattern of static critical properties (low angle scattering intensity and static correlation, ξ_s) as a function of reduced temperature. Good qualitative accord is observed between our DLS measurements and the KF theory. In particular, we observe that the collective diffusion coefficient D_c of the PC solutions obeys the generalized Stokes-Einstein equation (GSE), D_c = k_BT/6πηξ_s, where ξ_s is specified from our previous measurements and where η is measured by capillary rheometry under the same thermodynamic conditions as in our previous study of these solutions, allowing for a no-free-parameter test of the GSE. We also find that even the wavevector (q)-dependent collective diffusion coefficient D_c(q), measured by varying the scattering angle in the DLS measurements over a large range, is also well-described by the mean-field version of the KF theory. We find it remarkable that the KF theory provides such a robust description of collective diffusion in these complex charged polyelectrolyte blends under near-critical conditions given that charge fluctuations and association of the polymers might be expected to lead to physical complications that would invalidate the standard model of uncharged fluid mixtures.

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D(T)) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D(T) is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D(T)(0,infinity) = -1.69 x 10(-7) cm2(sK)(-1). The Soret coefficient S(T) of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).

Critical structure factor in using systems

We perform a large-scale Monte Carlo simulation of the three-dimensional Ising model on simple cubic lattices of size L(3) with L=128 and 256. We determine the corresponding structure factor (Fourier transform of the two-point function) and compare it with several approximations and with experimental results. We also compute the turbidity as a function of the momentum of the incoming radiation, focusing in particular on the deviations from the Ornstein-Zernike expression of Puglielli and Ford.

Turbidity and critical behavior of a colloid-polymer system

The osmotic compressibility and correlation length of a colloid-polymer system, consisting of grafted silica particles in cyclohexane in the presence of the soluble polymer polydimethylsiloxane, are determined by turbidity measurements in the entire one-phase liquid region, with emphasis on the critical region. The renormalized critical exponents of the osmotic compressibility and the correlation length are found to be respectively gamma(*)=1.39+/-0.01 and nu(*)=0.71+/-0.01, while the amplitude of the correlation length is 16.0+/-0.3 nm. Comparison is made with theoretical predictions.