Coupled non-equilibrium fluctuations in a polymeric ternary mixture

Abstract

We investigate by dynamic shadowgraphy the non-equilibrium fluctuations at the steady state of a thermodiffusion experiment in a polymeric ternary mixture of polystyrene-toluene-nhexane. The structure function of the refractive index reveals the existence of quite different decay times, thus requiring the analysis of a wide range of correlation times. This is related to the simultaneous presence of three distinct decay modes corresponding to (from fastest to slowest) relaxation of temperature fluctuations, of the concentration fluctuations of the mixed solvent, and of the concentration fluctuations of the polymer in the binary solvent. An investigation of the decay times at the corresponding diffusive regimes provides a measurement of the thermal diffusivity and the two eigenvalues of the mass diffusion matrix of the ternary mixture. Similar experiments were performed in the past but here, to suppress the confinement effect and obtain a more direct comparison with the theory, a thicker sample is studied. Moreover, also a faster camera is used allowing the experimental observation of faster modes, like the propagative ones. The experimental values of the decay times are eventually compared with those predicted by different available theories. Finally, we present a more complete theoretical model to describe the non-equilibrium fluctuations in the bulk of a ternary mixture at the steady state of a thermodiffusion experiment.

Stabilized convection in a ternary mixture with two Soret coefficients of opposite sign

“…Following the results from [ 11 ], close to infinite dilution of polystyrene, matches the Fick diffusion of the binary mixture toluene-cyclohexane and the tracer diffusivity of polystyrene [ 12 , 13 ]. The latter value has been determined by the Stokes–Einstein relation using the hydrodynamic radius of polystyrene derived from diffusivity data of polystyrene in toluene [ 14 , 15 ] and density data from [ 10 ].…”

“…The polystyrene solutal diffusive time can also be computed by multiplying the thermal one by the relevant Lewis number or by multiplying the binary solvent solutal diffusive time by the diffusion eigenvalue ratio [ 13 , 31 ].…”

The modern structurator: increased performance for calculating the structure function

“…At the same time, it was proposed to develop "structurators" in place of the more widely known correlators [3]. With the spread of pixelated detectors, imaging techniques like dynamic shadowgraphy, dynamic Schlieren [4][5][6][7][8][9], and differential dynamic microscopy (DDM) [10][11][12] have taken advantage of the use of the structure function because of its improved robustness for data analysis in terms of rejection of background signal deriving from steady-state and slow-drift noise sources as compared to the autocorrelation function approach [2,13]. This is due to the intrinsic nature of the structure function that is based on the difference of signal elements of increasing time delay so that any spurious signal changing on times longer than the utilized time delay is subtracted.…”

Data quality assessment of Diffusion Coefficient Measurements in ternary mIXtures 4 (DCMIX4) experiment

“…Bou-Ali (MMBA), from Mondragon Goi Eskola Politeknikoa (MGEP), Spain. The ternary mixture of polystyrene-toluene-cyclohexane has been chosen mainly because the two eigenvalues of the mass diffusion coefficients matrix are expected to be well separated, by a factor of about 10, as this mixture includes a polymer as one of the components, namely the polystyrene, having a much larger molecular weight than the other two [10][11][12]. This implies that the time evolution of the concentration profiles measured by SODI two-wavelength diagnostics will be easier to analyse and interpret, as the different contributions can be also separated on the basis of their kinetics.…”