Concentration Fluctuations in a Polymer Solution under a Temperature Gradient

Abstract

We have performed small-angle Rayleigh light-scattering measurements in polymer solutions under various externally applied temperature gradients. Our experiments confirm the existence of an enhancement of the concentration fluctuations. The nonequilibrium concentration fluctuations are proportional to ͑=T͒ 2 ͞k 4 , where =T is the applied temperature gradient, and k is the wave number of the fluctuations. The measured strengths of the nonequilibrium fluctuations in the dilute and semidilute concentration regime agree with the strengths calculated from fluctuating hydrodynamics.[ S0031-9007(98) PACS numbers: 61.25. Hq, 05.70.Ln, 66.10.Cb During the past decade, considerable theoretical and experimental effort has been devoted to the study of fluctuations in fluids in nonequilibrium steady states, in particular, when subjected to a constant temperature gradient =T . It is now known that the correlation functions become spatially long ranged [1][2][3], because microscopic detailed balance is violated. These nonequilibrium correlation functions can be observed by small-angle Rayleigh light scattering. Experiments have been carried out with simple fluids, in which case excellent agreement with the theory has been found [4,5].In fluid mixtures, the situation is more complicated because the temperature gradient induces a concentration gradient through the Soret effect. Hence, in addition to nonequilibrium entropy and viscous fluctuations, which are also present in one-component fluids, nonequilibrium concentration fluctuations are present in mixtures [6]. All of these nonequilibrium fluctuations have intensities proportional to ͑=T ͒ 2 ͞k 4 , where k is the wave number of the fluctuations. The existence of these nonequilibrium fluctuations and their dependence on ͑=T ͒ 2 ͞k 4 have been checked experimentally, but the quantitative values of the observed strengths of the nonequilibrium concentration fluctuations were not in agreement with the theory [5,7,8].Dilute polymer solutions appear to be a more suitable system to check the theory for nonequilibrium concentration fluctuations, because the expression for the dynamic correlation function C͑k, t͒ as a function of time is simpler. When the polymer concentration is below the overlap concentration, viscoelastic and entanglement effects are negligible, and ordinary fluctuating hydrodynamics should be applicable to describe the nonequilibrium fluctuations. Furthermore, the collective mass-diffusion coefficient is so small and the Rayleigh ratio so large that, in practice, the concentration fluctuations are dominant. Therefore, for polymer solutions at sufficiently low concentrations, the equations in Refs. [5,6] can be simplified, yielding the following for fluctuations with a wave vector perpendicular to =T :where C 0 is the ratio of the signal to the local oscillator background, which corresponds to the amplitude of the experimental equilibrium correlation function; D is the collective mass-diffusion coefficient, and A c is the nonequilibrium enhancement. A c may be ...

Concentration fluctuations in nonisothermal reaction-diffusion systems

“…Indeed, in ordinary liquid mixtures concentration fluctuations usually dominate, and temperature fluctuations are more difficult to observe by the ordinary techniques like light scattering. [41][42][43] The same has been found from nonequilibrium molecular dynamics simulations. 44 Further details concerning this approximation scheme can be found in the relevant literature.…”

“…The validity of such an extension of the fluctuation-dissipation theorem has been confirmed experimentally for ͑nonreacting͒ fluids in a temperature gradient. 4,42,48 In this same context, we also remind the reader that effects due to nonlinearities such as inhomogeneously correlated thermal noise 49 are completely negligible when there exists a coupling in nonequilibrium between fluctuating fields via the balance laws, 3 such as the one we found in Eq. ͑52a͒ and ͑52b͒.…”

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

“…Indeed, in ordinary liquid mixtures concentration fluctuations usually dominate, and temperature fluctuations are more difficult to observe by experimental techniques, such as light scattering. [36][37][38] The same has been found from non-equilibrium molecular dynamics simulation. 39 Further details concerning this approximation scheme can be found in the relevant literature.…”

Gravity effects on Soret-induced non-equilibrium fluctuations in ternary mixtures

“…Indeed, it has been the systematic application of FHD that allowed the investigation of fluctuations in systems out of (global) equilibrium. The validity of this non-equilibrium extension of FHD, in the case of binary liquid mixtures, has been confirmed by a series of pioneering experiments [18][19][20][21][22]. One other notable example of FHD success is the prediction of the influence of gravity on the fluctuations [23], an effect initially considered to be not accessible to experiments, and later confirmed by novel optical techniques [24].…”