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Register a new userLight Scattering from Nonequilibrium Concentration Fluctuations in a Polymer solution
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Added by
Jose M. Ortiz de Zarate
Publication date
2000
fields
Physics
and research's language is
English
Authors
W.B. Li
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We have performed light-scattering measurements in dilute and semidilute polymer solutions of polystyrene in toluene when subjected to stationary temperature gradients. Five solutions with concentrations below and one solution with a concentration above the overlap concentration were investigated. The experiments confirm the presence of long-range nonequilibrium concentration fluctuations which are proportional to $( abla T)^2/k^4$, where $ abla T$ is the applied temperature gradient and $k$ is the wave number of the fluctuations. In addition, we demonstrate that the strength of the nonequilibrium concentration fluctuations, observed in the dilute and semidilute solution regime, agrees with theoretical values calculated from fluctuating hydrodynamics. Further theoretical and experimental work will be needed to understand nonequilibrium fluctuations in polymer solutions at higher concentrations.
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This article focuses on a preaveraging description of polymer nonequilibrium stretching, where a single polymer undergoes a transient process from equilibrium to nonequilibrium steady state by pulling one chain end. The preaveraging method combined with mode analysis reduces the original Langevin equation to a simplified form for both a stretched steady state and an equilibrium state, even in the presence of self-avoiding repulsive interactions spanning a long range. However, the transient stretching process exhibits evolution of a hierarchal regime structure, which means a qualitative temporal change in probabilistic distributions assumed in preaveraging. We investigate the preaveraging method for evolution of the regime structure with consideration of the nonequilibrium work relations and deviations from the fluctuation-dissipation relation.
We analyse the dynamics of polymer translocation in the strong force regime by recasting the problem into solving a differential equation with a moving absorbing boundary. For the total translocation time, $tau_{rm tr}$, our simple mean-field model predicts that $tau_{rm tr}sim$ (number of monomers)$^{1.5}$, which is in agreement with the exponent found in previous simulation results. Our model also predicts intricate dependencies of $tau_{rm tr}$ on the variations of the pulling force and of the temperature.
A widely spread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. Nucleation process, polymorph selection, and crystal habits depend crucially on this thermodynamic parameter. When performing simulations in the canonical ensemble as the crystalline phase is deposited the solution is depleted of solutes. This unavoidable modification of the thermodynamic conditions leads to significant artifact. Here we adopt the idea of the constant chemical potential molecular dynamics approach of Perego et al. [J. Chem. Phys. 2015, 142, 144113] to the study of nucleation. Our method allows determining the crystal nucleus size and nucleation rates at constant supersaturation. As an example we study the homogeneous nucleation of sodium chloride from its supersaturated aqueous solution.
The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive Molecular-Dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, $s(t)$, that have passed through the pore at time $t$ due to a driving force $f$. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity $v=dot{s}(t)$ is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a {em time-dependent} diffusion coefficient $D(t)$. Our MD simulation reveals that the driven translocation process follows a {em super}diffusive law with a running diffusion coefficient $D(t) propto t^{gamma}$ where $gamma < 1$. This finding is then used in the numerical solution of the FPE which yields an important result: for comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent $alpha$ which describes the scaling of the mean translocation time $<tau>$ with the length $N$ of the polymer, $<tau> propto N^{alpha}$ is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the non-driven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).
We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with sub-nanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G=0.11 +/- 0.03 Pa and 0.17 +/- 0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G(omega) as omega^(3/4) at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G(omega) as omega^(1/2), consistent with the predictions of the Rouse model for flexible polymers.
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