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Register a new userSelf-diffusion and Cooperative Diffusion in Semidilute Polymer Solutions as measured by Fluorescence Correlation Spectroscopy
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We present a comprehensive investigation of polymer diffusion in the semidilute regime by fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Using single-labeled polystyrene chains, FCS leads to the self-diffusion coefficient while DLS gives the cooperative diffusion coefficient for exactly the same molecular weights and concentrations. Using FCS we observe a new fast mode in the semidilute entangled concentration regime beyond the slower mode which is due to self-diffusion. Comparison of FCS data with data obtained by DLS on the same polymers shows that the second mode observed in FCS is identical to the cooperative diffusion coefficient measured with DLS. An in-depth analysis and a comparison with current theoretical models demonstrates that the new cooperative mode observed in FCS is due to the effective long-range interaction of the chains through the transient entanglement network.
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We discuss the manner in which the dynamics of tracer polystyrene chains varies with the concentration of matrix polystyrene chains dissolved in toluene. Using fluorescence correlation spectroscopy and theory, it is shown that the cooperative diffusion coefficient of the matrix polystyrene chains can be measured by fluorescence correlation spectroscopy in the semidilute entangled concentration regime. In addition the self-diffusion coefficient of the tracer polystyrene chains can be detected for arbitrary concentrations. The measured cooperative diffusion coefficient is independent of the molecular weight of the tracer polystyrene chains because it is a characteristic feature of the transient entanglement network.
The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.
The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $alpha = 2/(2 u+2-gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $<s(t)>$, and $<s^2(t)> - < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.
We investigate the dynamics of nanoparticles in semidilute polymer solutions when the nanoparticles are comparably sized to the polymer coils using explicit- and implicit-solvent simulation methods. The nanoparticle dynamics are subdiffusive on short time scales before transitioning to diffusive motion on long time scales. The long-time diffusivities scale according to theoretical predictions based on full dynamic coupling to the polymer segmental relaxations. In agreement with our recent experiments, however, we observe that the nanoparticle subdiffusive exponents are significantly larger than predicted by the coupling theory over a broad range of polymer concentrations. We attribute this discrepancy in the subdiffusive regime to the presence of an additional coupling mechanism between the nanoparticle dynamics and the polymer center-of-mass motion, which differs from the polymer relaxations that control the long-time diffusion. This coupling is retained even in the absence of many-body hydrodynamic interactions when the long-time dynamics of the colloids and polymers are matched.
The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an aging regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the aging dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic time scale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the Probability Density Function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters (dynamic heterogeneity), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function.
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