Molecular Tracer Diffusion in Nondilute Polymer Solutions: Universal Master Curve and Glass Transition Effects

A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter

Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξ_f and t_f. We find that ξ_f stays constant, whereas t_f grows as the inverse of the long-time diffusion coefficient t_f ∝ D^-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.

Nanoparticle diffusion in polymer melts in the presence of weak nanoparticle-monomer attractive interactions: A mode-coupling theory study

Mode-coupling theory is developed and employed to compute the nanoparticle diffusion coefficient in polymer solutions. Theoretical results are compared with molecular dynamics simulation data for a similar model. The theory properly reproduces the simulated effects of the nanoparticle size, mass, and concentration on the nanoparticle diffusion coefficient. Within the mode-coupling theory framework, a microscopic interpretation of the nonmonotonic dependence of the diffusion coefficient on the nanoparticle concentration is given in terms of structural and dynamic effects. Both the size dependence and mass dependence of the diffusion coefficient indicate a pronounced breakdown of the Stokes-Einstein relation for the present model.

A blob model to parameterize polymer hole free volumes and solute diffusion

Solute diffusion in solid polymers has tremendous applications in packaging, reservoir, and biomedical technologies but remains poorly understood. Diffusion of non-entangled linear solutes with chemically identical patterns (blobs) deviates dramatically in polymers in the solid-state (α_lin > 1, Macromolecules 2013, 46, 874) from their behaviors in the molten state (α_lin = 1, Macromolecules, 2007, 40, 3970). This work uses the scale invariance of the diffusivities, D, of linear probes D(N·M_blob + M_anchor,T,T_g) = N^{-α_lin(T,T_g)}D(M_blob + M_anchor,T,T_g) comprising N identical blobs of mass M_blob and possibly one different terminal pattern (anchor of mass M_anchor) to evaluate the amounts of hole-free volume in seven polymers (aliphatic, semi-aromatic and aromatic) over a broad range of temperatures (-70 K ≤T-T_g≤ 160 K). The new parameterization of the concept of hole-free volumes opens the application of the free-volume theory (FVT) developed by Vrentas and Duda to practically any polymer, regardless of the availability of free-volume parameters. The quality of the estimations was tested with various probes including n-alkanes, 1-alcohols, n-alkyl acetates, and n-alkylbenzene. The effects of enthalpic and entropic effects of the blobs and the anchor were analyzed and quantified. Blind validation of the reformulated FVT was tested successfully by predicting from first principles the diffusivities of water and toluene in amorphous polyethylene terephthalate from 4 °C to 180 °C and in various other polymers. The new blob model would open the rational design of additives with controlled diffusivities in thermoplastics.

Diffusion of small particles in polymer films

The motion of small probe molecules in a two-dimensional system containing frozen polymer chains was studied by means of Monte Carlo simulations. The model macromolecules were coarse-grained and restricted to vertices of a triangular lattice. The cooperative motion algorithm was used to generate representative configurations of macromolecular systems of different polymer concentrations. The remaining unoccupied lattice sites of the system were filled with small molecules. The structure of the polymer film, especially near the percolation threshold, was determined. The dynamic lattice liquid algorithm was then employed for studies of the dynamics of small objects in the polymer matrix. The influence of chain length and polymer concentration on the mobility and the character of motion of small molecules were studied. Short- and long-time dynamic behaviors of solvent molecules were also described. Conditions of anomalous diffusions' appearance in such systems are discussed. The influence of the structure of the matrix of obstacles on the molecular transport was discussed.

Scale-dependent rotational diffusion of nanoparticles in polymer solutions

It is shown that the rotational diffusivity of nanoparticles in polymer solutions spanning the dilute to semi-dilute regimes deviates from the predictions of the Stokes-Einstein (SE) relationship, and that this deviation can be explained by the existence of a polymer depletion layer with the viscosity of the bath solvent. The measurements of the rotational diffusion coefficient of poly(ethylene glycol) (PEG) grafted magnetic nanoparticles in PEG solutions spanning the dilute to semi-dilute regimes and a wide range of polymer molecular weights were obtained from the dynamic magnetic response of the nanoparticles to alternating magnetic fields. Experimental rotational diffusion coefficient values were compared with those predicted by the SE relation using the macroscopic viscosity of the polymer solutions and the hydrodynamic radius of the nanoparticles. Deviations between experimental and SE rotational diffusivity values were observed for nanoparticles in polymer solutions where the radius of gyration of the polymer exceeded the hydrodynamic radius of the particles. A simple model for the rotational hydrodynamic drag on a particle surrounded by a polymer depletion layer was found to describe the experimental rotational diffusivities well, suggesting that the observed phenomenon arises due to the formation of a polymer depletion layer around the nanoparticles.

Diffusive properties of solvent molecules in the neighborhood of a polymer chain as seen by Monte-Carlo simulations

The influence of both polymer chain length and concentration on the mobility of solvent molecules in polymer solutions was studied by Monte Carlo simulations with the use of the dynamic lattice liquid (DLL) model. The poly(vinylmethylether)-water system was used as a model. Two different solvent (water) states with differing mobilities were distinguished in polymer solutions. The first one with high molecular mobility independent of polymer concentration corresponds to bulk solvent in real systems. The second state relates to so called bound solvent. In this case the solvent diffusivity decreases with polymer content. For diluted solutions the diffusion of bound solvent is affected by polymer chain length, precisely, by the ability of the polymer chain to undergo coil formation.