Probe molecules in polymer melts near the glass transition: A molecular dynamics study of chain length effects

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Translation-rotation decoupling of tracers reflects medium-range crystalline order in two-dimensional colloid glasses

The dynamic heterogeneity and the translation-rotation decoupling are the dynamic signatures of glasses and supercooled liquids. Whether and how the dynamic heterogeneity would relate to the local structure of glasses has been a puzzle for decades. In this work we perform molecular dynamics simulations for tracers in both two-dimensional polydisperse colloids (2DPC) and two-dimensional binary colloids (2DBC). In 2DPC glasses, hexatic local structures develop at low enough temperatures and grow quickly along with the dynamic correlation length of the 2DPC, which is well known as the medium-range crystalline order (MRCO). In 2DBC glasses, on the other hand, any explicit local structure has not been reported to grow significantly with the dynamic correlation length at low temperatures. We introduce two different types of tracers into colloidal systems: A diamond tracer that resembles the MRCO of 2DPC glasses and a square tracer that is dissimilar to any local structure of glasses. The translation-rotation decoupling of the diamond tracer in 2DPC glasses is much more significant than that of the square tracer in the same 2DPC glasses. On the other hand, such a tracer shape-dependence of the decoupling is not observed in 2DBC glasses where the local hexatic structure does not develop significantly. We introduce a shape-dependency parameter of the decoupling and find that the shape-dependency parameter grows along with the dynamic correlation length in 2DPC glasses but not in 2DBC glasses. This illustrates that the dynamic heterogeneity and the translation-rotation decoupling of tracers could reveal the local structure that develops in glasses.

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.

Nanoparticle diffusion in polymer melts: Molecular dynamics simulations and mode-coupling theory

Nanoparticle diffusion in polymer melts is studied by the combination of Molecular Dynamics (MD) simulations and Mode-Coupling Theory (MCT). In accord with earlier experimental, simulation, and theoretical studies, we find that the Stokes-Einstein (SE) hydrodynamic relation D_n ∼ 1/R_n holds when the nanoparticle radius R_n is greater than the polymer gyration radius R_g, while in the opposite regime, the measured nanoparticle diffusion coefficient D_n exceeds the SE value by as much as an order of magnitude. The MCT values of D_n are found to be consistently higher than the MD simulation values. The observed discrepancy is attributed to the approximations involved in constructing the microscopic friction as well as to the approximate forms for dynamic structure factors used in MCT. In a thorough test of underlying MCT assumptions and approximations, various structural and dynamical quantities required as input for MCT are obtained directly from MD simulations. We present the improved MCT approach, which involves splitting of the microscopic time-dependent friction into two terms: binary (originating from short-time dynamics) and collective (due to long-time dynamics). Using MD data as input in MCT, we demonstrate that the total friction is largely dominated by its binary short-time term, which, if neglected, leads to severe overestimation of D_n. As a result, the revised version of MCT, in agreement with the present MD data, predicts 1/R_n ² scaling of the probe diffusion coefficient in a non-hydrodynamic regime when R_n < R_g. If the total friction is dominated by the collective long-time component, one would observe 1/R_n ³ scaling of D_n in accordance with previous studies.

A practical method to account for random phase approximation effects on the dynamic scattering of multi-component polymer systems

Investigations of polymer systems that rely on the interpretation of dynamical scattering results as, e.g., the structure factor S(Q, t) of single chains or chain sections may require the inclusion of effects, as described within the framework of the random phase approximation (RPA) for polymers. To do this in practice for the dynamic part of S(Q, t) beyond the initial slope is a challenge. Here, we present a method (and software) that allows a straightforward assessment of dynamical RPA effects and inclusion of these in the process/procedures of model fitting. Examples of applications to the interpretation of neutron spin-echo data multi-component polymer melts are shown.

Glassy dynamics of model colloidal polymers: The effect of "monomer" size

In recent years, attempts have been made to assemble colloidal particles into chains, which are termed "colloidal polymers." An apparent difference between molecular and colloidal polymers is the "monomer" size. Here, we propose a model to represent the variation from molecular polymer to colloidal polymer and study the quantitative differences in their glassy dynamics. For chains, two incompatible local length scales, i.e., monomer size and bond length, are manifested in the radial distribution function and intramolecular correlation function. The mean square displacement of monomers exhibits Rouse-like sub-diffusion at intermediate time/length scale and the corresponding exponent depends on the volume fraction and the monomer size. We find that the threshold volume fraction at which the caging regime emerges can be used as a rescaling unit so that the data of localization length versus volume fraction for different monomer sizes can gather close to an exponential curve. The increase of monomer size effectively increases the hardness of monomers and thus makes the colloidal polymers vitrify at lower volume fraction. Static and dynamic equivalences between colloidal polymers of different monomer sizes have been discussed. In the case of having the same peak time of the non-Gaussian parameter, the motion of monomers of larger size is much less non-Gaussian. The mode-coupling critical exponents for colloidal polymers are in agreement with that of flexible bead-spring chains.

Simulated glass-forming polymer melts: dynamic scattering functions, chain length effects, and mode-coupling theory analysis

We present molecular-dynamics simulations for a fully flexible model of polymer melts with different chain length N ranging from short oligomers (N = 4) to values near the entanglement length (N = 64). For these systems we explore the structural relaxation of the supercooled melt near the critical temperature T c of mode-coupling theory (MCT). Coherent and incoherent scattering functions are analyzed in terms of the idealized MCT. For temperatures T > T c we provide evidence for the space-time factorization property of the β relaxation and for the time-temperature superposition principle (TTSP) of the α relaxation, and we also discuss deviations from these predictions for T ≈ T c. For T larger than the smallest temperature where the TTSP holds we perform a quantitative analysis of the dynamics with the asymptotic MCT predictions for the late β regime. Within MCT a key quantity, in addition to T c, is the exponent parameter λ. For the fully flexible polymer models studied we find that λ is independent of N and has a value (λ = 0.735 ) typical of simple glass-forming liquids. On the other hand, the critical temperature increases with chain length toward an asymptotic value T c (∞) . This increase can be described by T c (∞) - T c(N) ∼ 1/N and may be interpreted in terms of the N dependence of the monomer density ρ, if we assume that the MCT glass transition is ruled by a soft-sphere-like constant coupling parameter Γ c = ρ c T c (-1/4), where ρ c is the monomer density at T c. In addition, we also estimate T c from a Hansen-Verlet-like criterion and MCT calculations based on structural input from the simulation. For our polymer model both the Hansen-Verlet criterion and the MCT calculations suggest T c to decrease with increasing chain length, in contrast to the direct analysis of the simulation data.

Electron transfer-based single molecule fluorescence as a probe for nano-environment dynamics

Electron transfer (ET) is one of the most important elementary processes that takes place in fundamental aspects of biology, chemistry, and physics. In this review, we discuss recent research on single molecule probes based on ET. We review some applications, including the dynamics of glass-forming systems, surface binding events, interfacial ET on semiconductors, and the external field-induced dynamics of polymers. All these examples show that the ET-induced changes of fluorescence trajectory and lifetime of single molecules can be used to sensitively probe the surrounding nano-environments.

Heterogeneity in Single-Molecule Observables in the Study of Supercooled Liquids

Bulk approaches to studying heterogeneous systems obscure important details, as they report average behavior rather than the distribution of behaviors in such environments. Small-molecule and polymeric supercooled liquids, which display heterogeneity in their dynamics without an underlying structural heterogeneity that sets those dynamics, are important constituents of this category of condensed matter systems. A variety of approaches have been devised to unravel ensemble averaging in supercooled liquids. This review focuses on the ultimate subensemble approach, single-molecule measurements, as they have been applied to the study of supercooled liquids. We detail how three key experimental observables (single-molecule probe rotation, translation, and fluorescence lifetime) have been employed to provide detail on dynamic heterogeneity in supercooled liquids. Special attention is given to the potential for, but also the challenges in, discriminating spatial and temporal heterogeneity and detailing the length scales and timescales of heterogeneity in these systems.

Manifestations of probe presence on probe dynamics in supercooled liquids

Experimental studies that follow behavior of single probes embedded in heterogeneous systems are increasingly common. The presence of probes may perturb the system, and such perturbations may or may not affect interpretation of host behavior from the probe observables typically measured. In this study, the manifestations of potential probe-induced changes to host dynamics in supercooled liquids are investigated via molecular dynamics simulations. It is found that probe dynamics do not necessarily mirror host dynamics as they exist either in the probe-free or probe-bearing systems. In particular, for a binary supercooled liquid, we find that smooth probes larger than the host particles induce increased translational diffusion in the host system; however, the diffusion is anisotropic and enhances caging of the probe, suppressing probe translational diffusion. This in turn may lead experiments that follow probe diffusion to suggest Stokes-Einstein behavior of the system even while both the probe-free and probe-bearing systems exhibit deviations from that behavior.