Mode-coupling approach to polymer diffusion in an unentangled melt. I. The effect of density fluctuations

Non-Rouse behavior of short ring polymers in melts by molecular dynamics simulations

Short ring polymers are expected to behave nearly Rouse-like due to the little effect of topological constraints of non-knot and non-concatenation. However, this notion is questioned because of several simulation and experiment findings in recent times, which requires a further more quantitative study. Therefore, we perform a deep investigation of statics and dynamics of flexible short ring polymers (N < 2Ne) in melts via molecular dynamics simulations by further taking linear analogues as well as all-crossing ring and linear polymers with switched off topological constraints for comparisons and demonstrate the noticeable deviations from the Rouse model in terms of local and global scales. Although the overall size is compact, the subchains are swollen, which is traced back to the deeper "segmental correlation hole" effect. The same scaling relationship of the non-Gaussian deviation of the static structure factor holds, but the deviation magnitude of rings is larger than that of linear analogues. By checking the non-Gaussian parameter and autocorrelation function of center-of-mass velocity, the physical origin of anomalous sub-diffusions of short rings is identified as unscreened viscoelastic hydrodynamic interactions and not correlation hole effects, like linear analogues.

Glassy dynamics of sticky hard spheres beyond the mode-coupling regime

Sticky hard spheres, i.e., hard particles decorated with a short-ranged attractive interaction potential, constitute a relatively simple model with highly non-trivial glassy dynamics. The mode-coupling theory of the glass transition (MCT) offers a qualitative account of the complex reentrant dynamics of sticky hard spheres, but the predicted glass transition point is notoriously underestimated. Here we apply an improved first-principles-based theory, referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres. This theoretical framework seeks to go beyond MCT by hierarchically expanding the dynamics in higher-order density correlation functions. We predict the phase diagrams from the first few levels of the GMCT hierarchy and the dynamics-related critical exponents, all of which are much closer to the empirical observations than MCT. Notably, the prominent reentrant glassy dynamics, the glass-glass transition, and the higher-order bifurcation singularity classes (A3 and A4) of sticky hard spheres are found to be preserved within GMCT at arbitrary order. Moreover, we demonstrate that when the hierarchical order of GMCT increases, the effect of the short-ranged attractive interactions becomes more evident in the dynamics. This implies that GMCT is more sensitive to subtle microstructural differences than MCT, and that the framework provides a promising first-principles approach to systematically go beyond the MCT regime.

Dynamics of poly[n]catenane melts

Inspired by advances in the chemical synthesis of interlocking polymer architectures, extensive molecular dynamics simulations have been conducted to study the dynamical properties of poly[n]catenanes-polymers composed entirely of interlocking rings-in the melt state. Both the degree of polymerization (number of links) and the number of beads per ring are systematically varied, and the results are compared to linear and ring polymers. A simple Rouse-like model is presented, and its analytical solution suggests a decomposition of the dynamics into "ring-like" and "linear-like" regimes at short and long times, respectively. In agreement with this picture, multiple sub-diffusive regimes are observed in the monomer mean-squared-displacements even though interchain entanglement is not prevalent in the system. However, the Rouse-type model does not account for the topological effects of the mechanical bonds, which significantly alter the dynamics at intermediate length scales both within the rings and at the chain segment scales. The stress relaxation in the system is extremely rapid and may be conveniently separated into ring-like and linear-like contributions, again in agreement with the Rouse picture. However, the viscosity has a non-monotonic dependence on the ring size for long chains, which disagrees strongly with theoretical predictions. This unexpected observation cannot be explained in terms of chain disentanglement and is inconsistent with other measures of polymer relaxation. Possible mechanisms for this behavior are proposed and implications for materials design are discussed.

Self-consistent molecular dynamics calculation of diffusion in higher n-alkanes

Diffusion is one of the key subjects of molecular modeling and simulation studies. However, there is an unresolved lack of consistency between Einstein-Smoluchowski (E-S) and Green-Kubo (G-K) methods for diffusion coefficient calculations in systems of complex molecules. In this paper, we analyze this problem for the case of liquid n-triacontane. The non-conventional long-time tails of the velocity autocorrelation function (VACF) are found for this system. Temperature dependence of the VACF tail decay exponent is defined. The proper inclusion of the long-time tail contributions to the diffusion coefficient calculation results in the consistency between G-K and E-S methods. Having considered the major factors influencing the precision of the diffusion rate calculations in comparison with experimental data (system size effects and force field parameters), we point to hydrogen nuclear quantum effects as, presumably, the last obstacle to fully consistent n-alkane description.

The universal trend of the non-exponential Rouse mode relaxation in polymer systems: a theoretical interpretation based on a generalized Langevin equation

We show that the universal behavior of the Rouse-mode relaxation in polymer systems - which has been recently reported from experimental data [S. Arrese-Igor, et al., Phys. Rev. Lett., 2014, 113, 078302] - can be quantitatively explained in the framework of a theoretical approach based on: (i) a generalized Langevin equation formalism and (ii) a memory function which takes into account the coupling between intra-chain dynamics and collective dynamics. This approach opens the way for generalizing the magnitudes probing chain dynamics in polymer systems.

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.

Collective intermolecular motions dominate the picosecond dynamics of short polymer chains

Neutron scattering and extensive molecular dynamics simulations of an all atom C(100)H(202) system were performed to address the short-time dynamics leading to center-of-mass self-diffusion. The simulated dynamics are in excellent agreement with resolution resolved time-of-flight quasielastic neutron scattering. The anomalous subdiffusive center-of-mass motion could be modeled by explicitly accounting for viscoelastic hydrodynamic interactions. A model-free analysis of the local reorientations of the molecular backbone revealed three relaxation processes: While two relaxations characterize local bond rotation and global molecular reorientation, the third component on intermediate times could be attributed to transient flowlike motions of atoms on different molecules. The existence of these collective motions, which are clearly visualized in this Letter, strongly contribute to the chain relaxations in molecular liquids.

Mode-coupling approach to polymer diffusion in an unentangled melt. II. The effect of viscoelastic hydrodynamic interactions

A mode-coupling theory (MCT) version (called hMCT thereafter) of a recently presented theory [Farago, Meyer, and Semenov, Phys. Rev. Lett. 107, 178301 (2011)] is developed to describe the diffusional properties of a tagged polymer in a melt. The hMCT accounts for the effect of viscoelastic hydrodynamic interactions (VHIs), that is, a physical mechanism distinct from the density-based MCT (dMCT) described in the first paper of this series. The two versions of the MCT yield two different contributions to the asymptotic behavior of the center-of-mass velocity autocorrelation function (c.m. VAF). We show that in most cases the VHI mechanism is dominant; for long chains and prediffusive times it yields a negative tail ∝-N^{-1/2}t^{-3/2} for the c.m. VAF. The case of non-momentum-conserving dynamics (Langevin or Monte Carlo) is discussed as well. It generally displays a distinctive behavior with two successive relaxation stages: first -N^{-1}t^{-5/4} (as in the dMCT approach), then -N^{-1/2}t^{-3/2}. Both the amplitude and the duration of the first t^{-5/4} stage crucially depend on the Langevin friction parameter γ. All results are also relevant for the early time regime of entangled melts. These slow relaxations of the c.m. VAF, thus account for the anomalous subdiffusive regime of the c.m. mean square displacement widely observed in numerical and experimental works.