Coarse-grained Polymer Melt Research Articles

Comparison of Friction Parametrization from Dynamics and Material Properties for a Coarse-Grained Polymer Melt.

In this work, we extend an approach to coarse-grained (CG) modeling for polymer melts in which the conservative potential is parametrized using the iterative Boltzmann inversion (IBI) method and the accelerated dynamics inherent to IBI are corrected using the dissipative Langevin thermostat with a single tunable friction parameter (J. Chem. Phys. 2021, 154, 084114). Diffusive measures from picoseconds to nanoseconds are used to determine the Langevin friction factor to apply to the CG model to recover all-atom (AA) dynamics; the resulting friction factors are then compared for consistency. Here, we additionally parametrize the CG dynamics using a material property, the zero-shear viscosity, which we measure using the Green-Kubo (GK) method. Two materials are studied, squalane as a function of temperature and the same polystyrene oligomers previously studied as a function of chain length. For squalane, the friction derived from the long-time diffusive measures and the viscosity all strongly increase with decreasing temperature, showing an Arrhenius-like dependence, and remain consistent with each other over the entire temperature range. In contrast, the friction required for the picosecond diffusive measurement, the Debye-Waller factor, is somewhat lower than the friction from long-time measures and relatively insensitive to temperature. A time-dependent friction would be required to exactly reproduce the AA measurements during the caging transition connecting these two extremes over the entire timespan at this level of coarse-graining. For the polystyrene oligomers for which we previously characterized the diffusive friction, the viscosity-parametrized frictions are consistent with the diffusive measures for the smallest chain length. However, for the longer chains, we find different trends based on measurement method with friction derived from rotational diffusion remaining nearly constant, friction derived from translational diffusion showing a modestly increasing trend, and viscosity-derived friction showing a modest decreasing trend. This seems to indicate that there is some sensitivity of the friction measurement method for systems with increased relaxation times and that in particular, the unsteady dynamics of the individual parametrization schemes plays a role in this. Increased difficulty in applying the GK method with increasing relaxation time of the longer chain systems is also discussed. Overall, we find that when the material is in a high-temperature melt state and the viscosity measurement is reliable, the friction parametrization from the diffusive friction measures is consistent and the lower cost diffusive parametrization is a reliable means for modeling viscosity. Our data give insight into the time-dependent friction one might compute using a non-Markovian approach to enable the recovery of AA dynamics over a wider range of time scales than can be computed using a single friction.

Explaining the Sensitivity of Polymer Segmental Relaxation to Additive Size Based on the Localization Model.

We use molecular simulations to examine how the dynamics of a coarse-grained polymer melt are altered by additives of variable size and interaction strength with the polymer matrix. The effect of diluent size σ on polymer dynamics changes significantly when its size is comparable to the polymer segment size. For each σ, we show that the localization model (LM) quantitatively describes the dependence of the segmental relaxation time τ on temperature T in terms of dynamic free volume, quantified by the Debye-Waller factor ⟨u^{2}⟩. Within this model, we show that the additive size alone controls the functional form of the T dependence. The LM parameters reach asymptotic values when the diluent size exceeds the monomer size, converging to a limit applicable to macroscopic interfaces.

Microrheology analysis in molecular dynamics simulations: Finite box size correction

In single-particle microrheology, the viscoelastic properties of a complex fluid can be extracted using the generalized Stokes–Einstein (GSE) relation by embedding a micrometer-sized particle and tracking its motion through the fluid. Applying the same analysis to molecular dynamics simulations can result in overestimated G∗ values because of the hydrodynamic interaction between the probe bead and its periodic images. We derive a simple correction to the GSE equation by implementing an analytical solution for Stokes drag on a periodic array of spheres, which allows smaller box sizes to be simulated while still retaining accuracy. Fluid and particle inertia are neglected, although the approach used here might be generalized to include them. The correction is applied to molecular dynamics simulations of a coarse-grained polymer melt. For several bead-to-box-size ratios R/L and two probe sizes, we measure the mean squared displacement and calculate G∗ using both the original GSE and the corrected hydrodynamic Stokes–Einstein (HSE) equations. These results are compared to small amplitude oscillatory non-equilibrium molecular dynamics (NEMD) simulations, which show that the HSE analysis correctly predicts the G∗ values at low frequencies but breaks down when either fluid inertia is important or the bead size is too small to “see” a continuum. For small R/L, the GSE and HSE results are similar, although a small correction is still required for the finite box size and computational cost is significantly larger. The HSE equation allows the use of smaller box sizes, reducing computational costs by more than an order of magnitude.

Equation of State and Entropy Theory Approach to Thermodynamic Scaling in Polymeric Glass-Forming Liquids

We show that thermodynamic scaling can be derived by combining the Murnaghan equation of state (EOS) with the generalized entropy theory (GET) of glass formation. In our theory, thermodynamic scaling arises in the non-Arrhenius relaxation regime as a scaling property of the fluid configurational entropy density $s_c$, normalized by its value $s_c^*$ at the onset temperature $T_A$ of glass formation, $s_c / s_c^*$, so that a constant value of $TV^{\gamma}$ corresponds to a \textit{reduced isoentropic} fluid condition. Molecular dynamics simulations on a coarse-grained polymer melt are utilized to confirm that the predicted thermodynamic scaling of $\tau_{\alpha}$ by the GET holds both above and below $T_A$ and to test whether the extent $L$ of stringlike collective motion, normalized its value $L_A$ at $T_A$, also obeys thermodynamic scaling, as required for consistency with thermodynamic scaling. While the predicted thermodynamic scaling of both $\tau_{\alpha}$ and $L/ L_A$ is confirmed by simulation, we find that the isothermal compressibility $\kappa_T$ and the long wavelength limit $S(0)$ of the static structure factor do not exhibit thermodynamic scaling, an observation that would appear to eliminate some proposed models of glass formation emphasizing fluid `structure' over configurational entropy. It is found, however, that by defining a low temperature hyperuniform reference state, we may define a compressibility relative to this condition, $\delta \kappa_T$, a transformed dimensionless variable that exhibits thermodynamic scaling and which can be directly related to $s_c / s_c^*$. Further, the Murnaghan EOS allows us to interpret $\gamma$ as a measure of intrinsic anharmonicity of intermolecular interactions that may be directly determined from the pressure derivative of the material bulk modulus.

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear.

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated β-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the "stretching exponent" β quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

Influence of knot complexity on glass-formation in low molecular mass ring polymer melts.

We perform molecular dynamics simulations on a coarse-grained polymer melt to study the dynamics of glass-formation in ring polymer melts of variable knot complexity. After generating melts of non-concatenated polymeric rings having a range of minimum crossing number values, mc, we compute the coherent intermediate scattering function, the segmental α-relaxation time, fragility, and the glass transition temperature as a function of mc. Variation of knot complexity is found to have a pronounced effect on the dynamics of polymer melts since both molecular rigidity and packing are altered, primary physical factors governing glass-formation in polymeric materials.

Why we need to look beyond the glass transition temperature to characterize the dynamics of thin supported polymer films

There is significant variation in the reported magnitude and even the sign of [Formula: see text] shifts in thin polymer films with nominally the same chemistry, film thickness, and supporting substrate. The implicit assumption is that methods used to estimate [Formula: see text] in bulk materials are relevant for inferring dynamic changes in thin films. To test the validity of this assumption, we perform molecular simulations of a coarse-grained polymer melt supported on an attractive substrate. As observed in many experiments, we find that [Formula: see text] based on thermodynamic criteria (temperature dependence of film height or enthalpy) decreases with decreasing film thickness, regardless of the polymer-substrate interaction strength ε. In contrast, we find that [Formula: see text] based on a dynamic criterion (relaxation of the dynamic structure factor) also decreases with decreasing thickness when ε is relatively weak, but [Formula: see text] increases when ε exceeds the polymer-polymer interaction strength. We show that these qualitatively different trends in [Formula: see text] reflect differing sensitivities to the mobility gradient across the film. Apparently, the slowly relaxing polymer segments in the substrate region make the largest contribution to the shift of [Formula: see text] in the dynamic measurement, but this part of the film contributes less to the thermodynamic estimate of [Formula: see text] Our results emphasize the limitations of using [Formula: see text] to infer changes in the dynamics of polymer thin films. However, we show that the thermodynamic and dynamic estimates of [Formula: see text] can be combined to predict local changes in [Formula: see text] near the substrate, providing a simple method to infer information about the mobility gradient.

String-like collective motion in the α- and β-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Influence of Cohesive Energy on Relaxation in a Model Glass-Forming Polymer Melt

The wide range of chemical compositions exhibited by polymers enables the fabrication of materials having highly tunable cohesive energy strength ϵ, and many of the properties that make polymers so useful as structural and responsive materials in both manufacturing and living systems derive from the variability of this basic property. The design and characterization of polymer materials then inevitably leads to a consideration of how ϵ impacts the thermodynamic and relaxation properties of polymer liquids. Our prior paper uses molecular dynamics simulations of a model coarse-grained polymer melt to systematically investigate the dependence of commonly measured thermodynamic properties on ϵ, while the present work focuses on the relaxation dynamics of the same molecular model. After demonstrating, as expected, that ϵ greatly influences the segmental relaxation time, we obtain a universal reduction of all our data for relaxation in terms of an activated transport model in which the activation free energy is...

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

The study of glass formation is largely framed by semiempirical models that emphasize the importance of progressively growing cooperative motion accompanying the drop in fluid configurational entropy, emergent elasticity, or the vanishing of accessible free volume available for molecular motion in cooled liquids. We investigate the extent to which these descriptions are related through computations on a model coarse-grained polymer melt, with and without nanoparticle additives, and for supported polymer films with smooth or rough surfaces, allowing for substantial variation of the glass transition temperature and the fragility of glass formation. We find quantitative relations between emergent elasticity, the average local volume accessible for particle motion, and the growth of collective motion in cooled liquids. Surprisingly, we find that each of these models of glass formation can equally well describe the relaxation data for all of the systems that we simulate. In this way, we uncover some unity in our understanding of glass-forming materials from perspectives formerly considered as distinct.

String model for the dynamics of glass-forming liquids.

We test the applicability of a living polymerization theory to describe cooperative string-like particle rearrangement clusters (strings) observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann "entropy crisis."

Quantitative Model for Clusters of String-like Cooperative Motion in a Coarse-Grained Glass-Forming Polymer Melt

ABSTRACTWe apply a living polymerization theory to describe cooperative string-like particle rearrangement clusters observed in simulations of a coarse-grained polymer melt. The theory quantitatively describes the interrelation between the average string length L, configurational entropy Sconf, and the order parameter for string assembly Φ without free parameters. Combining this theory with the Adam-Gibbs (AG) model allows us to predict the relaxation time τ in a lower temperature T range than accessible by current simulations. In particular, the combined theories suggest a return to Arrhenius behavior near Tg and a low T residual entropy, thus avoiding a Kauzmann ‘entropy crisis’.

Nature and interrelations of fast dynamic properties in a coarse-grained glass-forming polymer melt

Recent experimental studies have demonstrated that the dynamics of glass-forming liquids on fast picosecond timescales are directly relevant to developing effective formulations for protein drug preservation. In these systems, short-time dynamic properties, including the Debye–Waller factor, non-ergodicity parameter, and the ‘fast beta’ relaxation time, are ‘tuned’ by the addition of antiplasticizer additives, with associated improvements in protein preservation. We employ molecular dynamics simulations of a coarse-grained polymer melt with and without the addition of an antiplasticizer additive to characterize how these fast dynamic properties interrelate and how they are altered by the addition of antiplasticizer additives. We find that the Gaussian approximation for the van Hove correlation function holds to an excellent approximation at short times, facilitating the establishment of precise interrelations between these properties and the characterization of their temperature and composition dependence. Following previous studies, we first fit the fast relaxation process to an empirical ‘stretched Gaussian’ form (exp[−(t/τ)β] with 1 < β < 2) and find that β equals 3/2 over a wide range of temperature for the post-inertial relaxation process. We then consider a more theoretically motivated description of fast beta relaxation inspired by an earlier model for the relaxation of a fractal network of elastic clusters in glass-forming colloids, and we find that this description provides an excellent fit to the entire short time relaxation over a large range of temperatures with physically meaningful parameters. Finally, we show that it is possible to tune the fast beta relaxation process with antiplasticizer additives, resulting in effects that rationally enhance protein preservation in glassy sugar matrices.

Onset of Entanglements Revisited. Dynamical Analysis

In a series of two papers, we study the onset of entanglements and the transition from Rouse-type to reptation dynamics, in the context of dissipative particle dynamics (DPD) simulations of a coarse-grained polymer melt. A set of monodisperse systems with increasing chain length is examined. We consider both static and dynamic aspects of the problem. Part I, the preceding paper (DOI: 10.1021/ma901131c), presents a topological analysis of our systems. It deals with the continuous transition from unentangled to entangled topology, as chain length increases, at the level of primitive paths (PPs). In part II, this paper, we present the dynamics of our systems, and a comparison between topological and dynamical analysis. We utilize a coarse-grained model of polyethylene, based on the blob (or bead) picture of a polymer chain. The conservative potentials describing bead interactions are derived by a bottom-up approach. Each bead corresponds to 20 carbon atoms. Because of the large coarse-graining level, beads can easily overlap and chain contours can cross each other. We maintain chain uncrossability by introducing a segmental repulsive potential (SRP), adapted to our model. It is demonstrated that suitable parametrization of this potential can reproduce the dynamical transition from Rouse to reptation dynamics. For short chain unentangled systems, we observe a deviation from the pure Rouse behavior, attributed to the presence of chain stiffness, nonbonded interactions, and chain uncrossability, which are not considered by the Rouse model. For long chain systems, global dynamics is typical of reptation. The chain length dependence of viscosity and self-diffusion is described by power laws, with exponents equal to +3.2 and −2.3, respectively. A global and local (Rouse-mode) dynamical analysis, a static topological analysis, and the comparison between them, shows that topological constraints alter polymer dynamics at length scales much shorter than the length scales implied by the reptation model. This is evidenced by a slowing down of Rouse modes, which is maximum at the length scale where the underlying system of interpenetrating PPs appears as a network of topological constraints.

Onset of Entanglements Revisited. Topological Analysis

In a series of two papers, we study the onset of entanglements and the transition from Rouse-type to reptation dynamics, in the context of dissipative particle dynamics (DPD) simulations of a coarse-grained polymer melt. A set of monodisperse systems with increasing chain length is examined. We consider both static and dynamic aspects of the problem. Part I, this paper, deals with the continuous change of the polymer topology, from unentangled (short chains), to entangled (long chains). We show that as chain length increases the rate of increase of chain overlap increases asymptotically. It becomes constant when chains are sufficiently long, and in this regime a long chain topology is established. Next, we examine the onset by probing static length scales at the level of primitive paths (PPs). A simple scaling model based on a transformation of PPs from thin rods (short chains) to random walks (RWs) (long chains) is discussed qualitatively and quantitatively. The model predicts a crossover in the underlyi...

Structure of an Associating Polymer Melt in a Narrow Slit by Molecular Dynamics Simulation

Molecular dynamics simulation has been used to study the equilibrium properties of a generic coarse-grained polymer melt with associating terminal groups, confined in a narrow slit by two atomically smooth walls. Simulations were carried out as a function of wall separation and attracting strength as well as polymer end-end interaction strength. We find that confinement has an important effect on the melt properties. In particular, strongly attracting walls can produce radical changes in chain conformation, the nature of the transient network, and the structure of the aggregates formed by the associating terminals.