Dynamic Heterogeneity in Ring-Linear Polymer Blends

We present results from a direct statistical analysis of long molecular dynamics (MD) trajectories for the orientational relaxation of individual ring molecules in blends with equivalent linear chains. Our analysis reveals a very broad distribution of ring relaxation times whose width increases with increasing ring/linear molecular length and increasing concentration of the blend in linear chains. Dynamic heterogeneity is also observed in the pure ring melts but to a lesser extent. The enhanced degree of dynamic heterogeneity in the blends arises from the substantial increase in the intrinsic timescales of a large subpopulation of ring molecules due to their involvement in strong threading events with a certain population of the linear chains present in the blend. Our analysis suggests that the relaxation dynamics of the rings are controlled by the different states of their threading by linear chains. Unthreaded or singly-threaded rings exhibit terminal relaxation very similar to that in their own melt, but multiply-threaded rings relax much slower due to the long lifetimes of the corresponding topological interactions. By further analyzing the MD data for ring molecule terminal relaxation in terms of the sum of simple exponential functions we have been able to quantify the characteristic relaxation times of the corresponding mechanisms contributing to ring relaxation both in their pure melts and in the blends, and their relative importance. The extra contribution due to ring-linear threadings in the blends becomes immediately apparent through such an analysis

Computational study of structural relaxation and plastic deformation of glassy polymers

This thesis focuses on the study of glassy system dynamics and their mechanical properties via molecular dynamics simulations. In order to study the dynamics for large times we proposed the observation of the inherent structures picture (local minima of the potential energy). For the mechanical properties we conducted computational experiments in the elastic and the plastic region. For the experiments in the elastic region we confirmed that the inherent structure picture can predict the mechanical properties of glassy polymers. For the plastic region experiments we showed that for non-infinite deformation rates, we must redefine its probability distribution between the inherent structures during the application of external stress. This means that we must solve the problem of the dynamical evolution of the system between the inherent structures for such times that correspond to the deformation rates of interest. For the development of such methods we studied a simplified model system. We observed the dynamics of the model system by studying the mean squared displacement, which is connected with the self-diffusivity coefficient. For temperatures lower than the glass transition temperature (Tg?38.4 Κ) we have envisioned a model that describes the dynamics of the atomistic system as a series of transitions, following first-order kinetics and Poisson statistics, from one potential energy minimum to another. We provide the mathematical formulation for “lifting” the coarse-grained model and reproducing the full dynamics of the atomistic system. For temperatures around and over the glass transition temperature transitions between collections of basins are described by rare events statistics. We developed an automated, self-consistent method, allowing the identification of such collections and their characterization as a metabasin. Since the computational cost increases we developed a parallel method and we accelerated the execution times of our simulations more than 2 orders of magnitude. We developed a method of temperature acceleration of the system dynamics, which is connected with the parallel method. Temperature accelerated dynamics method, allows us to sample transitions in timescales inaccessible to conventional molecular dynamics. By knowing the rate constants from and to every sampled state, our system is by definition ergodic, if we have the ability to observe it in such times, so that the transitions from all states to all states are probable.Στην παρούσα διδακτορική διατριβή εξετάζεται η δυναμική και οι μηχανικές ιδιοτήτες υαλωδών υλικών, μέσω προσομοιώσεων μοριακής δυναμικής. Για την μελετη της δυναμικής σε μεγάλους χρόνους προτάθηκε εικόνα των εγγενών δομών (ελαχίστα της δυναμικής ενέργειας του συστήματος). Για τις μηχανικές ιδιότητες διεξήχθησαν υπολογιστικά πειράματα στην ελαστική και στην πλαστική περιοχή. Για τα πειράματα στην ελαστική περιοχή επιβεβαιώθηκε πως η εικόνα των εγγενών δομών είναι ικανή για την πρόβλεψη των μηχανικών ιδιοτήτων υαλωδών πολυμερών. Για πειράματα πλαστικής παραμόρφωσης δείξαμε πως, για ρυθμούς παραμόρφωσης που δεν είναι άπειροι, πρέπει να δοθεί η δυνατότητα στο σύστημα να ανακατανείμει την πληθυσμιακή του κατανομή μεταξύ των εγγενών δομών κατά την επιβολή εξωτερικής τάσης. Προκύπτει, λοιπόν, η ανάγκη δημιουργίας μεθόδων οι οποίες επιτρέπουν την επαρκή δειγματοληψία της δυναμικής υαλωδών υλικών, για χρόνους που αντιστοιχούν στην τιμή του ρυθμού παραμόρφωσης που μας ενδιαφέρει. Για την ανάπτυξη τέτοιων μεθόδων μελετήθηκε ένα πρότυπο σύστημα. Η μελέτη της δυναμικής του πρότυπου συστήματος έγινε εξετάζοντας τη μέση τετραγωνική μετατόπιση, που συνδέεται με τον συντελεστή αυτοδιάχυσης. Για θερμοκρασίες μικρότερες της θερμοκρασίας υαλώδους μετάπτωσης (Tg?38.4 Κ) αναπτύξαμε ένα μοντέλο που περιγράφει τη δυναμική του ατομιστικού συστήματος, ως μια ακολουθία μεταβάσεων μεταξύ των εγγενών δομών, οι οποίες υπακούουν κινητική α΄ τάξης και στατιστική τύπου Poisson. Παρέχουμε το μαθηματικό φορμαλισμό για την «ανύψωση» του αδροποιημένου μοντέλου, της αλληλουχίας μεταβάσεων, για την αναπαραγωγή της πλήρους δυναμικής. Για θερμοκρασίες κοντά και πάνω από την Tg παρατηρήσαμε πως αποτελούν σπάνια γεγονότα οι μεταβάσεις μεταξύ συνόλων ελαχίστων. Αναπτύξαμε μια αυτοματοποιημένη-αυτοσυνεπή μέθοδο που επιτρέπει την ταυτοποίηση ενός τέτοιου συνόλου και το χαρακτηρισμό του ως μεταλεκάνη. Καθώς το υπολογιστικό κόστος αυξάνει αναπτύξαμε μια παράλληλη μέθοδο, επιταχύνοντας τον χρόνο εκτέλεσης κατά 2 τάξεις μεγέθους. Αναπτύξαμε μια μέθοδο θερμοκρασιακής επιτάχυνσης της δυναμικής η οποία είναι συνδεδεμένη με την παράλληλη μέθοδο. Η μέθοδος θερμοκρασιακής επιτάχυνσης επιτρέπει τη δειγματοληψία μεταβάσεων σε κλίμακες χρόνου απρόσιτες στη μοριακή δυναμική. Με τη γνώση των σταθερών ρυθμού από και προς κάθε κατάσταση, το σύστημα μας είναι εξ ορισμού εργοδικό, αν έχουμε την δυνατότητα παρατήρησης για τέτοιους χρόνους ώστε να είναι πιθανές οι μεταβάσεις από όλες προς όλες τις καταστάσεις

A new equation for the mean free path of air

A recent rigorous methodology for determining the mean free path, λ, of air at ambient conditions [Tsalikis, D. G., Mavrantzas, V. G., & Pratsinis, S. E. (2023). Physics of Fluids, 35, 097131] is extended to pressures, P, from 0.5 to 5 atm and temperatures, T, from 100 to 3000 K that are of environmental and industrial relevance, allowing to derive a new simple equation for λ as a function of T and P. This entails molecular dynamics (MD) simulations of air accounting for the actual shape and force field of nitrogen and oxygen and analysis of the computed microcanonical ensemble of free paths to derive λ at any P and T. Simulations are rigorously validated by comparing MD-predicted air densities, diffusivities and viscosities at various temperatures and pressures against experimental measurements, theoretical expressions and ab initio simulations. At all T and P, the MD-computed λ are systematically smaller (at least 40%) than those from classic kinetic theory and its variants. The new equation for λ is: λ (T, P) = 0.033916 x T¹.²³ P⁻¹ and can be also expressed in terms of the standard Jennings’ expression, λ = √(π/8) μ/u 1/√(ϱP) [Jennings, S. G. (1998). Journal of Aerosol Science, 19(2), 159–166], relating λ to air viscosity, μ, and density, ρ, using just a new value for its numerical factor u, u = 0.81475 ± 0.00288, which is 63% larger than the current u = 0.4987445.ISSN:0278-6826ISSN:1521-738

Threading of Ring Poly(ethylene oxide) Molecules by Linear Chains in the Melt

We report results from an atomistic molecular dynamics simulation study of ring-linear poly­(ethylene oxide) (PEO) melts followed by a topological reduction to ensembles of primitive paths and a detailed geometric analysis using vector calculus, which reveals considerable cyclic threading by the linear chains. The simulations have been conducted using ring-linear PEO blends of the same size, over a series of molecular lengths and compositions. For PEO melts characterized by molecular weight (MW) greater than 10044 g/mol, in particular, our computations reveal the occurrence of multiple threading events (penetrations). We further find that the time it takes a linear molecule that threads a cyclic one to fully pass through the latter can be more than 1 order of magnitude larger than the corresponding relaxation time of the ring in its own melt. Our analysis implies that dynamics in ring-linear polymer blends is highly heterogeneous, with many of the threadings being long-lived and with the linear chains (even when present in small amounts) dramatically obstructing the mobility of rings

On the Use of a Non-Constant Non-Affine or Slip Parameter in Polymer Rheology Constitutive Modeling

Since its introduction in the late 1970s, the non-affine or slip parameter, ξ , has been routinely employed by numerous constitutive models as a constant parameter. However, the evidence seems to imply that it should be a function of polymer deformation. In the present work, we phenomenologically modify a constitutive model for the rheology of unentangled polymer melts [P. S. Stephanou et al. J. Rheol. 53, 309 (2009)] to account for a non-constant slip parameter. The revised model predictions are compared against newly accumulated rheological data for a C48 polyethylene melt obtained via direct non-equilibrium molecular dynamics simulations in shear. We find that the conformation tensor data are very well predicted; however, the predictions of the material functions are noted to deviate from the NEMD data, especially at large shear rates

Microscopic Dynamics and Topology of Polymer Rings Immersed in a Host Matrix of Longer Linear Polymers: Results from a Detailed Molecular Dynamics Simulation Study and Comparison with Experimental Data

We have performed molecular dynamics (MD) simulations of melt systems consisting of a small number of long ring poly(ethylene oxide) (PEO) probes immersed in a host matrix of linear PEO chains and have studied their microscopic dynamics and topology as a function of the molecular length of the host linear chains. Consistent with a recent neutron spin echo spectroscopy study (Goossen et al., Phys. Rev. Lett. 2015, 115, 148302), we have observed that the segmental dynamics of the probe ring molecules is controlled by the length of the host linear chains. In matrices of short, unentangled linear chains, the ring probes exhibit a Rouse-like dynamics, and the spectra of their dynamic structure factor resemble those in their own melt. In striking contrast, in matrices of long, entangled linear chains, their dynamics is drastically altered. The corresponding dynamic structure factor spectra exhibit a steep initial decay up to times on the order of the entanglement time τe of linear PEO at the same temperature but then they become practically time-independent approaching plateau values. The plateau values are different for different wavevectors; they also depend on the length of the host linear chains. Our results are supported by a geometric analysis of topological interactions, which reveals significant threading of all ring molecules by the linear chains. In most cases, each ring is simultaneously threaded by several linear chains. As a result, its dynamics at times longer than a few τe should be completely dictated by the release of the topological restrictions imposed by these threadings (interpenetrations). Our topological analysis did not indicate any effect of the few ring probes on the statistical properties of the network of primitive paths of the host linear chains

Dynamics of molecular collisions in air and its mean free path

The mechanics and dynamics of molecular collisions in air are investigated by thoroughly validated atomistic molecular dynamics (MD) simulations that treat oxygen and nitrogen as true diatomic molecules accounting for their non-spherical shape and, most importantly, force field. Due to their rotational motion and non-spherical shape, molecules follow complex trajectories at close enough separations experiencing a great variety of collision events. Most of the collisions are bimolecular. However, some can involve up to four molecules as pairs (or even triplets) of molecules that collide repeatedly are observed. Following their initial encounter, these molecules separate briefly, come back, and collide again and again creating even “orbiting” collisions, before they split apart to collide with other molecules. Identifying such rather spurious collisions and filtering them by hazard plot analysis was a key step in correctly determining collision densities and accumulating collision event statistics. By systematically recording the distribution of free paths (distances traveled by molecules between genuine collisions), the mean free path, λ, of air is determined as 38.5 ± 1 nm at 300 K and 1 atm. This is 43% smaller than the 67.3 nm widely accepted λ today at these conditions and quite robust to the employed MD force field as long as it accurately matches the experimentally determined macroscopic properties of air (density, viscosity, and diffusivity).ISSN:1070-6631ISSN:1089-7666ISSN:0031-917