A computational study of the dynamics of entanglement networks in polymer melts

153 σ.Η βασική κατανόηση των ιδιοτήτων των πολυμερικών τηγμάτων και ελαστομερών, σε μοριακό επίπεδο, έχει να αντιμετωπίσει την ύπαρξη τοπολογικών περιορισμών οι οποίοι απαγορεύουν τη διασταύρωση των πολυμερικών αλυσίδων και είναι γνωστοί ως διαπλοκές. Στα περισσότερα μοντέλα της ρεολογίας και της δυναμικής των πολυμερών, τα φαινόμενα που προκαλούν οι διαπλοκές εισάγονται είτε ως ένα περιοριστικό μέσο πεδίο (σωληνοειδές μοντέλο), είτε ως δυαδικοί σύνδεσμοι κατά μήκος των αλυσίδων (ολισθαίνοντες σύνδεσμοι). Αρχικά αναπτύσσουμε έναν πρωτότυπο αλγόριθμο, ο οποίος μπορεί να εφαρμοστεί σε μεσοσκοπικό επίπεδο, στους πρωτογενείς δρόμους (ΠΔ) των αλυσίδων ενός οποιουδήποτε πολυμερικού συστήματος. Ο αλγόριθμος βασίζεται στην ιδέα της ολικής ακτίνας καμπυλότητας και έχει ως στόχο τον εντοπισμό στο χώρο και στο χρόνο των τοπολογικών περιορισμών που εμφανίζουν οι αλυσίδες και την αντιστοίχιση των περιορισμών αυτών σε μεμονωμένους τοπικούς συνδέσμους. Επίσης, ελέγχουμε την ευαισθησία του αλγορίθμου στις ελεύθερες παραμέτρους του, και εκτιμούμε την επίδρασή τους στα τελικά αποτελέσματα, η οποία είναι αμελητέα. Στη συνέχεια ακολουθεί μια μικροσκοπική, στατιστική μελέτη των φαινομένων διαπλοκής, σε επίπεδο ολισθαινόντων συνδέσμων, σε ένα τήγμα και ένα ελαστομερές πολυαιθυλενίου (PE). Ξεκινώντας από τροχιές μοριακής δυναμικής, και χρησιμοποιώντας τον αλγόριθμο που περιγράψαμε, αναγνωρίζουμε τους τοπικούς συνδέσμους στο χώρο και στο χρόνο. Δείχνουμε ότι: (α) οι διαπλοκές είναι συλλογικές με μια κυρίαρχη δυαδική συνιστώσα, (β) υπάρχουν ισχυρές και ασθενείς αλληλεπιδράσεις μεταξύ ζευγών αλυσίδων και (γ) ο σωληνοειδής περιορισμός μπορεί να αντιστοιχισθεί στις ισχυρότερες δυαδικές αλληλεπιδράσεις. Επίσης, παρουσιάζουμε μια αυτοσυνεπή μεθοδολογία για την επιλογή των κυρίαρχων συνδέσμων. Τέλος, μέσω της συνάρτησης αυτοσυσχέτισης, Φ(s,t), ερευνούμε τη δυναμική εξέλιξη του προσανατολισμού των ΠΔ, διαπλεγμένων και μη, αδροποιημένων πολυμερικών συστημάτων PE που έχουν δημιουργηθεί με τη μέθοδο Dissipative Particle Dynamics. Αρχικά αναγνωρίζουμε τους διάφορους μηχανισμούς χαλάρωσης και πως αυτοί επιδρούν στον προσανατολισμό των ΠΔ και συγκρίνουμε την Φ(s,t) που υπολογίσαμε, με τις προβλέψεις του σωληνοειδούς μοντέλου. Παρατηρούμε δυναμικά ότι οι ΠΔ των αλυσίδων που δεν εμφανίζουν διαπλοκές είναι ραβδόμορφοι, ενώ οι ΠΔ των διαπλεγμένων αλυσίδων έχουν τη μορφή τυχαίων περιπάτων. Τέλος, μέσω της Φ(s,t), παρουσιάζουμε μια μεθοδολογία για την εκτίμηση του κρίσιμου μοριακού βάρους (Μc).A basic understanding of the properties of polymer melts and networks, at the molecular level, requires dealing with uncrossability constraints and the entanglement concept. In the most successful models of polymer rheology and dynamics, entanglement effects are considered through a constraining mean field (tube model), or through binary links along the chain (slip links). Microscopically, though, the concept of entanglement is still elusive. We develop a novel algorithm which detects the microscopic topological constraints that give rise to the tube constraint. The constraints are identified at the level of Primitive Paths (PPs) and are mapped to local pairwise chain interactions (local links). It is shown quantitatively that the algorithm is very stable and that noise effects are small and do not affect any of our final results and conclusions. By applying this algorithm to Molecular Dynamics trajectories, which were first reduced to the corresponding trajectories of PPs, we present a microscopic, statistical study of entanglements in Polyethylene (PE) melts and rubbers. By analyzing the tube constraint as a complete set of local binary links, we show that: (a) entanglements are collective with a prevailing pairwise component; (b) there exist strong and weak pairwise chain interactions; (c) the tube constraint can be mapped to the prevailing, strong pairwise interactions. We also present a self-consistent methodology for the selection of the strong links. We then present a study of the onset of entanglements in a set of melt systems of increasing chain length, from the unentangled to the entangled regime. For each system a dynamical trajectory generated by the Dissipative Particle Dynamics method is mapped to a corresponding trajectory of PPs. The systems are studied at the level of the orientational autocorrelation function, Φ(s,t). First, we explain how the relaxation mechanisms of Constraint Release and Contour Length Fluctuations appear at the level of PPs and affect Φ(s,t) values. We find that, in the transition from the unentangled to the entangled regime, PP conformations transform from rods to random walks. A comparison against the predictions of the tube model shows that this transformation leads, to the form of Φ(s,t) described by strict reptation theory. Eventually, by exploiting the properties of Φ(s,t), we present a simple methodology for estimating the critical molecular weight, Mc.Στέφανος Δ. Ανωγιαννάκη

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models

Microscopic Description of Entanglements in Polyethylene Networks and Melts: Strong, Weak, Pairwise, and Collective Attributes

We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, or as certain pairwise uncrossability interactions, as in slip-link models. A <i>pairwise parameter</i>, which varies between these limiting cases, shows that, for the systems studied, the character of the entanglement environment is more pairwise than collective. We employ a novel methodology, which analyzes entanglement constraints into a complete set of pairwise interactions, similar to slip links. Entanglement confinement is assembled by a plethora of links, with a spectrum of confinement strengths, from strong to weak. The strength of interactions is quantified through a link “persistence”, which is the fraction of time for which the links are active. By weighting links according to their strength, we show that confinement is imposed mainly by the strong ones, and that the weak, trapped, uncrossability interactions cannot contribute to the low frequency modulus of an elastomer, or the plateau modulus of a melt. A self-consistent scheme for mapping topological constraints to specific, strong binary links, according to a given entanglement density, is proposed and validated. Our results demonstrate that slip links can be viewed as the strongest pairwise interactions of a collective entanglement environment. The methodology developed provides a basis for bridging the gap between atomistic simulations and mesoscopic slip-link models