An MD study of the polymer–polymer adhesion via connector chains: some aspects of the competition between bulk dissipation in the interphase and pull-out of interface-connecting molecules

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Highlights

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    Crazing shares similitudes with issues of polymer interface separation.

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    Molecular Dynamics simulations provide needful molecular details.

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    Two stretched polymers connected by coarse-grained molecules is a relevant representation.

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    The CPU time consumption is reasonable.

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    The strain rate controls pull-out and micro-bulk dissipation magnitude.

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    Temperature and connectors/fibrils length are fixed parameters.

Abstract

Atomistic simulation approach was used to analyze the separation behavior of polymer–polymer interfaces. This was achieved using coarse-grained molecular dynamics (MD) simulations of some connector chains embedded in two adjacent polymer entangled melts. To separate the contribution of polymer molecules pull-out from the micro-bulk dissipation in the viscoplastic interphase, surrounding the surface of separation, two kinds of simulations were considered: (a), simulations of the pull-out mechanism, where the extraction of the connectors out of the melts takes place through a complex mechanism of forced reptation only; (b), simulations of the full debonding process where the micro-bulk dissipation contributes to the overall crack opening and can skew the description of the interface separation by pure connector molecules pull-out. From the MD simulation results, some relevant parameters (e.g., a cohesive strength or an adhesion energy) of the separation behavior of the interface being modelized were extracted. In addition, one was able to separate quantitatively connector pull-out from micro-bulk dissipation (in the surrounding bulk region of the interface). This means that we were able to emphasize: (i) how the straining divides into interface opening and bulk deformation and (ii), how the macroscopic opening rate diffuses throughout the melts and the interface opening rate, since the mechanical behavior of polymers is strain-rate dependent. A comparison between two kinds of MD simulations, where a system is stretched along one direction, is shortly discussed as a necessary prelude to future investigations.

Introduction

This contribution is interested in fracture toughness and the fracture mechanisms of planar polymer interfaces. It represents an intermediate continuation of the already published work by Solar and van der Giessen [1], where a first insight of the competition between surface and bulk phenomena, involved in polymer interface separation problems, was presented for various separation velocities. Various stress measures were discussed and assessed at various locations of the heterogeneous system, as well.

Damaging or fracture in polymers is still a broad research topic. In comparison to metallic materials where fracture only consists of the propagation of a crack, the region at the front of a crack tip in a polymeric material, is made of two lips joined (on a very small characteristic distance) by isolated fibrils. This region is the so-called “craze” and is the prelude of a pure crack. This region propagates, strictly speaking, through a mechanism of “crazing” instead of “cracking”. Depending on the mode I, II or III of craze-opening, this mechanism of “crazing” is composed of the 3-D oriented translation of the front of the craze, in which one observes fibrils extraction from the lips or fibrils breaking and, after which the craze degenerates into a pure crack like in metallic materials. If one considers a schematic representation of the “crazing” propagation mechanism where a fibril is seen like a coarse-grained polymer molecule, one may find interesting similitude with the issue of polymeric interface separation, where some polymer molecules diffused at both sides of the interface.

The topic of fracture of planar polymer interfaces is hardly modelized by atomistic approaches, mostly because of increasing CPU time efforts for growing characteristic length scales of the simulated systems. In this situation, the phase field methods are relevant and, may be able to contribute as well [2]. Nevertheless, it was decided to use MD coarse-grained approach to modelize the separation behavior of polymer–polymer interfaces, through simulations of some connector chains embedded in two adjacent polymer entangled melts, see Fig. 1. Through the material force field between the particles, atomistic simulations are able to modelize internal cohesion forces in a material with a high level of accuracy indeed, more than Continuum Mechanics does. Atomistic (coarse-grained) approaches are thus helpfull and, contain exactly the molecular aspects needed to investigate and understand such a competition between viscoelastic deformation inside a polymer bulk-interphase and connector extraction out of this interphase.

Even though nice reviews on polymer adhesion can be found in the literature [3], [4] and some interesting theoretical and numerical predictions for mechanical behavior of separated interfaces and of strained polymer melts exist in the literature as well, see Refs. [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], the contribution of the viscoelastic deformation inside the polymers on either side of the interface are often disregarded or reduced to a simplified modeling. This last mechanism can be very important however, as the strain rate, the areal density or the connector chain length increase. This micro-bulk dissipation is not so obvious to determinate and, is taken under consideration in this manuscript.

In the manuscript proposed herein, our simulations of the failure of adhesion between two deformable melts develops a deeper insight in the competition between surface and bulk phenomena for a broader range of external conditions: this is the novelty of this contribution. Our investigations are aimed to improve further our study on the separate contributions of surface adhesion and bulk dissipation to the overall work of separation. This manuscript is divided into: (a), Section 2 describing some needful aspects on the computational efforts granted; (b), Section 3 synthesizing several aspects from the literature and proposing a short discussion on an over-simplified model derived from the literature; (c), Sections 4 Fracture kinematics of the polymer interfaces being modelized, 5 Some scaling laws of the polymer interfaces being modelized dealing with some kinematical aspects and scaling laws of the polymer interfaces being modelized. Finally, Section 6 presents the full interface separation behavior during pull-out and full debonding as an anticipation of the implementation of a new cohesive model, which will be the topic of further contributions to this manuscript.

Section snippets

Some aspects on the computational interface mechanics being modelized

Two amorphous polymer melts, stitched together by distinct connector molecules, are studied. This system is contained in an (initially orthorhombic) MD cell with a given cell matrix Hcell, see Fig. 1 and Ref. [16]. The melts are separated by an initial gap δgap=4.5σ before any deformation, to impose the presence of an interface/ a craze being opened. The system is deformed by imposing the straining of the MD cell through a uniform rate of deformation gradient, see A. The principles of the

Legacy from the literature and short discussion

In the literature of adhesion (see Refs. [34], [35], [36], [37], [38]), the Universal Binding Energy Relation (UBER) describes the energy W dissipated (per unit of area) during the interface separation mechanism as a function of the separation Δn (between the two surfaces).

Fracture kinematics of the polymer interfaces being modelized

In Section 2, we described how the cohesive behavior of our modelized interfaces was interpreted from MD simulation results. In Fig. 1, 2 one defined a (vertical) traction Tn, representing an averaged measure of stress at the connector molecules, a

Some scaling laws of the polymer interfaces being modelized

Our present investigations are based on the velocity (or macroscopic strain rates) dependencies of 〚Tn〛 (resp. W) as a function of the opening Δn. They are presented in Fig. 14, Fig. 15, Fig. 16 for T=0.3∊/kB and Nbconn=150, from where the results are combined into the results given in Fig. 13. An interesting first conclusion is that the “traction vs. opening” at the connectors during total debonding is still similar in shape to the “traction vs. opening” at the connectors during pull-out

Full interface separation behavior during pull-out and full debonding

One proposes here to analyze the cohesive law “〚Tn〛 vs. Δn” during pure pull-out and full debonding, as a prelude to the mapping to a future continuum model for interface separation., although it will be the scope of a further contribution. During a pull-out simulation, it was already observed that as the strain rate increases, the two melts can be crushed against the intermediate walls, because of a faster extraction of the connectors. Thus, this artefact should make the extraction of the

Conclusion

The MD simulation approach was used to analyze the separation behavior of some connector chains embedded in two adjacent polymer entangled melts. We focused (a), on the pull-out mechanism, where the extraction of the connectors out of the melts takes place through a complex mechanism of forced reptation only and (b), on the full debonding process, where a micro-bulk dissipation contributes to the overall crack opening and can skew the description of the interface separation by pure connector

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study. Nevertheless, the modified routines used in LAMMPS will be given to the LAMMPS users-community after valuable publication.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

This contribution was the fruit of a long collaboration with Prof. Erik van der Giessen 7. This project was supported between 2010 and 2011 by the Dutch Technology Foundation STW under the project “A Multiscale approach toward integrated cohesive interface elements” and, between 2017 and 2020 by the Institut Charles Sadron (Team MIM, Strasbourg, FRANCE).

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