Micromechanical molecular models

The aim of this chapter is to describe the micro-mechanical processes that occur close to an interface during adhesive or cohesive failure of polymers. Emphasis will be placed on both the nature of the processes that occur and the micromechanical models that have been proposed to describe these processes. The main concern will be processes that occur at size scales ranging from nanometres (molecular dimensions) to a few micrometres. Failure is most commonly controlled by mechanical process that occur within this size range as it is these small scale processes that apply stress on the chain and cause the chain scission or pull-out that is often the basic process of fracture. The situation for elastomeric adhesives on substrates such as skin, glassy polymers or steel is different and will not be considered here but is described in a chapter on tack . Multiphase materials, such as rubber-toughened or semi-crystalline polymers, will not be considered much here as they show a whole range of different micro-mechanical processes initiated by the modulus mismatch between the phases. 

CNTs have extremely high stiffness and strength, and are regarded as perfect reinforcing fibers for developing a new class of nanocomposites. The use of atomistic or molecular dynamics (MD) simulations is inevitable for the analysis of such nanomaterials in order to study the local load transfers, interface properties, or failure modes at the nanoscale. Meanwhile, continuum models based on micromechan-ics have been shown in several recent studies to be useful in the global analysis for characterizing such nanomaterials at the micro- or macro-scale. 

The DNF model incorporates the experimentally observed characteristics by using a micromechanism-inspired approach in which the material behavior is decomposed into a viscoplastic response, corresponding to irreversible molecular chain sliding due to the lack of chemical crosslinks in the material, and atime-dependent viscoelastic response. The viscoelastic response is further decomposed into the response of two molecular networks acting in parallel the first network (A) captures the equilibrium response and the second network (B) the time-dependent deviation from the viscoelastic equilibrium state. A onedimensional rheological representation of the model framework and a schematic illustrating the kinematics of deformation are shown in Fig. 11.6. 

In Odegard s study [48], a method has been presented for finking atomistic simulations of nano-structured materials to continuum models of tfie corresponding bulk material. For a polymer composite system reinforced with SWCNTs, the method provides the steps whereby the nanotube, the local polymer near the nanotube, and the nanotube/ polymer interface can be modeled as an effective continuum fiber by using an equivalent-continuum model. The effective fiber retains the local molecular stractuie and bonding information, as defined by MD, and serves as a means for finking tfie eqniv-alent-continuum and micromechanics models. The micromechanics method is then available for the prediction of bulk mechanical properties of SWCNT/polymer com-... 

Computational techniques have extensively been used to study the interfacial mechanics and nature of bonding in CNT-polymer composites. The computational studies can be broadly classified as atomistic simulations and continuum methods. The atomistic simulations are primarily based on molecular dynamic simulations (MD) and density functional theory (DFT) [105], [106-110] (some references). The main focus of these techrriques was to understand and study the effect of bonding between the polymer and nanotube (covalent, electrostatic or van der Waals forces) and the effect of fiiction on the interface. The continuum methods extend the continuum theories of micromechanics modeling and fiber-reirrforced composites (elaborated in the next section) to CNT/polymer composites [111-114] and explain the behavior of the composite from a mechanics point of view. 

The direct use of micromechanical models for nanocomposites is however doubtfid due to the significant scale difference between nanoparticles and macro-partides. As such, two methods have recently been proposed for modeling the mechanical behavior of polymer nanocomposites equivalent continuum approach and self-similar approach. In equivalent continuum approach, molecular dynamics (MD) simulation is first used to model the molecular interaction between nanopartide and polymer. Then, a homogeneous equivalent continuum reinforcing element (i.e., an effective nanopartide) is constmcted. Finally, micro-mechanical models are used to determine the effective bulk properties of a... 

Mechanical properties of polymer nanocomposites can be predicted by using analytical models and numerical simulations at a wide range of time- and length scales, for example, from molecular scale (e.g., MD) to microscale (e.g., Halpin-Tsai), to macroscale (e.g., FEM), and their combinations. MD simulations can study the local load transfers, interface properties, or failure modes at the nanoscale. Micromechanical models and continuum models may provide a simple and rapid way to predict the global mechanical properties of nanocomposites and correlate them with the key factors (e.g., particle volume fraction, particle geometry and orientation, and property ratio between particle and matrix). Recently, some of these models have been applied to polymer nanocomposites to predict their thermal-mechanical properties. Young s modulus, and reinforcement efficiency and to examine the effects of the nature of individual nanopartides (e.g., aspect ratio, shape, orientation, clustering, and the modulus ratio of nanopartide to polymer matrix). 

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