Interphase continuum mechanics

Due to the complexity of the formation of interphases, a completely satisfying microscopic interpretation of these effects cannot be given today, especially since the process of the interphase formation is not yet understood in detail. Therefore, a micromechanical model cannot be devised for calculating the global effective properties of a thin polymer film including the above-mentioned size effects governed by the interphases. On the other hand, a classical continuum-based model is not able to include any kind of size effect. An alternative to the above-mentioned classical continuum or the microscopical model is the formulation of an extended continuum mechanical model which, on the one hand, makes it possible to capture the size effect but, on the other hand, does not need all the complex details of the underlying microstmcture of the polymer network. 

In the present study an extended continuum mechanical model is derived which is able to predict either weak or stiff boundary layers in thin films. As a possible application, the formation of interphases in polymer films is investigated. In this case it was shown [7, 24, 37] that the local stiffness in the polymer depends on the combination of polymer and substrate. 

Nanoscopic particles, dispersed in a block copolymer, have dimensions that are appropriate for Brownian dynamics simulations (268). Clay composites have a range of length scales, but if the gallery spacing between the layers is not large, MD methods can be used (269) with periodicity in the directions parallel to the clay platelets. However, continuum mechanical models need to be invoked for the description of exfoliated clay systems (270). These materials have so much interfacial area that adhesion properties are very important (271). Traditional continuum bounds methods (130) usually ignore the interphases on the grounds that they comprise a very small volume fraction of the total material, and so are not expected to be very accurate for exfoliated clay systems. 

Many computer modeling and simulation methods have been developed to study polymer nanocomposites with different nanofiller geometries. Resulting information on molecular simulation is very useful to understand the level of interaction at the interphase between polymer matrix and nanofiller. Molecular simulations results have been incorporated by several authors into continuum mechanics-based models in order to predict the mechanical behavior of polymer nanocomposites. 

In the present conribution, we develop a continuum-based model to describe experimentally observable interphases in thin adhesive films. The model is based on an extended contiuum theory, i.e. the mechanical behaviour in these interphases is captured by an additional field equation. The introduced scalar order parameter models the microscopical mechanical properties of the film phenomenologically. 

CONTINUUM AND STATISTICAL MECHANICS-BASED MODELS FOR SOLID-ELECTROLYTE INTERPHASES IN LITHIUM-ION BATTERIES... 

Chapter 6. Continuum and statistical mechanics-based models for solid-electrolyte interphases in lithium-ion batteries... 

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