Using a pattern-based homogenization scheme for modeling the linear viscoelasticity of nano-reinforced polymers with an interphase

Moore

Journal of the Mechanics and Physics of Solids

2016

Inclusions comprised on filler particles and interphase regions commonly form complex morphologies in polymer nanocomposites. Addressing these morphologies as systems of overlapping simple shapes allows for the study of dilute particles, clustered particles, and interacting interphases all in one general modeling framework. To account for the material properties in these overlapping geometries, weighted-mean and additive overlapping conditions are introduced and the corresponding inclusion-wise integral equations are formulated. An extended micromechanics method based on these overlapping conditions for linear elastic and viscoelastic heterogeneous material is then developed. An important feature of the proposed approach is that the effect of both the geometric overlapping (clustered particles) and physical overlapping (interacting interphases) on the effective properties can be distinguished. We apply the extended micromechanics method to a viscoelastic polymer nanocomposite with interphase regions, and estimate the properties and thickness of the interphase region based on experimental data for carbon-black filled styrene butadiene rubbers.

Section: General Homogenizing Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An extended micromechanics method for probing interphase properties in polymer nanocomposites

Moore

Journal of the Mechanics and Physics of Solids

2016

Macromol. Rapid Commun.

“…The thickness of the interphase domain has been reported to have a wide range of values, from several nanometers to hundreds of nanometers in different material systems. [ 16,[32][33][34][35][36] And in thin polymer fi lms, some methods suggested strongly increased modulus, while others showed decreased modulus. The mechanisms causing the interphase, its extent, and magnitude of property changes imparted is still an open discussion in the literature.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Local Elastic Modulus in Confined Polymer Films via AFM Indentation

Cheng

Putz

Wood

et al. 2014

111

113

The properties of polymers near an interface are altered relative to their bulk value due both to chemical interaction and geometric confinement effects. For the past two decades, the dynamics of polymers in confined geometries (thin polymer film or nanocomposites with high-surface area particles) has been studied in detail, allowing progress to be made toward understanding the origin of the dynamic effects near interfaces. Observations of mechanical property enhancements in polymer nanocomposites have been attributed to similar origins. However, the existing measurement methods of these local mechanical properties have resulted in a variety of conflicting results on the change of mechanical properties of confined polymers. Here, an atomic force microscopy (AFM)-based method is demonstrated that directly measures the mechanical properties of polymers adjacent to a substrate with nanometer resolution. This method allows us to consistently observe the gradient in mechanical properties away from a substrate in various materials systems, and paves the way for a unified understanding of thermodynamic and mechanical response of polymers. This gradient is both longer (up to 170 nm) and of higher magnitude (50% increase) than expected from prior results. Through the use of this technique, we will be better able to understand how to design polymer nanocomposites and polymeric structures at the smallest length scale, which affects the fields of structures, electronics, and healthcare.

Journal of the Mechanics and Physics of Solids

“…By means of a combination of iterative and variational techniques, this fundamental dilute result is then utilized to generate in turn a solution for the homogenized nonlinear elastic response of non-Gaussian elastomers filled with an isotropic distribution of rigid particles and interphases at finite concentrations. Here, it is relevant to remark that the reinforcement of materials (not just elastomers) via the addition of inclusions bonded through finite-size interphases is a subject that has received considerable attention over the last three decades, but almost exclusively within the restricted small-deformation contexts of linear elasticity (see, e.g., Walpole, 1978;Mikata and Taya, 1985;Qiu and Weng, 1991;Herve and Zaoui, 1993;Duan et al, 2006) and linear viscoelasticity (see, e.g., Hashin, 1991;Diani et al, 2013;Diani and Gilormini, 2014).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Filled elastomers: A theory of filler reinforcement based on hydrodynamic and interphasial effects

Goudarzi

Spring

Paulino

et al. 2015

Experimental evidence has by now established that i) the hydrodynamic effect and ii) the presence of stiff interphases (commonly referred to as bound rubber) "bonding" the underlying elastomer to the fillers are the dominant microscopic mechanisms typically responsible for the enhanced macroscopic stiffness of filled elastomers. Yet, because of the technical difficulties of dealing with these fine-scale effects within the realm of finite deformations, the theoretical reproduction of the macroscopic mechanical response of filled elastomers has remained an open problem. The object of this paper is to put forward a microscopic field theory with the capability to describe, explain, and predict the macroscopic response of filled elastomers under arbitrarily large nonlinear elastic deformations directly in terms of: i) the nonlinear elastic properties of the elastomeric matrix, ii) the concentration of filler particles, and iii) the thickness and stiffness of the surrounding interphases. Attention is restricted to the prominent case of isotropic incompressible elastomers filled with a random and isotropic distribution of comparatively rigid fillers. The central idea of the theory rests on the construction of a homogenization solution for the fundamental problem of a Gaussian elastomer filled with a dilute concentration of rigid spherical particles bonded through Gaussian interphases of constant thickness, and on the extension of this solution to non-Gaussian elastomers filled with finite concentrations of particles and interphases by means of a combination of iterative and variational techniques. For demonstration purposes, the theory is compared with full 3D finite-element simulations of the largedeformation response of Gaussian and non-Gaussian elastomers reinforced by isotropic distributions of rigid spherical particles bonded through interphases of various finite sizes and stiffnesses, as well as with experimental data available from the literature. Good agreement is found in all of these comparisons. The implications of this agreement are discussed.