Nanocomposites analytical models

The analytical expressions of micromechanics are generally most accurate at low volume fractions of the filler phase. The details of the morphology become increasingly more important at higher volume fractions. This fact was illustrated by Bush [64] with boundary element simulations of the elastic properties of particulate-reinforced and whisker-reinforced composites. The volume fraction at which such details become more important decreases with increasing filler anisotropy, as was shown by Fredrickson and Bicerano [60] in the context of analytical models for the permeability of nanocomposites. 

Computational approach can play an important role in the development of the CNT-based eomposites by providing simulation results to help on the understanding, analysis and design of sueh nanocomposites. At the nanoscale, analytical models are difficult to establish or too complicated to solve, and tests are extremely difficult and expensive to eonduct. Modeling and simulations of nanoeomposites, on the other hand, ean be achieved readily and eost effectively on even a desktop computer. Characterizing the meehanieal properties of CNT-based composites is just one of the many important and urgent tasks that simulations can follow out [72]. 

Micromechanical models have been widely used to estimate the mechanical and transport properties of composite materials. For nanocomposites, such analytical models are still preferred due to their predictive power, low computational cost, and reasonable accuracy for some simplified stmctures. Recenfly, these analytical models have been extended to estimate the mechanical and physical properties of nanocomposites. Among them, the rule of mixtures is the simplest and most intuitive approach to estimate approximately the properties of composite materials. The Halpin-Tsai model is a well-known analytical model for predicting the stiffness of unidirectional composites as a function of filler aspect ratio. The Mori-Tanaka model is based on the principles of the Eshelby s inclusion model for predicting the elastic stress field in and around the eflipsoidal filler in an infinite matrix. 

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). 

Intercalated compounds offer a unique avenue for studying the static and dynamic properties of small molecules and macromolecules in a confined environment. More specifically, layered nanocomposites are ideal model systems to study small molecule and polymer dynamics in restrictive environments with conventional analytical techniques, such as thermal analysis, NMR, dielectric spectroscopy and inelastic neutron scattering. Understanding the changes in the dynamics due to this extreme confinement (layer spacing < Rg and comparable to the statistical segment length of the polymer) would provide complementary information to those obtained from traditional Surface-Force Apparatus (SFA) measurements on confined polymers (confinement distances comparable to Rp [36]. 

Polymer silicate nanocomposites offer unique possibilities as model systems to study confined polymers or polymer brushes. The main advantages of these systems are (a) the structure and dynamics of nanoconfined polymer chains can be conveniently probed by conventional analytical techniques (such as scattering, DSC, NMR, dielectric spectroscopy, melt rheology) (b) a wide range of different polymers can be inserted in the interlayer or end-grafted to the silicate... 

Conducting experiments for material characterization of the nanocomposites is a very time consuming, expensive and difficult. Many researchers are now concentrating on developing both analytical and computational simulations. Molecular dynamics (MD) simulations are widely being used in modeling and... 

Liu, H. and Brinson, L.C. (2006) A hybrid numerical-analytical method for modeling the viscoelastic properties of polymer nanocomposites. Journal of Applied Mechanics, 73 (5), 758-768. 

Eor example, the effective elastic properties of silica nanopartides-reinforced polymer nanocomposites were predicted by means of various FEM-based computational models [70], induding an interphase layer around partides as a third constituent material in the prediction of the mechanical properties. Boutaleb et al. [30] studied the influence of structural characteristics on the overall behavior of silica spherical nanoparticles-polymer nanocomposites by means of analytical method and FEM. They assumed that the interphase between silica partide and polymer matrix presents a graded modulus, ranging from that of the silica to that of the polymer matrix, for example, a gradual transition from the properties of the silica to the properties of the polymer matrix (Figure 5.6). The change in elastic modulus in the interphase was described by a power law introducing a parameter linked to interfacial features. 

Understanding the fundamental issues from the atomic or molecular scale to macroscopic morphology in such a complex system is challenging. Most analytical theories [11] are severely limited for such complex systems that exhibit linear and nonlinear response properties on different spatial and temporal scales. Computer simulations remain the primary choice to probe multiscale phenomena from microscopic characteristics of constituents to macroscopic observables in such complex systems. Most real systems [9] are still too complex to be fully addressed by computing and computer simulations alone. Coarse-grained descriptions are almost unavoidable in developing models for such nanocomposite systems. 

In the work of lie et al., quantum dot nanocomposite electrodes were functionalized with an antibody or a ligand for a receptor, and a decrease in ECL signal derived from the Cd8 or Cd8e nanocrystals was measured. Quantum dot nanocomposite ECL-based biosensors had a linear range of 0.002-500 ng mL" with a DL of 0.6 pg mL" using human IgG as a model analyte. ... 

Typical nonidealities such as polydispersity in filler size and conductivity, filler waviness and entanglements, and impurities impact the measured electrical properties of polymer nanocomposites. Most analytical and simulation studies of these nonidealities have been conducted for highly simplified systems, so that the extent to which these factors can modify composite properties, particularly within the context of more dominant factors such as filler dispersion and network stmcture, is unclear. To clarify the importance of these effects, theoretical analysis or modeling of more complex systems is required. Conducting parallel experiments in model systems can enhance the efficacy of such studies. 

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