Nanocomposites numerical methods

For appropriate comprehension of morphology and the concomitant structure-property correlations in nanocomposites, knowledge of the state and extent of nanofiller dispersion in the matrix is of paramount importance. Numerous methods have been reported in the literature in this regard, for instance, WAXD [6, 38], SAXS [8, 39], SANS [40], SEM, [6, 41], AFM [7, 42], HRTEM, STEM, EELS [43], SSNMR [44], EPRS [45], UV/vis/NIR, FTIR [46], Raman spectroscopy... 

On the basis of the theory of numerical methods and mathematical modeling the problem of the calculation and forecast of the distribution of the temperature field in a two-phase nanocomposite environment is solved. The mathematical statement of the problem is formulated as the integral equation of thermal balance with a heat flux taken into account, which changes according to Fourier s law. Jumps of enthalpy and heat conductivity coefficient are considered. Various numerical schemes and methods are examined and the best one is selected - the method of control volume. Calculation of the dynamics of the temperature field in the nanostructure is hold using the software. 

The molecular origins of mechanical reinforcement of polymer nanocomposites have been studied by various analytical and numerical methods, which led to two different opinions one attributes exclusively the reinforcement to nanoparticle... 

Numerous nanocomposite characterization methods are available thermogravimetric analysis (TGA), differential scanning calorimetry [DSC], transmission electron microscopy (TEM), scanning electron microscopy (SEM), X-ray diffraction (XRD), nuclear magnetic resonance (NMR), IR spectroscopy, Raman spectroscopy, X-ray photoelectron spectroscopy, dielectric relaxation spectroscopy, atomic force microscopy [AFM], electron spin resonance, continuous-wave and pulsed ESR spectroscopy and others [59]. Among all of the methods, TGA, DSC, wide-angle scattering diffraction [WAXS], and TEM are the most commonty used and will be discussed in detail. 

Applications. Numerous uses of x-ray analysis were reported for filled systems. They include orientation of talc particles in extruded thennoplastics, particle size deteimination in nanocomposites, crystallinity of talc nucleated PP, crystallinity of polymerization filled PE, diffraction pattern of filled PVA, structure of nanocomposites based on montmorillonite, degree of filler mixing, structural characteristics of fillers, structure of carbon black filled rubber, the effect of apatite concentration on the structure of wood pulp, and graphite as template. " This list shows the versatility of the method in applications to filled systems. 

Nanocomposites, in addition to small particle sizes usually are required to have a very uniform composition. These two requirements impose constraints on the methods of synthesis. In addition, the required form of the final product is given consideration in the choice of the method of their synthesis. These constraints resulted in numerous design strategies in methods of nanocomposite manufacture, discussed below. 

As for the linear properties, numerous approaches have been proposed to predict and explain the nonlinear optical response of nanocomposite materials beyond the hypothesis leading to the simple model presented above ( 3.2.2). Especially, Eq. (27) does not hold as soon as metal concentration is large and, a fortiori, reaches the percolation threshold. Several EMT or topological methods have then been developed to account for such regimes and for different types of material morphology, using different calculation methods [38, 81, 83, 88, 96-116]. Let us mention works devoted to ellipsoidal [99, 100, 109] or cylindrical [97] inclusions, effect of a shape distribution [110, 115], core-shell particles [114, 116], layered composites [103], nonlinear inclusions in a nonlinear host medium [88], linear inclusions in a nonlinear host medium [108], percolated media and fractals [101, 104-106, 108]. Attempts to simulate in a nonlinear EMT the influence of temperature have also been reported [107, 113]. 

Estimation of effective elastic moduli of nanocomposites was performed by the version of effective field method developed in the framework of qirasi-crystalline approximation when the spatial correlatiorts of inclrrsion location take particirlar ellipsoidal forms [71]. The independent justified choice of shapes of inclirsiorts arrd correlation holes provide the formttlae of effective modirli which are syrrrmetric, corrrpletely explicit, and easily to use. The parametric numerical analyses revealed the most sensitive parameters influencing the effective moduli which are defined by the axial elastic moduli of nanofibers rather than their transversal moduli as well as by the justified choice of correlation holes, concentration, and prescribed random orientation of nanofibers [72]. 

Considering the low physical characteristics of biopolymers, fillers are recommended for the reinforcement of their electrical, mechanical and thermal properties. Following the discovery of CNT, much work has been done regarding their application as fillers in other polymers, for improving the properties of the matrix polymer. At first CNT were used as a filler in epoxy resin, by the alignment method. Later on, numerous studies have focused on CNT as excellent substitutes for conventional nanofillers in nanocomposites and recently, many polymers and biopolymers have been reinforced by CNT. As already mentioned, these nanocomposites have remarkable characteristics, compared to the bulk materials, due to their imique properties. 

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