Mechanical Properties of Nano-composites and Size-dependencies

Mechanical Properties of Nano-composites and Size-

dependencies

Presented byBiplab Gogoi

Department of Physics,Tezpur University

IntroductionNanomaterials describe in principle the materials of

which a single unit is sized between 1-100 nm. Nanomaterial or particles often exist, the typical size

dependent properties, which are mainly due to their relatively larger surface area.

A lot of the mechanical and physical properties of nanoparticles are quite different from bulk materials yielding a wide variety of new application.

NanowiresNanowires have attracted

considerable interest as nanoscale

interconnects and active

components of optical electronic devices and nanoelectromechanical systems (NEMS), etc

The size dependence of their mechanical properties is important for applying nanowires in NEMS etc.

ZnO Nanowires

The experimental and

theoretical results, comparing

investigations on oxide are fairly rare.

The nanomechanical practices of

1 D ZnO nanomaterials have turned into the core interest of a few experimental and theoretical examines.In this project, Young’s modulus of ZnO NW with diameters

ranging from 17 to 550 nm has been studied.

The size-related elastic properties can be analysed with regard to the approximate core-shell composites NW model.

A NW with adjusted surface layers can be treated as a composite wire shown in Fig.1 with a core-shell structure composed of a cylinder core having modulus of bulk material E0 and a surface shell coaxial with the core having a surface modulus Es which is associated to the surface bond length contractions.

The Core-Shell Composite NW Model

Flexural rigidity is the governing parameter for transverse deformation. We define EI as the effective flexural rigidity of the composite NW, with E the effective Young’s modulus in the axial direction. Neglecting shear deformation, we obtain

EI = E0I0 + ESIS, (1)

Where I0 and Is are the geometrical moment of inertia of cross-section of the core and the shell, respectively

(a) (b)FIG. 1 (a) Schematic illustration of the core-shell composite NW model;

(b) the cross section.

Substituting the value of I0 and Is to the equation (1), expanding and rearranging we obtain,

(2)

Where, rs is the depth of the shell and D is the diameter of

the Nanowire. The value is a critical parameter determining the tendency of the size dependence of the Young’s modulus.

We know that, the aspect ratio of a geometric shape is the ratio of its sizes in different dimension. The aspect ratio of the NW is the ratio of its length and diameter.

i.e., Or (3)Substituting the value of diameter to equation (2), we obtain (4)

The optimized curve fitting yields,

E0 = 139 GPa, and, rs = 4.4 nm. Here the length of the nanowire is assumed to be, L = 1000 nm. By changing the diameter of ZnO NWs and putting the equation (4) obtain

Table 1:Sl. no Diameter (D)

(nm) 

Aspect Ratio (σ) Young’s Modulus(E) GPa

1 17 58.8 204.1

2 20 50 201.6

3 50 20 175.99

4 80 12.5 167.2

5 100 10 144.35

FIG. 3 The plot shows the variation on the effective Young’s modulus deduced from Eq. (4), as a function of aspect ratio.

FIG. 2 The plot shows the variation on the effective Young’s modulus deduced from Eq. (2), as a function of Diameter

Fig. 2, shows that the increase of Young’s modulus of the nanowire with decrease in the diameter. Hence the Young’s moduli of ZnO nanowires dependent on the diameter of the NWs. For 100 nm diameter of the nanowire we can see that the result of Young’s modulus of the nanowires becomes almost same at it’s bulk material limit.

Fig. 3, shows a significant increase in the Young’s modulus of the ZnO nanowire with the increase in the aspect ratio (σ). For small values of aspect ratio (10 to 12.5), the increase in Young’s modulus is very sharp with respect to a change in aspect ratio. After aspect ratio reaches 20 there is a continuous increase in Young’s modulus.

From the study of POM/ZnO, SiO2-GO and PVC/CaCO3 nanocomposites, we notice that the all three composites are changing in the order of weight %. We plot the data in the datasheet,

It can be seen that Young’s modulus of POM/ZnO, SiO2-GO nanocomposites increased with increasing filler content. Young’s modulus of the PVC/CaCO 3 nanocomposites is shown to increase with the loading of CaCO3 up to 5 wt% and then decrease marginally at 7.5 wt%.

Youn

g’s

mod

ulus

(E in

GPa

)

Weight (%)

FIG. 4 Variation of Young’s modulus of various Nanocomposite systems with different nanoparticle loading (weight %).

Conclusion We carried out a theoretical study on the size-

dependence of Young’s modulus of ZnO nanowires. we conclude that,

1. Young’s modulus of ZnO nanowires increase with increase in aspect ratio (σ) of the wires.

2. The increase in Young’s modulus of the nanowires with decrease in the diameter. Hence the Young’s modulus of ZnO nanowires depends on the diameter of the nanowires.

3. Young’s modulus of nanocomposites depends on the weight and increases with increase in the filler content in the nanocomposites systems.

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