Thermal and electrical properties of nanomaterials

Thermal and electrical properties of  nanomaterials

Thermal properties- An Introduction

                       Many properties of the nanoscale materials have been well studied, including the optical electrical, magnetic and mechanical properties. However, the thermal properties of nanomaterials have only seen slower progresses. This is partially due to the difficulties of experimentally measuring and controlling the thermal transport in nano scale dimensions.

                      Atomic force microscope (AFM) has been introduced to measure the thermal transport of nanostructures with nanometer-scale high spatial resolution, providing a promising way to probe the thermal properties with nanostructure. Moreover, the theoretical simulations and analysis and of thermal transport in nanostructures are still in infancy.

                     Available approaches including numerical solutions of Fourier’s law, computational calculation based on Boltzmann transport equation and Molecular-dynamics (MD) simulation, all have their limitations. More importantly, as the dimensions go down into nanoscale, the availability of the definition of temperature is in question.

Size – Nano Scale

                In nanomaterials systems, several factors such as the small size, the special shape, the large interfaces modified the thermal properties of the nanomaterials, rendering them the quite different behavior as compared to the macroscopic materials.    

                As mentioned above, as the dimension goes down to nano scales, the size of the nanomaterials is comparable to the wavelength and the mean free path of the photons, so that the photon transport within the materials will be changed significantly due the photon confinement and quantization of photon transport, resulting in modified thermal propeties.

Example

               For example, nanowires from silicon have a much smaller thermal conductivities compared to bulk silicon

Thermal Conductivity

•       Thermal Conductivity is the ratio of density of heat flow transmitted through the material to the temperature gradient in the material.

•       Unit- Wm^-1 K^-1

•       Nanowires from silicon have a much smaller thermal conductivities compared to bulk silicon.

                carbon nanotubes are carbon nanostructures relating to diamond and  graphite, which are well known for their high thermal conductivities.

                    The stiff sp3 bonds in diamond structure result in high phonon speed and consequently high thermal conductivities of the material. In carbon nanotubes, the carbon atoms are held together by the even stronger sp2 bonds, so that the nanotube structures, consisting of seamlessly joined graphitic cylinders are expected to have extraordinarily high thermal conductivities. The rigidity of the these nanotubes, combined with virtual absence of atomic defects or coupling to soft photon modes of the embedding medium, should make isolated nanotubes very good candidates for efficient thermal conductors.

       Figure. Temperature dependence of the thermal conductivity for a (10, 10) carbon nanotube for temperatures below 400 K.

      They concluded that the thermal conductivity of an isolated (10, 10) nanotubes was dependent on the temperature and an extraordinarily high value of ~6600W/mK was resultant at room temperature, shown in Figure

Temperature and thermal conductivity

                

v  Figure 1.8: the thermal conductance of an individual MWNT (d=14 nm).

v  Lower inset: Solid line represents thermal conductivity of an individual MWNT (d=14 nm). Broken and dotted lines represent small (d=80 nm) and large bundles (d=200 nm) of MWNTs, respectively.

v  Upper inset: SEM image of the suspended islands with the individual MWNT.

v   The scale bar represents 10 mm.

                 

              These experimental values were in the range of the theoretical calculations, proved the high thermal conductivity of the carbon nanotubes experimentally.

               Due to their high thermal conductivities, carbon nanotubes or nanotubes based nanocomposite could be promising candidates for heat transport management in many applications such as in the integrated circuits, optoelectronic devices and MEMS structures.

Specific Heat Capacity

•      The amount of heat required to raise unit temperature for unit mass of the material.

•      Unit- J Kg^-1 K^-1

Thermal diffusivity

•      When temperature of the material is raised , the heat spreads with time and the temperature will be uniform over the material, If it is adiabatic to the environment.

•      Thermal diffusivity  -   Time-dependent heat transfer

•      Unit – m^2 s^-1

Thermal Effusivity

•      The capability to absorb heat when surface of material is heated is the thermal effusivity.

ELECTRICAL PROPERTIES OF NANOPARTICLES

Electrical properties – An Introduction

            The electrical conductivity is a material- dependent property which for metallic conductors is independent of the applied voltage or the flowing electrical current. In contrast, for semiconductor or insulators the conductivity usually increases with increasing applied voltage. 

          When reducing the geometric dimensions of a wire to nanometer or molecular dimensions.  Ohms law is no longer valid in any case. Rather, the strictly linear relationship between current and voltage is replaced by a nonlinear, non-ohmic characteristic.

     In order to understand these phenomena, it is necessary first to consider the mechanism of electrical conductivity, the conventional macroscopic case.

                             V= I R = I (1 / G);    G = I / V            à1

Where V= Applied voltage; I= electric current

              R= Resistance        ; G= Electrical conductance

Note:  G depends on geometric parameters. (length & cross section). But σ (electrical conductivity) is material dependent property and it is independent of the applied voltage or the flowing electric current (for metal). For semiconductor σ usually increases with increasing the applied voltage.

Conduction Mechanism of Nanoparticles

            In the ballistic conduction the scattering phenomena are no longer observed, classically zero resistivity is expected, but this is not observed because now quantum mechanical phenomena are occurring. In order to understand this ballistic conductivity Eq: 1 must be rewritten in a form which takes into account the transport of electricity by electrons. That is the electrical current I transports within a time interval ∆t the charge Q.

Fig 2:  Ballistic conductivity of an electrical current in a small electrical conductor.  Ballistic conductivity is not characterised by scattering of the free electrons in the lattice, as the geometric dimensions of the conductor are smaller than the mean free path length of the electrons.

Finally we get              

                                        G = (Ne²/h) × (λ/L)

            Here (L/λ) = n is the electron wave mode number.  Each electron wave mode can have two modes (spin up and spin down) leading to N = 2n; therefore, one finally obtains for the conductance of a short, thin wire with one mode      

     G = 2e² /h.

  Assuming m active modes in a wire, the conductance is G = 2me² /h.

            From above discussion, there are no longer any variables depending on the material or the geometry of the wire.  It is clear that the electrical conductance of a small, thin wire increases with the increment G₀ = 2e² /h = 7.72 ×10^-5S. Hence the conductance decreases with increasing voltage.

Electrical Parameters

Nanoparticles array shows environment–dependent electrical properties

(conductivity). These properties are modified by the chemical species present in its vicinity. The

Conductivity of nanoparticles is believed to occur due to:

1. Tunneling of electrons through the metal core.

2. Hopping of the electrons along the atoms constituting the chain of the legend molecule encapsulating the nanoparticle.

By changing the parameters of the nanoparticle such as its particle diameter, space between the particles and the number of layers, the conductivity of the system can be altered. The analyte can be made to interfere with any one of the processes and hence can help vary the conductivity. This could lead to a sensing of the analyte.