^{1}

^{2}

^{*}

In this work, we had adopted solid states reaction kinetic model to calculate diffusion coefficient of graphite Gr in Gum Arabic (GA) as the function of temperatures and concentration D(
*t*, C). From the calculations we have found that the diffusion coefficient D increases with increasing temperature. At higher temperature the Gr atoms might get enough thermal energy to overcome the activation energy (Ea) barrier and hence can easily be transported to a new atomic position. Diffusion coefficient of Gr at high concentrations had exceeded that at low concentrations by more than two to three orders of magnitude. Such increase can be attributed to the large number of jumps or jump frequency which found to be directly proportion to the Gr concentration. Electric conductivity, calculated by Nernst-Einstein equation, at high concentration Gr had exceeded that at lower concentration. The decrease in conductivity with decreasing Gr concentration might be attributed to the effective charges interactions, which lead to enhance the recombination of charge carriers.

Carbon had remained to be important for various applications due to its novel physical and chemical properties of its different isomers [

Gum Arabic and Graphite powder of high purities have been supplied by the Sudanese Gum Arabic and local Techno-Chemical local companies, respectively. Samples were prepared by solid state reaction by blending 1 g fine powder GA with 0.01, 0.09 and 0.25 g fine powder Gr forming, S_{1}, S_{2} and S_{3} respectively. The samples were subjected to thermal treatment at different temperatures (kelvin) ranging from 300,600 degree K at equal rate of 10 seconds.

Let us consider any two elements A and B in solid phase and let A type atoms be a solute and B type be a solvent atoms which are to be subjected mixing and heating. Due to such physical processing type A and B atoms may react to form composite. In our case the B-type atoms are GA whereas the A type are Gr. GA has said to be natural polymer of a complex chemical structure composed of different molecular groups of different chemical bonds. Which are highly affected by thermodynamic conditions.

Their atomic diffusion has been activated thermally. According to the thermodynamics the information concerning microstates can be traceable by the grand thermodynamic function includes macrostates variables such as volume, temperature, pressure etc. We will try to drive solid state reaction rate from the function of weight fraction calculated from the ratio between the mass difference before and after thermal treatment [

α = m 0 − m T m 0 − m f (1)

where, m 0 and m T are the weights before and after thermal treatment, respectively whereas m f is the final weight obtained at the final thermal treatment stage [

g ( α ) = k t (2)

where,

g ( α ) = [ 1 − ( 1 − α ) 1 3 ] 2 (3)

Hence,

k = ( 1 − ( 1 − α ) 1 3 ) 2 t (4)

According to Arrhenius equation

k = A e − E a R T (5)

where, A , E a and R are the frequency factor, activation energy and gas constant, respectively. The activation energy and the frequency factor can be estimated from the linear plot relation between 1 T v s . ln ( k ) . The activation energy calculated were used for determining the atomic diffusivity (D) according to the equation

D = D 0 e − E a R T (6)

The direct relation between atomic diffusivity (D) and electrical conductivity ( σ ) is given by Nernst-Einstein equation

σ = D N q 2 K B T (7)

where, N_{A}, q and K_{B} are Avogadro’s number, charge number and Boltzmann constant, respectively.

Diffusion coefficient of Gr had been calculated using solid state reaction kinetic model based on the temperature dependent mass variations [_{3} had exceeded that of S_{2} and S_{1} by 10 to 100 orders of magnitudes as shown in

Such vacancies represent high potential sites for diffusing Gr atoms in GA [_{1}, S_{2} and S_{3} as being depicted in _{3} exceeds that of S_{1} and S_{2}.GA/Gr composites has said to be highly disordered, the charge transport might be due to the quantum hopping which is to be supported by the interaction of thermal phonons with charge carriers and accordingly it moves from one site to another site of same or different energies [

σ ( T ) = σ 0 exp [ ( − T 0 T ) γ ] (8)

where the exponent γ is related to the dimensionality and γ = 1 4 .

The decrease in conductivity with decreasing Gr concentration might be attributed to the effective charges interactions, which lead to enhance the

recombination of charge carriers.

This work we had pinned pointed the effect of continuous thermal treatment on the Gr diffusion coefficients in GA and its effect in electrical conductivity of the Ga/Gr composite. The results had showed increase in the diffusion coefficient with temperature at high Gr concentrations. The increase in Gr concentration might results in considerable charge carrier’s interactions. It was clearly seen that, the electrical conductivity calculations indicate that the GA/Gr composite had turn into a semiconductor. Such processing had produced novel engineering material.

This work is supported by the Material Science Research Laboratory of Al-Neelain University and the Ministry of Higher Education and Scientific Research of the.

Adham, B.I. and El-Khair, H.M. (2018) Atomic Diffusion and Electric Conductivity of Gum Arabic/Graphite Composite. Journal of Materials Science and Chemical Engineering, 6, 91-96. https://doi.org/10.4236/msce.2018.67010