### Carbon black (CB) main reinforcing fillers rubber

## Carbon black and Rubber

Carbon black (CB) and silica have been used as the main reinforcing fillers used to increase the performance of rubber. Since each filler has specific advantages, the use of silica/CB compounds improves the dynamic and mechanical properties of natural rubber vulcanization. However, the optimum ratio of silica to CB must be refined to provide optimum properties In this context, NR reinforcement with silica/CB hybrid in different ratios was studied to determine the optimal ratio. The total filling of the hybrid was 50 phr. The mechanical properties indicating the strengthening of NR vulcanizates such as tensile strength, tear resistance, wear resistance, crack growth resistance, increased thermal resistance and folding resistance were determined. The results showed that vulcanizates with 20 and 30 phr silica in the hybrid filler showed better mechanical properties.

## Effect of Carbon black mechanical and dynamic properties

Although natural rubber exhibits outstanding properties, reinforcing fillers are necessarily added to rubber in most cases to achieve appropriate properties in specific applications. A wide range of fine filler materials are used in the rubber industry for various purposes, which reduces material costs and improves the manufacturing process. Adding reinforcement fillers such as carbon black and silica in large amounts in tires results in special mechanical and dynamic properties in many rubber products. The prediction of the amount of rubber reinforcement is limited to the models for determining the elastic or viscoelastic behavior of polymer composites or It is rubber This is despite the fact that many characteristics, in addition to the filler volume fraction, are effective on the mechanical and dynamic properties of these composites. The main focus of this article is to review the impact of various filler characteristics, including surface chemistry, structure and shape, particle size, and especially the size distribution of filler particles on the reinforcement of different systems, including colloidal, polymer and rubber systems. Among the mentioned factors, the influence of the size distribution of filler particles in rubber systems has received more attention.

## Reinforcement models

Adding a hard filler to a soft matrix, either liquids or solids, increases the viscosity or elastic modulus of these materials. To estimate the properties of these composites, several models with specific assumptions have been presented, which are as follows:

The first model in this connection was presented by Einstein, in which the viscosity changes of a Newtonian fluid were calculated by adding hard spherical spheres without any interaction with each other, and the following equation was obtained.

## η_C=η_m (1+K_E V_p)

where η_c is the viscosity of the normal medium and η_m is the viscosity of the medium after the addition of spheres, KE is Einstein’s coefficient, which is equal to 2.5 for spherical particles, and ϕ is the volume fraction of spheres. Using the relationship = G_c/G_m η_C/η_m, equation (1) for the shear modulus of rubber solids by Einstein-Smallwood was expressed as follows:

## 2) G_C=G_m (1+2.5V_p)

In these two models, the effect of particle size in reinforcement is not considered, and also these models are used for low volume percentage of filler, because with the increase of volume percentage of filler, we will see the interference of the strain lines around the filler particles. Gut [11] In the following, he considered the effect of large amounts of filler and the interference of hydrodynamic effect for spherical particles and arrived at the following relationship.

## (3) G_c=G_M (1+K_E V_p+14.1V_P^2)

In the above relation, the term 〖V_P〗^2 expresses the effect of interaction between particles in a highly charged mixture. Guth further considered the effect of geometry and filler shape, which led to the following relationship

## (4) P>>1 G_C=G_M (1+0.67PV_P+1.62P^2 V_P^2)

For non-spherical particles, the shape factor p can be considered as the ratio of the length of the particles to their width.

G_c and G_m are the shear modulus of the filled rubber system and the system without filler, respectively. One of the equations that has various parameters to express the elastic behavior of composites with spherical particles in the matrix is Corner’s equation [1] for 〖G_P>G〗_m we have :

## (5) G_C=G_m(1+V_P/V_m (15(1-ν_m))/((8-10ν_m)))

where ν_m is Poisson’s ratio of the matrix. The above equation was modified by Nielsen as follows

## (6)(1+ABV_P)/(1-BδV_P) M=M_m

where the Bδ function depends on the percentage of particle arrangement and M is the modulus, which can be shear, elastic or bulk. Coefficient A is a function of factors such as filler geometry and Poisson ratio of the matrix, coefficient B is also a function of filler modulus and matrix modulus. To increase the accuracy of the hydrodynamic model in explaining the behavior of rubber-filled mixtures, Moony presented some amendments to model (1), similarity This model, with the corner model, was the presence of effects such as high filler concentration and the interference of the hydrodynamic effect of particles and the shape and aspect ratio of particles, which were not considered in Einstein and Smallwood’s equations.

## The effect of filler characteristics on the reinforcement of rubber compounds

## The effect of the specific surface of the filler

The specific surface of the filler has a great effect on the properties of the final mixture. It is generally believed that increasing the specific surface area of a filler increases the reinforcement of the final mixture. The effect of the specific surface area on the deformation of the filler network can be explained in such a way that with the increase of the specific surface area of the particles, their diameter decreases. In a certain structure and a certain amount of filler, with the decrease in the diameter of the particles, the size of the smaller filler clusters and their internal distances decrease. This increases the probability of forming a network of fillers, as a result, the dynamic modulus increases at low strains (G’0). Niedermeyer and Gotzer’s investigations on the SSBR mixture filled with different grades of carbon black, including N115, N220 and N339, which have the same structure but have different specific surface areas, are reviewed in the figure below [4]. As shown in Figure 1 given, in the case of the mixture containing N115 carbon black, G’0 increased with increasing the surface area or decreasing the size of the filler particles, and the phenomenon of pin or modulus loss due to the failure of the filler structure increased.