For the first time, the thermal conductivities of vulcanized polybutadiene and polyisoprene have been investigated according to their degree of crosslinking. The C-C and C-S-S-C crosslink bridges, which can be obtained via vulcanization processes using peroxides and sulfur, respectively, are considered. The temperature dependence of the thermal conductivity of soft rubber derived from molecular dynamics (MD) simulations is in very good agreement with the experimental results. The contributions of bonded and non-bonded interactions in the MD simulations and their influence on the thermal conductivities of polyisoprene and polybutadiene are presented. The details are discussed in this paper.

In this article, two main approaches to the prediction of thermal conductivities by molecular dynamics (MD) simulations are discussed, namely non-equilibrium molecular dynamics simulations (NEMD) and the application of the Green–Kubo formula, i.e., EMD. NEMD methods are more affected by size effects than EMD methods. The thermal conductivities of silicone rubbers in special were found as a function of the degree of crosslinking. Moreover, the thermal conductivities of thermoplastic polyurethane as function of the mass fraction of soft segments were obtained by those MD simulations. All results are in good agreement with data from the experimental literature. After the analysis of normalized heat flux autocorrelation functions, it has been revealed that heat in the polymers is mainly transferred by low-frequency phonons. Simulation details as well as advantages and disadvantages of the single methods are discussed in the article.

The thermal conductivities of untreated polyisoprene and polybutadiene were calculated by molecular dynamics (MD) simulations using a Green-Kubo approach between −10 °C and 50 °C at atmospheric pressure. For comparison, the thermal conductivities of untreated polyisoprene with a molecular weight of 54,000 g/mol and untreated polybutadiene with a molecular weight of 45,000 g/mol were measured by the transient hot wire method in similar conditions. The simulation results of both polymers are in good agreement with the experimental data. We observed that the MD simulations slightly overestimate the thermal conductivity due to the chosen force field description. Details are discussed in the paper.

Thermal conductivities of polybutadiene rubbers crosslinked by 2.4 and 2.8 phr of sulfur have been found to be functions of temperature via molecular dynamics (MD) simulations using the Green–Kubo method. From an analysis of the heat flux autocorrelation functions, it has been revealed that the dominant means of heat transport in rubbers is governed by deformations of polymeric chains. Thermal conductivities of rubber samples vulcanized by 2.4 and 2.8 phr of sulfur have been measured by the heat flow meter method between 0 ${}^{\circ }$C and 60 ${}^{\circ }$C at atmospheric pressure. The temperature dependencies of the thermal conductivities of rubbers and their glass transition temperatures derived from MD simulations are in good agreement with the literature and experimental data. Details are discussed in the paper.

Thermal conductivities of polybutadiene crosslinked with sulfur as a function of the heat flux autocorrelation function by using an equilibrium molecular dynamic (EMD) simulation were investigated. The Green–Kubo method was used to calculate thermal conductivities. All simulations were performed by applying the LAMMPS software (version 3 Mar 2020) package. The united-atom force field (OPLS-UA) from the Moltemplate software (version 2.20.3) was applied in the simulations. The influence of uniform and random distributions of sulfur in polybutadiene on the final value of thermal conductivities was studied by polymeric model structures with similar and variable degrees of crosslinking. The results showed that for identical degrees of crosslinking, the distribution of crosslinkers in the polymeric model structures significantly influenced the final value of thermal conductivity. Moreover, the influence of the crosslinking degree on the final value of thermal conductivity was studied by considering polymeric model structures with different degrees of crosslinking. The results demonstrate that by having a random distribution of sulfur, the thermal conductivity will be enhanced. However, by increasing the degree of crosslinking to the higher percentage in random crosslinked model structures, the value of thermal conductivity drops significantly due to possible higher crystallization of the model structures, which decrease the degree of freedom for phonon contributions.

The thermal conductivities and glass transition temperatures of polybutadiene crosslinked with randomly distributed sulfur chains having different lengths from mono-sulfur (S1) to octa-sulfur (S8) were investigated. The thermal conductivities of the related models as a function of the heat flux autocorrelation function, applying an equilibrium molecular dynamic (EMD) simulation and the Green–Kubo method, were studied for a wide range of temperatures. The influence of the length of sulfur chains, degree of crosslinking, and molar mass of the crosslinker on the glass transition temperature and final values of thermal conductivities were studied. First, the degree of crosslinking is considered constant for the eight simulation models, from mono-sulfur (S1) to octa-sulfur (S8), while the molar mass of the sulfur is increases. The results show that the thermal conductivities of the crosslinked structure decrease with increasing temperature for each model. Moreover, by increasing the lengths of the sulfur chains and the molar weight of the crosslinker, thermal conductivity increases at a constant temperature. The MD simulation demonstrates that the glass transition temperature and density of the crosslinked structure enhance as the length of the sulfur chains and molar mass of the sulfur increase. Second, the molar weight of sulfur is considered constant in these eight models; therefore, the degree of crosslinking decreases with the increase in the lengths of the sulfur chains. The results show that the thermal conductivities of the crosslinked structure decrease with the increase in the temperature for each model. Moreover, by increasing the lengths of sulfur chains and thus decreasing the degree of crosslinking, the trend in changes in thermal conductivities are almost the same for all of these models, so thermal conductivity is constant for a specific temperature. In addition, the glass transition temperature and density of the crosslinked structure decrease.