Table 1 Correlation among hybrid nanostructures and nanomaterials in polymers.

Density \(\left( \rho \right)\)

\(\rho_{hnf} = \left( {1 - \varphi } \right)\rho_{f} + \varphi \rho_{s}\)

Heat capacity \(\left( {\rho c_{p} } \right)\)

\(\left( {\rho c_{p} } \right)_{hnf} = \left[ {\left( {1 - \varphi } \right)\rho_{f} + \varphi \rho_{s} } \right]\left[ {\left( {1 - \varphi } \right)c_{pf} + \varphi c_{ps} } \right]\)

Viscosity \(\left( \mu \right)\)

\(\mu_{hnf} = \left( {1 - \varphi } \right)^{ - 2.5} \mu_{f}\)

Thermal conductivity \(\left( K \right)\)

\(K_{hnf} = \left[ {\frac{{k_{1} + \left( {n_{1} - 1} \right)k_{f} - \left( {n_{1} - 1} \right)\varphi_{1} \left( {k_{f} - k_{1} } \right)}}{{k_{1} + \left( {n_{1} - 1} \right)k_{f} + \varphi_{1} \left( {k_{f} - k_{1} } \right)}}} \right] \times \left[ {\frac{{k_{1} + \left( {n_{1} - 1} \right)k_{f} - \left( {n_{1} - 1} \right)\varphi_{1} \left( {k_{f} - k_{1} } \right)}}{{k_{1} + \left( {n_{1} - 1} \right)k_{f} + \varphi_{1} \left( {k_{f} - k_{1} } \right)}}} \right] \times k_{f}\)

Thermal diffusivity (\(D_{hnf}\))

\(D_{hnf} = \left( {1 - \varphi } \right)d_{f}\)

Electrical conductivity (\(\sigma_{hnf}\))

\(\sigma_{hnf} = \left[ {\frac{{\sigma_{2} + 2\sigma_{nf} - 2\varphi_{2} \left( {\sigma_{nf} - \sigma_{2} } \right)}}{{\sigma_{2} + 2\sigma_{nf} + \varphi_{2} \left( {\sigma_{nf} - \sigma_{2} } \right)}}} \right]\left[ {\frac{{\sigma_{1} + 2\sigma_{f} - 2\varphi_{1} \left( {\sigma_{f} - \sigma_{1} } \right)}}{{\sigma_{1} + 2\sigma_{f} + \varphi_{1} \left( {\sigma_{f} - \sigma_{1} } \right)}}} \right]\)