This research investigated comprehensively the fundamental science of estimating sorption, diffusion, and permeation of 1,3-butadiene and nitrogen in polydimethylsiloxane (PDMS), and zeolitic imidazolate frameworks (ZIFs) filled mixed-matrix membranes (MMMs). ZIF-8 and Ni-ZIF-8 nanocrystals were synthesized at room temperature and incorporated into PDMS at different loadings. The physical and chemical properties of both ZIFs have been studied by XRD, FTIR, SEM, EDX, and TGA, respectively. Synthesized Ni-ZIF-8/PDMS MMMs demonstrated homogeneous particle dispersion, improved particle-polymer adhesion, and better butadiene permeation under various testing conditions. 15% Ni-ZIF-8/PDMS MMM exhibits 1,3-butadiene permeance 323 GPU, which improved by 60% compared with PDMS, and 32% with 15% ZIF-8/PDMS MMM, while BD/N2 ideal selectivity of 19.5was higher 81% than PDMS, and 32% than 15% ZIF-8/PDMS MMM at 40°C and 1.5 bar. Additionally, Ni-ZIF-8/PDMS MMMs have improved the solution-diffusion properties of butadiene and decreased sorption enthalpy, entropy change, activation energies of diffusion, and permeability from PDMS and ZIF-8/PDMS.