  Lacking a band gap largely limits the application of graphene in electronic
devices. Previous study shows that grain boundaries (GBs) in polycrystalline
graphene can dramatically alter the electrical properties of graphene. Here, we
investigate the band structure of polycrystalline graphene tuned by externally
imposed strains and intrinsic mismatch strains at the GB by density functional
theory (DFT) calculations. We found that graphene with symmetrical GBs
typically has zero band gap even with large uniaxial and biaxial strain.
However, some particular asymmetrical GBs can open a band gap in graphene and
their band structures can be substantially tuned by external strains. A maximum
band gap about 0.19 eV was observed in matched-armchair GB (5, 5) | (3, 7) with
a misorientation of {\theta}=13o when the applied uniaxial strain increases to
9%. Although mismatch strain is inevitable in asymmetrical GBs, it has a small
influence on the band gap of polycrystalline graphene.
