Twisted quantum affine algebras and equivariant $\phi$-coordinated modules for quantum vertex algebras

This paper is about establishing a natural connection of quantum affine algebras with quantum vertex algebras. Among the main results, we establish $\mathrm{\hslash }$-adic versions of the smash product construction of quantum vertex algebras and their $\phi$-coordinated quasi modules, which were obtained before in a sequel, we construct a family of $\mathrm{\hslash }$-adic quantum vertex algebras $V_L[[\mathrm{\hslash }]{]}^{\eta }$ as deformations of the lattice vertex algebras $V_L$, and establish a natural connection between twisted quantum affine algebras of type $A,D,E$ and equivariant $\phi$-coordinated quasi modules for the $\mathrm{\hslash }$-adic quantum vertex algebras $V_L[[\mathrm{\hslash }]{]}^{\eta }$ with certain specialized $\eta$.