The analytical investigations of 3-miktoarm star (3-arm 𝜇-star) copolymers of type 𝐴₂𝐵 and 𝐴𝐵₂ are performed in the framework of mean-field approximation and Flory–Huggins theory. The total entropy of mixing and the Helmholtz free energy of interaction are calculated for the number 𝑁ᴀ monomers of type A and number 𝑁ʙ monomers of type B, respectively. The results confirm that the Helmholtz free energy of miktoarm star copolymers differs from that of polymer blends. The temperature dependence of the Helmholtz free energy allowed us to construct a phase diagram of the solution of miktoarm star copolymers, showing regions of stability, instability, and metastability. The analytical results confirm that a miktoarm star copolymer is not merely a mixture of different homo-arm star polymers and are consistent with a previous investigation performed by liquid chromatography under the critical conditions. Moreover, we performed molecular dynamics simulations of a dilute solution of 3-miktoarm star copolymer of type 𝐴₂𝐵 with a certain number of beads (300 + 300 + 200 + 1) and star copolymer of type 𝐴𝐵₂ with number of beads (300 + 200 + 200 + 1), accordingly. The calculations of the radius of gyration and monomer density profiles of the 3-miktoarm star copolymers of type 𝐴₂𝐵 and 𝐴𝐵₂ in confined geometry of two repulsive surfaces (Dirichlet–Dirichlet boundary conditions) and one repulsive and other one attractive surface (Dirichlet–Neumann boundary conditions) by molecular dynamics simulations are performed. The obtained analytical and numerical results indicate that a dilute solution of miktoarm star copolymers can be used in biotechnology and medicine for drug and gene transmission as well as for the production of new functional materials.
