Theoretical study and enhancement of the birefringence of fluorinated poly(methacrylate)

Abstract

In this paper, the birefringences of two fluorinated polymers, namely, poly(trifluoroethyl methacrylate) (PMATRIFE) and poly(methacrylate of pentafluorophenyl) (PMAPF), are studied. It is found that the molecular structure and molecular orientation of these polymers are the two main factors influencing the birefringence. The calculations show that the material birefringence (Δn) of PMAPF is greater than that of PMATRIFE by 0.00009, while the intrinsic birefringence (Δn ₀) of PMATRIFE is greater than that of PMAPF by 0.0378. The lower Δn ₀ of PMAPF is caused by the benzene ring in the repeat unit. On the other hand, the planarity of the benzene ring can enhance the degree of orientation of the PMAPF molecular chains, which is three times larger than that of PMATRIFE, and consequently a larger Δn of PMAPF. Furthermore, the effect of different shear rates on the birefringences of PMATRIFE and PMAPF is examined. The calculations reveal that their Δns are enhanced.

Appendix

Modeling procedure of the fluorinated polymer materials

The polymer material models were generated by a procedure involving three steps, namely, building the repeating unit model, polymer molecular chain model, and polymer material system with periodic boundary conditions.

The polymer molecular chain models were generated from the optimized repeat units shown in Fig. 2. Geometry optimizations of these molecular chain models were performed with the Forcite program available with MS (referred hereafter as MS/Forcite), using the parameters: convergence criterion of energy of 2 × 10⁻⁵ kcal/mol, convergence of maximum displacement of 10⁻⁵ Å, COMPASSII force field, the summation methods and the cutoff distances of electrostatic and vdW energies are both atom based and 18.5 Å. The optimized molecular chain structures are shown in Fig. 6.

Fig. 6

The optimized molecular chain models of a PMATRIFE and b PMAPF

The polymer material systems were built from the above optimized polymer molecular chains by generating a simulation cell containing m = 30 chains. Next, geometry optimization was performed for the polymer material models. The optimized fluorinated polymer materials are shown in Fig. 7. From Fig. 7, we can see that the molecules are separated by very large spaces. This is because the two fluorinated polymers have initial densities that are much less than the actual densities.

Fig. 7

The optimized polymer materials, including 30 molecular chains, of a PMATRIFE and b PMAPF

Therefore, in order to obtain a more realistic model of the fluorinated polymer materials, it was necessary to perform MD simulations using the optimized structures depicted in Fig. 7. The MD simulations involved three steps: a high temperature relaxation, an annealing process, and a MD at room temperature. The purpose of the high temperature relaxation is to balance the polymer system. The parameters of the high temperature relaxation with MS/Forcite were an NVT ensemble, temperature set to 800 K, time step of 0.1 fs, total simulation time of 150 ps, and NHL thermostat. The polymer material models obtained after the high temperature relaxation are shown in Fig. 8.

Fig. 8

The polymer material models of a PMATRIFE and b PMAPF after high temperature relaxation

After the high temperature relaxation, the polymer material systems were annealed to the room temperature. The annealing parameters used with MS/Forcite were an NPT ensemble, 298 K as the room temperature, 0.1 fs time step, 200 ps of total simulation times, and NHL thermostat.

Finally, MD simulation was performed for the two annealed fluorinated polymer materials. The MD parameters in MS/Forcite were an NPT ensemble, 298 K temperature, and 0.1 fs time step, and total simulation times of 30 and 40 ps for PMATRIFE and PMAPF, respectively. The all-atom models of the two fluorinated polymers obtained after MD are displayed in Fig. 4 in the main text.