Determination of the Mechanical Properties of Amorphous and Semi-crystalline Polymers

Researchers at DKI (Deutsches Kunststoff - Institut) have used Accelrys' Amorphous Cell to evaluate various methods for determining the mechanical properties of amorphous and semi-crystalline polymers.

The findings will aid the development of new and improved plastics.

The aim of this study [1,2] was to evaluate various methods for determining the mechanical properties of amorphous and semi-crystalline polymers.

Bulk amorphous polymer structures were generated using Amorphous Cell, which involves construction of chains in a periodic cell, taking account of bond torsion probabilities and bulk packing requirements. The models were then equilibrated by a series of energy minimization and molecular dynamics runs. The crystal structures for the semicrystalline polymers were generated by using Crystal Cell. The quality of the resulting structure for both amorphous and cystalline structures were tested by comparing the X-ray scattering patterns determined from the molecular models with experimental data.

The simulated bulk structures were then subjected to three different methods for evaluating their mechanical behaviour: the static method, developed by Theodorou and Suter[3]; the fluctuation method of Parinello and Rahman[4]; and the dynamic method, originally introduced by Berendsen et al.[5] and adopted by Brown and Clarke[6]. In the static method, each structure was subjected to a number of successive deformations followed by a reminimization in order to map out the energy hypersurface and subsequently determine the elastic modulus. The dynamic method involves using constant stress molecular dynamics to measure the stress-strain behavior of a material subjected to an applied load. For the dynamic method a force field (united atoms) and a software developed in the group of Professor J. H. R. Clark from Manchester University was used[7].The fluctuation method makes use of the fact that the elastic constants appear in the fluctuation formulae applied to statistical ensembles obtained by simulation. For the static method, the procedure is illustrated in Fig. 1 for the case of poly(-ether-sulfone-).

Fig. 1 Schematic illustration of the procedure applied in the simulation of the mechanical properties of amorphous poly(-ether-sulfone-): (a) the chemical formula and (b) energy minimized molecular model of the monomer; (c) an amorphous cell of polyethersulfone chains; (d) the X-ray scattering intensity determined from the amorphous cell compared with experimental data; (e) principle of the mechanical test; (f) the potential energy obtained from the mechanical properties simulation

The methods were tested on several amorpous and semicystalline polymers (polysulfone, polyethersulfone, polypropylene). Investigations for other polymers are in progress (PEEK, polyethylene). The dynamic method and the fluctuation method gave reasonable agreement with experimental measurements, whereas the moduli obtained with the static method are considerably too high and gave only an upper limit.

The case of semi-crystalline polymers was treated by independently simulating the crystalline and amorphous phases of isotactic polyproylene, and using the simulated elastic constants as input to micro-mechanical models[8]. The resulting composite behaviour was also found to be in good qualitative agreement with experiment.

This work was supported by the Bundesministerium für Wirtschaft through the Arbeitsgemeinschaft industrieller Forschungsgemeinschaften (AiF) Grants No 11314N and 12980N, and by the SUPERNET programm of the European Science Foundation (ESF).

References

1. I. Alig, M. Kröhn, R. Hentschke, and M. Soliman, "Molekulares Modellieren in der Polymerforschung", Spektrum der Wissenschaft, 6 (1996) 106.
2. I. Alig, M. Kröhn, and R. Hentschke, "Molekulares Modellieren in Polymersystemen", Spektrum der Wissenschaft Digest, 1 (2000) 78.
3. D.N. Theodorou, U.W. Suter; Macromolecules, 19 (1986) 139.
4. M. Parrinello, A. Rahman; J. Chem. Phys., 76 (1982) 2662.
5. H.J.C. Berendsen et al.; jJ. Chem. Phys., 81 (1984) 3684.
6. D. Brown, J.H.R. Clarke; Macromolecules, 24 (1991) 2075.
7. M. Kröhn, J.H.R. Clarke, ESF Resarch Report, June 2000.
8. J.C. Halpin, J.L. Kardos; J. Appl. Phys., 43 (1972), 2235.