Modified two-dimensional computational model for electrostrictive graft elastomer

A modified two-dimensional computational model is developed to calculate the electromechanical properties of the electrostrictive graft elastomer. The electrostrictive graft elastomer, recently developed by NASA, is a type of electro-active polymer. In a previous paper, the authors calculated electrostrictive graft elastomer electromechanical properties using a 2-D atomic force field. For this 2-D polymer structure, a much higher electric field was required to produce strain compared with that required in experiments. Two reasons could explain the higher electric field strength: (1) Polymer chain movement is restricted to a 2-D plane rather than to a 3-D plane. Out-plane dihedral torsional angle change would thus not be modeled. For this reason, 2-D polymer chains are less flexible than actual 3-D polymer chains. (2) Boundary effect of the computational model. In the original model, a unit cell consisting of a single graft unit was developed to simulate the deformation of the electrostrictive graft elastomer. The boundary of the unit cell would restrict the rotation of the graft unit. In this paper, a modified 2-D computational model is established to overcome the above problems. Firstly, three-dimensional deformations, induced by both bending angle and dihedral torsional angle changes, are projected onto a two-dimensional plane. Using both theoretical and numerical analyses, the projected 2-D equilibrium bending angle is shown to have the same value as the 3-D equilibrium bending angle. The 2-D equivalent bending stiffness is derived using a series model based upon the fact that both bending and dihedral torsion produce configuration change. The equivalent stiffness is justified by the characteristics of the polymer chain and end-to-end distance. Secondly, a self-consistent scheme is developed to eliminate the boundary effect. Eight images of the unit cell are created peripherally, with the original unit cell in the center. Thus the boundary can only affect the rotation of the eight images, not the central unit cell. The modified 2-D computational model is employed to determine the electromechanical properties of the electrostrictive graft elastomer. Relations between electric field induced strain and electric field strength is calculated. The effect of molecular scale factors, such as free volume fraction, graft weight percentage, and graft orientation are also discussed. The results should enable molecular scale design of the electrostrictive graft elastomer.