KEYWORDS: Polymers, Crystals, Electromechanical design, In vitro testing, Homogenization, Ferroelectric polymers, Data modeling, Computer simulations, Chemical elements
Polymer computational simulations enable the prediction of material properties, exploration of the microscopic and macroscopic phenomenon of materials, and guidance of in vitro macromolecular materials design. This paper presents a mesoscopic level, multiscale approach to generate a complex polymer morphology for future simulations of polymer chains aimed at the design of materials or the study of material properties, such as strain/stress relations and electromechanical properties. To generate a complex polymer morphology, a mesoscopic level model is developed, in which the polymer chains are modeled as one-dimensional homogeneous flexible chains, and the crystalline regions are modeled as rigid continuum bodies. The polymer domain is firstly discretized into a uniform mesh. Location, orientation, and size of crystalline regions can be either pre-defined or randomly distributed inside the polymer domain. Nodes of each cuboid element grid located within crystal units are marked as occupied. Then, a random walking process is applied to generate polymer chains. No overlap is permitted between polymer chains nor between polymer chains and crystalline regions. Chain propagation ceases upon reaching the crystal block surface. Polymer chain properties, such as longitudinal stiffness, bending stiffness, and torsional stiffness, are derived based on molecular structures. Interactions, those between polymer chains, and those between polymer chains and crystalline regions are derived based on Lennard-Jones forces. An explicit dynamic relaxation algorism is applied to minimize potential energy. This approach is much more efficient than MD simulation. The computing time required for this mesoscopic simulation is only 0.5-1% of MD simulation. Yet, nanoand micro-scale geometries of polymer morphology can still be analyzed in detail. Polyvinylidene difluoride (PVDF) is selected to demonstrate the efficiency and efficacy of this numerical model due to its high piezoelectric coefficient.
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.
The electrostrictive graft elastomer is a new type of electromechanically active polymer. Recently developed by NASA, it consists of flexible backbone chains, each with side chains, called grafts. Grafts from neighboring backbones physically cross-link and form crystal units. The flexible backbone chains and the crystal graft units are composed of polarized monomers, which contain atoms with electric partial charges, generating dipole moments. Polarized domains are created by dipole moments in the crystal units. When the elastomer is placed into an electric field, external rotating moments are applied to polarized domains. It stimulates the rotation of the polarized crystal graft units, which further induces deformation of the elastomer. In this paper, two-dimensional computational models are established to analyze the deformation mechanism of the graft elastomer.
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