Energetics In Computational Simulation Of Ionic Polymer

Electroactive Polymer (EAP)

Electroactive Polymer

Table 1. Comparison of the properties of EAP, SMA, and EAC

Property	EAP	SMA	EAC
Actuation strain	>10%	<8% short fatigue life	0.1-0.3%
Force (MPa)	0.1-3	about 700	30-40
Reaction speed	μsec to min	sec to min	μsec to sec
Density	1-2.5 g/cc	5-6 g/cc	6-8 g/cc
Drive voltage	2-7 V/10-150 V/ μm	not applicable	50-100 V
Consumed pwr.	m-watts	watts	watts
Fracture toughness	resilient, elastic	elastic	fragile

As an actuator, Ionic Polymer has greater actuation displacement and can be operated under much lower voltages than other electroactive materials.

EAP — Polymers that exhibit shape change in response to electrical stimulation:

• Electronic EAP (driven by electric field or Coulomb forces)
  • Ferroelectric Polymers: Piezoelectricity is found only in noncentro-symmetric materials and the phenomenon is called ferroelectricity when a nonconducting crystal or dielectric material exhibits spontaneous electric polarization. For expample: Poly(vinylidene fluoride)(PVDF) and its copolymers
  • Dielectric EAP: Polymers with low elastic stiffness and high dielectric constant can be used to induce large actuation strain by subjecting them to an electrostatic field. When a voltage is applied across the compliant electrodes on both side of the polymer film, the polymer shrinks in thickness and expands in area. For example: Dielectric elastomers

• Ionic EAP (involving mobility or diffusion of ions)
  • Ionic Polymer-Metal Composites (IPMCs)

Ionic polymers comprise the active layer in IPMCs

Applications

Applications of Ionic Polymers

• IPMCs
  • Artificial Muscles
  • Actuators
  • Biomimetic Sensors
• Polymer Electrolyte Membrane Fuel Cells (PEM FCs)
• Ion Exchange Membranes (IEMs)
  • Water Purification
  • Separation of CO2 from Flue Gas

The biocompatibility coupled with high gravimetric energy density and cryogenic functionality of ionic polymers, has led to considerable conjecture over potential applications. Despite the broad range of ionic polymer existing and potential applications, the physical mechanisms responsible for this material’s active response are not yet fully understood.

A better understanding of their mechanical properties is needed to fully exploit these applications.

Two Widely Used Ionic Polymers

• Nafion® (a sulfonated tetrafluorethylene copolymer by DuPont)
• Selemion® (a hydrocarbon type IEM by AGC)

Chemical Structure of Nafion

Chemical Structure of Selemion

Cluster Morphology

Cluster Morphology in Nafion® Polymer Model by Hsu and Gierke (1982)

• Polymer chains making up the material are composed of a hydrophobic backbone with side chains that terminate in hydrophilic ionic groups. These polymer chains interact with each other so that they form hydrophobic and hydrophilic regions.
• When the material is solvated with water, these hydrophilic ionic side groups and the water that has been taken up by the material cluster together.
• The embedded clusters are of essentially constant radius, uniformly distributed throughout the material, and interconnected by channels.

Cluster Shape
By minimizing the sum of (1) the electro-elastic interaction energy between an ionic cluster and the fluorocarbon matrix, and (2) the cluster surface energy, it is concluded that the effective cluster shape is spherical in the absence of an electric field.

Cluster Size
The cluster size is determined from the minimization of the free energy as a function of (1) the equivalent weight of Nafion®, (2) the volume fraction of water, and (3) the temperature, taking into account (1) the electrostatic dipole interaction energy, (2) the elastic polymer chain reorganization energy, and (3) the cluster surface energy.

Calculation of Cluster size for Selemion

Multiscale Model

Nanoscopic Model for Estimating Chain Length

• Rotational Isomeric State (RIS) theory (by Flory, used to build atomic scale models to study deformation trends and material properties in polymeric materials)
  • Bond length lc-c=1.53 Å
  • Valence angle θ=116°
  • Rotation angle φ=±15 ° and ±120 °
  • Statistical Weight matrices Uj for bond j

The fundamental idea of this approach is that any given bond within a single polymer chain is restricted to a discrete number of possible low energy bond angles, dictated largely by the interaction with the nearest-neighbor bond.

• RIS-Monte Carlo (MC) theory by Mark and Curro (1983)
  • The stochastic element of the Monte Carlo simulation focuses on determining the angle of rotation φ for each bond by the weight matrices.
  • The previous bond rotational state determines which row of the matrix contains the probabilities to select the φ value for the current bond

Polymer Conformation -> end-to-end chain length r -> Probability Density Function P(r)

Macroscopic Model for Estimating Stiffness

• Boltzmann’s approach to statistical thermodynamics is used to relate the entropy of the chain to P(r)
• Under the assumption of rubberlike elasticity, the “three chain” model is applied.
• RIS theory assumes that under load, the rotation about a given bond is unrestricted and thus the Helmholtz free energy is strictly a function of entropy.

Stiffness Predictions
Please refer to the uploaded file Notes.pdf.

References

References

Ionic Polymer

• Introduction:
  • Y. Bar-Cohen: Electroactive polymer (EAP) Actuators as Artificial Muscles—Reality, Potential, and Challenges, SPIE, The International Society for Optical Engineering (Bellingham, WA, 2001).
  • Electroactive polymer: http://en.wikipedia.org/wiki/Electroactive_polymers
  • Ionic Polymer Metal Comosite (IPMC): http://en.wikipedia.org/wiki/Ionic_polymer-metal_composite
• Applications: Proton exchange membrane fuel cells (PEM FCs)
• Widely used ionic polymers: Nafion, Selemion

Computational Simulation

• P.J. Flory: Statistical Mechanics of Chain Molecules (Hanser Publisher, New York, NY, 1988).
• J.E. Mark and J.G. Curro: A non-Gaussian theory of rubberlike elasticity based on rotational isomeric state simulations of network chain configurations. I. Polyethylene and polydimehylsiloxane short-chain unimodal networks. J. Chem. Phys. 79(11), 5705 (1983).
• V.K. Datye and P.L. Taylor: Electrostatic contributions to the free energy of clustering of an ionomer. Macromolecules 18, 1479 (1985).
• J.Y. Li and S. Nemat-Nasser: Micromechanical analysis of ionic clustering in Nafion perfluorinated membrane. Mech. Mater. 32, 303 (2000)
• L.M. Weiland, E.K. Lada, R.C. Smith and D.J. Leo: Application of rotational isomeric state theory to ionic polymer stiffness predictions. J. Mater. Res. 20(9), 1 (2005).