Ionic polymer-metal composite (IPMC) is a polyelectrolyte (usually Nafion or Femion swollen by simple salt solution) strip or membrane with both sides plated with metal electrodes. It is a particular design of electroactive-polymer device rather than a new class of material. When a voltage is applied between its electrodes, it will bend toward either electrode depending on the polarity (anode for a negatively charged gel), and the magnitude of deformation could be controlled by the electric signal.  Reversely, the deformation of an IPMC can generate electric signal or even energy output [1-4].  Therefore IPMC has recently becomes a hot topic in actuation, sensor and energy harvesting applications, especially when integrated with the characteristics of certain gels that are responsive to other environmental stimuli such as pH value or temperature.

Compared to traditional actuation devices, the IPMC is small, simple, low-cost, resilient, noise-free, biocompatible, works at low voltage and capable of large deformation [a].  However, it also suffers from several problems: its actuation response is non-linear and also followed by non-controllable relaxation, its response is relatively slow, its working voltage is limited by the electrolysis of swelling media, its performance deteriorates in the long term as swelling media evaporates, its operation is time and history dependent, and so on [5, 6].  There have been numerous experimental efforts to overcome these problems by changing the swelling media or modifying the structures of polymer matrix and electrodes [7-10].

On the other hand, the underlying mechanism of IPMCs has yet to be fully understood.  Deformation theories of polyelectrolyte gel [b] were initiated almost at the same time as when Oguro published his first design of IPMC [11].  By using the same frame work, equilibrium and kinetics of bending of IPMC was then calculated [12, 13].  It is suggested that free ions drift under electric field, the concentration gradient creates osmotic pressure difference that drives the gel to bend, which is balanced by the elastic resistance of the matrix, while the kinetics is formulated by phenomenological law of porelasticity and diffusion rather than viscoelasticity [c].  Later another stress part is added to include the collective behavior of fixed charges [14-17].  A detail model of this stress is presented for Nafion by Nemat-Nasser [18], who assumes that Nafion contains solution clusters and a hydrophilic polymer matrix, with the detailed morphology determined by the level of hydration, as suggested by materials models [19, 20].  A double layer of ions forms at phase boundary where the electro-static interaction of the ordered polarized results in a net excess pressure.  Although the essential microstructural features are captured, more assumptions have to be made in order to incorporate this effect in the general framework of continuum theory.

A nonlinear field theory for polyelectrolyte gels recently proposed [21] provides a way of describing the deformation and electrochemistry of polyelectrolyte gels.  The theory suggests that the equilibrium behavior of a polyelectrolyte gel is fully determined by its free-energy density, as a function of strain, electric displacement, and concentration of mobile species.  The concept of osmotic pressure, which has often been used without a physical definition [22, d], is introduced as a Lagrange multiplier for the incompressibility constraint.  The equations that govern the evolution of polyelectrolyte gels in a nonequilibrium state are formulated, based on the conservation law of all mobile species and the kinetic equations that relates the diffusion flux of mobile species to its driving force, the gradient of the chemical potential.  A self-consistent model shall have the chemical potential derived from the free-energy function as well, containing contributions from the elasticity of the polymer, the concentration of mobile species, and the electric field.  If specific combinations of the free-energy function and the kinetic laws are chosen, one could recover the Nernst-Planck equation, an evolution equation often used in various models [15, 16].  Clearly, a gap exists between the microstructure of the material and its free-energy function / kinetic law.  The following questions may need to be answered before we can fill in this gap in theoretical understanding.

 1. The effect of the microstructure and thickness of the electrodes/interfaces

One of the important conclusions by existing models is that there is an ion-depletion region near the electrode and the deformation is determined by this boundary layer [18].  However, most models simply assume a sharp interface between electrode and polymer matrix.  Under such an assumption, in an equilibrium or steady state, the physical laws and a simple dimensional analysis will lead to a result that the bulk of a gel is electroneutral except for the boundary layer, characterized by the Debye length.  While an 1D analysis can estimate a bending moment induced by the ultra high stress in the thin boundary layer, 3D continuum mechanics indicates that a surface compressive stress may rather cause surface instabilities such as wrinkle and crease.  On the other hand, an effective IPMC design actually needs the electrode metal particles to infiltrate into polymer matrix, and experiments also suggest a strong correlation between the actuation strain and the morphology and thickness of electrodes [23, 24]. It is possible that the energy is majorly stored in the “vague” electrode-polymer interface, or the microstructured electrode with finite thickness, rather than in the thin boundary layer between the polyelectrolyte and a mathematically sharp interface?

 2. Are the basic laws of electrostatics still valid in an electrolyte-metal composite?

In most existing models of IMPC, the governing equation for the electric field, namely the Poisson-Boltzmann equation, is derived from the Gauss’s law of electrostatics.  A homogeneous polyelectrolyte mixture is sometimes treated as a dielectric medium when all charged particles are excluded [21].  However, for a material with microstructures of various length scales, the validity of such an assumption has never been discussed.  For example, the mixture of metal, polyelectrolyte, and ionic solution at the interfaces, which seems to play an important role, turns out to be a medium that is both an electric conductor and an ionic conductor.  Even for the case when the structure is random, a proper way of homogenization is a challenge.  Other examples include the microporous structure of Nafion, in which the mobile charges are distributed in order, and the distribution interacts with the macroscopic electric field.

 3. The origin and mechanism of the electrostatic and ionic contributions to force/stress 

The definition and notation of electrostatic forces in solids have always been controversial, as commented by Zhigang in his paper on deformable dielectrics.  In a system containing dielectric polymer and solvent, mobile and immobile ions, and even electronic conductors, the “force” or “stress” in a continuum mechanics manner is even hard to imagine.  Maybe one should rather avoid ambiguous terms like force and stress.  A question that arises naturally is how the charges carried by the polymer network and the mobile ions interact with each other and with external field, and further affect the system as a whole.  The answers to such a question have impacts much broader than just calculating the bending of a polymer strip.  For example, biological tissues are materials of similar or more complex structures.  Qualitatively, it has been argued that the main contributions include the electrostatic repulsions between fixed charges and the osmosis by the concentration difference of mobile ions in the solvent [25].

An approach often used (e.g. in multiphasic theories) is the introduction of the chemical expansion stress [26] or similarly the eigenstrain [e], the thermodynamic validity of which is put into question recently [27].  Another approach is the use of the Maxell stress in dielectrics through homogenizing the charge distribution.

Alternatively, one could start from the microstructure of the material and sum over all the ion-ion interactions, an approach similar to statistical physics or atomistic simulations [28].  However, similar as one calculating Maxwell stress, careful sum over all interaction pairs need to be performed, which also introduces the question of how microstructures (e.g. electric double layers) will evolve in response to the change in macroscopic fields.

IPMC is not only interesting in application, but also one of the model systems of natural soft materials with tunable parameters.  Modeling it may sever as the first step towards understanding the mechanics of soft matters.

Key References:

[a] M. Shahinpoor and K. J. Kim, “Ionic polymer-metal composite: I Fundamentals”, Smart Mater. Struct. 10, 819 (2001)

[b] M. Doi, M. Matsumoto and Y. Hirose, “Deformation of ionic polymeric gels by electric fields” J. Macrocol. 20, 5504 (1992):

[c] P. G. deGennes, K. Okumura, M. Shahinpoor and K. J. Kim, “Mechanoelectric effects in ionic gels”, Europhys. Lett. 50(4) 513 (2000)

[d] M. Shahinpoor, “Continuum eletromechanics of ionic polymeric gels as artificial muscles for robtotic applications”, Smart. Mater. Struct. 3, 367 (1994)

[e] S. Nemat-Nasser, “Micromechanics of actuation of ionic polymer-metal composites”, J Appl Phys 95 (5): 2899 (2002)

[f] K. J. Kim and M. Shahinpoor, “Ionic polymer-metal composite: II Manufacturing technique”, Smart Mater. Struct. 12, 65 (2003)

[g] M. Shahinpoor and K. J. Kim, “Ionic polymer-metal composite: III Modeling and simulations as biomemetic sensors, actuators, transducers and artificial muscles”, Smart Mater. Struct. 10, 819 (2001)

[h] M. Shahinpoor and K. J. Kim, “Ionic polymer-metal composite: IV industrial and medical applications”, Smart Mater. Struct. 13, 1362 (2004)

Other References:

[1] K. Asaka, K. Oguro, Y. Nishimura, M. Mizuhat and H. Takenaka, “Bending of polyelectrolyte membrane-platinum composites by electric stimuli I”, Polymer J. 27(4) , 436 (1995)

[2] K. Sadeghipour, R. Salomon and S. Neogi, “Development of a novel electrochemically active membrane and smart material based vibration sensor/damper” Smart Mater. Struct. 1, 172 (1992)

[3] M. Shahinpoor, Y. Bar-Cohen, J. O. Simpson and J. Smith, “Ionic polymer-metal composite as biomimetic sensors, actuators and artificial muscles – a review”, Smart Mater. Struct. 7, 15 (1998)

[4] M. Aureli, C. Prince, M. Porfiri and S. D. Peterson, “Energy harvesting from base excitation of ionic polymer metal composites in fluid environment”, Smart Mater Struct 19, 015003 (2010)

[5] Y. Bar-Cohen, S. Leary, A. Yavrouian, K. Oguro, S. Tadoro, J. Harrizion, J. Simith and J. Su, “Chanllenges to the application of IPMC as actuators of planerary mechanis”, Proc SPIE Smart Struc. Mater. Sympo. 3987-21 (2000)

[6] X. Bao, Y. Bar-Cohen and S. Lih, “Measurements and macro models of ionomeric polymer-metal composties”, Proc. SPIE Smart Struc. Mater. Sympo. 4695-27 (2002)

[7] S. Nemat-Nasser and Y. Wu, “Comparative experimental study of ionic polymer-metal composites with different backbone ionomer and in various cation forms”, J Appl. Phys. 93(9), 5255 (2003)

[8] B. J. Akle, M. D. Bennett and D. J. Leo, “High-strain ionomeric ionic liquid electroactive actuators”, Sens. Actuators, A 126(1), 173 (2006)

[9] N. Kamamichi, M. Yamakita, T. Kozuki, K. Asaka and Z. W. Luo, “Doping effects on robotic system with ionic polymer-metal composite actuators”, Adv. Rob. 21(1-2), 65 (2007)

[10] S. Liu, R. Montazami, Y. Liu, V. Jain, M. Lin, X. Zhou, J. R. Heflin, Q.M. Zhang, “Influence of the conductor network composites on the electromechanical performance of ionic polymer conductor network composite actuators”, Sensors and Actuators A 157, 267 (2010)

[11] K.Oguro, Y. Kawami and H. Takenaka, “Bending of an ion-conducting polymer film electrode composite by an electric stimulus at low voltage”, J. Micromachine SOC 5, 27 (1992)

[12] D. Segalman, W. Witkowski, D. Adolf, M. Shahinpoor, “Electrically-controlled polymeric gels as active materials in adaptive structures”, Smart Mater Struct 1, 95 (1992)

[13] M. Shahinpoor, “Continuum eletromechanics of ionic polymeric gels as artificial muscles for robtotic applications”, Smart. Mater. Struct. 3, 367 (1994)

[14] J. Firmrite, H. Struchtrup and N. Djilali, “Transport phenomena in polymer electrolyte membranes I medeling framework”, J Electrochem. SOC 152(9), A1804 (2005)

[15] R. Luo, H. Li and K. Y. Lam, “Modeling and simulation of chemo-electro-mechanical behavior of pH-electric-senstive hydrogel”, Anal. Bioanal. Chem. 398, 863 (2007)

[16] M. Porfiri, “Charge dynamics in ionic polymer metal composite”, J Appl Phys 104, 104915 (2008)

[17] T. Wallmersperger, A. Horstmann, B. Kroplin and D. J. Leo, “Thermodynamical modeling of the eletromechanical behavior of ionic polymer metal composites”, J Intell. Mater. Syst. Struct. 20(6), 741 (2009)

[18] S. Nemat-Nasser, “Micromechanics of actuation of ionic polymer-metal composites”, J Appl Phys 95 (5): 2899 (2002)

[19] W. Y. Hsu and T. D. Gierke, “Elastic theory for ionic clustering in perfluorinated ionomers”, Macromol. 15, 101 (1982)

[20] K. A. Mauritz and R. B. Moor, “State of understanding of Nafion”, Chem. Rev. 104, 4535 (2004)

[21] W. Hong, X. Zhao, Z. Suo, “Large deformation and electrochemistry of polyelectrolyte gels” J Mech. Phys. Solids. 58, 558-577 (2010).

[22] P.J. Flory, in “Principles of polymer chemistry”, Ithaca, New York, Come11 University Press (1953)

[23] N. Fujiwara, K. Asaka, Y. Nishimura, K. Oguro and E. Torikai, “Preparation of gold-solid polymer electrolyte composite as electric stimuli-responsive materials”, Chem. Mater. 12, 1750 (2000)

[24] K. Onishi, S. Sewa, K. Asaka, N. Fujiwara and K. Oguro, “Morphology of electrodes and bending response of the polymer electrolyte actuator”, Electrochimica Acta 46, 737 (2000)

[25] V. C. Mow and X. E. Guo, “Mechano-electrochemical properties of aritcular cartilage: their inhomogeities and anisotrpies”, Annu. Rev. Biomed. Eng. 4, 175 (2002)

[26] W. M. Lai, J. S. Hou and V. C. Mow, “A triphasic theory for the swelling and deformation behavior of articular cartilage”, J. Biomech. Engr. 113, 245 (1991)

[27] J. H. Huyghe and W. Wilson, “On the thermodynamical admissibility of the triphasical theory of charged hydrated tissues”, J Biomech. Engr. 131, 044504 (2009)

[28] S. A. Rice and N Nagasawa, in “Polyelectrolyte solution, a theoretical introduction”, Academic Press, New York (1961)

This review is completed with the help of Xiao Wang.