Macro-ion Characterization - American Chemical Society

Chapter 40 Biomimetic Macromolecular Actuators 1,2

1,2

Danilo De Rossi and Piero Chiarelli 1

Centro "E. Piaggio", Faculty of Engineering, University of Pisa, 56126 Pisa, Italy Institute of Clinical Physiology, CNR (Italian Research Council), 56126 Pisa, Italy

Downloaded by PURDUE UNIV on May 26, 2018 | https://pubs.acs.org Publication Date: December 13, 1993 | doi: 10.1021/bk-1994-0548.ch040

2

The dichotomy of man-made machines and biological machines is not an engineering dogma anymore. Recent research efforts in the field of molecular engineering led to substantial advances to the endevour of mimicking through synthetic pathways the functional characteristics of biological muscles. The effort to build sophisticated molecular engines has its foundation on methods techniques to synthesize, study and characterize new materials able to perform useful electromechanical work, starting from conformational changes on a molecular scale. An overview of electron-conducting polymer and polyelectrolyte gels based-actuators is presented. A continuum model of the electromechanical response and control strategies for polyelectrolyte gel actuators are discussed.

Organic materials can be used to create new sensors and actuators capable of measuring physical, chemical and biological parameters or of generating controllable forces and displacements. These novel transduction systems, which rise from research into intrinsic energy conversion characteristics of molecular aggregates and developments in molecular electronics, possess specific capabilities that may improve upon those of conventional materials. Whilst significant advances in solid state technology have allowed tremendous improvements in electronic processing, memory and display systems of modem instrumentation, this has not always been possible for transducers. In fact, transducers still remain highly specialized, delicate and costly and are often unreliable. Moreover, conventional transducers frequently limit the overall performance of an instrument and impose severe restrictions on its operating environment For decades the electronic applications of macromolecules made almost exclusive use of their dielectric properties and electrical insulation capacities. This general view of polymers changed when metal-like conductivity in doped polyacetylene was discovered in 1977. Electronic and ionic macromolecular conductors now offer much broader uses as actuation elements and are the subjects of intense investigation in several laboratories worldwide. Molecular based transducers are thus being studied in order to overcome measurement and actuation problems infieldssuch as bioengineering, advances robotics and pollution control, which inorganic materials cannot solve. 0097-6156/94A)548-0517$06.00A) © 1994 American Chemical Society

Schmitz; Macro-ion Characterization ACS Symposium Series; American Chemical Society: Washington, DC, 1993.

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MACRO-ION CHARACTERIZATION


Molecular Actuators The layman's view of a machine is a large, unwieldy and inefficient piece of equipment which converts an input energy into a lot of heat and noise and some useful work. Micro actuators and nano machines should someday replace this image with one of quiet efficiency and compactness, performing critical and delicate tasks. A great majority of the devices developed by man to convert chemical or electrical energy in mechanical work are thermochemical or electromagnetic machines. The physical principles exploited in such man-made machines are completely different from the ones which biological machines use to generate forces and accomplish work. Despite the advanced state of conventional motor technology, the development of mechanical actuators exhibiting biomorphic characteristics would provide a major advance and have important implications in several areas of technology. Although the end is not yet in sight, the two very promising young fields of nano and micro actuators are undergoing vigorous growth and popularity and some short term goals such as microtweezer and tnicropositioners based on polymers are nearing realization. Nanoactuators. The concept of nanoactuators was examined several years ago by K.E. Drexler, who is today one of the leading devotees of nanofabrication. Although it is by no means necessary to mimic nature's machines to the letter, they are near-perfect systems upon which we can model man-made nanomachines. The innate ability of biological organisms to move themselves is impelled by their exquisitely simple yet sophisticated biomolecular machines. Simple because the tiny machines found in nature are based on only a few molecules, and sophisticated because they are able to work in the environments present in vivo and use minimal energy to producerelativelylarge forces and displacements. Research in nanoactuation systems has only just begun to take off, with die participation of mainly Japanese and American groups. The ultimate man made molecular machine, according to Drexler (1), will eventually be self assembling and self repairing and will be used to direct chemicalreactions,repair organs, construct computers, transport reagents and generally perform a whole range of useful functions. Obviously, such a machine will take many years to develop, in the meantime this field is still in its infancy, and current efforts are devoted to replicating biological machines in the laboratory in order to better understand such systems. Two pioneering examples are myosin sliding machines and flagellar rotary motors and will be briefly described. Flagellar Rotary Motor. A group at the University of Tokyo has attempted toreconstructthe flagellar motor of bacteria in vitro (2) The flagellar motor, by which means a bacterium propels itself, is the only rotating type motor found in nature, and for its high speed and efficiency and low inertia merits study. The whole flagellum is composed of three parts: thefilament,the hook which connects the filament to the motor, and the motor itself, as illustrated in (Figure 1). The filament, which is not unlike a screw, was reconstructed in vitro by self assembly of its constituent proteins, which consist of identical subunits known as flagellin. The hook, which is a sort of universal flexible joint, is also made up of identical proteic subunits. It has not yet been possible to reconstruct the hook in areproduciblemanner. Several disk-like structures make up the motor unit including a shaft-like element, a bush and a rotor. The motor can rotate at speeds of up to 12000 rpm. By using genetic engineering techniques, genes encoding dierotorand shaft proteins were expressed in bacteria and amplified, and therotor,but not as yet the shaft, was successfully self assembled. These are thefirstpromising attempts at reconstructing a biological motor and have led to a further understanding of its mechanisms. This type ofresearchis a first step towards therealizationof nanomolecular machines.



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Biomimetic Macromolecidar Actuators 519

Myosin Sliding Machines. Muscle fibre consists of two protein containing filaments. One type of filament (the thin filament), contains the proteins actin, troponin and tropomyosin, and it consists of thin threads supporting globular proteins. A second type of filament, containing the protein myosin, consists of thicker rods that interdigitate with adjacent actin filaments. According to the sliding filament model of muscle contraction, during a contraction, actin filaments slide past myosin filaments through die generation of cross-bridges. In this manner, the entire muscle fibre contracts, and die process is driven by the hydrolysis of APT. In an attempt to comprehend this chemomechanical energy transduction process Ishijima et al. (3) have monitored the motions of individual actinfilamentsin vitro. In their experiments, a single fluorescent labelled actin filament is placed on a myosin coated surface. By means of fluorescent microscopy, the motions of the actinfilamentcan be observed, and it is also possible to measure the force produced by a single myosin molecules. In this system then, the coupling of the APT cycle to interaction between actin and myosin can be examined directly, thus furnishing insights into molecular mechanisms which drive muscle contraction. In the future they can perhaps be applied to molecular machines. Microactuators. There is growing demand, infieldssuch as anthropomorphic robotics, microrobotics and bioengineering, for muscle-like actuators with high power to weight ratios and a large degree of compliance. From a mechanical engineering point of view, muscle are very unconventional, actuators. They are neither pure force generators (like electric DC motors), nor pure motion generators (like stepper motors). In fact, they behave rather like springs with tuneable elastic parameters. This and the built-in compliance of muscles are winning features for achieving versatility and robustness and for affronting the complexity of sensory-motor problems, such as motor redundancy, trajectory formation, negotiation of impacts and motor learning. All this, though, is achieved at the cost of precision. Nonetheless, pure mechanical precision is unnecessary because what is of functional significance when confronted with an interacting object is a global characterization of the integrated sensory-motor system, rather than any accurate information on its location, shape or bulk and surface properties. Pseudomuscular actuators are intended to reproduce the salient features of biological muscles. Hence it is desirable to target performances which equal or even exceed those of muscles. These objectives thus provide the following set requirements for actuators (4) -large linear displacements -durable, with long lifetimes and high stability -built-in tuneable compliance -High power/volume ratio, and power/weight (O.l-l kW/kg) -high force density (0.1 MPa) -fast response time (a typical strain rate is 100%/s) -convenient, high density and environmentally safe energy source -efficient energy conversion (45-70%) Some of the criteria above have been met, but most of them are far too ambitious to be approached by currently available materials. In spite of several major advances in actuator performances in the last few years, a number of technical breakthroughs are needed before efficient and reliable devices can be implemented. At present, there are four different major classes of macromolecular materials that exhibit mechanical transduction (see Table I), three of which are discussed below. Piezoelectric Polymers. Piezoelectric polymers (5) are widely used as sensing devices and are common in medical ultrasonics. Their use as low frequency actuators is however limited because of the high driving voltages required to produce small strains (typically 2 kV for a 1 μπι linear displacement) and their lack of a steady state response.


520


Table I: Molecular Actuators Micro


electrostrictive materials polymer gels conducting polymers piezoelectric polymers

Nano

actin-myosin flagellar motor proton pumps in membranes

Nevertheless, they can be fast and highly reliable, and production technologies for piezoelectric polymers are quite advanced. In order to produce useful displacements, polyvinylidene fluoride, (PVDF) for example, can been formed into a bimorph. In (6) , two small PVDF strips with opposing axes were bonded together to produce a 13 μπι displacement with an applied voltage of 300 V. Their precision and reliability make piezoelectric polymers ideal for low mechanical impedance, small displacement, multidegree of freedom micromanipulators for cell handling (7), as illustrated in (Figure 2). Conducting Polymers. Conducting polymers (CP) have only recently been used for actuation, but have already shown to possess very high force generation capabilities (8) . π-electron conjugated polymers can exert tremendous forces, hundreds of times greater than those of muscles. In very thin CP fibres, where diffusion distances are minimized, response times can be compatible with the proposed application. They do however tend to have lower strain (1-10%) than polyelectrolyte gels, but not as low as those of piezoelectric polymers. Pei and Inganâs (9) have investigated the mechanical properties of a bilayer CP strip of polypyrrole. On application of 0.8 V vs S CE the strip bent by 0.5 cm. The process was fairly slow, but reversible. CP are rather solid compact polymers, and it is this which limits the responsetimesof anything other than very thin fibres. To circumvent this, a number of different approaches to designing CP actuators are being investigated. The synthesis of a polymer gel incorporating a CP backbone has been accomplished (10). However, this trial and error type approach may take several year before a useful polymer with adequate mechanical properties can be synthesized. Alternatively, it may be possible to produce a microporous CP structure, rather than a gel, using a phase inversion spinning process. This method would produce a polymer structure with a fast response time, at the expense of a slightly reduced force density. Polymer Gels. Polyelectrolyte gels have received much attention since the early 50"s, and, more recently have been incorporated into prototypes or demonstration robotic devices A polyelectrolyte gel is a cross-linked polyelectrolyte network permeated by an aqueous solution. The majority of gels investigated undergo chemomechanical (CM) conversion by ionization, redox reactions or photoisomerisation. Other mechanisms such as ionexchange and phase or order-disorder transitions also exist (12) . Under direct chemomechanical conversion, polymer gels are characterized by yielding large strain (50%) and force densities comparable to those in muscles. However, in spite of almost two decades of research, the mechanical strength and response times of these materials still leave much to be desired



DE ROSSI & CHIARELLI

Biomimetic Macromolecular Actuators

Figure 1. A natural flagellar rotary motor (adapted from ref. 26) STEEL SHEET

Figure 2. A micromanipulator that uses piezoelectric polymers



522


The CM conversion process is diffusion regulated so that the responsetimemay be increased by drawing the gels into very thin fibres and assembling bundles composed of several fibres. This poses severe technical problems, not least breakage of the fibres. Present efforts in thisfieldare dedicated to providing polymer gels with some sort of electrical drive in order to render them useful for various applications. In earlier attempts, metal electrodes were positioned in the gels. More recently, the electrochemomechanical (ECM) properties of a polymer gel with interpenetrating polypyrrole electrodes have been studied (13): In both cases although ECM conversion was achieved, the electro-chemical coupling mechanism was inefficient To date no experimental evidence related to the feasibility of electrically triggered chemically fueled ECM conversion has been reported, this problem poses a major limiting on polyelectrolyte gels for application to actuators. Notwithstanding recent advances in the science and technology of electrocontractile polyelectrolyte and conducting polymer gels, major progress has to be achieved in all aspects which are instrumental to die conception and implementation of muscle-like actuators. These aspects embrace various disciplines and their intimate interrelations pose additional difficulties. Pseudomuscular Gel Actuators For Advanced Robotics. In the course of a research aimed at developing muscle-like gel actuators, the following topics have been examined: -analysis of mechanisms eliciting electromechanochemical response in gels -formulation of continuum models describing gel rheology and electromechanochemistry -reduction of model complexity to a lumped parameter description of gel fiber actuators, useful for control purposes -formulation of control strategies forfinger-likekinematic chains driven by polymeric actuators -neural control of redundant, multi-actuator systems. Analysis of mechanisms eliciting electromechanochemical response in polyelectrolyte gels. The effects of interactions of electric fields with polyelectrolytes in solution or gel form can be summarized as: a) orientation of dipolar species b) deformation of polarizable species and orientation of induced dipoles c) alterations of the degree of dissociation of weak acids and bases d) motion and redistribution of mobile charged species. In addition, in the case of electricfieldsproduced by electrodes in contact with the solution or gels: e) electrochemical reactions at the interfaces. These effects can be associated with various modifications and structural readjustments at the molecular level which, in a gel, can manifest themselves macroscopically because of intermolecular bridges and crosslinks. Estimates in terms of orders of magnitude, although approximated, can offer useful indications for a comparative evaluation of electricfielddependence of the effects listed above. It is clearly understood that the large variety of physical and chemical properties of various polyelectrolyte moieties would require a detailed analysis, specific for each compound. The following analysis, however, is based on large categorizations and, although limited in their applicability and accuracy, results are easily obtained in an handy form (14).


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ROSSI & CHIARELLI

Biomimetic Macromolecular Actuators523


In its simplest form, the analysis is limited to synthetic polymers made by a unique monomeric unit possessing a permanent dipole moment which, as it occurs typically, has a value of a few Debye. In the process leading from a single monomer to a structural unit in a linear polymeric chain the dipole moment do of the monomer changes because of a diverse electronic distribution in the molecule and, in general, the structural unit assumes a moment given byd = Vdo (whereV~l). In the presence of an electric field each structural unit tends to rotate to align its dipole moment with the local field Ε and its energy decreases by an amount equal to d-E. The interaction with the electric field affects the rotational mobility of the structural unit. Since the elastic properties of the chain deriving from this mobility originate from thermal agitation, we may consider as a term of comparison the average energy of a structural unit equal to KT. We can so impose the condition: dE~KT 6

Assuming V = 1, do =3D and T=300° K, we obtain Ε ~ 10 V/cm. So, an electric field strength of 10 V/cm causes an approximate change of 1% of the average energy of the structural unit. Using similar arguments, the polarizability of an ionized polyelectrolyte chain and the influence of electric field changes on the dissociation constants in polyelectrolyte systems can be taken into account, leading to similar values of electric field strength needed to produce a 1% change in end-to- end distance in the macromolecule (see Table Π). 3

Table Π. Various Effects Related to Electric Field Dependence and TEFS

Effect

a) Deformation of chains containing permanent dipoles

electricfield(E) dependence

Ah/h-Em^do/SkT

TEFS*

HPVAan

b) Pdlarizability of a polyelectrolyte chain

Ah/h«E a/3kT

H^V/cm

c) Change in dissociation constant in a polyelectrolyte

AKaVKd- IB e^/ 8jceoe(kT)2

1Q4 v/cm

2

+

(ApBAp + B") * Typical electric field strength causing 1% change h = change end-to distance; εο = vacuum dielectric constants = dielectric constant e = electron charge; k = Boltzman constant; a= chain polarizability Τ = temperature °K Ka = dissociation constant do = permanent dipole of a chain Calculation performed as per Neuman (19).



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The arguments so developed indicate that structural modifications caused by electric field effects of classes a), b) and c) can reasonably be excluded if the field strength is below HPV/cm. Low intensity electricfields(below 10 V/cm), however, have been shown to cause sizable size and shape changes in polyelectrolyte gels. The interpretation of the mechanisms governing contractile phenomena and volume phase transitions, which occur in polyelectrolyte gels when in direct contact with an electrode is, however, controversial. Tanaka et al. (15) attributed the volume phase transitions they observed in an ionized polyacrylamide gel under electricfieldto electrostatic attraction between the positive electrode and the negatively charged gel, leading to imbalance of the equilibrium swelling pressure. We attempted to interpret experimentalfindingsrelated to contractile activity in polyelectrolyte gels under electric excitation, using the model proposed by Tanaka, reaching the conclusion that the electrostatic attraction model is inadequate to describe the kinetic and electricfielddependence of the observed phenomena. We investigated the origin of these electromechanical effects, and a conclusion has been reached which ascribes the observed contractile response primarily to spatio-temporal pH gradients created by electrochemical reactions as the electrodes (16). Continuum Models of Electrochemomechanical Response. Theoretical models to analyze the transient electrochemomechanical (ECM) response of polyelectrolyte gels have been formulated and their adequacy tested in experiments. Kinetic equations for chemical and electrochemical reactions and ion transport have been coupled to formulae governing the contraction and swelling of gels. The dynamics of swelling of a gel can be analyzed by recurring to continuum models which have their foundations in the poroelastic theory formulated by Biot (17). Grodzinsky (18) developed a continuum model which extended to charged gels, and was aimed at describing mechanical transients occurring in response to changes in the composition of the fluid permeating and surrounding the gel. According to the model, the total stress σ | j acting on a homogeneous, linear, isotropic gel can be expressed, in the small strain approximation, through the constitutive law: τ

oT

i

j

=

K(c)divu δ ] + 2 μ ο ( ϋ -l/3divu 8ij) - (B )+ P)6ij ί

(

ί ]

(C

where K(c) and μ(ο) are respectively the bulk and shear moduli of the solid polymer network, which depend on the concentrations of the ionic solution in the gel interpenetrating liquid. Β (C) is the chemical stress, which couples changes in local chemical concentrations to the local dilatation of the sample; u is the polymer displacement vector and 5j j the Kroneker index. The fluid pressure, Pf, is related to the difference between the hydrostatic pressure, P, inside the gel (relative to the bath pressure) and the osmotic pressure difference Δ π (between the inside and the outside of the sample) as: Pf = (Ρ - χ ( θ Δ π ) where χ (Q is the membrane reflection coefficient The fluid velocity is assumed to be related to the fluid pressure by Darcy's law: U = -(l/f APf) (C)


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Biomimetic Macromolecular Actuators 5 2 5

where U is the total-area averagedfluidvelocity relative to theflowoffluidwith respect to the solid matrix and 1/f (Q is the hydraulic permeability of the gel matrix (f is a polymer-solution friction coefficient). Conservation of mass, assuming both liquid and solid fractions are incompressible materials, and conservation of momentum, usually neglecting inertia! effects, complete the description of gel dynamics, thus leading to an equation of motion of the polymer network. In order to account for electrochemical changes generated by electrodes for driving the actuator through modulation of the material coefficients and the chemical stress, electrodiffusion-reaction and continuity equations have to be considered:


Ji = -Di gradCi +(Z/lZl)Q μι E + Q v and

3 C i / 3 t = - divJi + Gi - Ri where Ji is the flux of the species i, Z{ its valence, μΐ its mobility and Di its diffusion coefficient. Ε and ν are the local electric field and the local, velocity of the fluid respectively. Gi and Ri are the generation and recombination rates for the chemical reactions. The concentrations of ions inside the gel and in the external bath are linked through Donnan partition relationships. Coupling between die ion transport processes and the mechanical readjustment of the gel is taken into account by die dependence of the transport coefficients Di Άηάμΐ from the local dilatation field of the polymer network, and, hence, the local water volume fraction. Stating of appropriate initial and boundary conditions fully defines the problem. The solution of die coupled equation system is a challenging task, even using numerical methods. However, under appropriate conditions, ion transport and mechanical readjustment phenomena can be decoupled because of the large difference in the values of their rate limiting constants. Free swelling and stress relaxation experiments have been performed on thin cylindrical fibre, which are a suitable geometry for actuator construction. The elastic moduli and hydraulic permeability of the gel have thus been determined and used to calculate the isometric tensile force generated under rate limiting chemical stimuli (19). In the case of gels with high elastic moduli, the rate limiting phenomena in ECM experiments generally resides in the electrodiffusion-reaction. The requirement of high modulus fibre for actuator construction appears to favour a shorter mechanical time constant over the electrodiffusion-reaction time constant This implies a working mechanism in which the active dynamics of the actuator is essentially governed by time needed to modulate (in space as well as in time) the gel material parameters by the electrochemically generated species (20). The passive properties of the actuator are governed by the viscoelastic behavior in the following section. Dynamical Properties of Hydrogel Thin Fibres. The free swelling and stressrelaxation behavior of thin fibres of a hydrogel can be analytically described starting from the equation of motion of the gel network in a motionless fluid phase approximation: 2

p3 u/3t

2

T

= div a i j

where ρ is the density of the polymer network.


526


In the absence of chemical changes or concentration gradients, the chemical stress term can be omitted and the inertial term can usually be neglected, because phenomena are slow, to obtain the motion equation:


f du/dt = (Κ+μ/3) (grad(divu)) + μ div(gradu) This equation, combined with the linear constitutive law of the gel, Darcy's law, the equations of conservation of mass of both die liquid and solid components, and initial and boundary conditions, has been used to predict the time course of the force developed in a stress-relaxation experiment performed on thinfibresof gel [19]. The analytical expressions for the time course of the force are very complicated. Much simpler expressions have been obtained in two limiting cases which are, respectively, the recoil force immediately after the application of a step deformation and the force at time infinity when fluid flow has ceased and only the elastic recoil force of the polymer exists. The time constant for the stress-relaxation process above has also been calculated and has been shown to have a multiexponential behavior. The limiting (single exponential) time constant has been found to be (19). where d is thefibrediameter and Oo =0.767. 2

tb = (dV4ao% )(f^) A Lumped Parameter Model of the Mechanical Behavior of a Gel Fibre. The continuum approach is useful for determining the concentration of chemicals and the stress in the gel in space and time. Since dynamic control of the actuator requires a fast feedback loop, the complex equations describing the phenomena have to be reduced to a manageable form by appropriate simplifications. A lumped parameter model which is suitable for representing the passive viscoelastic behavior of a gelfibreis the standard viscoelastic solid (SVS) which is thought to hold when the solid polymer component behaves as an elastic material. Referring to (Figure 3) the dynamic equations of the SVS can be expressed as: F

f

a

= ^ a / S l o ) (lp+X-X )

Fb = (μο S/lo ) (lp +x-lo ) - ( μ S/lo) (χ') + F Η

F = F +F a

a

=0

b

where lo is the unstrained length, lp the pretensioned length, χ is the instantaneous length of the gelfibre,and x is thefictitiousinstantaneous length at the point A'. S is the resisting cross section of thefibreand μa, μb » ^ , are the elastic and viscous moduli of the SVS, respectively. The dependence of the parameters on the material coefficients of the gel, as they appear in the continuum model, can be deduced by assuming that, instantly, following the application of a step deformation, the gelfibre(at time t = 0+) behaves as an incompressible medium. Thus, by equating the resisting force of the linear viscoelastic solid submitted to a step elongation to the force calculated for the gelfibreattimet = 0+ (whose polymeric component has a bulk modulus k, a shear modulus μ, and a polymer-solution friction coefficient, 0 we have: 1

a


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Biomimetic Macromolecular Actuators

μa+μb=3μ Also equating at time t =00, the asymptotic force value of the linear viscoelastic solid with the corresponding expression for the gel fibre, we obtain: μ„=[9^/μ)/(1+3^/μ))]μ Then, by combining these equations it follows that μ =[3/(1+3(1 /μ))]μ 8

ί


Finally, by equating the time constant of the viscoelastic solid to the limiting stressrelaxation decay time constant of the gel fibre we obtain: 2

2

2

3

το=(

Macro-ion Characterization - American Chemical Society

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