Page 125 - The Mechatronics Handbook

0066_Frame_C08 Page 16 Wednesday, January 9, 2002 3:48 PM

s
s
where c are the mass fractions, V s are the partial molar volumes, M are the molar masses, and the index
0 refers to the initial value of a variable. Complete mathematical description of the polymer actuator
requires the solution of mass transport (diffusion) equation, momentum balance, and Poisson equation
for potential distribution, the discussion of which is beyond the scope of this book. An interesting
consequence of the addition of the chemical strain in (8.46) is the explicit appearance of the pressure
term in the electrochemical potential driving the diffusion. The total mass diffusion flux will have a
component proportional to the negative gradient of the pressure, which for the case of water, will result
in a relaxation phenomena observed experimentally. The total flux of component s is then given by
s s
s
--------------∇ m () +(
J = – rc W os T pV + RT ln ( fc ) + z Φ) (8.53)
s
s
s
M s
s
s
s
where W is the mobility of component s, z is the valence of component s, p is the pressure, f is the
activity coefficient, and Φ is the electric potential. We have omitted the cross-coupling terms that would
appear in a fully coupled Onsager-type formulation. Interested readers are referred to [Enikov 2000b] and
the references therein for further details.
8.6 Future Trends
The future MEMS are likely to be more heterogeneous in terms of materials and structures. Bio-MEMS
for example, require use of nontoxic, noncorrosive materials, which is not a severe concern in standard
IC components. Already departure from the traditional Si-based MEMS can be seen in the areas of optical
MEMS using wide band-gap materials, nonlinear electro-optical polymers, and ceramics. As pointed
earlier, the submicron size of the cantilever-based sensors brings the thermal noise issues in mechanical
structures. Further reduction in size will require molecular statistic description of the interaction forces.
For example, carbon nanotubes placed on highly oriented pyrolytic graphite (HOPG) experience
increased adhesion force when aligned with the underlying graphite lattice [Falvo et al. 2000]. The future
mechatronic systems are likely to become an interface between the macro and nano domains.

References

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Evans, T.H., Journal of Applied Mechanics, 6, p. A-7, 1939.
Enikov, E.T., Nelson, B., “Three dimensional microfabrication for multi-degree of freedom capacitive
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Enikov, E.T., Nelson, B.J., “Electrotransport and deformation model of ion exhcange membrane based
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2000.
Falvo, M.R., Steele, J., Taylor, R.M., Superfine, R., “Gearlike rolling motion mediated by commensurate
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