Page 124 - The Mechatronics Handbook

0066_Frame_C08 Page 15 Wednesday, January 9, 2002 3:48 PM

FIGURE 8.11 Nafion membrane with Pt electrode.

_
+

6H 2 O(liq.) → 4H 3 O + + 4e − + O 2 (gas) e − Surface Electric Current (electrons) H O + Electroosmotic Drag e − Surface Electric Current (electrons) 4H 3 O + + 4e − → 4H 2 O(liq.) + 2H 2 (gas) Li + + OH − → LiOH
+
+
Li
H
2
H O
2
pressure gradient)

Anode D'Arcy Flow (osmotic Cathode

FIGURE 8.12 Ion transort in nafion.

The deformation of the polymer-metal composite can be attributed to several phenomena, the dom-
inant one being differential swelling of the membrane due to internal osmotic pressure gradients [Eik-
erling 1998]. A schematic representation of the ionic processes taking place inside the polymer is shown
in Fig. 8.12. Under the application of external electric field a flux of cations and hydroxonium ions is
generated towards the cathode. At the cathode the ions pick up an electron and produce hydrogen and
free water molecules. On the anodic side, the water molecules dissociate producing oxygen and hydrox-
onium ions. This redistribution of water within the membrane creates local expansion/contraction of
the polymer matrix. Mathematically, the deformation can be described by introducing an additional
strain (eigen strain) term in the expression of the total strain. Thus the total strain has two additive parts:
elastic deformation of the polymer network due to external forces (mechanical, electrical) and chemical
strain proportional to the compositional variables

s
V
e ij = e ij elast + r 0∑ --------- c –( s c 0 )d ij (8.52)
s
3M s
s
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