Chemistry Reference
In-Depth Information
(
is the charge transfer coefficient) and
E
ohm
aL
:
j
¼
ð
4
:
7
Þ
These two equations can be combined with regard to E
¼
E
a
þ
E
ohm
to
obtain
þ
RT
L
nF
j
0
Mat
jL
E
¼
yF
ln
ð
4
:
8
Þ
Eliminating j from Eqs. 4.6 and 4.7 leads to a transcendental equation for L:
L
2
RT
L
nF
j
0
Mat
nF
Mat
¼
þ
ð
:
Þ
E
yF
ln
4
9
Unfortunately, it cannot be solved analytically, but for E
a
!
0orL
0, the
K
0
p
t (cf. Eq. 4.4). On the other
first term can be neglected, which gives L
hand, for large E
a
or L
!
0 (short time) the second term can be neglected,
and we obtain
¼
j
0
tMa
exp
nFE
RT
L
¼
nF
K
1
t
:
ð
4
:
10
Þ
The reactions exhibiting linear film growth (Eq. 4.10) are listed in
Table 4.2
.
Most of them comprise reactions of Li-amalgam with various fluoro-
carbons. Only the perfluoro-2-butyne reacts with Li-amalgam according to
Eq. 4.4 with K
0
¼
120 nm/s
1/2
forward: the faradaic carbonization of perfluoro-2-butyne is so fast that the
overall kinetics is controlled by E
ohm
(Li
þ
transport in the growing film) and
not by E
a
. While most tested reaction systems follow unique kinetics (either
Eq. 4.4 or Eq. 4.10) at all practically accessible film thicknesses, the reaction
of perfluoronaphthalene with Na-amalgam exhibits distinct linear kinetics
(with K
1
¼
0.3 nm/s) at early stages, but it changes to square-root kinetics
at later stages (with K
0
¼
18 nm/s
1/2
). In other words, the Na
þ
transport is
rate determining only for thicker films, but not for thinner films in this
particular case.
4.2 ELECTROCHEMICAL ROUTES TO CARBYNE-LIKE CHAINS
Carbyne is an ill-defined crystal containing sp-bonded all-carbon chains [16].
Species approaching this structure are carbon molecules in the carbon melt
[17], vapor, or in inert matrices at low temperatures [18,19] and end-capped
oligoynes [20,21]. An ''infinite'' sp-bonded carbon chain has two possible
Search WWH ::
Custom Search