Question:
Uh, it looks to me like ANY use of pulsed waveforms or ac currents or
any other strange waveforms in a hydrogen electrolysis cell HAS to end
up inherently inefficient.
The reasoning is as follows. At a DC level of 1.23 volts, hydrogen
generation is one sixth endothermic and at maximum efficiency. At 1.5
volts, hydrogen generation takes all of its energy from the electricity
and none from ambient waste heat. Above 1.5 volts, hydrogen generation
exothermically produces new heat and wastes electricity.
Curves for this are in Peavey and elsewhere.
Seems like any pulse or ac waveform would spend most of its time away
from the optimal voltage point, and thus end up totally useless. This
suggests that carefully regulated DC is the only way to go for decent
efficiency.
One question though: What is the time constant of hydxrogen generation?
Say you suddenly shift your cell voltage from 1.3 to 1.5 volts. What
does the current waveform look like? Is this time constant electrically
or electrochemically defined?
Are there integration effects that makes the above analysis wrong?
If so how?
Answer:
Boy do you ask a lot of questions (which would take a tome to answer
properly) (GG). The simplest "equivalent circuit" for an electrode
surface is a resistor (R1) in parallel with a capacitor (C1). You have
one of these for each electrode (with different R1's and C1's) and
they are joined by another resistor in series (R2). R2 is the
simplest, it is essentially the ohmic drop due to the resistance of
the electrolyte solution between the electrodes. R2 depends mainly on
the chemical composition of the electrolyte, the concentration of the
electrolyte, and the spacing between the electrodes. R2 always
constitutes a "loss" so you want to make it as small as possible,
which is why cells usually have concentrated electrolyte solutions and
very small electrode spacings.
R1 and C1 are more complicated because they depend heavily on specific
chemical and surface properties. C1 is primarily the "double layer
capacitance" which occurs across the angstrom-level thickness of the
electrical double layer at the electrode surface (this is mainly due
to the electronic charge on the surface of the electrode opposite a
charge due to the layer of ions in solution). C1 is usually pretty
big; for a smooth electrode surface in aqueous solution it is upwards
of 20 microfarads per cm^2 of surface. R1 depends a lot on the
inherent rate of the electrochemical reaction at the surface. For
hydrogen evolution on metals, this rate can vary over many (10 or so)
orders of magnitude. It is fastest on Pt and related metals, which is
why people spend so much money on their electrodes. It turns out that
this component of R1 is actually nonohmic at potential drops more than
a few mV, further complicating things.
Another component of R1 involves the rate of transport of material to
the electrode surface; the surface can get "starved" for material to
electrolyze if you try to force more current through it than mass
transport of the reacting species can afford. This produces a
time-dependent "resistance".
Running out of breath here, so anyway, if you apply a controlled
voltage step to your cell, you should see an initial spike in current
due to charging C1's, and limited mainly by R2. As time goes by, the
current will become more limited by the R1's (which, remember, is
complex quantity and can vary with time). If you apply a constant
current pulse, the initial jump in potential will be due to R2 (being
ohmic, it has a submicrosecond time constant), followed by a slower
rise determined mainly by C1 and an ultimate (time dependent) voltage
drop usually dominated by R1. These time constants depend on a lot of
things, as you can see, but speaking roughly they are on the
millisecond to second range. After a few seconds the mass transport
can become convective and things get real complicated.
Electrochemists apply all sorts of a waveforms to electrodes as a
means of characterizing them and the reactions occurring on them.
There are some practical applications for non-steady state
electrolysis (including "pulse plating"). There may even be some small
gains in efficiency to be made in applying them to other types of
electrolysis (due to the time dependence of the mass transfer
component), but I am not personally aware of credible research in this
area with regard to water electrolysis.
