Don't think it's trustworthy, though; a bit of load, and the battery will outgas (and burp); you can get a pretty nice sawtooth characteristic from a 'sealed' battery design. Either mercury cells (hard to find, now) or vented battery designs are better in terms of constant voltage.
The dielectric constant of water drops fast with frequency. I wonder what the step response of the conductivity of a water solution is like. I meant to do that as a high school physics project, but never got around to it. [1]
Time domain Hall effect might be interesting, too.
[1] I did have some fun with Kerr cells. It's amazing that I didn't poison myself with the nitrobenzene. Somebody was murdered in a Nero Wolfe mystery, a dish nitrobenzine on a car visor shade, with a layer of water on top to supress the odor.
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Metal-aqueous junction effects are quite strange. Impedance plots show fractional-pole slopes over many decades, with a nearly constant ratio between resistive and capacitive impedance. The slope depends on the metal. Step responses are problematic because of some serious nonlinearities once you get beyond some modest current densities.
Excluding the nonlinearities, you can make a fairly good equivalent circuit with a RC ladder network where each section can be calculated from the last, the RC product getting shorter by a fixed factor. Then you can use spice...
I've tried getting some better understanding of the underlying electrochemistry but have yet to "get it". I'm not sure that anyone has an explanation based on fundamental principles.
Of course, these surface effects are almost certainly different than bulk effects - but it's hard to get to the latter without tripping over the former. If you use metals that form stable junction potentials (Ag-AgCl) you'd be farther ahead.
Don't liquid polar molecules have inertia and viscoscity and Brownian things going on?
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John Larkin Highland Technology, Inc
jlarkin at highlandtechnology dot com
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Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
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Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro acquisition and simulation
There are explanations that are firmly tied to fundamental principles, but the math gets messy for concentrated solutions, which is what you've got in batteries.
For my own purposes I'd be happy to understand say, 0.1 - 1 molar. If you know of any reference that quantitatively explains the origin of this strange fractional pole response I'd appreciate it! {especially if it's accessible to someone who is not an electrochemist!}
A distribution of time constants gives rise to 1/f noise, which is a pretty good fractional pole.
Cheers
Phil Hobbs
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No, but it gives you a useful search string. I spent an afternoon in the Nijmegen University Chemistry department library browsing electrochemistry textbooks finding it, along with a lot of other interesting stuff. You probably need to find your own university library.
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They do exist, but it's more than ten years since I looked at any of them.
There are other diffusion situations that give a 1/2 pole rolloff, e.g. if you have a heat source at the surface of a semi-infinite piece of some material. Anywhere inside the material, the frequency response rolls off exponentially, but right at the surface it goes as 1/sqrt(f). The reason for this is that since diffusion is slow, the amount of material that actually responds significantly to the thermal forcing goes down with frequency.
I went through the math of this once--it's in my thermal control chapter,
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Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics
160 North State Road #203
Briarcliff Manor NY 10510 USA
+1 845 480 2058
hobbs at electrooptical dot net
http://electrooptical.net
I'm not sure I quite get the fractional pole response. (Impedance looks weird at all time scales?) But I'm wondering if there are some space charge effects in batteries. (It's been way too long since I did a space charge thing, but I seem to recall it gives a non-linear I- V curve.)
Yes, I've spent quite a few hours in our local Chem library. I've yet to find anything that explains this peculiar response - at least in a form that I could recognize. I've spoken with some people with chemistry PhDs whose expertise (if not exactly electrochemistry) was closely related, and they haven't been able to help.
Again, a _description_ (that works in over a small but poorly articulated domain) does not constitute an explanation!
The linear model that I mentioned is weird in itself - but fails to predict where the linearity breaks down and doesn't describe what happens when it does :( There's another basic distinction between the "battery" application and the polarizable electrode application that is my main interest - in batteries, the electrodes are made of materials (think metallic salts grown on metals) that form stable junctions with ionic solutions. These behave very differently than nonreactive metals in solutions. Sorry if my question confused matters for those interested in battery technology.
Yes, the math is pretty similar, and the connection to diffusion processes is highly suggestive. Where it's lacking is predicting how this can fall apart and what happens when it does (as when current densities get "too high").
I also find it extremely bizarre that different metals produce somewhat different slopes - they are _not_ all 1/2 pole.
For what it's worth, the book that proved most useful was a collection of papers editied by a guy that I'd known socially - as another post- doc - when I was a post-doc in the Southampton University Chemistry Department. The professor of electrochemistry there then went on to become notorious for claiming to have invented cold fusion - Martin Fleischmann - and I had to go to the cold fusion entry on Wikipedia before I could remember his name. in 1971-72 he ran a very good electrochemistry department.
I didn't claim to give you an explanation, I merely pointed you at a useful search string. Checking out the next few entries it throws up on Google it points you at a bunch of electrochemistry lecture series, which do try to present an explanation. I'm not interested enough to try to make sense of any of them.
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