Infinite dielectric permittivity?

[Moreno]

If there exist materials with infinitely low dielectric strength (superconductors), can there be a "superdielectrics" with opposite effect? Materials with infinite dielectric permittivity and reasonable dielectric strength in the same time? Or it's proved that such thing is theoretically impossible?

[John Cuthber]

Imagine that you had such a material, and you made a capacitor using it as the dielectric.

The energy stored in a capacitor is proportional to the permittivity if the dielectric.
Putting any voltage on a capacitor with an infinite permittivity would require an infinite amount of energy.

Since that's not available either the permittivity must be finite or the "capacitor" has the strange property of never having a voltage across it.

So I don't think an infinite permittivity is possible.

[Moreno]

Imagine that you had such a material, and you made a capacitor using it as the dielectric.

The energy stored in a capacitor is proportional to the permittivity if the dielectric.

Putting any voltage on a capacitor with an infinite permittivity would require an infinite amount of energy.

Since that's not available either the permittivity must be finite or the "capacitor" has the strange property of never having a voltage across it.

So I don't think an infinite permittivity is possible.

What do you mean by this? That we cannot save some reasonable or even small amount of energy if we have capacitor with infinite permittivity? That we are obligated to apply infinite amount of energy whatever amount of energy we want to save? How come?

 

Dielectric permittivity of the metals claimed to be taken for infinity, conditionally. However, their dielectric strength approaches zero. Dielectric permittivity of ferroelectrics claimed approaches infinity near Curie point. I don't know what happens to their d. s-h. at the same time. What if we have metal pieces embedded in ceramics?

It is claimed that "superinsulator" was discovered, but I'm not sure it does have some relation to permittivity.

https://en.wikipedia.org/wiki/Superinsulator

 

Debye (1912 ▶) hypothesized that the latter property must be due to a permanent electric dipole moment set up by the molecules in the crystal, and further that there must be a critical temperature for which the dielectric constant goes to infinity, hence an analogy with the Curie temperature of a ferromagnet.

 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4285877/

Edited March 4, 2017 by Moreno

[Enthalpy]

Ceramic capacitors do exploit permanent electric dipoles in the material, interacting enough to make a ferroelectric material (BaTiO₃, SrTiO₃, few more) if the temperature isn't too low. By adjusting the Curie temperature near the operation temperature (with Ba to Sr proportion); some achieve a permittivity like 200 000 but not infinity.

 

The heterogeneous nature of ferroelectric materials must be the limit. The Curie transition is between "capacitive" and "permanent polarization" and it happens at different temperatures across the capacitor. These type II and type III capacitors are known by (some) users to show dielectric polarization, high losses and big temperature drift.

 

Maybe a hypothetical homogeneous material would show one single transition temperature, but the permittivity would increase only at that temperature, and just below, it would bring pure losses.

[KipIngram]

Power is voltage times current. So you can write the power flow into a capacitor as (capacitor voltage) * (current into capacitor). An infinite permittivity capacitor would have zero voltage, so the power flow into it would always be zero. So you would never get any energy stored.

 

Another way of seeing this is to write capacitor energy in terms of charge: E = Q^2/2*C. For any non-infinite charge your energy is zero.

 

This hypothetical capacitor would behave exactly like a short circuit. But I agree with the above assertions that it's not physically possible anyway.

[Moreno]

Power is voltage times current. So you can write the power flow into a capacitor as (capacitor voltage) * (current into capacitor). An infinite permittivity capacitor would have zero voltage, so the power flow into it would always be zero. So you would never get any energy stored.

 

Another way of seeing this is to write capacitor energy in terms of charge: E = Q^2/2*C. For any non-infinite charge your energy is zero.

 

This hypothetical capacitor would behave exactly like a short circuit. But I agree with the above assertions that it's not physically possible anyway.

 

For practical reasons I don't stick to absolutes. I think about capacitor which would be comparable to the best batteries in energy density.

[KipIngram]

 

For practical reasons I don't stick to absolutes. I think about capacitor which would be comparable to the best batteries in energy density.

 

"Infinite" is an absolute. "Very high" permittivity is great; you will get a non-zero voltage and thus can deliver and extract power. But your word was "infinite."

[Moreno]

 

"Infinite" is an absolute. "Very high" permittivity is great; you will get a non-zero voltage and thus can deliver and extract power. But your word was "infinite."

 

Could you calculate, what value dielectric constant have to be equal to in order for capacitor to have 1.000 Wh/kg energy density?

[KipIngram]

That would require assuming a density as well, wouldn't it? And a voltage of course.

[Moreno]

That would require assuming a density as well, wouldn't it? And a voltage of course.

 

Let say 10V or 100V, for example. Density could be equal to 3g per cm3. Dielectric materials are dense, commonly.

[KipIngram]

Ok, so sure - let's play with that. C = eA/L, where e is permittivity, A is area, and L is plate separation. We'll consider only dielectric mass (ignore the plates). If d is density, then mass is d*A*L. Energy is C*V^2/2, so energy density (D) is:

 

D = (C*V^2/2) / (d*A*l) = (e*A*V^2) / (2*d*A*L^2) = (e*V^2) / (2*d*L^2) = (e/2*d) * (V/L)^2.

 

We could plug numbers at this point, but you're going to wind up with the energy density going as 1/L^2; the thinner you make your dielectric layer the higher your energy density will be. What I'm inclined to do at this point is define V/L as b, the dielectric strength of the material. Then your limiting energy density is

 

D = (e*b^2) / (2*d)

 

and you have everything in terms of material properties. If you look at the Wikipedia article on dielectric strength, you see that "vacuum" has a value of 10^12, but that seems to be "perfect vacuum" - higher up in the table is an entry for "high vacuum (field emission limited)" and the value there is only 20-40 MV/m. Otherwise diamond is far and away the highest value in the list, at 2000 MV/m. The article on permittivity gives diamond a relative permittivity of 5.5-10, so let's say 10 since we're optimists. Density of diamond is 3.5 g/cm^3 or 3500 kg/m^3. Plugging and chugging,

 

D = (10*8.854*10^-12) * (2*10^9)^2 / (2*3500) Units: (C^2 N^-1 m^-2) * (V^2 m^-2) / (kg m^-3)

 

The fastest way to simplify the units is to note that a volt has units N*m/C; then those units at the right fall right down to J/kg.

 

D = 50.6 kJ/kg.

 

You can play with other materials, but on a quick peek it looked to me like diamond's b=2000 probably outweighed any shortcomings it had in its other parameters. Note that its density is right in the range you suggested.

 

Now compare that to gasoline, which has D = 46.4 MJ/kg (order of 1000 times the diamond capacitor). You see pretty quickly why chemical energy storage carries the day.

Edited April 15, 2017 by KipIngram

[Moreno]

D = 50.6 kJ/kg.

 

You can play with other materials, but on a quick peek it looked to me like diamond's b=2000 probably outweighed any shortcomings it had in its other parameters. Note that its density is right in the range you suggested.

 

Now compare that to gasoline, which has D = 46.4 MJ/kg (order of 1000 times the diamond capacitor). You see pretty quickly why chemical energy storage carries the day.

This is what a bit strange to some extent. Theoretically, energy of atomic orbital restructuring cannot be greater than energy of atomic orbitals deformation. For example, when you burn hydrogen and atoms combine to create water molecules you obtain X amount of energy. But to break down water molecule back to hydrogen and oxygen you will need to spend even higher amount of energy, practically. Theoretically, the energy is the same, but practically it is even higher. This is how capacitors store energy in my understanding. Intermolecular bonds are subjected to deformation, well below their breakdown limit. So, theoretically capacitors can get quite close to chemical fuel energy systems. Currently, graphene supercaps reached the level of lead-acid batteries, which is still well below the best Li-ion batteries. I think the main breakthrough in field of capacitor will happen when a capacitor will be created, designed to satisfy to two main qualities:

 

1)It suppose to store energy in a safe form. There suppose to be almost no "weak places" in a capacitor.

2) Almost all atoms and molecules of a capacitor suppose to carry the useful load.

 

For now even graphene capacitors do not completely satisfy to these criterions as there are still plenty of bulk "ballast" molecules which carry no useful load.

[KipIngram]

I did some electric vehicle work while I was working for UT Austin's Center for Electromechanics. There's so much to love about them. Most obviously, electric motors can reach efficiency levels well above internal combustion engines. But the energy storage problem is a bear. Lots of hurdles to get over there. For example, let's say you have your fantastic capacitor that can store the energy. Now you're on a road trip, in your regular internal combustion car, and you get low on gas. So you pull into the first station you come to, pop the pump nozzle into your tank, and squeeze the trigger. What's happening there?

 

Well, my tank holds 15 gallons and it takes maybe two minutes to fill it, so let's say your pumping gasoline at 7.5 gallons per minute. Gasoline has about 132 MJ/gallon of energy content. So (7.5 gallons/minute) * (132*10^6 J/gallon) / (60 seconds/minute) = 16.5 megawatts.

 

So to have that same experience in an electric car you have to have a cable from the charging unit to your car, and a connector where the connection is made, that can handle order of 10 megawatts. That's some serious power flow. Obviously if you're willing to wait longer you can bring that down, but meanwhile all the other customers are waiting in line, and so on. Let's say we're charging at 500V (which would raise serious safety issues) you're looking at over 40 kA of current flow.

 

So it's not just a matter of making the car work - there's an entire infrastructure that has to be brought into existence. I have a feeling electric cars will find a place in our world, but tI think they'll be used primarily for "around town" runs that allow the car to be charged overnight in the garage for the next day's running about. That automatically limits them to people who can afford multiple vehicles, since most people will still want to have their "out of town" capable car.

 

I will say that I think you're looking at the right part of the problem - the batteries are the weak link in the current generation of electric vehicles. I owned a Honda Civic hybrid a while back, and the batteries just didn't last. I was bitterly disappointed - I'd been excited about the whole idea. But when it came time to buy another car I went back to internal combustion.

[Moreno]

 

So it's not just a matter of making the car work - there's an entire infrastructure that has to be brought into existence. I have a feeling electric cars will find a place in our world, but tI think they'll be used primarily for "around town" runs that allow the car to be charged overnight in the garage for the next day's running about. That automatically limits them to people who can afford multiple vehicles, since most people will still want to have their "out of town" capable car.

 

Sure. Plug-in hybrids will be the main line of research in the next few decades. They don't have such as limited range as EV's.

I think plug-ins may become the most common type of vehicle when a relatively inexpensive energy storage will be developed with 400-500 Wh-kg energy density and 10.000 cycle life. Then 100 kg battery or capacitor will give you at least 100 km range.

With that range 80-90% of organic fuel could be saved monthly (depending on weather). Currently, it's difficult to predict what exactly energy storage will it be. A rechargeable Zinc-air batteries still remain a "dark horse" and some claims have to be proved yet. Recently, I've obtained a patent on a novel kind of supercapacitor and currently looking for R&D (investors).

Maybe my view will seem a bit revolutionary to you, but I would not be wondered if in a few decades a typical plug-in will include at least three main features:

 

1) An advanced and relatively inexpensive supercapacitors to store electric energy.

2) A highly efficient MHD generator (instead of ICE) to charge supercapacitors.

3) An advanced methane storage device. Ultimately, methane may become the most common fuel for hybrids.

 

Another interesting possibility switch to all-electric at present level of technology is mechanically rechargeable metal-air fuel cells.

But it will require to create a huge infrastructure from the scratch.

 

In more distant future such new possibilities may appear as:

 

1) Long distance wireless energy transfer.

2) Portable primary energy sources similar to nuclear fission or fusion. Some kind of "cold fusion", for example.

Edited April 17, 2017 by Moreno

[KipIngram]

Well, yeah - if we can all have our own Mr. Fusion then it's a whole new world. Sounds great. But I still think you're vastly overestimating the future capability of capacitors. It's not the case that the processes that occur in a capacitor as it's charged can "approach" those that occur in chemical energy storage. With real chemical energy storage you are working with real chemical reactions. You're actually changing the chemical composition of the materials. That brings the energy of covalent bonds to the table. With capacitor dielectric, you are merely "stretching" the chemical bonds, so to speak. It's a process of an entirely different nature. I think our earlier calculation was pretty sound, and that something on the order of 100 kJ/kg will prove to be the limit. A watt-hour is 3600 Joules, so the number you just threw out (400-500 Wh/kg) is equivalent to 1.6 MJ/kg.

[Moreno]

Well, yeah - if we can all have our own Mr. Fusion then it's a whole new world. Sounds great. But I still think you're vastly overestimating the future capability of capacitors. It's not the case that the processes that occur in a capacitor as it's charged can "approach" those that occur in chemical energy storage. With real chemical energy storage you are working with real chemical reactions. You're actually changing the chemical composition of the materials. That brings the energy of covalent bonds to the table. With capacitor dielectric, you are merely "stretching" the chemical bonds, so to speak. It's a process of an entirely different nature. I think our earlier calculation was pretty sound, and that something on the order of 100 kJ/kg will prove to be the limit. A watt-hour is 3600 Joules, so the number you just threw out (400-500 Wh/kg) is equivalent to 1.6 MJ/kg.

You are a bit pessimistic about caps. Some laboratories are more optimistic and hope to achieve 350 W-h/kg with graphene supercaps, ultimately.

https://www.quora.com/What-is-the-highest-energy-density-supercapacitor

 

Some researches hope to achieve 500 W-h/kg.

http://www.idtechex.com/research/articles/supercapacitors-can-destroy-the-lithium-ion-battery-market-00006649.asp

 

I don't claim they will succeed anytime soon, though.

 

I think it may be needed to invent completely new type of supercapacitor. One of the goals is to move away from expensive and

flammable organic electrolyte and make a supercap all-solid state device where distance between imaginable "electrodes" will be reduced to atomic distances.

[KipIngram]

Well, I think it would be great if we can have that. And I am not as up-to-date on the latest as you seem to be. My work storing serious energy (for electric launchers and so on) in capacitors was in graduate school, in the late 1980s. And my research group was primarily focused on rotating machinery energy storage (homopolar generators, and one we invented ourselves that we called the compulsator, for compensated pulsed alternator - it had higher output voltage than HPGs).

 

So I should have mentioned earlier, just to complete the picture, that capacitors store energy in the dielectric by stretching the bonds (loosely speaking), and the limit (the dielectric strength) is more or less where the bond strength is exceed and the bonds break. So those really are very fundamental things. Any given material has what it has. So improvements will fall into the realm of material science. Graphene has a relationship to carbon nanotubes, and they're flipping strong, so it wouldn't surprise me too much to learn that similar payoffs can be had in arenas less directly mechanical.

 

Of course, I mentioned diamond, and it's carbon-based as well. Carbon really does seem to be sort of the "super element" in a lot of ways.

[Moreno]

So I should have mentioned earlier, just to complete the picture, that capacitors store energy in the dielectric by stretching the bonds (loosely speaking), and the limit (the dielectric strength) is more or less where the bond strength is exceed and the bonds break. So those really are very fundamental things. Any given material has what it has. So improvements will fall into the realm of material science. Graphene has a relationship to carbon nanotubes, and they're flipping strong, so it wouldn't surprise me too much to learn that similar payoffs can be had in arenas less directly mechanical.

 

Of course, I mentioned diamond, and it's carbon-based as well. Carbon really does seem to be sort of the "super element" in a lot of ways.

It depends on what you mean as a "dielectric". Supercapacitors have no dielectric between their plates. Instead it is the electrolyte

breakdown voltage what usually the main limit which limits the working voltage of the supercaps. Organic electrolytes limit is usually

4-5 V. Ionic liquids withstand 6 V. Solid electrolytes (glass based, for example) may withstand 10 V.

 

Carbon is a wonder element with no doubt, but I wouldn't make all the wages on it. I wouldn't be wondered if "ultimate" supercap will

be something like an all-solid state device and the main material will be some exotic metal alloy or a semiconductor.