Why do capacitors have less energy density than batteries?

Question

The basic operating principle of a battery is, in order to charge it, the electrons are removed from cathode and moved to anode by applying voltage. And to discharge, the electrons move from cathode to anode creating an electric current.

This principle is extremely similar to what happens in a capacitor. Even though there are high energy density capacitors, their energy density never matches with, say Li-ion batteries. Why is this?

Answer 1

This is more of a chemistry question, but the basic idea is, well, chemistry.

A capacitor imposes an electric field around a dielectric, which can only store energy until it breaks down (typically a runaway ionization process). Ionization requires a few eV/atom to occur, but it can be triggered at much lower field strengths per atom/molecule, because a free charge moving through the dielectric is accelerated by the field and able to cause much more damage (i.e., an avalanche cascade).

Thus, capacitance is limited by surface area, and surface area is limited by how well it can be connected (the metal has to be nonzero thickness), and the minimum thickness of dielectric required to hold off the rated voltage.

There are also mechanical limitations, like for very low voltages, dielectrics can't be made thin and perfect enough, and density tends to suffer. Across most dielectric types, modest-voltage capacitors (a few hundred volts, ballpark) have the best CV² (energy) product per volume. CV (charge) also tends to go up with rating.

Whereas batteries store energy by chemical reaction: a redox potential of up to several volts per atom, and thus several eV per electron exchanged. Not all atoms in the electrodes can participate -- some structure must remain to be restored during charging, for reusable chemistries anyway -- but a sizable fraction can, and with several eV/atom, the density is vastly higher. The downside is, it's a material-transport limited process. Diffusion being the dominant transport mechanism on the smallest scales (which is directly sensible as the Z ~ 1/√f internal impedance characteristic of most batteries). Material transport is also part of why rechargables wear so notoriously (as mentioned above, some structure is required, but that structure gets distorted as material is cycled through it), among other reasons: there are also side reactions, like lead-acid sulfation, or lithium ion metal dendrite formation or electrolyte decomposition, etc.

Is there an inbetween case? Yes! We can cause ions to migrate subject to an electric field (double layer effect). The maximum potential is quite low (comparable to battery terminal voltage: 2.5V or so for typical electrolytes in use), but this corresponds to the energy per ion, roughly speaking. The hard part is influencing enough ions to make a dent. And this is where surface area comes into play: an extremely porous material like activated charcoal, which also happens to be conductive, serves as the electrode. Downside: the pores are extremely deep, so it takes a very long time for charge to equalize.

A typical experiment is to take commercial ingredients (activated charcoal, salt water, ionic membrane) and construct such a capacitor; while the capacity is impressive for such meager materials (it can be in the kF/cm³ range!), the charge rate is incredibly low: you'll only measure such large capacitances over time periods of days. (Water is also a poor electrolyte, breaking down at ~1.2V. But within that 1.2V range, yeah, it works.)

There are even more direct hybrid types, which I don't know the particulars of, but a good jumping-off point is Supercapacitor | Wikipedia.

In general, speed and density are in an inverse relationship. Transmission lines, and ceramic and film capacitors, are the fastest possible materials and structures (sub-ns to µs). Type 2 ceramic and cheaper grades of film are denser but slower (~µs), and aluminum electrolytic slower still (~µs to ~ms). Supercaps are slower still (~s), and batteries slowest (~ks).

Answer 2

The basic operating principle of a battery is, in order to charge it the electrons are removed from cathode and moved to anode by applying voltage. And to discharge the electrons move from cathode to anode creating an electric current.

This account is missing something very crucial. When a battery is charged or discharged, chemical reactions take place, either at the anode, the cathode, or both. Most of the stored energy that is available in a battery is in the form of chemicals that can potentially react with each other, rather than in the form of an electric field, as in a capacitor. Yes, electrons move in charging and discharging process of a battery, but the chemical reactions are what are what make a battery distinctive and different from a capacitor.

even though there are high energy density capacitors their energy density never matches with say Li-ion batteries. Why is this?

I don't believe there is a physical law that is responsible for batteries being more energy dense than capacitors, but rather the materials we have at our disposal at this point in history that the case.

The energy in a capacitor depends upon the surface area of the plates, their distance apart, the dielectric constant of the dielectric and the break-down voltage of the dielectric. The energy in a battery depends upon the chemistry of the battery and the mass of the reacting chemicals. It just so happens that in this day and age, the battery wins in the energy density competition. However, if we were to discover tomorrow some materials with orders of magnitude higher dielectric constant, or orders of magnitude higher break-down voltage, the winner in the competition would be capacitors.

Answer 3

A very, very simplified picture:

A capacitor stores energy by deforming existing chemical bonds. This is how charged particles in a dielectric react to the electrical field. One can tension them only so much before some of them break (and this amounts to a capacitor failure). Pretty much analogous macroscopic process is the elastic deformation.

On the other hand, a battery stores energy by rearranging (i.e. completely removing and creating new) chemical bonds in an orderly manner. This process involves much more energy per chemical bond (or, generally, per amount of substance). Analogous to e.g. burning.

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So the capacitor and battery energy capacity compare generally like e.g. a rubber piece being used as a spring and the same being used as a fuel.

Answer 4

• Capacitors working principle is a Electrostatic Potential Differential developing along two isolated same-material conductors surface-area sepparated by a dielectric (a non conducting insulating material); the dielectric material occupies a big part of its volume along the polar surface areas. It suffers no chemical reactions on its inside since it works on a fundamental physical principle, the electrostatic force by the means of a electron mobility principle called Faraday Law. Then Capacitors are simplistic devices working on a fundamental force of nature as its principle, with a metallic surface-area which suffers polarization; Due a voltage the dielectric (insulating material) sustains the electrostatic force as a form of potential energy C (The capacitance) developing betwen attracting polar surface-areas distant by a dielectric e due Lenz Principle.
• Batteries do not have a dielectric instead their working principle depends on electrochemical mobility (electron holes, not differential potential) which is a form of conductance not dielectric. Being usually made from composite materials where one is electropositive the other electronegative, normally mantaining it's electrochemical reaction potential untouch until the circuit is closed and electronegative compound commences leveling the chemical potential of Charged atoms (Lorenz force) by easing electron flow to the electron-deficient cathode by the means of Strong chemical electron exchange being that times stronger than Electrostatic thus achieving higher currents, and lot of heat as byproduct. The heat itself is compensated in the battery chemical compound itself otherwise the battery would short.
  
• The case of lithium-ion batteries is identical to the working principle of batteries but under chemical restrictions for charge-discharge due heat produced by the aditional charge lithium permits; discharging then through an enhanced conductive material through its anode some considerable amounts of current flow as the compound itself is nanoengineered to achieve the thermal/flow performance.

Answer 5

There have been some REALLY good indepth answers here.

Caps have a low internal resistance... so they can discharge / charge a stack of current really quickly (much quicker than a battery). This is their job.

of course I'm over simplifying... depends on the cap... depends on the battery.