Theoretical physics for better batteries? It is Earth day, so I started thinking about the theoretical physics problems that could help reduce greenhouse-gas emissions and fight climate change. 
We actually have a reasonable range of ways to generate energy without fossil fuels. The problem is, however, that the energy is generated by large immovable plants and that these plants cannot be just switched on and off at our convenience. This is quite unlike fossil fuels, which can be ignited and put out very quickly, and which also have a very high energy density so that they can be just carried around by various vehicles as an energy source. 
For example, this means that renewable sources such as solar or wind, which output unevenly throughout the year or even the day, often have to be backed and strongly assisted by fossil fuels either way. On the other hand, nuclear fission reactors really cannot be turned off for the few hours of electricity usage dips during the day and night. Things such as pumping water up dams at some loss then have to be done with the energy surplus. This so-called pumped-storage hydroelectricity seems to be a reasonable solution to even out the electricity demand but its availability may depend on geography and a number of other factors. Either way, we still need an energy source for vehicles.
It seems that the most realistic option is to replace fossil fuels in vehicles by batteries that are charged through an electric grid. These should then power our vehicles and also possibly assist with the fluctuations of electricity needs during the day. However, there is a number of challenges. Batteries currently do not have the same energy density as fossil fuels and they tend to be relatively short-lived. For instance, commercial airliners will never go electric with current technology because the batteries are simply too heavy. Batteries also require rare materials and elements to be built. 
I believe that most of the development of new batteries is on the side of engineering or experimental physics. However, are there any theoretical-physics problems that stand in the way? Is there a problem in theoretical physics whose solution would allow to make batteries lighter, simpler to make, and/or long-lived? Are there promising lines of theoretical research in this direction?
 A: You suggested correctly that producing better batteries (in terms of their capacity and cycle life) is more of an engineering problem than a theoretical physics one. Still, it's useful to understand where the faults of existing batteries come from.
The sources of bad performance for existing batteries are:


*

*defects in electrode composition

*loss of electric contact between electrode parts

*side reactions at the interface between the electrode and the electrolyte
Basically, it boils down to a simple fact that we cannot precisely control where the atoms of the battery materials are located. If we could, battery scientists would come up with an optimal electrode and electrolyte material, optimal distribution of defects and dopants in them, optimal structure and shape of their assembly, and optimal interface between the electrode and the electrolyte.
The term for the idea is atomically precise manufacturing, and researchers have been working towards it, either by looking at self-assembling systems or by upgrading existing scanning probe microscopes to move individual atoms. There's a number of works on battery self-assembly (1, 2), material creation with biological vectors and atomic layer deposition. In particular, atomic layer deposition is an obviously physical approach to atomically precise manufacturing. It is painfully slow, but it may work fine enough to produce thin film batteries, with the thicknesses of electrodes and electrolyte layer in the range of several hundred nanometers. These are suitable for thin-film all-solid-state batteries. 
I haven't found any evidence that atomically precise manufacturing has been researched for molten salt batteries. There is some traction that I have found outside of my usual lithium-ion interests: there's a need to create atomically precise arrays of nanopores for membranes to be installed in fuel cells, and redox flow batteries apparently need atomically reproducible molecular clusters to be used in catholytes.
I don't know how the future atomically precise manufacturing technology is going to work, but the tech we have now -- self-assembly, bio-inspired and ALD -- will likely be the precursors for the upcoming new tech.
A: Room temperature superconductors for SMES, superconducting magnetic energy storage, would be nice. They'd also make an international power grid practical. Such a grid would reduce the need for the storage systems that wind & solar power systems require.
A: The inner resistance of the battery can have a huge impact on its efficiency.
You may already know that resistance is  the constraint of charges flowing in a circuit. Depending on the current a battery can supply and the value of the internal resistance, it can become hot and therefore energy is transferred to heat. For batteries, this is problem which wants to be mitigated as much as possible.
If a battery has a tendancy to get hot when someone is using it to power their  circuit, some of the chemical energy is transferred to heat instead of electrical energy and is therefore lost reducing the useful energy out.
Also depending on the voltage rating of the battery, since Current = Voltage / Resistance, the higher the internal resistance of the battery, the lower the current which can be supplied to the circuit which can be problematic for some designs.
For example:
If a AA battery (1.5V) has a internal resistance of 30 ohms (made up resistance), it would only be able to supply 0.05A which is technically more than enough for a small circuit but if we were to change the resistance to a much higher value, the current would be much less. This is without factoring in the resistance of the circuit.
There are various ways in which this problem can be reduced which would greatly increase the efficiency of the battery, which would also make it a lot friendlier for the environment as many people dispose hundreds of alkaline batteries a year.
I would suppose that some of these batteries would have built in obsolescence sadly as of course the company who makes these batteries will still need a steady income of money.
I would hope that batteries, much like you said will improve allowing us to rely on more greener ways of producing electricity which would be of course much better for the world.
