I have an application where I need a rechargeable battery in a very tight space too small for two 18650’s but large enough for a single 26650 cell. I have done some research on these cells and currently the highest capacity commercial 18650 cells are pushing 3500mAh’s (and here). Since the 26650 cells have a little over twice the volume as an 18650, I expected the capacities to scale proportionally, but the highest capacity commercial cells are a little over 5500mAh. Why are these high cap cells not closer to 7000mAh?
If we just compare the two cells you linked, there is an obvious difference: The 18650 is rated for 5A continuous discharge while the (twice as big) 26650 is rated for 20 A - four times more. The size of a battery is not only determined by capacity (energy density), but also by its current output (power density). The inner structure has to be built in a more massive way if you want to draw a high current from the battery which requires a low internal resistance.
If you check typical applications for these batteries the large 26650 is normally not used in applications that are designed for long running time but rather in those using a lot of power like high-end flashlights.
Why are these high cap cells not closer to 7000mAh?
Because they are not "high cap", just bigger in physical size.
In order to have high power (i.e. high discharge) you have to have the correct Li-ion chemistry which, today, would be Lithium Nickel Manganese (NMC). NMC is a low energy chemistry.
It's the chemistry.
Not all Li-ion are the same. There are a variety of Li-ion chemistries. The lower energy chemistries are more likely to found in larger packages.
Notice the division between chemistries and cell size is at about 150 Whr/kg energy density. With lower energy a bigger cell is required for what a consumer expects to be a reasonable time between charges.
A 26650 Li-ion battery is typically a
LMO, 3.7V Li-manganese LiMn2O4 High power, less capacity, energy=100–150Wh/kg used in power tools. Varied packaging.
LFP, 3.2V Li-phosphate (LiFePO4) with high power (high discharge) but low capacity, high currents and endurance, energy=90–120Wh/kg Beginning to be used as a replacement for lead acid starter and deep cycle.
A 3.6V 18650 Li-ion can be either
NMC, Lithium Nickel Manganese (LiNiMnCoO2) High capacity and high power, energy=150–220Wh/kg
LCO, Li-cobalt (LiCoC2) High energy, limited power. energy=150–200Wh/kg
NCA, Li-aluminum (LiNiCoAlO2) Highest capacity with moderate power. energy=200-260Wh/kg
The above are not hard rules but typical of what is found in the market. There are also batteries that use mixed chemistries. NMC and LMO are often combined to balance capacity and power in a 18650 cell.
For more on Li-ion chemistry see: Types of Lithium-ion
It gets confusing when there are so many charlatans in the battery business. It just gets worse and worse as they try to one up each other with new and bigger lies.
You will find that most 3.7V Li-ion are actually 3.6V in the datasheet. It's the charlatan vendors. Technically only Li-manganese (LMO & NMC) cells are 3.7V.
Since the 26650 cells have a little over twice the volume as an 18650, I expected the capacities to scale proportionally,
The 18650 LCO cell has been around for 30 years so it is the preferred cell size. If you want more capacity or power you wire then in parallel. In the past 10 years newer chemistries have been developed like NMC. NMC and LMO manganese are lower capacity and were more commonly proprietary packaged and high priced. Look at the price of power tool replacement batteries at Home Depot, $100+. To meet consumer run time expectations lower capacity chemistries are packaged in larger cells such as 26650.
As 26650 get used in more consumer products you will see some very high capacity 26650 NMC cells. As the patents begin to run out you will see more licensing deals which will raise market share for NMC.
Patents should be running out an Panasonic's NCA Li-aluminum chemistry. A lot of R&D is currently focused on this highest capacity NCA. Tesla is pushing for it.