Do constant current batteries exist?
Do constant current batteries exist?


["Battery" used for "cell" in many places below]

Essentially, no.  

A battery could easily be made that had that characteristic by adding electronics in the battery housing, and 'for extra points' one could be devised which electrochemically did a good job of current limiting at a designed maximum current, which would then be a constant current battery. But, such devices are rare or nonexistent. 

A battery can be made to approximate a constant current source by adding a series resistance - the larger the resistance the better the approximation - and the lower the current. So very discharged batteries, with high internal resistances,  are better approximations to constant current sources than fully or partially charged ones.

A photovoltaic cell loaded past its maximum power point also acts as a constant current device. Whether that qualifies as a "battery" is debateable.

Image from Wikipedia - MPPT

V/I characteristics of a "solar cell". 
Here, for voltages below about 0.35 V,  as load increases voltage falls at about constant current. 
Family of lines shjow output at various light levels.



Batteries are also NOT constant voltage devices (see below) 


  If not why?


Simple answer: There are much better ways of implementing constant current energy sources when required. 

A battery is essentially an energy source with a defined voltage &amp; current profile across its discharge range. With the exception of exceedingly specialist reference cells such as the "Weston Cell" which are designed to be constant voltage sources, batteries are also not constant voltage sources - their voltage decreases with both increasing load and decreasing state of charge. While a battery may be optimised to produce a flatter voltage vs discharge curve the usual major aim in battery design is to optimise some mix of energy density*, power density*,  discharge rate, recharge rate, longevity and cost effectiveness.[* both per mass and per volume].  Constancy of discharge voltage is useful but tends to rank below most of these other factors. A lead acid battery is a reasonable approximation to a constant voltage source - but its much preferred LiIon replacement is much less so (4.2 to 3V discharge range or 29% decrease from fully charged). 

Constant current energy supply is much less useful and liable to be even less efficient in terms of the usual design parameters mentioned above. 

When a constant current source is required it can be implemented electronically in such a way as to optimise some mix of accuracy, energy efficiency and cost as required - and the result will be vastly better than could be achieved electrochemically.  This allows the battery design to be optimised for its energy sourcing capabilities. 

A constant current source has, by definition, a high open circuit voltage and operates at little or no output voltage if required when loaded heavily. The energy efficiency of an electrochemical product with this characteristic would be abysmal at low load resistances as the majority of the energy produced would need to be dissipated within the battery. The only alternative would be to in some way reduce the electro-potential of the "driving reactions" as load current exceeded the design current. Alchemists may have been able to achieve this but modern science may be challenged. 



Related:

Constant voltage cells:

Wikipedia - Weston Cell
Ugly truck 


Weston cell - constant voltage reference:   The original design was a saturated cadmium cell producing a convenient 1.018638 Volt reference and had the advantage of having a lower temperature coefficient than the previously used Clark cell.
The temperature coefficient can be reduced by shifting to an unsaturated design, the predominant type today. However, an unsaturated cell's output decreases by some 80 microvolts per year, which is compensated by periodic calibration against a saturated cell.






Wikipedia - Clark Cell


The Clark cell, invented by English engineer Josiah Latimer Clark in 1873, is a wet-chemical cell (colloquially: battery) that produces a highly stable voltage. In 1893, the output of the Clark cell at 15 C was defined by the International Electrical Congress as 1.434 volts, and this definition became law in the United States in 1894. This definition was later supplanted by one based on the Weston cell.1