Check out Robert Murray Smith on YouTube he has some great videos on building active materials for batteries and supercapaitors as well as other things.
Here are a few videos to get you started toward learning how to make the materials or improve on an already existing lead acid battery but make it better so it becomes a cross between a capacitor and a battery, you are supposed to be able to repeatedly completely drain them to 0 without damaging them as well as charge them super fast and make them last longer/increase the number of charge/discharge cycles.
How To Make An Ultrabattery
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How To Build A Better Battery
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Making High Performance Supercapacitor Materials
Here is a video on how to easily make activated carbon, it does not use an autoclave and I don't know if carbonizing under pressure makes any difference on the energy density of the finished carbon or not.
Making Activated Carbon from Food Waste (The CCC Method)
I'm just now getting started on trying to learn and experiment . According to Robert it is a lot better if you have some knowledge of chemistry which I don't have so for me it's just a matter of trial and error.