I do not find a Samuel Chapman in the 36th Illinois but do find him here:

Samuel Chapman

Residence Plato IL;
Enlisted on 8/17/1861 as a 1st Lieutenant.
On 9/23/1861 he was commissioned into "Smith's" Co. IL Indpt Cavalry
He Resigned on 4/1/1862

Sources used by Historical Data Systems, Inc.:
- Illinois: Roster of Officers and Enlisted Men