The 11th was on the Bloomsfield expedition in November 1861 while Grant was at Belmont, right?
Found these on the 'net, you may have seen these:
http://www.autographcollector.com/civilwar.html
http://www.geocities.com/cindyparkinson/
http://www.webbdeiss.org/webb/webbgallery/serv_rec2/
http://www.lib.ua.edu/libraries/hoole/findingaids/indexsql.php?alpha=k
Nathaniel C. Kenyon diary, 1862-1865, 1 item, 36 pieces; photocopy, typescript
Contains a photocopy of a typescript of the diary this Union officer with the 11th Illinois Infantry kept from before and during his capture in Tennessee. He provides fairly detailed descriptions of life as a prisoner of war in Tuscaloosa, Alabama, and other southern cities.
There is another diary I can't locate right now - it is Chicago Historical Society I think. An officer. There was an article in Company of Military Historians years back, if I recall correctly.
John