LESS THAN STANDARD SEPARATION BETWEEN COMMUTER AND GA TWIN. OPERATION ERROR.

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I AM A DEV TRNEE AT PHL TWR. I HAVE CERTIFIED THROUGH THE CTL TWR AND CURRENTLY TRNING IN THE TRACON WHERE I HAVE CERTIFIED ON 3 RADAR POSITIONS. I WAS WORKING MODENA SECTOR (N DEPS); WHICH I HAD BEEN CERTIFIED. IT WAS A BUSY SESSION INCLUDING WORKING OVERFLTS AS WELL AS DEPS. A COMMUTER WHICH DEPARTED PHL WAS INITIALLY GIVEN A CLB TO 6000'; THEN 7000' AND A WESTERLY HDG FOR IN TRAIL SPACING OVER THE PTW VORTAC. A TWIN ENG (LIGHT) WAS SBND ON V29 S OF PTW AT 7000' OVERFLYING PHL AIRSPACE. BOTH ACFT WERE IFR UNDER RADAR CONTACT. DURING COURSE OF EVENTS REALIZING SEP MAY BE LOST I ISSUED TFC TO THE COMMUTER; SUBSEQUENTLY DSNDING AND TURNING TO AVOID THE TWIN. IN TURN I ISSUED TFC AND VECTOR FOR THE TWIN; NO RESPONSE. HE WAS NEVER SWITCHED TO MY FREQ. SEP WAS LOST AND DETERMINED TO BE 7/10 MI LAT. THE VOL OF TFC AT THE TIME WAS 9-10 ACFT. BASICALLY THEY INCLUDED JETS AND COMMUTER PROPS. I HAD TAKEN ACTION TO ALLEVIATE SOME OF MY PROB BY STOPPING DEPS INTO MY SECTOR BEFORE THIS INCIDENT. BUT; BASICALLY I HAD REACHED MY LIMIT IN AIRPLANES AND SAW THE SITUATION A LITTLE LATE. I WANT YOU TO KNOW THAT I HAVE TAKEN FULL RESPONSIBILITY FOR THIS INCIDENT AND HOPE YOU RESPECT THE INTENT OF THIS LETTER.