THE CONTROLLER ISSUED A TAKEOFF CLEARANCE FOR SIMMONS 4085 TO FLY THE RUNWAY HEADING. UNITED 556 WAS NEXT TO TAKEOFF AND WAS ISSUED A CLEARANCE TO FLY A HEADING OF 140 DEGREES AFTER TAKEOFF. THE PILOT DID NOT TURN IMMEDIATELY TO 140 DEGREES AND SEVERAL ATTEMPTS BY THE CONTROLLER TO CONTACT THE FLIGHT WERE TO NO AVAIL. IN AN ATTEMPT TO PREVENT THE UNITED FLIGHT FROM OVERTAKING THE SLOWER SIMMONS FLIGHT, THE CONTROLLER STOPPED UNITED FROM CLIMBING. RADAR SEPARATION OF 3 MILES HAD ALREADY BEEN LOST BY TIME THE UNITED FLIGHT STOPPED ITS CLIMB.