FLC OF A CESSNA CITATION; CE750; DEVIATED FROM ASSIGNED HDG FOR TSTMS AFTER ATTEMPTING 3 TIMES TO NOTIFY APCH CTL OF THE NEED TO DO SO. APCH CTLR COULD NOT CLR THEM TO DEVIATE DUE TO THE CONFLICTION WITH DEPS.

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DURING OUR ARR INTO IAD ARPT ON MAY/XA/00 AT APPROX XA45Z; WE ADVISED ZDC OF THE POSSIBILITY OF NEEDING TO DEVIATE FOR WX IN THE AREA OF THE JASON ARR. WE WERE INFORMED THAT DULLES APCH WOULD BE TAKING THE 'HDOF' SHORTLY AND TO ADVISE THEM. AFTER INITIAL CONTACT ON THE ARR; APCH CHANGED OUR CLRNC TO 'DIRECT KNUCK INTXN' FOR THE ILS RWY 12. AFTER READING BACK THE CLRNC AND TURNING THE AIRPLANE TOWARDS KNUCK; WE REALIZED THIS WOULD PUT US RIGHT INTO SOME BUILDUPS THAT NEEDED TO BE AVOIDED ACCORDING TO OUR RADAR. WE TRIED TO CONTACT APCH 3 TIMES TO ADVISE THEM OF THE SMALL; BUT IMMEDIATE NEED TO DEVIATE TO AVOID THIS WX; BUT WITH NO RESPONSE. WE THEN MADE A SOUTHERLY TURN TO AVOID THE WX; AND WERE ABLE TO CONTACT APCH ON OUR 4TH ATTEMPT. WE ADVISED THEM OF THE NEED FOR THE TURN; AT WHICH POINT THEY RESPONDED WITH 'NEGATIVE; THERE IS DEPARTING TFC FROM DULLES TO THE S.' WE WERE ABLE TO RETURN TO COURSE AND AVOID THE WX SINCE WE HAD ALREADY MANEUVERED SOMEWHAT. A HEATED DISCUSSION THEN ENSUED FROM THE CTLR ABOUT 'HOW OTHER ACFT HAD NOT HAD ANY PROBS ON OUR TRACK AND HOW HE 'MUST BE CONTACTED BEFORE ANY DEVS ARE MADE.' WE DID TRY TO CONTACT HIM AND HIS 'NO RESPONSE' LEFT US NO CHOICE BUT TO DEVIATE FOR THE WX. CTLRS NEED TO BE SENSITIVE/RESPONSIVE TO AN ACFT'S NEED FOR WX AVOIDANCE. NO OTHER ACFT WERE INVOLVED IN THIS EVENT.