An A319 Flight Attendant; crew; and passengers reported a burning rubber smell starting in the aircraft's rear and eventually smelled in the flight station. An emergency was declared with a landing at a nearby airport.

Narrative

Shortly after climbing through 10;000 FT; the Flight Attendant In Charge reported that passengers in the rear of the cabin were complaining about an odd odor in the cabin. She went to the aft cabin for a firsthand observation. In the interim; we checked the applicable ECAM pages and noticed that everything was normal. When the Flight Attendant re-contacted the flight deck; she reported that the smell reminded her of rubber; like a tire smell. ZZZ1 Maintenance had changed a nose gear tire prior to the previous leg and I suggested that we maybe getting odors from the nose gear tire since it was vibrated quite a bit during deceleration after retraction. I asked her to let us know if conditions changed. Although not routine; it is not unusual to have passengers report odors and so at this point we continued on toward ZZZ1. The Flight Attendants notified the flight crew several more times that the odor was persistent; seemed to be moving forward in the cabin; and was detected by an increasing number of passengers. Each time; we checked the ECAM; found all systems normal. Asked the Flight Attendants if any of the passengers were experiencing problems and if the odor was constant. Discussed the sit; and agreed that we could proceed normally. However; about 80 miles from ZZZ; the Flight Attendants reported that the odor was getting stronger and smelled like burning rubber. I confirmed that they said it smelled like something was burning. They answered 'yes.' We agreed that the Flight Attendants would walk the cabin looking for hotspots and call back. I contacted ZZZ Center and told them we may have a problem and would like to begin a descent; just in case. We were cleared from FL390 to FL350 and initially put on a heading for traffic avoidance and then quickly recleared to FL250. After we notified Dispatch through ZZZ operations that we were diverting to ZZZ; the First Officer flew the aircraft while I reviewed/completed the applicable procedures in the Smoke/Fume Removal procedures in the Flight Manual. By this time; our descent was well underway; so I let the aircraft depressurize automatically and then followed the procedures once we reached 1.0 PSID. About 1/2 way through descent; the First Officer and I noticed the odor and donned our oxygen masks. The entire descent was completed in 'Open Descent' -- 'Selected Speed' (300-310 KTS) modes with spoilers fully deployed. During the descent we were recleared direct to ZZZ1. Since it was close to a straight line through ZZZ to ZZZ1 and I had not yet decided to divert; I accepted that clearance but was still positioning myself for ZZZ which was the best alternate given our altitude. The Flight Attendants completed their walkthrough and reported no hotspots; and I asked them again if it smelled like something was burning and if the odor was constant. They answered 'yes.' At this time I told Center that I wanted to divert to ZZZ and was cleared direct with a further descent to 11;000 FT. Around 11;000 FT we were handed off to Approach and I declared an emergency at that time. Continued the descent in open descent with spoilers fully deployed through 7;000 FT. We maintained 300 KTS until 7;000 FT and reported the airspeed deviation to Approach. Once we reached 1.0 PSID; I closed the air conditioning packs and opened the ram air valve to ventilate the cabin. We came off oxygen at this time. I contacted the Flight Attendants for the last time at approximately 10;000 FT to ask about conditions in the back; to ensure they had briefed the passengers on our divert into ZZZ; and to let them know we'd be landing in approximately 5 minutes. They reported the odors were abating and the passengers had been briefed. It was an uneventful visual approach and landing to Runway XXR at ZZZ. One fire truck followed us to the gate. Once clear of the runway; I spoke with the passengers and asked if anyone felt nauseous or ill to please let the Flight Attendant know immediately; so we could have paramedics meet the aircraft at the gate. No passengers reported ill. We had considered the possibility of a cargo fire; and so I asked operations to not open the cargo compartments until we were certain it was safe. At the gate; I spoke with one of the firemen; who agreed to scan the cargo compartments with a thermal scanner prior to opening. Maintenance met the aircraft and although they briefly noticed the odor; it was fairly well dissipated by the time we reached the gate and they could not identify it. Passengers were deplaned and follow-on arrangements were made. Once Maintenance was satisfied and signed off the write-up; we uneventfully repositioned the plane to ZZZ1.