I don't think there is much you can do. You can use the polymerized sand that okdokegal mentioned above,but don't expect to completely get rid of the problem. I have it between my pavers and last year grass managed to take roots between pavers. We cleaned it up and now we have to add some more sand since some of it comes out when you pull the weeds. From looking at your photo, I can't see if there is grass between pavers or moss. It looks like moss to me, which is due to humidity. If you have lowers spots with standing water and some shade, then moss will grow. That can be easily removed.

Does anyone know what type of grass this is? I live in Central NC and the grass is greener in the summer. There is also moss mixed in with the grass.

Actually i also do love moss growing in between pavers, it makes it cool to my eyes in contrast to the brick colors, but since u are eager to kill them, maybe try this, its even saving money, i accidentally threw a used liquid (or more likely the result of waterized moisture - http://www.amazon.co.uk/Interior-dehumidifier-Absorbs-damp-crystals/dp/B007JBIUSW) of dehumidifiers(if youre using it) to a patch or portion of grass which all of a sudden died, and until now( that was a year ago), there are no grass that even grow on it, i dont know much about the components of dehumidifiers, but i suggest be responsible.

Was this a hydroseeded lawn? It looks like it's not getting enough water there to keep the mixture wet so the grass seed can't sprout. It has to stay lightly moist, usually requiring water 4-6 times per day. If it did already sprout and somehow did not get enough water for whatever reason the grass seedlings could have died and will not grow back. Have you personally checked that sprinkler zone to make sure you're getting good coverage in that area or that wind is not blowing the water away from that area?