We have used neutron reflectivity to measure concentration profiles of brushes of grafted chains in the melt. A method has been developed for permanently grafting end-functionalized polymers to a silicon substrate. By changing the matrix polymer surrounding the brush, we have investigated how the conformation of the brush depends upon the interaction between the matrix and brush polymers. We have observed strong stretching of the blush chains when the matrix and brush interact favorably, and collapse of the brush onto the substrate when they are immiscible. Comparisons have been made with theoretical predictions for the height and width of the brush, and experimental profiles have been compared with numerical self-consistent field theory.