Using recently calculated rate coefficients for reactive coupling of c
hains at polymer-polymer interfaces, we describe the diffusion-control
led growth of diblock copolymer at the interface between dissimilar mo
lten homopolymer films. The growth exhibits several regimes, successiv
ely controlled by (1) the quasilocal reaction rate near the interface,
(2) center-of-mass diffusion of reactive homopolymer to the interface
, and (3) the diffusion barrier presented by the growing copolymer lay
er. Our results can be tested by time-dependent measurements of the co
polymer coverage or concentration of reacted coupling groups.