A theory is presented to describe the nucleation and subsequent growth of weakly inhomogeneous lamellar phases from a supercooled disordered phase. Detailed calculations are performed for the case of nearhyphen;symmetric diblock copolymer melts, although the results have relevance for other physical systems in the Brazovskii lsquo;lsquo;universality class.rsquo;rsquo; Nucleation phenomena in such systems are particularly interesting because the bulk phase transitions have a very weak, fluctuationhyphen;induced first order character. We find unusually small nucleation barriers and critically slowed growth kinetics. For a diblock copolymer melt with degree of polymerizationNand undercooling dgr;prop;(Ttminus;T)/TtLt;1, the barrier is of order Dgr;Fast;/kBTsim;Nminus;1/3dgr;minus;2. Our estimate for the completion time of the nucleation and growth processes is thgr;csim;N1/12dgr;minus;3/4tgr;dthinsp;exp(Dgr;Fast;/4kBT), where tgr;dis the copolymer terminal relaxation time.
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