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Using optical birefringence, small-angle neutron scattering, and field-theoretic methods, we study the effects of frustrating quenched randomness and connectivity on microphase ordering in copolymer melts. Our results show that randomly grafted copolymers are good model systems to examine these effects, and we find that these materials exhibit behavior different from that observed heretofore for other types of molten polymers. (S0031-9007(99)08822-5) PACS numbers: 61.41. + e, 61.12.Ex Mixtures of incompatible homopolymers form distinct macroscopic phases when cooled below a certain tempera- ture. In contrast, due to frustration presented by chain connectivity, molten copolymers comprised of incom- patible segments form ordered microphases when cooled below the phase transition temperature. The physics of microphase ordering in copolymers with ordered se- quence distributions (e.g., diblock copolymers) has been studied extensively, e.g., (1), and many exotic microstruc- tures with potential applications have been observed. Recent years have witnessed a surge of interest in copolymers with disordered sequence distributions. A simple example is provided by connecting two types of segments to form linear chains with disordered sequences (a linear random copolymer or LRC). The disordered se- quence distribution is quenched and leads to frustrations not present in copolymers with ordered sequence distri- butions. Fundamental interest in systems with quenched disorder and the relevance of LRCs as models to study protein folding have motivated many theoretical studies, e.g., (2). The effects of frustrating quenched randomness and chain connectivity on microphase ordering in LRCs have been considered by theorists, e.g., (3). Theorists have also examined the disordered molten state of polymers with quenched randomness and branched architectures, e.g., (4- 6). However, experiments probing microphase ordering in copolymers with disordered sequences have not been conducted, largely because of the difficulty of synthesiz- ing LRCs with controlled sequence statistics. We consider a class of copolymers that embodies competing interactions and frustrating sequence disorder that can be synthesized with well-characterized sequence statistics. Specifically, we have a homopolymer backbone (A-type segments) of length N onto which are grafted p branches (B-type segments) of length M. The branch points are randomly located on the backbone and cannot anneal after synthesis is complete. Each chain in a melt of these copolymers has a different sequence of branch points. We refer to these materials as randomly grafted copolymers (or RGCs). An RGC was synthesized by a combination of anionic polymerization and selective silane coupling (7). Microphase ordering in this well- characterized RGC melt wherein the branch point fluctuations are short range correlated with a mean value of pyN is then studied by optical birefringence and small-angle neutron scattering (SANS). We also develop a field-theoretic model for describing microphase ordering in such RGCs. Our analysis shows that as the system is cooled below the microphase transition temperature, the length scale on which the system orders is first strongly temperature dependent and then becomes essentially tem- perature independent. In the latter region, the theoretical analysis is in excellent agreement with our SANS data. We discuss the physical origin of the observed behavior which is different from that predicted for LRCs and that observed for diblock copolymers. Consider Np chains, with risnd being the spatial loca- tion of the nth segment on the backbone of the ith chain, and let rijsmd be the spatial location of the mth segment of the jth branch on the ith chain. Let the set hnijj represent the quenched locations of the branch points. The partition function for a particular realization of branch point loca- tions can be written as

Microphase Ordering in Melts of Randomly Grafted Copolymers