Simulation of Dynamic Scattering from Homopolymer and Symmetric Diblock Copolymer Solutions with the Bond Fluctuation Model Ana M. Rubio, J. Felicity M. Lodge, and Juan J. Freire* Departamento de Quı ´mica Fı ´sica, Facultad de Ciencias Quı ´micas, Universidad Complutense, 28040 Madrid, Spain Received December 6, 2001; Revised Manuscript Received March 25, 2002 ABSTRACT: The dynamic Monte Carlo algorithm is employed to explore the dynamic scattering of dilute and nondilute solutions of flexible linear chains. The chains are represented by the bond fluctuation model with and without attractions between nonbonded units placed at close distances, to describe different types of thermodynamic conditions (Θ or good solvents). This mimics the behavior of real chains in the different types of solvents. We also consider symmetric diblock copolymer chains in a nonselective good solvent, where the differences between the blocks are introduced in the scattering factors of the beads and, also, through a net repulsion between units belonging to different blocks. The analysis of the dynamic scattering functions for semidilute solutions reveals the presence of at least two different modes. In the homopolymer chains, one of the modes follows the behavior expected for the osmotic mode in the gel regime. The other mode seems to correspond to the structural relaxation, in the case of Θ systems at low values of the scattering, q. At higher q and for good solvents this mode is faster than expected from theory. It can tentatively be assigned to chain end effects. The total intensity at q ) 0 gives results consistent with the scaling theory for good solvent. The Θ systems show a dramatic increase for this intensity, which is mainly manifested in the slowest collective mode, due to the proximity of critical conditions. For the copolymer chains, we observe a main internal mode, related with the longest Rouse relaxation, and a secondary faster mode that can be due to the accumulation of shorter Rouse motions. The introduction of a moderate repulsion between units in different blocks is manifested through a more prominent peak in the total intensity. Some decrease of the rates is also observed for the same q values, probably caused by the onset of the order-disorder transition. Introduction Scattering radiation experiments are currently con- sidered powerful techniques to study the dynamics of a great variety of polymer systems. 1 The “coarse-grained” nature of polymer systems at not very short distances can be adequately monitored through light or neutron experiments. The experiments yield decay curves that, in many cases, can be related with theoretical time- correlation functions generally denoted as dynamic scattering functions. 2 For chains in dilute solutions, these functions can be easily calculated with the simple Rouse or Zimm models. 3 However, the dynamics of semidilute solutions is considerably more complex, 3,4 though many features of the dynamic scattering behav- ior have been predicted through the application of approximate theories. 5,6 On the other hand, these systems can also be studied by computer simulation. 7 The dynamic trajectories can yield “collective” dynamic scattering functions, 8 directly comparable to the experi- mental data, and also “intermediate” scattering factors, the latter being the contribution to the scattering from individual chains, averaged on the system. The inter- mediate scattering factors can be related with experi- mental neutron scattering from labeled chains or, sometimes, with light-scattering experiments, if the contributing modes are not sensitive to intermolecular interferences. However, the time scales involved in the simulation of scattering functions are very long and purely dynamic simulations, i.e., molecular dynamics, cannot be practi- cally employed. 7 For this reason, only dynamic Monte Carlo methods with coarse-grained models are presently adequate to accomplish this type of study. These meth- ods rely on the use of “single jump” moves that try to mimic small stochastic perturbations on real polymer beads, and therefore, the choice of a particular coarse- grained model may be important to their actual ap- plicability. Lattice models are particularly useful from the computational point of view, being the only ones that can provide an efficient description of relatively large systems. The choice of elementary moves for individual units is, however, an artificial characteristic of conven- tional lattice methods. For instance, the simple cubic lattice model has to combine elementary “bents” and “crankshaft” in order to ensure a close-to-ergodic algo- rithm. 9 The bond fluctuation model 7,10 was devised to offer the computational benefit of lattices and the more realistic characterization of systems represented by the open space simulations. This model offers a considerably higher number of empty positions available around an occupied site and, furthermore, it only needs a single and simple form of elementary move. These character- istics make this model adequate for Monte Carlo dynamics, especially if interactions between nonbonded units are included, as it is required to study the influence of solvent quality. In the present article, we report the results obtained for dynamic scattering functions of several different types of many-chain systems in the diluted, semidilute or concentrated regimes. We have considered homopoly- mer chains in good and Θ solvents. The good solvent systems are represented by self-avoiding walk (SAW) chains. The Θ systems include additional attractions between nonbonded units placed at short distances. 11,12 Also, we have studied symmetric diblock copolymer 5295 Macromolecules 2002, 35, 5295-5303 10.1021/ma0121262 CCC: $22.00 © 2002 American Chemical Society Published on Web 05/25/2002