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