Fluorescence Spectroscopy as a Tool for Investigating the Self-Organized Polyelectrolyte Systems - Self Organized Nanostructures of Amphiphilic Block Copolymers - page 227

Fig. 19 Polymer model used in the simulations. Red uncharged monomer units, blue charged
monomer units, grey counterions, brown fluorophore

4.1.1 The Model

In the simulation study of fluorescence anisotropy decay, a generic bead-spring
model of the polymer was used. It is schematically shown in Fig. 19 . Each bead
can represent one or several monomer units in a real polymer. The degree of disso-
ciation, , is defined as the fraction of monomer units carrying electric charges. The

interaction between monomer units of the polymer is modeled by the Lennard-Jones
potential and the solvent quality is controlled by the depth of this potential,

α

ε .As

shown by Micka, Holm and Kremer, 0.34 corresponds to the theta state [ 146 ] .

The simulation study was performed for several values of

ε ≈

0.33, i.e., under poor
solvent conditions. The simulation technique used was MD coupled to a Langevin
thermostat, i.e., the polymer was simulated in an implicit solvent. The counterions
were simulated explicitly. A more detailed description of the polymer model can be
found in the original paper [ 87 ] .
The fluorophore was modeled by two beads that are attached as a short pendant
side-chain (tag). Both the absorption and emission dipole moments of the fluo-
rophore are defined by the direction of the tag (parallel), as indicated by the vector
in Fig. 19 , and the fluorescence anisotropy was calculated from its orientation au-
tocorrelation function. For simplicity, we assumed that the reorientaional motion of
the fluorophore is the only source of fluorescence depolarization. We neglected en-
ergy transfer and other processes that might occur in real systems. The fluorescence
anisotropy decays were interpreted using the mean relaxation time, defined as:

ε >

A i τ i

∑ i

∞

=

A i =

( ) .

τ r t d t (18)

mean

∑ i

0