Fluorescent J-Aggregates and Their Biological Applications - Advanced Fluorescence Reporters in Chemistry and Biology - page 136

1 Introduction

The dyes exhibiting response manifested in change in one or several parameters of their
fluorescence spectrum (quantum yield, maximum wavelength, excited state lifetime,
etc.) are widely used in sensing. This response can be caused by various reasons. Here,
one kind of dye response will be discussed, i.e., the formation of their associates
or aggregates that often leads to drastic changes in the spectroscopic properties.

2 Molecular Aggregates and Their Spectroscopic Properties

Molecular aggregates are the stable structures formed by a number of molecules
noncovalently, i.e., by van der Waals, hydrophobic, and Coulombic interactions.
The effect of such assembling of several identical molecules into an associate
strongly depends on several factors, first of all on the interaction energy. This
dependence could be understood in the terms of the exciton theory, developed by
Frenkel [ 1 , 2 ] and then by Davydov [ 3 ], that describes the structure of energy levels
of the infinite crystal based on one molecule in an elementary cell. If we consider
the energy of intermolecular interaction in an aggregate to be much smaller than
that of the intramolecular one, we could regard the wave function of the aggregate
to be equal to the product of wave functions of the molecules, and the intermole-
cular interaction energy as the small perturbation of the internal energy of the
molecules. Then, the Schr¨dinger equation applied for the ground and excited states
of an aggregate gives the energy of these states, the difference of which equals to

E f ðk L f ðk D Þ¼De f þ D f þ Þ:

De f being the difference between the energies of ground and excited states of a
monomer molecule, D f accounts for the change in the energy of the molecule's
interaction with its neighbors upon excitation, and

X

L f ðk e ikðnmÞ :

M f nm Þ¼

m;m6¼n

m determine the positions of n -th and m -th molecules, and M f nm is the matrix
element describing the excitation transfer from the n -th molecule to the m -th one:

~ n and ~

Z

M f nm ¼ f n f m V nm f

o
m

f
n d

f t

f m are the wave functions of n -th and m -th molecules in the
ground and excited states, respectively, V nm is the operator of n -th and m -th molecules
interaction energy, and d

n m f n and

where ' ;' ;' '

t

is the elementary volume. If the one-dimensional