Abstract
The impressive photopysical properties offered by semiconductor
quantum dots (QDs) when compared with traditional organic
dyes have seen them emerge as viable alternatives to their organic
counterparts in biolabelling and sensing applications [1-3]. In
particular, the broad absorption spectra of QDs, coupled with their
narrow size-dependent emission spectra, mean they are ideal for
use as energy donors in Förster (or fluorescence) resonance energy
transfer (FRET) applications. FRET involves the non-radiative
transfer of excitation energy from an energy donor to the ground state
of a nearby acceptor molecule through a dipole-dipole interaction
[4]. The efficiency of energy transfer between the two fluorophores
is governed by two main factors: (1) the distance between the donor
and acceptor molecules and (2) a good spectral overlap between
the donor’s emission and acceptor’s absorption spectra. In addition
to these criteria, it is essential that the dipoles of both donor and
acceptor molecules are parallel to each other for efficient energy
transfer to occur. Should the dipoles be perpendicular the energy
transfer efficiency is zero. The FRET efficiency (E) can be calculated
using Eq. 5.1 [4]:
E = 6011 + ( / )r R (5.1)
where r is the actual donor-acceptor separation distance (in Å)
and R0 is the donor-acceptor separation, i.e., the distance when the
energy transfer is 50% (the Förster radius). R0 can be found from
Eq. 5.2: [4]:
26 00 5 4 A9000 (ln10)128Q K JR n N= (5.2)
where Q0 is the fluorescence quantum yield of the donor in the
absence of the acceptor, K2 is the dipole orientation factor (which
varies from 0 for perpendicular alignment of the D-A dipoles to 4
for parallel alignment), n is the refractive index of the medium, NA
is Avogadro’s number and J the spectral overlap integral that can be
found from Eq. 5.3 [4]: 4D A( ) ( )J f d= ∫ l e l l l (5.3)
where ƒD is the normalised donor emission spectrum and eA is the
acceptor molar extinction coefficient.
Experimentally, E can be measured using either steady-state
(Eq. 5.4) or time-resolved (Eq. 5.5) fluorescent experiments [5]: DA
1 F
E
F
−= (5.4)
1
E
−=
(5.5)
where FDA and FD are the fluorescence intensity of the donor in the
presence and the absence of the acceptor, respectively, while τDA and
τD are the fluorescence lifetime of the donor in the presence and
absence of the acceptor, respectively.
In spectroscopic terms, an increase in E will manifest itself in
a reduction in the donor fluorophore emission with a concomitant
increase in the emission from the acceptor fluorophore. From
Eq. 5.1, it can be observed that there is a sixth power dependence
of E on the donor-acceptor separation distance meaning that
small changes in this separation can manifest itself in a significant
modulation of the acceptor emission. Thus, FRET has earned
the term “spectroscopic ruler” as it can be used to probe separation
distances between 10 and 100 Å in biomolecules and provide
information on their conformational arrangement in different
environments or upon binding a target molecule [4].
Although the dipole-dipole interaction and sixth power
dependence of the donor-acceptor separation distance are features
of the FRET mechanism that have been determined by analysis of
pairs of organic fluorophores, they have also been proven to be
applicable with significantly larger QDs [6]. In addition, there are
several significant benefits of including QDs as energy donors in
FRET pairs:
1. The broad absorption spectra of QDs means they can be
excited with any wavelength less than their emission
wavelength. This flexibility of selecting an excitation
wavelength that can be hundreds of nanometres less than the
emission wavelength means QDs possess enormous Stokes
shifts. This feature significantly reduces the “direct excitation
contribution to acceptor photoemission” that is common
with all organic donor-acceptor pairs due to their small
Stokes shifts and broad absorption spectra [7, 8]. As a result,
complicated deconvolution is often required to separate the
donor and acceptor emissions thus reducing the effectiveness
of the technique.