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.
