Discussion

An estimate for the enhanced absorption of a LH2 complex in the vicinity of a AuNP can be obtained by considering a metallic sphere that is illuminated by a plane wave 𝐸⃗ _{𝑛𝑜𝑁𝑃}= 𝐸⃗ ₀𝑒^{−𝑖𝜔𝑡} = 𝐸₀𝑛̂_𝐸0𝑒^{−𝑖𝜔𝑡}. Here 𝐸₀ denotes the amplitude of the incident electric field, which is linearly polarized along the direction of the unit vector 𝑛̂_𝐸0. In the limit where the size of the NP is much smaller than the wavelength of light, the dominating contribution to the scattered field comes from the dipolar component [173]. Within this approximation the electric potential in presence of the NP is given by [174]

Figure 5.7: Comparison of the distributions of the fluorescence response from individual LH2 complexes from Rb. sphaeroides on bare SiO2 substrates (grey bars, 745 complexes) and on AuNP-covered SiO2 substrates with a (20 ± 5) nm PVA spacer layer between LH2 and the AuNPs (green bars, 777 complexes). Intensities are given in units of 〈𝐼_𝑟𝑒𝑓〉, which corresponds to the mean of the intensity distribution obtained from LH2 on bare SiO2 (grey bars). The mean (standard deviation) of the histograms are 1.0 (0.5) (grey) and 0.9 (0.5) (green), respectively. The negative values on the abscissa are an artefact that occurs for low intensity complexes that undergo blinking. This is not relevant for the conclusions. Figure from [131].

5.4 Discussion 75

𝜑_𝑁𝑃 = 𝜑_{𝑛𝑜𝑁𝑃}+ 𝜑_{𝑠𝑐𝑎𝑡𝑡𝑒𝑟} = −𝐸⃗ ₀⋅ 𝑟 + 𝑅^{3 𝜀}_2𝜀^{𝑁𝑃−𝜀𝑀𝑒𝑑𝑖𝑢𝑚}

𝑀𝑒𝑑𝑖𝑢𝑚+𝜀_𝑁𝑃 𝐸⃗ ₀⋅𝑟

𝑟³ 5.1

Here 𝜑_{𝑛𝑜𝑁𝑃} corresponds to the electric potential without NPs, 𝜀_𝑁𝑃 and 𝜀_{𝑀𝑒𝑑𝑖𝑢𝑚} denote the dielectric functions of the NP and the surrounding medium, respectively. 𝑅 corresponds to the radius of the NP, and 𝑟 = 𝑟𝑛⃗ _𝑟 refers to the radius vector from the origin, which is placed in the centre of the NP. For brevity the time dependence of the electric field has been omitted. The amplitude of the electric field in the presence of the NP follows from 𝐸⃗ _𝑁𝑃 = −∇𝜑_𝑁𝑃 which yields

𝐸⃗ _𝑁𝑃= 𝐸⃗ ₀− 𝛽^𝑅_𝑟3³𝐸⃗ ₀+ 3𝛽^𝑅_𝑟³₅(𝐸⃗ ₀⋅ 𝑟 )𝑟 5.2 using the abbreviation 𝛽 = (𝜀_𝑁𝑃− 𝜀_{𝑀𝑒𝑑𝑖𝑢𝑚})/(2𝜀_{𝑀𝑒𝑑𝑖𝑢𝑚}+ 𝜀_𝑁𝑃). The enhancement factor of the intensity of the electric field due to the presence of the NP can be defined as 𝑃 = |𝐸⃗ _𝑁𝑃|²/|𝐸⃗ _{𝑛𝑜𝑁𝑃}|² which reads in this approximation

𝑃 = 1 − 2^𝑅_𝑟³₃Re(𝛽) [1 − 3(𝑛̂_𝐸0 ⋅ 𝑛̂_𝑟)²] +^𝑅_𝑟6⁶|𝛽|²[1 + 3(𝑛̂_𝐸0⋅ 𝑛̂_𝑟)²] 5.3 Averaging this expression over all directions finally yields

〈𝑃〉_𝑟 = 1 + 2^𝑅_𝑟6⁶|𝛽|² 5.4

which gives the enhancement factor of the intensity of the electric field as a function of the distance of the chromophore from the NP.

Using equation 5.4 one can calculate the distribution of the enhancement factors

〈𝑃〉_𝑟 within a spherical shell that surrounds the NP concentrically with an inner radius 𝑅 + 𝜌 and a thickness 𝑑 (see Figure 5.8b for comparison). For 𝜀_𝑁𝑃 the dielectric function of gold as given in ref [175] was used (𝜀_𝑁𝑃 = −3.95 + 2.58𝑖) and 𝜀_{𝑀𝑒𝑑𝑖𝑢𝑚} was set to 𝜀_𝑃𝑉𝐴 = 2.19. The distance 𝜌 between the inner surface of the shell and the surface of the NP was set to 3 nm, which takes into account that the pigments are embedded in a protein matrix that is surrounded by a cage of surfactant molecules.

76 5 Hybrid Nanostructures: Plasmon Enhancement of LH2 Fluorescence

However, when trying to relate the calculated distribution of the enhancement factors to the experimentally observed intensity distribution of the LH2 fluorescence, one faces the problem that the fluorescence intensity from individual LH2 complexes already features a distribution without any NPs, see Figure 5.5a (grey bars). Therefore the simulated distribution for the enhancement factors was convoluted with the distribution of the fluorescence intensity of the LH2 complexes that is observed on bare SiO₂ substrates NPs.

The result of this procedure is shown in Figure 5.8 for 𝑑 varying from 0.5 to 11 nm, together with the measured reference distributions of the fluorescence intensity in the

Figure 5.8: Calculated intensity distributions for the fluorescence enhancement of LH2 complexes (black) as a function of their distance from a single AuNP. The calculations were performed using a dipole approximation as explained in the text. The LH2 complexes were located within a shell of finite thickness d (grey area) that accommodates the AuNP (yellow) in its centre. The distance between the surface of the AuNP and the inner surface of the shell was set to 3 nm, while the thickness d of the shell was varied from 11 nm (top left) to 0.5 nm (bottom right). The intensities are given in units of 〈𝐼_𝑟𝑒𝑓〉, which corresponds to the mean of the intensity distribution obtained experimentally from LH2 on bare SiO2 (grey). The mean (standard deviation) of the simulated histograms are (a) 1.1 (0.6), (b) 1.4 (0.7), (c) 1.7 (0.9), and (d) 2.0 (1.0). Figure adapted from [131].

5.5 Conclusion 77

absence of NPs (light grey). An enhancement of the LH2 fluorescence that resembles the experimentally obtained intensity distribution is found only if the distance between the AuNP and the pigments falls into the range of 3-5 nm. This finding is consistent with the result from the control experiment with the extra PVA layer. The conjecture that the LH2 complexes seem to stick to the AuNPs within a thin layer of only a few nanometres thickness is in line with the well-known fact that proteins tend to adsorb on noble metal surfaces [176].

5.5. Conclusion

In a systematic study, we could show plasmonic fluorescence enhancement of individual LH2 complexes by gold nano spheres. We took great care to precisely define the system under investigation by using monodisperse, non-interacting AuNP, that could only interact with a single LH2 at a time. Using a high throughput single molecule approach, we obtained clear and meaningful statistics and could bypass the disadvantages of ensemble measurements.

Excitation of LH2 in resonance with the AuNPs’ plasmons in average resulted in a fluorescence enhancement factor of 2, while off-resonant excitation showed no fluorescence enhancement at all. Introducing a spacer layer of 20 nm between AuNP and LH2 efficiently prevented fluorescence enhancement, even when the LH2 complexes were excited in resonance with the plasmon. In combination with model calculations this led to the conclusion that the LH2 complexes adsorb to the AuNP and are located within a thin shell around the individual particles. The fact, that the experimental data is well reproduced by the model calculations gives rise to the assumption, that the LH2 complexes only witness an absorptive enhancement, as only this contribution was taken into account in the model. The quantum yield and thus the radiative rate of LH2 seem to remain unchanged.

This study marks a first step in the use of noble metal nanoparticles for tuning the photophysical properties of integral membrane antenna complexes in a well-defined

78 5 Hybrid Nanostructures: Plasmon Enhancement of LH2 Fluorescence

way. In combination with other recent studies [17,177–180] it shows the way on how we can manipulate nature to build novel biohybrid light-harvesting architectures.

79

6. Artificial System: Photophysical Characterisation of