Transition Dipole Imaging of Carbon Nanodots

4.5 Transition Dipole Imaging of Carbon Nanodots

Carbon Nanodots (CNDs) are fluorescent carbon nanoparticles which have recently at-tracted enormous attention due to their bright photoluminescence (PL), solubility in water, low toxicity, easy functionalization, chemical inertness and one-step prepara-tion [153–155]. In order to fully understand the origin of their PL, we investigated the dimensionality of their transition dipole moments (p_exc and p_em). Depending on the origin of the PL, the dimensionality of the TDM changes [156, 157] from one di-mensional dipole for single chromophores for example, to an isotropic distribution of emission probability in a highly symmetric emitter such as silicon nanocrystals [158].

Molecules such as benzene and crystal violet show two-dimensional degenerate TDMs due to their symmetrical planar structures [159].

Figure 4.43: The left image shows intensity patterns of CNDs scanned by a radially polarized laser.

The image size is 12.5×12.5µm²with a pixel size of 50 nm and a pixel dwell time of 5 ms. The excitation was done using a 488 nm laser at a power of∼5 kWcm². The top right image shows the lifetime image with the calculated lifetime values for each single emitter. The right bottom graph shows the histogram of all the lifetimes of all the emitters identified. 62 intensity patterns were identified using the pattern matching algorithm.

The synthesis of carbon dots is given in detail in the supplementary information of Ghosh et al. [160]. Samples were prepared by spin-coating a droplet of an aqueous solution of these particles on a glass coverslide. Thereafter, we scanned the sample with a focused radially polarized laser beam with wavelength of 488 nm. Figure 4.43 shows one such a scan performed with a 488 nm radially polarized laser. The image clearly shows fixed single dipole p_exc behavior. More than that, one sees that no CND has

4.5. EXC-EM OF CNDS CHAPTER 4. SM ORIENTATION

Figure 4.44: Top row shows scans of 5 carbon dot particles with radially polarized laser with a wavelength of 488 nm. The orientations of the p_exc for these patterns are shown with the double arrows. The bottom row shows the defocused images of the corresponding molecules together with the orientations of thep_emshown by the double arrows. [This figure has been published in the article [160].]

more than one emission center. Of course, one can argue that there might be multiple emitters oriented in same direction, for which one needs to perform careful antibunching measurements or step-wise bleaching experiments. Some intensity time traces are shown in the supplementary figure S5 in [160] which prove that the CNDs have single emission centers. The presence of single dipole p_exc indicates that the PL originates from charge recombination of defect centers in the CND. Further, we performed experiments to determine the p_exc and p_em simultaneously on individual particles. Figure 4.44 shows scans of 5 particles with radially polarized laser excitation and their corresponding defocused images which also show single dipole behavior. The defocusing value was approximately 0.9µm above the focal plane. The figure shows that the excitation and emission takes along a particular orientation in each particle. The angle between these both TDMs does not exceed 5^◦ for these particles.

5 Discussion and Outlook

5.1 MIET on Metal Thin Films

The quenching of fluorescence and the modification of emission rates of a dye molecule depend on several factors such as the refractive index and thickness of the metal film, the layers and thicknesses the media above and below, the emission wavelength and quantum yield of the dye. Depending on the requirement of the experiment (the axial resolution desired, the maximum height range, refractive index of the medium) and dye characteristics one must to calculate the MIET calibration curves in order to find the most suitable metal film and its thickness. Even though it is difficult to predict a suitable metal, a few general trends can be speculated based on their properties. In order to simplify the situation, let us fix the emission wavelength and thickness of the metal film to 690 nm and 10 nm respectively. We assume that the thin metal film is deposited on top of glass (n = 1.52) and the medium above is water (n = 1.33). We further take the quantum yield of the emitter as unity. The refractive index of these metals at this wavelength are listed in the form of a table below¹².

Metal Refractive index (690 nm) Aluminum 1.58 + 7.93i

Beryllium 3.43 + 3.24i Chromium 3.63 + 4.26i Copper 0.22 + 4.00i

Gold 0.17 + 3.79i

Nickel² 2.15 + 3.93i Palladium 1.94 + 4.47i Platinum 2.50 + 3.93i Silver 0.17 + 4.22i Titanium 2.18 + 3.27i Tungsten 3.66 + 2.79i

1The refractive indices were calculated using the Brendel-Bormann model using the values given in [123].

2We assume the relative magnetic permeability as unity for the case of Nickel.

5.1. MIET ON METAL THIN FILMS CHAPTER 5. DISCUSSION AND OUTLOOK

Figure 5.1 shows the variation of lifetimes for an isotropic emitter, or a dipole that is rotating faster than its excited state lifetime so that it can be considered as an isotropic emitter. From Hagen-Rubens relationship, the conductivity of a metal is related to the reflection coefficient (at normal incidences).

|R| ≈1−2 r ω

2πσ (5.1)

where ω is the angular frequency of light. Therefore, at a particular wavelength, the conductivity is roughly proportional to the inverse of the transparency of the metal.

Since, |T| ∝1− |1− |n|/1 +|n||², it gives us that silver is the best conductor, closely followed by gold and then copper, at the chosen wavelength. Tungsten, beryllium and chromium are the least conductive materials in the list. Thus, from the curves shown in figure 5.1, one can vaguely state that the steepness of the lifetime variation with distance is closely related to the conductivity of the metal. Clearly, the higher the conductivity of the metal, the longer the distance range where it effects the fluorescence. However, aluminum acts as an exception to this trend. This is due to its exceptionally high imaginary part of refractive index.

Figure 5.1: Calculated relative lifetime values as a function of distance from the surface of various metals.

Most of the fluorescent dyes exhibit an excited state lifetimeτ_f in the range of 1-5 ns.

The precision of estimating lifetime values depends on the number of photons collected.

CHAPTER 5. DISCUSSION AND OUTLOOK 5.1. MIET ON METAL THIN FILMS

Assuming pure Poisson statistics, the error of lifetime estimation is given by:

∆τ > τ_f

√

N (5.2)

where N is the total number of photons. The equality occurs only if the statistics is ideal and there is no background, in the presence of which the error increases. This means that if one has approximately 1000 photons, the relative error within which the lifetime values can be estimated cannot be less than 0.03. Using the MIET curves, this error can be translated into axial errors. For a single molecule, immobilized in a polymer over glass substrate, one collects approximately 10⁴ photons before bleaching it. However, due to the quenching of fluorescence in the presence of the metal film, one collects less photons from the same single molecule. This means that the axial localization error of a molecule close to the metal surface is higher. The axial error is also high if the variation of the lifetime curve with height is low. This is shown in figure 5.2. We calculated the number of photons one collects from a single molecule before it bleaches based on the relative intensity that one observes for dipoles above these metal layers, which gives us the relative error of lifetime estimation at each height. Thereafter, this lifetime error was converted into axial localization error by taking the derivative of height with respect to lifetime. In this way, we get an estimate of axial localization error that one would likely measure as a function of the molecule’s position on top of the metal surface. We performed the same calculations for air as a medium on top of the metal films shown in figure 5.1. Note that these calculations were performed assuming quantum yield as unity and for a metal thickness of 10 nm. The lifetime curves will show different behavior for a different quantum yield and film thickness, which would result in a different axial error.

Figure 5.2: Left figure shows the plots of relative intensity of a single molecule that one observes through a 10 nm of metal layer on top of glass with a 1.49 N.A. objective, as a function of distance.

The values are normalized to a dipole in water (n= 1.33) without any metal film. The right figure shows the plot of axial localization errors as a function of distance above the metal films.

5.1. MIET ON METAL THIN FILMS CHAPTER 5. DISCUSSION AND OUTLOOK

Figure 5.3: The same as figure 5.2, but for air on top of the metal films.

From these simple calculations, we see that gold shows the highest axial error within the range of 10 to 30 nm. The error calculated is extremely high below 5 nm for both, water and air environments. For this reason, while measuring axial positions of dye molecules or labeled biological structures, one usually evaporates a thin layer (at least 10 nm) of transparent SiO2 as a spacer on top of a gold/copper thin film. However, the advantage of a gold/copper thin film in a MIET experiment is that the lifetime values increase monotonically up to a height of 150 nm as in contrast to most other metals considered here. Morevover, the variation of lifetimes with height is maximal in the range between 40 and 70 nm, which translates to an axial localization precision of less than 5 nm in water and 2 nm in air (see figures above). This makes them useful for live cell nanoscopy [161] where one would like to investigate the structure of biological entities of a cell on top of a surface. For such experiments, an error of 5 nm is tolerable.

Aluminum, on the other hand can be used to measure smaller distances, upto 1 nm, between a range of 10 to 30 nm. As can be seen in the figures, the relative intensity in water that one measures through this metal is much higher in comparison to the case of a gold film. The steep variation of the lifetime values with distance from aluminum surface can be useful for achieving a higher resolution in height variation, making it a potential candidate for single-molecule measurements in these conditions. The precaution one must take while working with silver thin films is that they easily form a thin layer of the silver oxide while reacting with oxygen present in the ambient air or dissolved in water over time. This affects the transparency and the overall fluorescence lifetime behavior over the surface. Therefore, one usually evaporates a thin layer (10-20 nm) of transparent SiO₂additionally on top of an evaporated silver thin film in order to prevent such a layer. This oxidation process is however not a problem in the case of aluminum, in which case the layer of alumina formed is transparent in the visible wavelengths. In any case, the axial error as we calculated for the figures above can be used as a way to