Determination of all Dimensions of CdSe Seeded CdS Nanorods Solely via their UV/Vis Spectra

1 Introduction

Semiconductor nanoparticles are a broadly researched material class nowadays. Their unique properties make them interesting candidates for fundamental research as well as for various applications (e.g. solar cells, LEDs, photocatalysis, etc) [1]. The synthesis of these nanoparticles through the so-called “hot-injection” method is preferential because of the good control of their shape, size and composition while having a low degree of polydispersity. By means of the hot injection method, a large variety of semiconductor nanoparticles is accessible. Thus, starting from 0-dimensional quantum dots (homogenous [2] as well as heterogeneous core/shell quantum dots [3], [4]), 1-dimensional homogenous [5] and heterogeneous nanorods [6], [7], [8] and –wires, 2-dimensional nanoplatelets [9], [10] and even different branched nanoparticles like tetra-[11], [12], [13] and octapods [14] can be synthesized today.

In this article, we concentrate on CdSe seeded CdS nanorods. These nanoparticles are of particular interest due to their high photoluminescence (PL) quantum efficiencies [11]. Based on these particles many groups investigate further effects like cation exchange reactions, [15], [16] phase transfer reactions [17] and the formation of superstructures [18]. Also many researchers investigated metal growth on these structures [19].

These are only few examples for the use of CdSe seeded CdS nanorods in the recent literature. Almost every study starting from CdSe seeded CdS nanorods first relies on a determination of the heteronanorods’ dimensions and their concentration in colloidal suspension. Up to now, only the combination of imaging techniques, like transmission electron microscopy (TEM), and quantitative analysis, like atomic absorption spectroscopy (AAS), leads to the complete understanding of the dimensionalities of CdSe seeded CdS nanoparticles.

For spherical Cd chalcogenide quantum dots size determination is easily done, because based on the quantum size effect, the size and concentration can be calculated from the first absorption maximum of the spectrum through empirical equations [20], [21], [22]. For elongated pure CdSe nanorods similar investigations showed that their diameter can be calculated from the first extinction maximum while with a known particle concentration the high energy extinction (e.g. at 350 nm) can be correlated to the total volume of the nanorods which eventually leads to information about the rod length [23]. Spherical CdSe seeded CdS quantum dots were also examined in this direction, and here the thickness of the CdS shell correlated to the shift of the first absorption maximum of the CdSe core (for sufficiently thin CdS shells) [24]. It was also shown in heterostructures consisting of CdSe and CdTe that irrespective of the shape of the particles the extinction coefficient increases proportionally to the added amount of shell material [25]. Later this was researched in detail showing that, up to the third, with each added monolayer of CdS the first absorption band of the CdSe core shifts and afterwards stays constant [26].

To be able to determine all size parameters of CdSe seeded CdS nanorods from their UV-Vis spectra, we first need to correlate the shifted CdSe band gaps to the original seed sizes. In the next step we have to find a way to detect the width and the length of the nanorods. Finally, by finding the correct relation between the particles’ volumes and their extinction coefficients we can then calculate the particle concentration and thus also the Cd concentration.

In this article, we demonstrate that it is possible to derive all needed dimensions solely from the extinction spectra of the particles.

2 Results and discussion

In the following part we will analyze UV-Vis absorbance spectra of heterogeneous CdSe seeded CdS nanorods thoroughly to show that all necessary information can be derived from them. Starting from the low energy (high wavelengths) part and going to higher energies (lower wavelengths) we will examine four specific areas in depth (see Figure 1).

Fig. 1:

(top) Typical extinction spectrum of CdSe seeded CdS nanorods with marked points of interest from which we can derive their size and concentration. The inset shows the magnification of the extinction maximum of the CdSe seed. (bottom) Scheme of a CdSe seeded CdS nanorod with the range of the size parameters which can be calculated within an acceptable margin of error through the method presented in this article.

We will begin with the first small local extinction maximum (usually between 550 and 650 nm) for which the CdSe core of the nanorod is responsible. The position of this peak is correlated to the size of the CdSe core. The width of the CdSe seeded CdS nanorods is derived from the position of the intercept of a tangent trough the inflection point of the low energy side of the CdS related absorption band with the x-axis. The same band’s peak extinction value is connected to the volume of the nanorods and through calculations assuming cylindrical shape leads to the length of the nanorods. Finally, the extinction coefficient at around 350 nm was found to be more or less independent on the rods dimensions and to only depend on the overall material concentration and can thus be used to determine the particle concentration once the particle dimensions are known. A detailed analysis of the data obtained for each of these points is shown in the following paragraphs.

CdSe seeded CdS nanorods have been synthesized according to the procedure developed by the Manna group by first synthesizing CdSe seeds via a hot injection approach and then synthesizing CdSe seeded CdS rods via a seed mediated growth approach (see experimental section and supporting information for details) [8]. The most easily accessible particle types are short and thick nanorods with a deep red color and high photoluminescence quantum yields (PL QY). They are synthesized with large CdSe seeds which are more easily produced due to the longer reaction time. Longer nanorods which are narrower are synthesized with small CdSe seeds. These can be obtained through very quick quenching of the CdSe seed synthesis with reaction temperatures not as high as those for large seeds. To produce nanorods which are thick and also long or thin and short the reaction parameters of the nanorod synthesis have to be modified slightly. For thick as well as long nanorods the amount of CdO has to be increased significantly, for thin and short nanorods it has to be decreased. In Figure 2, overview TEM images of four representative samples of nanorods are shown. Panel A displays nanorods which have a medium length and width, in Panel B we can see strongly elongated nanorods, whereas in Panel C very short and thick nanorods are presented. Finally, Panel D shows thick nanorod with a medium length. These four samples also represent the limitations of this synthetic route. Panels A and C show samples which are easily accessible just by varying the CdSe seed sizes and yield in high monodispersity. In Panel B, we already see that elongated particles tend to break off smaller pieces as well as lose their straightness. In Panel D an example for thick nanorods which were synthesized using higher amounts of the precursors can be seen. The growth of the CdS occurs inhomogeneously in these particles leading to an irregular thickness over the length. In total we analyzed 35 samples of CdSe seeded CdS nanorods with different widths and lengths which have been synthesized from nine different CdSe core sizes. A representative UV-Vis spectrum of nanorods obtained with this procedure is shown in Figure 1. We will now proceed to analyze these spectra in depth.

Fig. 2:

TEM images of four representative CdSe seeded CdS nanorod samples showing thin and short nanorods (Panel A), thin and long nanorods (Panel B), thick and short nanorods (Panel C) and thick and long nanorods (Panel D).

Starting at the first significant point in the spectra, the lowest energy absorption maximum, it is shown in Figure 3 that this small peak in the low energy region of the spectrum is significantly dependent on the CdSe core diameter. Earlier investigations show that in spherical CdSe seeded CdS quantum dots the CdSe band of the underlying seeds shift to lower energies with each added monolayer of the shell until as much as three monolayers. Afterwards the positions of the CdSe band stays almost constant [24]. In the case of the anisotropic CdSe seeded CdS nanorods the particles are capped with phosphonic acids during the nanorod synthesis to facilitate the growth along the c-axis by blocking the side facets of the particles. This leads to a thick shell along the nanorod axis. But the width of the nanorods merely increases by up to 2 nm which translates to around three monolayers of CdS. Accordingly, we find that the position of the low energy transition depends only slightly on variations of the width of the rods (and hence the CdS shell thickness perpendicular to the rods axis) as it can be seen by the relatively small variance of the peak positions of seeded rods with similar core diameters (black dots in Figure 3 bottom panel). Especially it can be seen in Figure 3 (bottom panel) that already for the pure CdSe seeds the deviation of the seed diameters from a Brus-type fitting curve is quite high (and especially higher than the variance between the absorption signals position for seeded rods with the same seed diameter) which is likely to be caused by inaccuracies in determining the particle diameter from TEM images. Hence we conclude that the original seed diameter can be extracted from the position of the lowest energy absorption signal with sufficient high accuracy (e.g. not less accurate than e.g. via TEM measurements of the original seeds). From a practical point of view however, the determination of the seed diameter from the spectra of the seeded rods is often not needed as the seed core diameter can of course normally be easier determined from the absorption spectrum of the original seeds. Therefore the here proposed method would only be necessary when the original seeds are not available.

Fig. 3:

(top) Exemplary absorption spectra of CdSe seeded CdS nanorods with different CdSe core diameters, in the spectral range between 550 and 625 nm. (bottom) Plot of the CdSe core diameter versus the peak position of the CdSe related absorption band of all investigated CdSe seeded CdS nanorods (black dots). Absorption peak positions for the original CdSe seeds (red dots). The lines show the respective fitting curves obtained through the Brus equation (Details for the extracted fitting parameters (which in principle correlate to the effective masses and dielectric constants of the material) are shown in the supporting information, Figure SI 1 and its discussion). The errors range between 0.4 and 0.7 nm depending on the quality of the TEM images on which the measurements were based.

In the next step we will determine the overall width of the nanorods. Especially for wider rods no distinct absorption maximum can be found at the position in the spectrum where the CdS starts to absorb but only a more or less pronounced shoulder can be identified. We have found that the intercept of a tangent through the inflection point of the low energy side of the CdS related absorption band (which can also be constructed for shoulder type absorption bands) with the x-axis of the absorption spectrum allows the determination of the rod width. As the width is the by far stronger restricting dimension of the nanorods, the position of the above mentioned intersection changes due to size quantization for differently thick nanorods.

This calibration curve allows the determination of the width of CdSe seeded CdS nanorods with acceptable accuracy in the width range of 4–7 nm. Extrapolation for thinner rods should be easily possible which however can synthetically almost not be realized. Extrapolation for thicker rods might also be possible, but also those are not easily accessible synthetically and also size quantization becomes weaker and weaker with increasing thickness, and therefore the width determination becomes less and less accurate for thicker rods. It should also be mentioned that especially for very long rods, sometimes rods with inhomogeneous thickness over the whole rod length are obtained which can naturally not be analyzed by this method.

In Figure 5 we show the dependency of the volume ratio between CdSe and CdS on the ratio of the extinction values of the corresponding absorption bands. In the case of thick and short nanorods the CdS band does not show a distinct maximum. Here the crossing of the tangent at the inflection point of the CdS band with the tangent extrapolated from the high energy side of the band is used as extinction value. The two ratios can be roughly fitted using a linear fit. The fitting linear equation is

which indicates a molar extinction coefficient of the CdSe which is by a factor of 1.34 higher than for the CdS.

As the volume of the CdSe core is already known, the volume of the CdS and thus the total volume of the nanorod can be calculated. Together with the width of the nanorod, the length is then also accessible assuming as a good approximation cylindrical rod shape. Hence, at this point, we know all dimensions of the CdSe seeded CdS nanorods. It should be noted that the last step mentioned is only possible in CdSe seeded CdS nanorods and not in e.g. pure CdS nanorods (for the latter ones, a length determination solely from the absorption spectrum would be impossible).

In the lower panel of Figure 4 it is noticeable, that there are some data points strongly deviating from the fitting. Long nanorods, especially when they are synthesized with large CdSe seeds, have a strong tendency to have inhomogeneous thicknesses along their length. Two types of behaviors were observed. In the one case, the nanorods grow thinner towards the end leading to more cone than cylinder shaped nanorods. This falsifies the CdS/CdSe volume ratio to higher values. In the other case, the particles are narrower in the middle part than at the ends. The small width of these narrow middle parts is measured as the allover width of the nanorods, therefore the CdS/CdSe volume ratio is falsified to lower values. Both type of derivation show again that our method naturally covers only such seeded rods with a homogenous rod width, as we already observed during the rod width determination.

Fig. 4:

(top) Exemplary extinction spectra of CdSe seeded CdS nanorods. (bottom) Plot of the intercepts of the tangents through the inflection points of the lower energy side of all CdS bands versus the measured widths of the nanorods. The line is obtained by fitting a Brus type fit through all data points (for fit details see supporting information Figure SI 2.

Finally, once all dimensions of the nanorods are known, also the molar concentration in solution can be calculated. The best way to do this is to measure the extinction value at high energies, e.g. at 350 nm, since the high energy absorption has already been shown also for homogenous rods to be more or less independent from the rod dimensions and only dependent on the overall amount of material present in solution. Figure 6 shows the dependency of the molar extinction coefficient at 350 nm from the nanorod volume for all investigated samples. For CdSe seeded CdS nanorods we find the more or less shape independent extinction coefficient of the particles at 350 nm to be:

where V is the already determined total rod volume in nm [3]. As already seen in Figure 5 (bottom panel), in Figure 6 there are also some data points which deviate strongly from the trend line shown as gray data points. Again we can see that particles which are not homogeneous in their shape and samples which are not sufficiently monodisperse do not match the fitting line. This happens more often in nanorods which are synthesized from large CdSe seeds and are long as well.

Fig. 5:

(top) Exemplary extinction spectra of CdSe seeded CdS nanorods showing the ratio of the absorption of the CdS band at around 450 nm compared to the absorption of the CdSe band (see inset), which is also used for normalization of the spectra. (bottom) Plot of the extinction ratio of CdS and CdSe versus the volume ratio of CdS and CdSe for all nanorods. The gray dots mark samples which do not match the pattern of behavior due to a lack of monodispersity and/or inhomogeneity of the particles.

Fig. 6:

Plot of the molar extinction coefficient at 350 nm calculated through the combination of TEM and AAS results versus the total volume of the nanorods. The line shows the linear fitting. The gray dots show samples which do not match the common trend.

Once the molar extinction coefficient is known the particle concentration in solution can be directly calculated.

3 Conclusion

To summarize, we have shown that all information concerning the size and concentration of CdSe seeded CdS nanorods can be derived from their UV-Vis spectra only. First, the CdSe core diameter has to be determined from the lowest energy absorption maximum using the calibration curve shown in Figure 3. Next, the rod width is determined by the position of the CdS related absorption band using the calibration curve from Figure 4. The overall rod volume can be estimated by the ratio of the maximum extinction values of the two aforementioned absorption bands by using the calibration curve from Figure 5. Once all dimensions are known the particles concentration can be determined by the optical density at high energy by using the calibration curve in Figure 6. Our method works with an accuracy which is high enough for certain applications of nanorods as long as they stay in the specified size regime and as long as their shape is more or less cylindrical. This might allow researchers to avoid time and resource consuming TEM analysis as long as not too high accuracy is required.

4 Experimental section