Carmine Serio
email: carmine.serio@unibas.it

Guido Masiello

Pietro Mastro

Sauveur Belviso

Marine Remaud

Seasonal variability of degrees of freedom and its effect over time series and spatial patterns of atmospheric gases from satellite: application to carbonyl sulfide (OCS)

Keywords: Satellite, atmospheric gases, carbon cycle, carbonyl sulfide, infrared, sounders, forward modeling, inverse problems, optimal estimation

teaching and research institutions in France or abroad, or from public or private research centers.

Seasonal variability of degrees of freedom and its effect

over time series and spatial patterns of atmospheric gases from satellite: application to carbonyl sulfide (OCS)

INTRODUCTION

Nowadays, satellite level 2 algorithms for the estimations of gas species and thermodynamic parameters make widespread use of Optima Estimation or OE, 1 a Bayesian approach that constrains the solution through the background state, which is our best prior knowledge about the parameters. In this context, the concept of degrees of freedom or d.o.f. of satellite-based retrievals is used, which measures the independence of the background from the final or level 2 product we get through the inversion process. Usually, the background constraint is a static feature of the inversion process, and therefore, in principle, it should not affect, e.g., the seasonality of the retrieved quantities, although a too much strong constraint can attenuate the dynamic of the estimated products, hence the amplitude of the seasonal cycle. However, we will show that there are other factors which do not depend on the background but on the atmospheric state, which can even change the phase of the seasonal cycle. Understanding and assessing the role of the background is an important issue, e.g., when we need to analyze the seasonal cycle of a given atmospheric gas, such as CO 2 or other greenhouse gases. Then, we can be confident that the variability we see in the satellite products is a natural effect coming from the observations and not the background. In effect, even if the background is static, it could add artifacts to the retrievals, which modify the seasonal cycle or the spatial patterns of 2-D fields. To avoid any spurious behaviors, we simultaneously need the background to be static and d.o.f. to have precisely the same value for every retrieval. In case the d.o.f. changes over time and spatial locations, the retrievals can be modulated by the d.o.f. variability to the extent that what we see in the time series or spatial fields is nothing but the d.o.f. behavior. The issue has been addressed with an analytical treatment based on the OE theory. We derive formulas, which allow us to assess the modulation introduced by d.o.f. variability. The Infrared Atmospheric Sounder Interferometer (IASI) 2 on board the European MetOp satellites have been used to analyze the problem quantitatively. Both time series and 2-D fields of observations will be considered. The analysis is extended to tropical and Mid-Lat regions to exemplify the effect of seasonal variability of d.o.f.. Although the methodology we will discuss is quite general, the study will focus mainly on retrieving carbonyl sulfide or OCS, which is of primary interest to the carbon cycle and the climate. In effect, OCS is receiving increasing attention (e.g., see Refs. [START_REF] Asaf | Ecosystem photosynthesis inferred from measurements of carbonyl sulphide flux[END_REF][START_REF] Berry | A coupled model of the global cycles of carbonyl sulfide and co2: A possible new window on the carbon cycle[END_REF][START_REF] Campbell | Atmospheric carbonyl sulfide sources from anthropogenic activity: Implications for carbon cycle constraints[END_REF] because (1) the fluxes of CO 2 and OCS into leaves follow similar pathways through plant stomata and (2) the enzyme carbonic anhydrase catalyses both the hydration of CO 2 and the hydrolysis of OCS. However, unlike CO 2 hydration, the hydrolysis of OCS is an irreversible reaction, which means that the captured OCS can no longer be released back to the atmosphere. Thus, the OCS absorption by plants is a potentially helpful proxy of CO 2 absorption, and therefore it is directly related to gross primary production (GPP). Attempts to retrieve OCS from the satellite are relatively recent, e.g., see Refs. 6-11, although the quality and reliability of the retrieval have not yet been assessed accurately. This gap will be filled in the present paper. The study is organized as follows. Section 2 will deal with data and methods, whereas results will be shown in section 3. Finally, conclusions will be drawn in section 4.

DATA AND METHODOLOGY

Data: in situ observations

Representative OCS flask monthly data (e.g., see Ref. 12) were collected at the station of Mauna Loa (short name MLO, 19.5362 N, 155.5763 W, 3397 m asl). MLO observatory (see Fig. 1) in Hawaii is part of NOAA Earth System Research Laboratory (ESRL) and Global Monitoring Division (GMD). The data considered in this analysis refers to the period 2014-2019.

In addition to the tropical OCS data, we have also collected observations from a mid-lat station located at Gif-sur-Yvette, France (short name GIF, 48.701N, 2.1475 W, 165 m asl, 7 m agl). At GIF station (see Fig. 1), hourly measurements have been performed for six and a half years (starting from 2014) using online gas chromatography with Pulsed Flame Photometry detection (see Ref. [START_REF] Belviso | A topdown approach of surface carbonyl sulfide exchange by a mediterranean oak forest ecosystem in southern france[END_REF]). More detailed information about the calibration method can be found in Ref. [START_REF] Belviso | A topdown approach of surface carbonyl sulfide exchange by a mediterranean oak forest ecosystem in southern france[END_REF]. It is worth noting that data accuracy was systematically assessed using a NOAA/ESRL certified standard for COS, proven to exhibit no long-term drift, as target gas (e.g., see Ref. [START_REF] Belviso | A top-down approach of sources and non-photosynthetic sinks of carbonyl sulfide from atmospheric measurements over multiple years in the paris region (france)[END_REF]). Hence, we can state that in that sense, GIF data are calibrated on the NOAA-2004 scale.

Data: IASI observtaions

For comparison, IASI OCS observations were obtained for the GIF and Hawaii target areas shown in the map of 1. The IASI soundings cover 2014-2019. Only clear sky soundings have been considered. To check the impact of spatial degrees of freedom variability, we have also considered IASI soundings for the European and Mediterranean (Euro-Med) area shown in Fig. 2. The data acquired for this area refers to February 2020. We stress that all the IASI data used in this paper consist of clear sky soundings. Spectra were filtered for the clear sky by using the native cloud mask of IASI Level 1C data. This cloud mask is released by EUMETSAT and is based on the Advanced Very High-Resolution Radiometer or AVHRR imagery. A further cloud detection scheme was also used (e.g., see Refs. [START_REF] Masiello | Qualifying img tropical spectra for clear sky[END_REF][START_REF] Amato | Cloud mask via cumulative discriminant analysis applied to satellite infrared observations: scientific basis and initial evaluation[END_REF][START_REF] Mastro | Cloud detection from IASI hyperspectral data: a statistical approach based on neural networks[END_REF] and applied sequentially to the previous one to improve the quality of the final results.

Basic Methodology

OCS retrievals from IASI have been obtained through an inversion algorithm, combining a fully analytical, monochromatic radiative transfer model and an Optimal Estimation (OE) module. 1 The radiative transfer model is called IASI 9, 18 and is a fast model, which uses a pre-computed look-up table for the optical depth calculation. The look-up table is derived from LBLRTM (Line-by-Line Radiative Transfer Model, e.g., see Refs 19,[START_REF] Alvarado | Performance of the line-by-line radiative transfer model (lblrtm) for temperature, water vapor, and trace gas retrievals: recent updates evaluated with IASI case studies[END_REF], using the line compilation aer 3.2 (see e.g., http://rtweb.aer.com/line_param_frame.html). The forward module computes the radiance after discretizing the radiative transfer equation on a fixed grid made up by N L = 60 pressure layers, which spans the atmosphere from 1050 to 0.005 hPa. The forward model yields spectral radiances and analytical Jacobians concerning surface temperature, emissivity, and any atmospheric parameter, including the volume mixing ratio of the gases mentioned above. In its latest version, 9 σ-IASI also considers the sun spectral radiation, which may add an essential contribution in the spectral interval 2000 to 2240 cm -1 , which contains most information for retrieving OCS. The inversion scheme, called δ-IASI, 21 implements an iterative algorithm for the optimal estimation of the thermodynamic state of the atmosphere and its composition. The model δ-IASI performs the mathematical inversion of the whole IASI radiance spectrum (8461 channels) to simultaneously retrieve the state vectors (ε, T s , T, Q, O, HDO, CO 2 , N 2 O, CO, CH 4 , SO 2 , HN O 3 , N H 3 , OCS, CF 4 ). A critical aspect of the retrieval scheme, which is relevant to the estimation of trace gases, is the use of background and first guess state vectors in the linear region of the radiative transfer equation. Towards this objective, we use ECMWF (European Centre for Medium range Weather Forecasts) analysis for (T, Q, O) collocated in space and time with the IASI soundings (see, e.g., Refs. 9, 10 for details). ECMWF (T, Q, O) analysis provides a strong constraint in the inverse scheme, and we think that the corresponding profiles are reliable and allow us to relax the conditioning for the trace gases. In effect, minor and trace gas profiles are usually adjusted starting from a climatology as a first guess. The retrieved profiles reach their final values in one iteration. For OCS, the background profile for the corresponding part of the state vector is set equal to the reference profile (see Fig. 3).

In addition to the background state, we also need to specify a proper background covariance matrix. We consider a Markov-type matrix, and we refer the interested reader to Ref. [START_REF] Camy-Peyret | Assessment of IASI capability for retrieving carbonyl sulphide (OCS)[END_REF] for further details about this matrix. It should be stressed that the covariance matrix is set so that it applies a loose constraint. Because of the possible d.o.f. modulation over the retrieval, our objective is to set up a covariance matrix so that the final OCS product is as much as possible independent of the a prior profile.

OCS retrieval details: the role of the data and the background

This section aims at deriving a set of equations that can give us a quantitative measure of the contribution of the background and data to the column amount retrieval of the prescribed gas species or atmospheric parameter. An essential aspect of the derivation presented in this section is how to formalize, with appropriate equations, the time-space evolution of the contribution coming from the a prior constraint. In effect, one could argue that based on Fig. 3, and considering that we have fixed the background, its contribution needs to be static. However, we will show that this is not the case because the background contribution to the retrieval also depends on the given state of the atmosphere, which can change with season and space.

To begin with, we note that in our scheme, an optimal estimate of the column amount of OCS, XOCS is obtained from a retrieved vector-valued profile qOCS of size N L (i.e., the number of layers in our forward model)

XOCS = h t qOCS ; var( XOCS ) = h t S qh (1)
where S q is the retrieval covariance matrix, h the averaging operator (e.g., see Ref. 10) and var(•) stands for variance. Because our methodology can be applied to any parameter, hereafter, the subscript OCS will be omitted for the sake of generality. Having said that, the column amount XOCS is corrected for the effect of moist air, as shown in Ref. [START_REF] Camy-Peyret | Assessment of IASI capability for retrieving carbonyl sulphide (OCS)[END_REF]. The averaging operator, h is defined according to the quadrature formula we use to compute the column amount from the mixing ratio profile, that is

X = - 1 p 1 -p N L +1 p N L +1 p1 qdp = 1 p 1 -p N L +1 N L i=1 qi (p i+1 -p i ) (2)
with p i the pressure of the level i, i = 1, . . . , N L . We define

h i = p i -p i+1 p 1 -p N L + 1 (3)
(with p 1 the surface pressure), and Eq. ( 2) becomes,

X = N L i=1 h i qi = h t q (4)
It should be also noted that because of its definition, we have

N L i=1 h i = 1 (5)
which means that the weights are appropriately normalized.

Figure 3b shows a typical Averaging Kernels (AK) for the retrieved OCS profile, from which we derive a value ≈ 1 for the degrees of freedom, computed as the trace of AK. However, we are mostly interested in the retrieval of the column amount, and, therefore, in the Averaging Kernel for X. Towards this objective, if A is the averaging kernels matrix for OCS profile, that for the column amount is h t A and is plotted in Fig. 4. For shortening notations, we put For a perfect retrieval, A would be the identity matrix, and we should have h t A = w = h t . It is interesting to see that the weights h t A remains positive (e.g., see Fig. 4) and different from zero throughout the atmosphere. They are smaller in the lower troposphere because, for each pressure layer i, they are proportional to ∆p i , as shown in Eq. (3), and ∆p i is not constant along the vertical spatial coordinate because the pressure-altitude grid step is uneven. To avoid this effect, we can normalize the elements of the vector, h t A to the corresponding ∆p i (e.g., see Ref. [START_REF] Connor | Orbiting carbon observatory: Inverse method and prospective error analysis[END_REF], to have the Averaging Kernel per unit (1 hPa) layer pressure depth. Considering the definition of the averaging operator h (see Eq. ( 3), the normalization can be achieved simply by defining a new vector w h , whose elements, w h,i are defined according to

w = h t A (6)
w h,i = w i h i (7)
It should be stressed that in case of a perfect retrieval, we should have w h,i , for each layer. For an actual retrieval, w h,i can be greater or lower than 1, and it is expected to be very small or close to zero in the pressure range from where no contribution is coming to the retrieval. The normalized averaging kernel w h is also shown in Fig. 4, to be compared with h, and we see that the retrieval X receives information from the whole atmosphere, but the lower part where w h tends linearly to zero. To have further insights into understanding the meaning of w and w h let us consider the linear approximation of the retrieval q, namely (e.g., see Ref. 1)

q = q a + A(q -q a ) = (I -A)q a + Aq (8)
where q, q a , q, are the estimated background and true OCS profiles, respectively; furthermore, I is the identity matrix. We can pass to the estimation of the column amount, X multiplying both sides by the averaging operator,

h t , X = h t q = h t (I -A)q a + h t Aq = X bg + X t (9)
with X bg and X t , the contribution for the background and the true profile, respectively. It is interesting to note the background term, X bg can be further split into two terms,

X bg = h t Iq a -h t Aq a = X bg1 + X bg2 (10)
It is seen that X bg1 depends solely on the background state vector, hence if q a is a static feature, the term X bg1 cannot change with time and space. The second term, X bg2 depends on the background covariance matrix (again a static feature) and the Jacobian derivative of the atmospheric state. The Jacobian matrix can change with time and space, hence can modulate the overall background term, X bg in a way that alters the time-space dynamic of the signal.

From Eq. ( 9), we can soon derive the sensitivity of X to the true and background profiles,

∂ X ∂q = h t A = w t ; ∂ X ∂q a = h t -h t A = u t (11)
It is interesting to note that we have

w + u = h (12)
and

N L i=1 w i + N L i=1 u i = N L i=1 h i (13)
Therefore, if according to the usual meaning of degrees of freedom, e.g. ref.

1, we define

dof X = N L i=1 w i (14)
we have that for a given retrieval, a fraction contribution equal to dof X is given by the true profile, whereas a fraction 1 -dof X is because of the background. Similarly for w, u can also be normalized to h yielding the vector u h . With this in mind, Fig. 4a, ehich refers to the GIF area, shows the vectors, w, w h , u, u h . For the case shown, we have dof X =0.93, and we note that the background weights, u changes sign along the vertical so that it sums to +0.07. Conversely, the weights w are always positive, and they sum to 0.93, so that w + u is exactly equal to 1. For completeness, Fig. ??b) shows an example for the Hawaii target area (tropics). For this case, we have dof X =1.02 and now the background weights, u sums to -0.02 and those corresponding to w 1.02, so that, again, w + u is exactly equal to 1. The example also shows that dof X can attain values greater than one, but only because the background contribution is negative, in such a way that the constraint imposed by Eq. ( 12) is satisfied. From a comparison of Fig. 44a and Fig. 4b, we see that the shape of w h changes according to the latitude belt. In addition, they show that the contribution to the column amount dof X from the true profile comes from everywhere in the atmosphere, although with different weights. The weights tend to be greater in the upper-middle troposphere and goes to zero at the surface.

The set of equations from 9 to 14 is the most important methodological result of the present study. They show that the background contribution X b g has a direct dependence on the averaging kernels, A, which in turn depend on the atmospheric state. This aspect was also evidenced in Ref. [START_REF] Serio | CO2 spectroscopy and forward/inverse radiative transfer modelling in the thermal band using IASI spectra[END_REF] when dealing with the column amount retrieval of CO 2 , and it cannot be simply ignored, as it will be exemplified in the results section.

RESULTS

Assessing the d.o.f. dynamic-variability on the time-behavior of retrievals

Figure 5 shows the comparison of the IASI OCS (monthly means) and the in situ GIF observations (monthly averaged). Although the range and cycle amplitude are correct, we see a delay between the two-time series, which is of the order of 2 months. IASI data points exhibit a peak in February and a trough in August, whereas the same characteristics are shown in April and October, respectively, for the GIF observations. If we consider the linear correlation between the two series, we find it equal to 0.45. What we see in Fig. 5 is a subtle aspect of the seasonal variability of the information content, that is dof X . In effect, especially for land surface retrievals outside the tropical belt, the strong seasonal contrast of the surface temperature and emissivity can modulate Jacobian, hence the kernel w, and introduce a seasonal cycle, which overlaps that of the OCS. This seasonal effect is exemplified in Fig. 6, where we show the monthly time series of X bg for the period 2014-2019 for the GIF station. For comparison, the same figure also shows the case of MLO (tropical belt).

In effect, Fig. 6 shows that the phenomenon is most seen on land and outside the tropical belt, in this latter case, the uniform climate all around the year does not introduce seasonal variability in A, hence dof X remains fairly constant. We stress again that the background state is a static feature, not changing with time; therefore, if we see seasonal effects in X bg , it is because they are introduced by a seasonal behavior of dof X . It also has to be stressed that the seasonal cycle shown by X bg has peaks in February and troughs in August; therefore, the OCS dynamics (see Fig. 5) is dominated by the X bg cycle rather than the data. We see that for the tropical station, the contribution from the background remains confined to the values of 1-2% of X. Conversely, for the mid-lat station, X bg can reach values as large as 20-25% and is strongly modulated with the seasons. In effect, this behavior is the result of the variations in dof X with the season. As further exemplified in Fig. 7, dof X undergoes very little changes at tropics, whereas at mid-lat it can reach values as low as 0.80.

To avoid the inclusion of spurious seasonal variations in the time series of X we need to perform the analysis at constant dof X . Towards this objective, the retrievals have been filtered according to the criterion 0.98 ≤ dof X ≤ 1.02 [START_REF] Masiello | Qualifying img tropical spectra for clear sky[END_REF] The effect of this criterion once applied to the GIF station is seen again in Fig. 6 and Fig. 7 Again, we see that the background contribution goes down to ≈ 8%, with no critical cyclic components.

Figure 8 is the same as Fig. 5, but now the OCS retrievals have been filtered according to the condition of Eq. ( 15). In addition, the IASI OCS time series have been smoothed with a moving average window with a time span of 3 months to reduce its random variability. We see that the cycle amplitude seen from IASI is smaller than that explained from the in situ observations. However, now the cycle goes into phase, and the correlation is raised to 0.74. IASI retrievals show an amplitude of the cycle, smaller than in situ GIF data because the IASI estimate is integrated over the whole atmospheric column, whereas GIF measurements are taken in the boundary layer. Also, the atmospheric column above the GIF area can receive the contribution from the many local sources in North-East Europe because of air mass transport. The vertical distribution is neither uniform nor stationary.

In contrast, when we analyze a target area far from anthropogenic sources, the vertical profile shows a smaller gradient. Therefore, we expect a more consistent satellite agreement with in situ observations. When we look at the results of Fig. 9, which refers to the MLO tropical station, we see that IASI and in situ agree with each other much better than for the GIF case; the cycle is better reproduced, and the correlation reaches the value of 0.82. We also stress that this time, the criterion of Eq. ( 15) has not been applied.

Assessing the d.o.f. spatial-variability on the space-behavior of retrievals

Figure 10 shows a scatter map of dof X for the Euro-Med target area (see, e.g., Fig. 2). The mapping does not involve any averaging operation; therefore, it shows the dof X corresponding to each IASI sounding. It should be noted that at given locations many IASI soundings can overlap, which have different dof X .

From Fig. 10a (no thresholding applied), we see that dof X has a large variability over land, where it can be as low as 0.4. The more considerable variability is seen in the East part of Europe, but also over mountains. In contrast, over the ocean, dof X is uniformly close to 1. Figure 10b shows the scatter map of dof X after thresholding with the criterion of Eq. [START_REF] Masiello | Qualifying img tropical spectra for clear sky[END_REF]. It is seen now that valid IASI soundings Eq. dof X ≈ 1 do not cover a large part of Eastern Europe on the map. If we try to build up a map without thresholding, the result would be highly biased, with patterns reproducing the d.o.f. variability, rather than the natural spatial dynamics of OCS. In fact, according to Eq. ( 9), the smaller the dof X , the larger the bias.

We also stress that Fig. 10a might lead to the wrong conclusion that we should have significant gaps over Spain and some parts of North Africa because of the many dof X below thresholds. However, as said before, IASI footprints can overlap; therefore, after thresholding, the remaining good footprints are revealed.

An analysis in terms of the background contribution, X bg is provided in Fig. 11. The scatter maps show the ratio (see Eq. ( 9)

100 × X bg X ( 16
)
for both cases without (left) and with (right) thresholding according to Eq. [START_REF] Masiello | Qualifying img tropical spectra for clear sky[END_REF]. It is seen that without thresholding, the background state can dominate the final estimate with a fractional contribution larger than 50%. In addition, the presence of thick patterns over mountains and the North-East side of Europe are identified.

In contrast, when we apply thresholding, the contribution of X bg to the final estimate is less than 10%. Again, we see that thresholding leaves gaps primarily at mountains sites and over the Eastern part of Europe.

Finally, Fig. 12 shows the OCS monthly map after thresholding to avoid artifacts added by the background rather that actual observations. The map has been obtained by using the methodology of optimal interpolation developed in [START_REF] Carissimo | The physical retrieval methodology for IASI: the δ-IASI code[END_REF][START_REF] Connor | Orbiting carbon observatory: Inverse method and prospective error analysis[END_REF], with two different length scales, which determine the spatial correlation extend, namely 16) without (left) and with thresholding (right) according to the criterion of Eq. ( 15). 1 • and 0.1 • . With the 1 • map we can fill the gaps left after thresholding (see Eq. ( 15). However, the spatial resolution is degraded at the expense of the uniform coverage. In contrast, the 0.1 • map still contains gaps, but now the spatial resolution is improved of a factor of ten. Despite the different spatial resolution, we see that there is a relatively large concentration of OCS over the North-East corner of Europe, which could be the results of emissions from biomass and coal power stations plants. We also see a striking feature over the North-Africa, the delta of the Nile, and the Sinai region. The OCS pattern over North Africa has also been identified by concurrent analysis with IASI (see, e.g., Ref. 8) and other satellite instrumentation (e.g., Ref. 24). It is not yet clear if the pattern is locally produced, e.g., because of the presence of oil and gas fields, or it is a result of atmospheric transport, as suggested in Ref. [START_REF] Glatthor | Tropical sources and sinks of carbonyl sulfide observed from space[END_REF]. However, our analysis now shows that it is not an artifact of d.o.f. variability but is a real phenomenon still to be understood as an additional, until now unknown, source of OCS. In effect, the much more resolved 0.1 • . The OCS pattern over North Africa has also been identified by concurrent analysis with IASI (see, e.g., Ref. 8) and other satellite instrumentation (e.g., Ref. 24). It is not yet clear if the pattern is locally produced, e.g., because of the presence of oil and gas fields, or it is a result of atmospheric transport, as suggested in Ref. [START_REF] Glatthor | Tropical sources and sinks of carbonyl sulfide observed from space[END_REF]. However, our analysis now shows that it is not an artifact of d.o.f. variability but is a real phenomenon still to be understood as an additional, until now unknown, source of OCS. In effect, the much more resolved 0.1 • map shows that the pattern follows the regions where oil and gas methane fields are active. It is well known that the oil and gas refinery produces CS 2 , which upon oxidation with OH, transforms to OCS (see Ref. [START_REF] Rich | Carbon disulfide (CS2) mechanisms in formation of atmospheric carbon dioxide (CO2) formation from unconventional shale gas extraction and processing operations and global climate change[END_REF][START_REF] Khan | Global analysis of carbon disulfide (CS2) using the 3-d chemistry transport model stochem[j][END_REF]. Also, the potential CS 2 source from the Libyan oil and gas field seems to have been overlooked until now as a potential source of OCS (e.g., see Ref. 27). In effect, the most recent OCS inventory 27 of anthropogenic OCS fluxes identifies the delta of the Nile river (as seen in our analysis) as a source of OCS but fails to show a possible contribution from the Libyan oil fields.

CONCLUSIONS

We have analyzed and assessed the effect of d.o.f. variability over retrievals from satellite high infrared spectral resolution sensors. Although the methodology has been exemplified with the case of atmospheric OCS, the approach is quite general and can be extended to any atmospheric parameter retrieved, e.g., on the basis of OE. We have shown that even in the case the background constraint is a static feature of the inverse system, it can introduce dynamical biases, which can alter the natural annual cycle of the given parameters. The problem also affects spatial fields because the atmospheric state can rapidly change because of a complex surface and meteorological conditions, especially over land. The issue should not be confused with the "smoothing" introduced by the constraint, which depends solely on the covariance matrix of the background (a static feature itself). The effect we are dealing with has to do with the variability of the state vector. Also, in our analysis, the covariance matrix is prescribed to have large variances to implement a very loose constraint.

We have shown that coherent dof X patterns can extend to large spatial scales, introducing biases that cannot be smoothed by considering reliable neighbour data points. An adequate way to come up with this bias is to apply a threshold criterion, which selects soundings with dof X ≈ 1 and ensure that retrievals are mainly depending on the data alone.

Our analysis of the OCS map on February 2020 shows a relevant atmospheric concentration of OCS over North-East Europe, which is in agreement with the most recent inventory of anthropogenic OCS sources. However, we have also found a relatively large and thick concentration of OCS over the Libyan oil and gas fields, which seems to be previously unnoticed. Finally, it is fair to say that this thick concentration could also result from atmospheric transport; therefore, more analysis is needed to draw a firm conclusion.

Figure 1 .

 1 Figure 1. Left: GIF target area; right: Hawaii target area. The yellow box shows the site for which IASI soundings have been acquired. In both figures, the red tag indicates the location of the OCS monitoring stations.

Figure 2 .

 2 Figure 2. Euro-Med target area (red box) used to assess the effect of d.o.f. variability on spatial patterns.

Figure 3

 3 Figure 3. a)-OCS background profile used for the retrieval from IASI data. b)-Example of Averaging Kernels for OCS.

Figure 4 .

 4 Figure 4. Comparison of the Averaging Kernels, w, w h , u, u h of the OCS integrated column amount. The case shown refers to the GIF (panel a) and Hawaii (panel b) for February 2014. The results shown in figure have been averaged based on 304 (a) and 519 (b) retrievals. Therefore, the values shown are representative of the average condition in February time.

Figure 5 .

 5 Figure 5. Comparison of IASI and in situ OCS (monthly means) for the GIF target area. White segments on the blue line (GIF in situ) correspond to missing data.

Figure 6 .

 6 Figure 6. Background contribution to the column amount X bg as a function of the month (2014 to 2019) for the MLO (tropics) and a GIF (Mid-Lat stations), respectively.

Figure 7 .

 7 Figure 7. Monthly series of dof X (2014 to 2019) for a tropical and a mid-lat station, respectively.

Figure 8 .

 8 Figure 8. Comparison of IASI and in situ OCS (monthly means) for the GIF target area. IASI have been filtered according to the criterion of Eq.[START_REF] Masiello | Qualifying img tropical spectra for clear sky[END_REF]. White segments on the blue line (in situ data) correspond to missing data.

Figure 9 .

 9 Figure 9. Comparison of IASI and in situ OCS (monthly means) for the MLO target area.

Figure 10 .

 10 Figure 10. Scatter map of dof X without (left) and with thresholding (right) according to the criterion of Eq. (15).

Figure 11 .

 11 Figure 11. Scatter map of the ratio defined by Eq. (16) without (left) and with thresholding (right) according to the criterion of Eq. (15).

Figure 12 .

 12 Figure 12. Monthly OCS map at different spatial resolution and after thresholding application; (left) the correlation length scale is 1°; (right) the correlation length scale is 0.1•.

ACKNOWLEDGMENTS

In situ observations recorded at Mauna Loa Observatory in Hawaii have been downloaded from the web page http://www.esrl.noaa.gov/gmd/obop/mlo/. The station is part of the National Oceanic and Atmospheric Administration (NOAA), the Earth System Research Laboratory (ESRL) and the Global Monitoring Division (GMD). We give credit to the National Oceanic and Atmospheric Administration (NOAA)/Global Monitoring Division (GMD) in Boulder as a source of the data. IASI has been developed and built under the responsibility of the Centre National d'Etudes Spatiales (CNES, France). It is flown onboard the Metop satellites as part of the EUMETSAT Polar System. The IASI L1C data are received through the EUMETCast near real-time data distribution service. This research was carried out in the framework of the project 'OT4CLIMA' which was funded by the Italian Ministry of Education, University and Research (D.D. 2261 del 6.9.2018, PON R&I 2014-2020 and FSC).


Jonas Hoffmann

Bernard Geffroy

Emmanuel Jaques

Muriel Hissler
email: muriel.hissler@univ-rennes1.fr.

Anne Staubitz
email: staubitz@uni-bremen.de.

Tuning the Aggregation Behaviour of BN-Coronene Diimides with the Imide Substituents and their Performance in Devices (OLED, OFET)

Compared to perylene diimides (PDIs), the coronene diimides (CDIs), which can be viewed as a lateral core extension, show undesired effects for optoelectronic devices such as the decrease of the absorption and a hypsochromic shift. Here, we demonstrate that if the core is extended with two BN units as opposed to two CC units, the opposite is true: Large bathochromic shifts can be achieved, together with higher molar extinction coefficients and beneficial luminescence properties, e.g. a small Stokes shift and high quantum yields (lum >94%). These effects can be explained by the influence of the BN-unit onto the frontier molecular orbitals of the BNCDI. Different substitution motifs at the imide-position, cylcohexyl and 2,6-diisopropylphenyl, although they had no influence on the optical properties on a single molecule level, influenced the aggregation substantially so that the optical properties in the solid-state and the performance in organic devices (OLED and OFET) differed considerably. In combination with host matrices devices with EQE up to 1.5% and white light emission (0.317; 0.346) were obtained. The developed synthetic route starting from a regioisomeric pure 1,7substituted PDI leads to BNCDIs in good yields, which makes this class of compounds very promising.

Introduction

Polycyclic aromatic hydrocarbons (PAHs) have a leading role as active components in organic electronics due to their excellent electronic and optoelectronic properties. [1][2][3][4][5] The molecular engineering of PAHs allows tuning the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) respectively. 6 This promoted the application of PAHs in organic electronics such as in organic solar cells (OSC), organic field-effect transistors (OFET), and organic light-emitting devices (OLED). [7][8][9][START_REF] Müllen | Organic Light Emitting Devices: Synthesis, Properties and Applications[END_REF][START_REF] Chen | [END_REF] However, the variety of PAH-based -conjugated non-fullerene electron acceptors remains limited. The most popular class of these compounds are rylene diimides, which are polycyclic aromatic chromophores based on two, side-on fused naphthalene units that are capped with two imide groups. These PAHs are widely used in the dye industry, 12 fluorescence labelling, 13, 14 and foremost in organic semiconducting devices. 15 In particular, perylene diimides (PDIs) and naphthalene diimides (NDIs) are the most prominent rylene diimides because of their outstanding photochemical and thermal stability. 16 Extending rylene diimides in their long molecular axis narrows the HOMO-LUMO gap, while the extension of the short molecular axis widens the HOMO-LUMO gap. 17, 18 In the case of PDI and coronene diimide (CDI), this leads to a blueshift of the absorption maximum from 525 nm (in PDIs) to 494 nm (in CDIs), a threefold decrease of the extinction coefficient, and a hypsochromic effect on the maximum of emission (532 nm to 500 nm) (Fig. 1). Moreover, a reduction of the fluorescence quantum yield ( lum = 0.98 to 0.69) occurs, which is detrimental for many devices. 19 The main reason for such photophysical changes can be found in the organization of the frontier orbitals. While the bay-extension from PDI to CDI leaves the LUMO unchanged, it influences the orientation of the HOMO level: In PDIs the HOMO level is located along the molecular axis, but in CDIs it is oriented along the short molecular axis leading to a reduced orbital coefficient in the HOMO-LUMO. 20, 21 An alternative to the extension of the system of the carbon scaffold is the integration of heteroatoms (B, N, Si, P) which effectively modifies the HOMO-LUMO gap. 22 In addition, the combination of two heteroelements represents a versatile tool to influence the frontier orbitals of a PAH, but is less likely to distort the flat geometry of the molecule. In particular, the isoelectronic substitution of a C=C unit with a B=N unit (BN/CC isosterism) became a prominent design principle in recent years. [23][24][25][26][27] This isoelectronic substitution can alter the frontier-orbital energies, stabilize the HOMO, [28][29][30][31][32] and significantly alter the orbital distribution of the resulting BN-PAH compared to the corresponding carbonaceous congeners. 33, 34 In fact, it was found that as a general rule, BN-substitution provides a bathochromic shifted absorption, higher fluorescence quantum yield and high hole mobility maintaining high thermal and photochemical stability.

Fig. 1 The bay extension from perylene diimide (PDI) 41 via benzannulated perylene diimide (benzPDI) 19 to coronene diimide (CDI) 42 led to a hypsochromic shift of the absorption. contrarily, the bay extension from perylene diimide (PDI), via BNPDI to the BN-coronene diimide (BNCDI) (this work) resulted in a red-shifted absorption.

In fact, a boron/nitrogen-mono-substituted PDI (BNPDI) has already been reported, which had a substantial bathochromic shift (61 nm) compared to the respective all-carbon benzPDI.

19, 43 The integration of the cyclohexyl-substituted BNPDI Cy in OLED devices, revealed aggregation-caused quenching (ACQ) effects which reduced the overall performance in OLED devices. Such an aggregation phenomenon is well investigated in PAHs, 44 especially rylene diimides, as they have a strong tendency to undergo intermolecular - stacking. 45 While these aggregates are desirable for charge transport, 46, 47 they result in adverse photophysical properties of the rylene diimides when aggregated, e.g. ACQ, and further hamper their device processing. To prevent aggregation of rylene diimides, the functionalization of the bay-area, The latter method has the advantage that it leaves the rylene core unaffected as the imide substituent is electronically decoupled from the rylene core.

54

The effect of a BN-substitution of coronene diimide (CDI) to give the BN-analog BNCDI and the resulting optoelectronic properties were studied. This should provide a deeper insight into how BN-substitution alters the HOMO/LUMO levels of PAHs. Furthermore, two different imide substituents and their effect on the solid-state properties of the BNCDIs was investigated.

As examples, the structures of the thienyl-substituted BNCDIs with prominent cyclohexyl (Cy) or diisopropylphenyl (Dip) substituents 19 at the imide's nitrogen were chosen (Fig. 2).

Results and Discussion

Synthesis of the BNCDIs

Starting from the regioisomerically pure 1,7-brominated PDIs (1,7-DB-PDI Cy/Dip ), generated via bromination of perylene tetraesters, 55 we implemented the nhexylamino moiety by an aromatic nucleophilic substitution (Scheme 1). Although several protocols for the reaction of neat primary alkylamines and 1,7-brominated PDIs at high temperatures were published, [56][57][58] the yields and high formation of side products (monosubstitution and dehalogenation forming the 1alkylamino-PDI) were unsatisfactory. To prevent the dehalogenation of the intermediary 1-alkyl-7-bromo-PDI (1,7-DB-PDI Cy/Dip ), we lowered the reaction temperature to 60 °C with a concomitant extension of the reaction time to 3 d. Using this protocol, we The resulting purple/red amorphous powders showed good solubility in halogenated solvents, toluene, and THF. Furthermore, BNCDIs showed stability against moisture, strongly acidic and basic conditions. We fully characterized the BNCDIs by 1 H/ 11 B/ 13 C NMR-, and FTIR spectroscopies and highresolution mass spectrometry. Since the aromatic perylene protons gave rise to only two proton signals and the carbon atoms located at the imide position gave rise to also only two signals, both BNCDIs were of C 2 -symmetry and were therefore regioisomerically pure (see also the ESI for detailed experimental conditions and full characterization of all compounds). Attempts to grow crystals failed throughout using different techniques as only aggregates were observed.

Optical properties of the BNCDIs in solution

To evaluate the effect of the BN-substitution on the CDI scaffold, the optical properties of the BNCDIs were analyzed by UV/Vis absorption and fluorescence spectroscopy in DCM. The absorption spectra of both BNCDIs were characterized by their intense maxima at 535/538 nm (BNCDI Cy /BNCDI Dip ) and high extinction coefficients ( ≈ 70794-74131 M -1 cm -1

) (Fig. 3, Table 1) The absorption bands exhibited well-resolved typical vibronic fine structures with the strongest transition (S 0 S 1 ) at 535/538 nm with further transitions at 498/501 nm and 466/470 nm from the 0-0, 0-1 and 0-2 vibronic bands. The higher energetic transitions (S 0 S 2 ) occurred at 425/426 nm and 401/401 nm for the respective 0-0 and 0-1 vibronic transitions.

59, 60 Moreover, a distinct absorption band is found between 300-350 nm. As expected, the effect of the imide sub- As expected for such a system, the bands were mirror images of the absorbance spectra including the vibronic fine structure with bands at 545/546 nm, 585/588 nm and 634/638 nm. This was attributed to the S 1 S 0 transitions and the respective vibronic bands.

61

In general, the absorption maxima of the here presented BNCDIs were red-shifted compared to their CC-analog CDI Dip ( abs = 494 nm), 62 the PDI Cy ( abs = 525 nm), 41 the CN-isoster diaza-CDI ( abs = 488 nm) 63 and previously reported BNmonosubstituted BNPDI Cy ( abs = 529 nm) 43 . Compared to all carbon PDI Dip ( lum = 0.98) 41 and CDI Dip ( lum = 0.69) 62 similar or higher quantum yields were observed. However, the R-C=Nisosteric compound CN-CDI ( lum = 0.25) 63 was less emissive.

Overall, the bathochromic shift of the absorption maxima  abs (BNCDI) = 535/538 nm) of the BNCDIs compared to the allcarbon CDI ( abs (CDI) = 494 nm) 62 was distinct. This effect was attributed to the decrease of the HOMO-LUMO gap due to the BN units, an increased dipole moment but foremost to the orientation of the frontier orbitals (see below).

If one compares the characteristics of the absorption spectra of BNCDIs and CDI, systematic differences are found. In fact, the absorption spectra of both BNCDIs resembled more closely the absorption spectrum of a PDI than a CDI. Therefore, it was concluded that upon adding two BN units to a perylene core and extending the -conjugated system in a lateral fashion, the absorption properties of the perylene core persist. This is not the case for the respective CDI. However, the absorption bands of BNCDIs at 350 nm and 425 nm are both absent in the absorption spectrum of PDI but are found in the absorption spectrum of the reported CDI unit.

Theoretical Calculations

To understand the optoelectronic properties of BNCDIs in comparison with their C=C congener CDI, theoretical calculations using density functional theory (DFT) and timedependent DFT (TD-DFT) were conducted. The ground stategeometry was optimized, and the respective frontier orbitals and energies were extracted to investigate the effect of the BN units on the coronene core (Fig. 4). The electronic effect of the BN-substitution of the coronene core was clearly visible by comparing the LUMO/HOMO energy levels of BNCDI and CDI. It became evident that an isoelectronic substitution of two C=C-units by two BN units stabilized the LUMO level (-3.06 eV vs. -2.91 eV) and destabilized the HOMO level (-5.69 eV vs. -5.97 eV) resulting in a smaller HOMO-LUMO gap (2.63 eV vs.

eV).

To explain the absorption spectra of CDI and BNCDI, the frontier orbitals of both motifs were considered and TD-DFT calculations were performed. Initially, in both cases, the imide substituents displayed a node located at the imide's nitrogen which underlined the fact that imide substituents are barely interacting with the electronical features of these systems, which is in perfect agreement with the observed optical properties (Fig. 3). The topology of the LUMO in both structures was similar to the one in rylene diimides 20 and therefore barely affected by the BN-substitution. In contrast, the nature of the HOMO changed drastically: The all-carbon coronene core of CDI exhibited a coronene-like organization of the HOMO whereas the HOMO of the BNCDI was more related to the typical HOMO of PDIs 64 . In fact, the coronene-like topology in CDIs is the reason for a hypsochromic shifted absorption in contrast to common PDIs. 20 The respective coronene-like HOMO of the BNCDI was found in the HOMO-4 whereas the perylene-like HOMO of the CDI is displayed in the HOMO-1. Additionally, the present S 0 S 2 transition (420 nm, Fig. 3), which might occur from the HOMO-4 to the LUMO level, and was similarily described for a more general CDI motif. 21 These findings were in agreement with the performed TD-DFT calculations which support the discrepancy between a coronene-like HOMO and a perylenelike LUMO indicated by the reduced oscillator strength (Fig. 4).

Finally, this highlights how BN-units can shift the photophysical properties of PAHs by influencing the alignment of the frontier orbitals in addition to merely influencing the dipole moment. This could also explain the drastic bathochromic shifted absorption from benzPDI to its BN-congener BNPDI BNCDIs exhibited two fully reversible distinctive reductive waves which is typical for rylene diimide systems 54 as both imides are reduced (Fig. 5). The onset potentials for the first reductive wave were E red, onset =-1.10/-1.05 V and therefore the energy level of the LUMO (E LUMO = -3.69/-3.75 eV) could be stimated (Table 2). The electrochemical oxidation of both BNCDIs led to irreversible processes (E ox,onset = 0.74/0.82 V) giving rise to the respective HOMO levels (E HOMO = -5.54/-5.62 eV). Evidently, only a marginal effect of the imide substit- tuents on the oxidation/reduction was found since the HOMO-LUMO gap was constant (E = 1.85/1.87 eV). In comparison with the conventional CDIs, the LUMO level (E LUMO = -3.69 eV) was unchanged. 42 But since CDIs optical gap (E opt = 2.46 eV) 42 was larger than for the BNCDIs (E opt ≈ 2.23 eV), it can be concluded that the BNCDIs have a destabilized HOMO and therefore lower the HOMO-LUMO gap. This was in good agreement with the calculation presented above. The same trend was observed for the CN-isoster of the BNCDIs, the diaza-CDI, where a similar LUMO level (E LUMO = -3.69 eV) and larger optical gap (E opt = 2.47 eV) were reported. 63 These electronic effects of the BN-substitution on the CDI were in great agreement with the above-mentioned theoretical investigations.

Optical Properties of the BNCDIs in Aggregated State

Expecting increased luminescence response of the novel BNCDIs at a lower temperature than at ambient conditions, we analyzed BNCDIs using isopentane, which forms a glassy state when frozen, as solvent. Surprisingly, we observed complete luminescence quenching of the BNCDIs at 150 K, where isopentane is still in a liquid state. Detailed temperature resolved investigation showed that the luminescence intensity decreases according to temperature but no appearance of other emission bands supporting an aggregation-caused quenching (ACQ) 69, 70 process due to the reduced solubility of the BNCDIs was found. Further investigation showed that this quenching effect correlated with the nature of the imide group. The BNCDI Cy quenched its luminescence way faster than the BNCDI Dip upon cooling down (see ESI, Fig. SI37). The result that emerges from these experiments was that the cyclohexyl substituent prevents less effectively the formation of aggregates than the diisopropylphenyl group and was an indication for the application in devices, where morphology effects are harder to predict. The initial observations on this ACQ behavior brought us to the idea to generate high luminescence solid-state materials by dispersing the BNCDIs in poly(methylmethacrylate) (PMMA) matrix. The blending experiments were performed with dopant ratios of 0.75%, 1.5%, 4.8%, 9.0% and 50%). The emission properties of BNCDI Cy and BNCDI Dip in wavelength and intensities of the emitted light were visible to the naked eye (Fig. 6). In fact, the luminescence of the BNCDI Dip changed from yellow-greenish to a deep red while the luminescence of the BNCDI Cy was barely visible and underlined the aggregation-caused quenching in this BNCDI derivative. Compared to the optical properties observed in solution, a low amount of BNCDI Cy (0.75%) in PMMA resulted in a red-shifted emission with a broad signal around 605 nm (Fig. 7, top). This represented a shift of approximately 80 nm towards the signal observed in DCM solution (Fig. 3) and might arise from aggregates emission. 71 Upon increasing the dopant rate, bathochromic shifts and broadening of the signals towards the NIR region were noticed. Using an equal amount of BNCDI Cy and PMMA a new band could be observed at 750 nm covering the whole emission spectra from 600 nm to 800 nm whilst the fluorescence was barely visible because of ACQ effects.

Repeating the experiment but changing the imide substituent from cyclohexyl to diisopropylphenyl moiety, drastic changes in the solid-state emission were observed. In the marginal dopant rate of 0.75%, the emission spectrum of BNCDI Dip was only slightly red-shifted (Fig. 7, bottom) and exhibited the same characteristics as in solution (Fig. 3). Since the vibrionic transitions were clearly observable, it was assumed that only monomeric emission occurred. Doubling of the BNCDI Dip dopant rate (1.5%) resulted in a small bathochromic shift of the first emission band and an increase of the 0-1 transition. However, when such monomers begin to aggregate, the 0-1 transition commonly increases as it was for similar aggregated PDIs. The difference between the BNCDI Cy and BNCDI Dip in the PMMA films was also investigated by optical microscopy. In the BNCDI Cy /PMMA blend needle-like agglomerates 75 were observed whereas nano-spheres 76 in the BNCDI Dip /PMMA blend could be detected (see ESI, Fig. SI36).

From the luminescence experiments at low temperature and in PMMA blends, the conclusion could be drawn that the imide substituents had a strong influence on the aggregation in the solid-state resulting in tuning the luminescence properties. These preliminary experiments were good indicators for the performance of both BNCDIs in organic light-emitting diodes (OLEDs).

Thermal properties

The thermal properties of both BNCDIs were investigated to evaluate their stability towards evaporation for organic devices. For both BNCDIs decomposition occurred at temperatures higher than 390 °C, indicated by 5% mass loss which are comparable to the respective PDI Dip and PDI Cy (see ESI, Fig. SI44). This analysis underlines the concept of condensing labile azaborine units with thermally stable PAH structures and suggested sufficient stability for thermal evaporation processes. Additionally, in a dynamic scanning calorimetry (DSC) experiment, no glass-transition temperature (T g ) in the range of -80 °C to 300 °C could be measured (see ESI, Fig. SI45 andSI46). Due to their amorphous characteristics, their morphological stability during the fabrication processing of OLEDs was therefore envisaged.

Organic Field Effect Transistor (OFET)

To study the charge transport ability of BNCDIs, the material that was shown to aggregate more, BNCDI Cy was integrated into a bottom-gate bottom-contact n-type OFET device. The characteristics of the OFET were measured in linear and saturated regime (i.e. V DS = 20 V and V DS = 50 V).

The linear field-effect mobility was estimated to be µ FE = 1.02 x 10 -8 cm 2 V -1 s -1 while in the saturated regime, fieldeffect mobility was µ FE = 4.34 x 10 -8 cm² V -1 s -1 . The classical electrical parameters of OFET were defined by its low conductivity (µ e = 3.42 x 10 -6 cm 2 V -1 s -1

), low on/off-current ratio (I on /I off = 36) and high threshold voltage (V th ≈ 21 V). The OFET device was also annealed at 150 °C to induce reorganization of the semiconducting layer. At this temperature, the linear field-effect mobility was slightly increased to µ FE = 2.68 x 10 -8 cm 2 V -1 s -1 and the threshold voltage was shifted (V th ≈ 16 V) due to a decreased defect density in the device. This result showed that the BNCDIs in general are capable of electron transportation in organic devices.

Organic Light Emitting Diode (OLED)

After the preliminary evaluation of the solid-state luminescence in the PMMA matrix had revealed promising optoelectronic and thermal properties, we used both BNCDIs in multilayer organic light-emitting devices (OLEDs). Because no oxidation was recorded, the use of a host matrix with matching HOMO-LUMO levels was necessary; moreover; this was expected to prevent ACQ effects. Therefore, 4,4'-bis(Ncarbazolyl)- . The raise of the dopant rate to 9.3% (device E) decreased the overall performance of the device (Table 3). Presumably, with a higher dopant ratio of BNCDI Cy , ACQ processes are favoured which was Table 3 Electroluminescent performance of devices A-J. The best parameters are highlighted bold.

a Recorded at 10 mA/cm 2 . b Recorded at luminance of 0.1 cd/m 2 (± 0.2 V). c Recorded at 30 mA/cm 2 .

expected from the experiments in the PMMA blend and as well in the OLED consisting of BNPDI Cy . 43 Since the best matrix/dopant interaction was obtained with DPVBi in the previous devices, devices F-J with BNCDI Dip were fabricated with the same matrix. Since the only difference between BNCDI Cy and BNCDI Dip was in their supramolecular arrangement and not their optoelectronic properties, a direct conclusion towards the effect of the imide bands can be drawn. Interestingly, device F exhibited also two main bands located at 460 nm and with slightly higher intensity at 560 nm resulting from the matrix and the BNCDI Dip (Fig. 8, right). The latter band showed a small shoulder which might be related to the vibronic structure of the BNCDI core. The CIE coordinates (device F: x = 0.317; y = 0.346) are close to white light (x = 0.330; y = 0.330). Moreover, device F exhibited an EQE of 1.5%, a brightness of 800 cd m -2

, and a power efficiency of 1.3 lm W -1

. Upon increasing the amount of BNCDI Dip (devices G-J)

the overall intensity decreased whereas a new band at 690 nm occurred. This might be related to aggregation processes since a similar band was observed in the blend of BNCDI Dip with PMMA (Fig. 7). By increasing the dopant ratio, the performance of these devices decreased significantly. Interestingly, devices G-J showed light emission at the region of white light (all CIE charts are to be in the ESI, Fig. SI52 andSI53).

Discussion of the device performances

The observed smaller HOMO-LUMO gap induced by the lateral BN-expansion of a PDI to a BNCDI and enhanced photophysical properties compared to the CDI motif could be transferred to several organic light-emitting devices using a host-guest setup. We observed, however, that the integration of two hexyl chains on the BN-motif could not overcome the general problem of aggregation which is common in rylene diimides due to strong - interactions. This diminished the performance of the OLED devices with increasing doping rate of BNCDI. This is in line with the poor electron mobility (µ e = 10 -6 cm 2 V -1 s -1

) of the neat material in an OFET device which is most likely due to morphological disadvantages. Furthermore, this is also supported by the fact that an improved performance after the reorganization of the film via annealing was observed (see ESI). To obtain higher electron mobility, appropriate (fluorinated) alkyl chains could be introduced to the nitrogen atom of the BN-motif or on the imide position of the BNCDI. While this is likely to increase OFET performance, a decrease in the performance in an OLED device due to a dense packing of the cores is to be expected. ) to CDI (µ e = 10 -4 cm2 V -1 s -1

) 77 .

However, in combination with matrices, better OLED performance properties could be accessed (EQE up to 1.5%) compared to common PDIs (EQE up to 0.638%) 78 or heteroatom bay-annulated PDI (EQE up to 0.06%).

79

Conclusions

In summary, we present the synthesis of regioisomerically pure BNCDIs via a BN-annulation reaction starting from PDI precursors. Initially, the optoelectronic properties BNCDIs were investigated and compared to its all-carbon coronene diimides: A large bathochromic shift (40 nm) and a higher compared to their carbonaceous congeners were observed. In fact, it was found that the BN-extension overcame the inferior photophysical properties which were observed for the CC-extension from PDI to CDI. DFT calculations showed that the BN-substitution stabilized a perylene-like HOMO whereas a CC-substitution leads to a coronene-like HOMO. This concept might be extendable to all cases where lateral -extension of PAHs leads to inferior optical properties. Moreover, the effect of the imide substituents (cyclohexyl or diisopropylphenyl) for the BNCDIs was investigated in solution (ambient and low temperature) and solid-state matrices (OLEDs and PMMA): It was found that the cyclohexyl motif was less effective in preventing aggregation-caused quenching (ACQ) than the diisopropylphenyl substituent.

In addition to the examination of their redox properties, thermal stability (T 95 >390 °C), the charge transfer behaviour was investigated in a n-type OFET (µ e = 10 -6 cm 2 V -1 s -1

). The rich chemistry for postfunctionalization of rylene diimides 80 should allow further modification for this n-type organic semiconductor to access lower lying LUMOs by stabilizing it with cyano groups 81 or halides.

Both BNCDIs were deployed in host matrices in a multi-stack OLED setup. Apart from being non-luminescent in the aggregated state, by blending the BNCDIs with a blue-emitting matrix it was demonstrated that white light emission in a multi-layered OLED device (x = 0.317; y = 0.346) could be achieved. Overall, the OLED performance was characterized with a maximum EQE of 1.5%, low turn-on voltage (V on = 3.6 V) and a luminance up to 1001 cd/m

Fig. 2

 2 Fig. 2 Molecular structures of BNCDI Cy and BNCDI Dip which only differ in their imide functionality. could obtain both 1,7-di(nhexylamino)-PDIs (1,7-DHA-PDI Cy/Dip ) in a moderate yield of 51% after intense column chromatography. In a final step, the BNCDIs were formed by the reaction of 1,7-DHA-PDI Cy/Dip with 2-thienyldichloroborane (TphBCl 2 ) and triethylamine as a base in high yields (97%/83%).The resulting purple/red amorphous powders showed good solubility in halogenated solvents, toluene, and THF. Furthermore, BNCDIs showed stability against moisture, strongly acidic and basic conditions. We fully characterized the BNCDIs by

a

  Measured in DCM (1.0 x 10 -6 M). b Obtained from the offset wavelength derived from the low energy absorption band. c Referenced against fluorescein in 0.1 M NaOH.

Fig. 3

 3 Fig. 3 Absorption and emission spectra of compounds BNCDI Cy and BNCDI Dip . Photographic images of both BNCDIs at ambient light (left) and with irradiation of light (365 nm) exhibiting green luminescence (right). stituents (Cy or Dip) on the optical properties was marginal in solution. 41 Both BNCDIs exhibited a strong luminescence ( lum (BNCDI Cy /BNCDI Dip ) = 0.94/0.95) and small Stokes shifts ( Stokes (BNCDI Cy /BNCDI Dip ) = 310/272 cm -1 ) in DCM solution indicating a high rigidity of the molecule in the ground state and the excited state.As expected for such a system, the bands were mirror images of the absorbance spectra including the vibronic fine structure with bands at 545/546 nm, 585/588 nm and 634/638 nm. This was attributed to the S 1 S 0 transitions and the respective vibronic bands.

Fig. 4

 4 Fig. 4 Display of the frontier orbitals of BNCDI Cy and CDI Cy calculated with B3LYP 6-31G* at an isovalue of 0.02. The transitions calculated via TD-DFT are indicated.

43 .

 43 Furthermore, nuclear independent chemical shift (NICS) 65-67 calculations for both BNCDI and CDI were conducted. They revealed that the aromaticity of the annulated rings decreased for the BN-derivatives: The azaborine ring had a NICS(0) = -3.25 ppm and NICS(1) = -6.01 ppm whereas the same ring in the CDI showed a NICS(0) = -8.68 ppm and NICS(1) = -11.09 ppm. The reduced aromaticity of the BN-structure is a result of the more localized -electrons on the B-N bond. A detailed NICS analysis of all rings for both BNCDIs and CDIs is shown in the ESI. Electrochemistry To further estimate the influence of the BN unit on the CDI motif, the redox properties of BNCDI Cy and BNCDI Dip were investigated using cyclic voltammetry experiments. Both

a

  In DCM with nBu4NPF6 (0.2 M), a scan rate of 200 mV/s and ferrocene/ferrocenium as reference. For further details see ESI. b Derived from ELUMO= -4.8 eV-Ered,ons and EHOMO= -4.8 eV -Eox,ons. 68c See also footnote ‡ .Temperature where 95% of the mass was still present at 10 K/min and 20 mL/min nitrogen flow.

Fig. 5

 5 Fig. 5 Cyclic voltammogram of BNCDI Cy (red) and BNCDI Dip (black) in DCM with nBu4NPF6 (0.2 M) as conducting salt using platinum working electrodes at 200mV/s sweep rate.

Fig. 6

 6 Fig. 6 Image of the PMMA films with different weight ratios (from left to right: 0.75%, 1.5%, 4.8%, 9.0% and 50%) of both BNCDIs under irradiation of UV light (365 nm) (top row: BNCDI Cy , bottom row: BNCDI Dip ).

Fig. 7

 7 Fig. 7 Emission spectra of the PMMA blends of BNCDI Cy (top) and BNCDI Dip (bottom) with different dopant ratios.

Fig. 8

 8 Fig. 8 Electroluminescence spectra of devices A-B (left) with BNCDI Cy and CBP matrix, devices C-E (middle) with BNCDI Cy and DPVBi matrix, devices G-J (right) with different dopant rate of BNCDI Dip in DPVBi matrix.

Scheme 1 Synthesis of BN-substituted BNCDIs through amination of 1,7-DB-PDI and ring annulation reaction of 1,7-DHA-PDI with TphBCl2. Tph

  : Thiophenyl. Details can be found in the ESI.

Table 1

 1 Overview of photophysical properties of both BNCDIs.

Table 2

 2 Overview of electronic and thermal properties of both BNCDIs.

  Despite advantages in fluorescence quantum yields and excitation energy gap reduction, a planar BN-coronene core in itself seems insufficient to increase the electron mobility; the values obtained by us are similar to a structurally similar thiophene-substituted PDI (µ e = 10

				-6 cm 2 V	-1 s	-1
	Host		Doping ratio (%)	EQE	a (%)		cd/A a	lm/W	a	V on b (V)	Luminance c (cd/m	2 )	CIE	c (x; y)
	CBP:		1.5 A	0.7		1.5	0.5		5.0	442		0.309; 0.415
	BNCDI	Cy	3.0 B	0.6		1.3	0.4		6.0	371		0.308; 0.417
	DPVBi: Cy BNCDI	1.1 C 1.4 D 9.3 E	1.4 1.4 0.3		3.3 2.7 0.4	1.3 1.1 0.1		4.2 4.3 4.8	1001 842 117		0.374; 0.431 0.327; 0.416 0.298; 0.339
			0.6 F	1.5		2.7	1.3		3.7	800		0.317; 0.346
	DPVBi: Dip BNCDI	1.1 G 1.2 H 2.1 I	1.3 1.1 0.9		1.8 1.6 1.3	0.9 0.7 0.6		3.7 3.6 3.7	530 480 380		0.347; 0.336 0.357; 0.336 0.376; 0.342
			3.0 J	0.8		1.0	0.5		4.0	275		0.375; 0.324

. However, to further increase the efficiency of BNCDIs in OFETs/OLEDs, modification of the imide function, e.g. by sterically demanding terphenyl imide substituents, 52, 83 can be directly implemented.

† Electronic supplementary information (ESI) available. See DOI: 10.1039/x0xx00000x ‡ Although this is often referred to as the LUMO, and Table2is resented as E LUMO , we wish to point out that actually the LUMO cannot be measured in this way, as it is not defined electrochemically.

Acknowledgements

The Authors thank Prof. F. Sönnichsen and his support with the 11 B NMR measurements. A. S. thanks the German research Foundation (DFG) for and Emmy-Noether grant (STA1195/2-1). J.H. acknowledges funding for a Short-Term Scientific Mission from the COST action COST 1302: "European Network on Smart Inorganic Polymers". This work is supported by the Ministère de la Recherche et de l'Enseignement Superieur, the CNRS, the Region Bretagne, and COST CM 1302 (SIPS).

Conflicts of Interest

There are no conflicts to declare.