Sudhanya Chatterjee
email: sudhanya.chatterjee@irisa.fr

Olivier Commowick

Onur Afacan

Benoit Combes

Simon K Warfield

Christian Barillot

A three year follow-up study of gadolinium enhanced and non-enhanced regions in multiple sclerosis lesions using a multi-compartment T 2 relaxometry model

Demyelination, axonal damage and inflammation are critical indicators of the onset and progress of neurodegenerative diseases such as multiple sclerosis (MS) in patients. Due to physical limitations of imaging such as acquisition time and imaging resolution, a voxel in a MR image is heterogeneous in terms of tissue microstructure such as myelin, axons, intra and extra cellular fluids and free water. We present a multi-compartment tissue model which estimates the water fraction (WF) of tissues with short, medium and high T 2 relaxation times in a T 2 relaxometry MRI voxel. The proposed method is validated on test-retest data of healthy controls. This model was then used to study longitudinal trends of the tissue microstructures for two sub-regions of the lesions: gadolinium enhanced (E+) and non-enhanced (L-) regions of MS lesions in 10 MS patients over a period of three years. The water fraction values in E+ and L-regions were found to be significantly different (p < 0.05) over the period of first three months. The results of this study also showed that the estimates of the proposed T 2 relaxometry model on brain tissue microstructures have potential to distinguish between regions undergoing active blood brain barrier breakdown from the other regions of the lesion.

Introduction

Magnetic resonance imaging (MRI) is one of the most widely used in-vivo imaging method for obtaining information on brain health. However, MRI voxels have limited resolution due to physical constraints. Use of advanced MRI techniques such as T 2 relaxometry and diffusion weighted MRI can address this issue by providing quantitative estimates on brain tissue microstructures such as myelinated and unmyelinated axons, brain fiber orientation etc [START_REF] Tofts | Quantitative MRI of the brain: measuring changes caused by disease[END_REF]. In patients with neurodegenerative diseases (such as multiple sclerosis (MS)), obtaining information on health of axons and myelin using in-vivo imaging techniques can improve our understanding of the current status and the progress of the disease in the patients. Obtaining this information can provide critical knowledge on the brain health.

The myelin, axons and fluids in the brain can be distinguished based on the nature of their water content. Myelin is a tightly wrapped structure around the axons. The water in myelin is very tightly bound to its surface. Hence myelin has a very short T 2 July 4, 2018 1/14 relaxation time compared to the other brain tissue structures. The axons, gray matter cells and other cells in the brain have a higher T 2 relaxation time than that of myelin but less than that of the fluids. Free fluids have the largest T 2 relaxation time. Hence, based on the T 2 relaxation time brain tissues can be broadly classified into three categories, short-, medium-and high-T 2 components [START_REF] Whittall | In vivo measurement of T2 distributions and water contents in normal human brain[END_REF][START_REF] Mackay | Magnetic Resonance of Myelin Water: An in vivo Marker for Myelin[END_REF]. Since a voxel in a MR image of the brain is heterogeneous, there is a certain amount of the three T 2 components present in each voxel. In addition to these, in presence of an infection there might also be some fluid accumulation. Hence a quantitative metric that conveys information on the condition of these tissues can provide useful insights into the current brain tissue health.

Quantitative T 2 relaxometry MRI sequences offer the capability to distinguish tissues based on their T 2 relaxation times. T 2 relaxometry MRI has been used effectively to calculate the myelin water fraction using a variety of approaches. Whittall et al. and MacKay et al. [START_REF] Whittall | In vivo measurement of T2 distributions and water contents in normal human brain[END_REF][START_REF] Mackay | In vivo visualization of myelin water in brain by magnetic resonance[END_REF] obtained myelin water fraction using a multi-component T 2 model [START_REF] Whittall | Quantitative interpretation of NMR relaxation data[END_REF]. The multicomponent T 2 model describes the observed T 2 decay curve as a weighted sum of an arbitrary number of decay curves. The weight of each T 2 decay curve is obtained using non-negative least squares (NNLS). Whittall et al. obtained myelin water fraction of the brain tissues by assuming the T 2 values of water in myelin to be in the range of 10 -55 milliseconds [START_REF] Whittall | In vivo measurement of T2 distributions and water contents in normal human brain[END_REF]. The multi-component T 2 models select an arbitrary number of T 2 decay curves to model the observed decay signal [START_REF] Whittall | Quantitative interpretation of NMR relaxation data[END_REF]. For example, Whittall et al. [START_REF] Whittall | In vivo measurement of T2 distributions and water contents in normal human brain[END_REF] considered 80 logarithmically spaced values between 15 milliseconds and 2 seconds. Since the number of parameters to be estimated considerably outweighs the number of observations (i.e. number of echoes), some regularization is mandatory. However, the choice of the regularization term and its extent affects the fitting measure [START_REF] Does | Inferring brain tissue composition and microstructure via MR relaxometry[END_REF].

An alternate approach is a multi-compartment T 2 relaxometry model where the different T 2 water pools in brain tissues are modeled as a weighted mixture of pre-defined continuous functions. Stanisz and Henkelman [START_REF] Stanisz | Diffusional anisotropy of T2 components in bovine optic nerve[END_REF] fitted two T 2 components (short and long T 2 in bovine optic nerve), each having a gaussian distribution on a logarithmic scale. Akhondi-Asl et al. proposed a framework to calculate myelin water fraction by modeling the R 2 space as a weighted mixture of inverse Gaussian distribution of fast-, medium-and slow-decaying components with respect to T 2 relaxation times [START_REF] Akhondi-Asl | Fast myelin water fraction estimation using 2D multislice CPMG[END_REF]. Layton et al. proposed a maximum likelihood estimation approach to estimate the myelin water fraction values [START_REF] Layton | Modelling and Estimation of Multicomponent T 2 Distributions[END_REF]. They obtained the Cramér-Rao lower bounds of the variables to establish the difficult nature of simultaneously estimating the model parameters and weights for each compartment for such models. In contrast to the multiple exponential T 2 fitting approach, these models do not suffer from the ill-posed weights estimation problem. In these models, the regularization is performed a priori rather than a posteriori.

In this work, we propose a method for computing water fractions corresponding to fast-, medium-and slow-decaying components with respect to T 2 relaxation times from T 2 relaxometry MRI data acquired using 2D multislice Carr-Purcell-Meiboom-Gill (CPMG) sequence. In this estimation framework, the T 2 space is modeled as a weighted mixture of three continuous probability density functions (PDF) representing the three T 2 compartments. For such models, the robustness and accuracy of the implementations to simultaneously estimate the weights and parameters of the distributions was found to be non-trivial and not reliable [START_REF] Layton | Modelling and Estimation of Multicomponent T 2 Distributions[END_REF]. We therefore chose to take advantage of the earlier studies performed in this field to fix the parameters of the distributions representing the T 2 relaxation components [START_REF] Mackay | Magnetic Resonance of Myelin Water: An in vivo Marker for Myelin[END_REF][START_REF] Lancaster | Three-pool model of white matter[END_REF][START_REF] Laule | Magnetic resonance imaging of myelin[END_REF]. Hence only the estimation of weights remain, making the estimation model robust. In our work, we need to correct for the effect of the stimulated echoes due to imperfect refocusing (due to the B 1 inhomogeneities) that leads to errors in T 2 estimation [START_REF] Crawley | Errors in T2 estimation using multislice multiple-echo imaging[END_REF]. The EPG algorithm is used to account for these July 4, 2018 2/14 stimulated echoes [START_REF] Prasloski | Applications of stimulated echo correction to multicomponent T2 analysis[END_REF]. The field inhomogeneity (B 1 ) is estimated numerically. Since the T 2 space is modeled as a weighted mixture of three continuous PDFs representing the three components, the proposed model does not include any regularization on the water fractions. The estimated weights of each compartment provide a quantitative estimate of the tissue microstructure in a voxel. Experiments were carried out to evaluate repeatability of the quantitative markers on healthy controls.

In the last part of this work, we show an application of the method on MS patients. We report observations on the evolution of the quantitative markers obtained from the model in enhancing (MS lesion regions undergoing active blood brain barrier breakdown) and non-enhancing MS lesion regions. Vavasour et al. studied the MWF and total water content in three new MS lesions in two patients over a year [START_REF] Vavasour | Longitudinal changes in myelin water fraction in two MS patients with active disease[END_REF]. Levesque et al. studied evolution of MWF and geometric mean of T 2 values of gadolinium enhancing lesions in five MS patients over a period of one year [START_REF] Levesque | Quantitative magnetization transfer and myelin water imaging of the evolution of acute multiple sclerosis lesions[END_REF]. Although MWF was found to be quite informative in suggesting changes in active lesions, the geometric mean T 2 values was sensitive to changes in the active lesions. Vargas et al. studied MWF of gadolinium enhancing and non-enhancing lesions [START_REF] Vargas | Measuring longitudinal myelin water fraction in new multiple sclerosis lesions[END_REF]. Measurements were compared for two acquisitions with median duration of around 6 months between the scans. Authors found that contrary to the non-enhancing lesions, there was significant improvement in MWF of enhancing lesions between the two scans. Vargas et al. also mention that MWF is a combined measure of edema and demyelination [START_REF] Vargas | Measuring longitudinal myelin water fraction in new multiple sclerosis lesions[END_REF]. The MWF is a relative measure and a change in its values should be studied in conjunction with the remaining water fraction measures. In our analysis, we observed and compared the change in water fractions of tissues with short, medium and high T 2 values in enhancing and non-enhancing regions of lesions in 10 MS patients over a period of 3 years.

Materials and methods

Estimation framework

Signal model We model the T 2 space as a weighted mixture of three continuous probability density functions (PDF) representing the three T 2 relaxometry compartments. The compartments represent tissues with short, medium and high T 2 relaxation times. The weight of the j-th distribution is denoted by w j . The weights are normalized such that j w j = 1.The signal of a voxel at the i-th echo time (t i ) is therefore given as:

s (t i ) = M 0 3 j=1 w j   ∞ 0 f j (T 2 ; p) EP G (T 2 , T E, i, B 1 ) dT 2   (1)
where t i = i × T E and T E is the echo spacing. Each f j (T 2 ; p) is the chosen PDF with parameters p. As mentioned in the introduction, for robustness reasons, the PDF parameters are pre-selected and fixed keeping in mind histology findings reported in the literature [START_REF] Mackay | Magnetic Resonance of Myelin Water: An in vivo Marker for Myelin[END_REF][START_REF] Laule | Magnetic resonance imaging of myelin[END_REF]. In Eq. ( 1), M 0 is the magnetization constant. EP G(•) represents the stimulated echo computed at the time point (t i = i × T E) using the EPG algorithm [START_REF] Prasloski | Applications of stimulated echo correction to multicomponent T2 analysis[END_REF]. B 1 is the field inhomogeneity.

Optimization Without any loss of generality, M 0 and {w j } 3 j=1 in Eq. ( 1) can be combined into a single term, {α j } 3 j=1 ∈ R + . The weight corresponding to each compartment can then be obtained as, w j = α j / i α i and M 0 as i α i . The signal of July 4, 2018 3/14 the voxel at time t i is expressed as:

s (t i ) = 3 j=1 α j   ∞ 0 f j (T 2 ; p) EP G (T 2 , T E, i, B 1 ) dT 2   (2)
The parameters to be estimated in Eq. ( 2) are: {α j } 3 j=1 , B 1 . The optimization is thus formulated as a least square problem:

α, B1 = arg min α,B1 m i=1 (y i -s (t i )) 2 = arg min α,B1 Y -Λ (B 1 ) α 2 2 (3)
where m is the number of echoes; Y ∈ R m is the observed signal; 3) is computed as:

α = {α 1 , α 2 , α 3 } ∈ R + 3 . Each element of Λ (Λ ij = λ j (t i ; B 1 ) ; i = {1, ..., m}, j = {1, 2, 3}) in Eq. (
λ j (t i ; B 1 ) = ∞ 0 f j (T 2 ; p) EP G (T 2 , T E, i, B 1 ) dT 2 (4)
The parameters to be estimated in the least squares optimization problem stated in Eq. ( 3), α and B 1 , are linear and non-linear in nature respectively. However they are linearly separable. Hence optimization for α and B 1 is performed alternatively until convergence is obtained in a desired error limit. In the first step, α is computed by non-negative least squares (NNLS) optimization [START_REF] Lawson | Solving least squares problems[END_REF] with a fixed B 1 value. In the next step, the weights computed in the first step are used to compute B 1 by a gradient free optimizer (BOBYQA). We choose to perform a numerical optimization to obtain B 1 as it does not have any closed form solution [START_REF] Prasloski | Applications of stimulated echo correction to multicomponent T2 analysis[END_REF]. The integral in Eq. ( 4) also does not have a closed form solution. Hence the integral is computed using the Riemann sum approach by dividing the T 2 region into rectangles of finite width (= 0.33ms in our case) over the range of [0, 2500] ms.

In this work, the PDFs to represent each T 2 relaxometry compartment ({f j (•)} 3 j=1 in Eq. ( 1)) are chosen as Gaussian PDFs. The mean and standard deviations are chosen for the three compartments based on histology findings reported in the literature [START_REF] Mackay | Magnetic Resonance of Myelin Water: An in vivo Marker for Myelin[END_REF][START_REF] Lancaster | Three-pool model of white matter[END_REF][START_REF] Laule | Magnetic resonance imaging of myelin[END_REF] and are set as µ = {20, 100, 2000} and σ = {5, 10, 80} (all values in milliseconds). The proposed method was implemented in C++ and is made available as an open source library Anima 1

Experimental Methods

Repeatability is an important aspect of quantitative MRI techniques. In the first experiment we carried out test-retest experiments to assess the repeatability of the proposed method. An important motivation of this study is to gain more insights into the neurodegenerative disease phenomenon using the tissue microstructure information. Hence, in the second experiment we performed a 3-year follow-up study on 10 multiple sclerosis patients.

Experiment-1: Repeatability test

The objective of this experiment is to observe whether the proposed model is repeatable in terms of estimation of the microstructure maps. For that purpose, test retest T 2 relaxometry scans of 4 healthy controls were obtained to evaluate the repeatability of the proposed method. Analysis A Bland-Altman plot was used to observe the repeatability of the estimations over the ROIs. From the plot we obtained the mean deviation (m d ) of the test retest values for the ROIs and checked whether there are noticeable systematic changes in the estimations. We further look at the limits of agreement (LoA) between the test retest estimations from the plot.

Experiment-2: Application to Multiple Sclerosis (MS)

Multiple sclerosis lesions are focal lesions and grow in a concentric manner [START_REF] Guttmann | The evolution of multiple sclerosis lesions on serial MR[END_REF]. In the early stages, brain tissues in the MS lesions undergo active blood brain barrier breakdown [START_REF] Guttmann | The evolution of multiple sclerosis lesions on serial MR[END_REF][START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. Surrounding the core of the lesion is the edema as a result of tissue inflammation due to ongoing tissue damage. As compared to the normal appearing brain matter, the entire MS lesion regions appear hyper-intense on T 2 weighted MRI.

However, only the regions of the lesion undergoing active blood brain barrier breakdown appear hyperintense on T 1 weighted MRI acquired post Gd injection. Hence, lesions in active state have two regions, a region which actively undergoes blood brain barrier breakdown and the regions which do not.

The objective of this experiment is to study the evolution of compartments' water fractions in regions of lesions in MS patients undergoing active blood brain barrier breakdown and the regions which are not. In addition to that, we shall observe whether the water fraction values of the compartments for the two regions are in confirmation with the pathological knowledge of MS lesions.

July 4, 2018 5/14

Patient Data We studied 10 MS patients over a period of 36 months. All patients included in this study had an episode of clinically isolated syndrome (CIS). The patient cohort comprised of an equal number of male and female subjects and their median age was 28 years. All participants of this study gave their written consent. Data was acquired at eight time points over a period of 36 months. An acquisition at the baseline was followed by acquisitions at 3, 6, 9, 12, 18, 24 and 36 months from the baseline. The lesions in patient scans were marked by an expert radiologist on T 2 weighted images at the baseline. All participants were informed and provided their written consent for the study. The lesion ROIs are marked at baseline and the same region is observed over a period of three years. In the 10 MS patients, we observed 229 L-and 25 E+ lesion regions.

Since the lesions were marked on T 2 weighted images, all processed images were registered to the T 2 images using a block matching algorithm [START_REF] Ourselin | Block matching: A general framework to improve robustness of rigid registration of medical images[END_REF][START_REF] Commowick | Block-matching strategies for rigid registration of multimodal medical images[END_REF].

3 Results

Experiment-1: Repeatability test

The Bland-Altman (BA) plots for short, medium and high-T 2 water fraction estimates over the ROIs are shown in Fig. 3. BA plots are scatter plots between the average This table summarizes the statistics of the Bland-Altman (BA) plots shown in Fig. 3 for short, medium and high-T 2 water fraction estimates.

Experiment-2: Application to Multiple Sclerosis (MS)

In this experiment we observed and compared the evolution of water fraction maps of The common language (CL) effect size are reported for the measurements which were significantly different for E+ and L-. In this work, the CL effect size denotes the percentage of times a randomly selected sample from L-is greater than a random selection from E+ group. of the water fraction values to reject the null hypothesis, the effect size is a measure of the magnitude of the difference. We used the common language (CL) effect size statistic and the associated p-values to observe the group differences [START_REF] Mcgraw | A common language effect size statistic[END_REF][START_REF] Grissom | Effect sizes for research: A broad practical approach[END_REF]. The CL effect size July 4, 2018 10/14

for the groups that were found to be significantly different from the Mann-Whitney U test is shown in Table 2. In this work, the CL effect size value denotes the percentage of times the w f value of L-is higher than E+ when both samples are selected at random from each group. It can hence be interpreted as the probability of superiority of Lover E+ for a measurement.

Discussion

The test-retest experiment results show that the quantitative MRI markers estimated by the proposed method is repeatable. For all the markers estimated, the zero level was comfortably inside the 95% confidence interval of the mean difference observed between the test and retest values of the marker for the 15 ROIs (refer the Bland-Altman plots in Fig. 2). Hence there are no noticeable systematic changes in the estimated markers for the test and retest data [START_REF] Lexell | How to assess the reliability of measurements in rehabilitation[END_REF].

In Section 3.2 the evolution of water fraction markers in MS lesion regions which are undergoing active blood brain barrier breakdown are compared to the MS lesion regions in the later stages. At the baseline scan, the E+ lesion regions are prone to having lower short-T 2 water fraction values as compared to L-regions (p = 0.014, CL = 65.05%). This might indicate that regions of the lesion undergoing active blood brain barrier breakdown have undergone greater demyelination. However, there seems to be no significant difference between the two groups with respect to the short-T 2 water fraction values for all scans three months after the baseline. The E+ lesion regions tend to have significantly higher values for high-T 2 water fraction as compared to L-at the baseline scan (p < 0.01, CL = 31.51%). The demyelination of MS lesions is accompanied by inflammation due to increased macrophage intervention [START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. This might explain the low and high values of short-T 2 and high-T 2 water fraction values observed at the baseline scan for E+ lesion regions. The gain in short-T 2 water fraction values for E+ lesion regions between the scans at M00 and M03 is significantly greater than that for L-(p < 0.01, CL = 34.25%). The increase in short-T 2 values in this period is accompanied by a considerable drop in high-T 2 values for the E+ lesion regions. The drop in high-T 2 water fraction values between the baseline and the next scan for E+ is significantly larger than that of L-(p < 0.01, CL = 66.08%). All E+ lesion regions incur a decrease in high-T 2 values over the first six months of observation. Hence, the observations from the change in water fraction values between consecutive scans are: (i) although both groups show indications of remyelination, E+ lesion regions undergo significantly greater remyelination as compared to L-between the baseline and scan at M03, (ii) there is a considerable reduction of inflammation in E+ over the first three months but L-show little or no change in this aspect. The myelination activity of E+ and L-is similar three months after baseline. However, the inflammation activity seems to continue for 9 months from baseline scan time. Some L-lesion regions observed at the baseline scan would have been in the E+ stage at some point of time. This explains the similar water fraction values for E+ and L-by the end of three years. Unlike short-T 2 and high-T 2 water fraction values, the medium-T 2 water fraction values for E+ and L-lesion regions never show any significant difference, which might be attributed to the fact that in terms of T 2 values considered, the medium-T 2 water pool is highly heterogeneous. It conveys information on unmyelinated axons, glia, interstitial and extra-cellular matters [START_REF] Lancaster | Three-pool model of white matter[END_REF].

Our study on MS patients has certain limitations. First, the clinical data available was not of the highest quality possible due to acquisition time constraints in a clinical setting. T 2 relaxometry data with a higher number of echoes and shorter echo times are favorable for multi-compartment models. Second, the time gap between the first and second scan was three months. A shorter interval between successive acquisitions would July 4, 2018 11/14 be beneficial to study the fast evolving active lesions.

Conclusion

In this work we proposed a multi-compartment T 2 relaxometry model to obtain quantitative estimates on brain tissues with short, medium and high T 2 relaxation times. Test retest experiment results showed that the proposed method does not suffer from any noticeable systematic changes in terms of the markers estimated. The study of the evolution of multi-compartment T 2 relaxometry markers on 10 MS patients over a period of 3 years had two important observations: (i) the markers have the potential to distinguish between gadolinium enhanced and non-enhanced regions in MS lesions and (ii) both lesion regions have similar water fraction values by the end of the third year and show little distinction after 3 months from baseline scan. The later observation from the longitudinal study shows that the biomarkers obtained from this model explains the MS lesion evolution along the lines reported in the pathological and radiological studies on MS lesions [START_REF] Guttmann | The evolution of multiple sclerosis lesions on serial MR[END_REF][START_REF] Lassmann | Heterogeneity of multiple sclerosis pathogenesis: Implications for diagnosis and therapy[END_REF]. The former observation on the other hand motivates us to investigate methods by which biomarkers from multi-compartment models based on advanced MRI techniques can help distinguish between lesion regions undergoing active blood brain barrier breakdown without injection of contrast enhancers in MS patients, which we shall investigate in our future studies.

1

  Fig 1. Assessing repeatability from test-retest data Test retest scans were performed for 4 healthy controls to study the repeatability of the proposed method.This figure shows the 15 regions which were marked on the healthy controls over which the repeatability was studied.

Fig 2 .

 2 Fig 2. MS patient study designThe MS lesions were marked on T 2 weighted on gadolinium post contrast T 1 spin echo MR images of the patients acquired at the first visit (i.e. M00). Eight scans are obtained from time of the first visit over a period of 36 months for each patient at intervals shown in the figure. The region of interest (ROI) marked at M00 is studied over the period of 36 months. Two ROIs are studied in this work: (i) region of the lesion which appears on the gadolinium post contrast T 1 weighted spin echo images. These are the regions of the lesions undergoing active blood brain barrier breakdown, (ii) lesion region appearing on T 2 weighted MR images but not on gadolinium post contrast images.

Fig 3 .

 3 Fig 3. Bland-Altman plots comparing test-retest estimations Bland-Altman (BA) plots for (a) short, (b) medium and (c) high-T 2 water fraction estimations are shown here. 15 ROIs (see Fig. 1) are evaluated for repeatability of the estimated water fractions in 4 healthy controls. The mean level (m d ) is the mean of the differences between test and retest values. The gray region around m d is its 95% confidence interval (CI). The limits of agreement (LoA) levels are computed as m d ± 1.96SD, where SD is the standard deviation of the difference in test and retest values. The yellow region around the LoAs are its 95% CI. The BA plot statistics are summarized in Table1.

  the three compartments between E+ and L-MS lesion regions in 10 patients over a period of 3 years. We observed the water fraction values for E+ and L-at each scan point. In addition to it, we also observed the change in the water fraction values (for E+ and L-) between consecutive scans which is computed as: ∆w f,i = w fscan i+1 -w fscan i . Hence positive values indicate a gain in the water fraction values between consecutive scans. The E+ and L-group difference analysis was performed using Mann-Whitney U test.

Fig 4 .Fig 5 .Fig 6 .Fig 7 .

 4567 Fig 4. Healthy subject and MS patient A comparison between water fraction maps for (a) healthy subject and (b) MS patient is shown.

Table 1 .

 1 test-retest measurement and the difference between test-retest measurements. We measured the means of the estimated values of 15 ROIs in 4 healthy controls. The BA plots for short, medium and high-T The gray area around the mean error level is its 95% confidence interval (CI). Along with m d , the m d ± 1.96 × σ d levels are also shown and are referred to as levels of agreement (LoA). σ d is the standard deviation associated with the errors observed in the test-retest measurements. LoA is thus an empirical estimate of the range around m d within which 95% of the differences are expected to exist. The 95% CI of the LoAs for each plot is shown with a yellow shade around LoA in the plots. The BA plot statistics are summarized in Table1. From Fig.3, we observe that the mean bias of difference between the test-retest ROI mean values (m d ) is close to zero for short, medium and high-T 2 water fraction estimates. For all three water fraction estimations, the zero level lies comfortably inside the 95% CI of the m d . The test retest differences lie within the LoA and its 95% CI.

2 water fraction estimates for the 15 ROIs are shown in Fig. 3(a), 3(b) and 3(c) respectively. The plots shows the level of mean error (m d ) July 4, 2018 7/14 observed.

Table 1 .

 1 Bland-Altman plots statistics for repeatability experiment

		Mean bias (m d )	95% CI around m d	Limits of agreement (LoA)
	Short-T2 water fraction	-2.27 × 10 -4	-4.92 × 10 -3 , 4.46 × 10 -3	1.65 × 10 -2
	Medium-T 2 water fraction	2.34 × 10 -4	-4.45 × 10 -3 , 4.91 × 10 -3	1.65 × 10 -2
	High-T 2 water fraction	-0.07 × 10 -4	-0.11 × 10 -3 , 0.09 × 10 -3	0.01 × 10 -2

Table 2 .

 2 Common language effect size and p-values

	Value	p-value CL effect size
	Short-T 2 water fraction (w s ) at M00	0.014	65.05%
	∆w s between M00 and M03	0.009	34.25%
	High-T 2 water fraction (w h ) at M00	0.002	31.51%
	∆w h between M00 and M03	0.008	66.08%
	∆w h between M03 and M06	0.011	65.51%
	∆w h between M06 and M09	0.011	34.55%

Acknowledgments

The clinical MS study was supported by a grant from Fondation pour l'Aide à la Recherche sur la Sclérose en Plaques (ARSEP). The authors acknowledge Neurinfo MRI research facility for logistic support and MRI data acquisition. This research was supported in part by the grants NIH R01 EB019483 and NIH R01 NS079788.


Romain Nandillon
email: romain.nandillon@iddea-ingenierie.fr

Manhattan Lebrun
email: manhattan.lebrun@etu.univ-orleans.fr

Florie Miard
email: florie.miard@univ-orleans.fr

Marie Gaillard
email: marie.gaillard@iddea-ingenierie.fr

Stéphane Sabatier
email: stephane.sabatier@iddea-ingenierie.fr

Sylvain Bourgerie
email: sylvain.bourgerie@univ-orleans.fr

Fabienne Battaglia-Brunet

Domenico Morabito
email: domenico.morabito@univ-orleans.fr

Effect of wood biochar associated to compost on the phytotoxicity of a mining technosol mainly contaminated by Pb and As

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Extended Abstract

Mining activities are one of the main sources of environmental contamination through metal(loid)s released due to soil erosion. High concentrations of metal(loid)s in soils and consequently into groundwater could have negative effects on terrestrial ecosystems and could pose potential health risks. Consequently depollution techniques such as physical or chemical methods have been developed to reduce the impact of such pollutions. However these techniques are expensive and disturb the normal biological soil activities. Phytoremediation techniques, which use specific plants and the associated microorganisms to control soil metal(loid)s availability in situ, are low cost alternative technologies. However few physicochemical characteristics of tailings such as low pH, and metal(loid)s toxicity could limit this strategy. Moreover, polluted soils are often agronomically poor, that is why often amendments either organic or inorganic must be applied to allow the establishment of vegetation. Among the amendments used, biochar has attracted attention in recent years because of its beneficial effects on soil fertility but also as a metal(loid)s sorbent.

In particular cases, biochar application to contaminated soils does not contribute effectively by itself to the growth of plants and sometimes the soil must be supplemented by other amendments such as compost. Therefore, the combination of amendments seems a better option for improving the agronomic capacity of a technosol while maintaining the biochar capacity to immobilize the metal(loid)s pollutants.

The objectives of our study were to evaluate, in pots, the capacity of dwarf bean as a plant indicator to germinate and grown on a mining technosol (Pontgibaud, France; mainly contaminated by Pb and As) amended by biochar +/-compost; and to characterize soil phytotoxicity.

When biochar was added to the technosol, soil pore water (SPW) pH and electrical conductivity increased significantly whereas lead SPW concentration decreased almost by 90%. In the opposite, SPW arsenic concentration increased after biochar addition but remains lower when compared to the biochar + compost amendments. The aerial dwarf bean dry biomass was ameliorated on technosol amended by biochar or by the biochar + compost association compared to the non-amended technosol. For all conditions, root biomasses were also ameliorated with amended technosol. In the aerial organs, arsenic and lead concentrations were less important or equal to the concentrations measured when dwarf bean were grown on non-amended technosol. For the two amended conditions, arsenic concentrations in roots were equal or significantly lower compared to non-amended technosol.

In conclusion, biochar and compost addition to the Pb and As contaminated soil allows the dwarf bean growth. Such amendments reduced the technosol phytotoxicity by decreasing Pb disponibility in SPW. However biochar addition allow arsenic remobilization. As alternatives, other amendments such as iron are under investigation in addition to biochar to decrease As SPW disponibility.


Urszula Szczepaniak
email: urszula.szczepaniak@u-psud.fr

Robert Kołos

Marcin Gronowski

Michèle Chevalier

Claude Guillemin

Claudine Crépin

Synthesis and Electronic Phosphorescence of Dicyanooctatetrayne (NC 10 N) in 1 Cryogenic Matrices 2 3

5 nm).

ACS Paragon Plus Environment

The Journal of Physical Chemistry INTRODUCTION 28 Hydrogenless centrosymmetric dicyanopolyyne chains (NC 2n N) constitute a unique series of well-29 defined linear molecules of closed-shell electronic structure. They are kinetically more stable, at 30 least as judged by the first elements of the series, than respective isoelectronic species of the related 31 monocyanopolyyne (HC 2n+1 N) or polyyne (HC 2n H) series. [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF] For example, while working with 32 dicyanoethyne (NC 4 N) [START_REF] Turowski | Low-Temperature 362 Phosphorescence of Dicyanoacetylene in Rare Gas Solids[END_REF] we could observe that it is much less susceptible to decomposition (by 33 polymerization) than cyanobutadiyne (HC 5 N) [START_REF] Trolez | Synthesis and Characterization of 2,4-Pentadiynenitrile-A Key 365 Compound in Space Science[END_REF] or hexatriyne (HC 6 H). [START_REF] Hunsmann | Nachweis Und Synthese Des Triacetylens[END_REF] Rod-like NC 2n N chains, with 34 their highly conjugated bonding and the ensuing semiconductive properties, are interesting from 35 purely theoretical/spectroscopic point of view, but potential applications, as nanowires, [START_REF] Ding | Gas Phase Electronic Spectrum of 368 the Nitrogen Terminated Nanowire NC 16[END_REF] were also 36 hypothesized. Moreover, dicyanopolyynes are molecules of astrochemical interest. [START_REF] Duley | Chemical Evolution of Carbonaceous Material in Interstellar Clouds[END_REF] However, while 37 the presence of HC 2n+1 N nitriles in interstellar gas clouds has been confirmed with microwave 38 spectroscopy up to n = 4, [START_REF] Turner | Detection of Interstellar Cyanoacetylene[END_REF][START_REF] Dickinson | Detection of Cyanoacetylene at 18 GHz[END_REF][START_REF] Mcgee | Interstellar Cyanoacetylene J=2→1, J=4→3 374 Transitions[END_REF][START_REF] Gardner | Observations of the J = 1→0 Transitions of the (13) C 376 Isotopic Species of Cyanoacetylene (HCCCN) in the Direction of Sagittarius B2[END_REF][START_REF] Mauersberger | Dense Gas in Nearby Galaxies. III -HC 3 N as an 379 Extragalactic Density Probe[END_REF][12][START_REF] Snell | Observations of HC 3 N, 385 HC 5 N, and HC 7 N in Molecular Clouds[END_REF][START_REF] Broten | The Detection of HC 9 N 387 in Interstellar Space[END_REF][START_REF] Graham | HC 9 N from the Envelopes of IRC+10216 and 389 CRL:2688[END_REF][START_REF] Bell | The Excitation Temperature of 391 HC 9 N in the Circumstellar Envelope of IRC + 10216[END_REF] little is known about centrosymmetric NC 2n N molecules in any 39 extraterrestrial sources, apart from a tentative identification [START_REF] Khanna | Vibrational Infrared and Raman Spectra 393 of Dicyanoacetylene[END_REF] of dicyanoacetylene (NC 4 N) in the 40 atmosphere of the Saturn's moon Titan. Aerosols build-up from related, highly unsaturated carbon-2 nitrogen polymers may contribute to the Titan's characteristic orange haze. [START_REF] Waite | The Process of Tholin Formation in Titan's Upper Atmosphere[END_REF] Some information 42 about NC 2n N molecules in space can be obtained by observation of their protonated forms. 18 43 Certain molecular properties were theoretically predicted for NC 2n N molecules, including the 44 geometry, vibrational modes, and electronic transition energies; some of these were derived up to n 45 = 8. [START_REF] Ding | Gas Phase Electronic Spectrum of 368 the Nitrogen Terminated Nanowire NC 16[END_REF][START_REF] Woon | Quantum Chemical Predictions of the Properties of Known and 401 Postulated Neutral Interstellar Molecules[END_REF][START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF][START_REF] Turowski | Formation and Spectroscopy of 406 Dicyanotriacetylene (NC 8 N) in Solid Kr[END_REF] NC 2 N, NC 4 N, and (to a lesser extent) NC 6 N are rather well experimentally characterized, 46 being available in macroscopic quantities via preparative organic synthesis. In particular, these are 47 known to emit strong phosphorescence under cryogenic isolation conditions. [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF][START_REF] Chang | The C 2 N 2 a 3 Σ u + -X ෩ 1 Σ g + Chemiluminescence in Matrices[END_REF][START_REF] Smith | Infrared Spectral Evidence of 410 N≡C-C≡C-N≡C: Photoisomerization of N≡C-C≡C-C≡N in an Argon Matrix[END_REF] Experimental 48 data reported for larger (n > 3) members of the series are limited to NMR spectroscopy (in CDCl 3 , n 49 ≤ 9), [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF] IR spectra of solid substances in NaCl (n ≤ 9), [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF] electronic absorption spectra in liquid organic 50 solvents [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF][START_REF] Cataldo | A New Class of Carbon Allotropes. About the Formation of 413 Dicyanopolyynes from an Electric Arc between Graphite Electrodes in Liquid Nitrogen[END_REF][START_REF] Cataldo | Polyynes and Cyanopolyynes: Their Synthesis with the Carbon Arc Gives the 416 Same Abundances Occurring in Carbon-Rich Stars[END_REF][START_REF] Forte | The Effects 419 of Liquid Environments on the Optical Properties of Linear Carbon Chains Prepared by Laser 420 Ablation Generated Plasmas[END_REF] (n ≤ 9) and in the gas phase (n = 8), [START_REF] Ding | Gas Phase Electronic Spectrum of 368 the Nitrogen Terminated Nanowire NC 16[END_REF] and low temperature electronic phosphorescence 51

(n = 4). [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF][START_REF] Turowski | Formation and Spectroscopy of 406 Dicyanotriacetylene (NC 8 N) in Solid Kr[END_REF][START_REF] Smith | Infrared Spectral Evidence of 410 N≡C-C≡C-N≡C: Photoisomerization of N≡C-C≡C-C≡N in an Argon Matrix[END_REF] Very recently, traces of a long-lived luminescence attributable to NC 10 N were 52 observed by us in a study primarily devoted to HC 9 N spectroscopy. [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF] In each of these cases, 53 electronic emission was characterized by at least one prominent vibronic progression with a spacing 54 of 2000 -2300 cm -1 , typical of CC or CN triple-bond stretching modes. Luminescence was also 55 observed for C 4 N 2 + , C 6 N 2 + , and C 8 N 2 + in cryogenic Ne matrices. 29,30 56 Here we report on synthesizing NC 10 N (1,8-dicyano-octa-1,3,5,7-tetrayne or deca-2,4,6,8-tetrayne- 57 1,8-dinitrile) in noble gas (Ar and Kr) matrices, using the method of cryogenic photochemical 58 coupling, already proved useful for C 6 N 2 , [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF] as well as for the monocyanopolyynes HC 5 N, 21,31 59 HC 7 N, [START_REF] Couturier-Tamburelli | 432 Synthesis and Spectroscopy of Cyanotriacetylene (HC 7 N) in Solid Argon[END_REF] and HC 9 N. [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF] Since NC 6 N appeared in photolysed matrices doped with HC 3 N, [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF] NC 10 N 60 formation from HC 5 N was anticipated, even though HC 5 N molecules are larger than HC 3 N and their 61 movement in a matrix is even more restricted. The spectroscopic identification of products has been 62

supported using density functional theory calculations of electronic and vibrational energy levels. 63

64

EXPERIMENTAL METHODS 65

Experimental details regarding matrix preparation and spectroscopic characterization of the 66 photochemical products are only briefly summarized here, as these were recently described in our 67 reports on HC 9 N 28 and CH 3 C 7 N. [START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF]

68

Precursor molecule, HC 5 N, was prepared with the method developed by Trolez and Guillemin. [START_REF] Trolez | Synthesis and Characterization of 2,4-Pentadiynenitrile-A Key 365 Compound in Space Science[END_REF] It 69 was purified by pumping while kept at T<200K, directly before the experiment. Solid krypton has 70 been shown to permit strong and spectrally well-resolved luminescence of embedded 71 cyanopolyynes. [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF][START_REF] Turowski | Formation and Spectroscopy of 406 Dicyanotriacetylene (NC 8 N) in Solid Kr[END_REF] Therefore, it was used here (4.0, Messer), along with, more commonly applied 72 in matrix-isolation spectroscopy, argon (6.0, Messer). 73 HC 5 N molecules were mixed with noble gases at a ratio of 1:1000 to 1:500. [START_REF] Frisch | [END_REF] program package. Time-dependent methodologies 36-38 98 and the B3PW91 functional of Perdew and Wang [START_REF] Perdew | Electronic Structure of Solids[END_REF][START_REF] Perdew | Molecules, Solids, and Surfaces: Applications of the Generalized 456 Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the 459 Generalized Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Generalized Gradient Approximation for the Exchange-462 Correlation Hole of a Many-Electron System[END_REF] were applied for singlet excited electronic 99 states. Energetic separations between the ground and the lowest triplet states were derived 100 employing the CAM-B3LYP [START_REF] Yanai | A New Hybrid Exchange-correlation Functional Using 464 the Coulomb-Attenuating Method (CAM-B3LYP)[END_REF] functional. Computations made use of the aug-cc-pVTZ [START_REF] Dunning | Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The 466 Atoms Boron through Neon and Hydrogen[END_REF][START_REF] Kendall | Electron Affinities of the First-row Atoms 468 Revisited. Systematic Basis Sets and Wave Functions[END_REF] basis set. 101

This approach supplied molecular geometries, harmonic vibrational wavenumbers, and energies of 102 transitions from the ground to excited electronic states. Additionally, IR absorption intensity and 103 Raman activity values were predicted for the ground electronic state (B3PW91/aug-cc-pVTZ). To 104 account for anharmonicity and inherent deficiencies of the involved theoretical approach, vibrational 105 wavenumbers were scaled with the factor of 0.96. [START_REF] Andersson | New Scale Factors for Harmonic Vibrational Frequencies Using 470 the B3LYP Density Functional Method with the Triple-ζ Basis Set 6-311+G(d,P)[END_REF][START_REF] Merrick | An Evaluation of Harmonic Vibrational Frequency 473 Scale Factors[END_REF] Linearity of the carbon-nitrogen backbone in 106 excited singlet electronic states was verified by performing CIS/aug-cc-pVDZ [START_REF] Dunning | Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The 466 Atoms Boron through Neon and Hydrogen[END_REF][START_REF] Kendall | Electron Affinities of the First-row Atoms 468 Revisited. Systematic Basis Sets and Wave Functions[END_REF][START_REF] Foresman | Toward a Systematic Molecular 475 Orbital Theory for Excited States[END_REF] optimizations 107 (starting from a bent structure) and by looking, at both CIS and DFT levels, for the degeneracy of 108 bending modes. Optimized structures were also checked for the absence of imaginary vibrational 109 frequencies. Vertical excitation energies, together with the corresponding oscillator strengths, were 110 additionally derived at the ab-initio level CC2 [START_REF] Christiansen | The Second-Order Approximate Coupled Cluster 477 Singles and Doubles Model CC2[END_REF][START_REF] Christiansen | Large-479 scale Calculations of Excitation Energies in Coupled Cluster Theory: The Singlet Excited 480 States of Benzene[END_REF][START_REF] Christiansen | Integral-Direct Coupled 482 Cluster Calculations of Frequency-Dependent Polarizabilities, Transition Probabilities and 483 Excited-State Properties[END_REF][START_REF] Hald | Triplet Excitation Energies in the Coupled Cluster Singles 485 and Doubles Model Using an Explicit Triplet Spin Coupled Excitation Space[END_REF] (cc-pVTZ basis set), using the Dalton2016 Theoretical results concerning the electronic states of NC 10 N are collected in Table 1 and Figure 1. 119

The first fully allowed electronic excitation of a ground-state molecule is predicted at 4.65 eV (267 120 nm). We have checked that the energy of the next allowed transition is around 6.2 eV (vertical 121 approximation), and no transition with oscillator strength similar to that characterizing ܪ ෩ -ܺ ෨ is 122 predicted up to around 7 eV. Formerly reported UV-Vis absorption of NC 10 N in acetonitrile [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF] and in 123 n-octane solution [START_REF] Cataldo | A New Class of Carbon Allotropes. About the Formation of 413 Dicyanopolyynes from an Electric Arc between Graphite Electrodes in Liquid Nitrogen[END_REF] is energetically close to the currently predicted ܪ ෩ -ܺ ෨ excitation. Electronic 124 structures characterizing states ܣ ሚ , ܤ ෨ , ܽ , and ܪ ෩ originate mainly in the HOMO-LUMO excitation. ܪ ෩ 125 state features the smallest deviation from the ground state geometry (see Figure 1), just as reported 126

for the analogous ܧ( ෨ ) state of HC 9 N. [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF] Transitions to the three lowest excited states ܣ( ሚ , ܤ ෨ , and ܽ ) 127 result in mutually similar changes of geometry (in analogy to what was observed for several alike 128 carbon-nitrogen chains [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF][START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF][START_REF] Turowski | Electronic 496 Spectroscopy of Methylcyanodiacetylene (CH 3 C 5 N)[END_REF] ). 129 The observed main vibronic spacing (see Figure 2) may originate in one of the two gerade 173 stretchings, either ν 3 or ν 2 , with DFT-predicted wavenumbers of 2115 cm -1 and 2140 cm -1 , 174 respectively. Although this last value better matches the observed separation of progression 175 elements, the former is preferred, based on its particular molecular distortion pattern: alternate 176 shrinking-expansion of interatomic distances along the chain (see Table S2), qualitatively similar to 177 the geometry change experienced by NC 10 N upon the transition from ܺ ෨ to ܽ (Figure 1). Moreover, 178 the ν 3 stretching is distinct by its highest Raman scattering activity (see Table 2), and such modes 179 were already shown to shape the main vibronic progressions of phosphorescence emitted by shorter 180 NC 2n N molecules. [START_REF] Turowski | Low-Temperature 362 Phosphorescence of Dicyanoacetylene in Rare Gas Solids[END_REF][START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF][START_REF] Turowski | Formation and Spectroscopy of 406 Dicyanotriacetylene (NC 8 N) in Solid Kr[END_REF][START_REF] Chang | The C 2 N 2 a 3 Σ u + -X ෩ 1 Σ g + Chemiluminescence in Matrices[END_REF][START_REF] Turowski | Niskotemperaturowe Badania Fotochemii i Spektroskopii Cyjanoacetylenów o 498 Znaczeniu Astrofizycznym[END_REF] a From Ref. [START_REF] Turowski | Electronic Absorption and Phosphorescence of 502 Cyanodiacetylene[END_REF] . b From Ref. [START_REF] Turowski | Low-Temperature 362 Phosphorescence of Dicyanoacetylene in Rare Gas Solids[END_REF] . c From Ref. [START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF] . d From Ref. [START_REF] Turowski | Niskotemperaturowe Badania Fotochemii i Spektroskopii Cyjanoacetylenów o 498 Znaczeniu Astrofizycznym[END_REF] . e From Ref. [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF] . f This work.

205 206 A systematic change of electronic transition energy with the molecular size is expected to occur in 207 homologous series (in particular those of unsaturated carbon-chain molecules) for vibrationless 208 transitions sharing a common electronic provenance. [START_REF] Murrell | The Theory of the Electronic Spectra of Organic Molecules[END_REF] Such regularities can be simplistically 209 described either by a particle-in-a-box model (where a 'particle', i.e. an electron, is delocalized in a 210 'box' formed by a system of conjugated bonds) [START_REF] Kuhn | A Quantum-Mechanical Theory of Light Absorption of Organic Dyes and Similar 506 Compounds[END_REF] or by a harmonic oscillator model (with electrons 211 oscillating within π orbitals). [START_REF] Lewis | The Color of Organic Substances[END_REF] It should then be manifested, respectively, by the linear correlation of 212 chain size with either ߣ ୭୰୧୧୬ or ߣ ୭୰୧୧୬ ଶ . Forney et al. [START_REF] Forney | Electronic Absorption Spectra of Cyano-509 substituted Polyacetylene Cations in Neon Matrices[END_REF] reported on linear ߣ ୭୰୧୧୬ vs. n relations for 213 the first allowed electronic absorption systems in several series of highly unsaturated carbon-214 backbone molecules: HC 2n+1 N + , NC 2n N + , HC 2n N + , and NC 2n+1 N + . The same properties have been 215

found for C 2n H -, C 2n+1 H -, HC 2n H -, HC 2n+1 H + , HC 2n+1 H, C 2n+1 , and C 2n+1 -families. [START_REF] Pino | Electronic Spectra of the Chains HC 2n H (n=8-13) 511 in the Gas Phase[END_REF] This can be 216 rationalized in terms of a high delocalization of electrons involved in the considered transitions. On 217 the other hand, certain curvature of ߣ ୭୰୧୧୬ vs. n plots, evident for n > 4 in the neutral polyyne 218 (HC 2n H) series, was associated by Pino et al. [START_REF] Pino | Electronic Spectra of the Chains HC 2n H (n=8-13) 511 in the Gas Phase[END_REF] with more pronounced localization of π orbitals. In 219 such cases, as demonstrated by Hausser et al. [START_REF] Hausser | Lichtabsorption Und Doppelbindung. V. Über Die 513 Absorption von Verbindungen Min Konjugierten Kohlenstoffdoppelbindungen Bei Tiefer[END_REF] for diphenylpolyenes, a ߣ ୭୰୧୧୬ ଶ

vs. n relation (Lewis-220

Calvin plot) is expected to offer good linearity. Figure 3

233

Lines defined by NC 2n N and HC 2n+1 N data (Figure 3) appear to be parallel to each other (with a 234 slope of approx. 75 000 nm 2 /triple bond). This can be interpreted as the inclusion of an extra -C≡C-235 unit having the same effect in both series. It makes yet another similarity between the 236 phosphorescence properties of respective di-and monocyano species. In case of the first fully 237 allowed ( 1 Σ u + -1 Σ g + ) system observed for NC 2n N (n = 3 to 8) solutions in acetonitrile (Ref. [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF] ), the 238 slope of a Lewis-Calvin plot is much lower (~12 000 nm 2 /triple bond) than for the presently 239 discussed phosphorescence, reflecting differences in electronic structure of the lowest triplet

( 3 Σ u + ) 240
and the lowest singlet ( 1 Σ u + ) state (evidenced also by their dissimilar geometries; see Figure 1). 241

C. Singlet excited electronic states 243

The phosphorescence excitation spectrum of Kr matrix-isolated NC 10 N is shown in Figure 4. The 244 first intense band falls around 38 500 cm -1 (4.77 eV, 260 nm), in good agreement with the predicted 245 vibrationless onset of the fully allowed ܪ ෩ 1 Σ u + -ܺ ෨ 1 Σ g + system (4.65 eV). When identifying other 246 vibronic bands, one should only consider the involvement of g-symmetry vibrations, i.e. those 247 preserving the general g↔u selection rule. The proposed assignments are presented in Table 5. We 248 identify the ܪ ෩ -state mode responsible for the main progression as ν 2 , considering that it distorts the 249 molecule in the same way (all in-phase C≡C stretches; see Table S2 of the Supporting Information) 250 as does the ν 3 mode of state ܺ ෨ , recognized as the one shaping the vibronic structure of 251 phosphorescence. Also, the calculated wavenumber of ܪ ෩ -state ν 2 better matches the obtained 252 spectral data than that of ν 3 . A weak distinct band observed to the red of the identified ܪ ෩ -ܺ ෨ origin 253 may be tentatively interpreted as due to a lower-lying electronic state, the excitation of which could 254 gain probability via Herzberg-Teller vibronic coupling (analogous effects were already evidenced in 255 10 HC 2n+1 N (n = 3, 4) excitation spectra in the region of the first allowed electronic bands). [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF][START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF] Weak 256 features detected to the blue of the main vibronic bands supposedly come from the coupling with 257 phonons and/or from the combination with low frequency bending modes; no reliable assignments 258 can be proposed. 259

Comparing Ar and Kr matrices, one can notice large differences (up to ~1000 cm -1 ) in the position 260 of detected spectral features. Moreover, spectral splittings, observed in solid Kr, coming from 261 dissimilar surroundings of embedded molecules (matrix sites) vary between 20 and 180 cm -1 (see 262 Table 5). This evidence points to substantial influence of the microenvironment on electronic 263 transitions of this highly polarizable [START_REF] Woon | Quantum Chemical Predictions of the Properties of Known and 401 Postulated Neutral Interstellar Molecules[END_REF] molecule. The role of environment was also demonstrated by 264 slightly differing band wavenumbers, from one sample to another. Due to all these effects and to the 265 high photon energy in the discussed spectral range, the error of measured wavenumber distances 266 could reach 30 cm -1 . Nevertheless, systematic irregularities observed in vibronic spacing reflect the 267 contributions from anharmonic interactions. As expected, Kr-to-Ar matrix shifts are larger for 268 ܪ ෩ -ܺ ෨ than for ܽ -ܺ ෨ transitions. The present Kr-matrix spectrum is compared in Figure 4 given in Ref. [START_REF] Cataldo | A New Class of Carbon Allotropes. About the Formation of 413 Dicyanopolyynes from an Electric Arc between Graphite Electrodes in Liquid Nitrogen[END_REF] seems to be erroneous. Additionally, a 1 Σ u + -1 Σ g + origin in the vicinity of 240 nm 276 can be deduced for gas-phase NC 10 N from the interpolation of experimental data reported in Ref. [START_REF] Ding | Gas Phase Electronic Spectrum of 368 the Nitrogen Terminated Nanowire NC 16[END_REF] , 277 indicating a gas-to-Kr matrix shift of ca. -3200 cm -1 . This large redshift is smaller than that due to 278 the matrix (>4000 cm -1 ) observed for the origin of allowed NC 6 N absorption (205 nm in Kr [START_REF] Turowski | Niskotemperaturowe Badania Fotochemii i Spektroskopii Cyjanoacetylenów o 498 Znaczeniu Astrofizycznym[END_REF] , 188 279 nm in gas phase [START_REF] Connors | Vacuum Ultraviolet Spectroscopy of Cyanogen and 516 Cyanoacetylenes[END_REF] ). 280 286 287 Based on previous similar considerations [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF][START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF] , one can propose the following NC 10 N formation 292 scheme: 293 (3) 297 also has to be considered. This would be analogous to the formation of NC 6 N from two C 3 N • 298 radicals, elucidated basing on the kinetics of HC 3 N photolysis in rare gas matrices. [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF] Reaction 3 is 299 however not expected to be of chief importance here, considering the shape of the curve of growth 300 obtained for the NC 10 N phosphorescence during the photolysis of HC 5 N in solid Kr (Figure 5). If the 301 photolysis of matrix-isolated HC 5 N molecules had led to NC 10 N via the recombination of C 5 N • 302 radicals then, assuming the validity of arguments provided in Ref. [START_REF] Crépin | UV-Induced Growth of Cyanopolyyne Chains in Cryogenic Solids[END_REF] (reporting on the appearance of 303 NC 6 N in irradiated HC 3 N), one would have seen the original increase of the dinitrile production rate 304 with photolysis time. In the present case, the production rate steadily decreases from the very onset 305 of irradiations. 306 Creation of the discussed long, all-heavy-atom chain species requires substantial mobility of the 307 involved precursor chains, apart from their dehydrogenation. Locally increased mobility of reaction 308 partners may be understood in terms of matrix "melting" resultant from the dissipation of the 309 electronic excitation energy. Other products (including mono-and dicyanopolyynes) were detected 310 in the described experiments, but it was not possible to thoroughly investigate their formation 311 efficiencies in terms of kinetics and relative quantum yields. 312

HC 5 N + hν → H • + C 5 N • , (1) 294
It is also possible that the precursors, instead of being dissociated into free radicals, are excited to 313 high electronic energy levels and then undergo reactions analogous to Reaction 2. In experiments 314 described here, it is not possible to differentiate between the two cases. 315 Vibronic patterns in phosphorescence and phosphorescence excitation spectra were partly 324 interpreted with the assistance of quantum chemical calculations. Among some general trends 325 observed in the series of cryogenic matrix-isolated NC 2n N molecules is the lack of fluorescence, 326 which seems to be due to efficient intersystem crossing. Phosphorescence is dominated by a 327 vibronic progression involving a specific σ g mode (an in-phase C≡C stretching). With increasing 328 length of the chain: 329 (i) the wavenumber of that particular mode decreases, approaching the limit defined by the pure 330 collective C≡C stretch of an infinite chain, with vanishing contributions from terminal C≡N groups; 331 (ii) phosphorescence origin bands become more and more prominent; their wavelengths closely 332 follow a Lewis-Calvin relation (linearity of ߣ ୭୰୧୧୬ ଶ vs. n); 333 (iii) energy of the first allowed ( 1 Σ u + -1 Σ g + ) transition decreases. 334 Vibronic progressions observed for the [START_REF] Schermann | Dicyanopolyynes: A Homologuous Series 360 of End-Capped Linear sp Carbon[END_REF]

Figure 1 .

 1 Figure 1. NC 10 N geometry in its ground and selected excited electronic states as derived at the B3PW91/aug-cc-

Figure 2 .

 2 Figure 2. Luminescence, assigned to NC 10 N phosphorescence, from a previously photolysed (193 nm) Kr/HC 5 N

PageFigure 3 .

 3 Figure 3. The dependence of phosphorescence wavelength ܖܑܑܚܗ (left panel) and ܖܑܑܚܗ (right panel) on

Figure 4 .

 4 Figure 4. Excitation spectrum of luminescence assigned to NC 10 N phosphorescence detected at 16 183 cm -1 (2.01

C 5 N

 5 • + HC 5 N → NC 10 N + H • . (2) 295 Radical recombination 296 C 5 N • + C 5 N • → NC 10 N

Figure 5 .

 5 Figure 5. Time evolution of NC 10 N formation, as monitored by intensity of phosphorescence emitted from

  a sample kept at 7 K. Of note, the formation of NC 10 N was also observed in 80 experiments aimed at HC 9 N and CH 3 C 7 N, involving HC 5 N co-deposited with, respectively, 81 diacetylene (see Ref.[START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic Spectroscopy of 423 Cyanotetracetylene[END_REF] ) and methylacetylene (see Ref.[START_REF] Szczepaniak | Low Temperature 435 Synthesis and Phosphorescence of Methylcyanotriacetylene[END_REF] ). Certain thus far unpublished results 82 coming from these studies are included in the present report. 83

	74 75 84 85 86 87 88 89 90 91 92 93 94 95 96 97	The mixture was subsequently trapped on a sapphire substrate window held at either 30 K (Kr) or at 22 K (Ar) inside The Journal of Physical Chemistry were recorded for The identification of photolysis products relied on selectively excited electronic luminescence, by means of an optical parametric oscillator (OPO). Dispersed phosphorescence was searched for in the 380 -800 nm range with a resolution of approx. 0.04 nm. The observed emission was also registered as a function of the excitation wavelength (192 -280 nm), yielding phosphorescence excitation spectra. Time synchronization between laser pulses (193 nm excimer laser for photolysis and a tunable OPO for spectroscopy), as well as the acquisition of phosphorescence signals (with a CCD camera) were provided by a home-made triggering device. COMPUTATIONAL DETAILS Although certain theoretical studies devoted to NC 10 N have already been reported, 20 these did not comprise excited electronic states. Here, experiments implicated electronic excitation, respective quantum chemical calculations were therefore performed; for consistency, predictions concerning the ground electronic state have also been included. Quantum chemical computations were carried out mainly at the density functional theory (DFT) 34 a closedPage 8 of 24 level, with the GAUSSIAN 09 (Rev. B. 01)
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-cycle helium refrigerator equipped with external CaF 2 windows. The typical amount of 76 deposited gas was 6-8 mmol. Composition of the samples was verified with FTIR spectroscopy. The 77 photochemical transformations were induced with UV irradiation of cryogenic matrices (30 K for 78 Kr; 22 K for Ar) by means of an ArF excimer laser (193 nm, 10 Hz, <5mJ/cm 2 per pulse). Spectra 79

Table 1 . Theoretical Predictions a of Energy (in eV), Wavelength (in nm), and Oscillator Strength (f) for 130 Electronic Transitions of NC 10 N Departing from the ෩ 1 Σ g + State b .

 1

	131
								CC2/cc-pVTZ		DFT
	State	Dominant orbital excitation	Vertical transition energy (wavelength)	f	Vertical transition energy (wavelength)	f c	0-0 transition energy (wavelength)
	ܣ ሚ 1 Σ u	-	3π g →1π u	*	3.27 (379)	0	2.62 (473)	0	2.18 (569)
	ܤ ෨ 1 ∆ u	3π g →1π u	*	3.39 (366)	0	2.71 (458)	0	2.30 (539)
	ܥ ሚ 1 Σ g -	3π u →1π u	*	4.64 (267)	0	4.01 (309)	0	3.74 (332)
	ܦ ෩ 1 ∆ g	3π u →1π u	*	4.84 (256)	0	4.16 (298)	0	3.90 (318)
	ܧ ෨ 1 Σ g -	3π g →1π g *	5.92 (209)	0	4.81 (258)	0	4.53 (274)
	ܨ ෨ 1 ∆ g	3π g →1π g *	6.01 (206)	0	4.82 (257)	0	4.54 (273)
	ܩ ෨ 1 Σ g +	3π u →1π u 3π g →1π g * *	5.32 (233)	0	4.84 (256)	0	4.56 (272)
	ܪ ෩ 1 Σ u	+	3π g →1π u	*	5.30 (234)	6.1	4.80 (258)	5.2	4.65 (267)
	ܽ 3 Σ u	+	3π g →1π u	*	2.59 (479)		2.04 (608)

a Obtained with DFT (B3PW91/aug-cc-pVTZ for excited singlet states, CAM-B3LYP/aug-cc-pVTZ for ܽ 3 Σ u 5 139

20 Geometry 142 predicted for other electronic states listed in Table 1 can be found in Figure S1 of the Supporting Information. 143

144

Table

2

lists DFT-derived wavenumbers, IR intensities and Raman activities for the vibrational 145 modes of the ground electronic state, together with respective ܪ ෩ -state values (see Table S1 of the 146 Supporting Information for the data concerning other excited electronic states). The visualization of 147 vibrational modes is presented in Table S2 of the Supporting Information. 148 IR absorption measurements for NC 10 N dispersed in a solid NaCl film 1 pointed to the spectral 149 features at 2237 cm -1 (the strongest one, assigned to CN stretching), 2186, and 2120 cm -1 ; the first 150 two match well our present prediction of the strongest IR fundamentals (ν 7 and ν 8 ). 151

Table 2 . Wavenumbers a of Vibrational Modes ( , in cm -1 ; scaled by 0.96) for ෩ 1 Σ g + and ෩ 1 Σ u + Electronic States 152 of NC 10 N. b Absolute IR Absorption Intensity (in km/mol) and Raman Scattering Activity (in Å 4 /amu) Values a for 153

 2 See TableS2of the Supporting Information for the visualization of vibrational modes.

	154	෩ 1 Σ g	+ State.
						ܺ ෨	ܪ ෩
		Mode Symmetry	ߥ	IR intensity Raman activity	ߥ
						σ symmetry
		ν 1		σ g	2254	0	7200	2194
		ν 2		σ g	2140	0	150	2067
		ν 3		σ g	2115	0	74000	2017
		ν 4		σ g	1414	0	25	1431
		ν 5		σ g	908	0	52	911
		ν 6		σ g	314	0	4.6	315
		ν 7		σ u	2241	280	0	2174
		ν 8		σ u	2199	20	0	2096
		ν 9		σ u	2061	0.015	0	1941
		ν 10	σ u	1180	0.016	0	1190
		ν 11	σ u	617	1.1	0	621
						π symmetry
		ν 12	π g	554	0	146	509
		ν 13	π g	512	0	1.8	462
		ν 14	π g	437	0	0.55	392
		ν 15	π g	222	0	0.61	210

Table 3 . Vibronic Bands in NC 10 N Phosphorescence. Relative Values Give the Distance from the Vibrationless 191

 3 Table 3 lists all vibronic bands presently identified in the ܽ 3 Σ u + -ܺ ෨ 1 Σ g + 181 system of NC 10 N. The appearance of only one strong progression governed by a single mode (C≡C 182 stretching), with very few other vibrations contributing to the recognized weak bands, is consistent 183 with the linearity of the lowest triplet state, predicted by DFT calculations. One can notice that in the 184 phosphorescence of NC 2n N molecules, relative intensity of bands that do not involve the specific 185 C≡C stretching (analogous to ν 3 here) diminishes with n growing from 2 to 5. 2,57 186Weak phosphorescence bands appearing in Kr matrices, blue-shifted from the main spectral 187 features, can be clearly assigned, to a minor matrix site (origin at 16220 cm -1 ), based on 188 phosphorescence excitation spectra (see below). In Ar-matrix spectra (the Kr-Ar matrix shift is quite 189 large, see Table3), only the strongest bands have been identified. 190

	192	Origin.
		Wavenumber [cm -1 ]
		Kr		Ar	Assignment
		Absolute Relative Absolute Relative
		16183	0	16324	0	0
		15897	286			20 ଶ
		15880	303		15 ଵ	16 ଵ
		15861	322			6 ଵ
		15699	484		14 ଵ	16 ଵ
		15617 a	566		6 ଵ	20 ଶ
		15585 a	598		6 ଵ	15 ଵ	16 ଵ
		15562 a	621			6 ଶ
		14046	2137	14186	2138	3 ଵ
		13941	2242			1 ଵ
		13760	2423		3 ଵ	20 ଶ
		13740	2443		3 ଵ	15 ଵ	16 ଵ
		13720	2463			3 ଵ	6 ଵ

a Weak band, observed with wide-open monochromator slits. 193 194

Table 4

 4 collects the results of phosphorescence lifetime measurements for solid Kr-isolated mono-195 and dicyanopolyynes. Within each of these families, emission lifetime markedly decreases with the 196 increase of polyyne length, a trend that may be explained considering the associated enhancement of 197 two factors promoting non-radiative T 1 → S 0 relaxation channels: reduction of the singlet-triplet gap 198 and the increasing number of vibrational degrees of freedom (leading to high density of states).

	199
	200	Monocyanopolyynes of Table 4 are characterized by faster phosphorescence decays than the
	201	respective (i.e. isoelectronic) dicyanopolyynes, which may again be due to the higher number of
	202	vibrational modes of the former. Moreover, one may point to a possible special role of large CH
	203	stretching quanta in coupling T 1 with the ground electronic state.

Table 4 . Phosphorescence Decay Time (in ms) for Mono-and Dicyanopolyynes Isolated in Solid Kr.

 4

	204
	HC n N	τ	NC n N	τ
	HC 5 N a 40 NC 4 N b 52
	HC 7 N c 8 NC 6 N d 35
	HC 9 N e 3.9 NC 8 N d 13
			NC 10 N f 4.4

  with the 269 UV absorption of NC 10 N in liquid acetonitrile 1 (maxima at 259, 246, 235 and 223 nm). Neglecting 270 the widths of spectral features, and hence the number of resolved details, the two spectra resemble 271 one another. Moreover, just as for cryogenic matrix sample, vibronic spacings observed in liquid 272 acetonitrile are not regular. Another NC 10 N absorption spectrum was reported 25 for a liquid n-octane 273 solution, with strong absorption bands at 283, 268, 253, 243, and 232 nm. However, an n-octane-to-274 acetonitrile shift of approx. -3300 cm -1 (283 nm 25 vs. 259 nm 1 ) is unrealistic, and the attribution 275

Table 5 . Vibronic Bands in NC 10 N Phosphorescence Excitation Spectrum, due to Dipole-Allowed ෩ 1 Σ u + -෩ 1 Σ g + 288 Transitions. Relative Wavenumber Values Give Distances from the Preceding Progression Elements.

 5

	289
				Wavenumber [cm -1 ]
		Kr matrix, main site Kr matrix, minor site	Ar matrix	Assignment
		Absolute Relative Absolute Relative Absolute Relative
		38 470	0	38 610	0	39430	0	0
		40 540	2070	40 700	2090	41440	2010	2 ଵ
		42 550	2010	42 730	2030	43510	2070	2	ଶ
		42 950	400	42 970	240			8	ଶ
		44 600	2050	44 700	1970	45480	1970	2	ଷ
		44 940	340	45 010	310			2 ଵ 8	ଶ
		46 580	1980	46 680	1980			2	ସ
		46 910	330					2	ଶ 8	ଶ
	290
	291	D. Formation

  Σ u + -1 Σ g + system are governed by the same specific σ g 335 stretching that shapes the phosphorescence spectrum. Its energy is lower in the excited state, 336 reflecting a decrease of the C≡C bond strength, compared to the ground state. 337 Phosphorescence measurement was a detection method of choice in this study aimed at molecule 338 coupling products. The quantity of synthesized C 10 N 2 was too low to produce a detectable IR 339 signature. The reported experimental approach can presumably be adopted to synthesize and study 340 the NC 2n N chains of n > 5; in particular, present results permit to expect the origin of NC 12 N 341 phosphorescence in solid Kr at about 670 nm. 342 343 ACKNOWLEDGMENTS 344 This work was financially supported by the Polish National Science Centre, project no. 345 2011/03/B/ST4/02763, French-Polish scientific cooperation programs Partenariat Hubert-Curien 346 Polonium (2012-2013) and PICS (2014-2016). U.S. is a beneficiary of the French Government 347 scholarship Bourse Eiffel, managed by Campus France, and of the project "Scholarships for PhD 348 students of Podlaskie Voivodeship" -the project is co-financed by European Social Fund, Polish 349 Government and Podlaskie Voivodeship. J.-C.G. acknowledges the financial support received from 350 the Centre National d'Etudes Spatiales (CNES) and from the French program Physique et Chimie du 351 Milieu Interstellaire (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. Geometry of NC 10 N in several electronic states; computed IR wavenumbers for the lowest excited 355 electronic states; visualization of vibrational modes in selected electronic states of NC 10 N. This 356 information is available free of charge via the Internet at http://pubs.acs.org.

	352
	353
	354	SUPPORTING INFORMATION AVAILABLE
	357
	358