Francisco Javier Ancin Murguzur
email: francisco.j.murguzur@uit.no

Arnaud Tarroux

Kari Anne Bråthen

Paco Bustamante

Sébastien Descamps

Using near-infrared reflectance spectroscopy (NIRS) to estimate carbon and nitrogen stable isotope composition in animal tissues

Keywords: isotopic analysis, dietary studies, NIRS

1. Stable isotopes analysis (SIA) of carbon and nitrogen provides valuable information about trophic interactions and animal feeding habits.

2. We used near-infrared reflectance spectroscopy (NIRS) and support vector machines (SVM) to develop a model for screening isotopic ratios of carbon and nitrogen (δ 13 C and δ 15 N) in samples from living animals. We applied this method on dried blood samples from birds previously analysed for δ 13 C and δ 15 N to test whether NIRS can be applied to accurately estimate isotopic ratios.

3.

Our results show a prediction accuracy of NIRS (R 2 > 0.65, RMSEP < 0.28) for both δ 13 C and δ 15 N, representing a 12% of the measurement range in this study.

4.

Our study suggests that NIRS can provide a time-and cost-efficient method to evaluate stable isotope ratios of carbon and nitrogen when substantial differences in δ 13 C or δ 15 N are expected, such as when discriminating among different trophic levels in diet.

Introduction

The analysis of stable isotope ratios of carbon (δ 13 C) and nitrogen (δ 15 N) is a widely used approach in trophic studies at various ecological scales, from individuals to entire food webs [START_REF] Boecklen | Use of stable isotopes in foraging ecology and food web analysis[END_REF][START_REF] Navarro | Comparison of ecosystem modelling and isotopic approach as ecological tools to investigate food webs in the NW Mediterranean Sea[END_REF][START_REF] Newsome | A Niche for Isotope Ecology[END_REF]. Stable isotope ratios in consumers' tissues reflect those of their prey and of the relative proportion of each prey in the consumers' diet [START_REF] Cozzolino | The use of near-infrared reflectance spectroscopy (NIRS) to predict the composition of whole maize plants[END_REF][START_REF] Deniro | Influence of diet on the distribution of nitrogen isotopes in animals[END_REF][START_REF] Kelly | Stable isotopes of carbon and in the study of avian and mammalian trophic ecology[END_REF]. Through a single sampling event, the measurement of isotopic ratios can provide dietary information integrated over a period of time. The time period represented depends directly on the turnover rate of the tissue sampled and the species. It typically ranges from a few days in blood plasma, to several weeks in red blood cells, and up to several years in metabolically inert tissues such as bone collagen, teeth, or baleen [START_REF] Hanson | Intrinsic and extrinsic forcing in life histories: Patterns of growth and stable isotopes in male Antarctic fur seal teeth[END_REF][START_REF] Trueman | Combining simulation modeling and stable isotope analyses to reconstruct the last known movements of one of Nature's giants[END_REF].

Although isotopic analyses of animal tissues shed light onto the dietary habits of individuals and populations, they require the use of a mass spectrometer in specialized laboratories. As an alternative, near-infrared reflectance spectroscopy (NIRS) can be used as a cost-and timeeffective method to measure tissue properties in animals and plants [START_REF] Chodak | Application of near infrared spectroscopy for analysis of soils , litter and plant materials[END_REF][START_REF] Cozzolino | The use of near-infrared reflectance spectroscopy (NIRS) to predict the composition of whole maize plants[END_REF][START_REF] Windley | A faecal index of diet quality that predicts reproductive success in a marsupial folivore[END_REF]. NIRS is a non-destructive method where a beam of light with known properties is shed on the sample, which will absorb or reflect different wavelengths with varying intensity depending on the composition of the organic bonds (e.g., C-H, N-H, O-H) [START_REF] Kaye | Near-infrared spectroscopy: Spectral identification and analytical applications[END_REF][START_REF] Kaye | Near infrared spectroscopy: Instrumentation and technique[END_REF]. The reflectance or transflectance values are registered in the visible and near-infrared spectrum (350-3000 nm), with the exact range and resolution dependent on the specific instrument used to measure the reflectance. The spectra obtained from the sample can subsequently be used to model other elements or molecules, given that a predictive model has been previously developed [START_REF] Foley | Ecological applications of near infrared reflectance spectroscopy -a tool for rapid, cost-effective prediction of the composition of plant and animal tissues and aspects of animal performance[END_REF]. The non-destructive nature of NIRS allows storing and reusing samples in further analyses, such as pollutant analyses. Although using NIRS as a method to estimate isotopic ratios is not new [START_REF] Fuentes | NIR Spectroscopy: An Alternative for Soil Analysis[END_REF][START_REF] Kleinebecker | Prediction of delta 13C and delta 15N in plant tissues with near-infrared reflectance spectroscopy[END_REF][START_REF] Sun | Classification of geographical origins and prediction of d13C and d15N values of lamb meat by near infrared reflectance spectroscopy[END_REF], to the best of our knowledge no study has explored the possibilities that NIRS offers for studying isotopic composition in wildlife animal populations.

In our study, we used blood samples previously collected in a study on a pelagic seabird, the Antarctic petrel (Thalassoica antarctica), to assess the suitability of NIRS to estimate stable isotopes in a free-living animal species. Seabird ecology often relies on stable isotope analyses to estimate seabird diet or feeding habitat [START_REF] Bond | Multi-tissue stable-isotope analyses can identify dietary specialization[END_REF][START_REF] Hovinen | Relationships between isotopic ratios, body condition and breeding success in a high arctic seabird community[END_REF]; a time and cost-efficient method for the estimation of δ 13 C and δ 15 N would facilitate ecological research on seabirds and on more wildlife in general.

Methods

Sampling and isotope measurements

Blood samples were collected during a previous study on Antarctic petrels (Thalassoica antarctica) at the Svarthamaren colony, Dronning Maud Land, Antarctica, and processed as described in [START_REF] Tarroux | Foraging tactics in dynamic seaice habitats affect individual state in a long-ranging seabird[END_REF]. Here, we used only the freeze-dried red blood cells (hereafter RBC), but otherwise the analytical procedure in the laboratory is identical to that described in [START_REF] Tarroux | Foraging tactics in dynamic seaice habitats affect individual state in a long-ranging seabird[END_REF]. We evaluated the overall precision of measurement by duplicating a random subset of 10 RBC samples [START_REF] Jardine | Analytical error in stable isotope ecology[END_REF]. The mean absolute difference between duplicates was 0.05 ‰ for both δ 13 C and δ 15 N (range = [0; 0.11] and [0; 0.09], respectively).

NIRS Scans

The freeze-dried samples were poured into 4-mm diameter custom-made black polyacetal sample holders. The powder was subsequently pressed with a metal rod against the bottom glass to create an even surface and reduce light scattering. Scans were taken using a FieldSpec 3 (ASD Inc, Boulder, CO, USA) spectrometer, which has a spectral range of 350-2,500 nm.

Spectra were registered at 1 nm interpolated resolution and saved as reflectance (R), with white reference measurements taken every 15 min to adjust for potential baseline drift. Each sample was scanned three times, rotating the sample holder between scans, to further reduce potential random light scattering effects.

Model development

All analyses were performed in R 3.5.1 (R Core Team, 2017). Model calibration was performed using support vector machines (SVM) contained in the e1071 package [START_REF] Meyer | e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071)[END_REF].

Spectral treatments such as smoothing and derivatives, together with the standard normal variate (SNV) treatment, were applied to the spectral library to optimize the model development contained in the prospectr package [START_REF] Stevens | An introduction to the prospectr package[END_REF]. We developed the NIRS models excluding the visible light region (i.e., 350-720 nm) and the regions where the spectrometer sensors overlap (i.e., 950-1,050 nm, 1780-1,880 nm, and 2,450-2,500 nm).

The blood scan database (n = 213) was split into a calibration and validation dataset using the Kennard-Stone algorithm [START_REF] Kennard | Computer aided design of experiments[END_REF] to ensure a high spectral variability included into the calibration dataset. We assigned 80% of the samples to the calibration dataset and 20% to the validation dataset, resulting in a calibration set of 171 samples and a validation set of 42 samples for both δ 13 C and δ 15 N.

We developed one distinct model for each isotope. Models were fitted using the calibration set and selected the kernel (i.e., linear, radial, polynomial, or sigmoid) based on its performance.

The SVM models were tested against the validation dataset: In addition to the R² value, we assessed the root mean squared error of the calibration (RMSEC) and the prediction (RMSEP), which measures the prediction error as integrated along the range of measured values with the formula:

𝑅𝑀𝑆𝐸 = √∑ (𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 -𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑) 2 𝑛 𝑛 𝑖=1
Furthermore, we assessed the range error ratio (RER), which is the ratio between the range for each calibration and the error (RMSEP). Models with RER values under 3 are considered unsuccessful, while RER values between 3 and 10 indicate limited applicability (e.g., screening)

and RER values higher than 10 are considered to characterize high-quality models [START_REF] Quentin | Application of near-infrared spectroscopy for estimation of non-structural carbohydrates in foliar samples of Eucalyptus globulus Labilladière[END_REF].

In addition, we computed the intercept and slope of the linear fit between predicted and measured values, as well as the bias (i.e., the systematic error of the predicted values) to estimate the suitability of NIRS to model δ 13 C and δ 15 N in future bird RBC samples.

Results

The RBC sample isotopic ratios ranged from -25.9 to -24.1 and from 8.4 to 10.9 respectively for  13 C and δ 15 N: both the δ 13 C (R 2 validation = 0.56, RMSEP = 0.24, RER = 5.45) and the δ 15 N (R 2 validation = 0.49, RMSEP = 0.29, RER = 5.93) models showed similar performances. The RMSEP in both cases represented an error of approximately 12% of the total range (ranges are 1.88

‰ for δ 13 C and 2.51 ‰ for δ 15 N), showing a linear relation between the measured and predicted values (Erreur ! Source du renvoi introuvable., Figs 1 and 2).

Discussion

Our results show that NIRS can be a suitable tool to estimate stable isotopes in RBC samples from a free-living animal population. Both δ 13 C and δ 15 N show an acceptable fit with RMSE values close to 0.25 and RER values in the acceptable range (5.45 for δ 13 C and 5.93 for δ 15 N),

showing that NIRS can be used to estimate stable isotope compositions in animal tissues, although the model accuracy is not high enough to substitute laboratory-grade measurements in studies addressing fine-scale variation in isotopic ratios. It is important to note that the model performance is likely underestimated in our study, owing to the narrow range of values for isotopic ratios in our study species. To our knowledge, the only feasibility study of NIRS for isotopic estimation on animal tissues was performed on cattle meat: Sun et al. ( 2012) created predictive models for δ 13 C and δ 15 N, with a broader range of values in both elements compared to our study. Although their models had higher R² values than ours (again, likely due to the limited range of predictor values in our case), their RMSEP values were more than twice as large, suggesting that our models do in fact perform better. This difference can stem from the structural complexity of the tissue they used: muscle (meat) contains different cell types such as myocytes or adipocytes as well as connective tissue (e.g., collagen) and has a heterogeneous physical structure, while RBCs constitute a more homogeneous matrix in comparison (>99% erythrocytes). On the other hand, the relationship between C and δ 13 C, and N and δ 15 N, have been hypothesized to be an underlying reason for the good results in NIRS models for isotopes both in plant tissues [START_REF] Hellmann | Retrieving nitrogen isotopic signatures from fresh leaf reflectance spectra: Disentangling δ 15 N from biochemical and structural leaf properties[END_REF] and soils [START_REF] Winowiecki | Landscape-scale assessments of stable carbon isotopes in soil under diverse vegetation classes in East Africa: Application of nearinfrared spectroscopy[END_REF], although it has not yet been demonstrated. In our case, we found a nearly non-existent correlation between δ 13 C and C (R² = 0.04) and δ 15 N and N (R² = 0.05) correlation in bird blood.

Several aspects make NIRS a very good candidate to estimate isotopic ratios of δ 13 C and δ 15 N in animal tissues. It is an easy-to-learn, quickly applicable tool: A short hands-on training is enough to learn the basic use of the instrument (i.e., the scanning process), and the conversion from raw scans to isotopic values can be streamlined with a simple R-code. Furthermore, since there is no need for reagents during the sample preparation or during the scanning process (other than the freeze-drying), the cost of the analyses is reduced to acquiring the instrument and the initial investment for the model creation; the maintenance costs of the instrument are low. Afterward, only a subset of samples should be analyzed with the traditional method to ensure that the model continues to perform within the expected accuracy. This approach would allow to process much larger numbers of samples to detect outliers, on which further, more detailed, analyses could be conducted. An added advantage of NIRS is that the scanning and predicting process is very quick (up to 30 samples/hr). Once the reflectance readings are stored, there is no sample degradation, which allows for future chemical and isotopic analyses.

Furthermore, a single NIRS scan can be used to estimate more than a single element or molecule [START_REF] Ancin-Murguzur | Towards a global arctic-alpine model for Near-infrared reflectance spectroscopy (NIRS) predictions of foliar nitrogen, phosphorus and carbon content[END_REF][START_REF] Foley | Ecological applications of near infrared reflectance spectroscopy -a tool for rapid, cost-effective prediction of the composition of plant and animal tissues and aspects of animal performance[END_REF]. In this study, we developed models for δ 13 C and δ 15 N, but other models could be developed and used to predict other elements or even more complex molecules [START_REF] Domján | Rapid Analysis of Whole Blood and Blood Serum Using near Infrared Spectroscopy[END_REF].

Although NIRS can be a cost-and time-effective tool, its accuracy is lower than the reference method when it comes to SIA. Nevertheless, isotopic variability can be high among populations [START_REF] Rey | Stable isotopes identify age-and sex-specific dietary partitioning and foraging habitat segregation in southern giant petrels breeding in Antarctica and southern Patagonia[END_REF] and also within populations [START_REF] Del Rio | Dietary and isotopic specialization: The isotopic niche of three cinclodes ovenbirds[END_REF] In such cases, this variability could be adequately captured by NIRS measurements. However, NIRS might not be able to identify subtle differences in isotopic composition among individuals or species with very, for example, closely related diets [START_REF] Young | Niche partitioning among and within sympatric tropical seabirds revealed by stable isotope analysis[END_REF], which would thus require proper SIA. That being said, the ability to increase the sample size with NIRS allows to obtain population-level information rather than relying on lower sample size due to the economical and logistical constraints inherent in SIA. An alternative to using freeze-dried blood is to use unprocessed blood, fresh blood: biomedical sciences routinely use NIRS for non-invasive blood analyses in screenings as a rapid analysis tool (e.g., [START_REF] Beć | Near-infrared spectroscopy in bio-applications[END_REF]. The ability to measure blood properties without sample preparation could simplify the data gathering process to simply extracting blood drops from an individual and directly scan it, either in situ with a portable instrument or in the laboratory afterward. It remains to be tested if NIRS could be used for rapid, screening of population characteristics using other tissues such as feathers and hair. Such tissues could be scanned directly and noninvasively in the field (e.g., in the case of feathers of colonial seabirds, directly on the nest). This would substantially decrease the potential impact on animal welfare, while increasing the sample size.

Conclusion

Our study shows that NIRS is a time-and cost-effective tool to estimate isotopic ratios of carbon and nitrogen in RBC samples, and we propose that it could be expanded to other tissues (e.g., feathers), leading to less invasive ecological studies on animals. Coupled with its portability and ease of use, NIRS can thus result in a highly useful and practical tool to better understand the trophic interactions between animals. Note: Eighty percent of the original dataset was used as the calibration dataset, while the remaining 20% was used for validation. R 2 cal = R² for calibration set, root mean squared prediction for the calibration (RMSEC) and validation (RMSEP) dataset, R²val = R² for validation set.

Fig 1

 1 Fig 1 Calibration (a) and validation (b) plots for the δ 13 C model based on NIRS scans. The solid line indicates the perfect (1:1) fit

Table 1 .

 1 Prediction performance for δ 13 C and δ 15 N in the calibration and validation datasets using freeze-dried bird RBC samples

	Model	R 2 cal	RMSEC	R 2 val	RMSEP	Bias	Intercept	Slope
	δ 13 C	0.66	0.24	0.56	0.24	0.05	1.78	1.07
	δ 15 N	0.67	0.26	0.49	0.29	-0.02	-3.37	1.34

Acknowledgements

We thank our dedicated field assistants S. Haaland, G. Mabille, T. Nordstad, E. Soininen, and J. Swärd. This project was funded by a grant from the Norwegian Research Council (Norwegian Antarctic Research Expedition program, grant number 2011/70/8/KH/is to SD). This study would not have been possible without support from the logistic department at the Norwegian Polar Institute (NPI) and the Troll Station summer and overwintering teams from 2011 to 2014. We are grateful to Sissel Kaino (University of Tromsø-The Arctic University of Norway) for help with the sample preparation. We thank M. Brault-Favrou from the platform "Analyses Elémentaires" and G. Guillou from the platform "Analyses Isotopiques" of LIENSs for their support in IR-MS isotope analyses. The Institut Universitaire de France (IUF) is acknowledged for its support to P. Bustamante as a Senior Member.

Data availability

The spectra, reference values, and scripts are available at UiT open data repository: https://doi.org/10.18710/5PX1GJ

Author contributions

KAB, FJAM and AT conceived the idea; AT and SD coordinated the sample collection; PB provided with reference measurements; FJAM scanned the samples and developed the models. All authors contributed critically to the drafts and gave final approval for publication.

Conflict of interest

The authors declare no conflict of interest.


Philippe Fabian

Georgios Z Papadopoulos

Patrick Savelli

Bernard Cousin

Performance Evaluation of Integrated Access and Backhaul in 5G Networks

Keywords: Integrated Access and Backhaul, 5G, 3GPP, Backhaul Adaptation Protocol, IAB, Routing

Integrated Access and Backhaul (IAB) allows to ease the deployment of gNodeBs (gNBs) in a 5G network by connecting them using cellular connectivity. The radio frequencies to achieve such a result can be the same as the ones used to connect User Equipment (UE) (in-band) or specific ones can be reserved (out-of-band). Both sub 6 GHz and millimeter wave (mmWave) frequencies can be used. IAB is relatively new and several contributions have been studying the lower layers (i.e. physical and link) in order to improve performance in scheduling and resource allocation. However, performance results are also very dependent on how the routing is implemented at the network layer which is an aspect that is not much studied in the state of the art. In this paper, we evaluate the performance of several IAB topologies against a topology without IAB-nodes. Results confirm the conclusions of the state of the art by showing that adding IABnodes significantly improve performance in terms of delay (more than 90 ms shorter delay) and Packet Delivery Ratio (PDR) (by up to 15%), and also allows to extend the coverage area. These results reveal the high potential of IAB that could be improved even more using efficient routing.

I. INTRODUCTION

5G networks are already being deployed as of the writing of this paper. Compared to 4G, 5G provides better performance overall [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF]. This, in turn, allows to extend current scenarios (higher density of devices, better support for mobility, higher throughput, etc.) and to enable new services such as Industry 4.0. The shorter range due to higher frequencies in 5G forces Internet Service Providers (ISPs) to deploy more antennae/gNBs in a given location (higher density). Doing so could imply the construction of costly wired links to connect the gNBs [START_REF][END_REF], [START_REF] Teyeb | Integrated access backhauled networks[END_REF]. However, thanks to IAB, it is possible to avoid this cost by connecting antennae with cellular connectivity [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF].

IAB uses the Backhaul Adaptation Protocol (BAP) [4] to route packets through the IAB topology (typically a tree, see Sec. II). The root is called Donor [START_REF]0, Backhaul Adaptation Protocol (BAP) specification (Release 16)[END_REF] and is a gNB connected to the Core Network (CN) through a wired link. It manages the topology by assigning BAP addresses to IAB-nodes (gNBs connect wirelessly to the Donor through one or several hops) and by setting paths on which packets are sent. It is possible to have several paths for a source-destination tuple. This increases reliability (for instance, in the case of a failure or radio interference) and flexibility (e.g. to dynamically change paths according to user needs).

The Donor is composed of a Central Unit-Control Plane (CU-CP), a CU-User Plane (CU-UP), one or several Distributed Units (DUs) and other functions depending on current needs Fig. 1: An example of an IAB topology. Blue links represent backhaul connections whereas red links represent access connections. This figure is taken from [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF].

(see Fig. 1 for an example of an IAB-Donor). Note that all these components are not necessarily on the same physical node, thanks to the extensive use of virtualization in 5G. This is useful to ensure better reliability (in case of equipment failure), to start/stop functions according to needs or to use additional physical resources whenever the demand increases and current hardware can not process requests fast enough. The DU part allows children nodes to connect to the current node. A child can either be an IAB-node or a UE. Each IAB-node has two parts: DU and Mobile Termination (MT). The DU part serves the same function as the one on the Donor (providing connectivity to IAB-nodes and UEs). The MT part is used to connect to the parent node (see [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF] for more details). The IAB topology and consequently the BAP protocol are transparent from the point of view of UEs.

Fig. 1 displays an example of IAB topology with 1 Donor, 5 IAB-nodes and 3 UEs. The DU and MT parts of the IAB-nodes are not shown on this figure, though. As mentioned earlier, the default topology is tree-shaped which makes upstream routing simpler because traffic only needs to be sent to the parent at each hop. However, routing is still needed to forward traffic downards and in the case several paths are created in the upstream direction. The choice of path to use is up to the network operator and thus depends on the chosen algorithms and the local needs.

In this paper, we evaluate the performance of IAB and stress the need to develop new routing solutions. We start by explaining how IAB works at the MAC and BAP layers before discussing state of the art papers. We then evaluate the performance of IAB through simulation and we point out the benefits of it. We also highlight new relevant features of 3GPP release 17. Our analysis leads to the conclusion that the routing aspect in IAB has a high potential. Indeed, we believe more research and new routing algorithms are needed in order to meet the stringent requirements of very dense 5G networks with a large number of IAB-nodes.

II. IAB DETAILS

In this section, we explain how IAB works. It is worth noting that the MAC layer and BAP are affecting one another. Indeed, the routing decisions taken at the BAP layer might result in sending more (or less) traffic to specific nodes. The resource allocation scheme must be properly set up to avoid congestion. On the other hand, feedback from the MAC to the BAP layer could impact the choice of paths (see Sec. IV-C).

A. Link Layer

The scheduling scheme needs to take into account interference [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF]. We can identify four cases concerning this issue:

• Out-of-band relaying [6]. IAB-nodes can use sub 6 GHz frequencies (more range, more resistant to blockage) to communicate amongst themselves and higher frequencies (mmWave) can be used for transmission between an IAB-node and its attached UEs. Note that this out-ofband separation does not solve the problem but rather decomposes it into two smaller (simpler) problems. • Time Division Multiplexing (TDM). A node can transmit on the whole range of frequencies but only during a limited time frame. In that case, it is possible to optimize downwards traffic by allocating the first time frames to the parent, then the next ones to the child so it can directly forward data from parent to next child. It is the same, respectively, for upwards traffic (first child, then parent). • Frequency Division Multiplexing (FDM). In that scheme, a node can transmit at any time but with a restrained bandwidth. As of the writing of this document, TDM is more in use compared to FDM (see Sec. III). • Spatial Division Multiplexing (SDM). This is possible by using beamforming techniques and allows different nodes to transmit and receive at the same time and on the same frequency. However, if many nodes transmit there will be more interference with increasing transmissions. Also, if we have to consider mobility (especially) on IABnodes, the variation in the distance between nodes might substantially increase the complexity of the beamforming algorithm.

Fig. 2: The BAP layer is located above the RLC layer. This figure is taken from [START_REF]Innovations in 5G Backhaul Technologies: IAB, HFC & Fiber[END_REF] and represents the user plane.

B. BAP Description

Routing in IAB is done at the BAP layer. Given this contribution focuses on the routing aspect, it is important to properly explain BAP and how it can be used to improve performance. Fig. 2 shows where the BAP layer is located in the network stack. This layer acts in a similar way as Internet Protocol (IP) and IAB-nodes are similar to routers in that they route and forward traffic (to other nodes) upwards or downwards if the packet has not reached its final destination yet. A UE does not have a BAP layer. In addition to routing packets, BAP supports flow control. Other functions are defined, see [4] Sec. 4.4 for more details. The possibility to choose the path to send packets is interesting as it allows to find the best one according to current needs (this will be covered more in details in Sec. IV). A reliable and/or stable default path can be established so there is always at least one possible path to reach the Donor and other nodes.

Fig. 3 illustrates a BAP control Packet Data Unit (PDU) used for flow control feedback. The Routing ID is the DESTINA-TION + PATH (from Fig. 4). This packet passes information to the Donor about the buffer usage of a given tuple [destination; path]. The Donor can use this information to adapt the resource allocation scheme if an IAB-node is congested or to avoid sending too much traffic their way. Note that there also exists a flow control PDU that associates an RLC channel ID to a buffer size but it is not shown here. It serves a similar purpose as the flow control PDU depicted on Fig. 3.

Fig. 4 shows a detailed view of a BAP data PDU that is 3 octets is size (plus the size of the data). The two fields of interest to us are DESTINATION (BAP address) and PATH. Both are coded on 10 bits, hence there are 1024 possible paths and there can be up to 1024 IAB-nodes including the Donor.

III. RELATED WORK

The following analyses several works aiming at improving some aspects within an IAB topology. However, they mostly focus on the PHY/MAC layers.

Islam et al. [START_REF] Islam | Investigation of performance in integrated access and backhaul networks[END_REF] study joint resource allocation and relay selection in IAB in order to show that it improves the mean data rate of UEs. They formulate the problem as an optimization one. The objective is to maximize the geometric mean of UEs' data rate. Two constraints are also formulated: the flow conservation (inbound traffic should be equal to outbound traffic) and the resource allocation constraint (a timeslot can not Fig. 3: A BAP control PDU for flow control purposes. This figure is taken from [4]. Note that there are several Routing IDs (octets 2-3 and octets 8-9) with their associated Buffer size (octets 5 to 7 and octets 11 to 13). Fig. 4: A BAP data PDU. The "data" field corresponds to the packet from the upper layer (e.g. IP). This figure is taken from [4]. be used simultaneously by two nearby nodes). The approach is based on TDM but authors claim it can be adapted to FDM as well. It is supposed that directional antennae are used. The authors compare a spanning tree versus mesh topology and conclude mesh yields better performance in terms of UE rate and latency. However, their approach is somewhat theoretical and real aspects such as buffering and mobility are not considered. Also, the connection of UEs is done through signal strength only.

In [START_REF] Li | Integrated access and backhaul optimization for millimeter wave heterogeneous networks[END_REF], authors formulate an optimization problem taking into account scheduling, resource allocation and routing. They use binary interference classification with the aforementioned elements. They also generate a conflict graph in which wireless links are represented as vertices. Two links are thus in conflict (interference, half-duplex constraint) if connected by an edge.

In practice, slots are allocated to groups of wireless links. Links within a group are not in conflict. Hence, different groups can transmit at the same time (SDM). Then, TDM is used to allocate timeslots to links within each group, proportional to their needs. Power allocation is finally computed to emit at optimal power levels. No interference should occur as they were eliminated thanks to the grouping from the previous steps. The authors also compute the best paths based on the maximum data rate (a high data rate on a link increases its weight, making it more interesting). However, performance evaluation is done using full buffer assumption and no UE mobility is considered.

Authors in [START_REF] Madapatha | On topology optimization and routing in integrated access and backhaul networks: A genetic algorithm-based approach[END_REF] design a genetic algorithm to resolve the placement of IAB-nodes and the distribution of non-IAB dedicated connections. The considered metric is the probability a UE receives satisfying data rate according to its needs ("coverage probability"). They use a radio model that accounts for path loss and blocking due to objects. This model includes blocking from vegetation as well. There are two genetic algorithms: the first iterates on the set of possible small base stations (i.e. IAB-nodes) to find where to place non-IAB links, and the second considers the possible location sets for the choice of small base stations. It is assumed IAB-nodes do not interfere with one another (directional antennae). Simulations are run to study the convergence of the algorithms and how well they improve performance of the network. However, they assume there is no interference between UEs which can be an issue in a high density setting such as music festivals or sport competitions. The proposed genetic algorithm is compared to exhaustive search only in terms of complexity. The proposed solution is based on planning the deployment of IAB-nodes: in a more realistic context it might not be possible to choose the locations of base stations, or some exceptional situations could degrade the system, making the planning obsolete or not usable. Also, although the theoretical model considers every UE has a potential need in terms of data rate that is different, this is not considered in the simulations, where the highest achievable data rates are studied. This is not adapted in the case where a differentiation of service is needed.

Pagin et al. [START_REF] Pagin | Resource Management for 5G NR Integrated Access and Backhaul: a Semi-centralized Approach[END_REF] design a semi-centralized scheduling algorithm where the Donor decides how the scheduling will be achieved. Then, each IAB-node is free to decide on how the actual MAC level scheduling is done locally. That is, some resources are allocated to a node and it decides how to use them to serve its UEs and children IAB-nodes. The allocation from the Donor is done through a priority scheme where nodes receive resource allocation in order of their position in the priority list (a node will get resources if there are some left). However, given the goal of this contribution, the authors have abstractly merged all UEs attached to one IAB-node into one node connected through one edge. Hence, individual UEs are not modeled.

In [START_REF] Liang | Dynamic routing and load balancing techniques for integrated access and backhaul network[END_REF], the author proposes to improve routing in IAB networks through two mechanisms. The first one is to use handover features from 5G specifications to change the parent of IAB-nodes in order to load balance the IAB topology. The second mechanism is the modification of the length of the transmission phases: an IAB-node can be allowed to transmit (upstream/downstream) more or less depending on the traffic. This allows to better utilize the time slots by assigning them where there is a higher need. However, only the data rate of UEs is considered to select links in the performance evaluation. This can be a problem when differentiation of service is required. No UE mobility is considered and the phase modification is run once after a handover happened. That is, if handovers are not possible for a relatively long duration, the load balancing can be compromised. Polese et al. [START_REF] Polese | Distributed path selection strategies for integrated access and backhaul at mmwaves[END_REF] consider the problem of selecting the best path from any IAB-node to a node connected (wired) to the core network. They define several strategies for an IAB-node to select a parent: highest SNR, lowest number of hops to reach a wired node, lowest number of hops (node with highest SNR closer to wired node) and highest possible data rate. However, considering the data rate and hop count is not enough to ensure Quality of Service (QoS) in realistic cases, and the results only show a study on the number of hops from IAB-nodes to a wired node.

As mentioned at the beginning of this section, these works focus on the lower layers (especially the MAC layer). Routing is not thoroughly studied and neither are routing algorithms. The next section will discuss these.

IV. STUDY OF IAB AND POSSIBLE DEVELOPMENTS

A. On the Validity of IAB

This subsection shows the results of four different scenarios. In scenarios 1 and 2 the Donor, IAB-node(s) and UEs are placed on a line. There is 1 IAB-node in scenario 1 (Fig. 5a) and there are 2 IAB-nodes in scenario 2 (Fig. 5b). All UEs are randomly placed inside a 100 m by 100 m "box". The distance between the Donor, each IAB-node(s) and the box of UEs is 100 m. In scenario 3 (Fig. 5c), UEs are split in two groups (each with half the total number of UEs). The distance between the Donor and IAB-nodes is 100 m. Thus, IAB 2 and IAB 3 have a horizontal and vertical distance of about 70.7 m from IAB 1 . The distance between IAB 2 and IAB 3 and their respective "box" of UEs is 50 m. In scenario 4 (Fig. 5d), the placement of the Donor and the boxes of UEs is the same as in scenario 3 but the three IAB-nodes have been removed. In all scenarios, distances are shown on Fig. 5. UEs are connected to the closest IAB-node (or the Donor in scenario 4). Simulations are done using the ns-3 simulator with the mmWave [START_REF] Mezzavilla | End-to-end simulation of 5g mmwave networks[END_REF] (5G) and IAB [START_REF] Polese | End-to-end simulation of integrated access and backhaul at mmwaves[END_REF] extensions. Table I depicts the most relevant parameters of the simulations. The x-axis on all graphs (Figs. 6 and7) represent the traffic load (bold text in Table I). Packets are sent at a Constant Bit Rate (CBA). A UE has a minimum distance from an IABnode (Donor in scenario 4) when it is on the center-left side of the box (or, in scenario 4, the lower-left corner for the upper box and upper-left corner for the lower box). The maximum distance is when a UE is on one of the right (lower or upper) corners of the box (except for scenario 4, where maximum distance is reached if a UE is placed on the upper-right corner for the upper box or the lower-right corner for the lower box). In scenario 4 the boxes of UEs are closer by 50 m to the left because the loss rate is greater (c.f. Figs. 7c and7d). Scenario 3 also has a 50 m shorter distance (compared to scenarios 1 and 2) to mirror scenario 4. UEs run a UDP client connected to a server on Internet. The delay and Packet Delivery Ratio (PDR) shown on the following graphs are computed from data packets in upload (UEs to server). The connection between the server and the Donor is a link at 10 Gbps with a delay of 2 ms.

The delay is computed from packets reaching the destination: if few packets arrive the results are less significant. In the graphs below, the value of one data point is the average of all runs. The value of one run is the averaged value (for delay) of all packets generated during that run. There is one PDR value per run. Concerning the asymmetrical error bars, the standard deviation is used. For each data point, the values of runs above (resp. below) the average have their standard deviation computed. The value of this standard deviation is the length of the error bar above (resp. below) the data point. Asymmetrical bars are more precise than symmetrical ones and prevent unrealistic values (e.g. negative delays).

Figs. 6a and 6b depict the case with 1 IAB-node. The PDR (Fig. 6a) is stable at 100% until the total traffic load reaches about 1.5 Gbps (2 UEs times 7.5 • 10 8 bit/s, or 4 UEs times (a) The PDR for scenario 1 (see Fig. 5a). (b) The delay for scenario 1 (see Fig. 5a). (c) The PDR scenario 2 (see Fig. 5b). (d) The delay scenario 2 (see Fig. 5b).

Fig. 6: Values of PDR and delay versus traffic load for scenarios 1 and 2. Note the vertical axis cut on PDR graphs (Figs. 6a and6c).

3.75 • 10 8 bit/s, etc.). The PDR starts to decrease because of congestion and more interference. The maximum achievable throughput is about 1.5 Gbps (this concurs with results from [START_REF] Mezzavilla | End-to-end simulation of 5g mmwave networks[END_REF]) so the limit is not on the Donor to Internet side (link at 10 Gbps as aforementioned) but rather on the IAB topology. On Fig. 6b, the delay is stable near 4-5 ms until congestion. Then, the value of delay increases to about 17 ms (2 UEs), 27 ms (4 UEs), 37 ms (6 UEs) and 47 ms (8 UEs). The average delay is higher with more UEs compared to fewer UEs because each one needs to wait for other UEs to be served before its own packets are processed. The delay reaches a top value because buffers are full and no new packets can be sent on the topology (thus the maximum waiting time is reached). Concerning scenario 2 (Figs. 6c and6d), the curves are similar to the case with 1 IAB-node (Figs. 6a and6b). There is a slight difference in the PDR, though, because there is one more hop to reach the Donor and thus the probability for a transmission error is higher. Delays are not significantly impacted because they increase mostly due to congestion.

Results from scenario 3 and 4 are shown on Fig. 7. Figs. 7a and 7b depict the results from scenario 3. They are better compared to scenario 4 (Figs. 7c and7d). However, they are worse compared to scenarios 1 (Fig. 5a) and 2 (Fig. 5b) because IAB-node 1 receives traffic from two IAB-nodes. Indeed, the PDR on Fig. 7a starts to decrease at about the same values compared to other graphs, but with a steeper slope. The delay with 2 UEs (on Fig. 7b) goes from about 4-6 ms at low charge (a) The PDR for scenario 3 (see Fig. 5c). (b) The delay for scenario 3 (see Fig. 5c). (c) The PDR scenario 4 (see Fig. 5d). (d) The delay scenario 4 (see Fig. 5d).

Fig. 7: Delay and PDR versus traffic load for scenarios 3 and 4. Note the cut on the vertical axis on PDR graphs (at 60% for Fig. 7a) and 40% for Fig. 7c.

up to about 18.75 ms. In comparison, 2 UEs on scenario 1 (Fig. 6b) have an average delay of about 4-5 ms at low charge and the delay increase up to 17.08 ms at maximum charge. Scenario 4 has much higher delays (Fig. 7d) compared to the other scenarios (up to 100 ms more compared to scenario 1, Fig. 6b). The PDR (Fig. 7c), considering error bars, is lower than all other cases (for 6 UEs, about 68.05% on average and about 44.69% considering variance). The PDR seems very high (above 85% at maximum load), but this is due to very few packets able to reach the Donor. Indeed, most are lost and do not even "leave" the UE 1 . In scenario 4, error bars are longer below the average. This is caused by few packets being correctly transmitted the first time and having a relatively low PDR (Fig. 7c) or delay (Fig. 7d). However, most packets have a value close to the average. These results highlight the benefits of deploying IAB-nodes for better performance and coverage rather than having long range (lossy) transmissions. More hops slightly decrease PDR (Fig. 6a versus 6c) but delay is not affected as long as there is no congestion. It is also interesting to see that there is a bottleneck when several IAB-nodes send traffic to a common parent: this shows the importance of robust routing on complex topologies with many IAB-nodes to help manage such issues.

B. 3GPP Release 17

Release 17 comes with several new features concerning IAB [START_REF] Dahlman | 5G evolution and beyond[END_REF], [START_REF] Bertenyi | 5G Evolution: What's Next?[END_REF], [START_REF]RP-211768, Enhancements to Integrated Access and Backhaul for NR[END_REF]. These features are expected to positively impact IAB by increasing performance and providing more flexibility and reliability to send data. The most relevant features are summarizedin the following list along with an explanation/example of how each one can be exploited:

• The radio spectrum is expanded to 71 GHz (from 52.6

GHz). This offers a higher flexibility in the choice of frequencies and it will increase achievable throughput. • Better support for simultaneous transmission and reception (i.e. full-duplex). This feature reduces latency and increases spectral efficiency. • Inter-Donor migration of IAB-nodes. This will allow to dynamically adapt the topology with a higher degree of flexibility compared to intra-Donor migration only. • Support for non-terrestrial networks. This feature enables the possibility to use drones as IAB-nodes. Disaster recovery or ensuring minimal service during a temporary failure are examples of use cases.

C. Future Research Axes

From all of the above, we can deduce a few potential research axes. Two of them are enhanced load-balancing and improved differentiation of service.

In Sec. III, we discussed paper [START_REF] Pagin | Resource Management for 5G NR Integrated Access and Backhaul: a Semi-centralized Approach[END_REF] in which the authors propose a solution where the Donor allocates resources to IABnodes. Ultimately, it is up to these nodes to decide how to schedule resources locally. This "micro" optimization could be combined with a more "macro" (global) optimization at the network (routing) level. A routing algorithm might be useful in load-balancing the traffic load given the scheduling scheme.

Another possibility is to use the differentiation of service to establish different (routing) paths. Fig. 8 depicts such an example where two paths have been established. On this example, we suppose service 1 needs a high throughput (e.g. downloading/uploading) and service 2 requires a short delay (such as a Voice over IP (VoIP) application). The blue path (Donor ↔ IAB 1 ↔ IAB 3 ) can achieve an end-to-end throughput of 100 Mbps and the total delay is 3 ms. On the green path (Donor ↔ IAB 2 ↔ IAB 3 ), the throughput can go up to 10 Mbps only but the end-to-end delay is 1 ms. The blue path is thus better suited for service 1 and the green path is more adapted for service 2. Such a solution could help in improving QoS and load-balancing might result as a consequence of choosing different paths to send traffic from the same source-destination tuple (one device can run several applications simultaneously).

V. CONCLUSIONS IAB is a solution with a very high potential. Several studies have been conducted to show how it can be used to improve performance, mainly at the MAC layer. Our results concur with these previous findings by showing improvements in terms of delay and PDR. IAB can also be used to extend coverage area and to dynamically adapt the topology of the access network. 3GPP release 17 will come with several new aspects to enhance the capabilities of IAB and we believe it can be further improved using an efficient routing algorithm.

  Scenario 3: 3 IABnodes placed in a Y-shape topology. Results are depicted on Figs. 7a and 7b. Scenario 4: There are no IAB-node. Results are shown on Figs. 7c and 7d.

Fig. 5 :

 5 Fig. 5: The four studied scenarios.

Fig. 8 :

 8 Fig.8: An example of a topology with 2 paths set up. Both paths can be optimized for a different service, improving QoS.

TABLE I :

 I Values of parameters. The physical and MAC models are described in [13]. † Only in scenario 3. Only relevant in scenario 4. Traffic load (packet/s) [10 4 ; 10 5 ] step 2500 [10 4 ; 10 5 ] step 2500

	Parameter Name	Value (scenarios 1 & 2)	Value (scenarios 3 & 4)
	Number of IABs	1 or 2	0 or 3
	Number of UEs	[2; 8] step 2	[2; 8] step 2
	Packet size	1500 bytes	1500 bytes
	Traffic model	CBA	CBA
	Distance between IABs	100 m	100 m
	Dist. UEs & nearest IAB	[100; 210.80] m	[50; 160.80] m †
	Dist. UEs & Donor	-	[221.67; 342.66] m
	Height of IABs	10 m	10 m
	Height of UEs	1.5 m	1.5 m
	Simulation time	3.6 s	3.6 s
	Number of repetitions/runs	10	10

More precisely, simulations on the line topology with 1 IAB-node gives about 75000 packets at maximum charge whereas the no IAB-node topology yields about 100 packets for the whole run.


Amer Sakr-Hamidi

Laure Biniek

Sadiara Fall

Martin Brinkmann
email: martin.brinkmann@ics-cnrs.unistra.fr

Precise control of lamellar thickness in highly oriented regioregular poly(3-hexylthiophene) thin films prepared by high temperature rubbing : correlations with optical properties and charge transport

Precise control of orientation and crystallinity is achieved in regioregular poly(3hexylthiophene) thin films by using high temperature rubbing, a fast and effective alignment method. Rubbing P3HT films at temperatures T R ≥ 144°C generates highly oriented crystalline films with a periodic lamellar morphology with dichroic ratio reaching 25. The crystallinity and the average crystal size along the chain axis direction, l c , were determined by High Resolution Transmission Electron Microscopy and Differential Scanning Calorimetry.

Figure for Title of content

Precise control of orientation and crystallinity is achieved in regioregular poly(3hexylthiophene) thin films by using high temperature rubbing, a fast and effective alignment method. Uniquely, the exciton coupling in P3HT is correlated to the length of the planarized chain segments in the crystals. The evolution of charge transport versus rubbing temperature is correlated to the crystal orientation and film nanomorphology.

The inverse of the lamellar period l scales with the supercooling and can accordingly be controlled by the rubbing temperature T R . Uniquely, the observed exciton coupling in P3HT crystals is correlated to the length of the average planarized chain segments l c in the crystals.

The high alignment and crystallinity observed for T R >200°C cannot translate to high hole mobilities parallel to the rubbing because of the adverse effect of amorphous zones interrupting charge transport between crystalline lamellae. Although tie chains bridge successive P3HT crystals through amorphous zones, their twisted conformation restrains inter-lamellar charge transport. The evolution of charge transport anisotropy is correlated to the evolution of the dominant contact plane from mainly face-on (T R ≤100°C) to edge-on (T R ≥170°C).

Introduction.

Semi-crystalline polymer semi-conductors are popular and key materials in the fabrication of low cost electronic devices. Mastering their charge transport properties in thin films is challenging as it is a complex multi-scale physical process that depends closely on the level of order achieved at multiple length scales. 1 At the molecular scale, intra-chain transport is favored by the chain planarization which can be enforced by crystallization for polymers such as poly(alkylthiophene)s (P3HT or pBTTT). 2,3 At the mesoscale, charge transport is further affected by the intrinsic semi-crystalline morphology of SCPs i.e. the fact that crystalline regions coexist with amorphous zones in the polymer. 4,5 Charges must therefore cross the boundaries between highly conductive crystalline and poorly conductive amorphous domains in the films and this is why controlling the nanomorphology of semi-conducting polymers (SCPs) is an important issue. 6 In this regard, molecular weight was found to influence strongly charge transport. This is because, depending on the average contour length of the chains, so-called tie-chains can link crystalline domains through the amorphous interlamellar zones and impact the charge transport in thin films. 7 Therefore, it is important to develop processing methods to control precisely the relative proportions of amorphous and crystalline fractions in SCPs i.e. to control the crystal size distribution and orientation in a thin film. In this perspective, the role of molecular weight is essential as it fixes the average contour length l chain with respect to the average crystal size along the chain direction l c . Furthermore, charge transport is highly anisotropic in systems such as P3HT, being most effective along the chain axis direction (c axis) and the -stacking direction (b axis) and poor along the insulating alkyl side chains (a axis). 8,9 Accordingly, a comprehensive approach to charge transport in SCPs requires to control both orientation and crystal dimensions in thin films.

The role of structural perfection on charge transport was recently addressed by Salleo and coworkers from the perspective of paracrystallinity along the -stacking direction. 1 Paracrystallinity is a measure of the lattice disorder obtained from the careful analysis of Xray diffraction peaks. Although correlations were observed for various polymers between charge mobility and paracrystallinity, it is surprising that no direct correlation between crystalline order along the chain direction and charge mobility was established so far. One of the reasons for this is that the precise control of both orientation and crystallite size is usually difficult to achieve in SCPs films. Moreover, crystal dimensions along the chain direction are virtually impossible to extract from classical Grazing Incidence X-ray diffraction data on unoriented films given the poor intensities of the 0 0 l reflections. But there exist means to align SCPs and thus enhance order along the chain direction, to cite but a few: nanoimprint lithography, 10 epitaxy 11 , flow coating, 12 strain orientation, 13 nanostructured confinement 14 and use of nanogrooved alignment layers. 15 One of the reasons for the rather low crystallinity in SCPs is their poor ability to nucleate intrinsically, especially from the melt, because of the entanglements between rigid chains that can hardly disentangle, even at elevated temperatures. In solution, control of nucleation and growth seems more straightforward and in the case of P3HT, it was demonstrated by Reiter and Ludwigs, that the density of nucleation of P3HT spherulites can be tuned by solvent vapor annealing. 16 Emerick et al. 17 as well as Stingelin et al. 18 showed that nucleation agents can be used either in solution or in the melt to favor crystallization of SCPs. Alternatively, Stingelin et al. proposed to use crystallization under pressure to promote extended chain crystallization of P3HT but with limited success. 18 Another approach to enhance the nucleation of polymer crystals consists in aligning the chains either by epitaxial interactions with a substrate or by using shear stress. 19 High crystallinity and orientation of P3HT were obtained by epitaxial crystallization whereby a crystalline substrate serves as a template to orient polymer chains acting as seeds for the subsequent growth. 5,11 Substrates of oriented polyethylene, 20 1,3,5-trichlorobenzene, 6,21 or carbon nanotubes 22 where successfully used to nucleate and align P3HT crystals from solution.

As an alternative, rubbing was proposed as an efficient method to align SCPs.

Rubbing is a well-known technique to prepare alignment layers of polyimides further used to orient liquid crystals. 23 Typically, a cylinder covered with a velvet cloth, rotates over a polymer film whereby surface alignment of polymer chains is induced. 18,[24][25][26] When applied to SCPs, it turned out that both temperature and molecular weight of the polymer are two key parameters controlling the level of alignment. 25,27,28 At high rubbing temperatures, polymer chains can disentangle (when the alkyl side chains of the SCPs are in a molten state) and align parallel to the rubbing direction. Bundles of aligned chains can then serve as seeds for the oriented crystallization of the SCPs. This work extends our previous studies on high-T rubbing by investigating the range of very high rubbing temperatures above 200°C and close to the melting of P3HT (240°C). To our surprise, it is observed that a solid state treatment such as high-T rubbing can generate very high levels of order in thin films that could usually only be observed in P3HT films processed from solution, not from the melt. Herein, precise control over lamellar periods is obtained for the first time by high-T rubbing of P3HT. Correlations between crystal dimension and the excitonic band width could be established. Moreover, the evolution of charge transport anisotropy with T R is correlated to the change of preferred contact plane of P3HT crystals in the oriented films.

Results and discussion.

Orientation and lamellar morphology at high rubbing temperature. a) Alignment versus rubbing temperature.

Improved orientation of P3HT at temperatures up to 180°C was recently demonstrated. 27,28 Hereafter, it is shown that using even higher temperatures close to the melting of the polymer can further modify crystallinity in the P3HT films to a level close to that usually observed in films prepared from solutions in organic solvents.

Figure 1.a and b depicts the changes in the UV-vis spectra of rubbed P3HT at various temperatures whereas Figure 1.c shows the TR-dependence of the dichroic ratio DR and the 3D order parameter S defined as S=(DR-1)/(DR+2). The change in the level of orientation is clear from the UV-vis spectra and the TR-dependence of DR and S. It shows that a maximum of orientation is achieved when TR reaches 171°C. Beyond this temperature, S tends to decrease slightly and levels at a value close to 0.8. Importantly, for TR ≥ 171°C, the absorption spectrum for  orientation does not show any vibronic structure and is peaked at 500 nm. As a matter of fact, for a polarization perpendicular to R, the film's color is orange, i.e. similar to the absorption of coiled P3HT in solution but it is red-shifted by 57 nm and significantly broader (See Figure S1). Such a spectrum indicates that the chains in the amorphous zones do not have a planar conformation but contain twists between successive thiophene units that break -conjugation along the chain, leading to a large distribution of conjugation lengths. Moreover, the spectrum is close to that obtained in spin-coated films of the hexane fraction of P3HT (Mn=5.6kDa) showing a poor crystallinity. 29 This suggests that the P3HT chains in the amorphous zones could be composed in majority of small Mw fractions i.e. those chains that are too short to crystallize at the rubbing temperatures (GPC results in Figure S2 indicate the presence of short chains in the samples). In other words, this would imply some type of Mw-fractionation during crystallization, the smaller P3HT chains being rejected to the amorphous interlamellar zones. These effects are somehow similar to that observed for crystallization of P3HT nanofibrils in solution in anisole. 30 Indeed, upon crystallization of P3HT nanofibrils in anisole, the low-Mw fractions of P3HT are left in solution. Despite the decrease in overall orientation for TR> 171°C, the intensity of the 0-0 component in the vibronic structure of the spectrum still increasing with TR. The spectrum observed in films rubbed at TR=217°C is similar to that observed in P3HT films cast from high boiling point solvents indicating that crystalline order is still improving.

The vibronic structure in the absorption of such rubbed films is significantly more pronounced when compared to that observed for P3HT films oriented by strain alignment, suggesting superior crystallinity in high-T rubbed P3HT films. 13 As shown hereafter, this trend is further supported by TEM in bright-field (BF-TEM) and diffraction.

b) Periodic lamellar structure.

P3HT is known to be a semi-crystalline polymer and its structure in films oriented by epitaxy was shown to consist of a periodic alternation of crystalline lamellae and amorphous interlamellar zones. 5 As seen in Figure 2, all the films rubbed at TR≥144°C exhibit a similar periodic lamellar morphology in BF whereas for TR≤125°C, no such morphology can be evidenced. Moreover, the contrast in the BF images between crystalline and amorphous domains tends to increase with TR. Figure 2 depicts the evolution of the lamellar structure in rubbed films as a function of TR whereas the plot in Figure 2.e shows the TR-dependence of the lamellar period l extracted from the fast Fourier transforms. The lamellar period l increases with TR, typically from 13 nm at 144°C to 26 nm at 217°C. The latter value is close to that observed in the semicrystalline films of P3HT prepared by directional epitaxial crystallization. For classical polymers such as polyethylene, the inverse of the lamellar period l is expected to scale with the supercooling following the relation

 l 1 (T m 0  T R )
where is the melting temperature of an infinite size crystal and T c is the crystallization temperature. [START_REF] Keller | Chain Folded Crystallization of Polymers, from discovery to the present day ; a personalized journey : Sir Charles Frank[END_REF][START_REF] Lotz | Structure of Polymer Single Crystals[END_REF] As seen in Figure 2.e, this relation is indeed verified for the films of P3HT and the fit yields a value Tm 0 =301°C±6°C. This value is found in excellent agreement with the value of 300°C extracted from Hoffman-Weeks plots by Malik and Nandi 33 and the value of 298°C obtained by Koch et al. from the extrapolation of the melting temperature of a set of oligo-P3HTs, 34 but it is above the value of 272±6°C reported by Snyder et al. 35 While such an evolution of lamellar period with crystallization temperature is well known for classical polyolefins such as polyethylene [START_REF] Lotz | Structure of Polymer Single Crystals[END_REF] , it is the first time that it is observed for a SCP such as P3HT.

Therefore, high-T rubbing is a unique method that allows to fine tune the lamellar period in semi-crystalline films of SCPs such as P3HT by adjusting the rubbing temperature. This is possible since the nucleation of crystalline domains, often difficult for such rigid polymers, is induced by mechanical rubbing at a sufficiently high temperature that allows P3HT to crystallize in the form of folded chain lamellae ultimately forming a regular lamellar semicrystalline morphology. Such a periodic lamellar morphology, also observed in epitaxied films, is different from the one found in cast and spin-coated films that consist of nanofibrils formed in solution under conditions that are far from equilibrium.

c) Electron diffraction.

Electron diffraction further evidences clear and remarkable structural variations in the rubbed films. Figure 3 shows the characteristic ED patterns versus TR. As noted in our original work on rubbing of P3HT at room temperature, no orientation of P3HT (48 kDa) is observed at TR=25°C. The ED pattern consists of an intense 0 2 0 Scherrer ring implying edge-on P3HT domains with random in-plane orientation. 36 For 98°C≤TR≤144°C, a set of equatorial h 0 0 reflections characteristic of face-on P3HT domains replaces progressively the 0 2 0 Scherrer ring associated with the non aligned edge-on P3HT domains. For all the films prepared at TR≤144°C, no well-defined 0 0 2 is observed. Therefore, the structure of these films resembles a highly strained smecticlike phase with the thiophene backbones oriented along the rubbing direction R but without well-defined translational order along the chain direction cP3HT between stacked polythiophene chains. 25 A remarkable structural change takes place for TR≥171°C. Beside the equatorial h 0 0 reflections, the ED patterns show several 0 k 2 reflections. For TR = 217°C, the 0 0 2 reflection becomes quite intense and sharp. More generally, the ED patterns show numerous mixed indexes reflections up to q= 1.3 Å -1 which could not be observed previously in oriented film (Mw=20 kDa) prepared by directional crystallization (see Figure 3.e). This indicates a very high level of crystalline order in P3HT films rubbed at 217°C, especially along the chain direction cP3HT. It also implies 3D order in the side chain packing. The enhanced sharpness of the 0 0 2 reflection along the meridian indicates larger crystals along cP3HT which is fully consistent with the larger lamellar periods seen in BF. Moreover, for TR=217°C, 0 2 l reflections appear on the equator beside the h 0 0 reflections (h=1-3), indicating that the films consist of aligned crystals (cP3HT//R) with face-on and edge-on orientations on the substrate. However, for TR=217°C, the films consist of a majority of aligned edge-on domains, as inferred from the strong intensity of the 0 2 0 equatorial reflection. The comparison of the 217°C ED pattern with the calculated fiber pattern (using the structure of form I by Kayunkid et al. 37 ) in Figure 3.f indicates that i) the films rubbed at 217°C have the characteristic form I crystal structure and ii) that they do not show a perfect fiber symmetry as can be inferred from the absence of certain h k 1 reflections. and the layers of alkyl side chains. 38,39 Therefore HR-TEM images show typical fringed patterns with a 1.65 nm period (corresponding to aP3HT). This methodology was applied here in the case of crystalline domains formed in high-T rubbed films. Figure 4 shows some representative low dose HR-TEM images and the extracted histograms of stem lengths (lc) for P3HT films rubbed at 144°C (a), 171°C (b) and 217°C (c). The statistical analysis shows that the average value of lc does indeed increase with the rubbing temperature. Importantly, a four-fold increase of lc is observed between 144°C and 217°C, corresponding to stems of 9 to 36 thiophene units in average, respectively. This result is in line with the ED observations showing enhanced diffraction at increased TR and a progressive increase of intensity and sharpening of the 0 0 2 reflection in the ED patterns.

Since we know the values of lc and l for various temperatures, it is possible to extract a crystallinity HRTEM = lc/l. This definition assumes that the crystalline order of the films along the a and b axes does not substantially change for 144°C≤TR≤ 217°C. The values given in Table 1 indicate that the crystallinity HRTEM is increasing with TR up to a value of 56% at 217°C. As shown below, the values of HRTEM are in close agreement with those obtained from the DSC analysis of the rubbed samples (vide infra). TR=171°C and c) TR=217°C.

Differential scanning calorimetry.

Having observed different morphological and structural features in the P3HT films rubbed at different temperatures, we have analyzed the rubbed films by DSC, in particular to follow the variation of crystallinity  DSC with TR. To this aim, only the first heating scan was considered as it is characteristic of the structural state of the sample after rubbing (the second heating scans of all rubbed films all looked similar with almost identical melting enthalpies, see Figure S3). Figure 4 illustrates the evolution of the DSC first heating scans as a function of the rubbing temperature TR. This exotherm is attributed to so-called cold crystallization of P3HT chains that have been pre-oriented by rubbing. This implies that there exists a fraction of highly oriented P3HT chains forming a metastable phase that crystallizes upon subsequent annealing during the DSC scan. In fact, both the cold crystallization exotherm and the 248°C melting endotherm appear and disappear concomitantly in the heating scans. Since the exotherm is associated to cold crystallization of aligned chains, the 248°C melting endotherm must correspond to the melting of the cold crystallized fraction during the DSC measurement.

The higher value of Tm might indicate that cold-crystallized P3HT chains form crystalline domains with more extended chains.

Despite the presence of the exotherm associated with the cold crystallization of rubbed P3HT, the total melting enthalpy ∆Hm was tentatively extracted from the entire endotherm peak (in pink). As seen in Figure 6, a rather clear evolution of ∆Hm is observed with TR. In the range 25°C -98°C, ∆Hm decreases to 3 J/g. Then, for TR≥98°C, ∆Hm increases with TR to a maximum value of 22 J/g.

The comparison of the structural information gathered by TEM allows us to rationalize the DSC results and propose the following rationale. Rubbing the films at TR=25°C leaves the films almost unaffected structurally without any alignment of the chains. Therefore the characteristics of the melting endotherm are similar to that of the non rubbed films in terms of peak position (endotherm at 241°C) and enthalpy.

For 98°C≤TR≤144°C, the film's structure consists of a fraction of non oriented crystalline phase (evidenced by the 0 2 0 Scherrer ring in the ED pattern) and an oriented "smectic-like" phase with face-on oriented domains. In the smectic-like phase, polythiophene backbones are -stacked into layers surrounded by layers of more or less disordered side chains. Inside a layer of -stacked chains, no translational order along the chain direction is observed between successive chains as inferred from the absence of the 0 0 2 reflection. 25 The non oriented P3HT crystalline phase gives rise to the melting endotherm at 241°C whereas both the exotherm due to cold crystallization and the melting endotherm at 248°C are attributed to the aligned smectic-like phase. The cold crystallization evidenced for films rubbed at 98°C≤TR≤171°C is therefore attributed to the crystallization of the aligned P3HT chains of the smectic-like phase during the heating scan. A second important result concerns the presence of a melting endotherm close to 248°C in the films rubbed at TR≤202°C. This endotherm might be linked with a fraction of highly oriented and possibly extended P3HT chains of the aligned smectic phase. In contrast to the folded chains found in the semi-crystalline phase with 3D order for TR≥144°C, the crystalline domains formed upon cold crystallization of the aligned smectic-like phase may involve a larger fraction of extended chains responsible for a higher melting temperature.

When TR ≥144°C, the periodic lamellar structure characteristic of semi-crystalline P3HT is formed. The size of the crystalline domains and of the total lamellar period l (crystalline + amorphous) increases with TR as does the melting enthalpy.

The melting endotherm of rubbed P3HT films with a semi-crystalline morphology is little affected by the increased lamellar periodicity for TR≥144°C. Only a slight shift of Tm is observed between 238.5 °C and 241.5°C for TR=144°C and 217°C, respectively. This situation is similar to that observed for powders of poly(3-octylthiophene) (P3OT) by Causin et al. 41 For P3OT films, a very small 2°C shift of the melting temperature Tm was evidenced when TC changes from 140°C to 170°C. enthalpy for an infinite P3HT crystal of 33 J/g. 40 Accordingly, it is possible to determine an apparent crystallinity  DSC and hence the average stem length in the crystalline regions lc defined as lc(DSC)= DSC l. Table 1 collects the values of  DSC and the average crystal size along the chain direction lc(DSC) versus TR. Interestingly, the crystal size lc increases substantially between 144°C and 217°C from 3 nm to 15 nm whereas the crystallinity  varies between 26 % and 66 %, respectively. Most interestingly, the average stem length lc(DSC) is in close agreement with the statistical stem length obtained from HR-TEM measurements, within experimental errors. This supports the total crystallinity values extracted from the DSC measurements on the films rubbed at various temperatures. The maximum crystallinity values obtained at 217°C are also in line with the X-ray values of 68-80% reported by Thurn-Albrecht and coworkers for powdered samples. 40 This result demonstrates that high-T rubbing allows to precisely tune the crystallinity of the P3HT samples in a reproducible way. The control of the rubbing temperature TR gives therefore a handle on the crystal size along the chain direction lc and on the total crystallinity We will now discuss the impact of crystal size on optical and charge transport properties in the oriented P3HT films.

Correlation between lc and excitonic band width W.

The optical absorption of P3HT films contains physical information on the polymer chain conformation. A random coiled P3HT chain in solution absorbs at 460 nm whereas planarization of the chains upon crystallization transforms the spectrum to a well-defined vibronic progression. The relative weight of the vibronic components A0-0 and A0-1 is a measure of the level of order, as inferred from studies on solvent cast films and crystallization of P3HT in solution. Large A0-0/A0-1ratios are observed in highly crystalline films of P3HT prepared from high boiling point solvents such as chlorobenzene, mesitylene or isodurene. 42,43 Although the importance of the solvent used for the processing is known, no correlation between the crystalline features of the films e.g. crystal dimensions and the optical properties has been established so far. As shown in the previous section, high-T rubbing gives a handle to control the size of the crystalline domains along the chain direction, hence, to investigate possible correlations with optical properties such as the exciton band with W extracted from the ratio A0-0 / A0-1.

Figure 7 depicts the evolution of the UV-Vis absorption spectrum with rubbing temperature (polarization parallel to the rubbing direction R). All spectra exhibit the characteristic vibronic structure with three dominant contributions associated to the 0-0, 0-1 and 0-2 transitions centered at 610 nm, 555 nm and 525 nm, respectively. For TR=98°C, both the 0-2 and 0-1 components are dominant whereas the 0-0 contribution is seen as a shoulder. Such a spectrum is similar to that observed in strain-aligned P3HT films. 13 The low intensity of the 0-0 component is in line with the limited crystallinity evidenced by TEM. Increasing TR results in the strong increases of the ratio A0-0/A0-1 and a decrease of A0-2/A0-1. For TR=217°C, the A0-0 component is very well defined, as for highly crystalline films of P3HT prepared by solvent vapor annealing. 14 The overall trend observed for the absorption spectrum follows the observed structural evolution seen by TEM: increasing TR above 171°C results in a remarkable increase in overall crystallinity of the rubbed films that show a periodic lamellar structure characteristic of a semi-crystalline polymer.

Referring to the weak H-aggregate model of Spano et al., 44 it is possible to extract information on the local intrachain order from the UV-Vis spectra. Indeed, Spano et al.

showed that the free exciton band width W for weak H-aggregates is related to the ratio A0-0/A0-1 following the equation :

 A 00 A 01  1 0.24 W / E p 1 0.073W / E p         2 (Eq. 1)
where Ep is the energy of the main intramolecular transition (corresponding to a symmetric C=C stretch). 42 Following the work by Clark et al., a decrease in W is associated to an increase in the effective conjugation length. In the present case, we observe that W decreases with increasing TR from 93 to a plateau value of 44 meV for TR=217°C. This value is remarkably small for such a high-Mw P3HT sample processed in the solid-state i.e. in absence of solvent. It is similar to that observed in P3HT spherulites grown by SVA. 16 It is therefore the fingerprint of high crystallinity in the films prepared at 217°C.

The excitonic coupling between planarized chain segments should decrease with the increasing length of the segments. Calculations of the excitonic coupling dependence with the extension of the planarized chain segments has been performed by Gierschner et al. and Beljonne et al. for various conjugated polymers such as polythiophene. 44,45 Since the size of the crystalline stems can be controlled in the rubbed P3HT films, we have a mean to probe how the limited crystal size impacts the value of W. Interestingly, our HRTEM results give a direct measure of the average planarized chain segments that can be approximated by lc. However, for TR=202°C, W reaches a plateau at 44 meV. Therefore, the value of lc at 202°C is an indirect measure of the maximum conjugation length achieved in semicrystalline P3HT films. This conjugation length is close to 10 nm and corresponds to 25 thiophene units. It must be stressed that this value is in good agreement with the conjugation length of the 40-60 monomer predicted by implementing Zerner's Intermediate Neglect of Differential Orbital method on P3HT films grown from isodurene solution (W=20 meV). 45,46 The lower value of W achieved in films cast from isodurene is related to the fact that, P3HT crystals grown from solution form fibrils with neatly folded chains and without extended amorphous interlamellar zones as observed in our rubbed films. In average, the width of P3HT fibrils, corresponding to lc, is in the range 18 -20 nm i.e. larger than the maximum value of lc observed in the rubbed films (16 nm). 47

Charge transport anisotropy.

To evaluate the impact of the controlled crystallinity and in-plane alignment on the charge transport properties, bottom-gate bottom-contact OFETs were fabricated using the rubbed P3HT films. It is worth mentioning that we did not aim at optimizing the transistor performances but mainly at correlating the structure, crystallinity and morphology of the films with charge transport properties observed in bottom-gate bottom-contact transistors. We probed the charge transport in both parallel (//) and perpendicular (┴) directions to the source-drain contacts. Some representative output and transfer curves of the rubbed samples in both directions are shown in Figure S4.

The output characteristics show good saturation behavior and "negligible" non linear characteristics in the low drain (VDS) voltage region. The field-effect mobilities were extracted from the transfer characteristics in the saturation regime by assuming a gate voltage independent transport and a negligible contact resistance (see Figure S4).

The evolution of the hole mobilities in both parallel (µ//) and perpendicular directions (µ ┴ ) as a function of rubbing temperature TR are shown in Figure 8. Except for the sample that was melt-annealed, all rubbed films exhibit some anisotropy of the charge mobility. The highest anisotropy is observed for the films rubbed at 50°C whereas the lowest anisotropy is observed for the sample prepared at 217°C. No direct correlation between the 3D order parameter extracted from the polarized UV-Vis absorption and the observed charge transport anisotropy could be evidenced. The only correlation might be that the decrease in orientation for TR≥171°C coincides with a corresponding decrease in the mobility anisotropy.

Surprisingly, the hole mobility in the direction parallel to R is not showing a strong variation for TR≤171°C. All values of µ// lie in the range 2-4 x10 -3 cm²/V . s. Also, the value of µ// is not found to surpass that of the as doctor bladed films. For TR>171°C, µ// decreases slightly and increases again after melting (240°C). Regarding hole transport in the direction perpendicular to the rubbing, the results in Figure 8 show a stronger impact of TR. For TR in the range 50°C-144°C, µ ┴ shows first an increase. Then, for 144°C≤TR≤198°C µ ┴ tends to level at a value of 5 x10 -4 cm 2 /V . s and finally, as TR approached the melting temperature, it is increasing again until it reaches a value close to µ// (as expected for an isotropic system after melting). In the following, the observed variations in charge mobilities are analyzed as a function of structural modifications evidenced by TEM (see Figure 9). For 144°C≤TR≤217°C where the semi-crystalline lamellar structure is progressively developing with an increase in lamellar thickness and overall crystallinity, µ// tends to decrease slightly whereas µ ┴ is increasing. This result indicates that the increase of both crystallinity and crystal size lc does not translate in an improved charge transport along the rubbing R but rather along the perpendicular direction. This result might be understood by considering the detrimental role of extended amorphous interlamellar zones on the macroscopic charge transport in the direction parallel to the rubbing.

Amorphous interlamellar zones contain chain ends, chain folds and tie-chains that bridge successive lamellae through the amorphous zones. As noted earlier by Kline et al., there is a need for tie chains or tie crystallites to bridge successive P3HT crystals to enhance macroscopic transport. 7 To evaluate the role of tie chains, it is instructive to compare the average contour length of the P3HT chains, L, and the lamellar periodicity in the samples. In the sample used herein, L  60-70 nm which is far superior to the largest value of the lamellar periodicity observed in the rubbed films (29 nm).

Therefore, for all rubbed samples showing a semi-crystalline morphology, some P3HT chains do necessarily bridge successive lamellae through the amorphous zones (see Figure 9). Second, when the applied electric field E is parallel to R, charges must channel through amorphous domains that systematically limit transport in this direction. Our UV-Vis absorption results suggest that the amorphous zones are possibly enriched in low-Mw fractions of P3HT that do not crystallize. The GPC trace further support this hypothesis since small polymer chain fractions can be seen at high retention time (Figure S2). It is known that the charge mobilities of such low-Mw fractions are usually quite low (10 -6 cm 2 /V . s for 3kDa P3HT). 6 Accordingly, the regular alternation of amorphous zones and crystalline domains must necessarily be detrimental for the large scale transport in the direction parallel to R. Despite the fact that in average, P3HT chains can bridge successive crystalline lamellae through amorphous zones in the direction parallel to R, the twisted conformation of the polythiophene backbone is highly unfavorable for charge transport between crystalline areas. This implies that the existence of only tie chains is not sufficient to efficiently channel the charges between crystalline domains, most important would be a planar conformation of such tie chains as could be observed in tie-crystallites. 38,39 The situation in the direction perpendicular to the rubbing is different. ED clearly shows that the proportion of edge-on crystals increases with TR. Accordingly, µ ┴ should progressively change from a value characteristic of transport along the alkyl side chains at low TR to a value typical of transport along the π-stacking direction at high TR, which explains in part the evolution of µ ┴ with TR. This situation is analogous to that of rubbed PBTTT showing a similar change in charge transport anisotropy when the dominant contact plane changes from mainly face-on to edge-on. 27 The progressive increase of µ ┴ with TR may have a second origin. The BF-TEM images show a high continuity of crystalline lamellae in the direction perpendicular to R, which should therefore be favorable for charge transport along that direction. In other words, whereas amorphous interlamellar zones interrupt transport in the direction parallel to R at a small length scale of max. 15-20 nm, the continuity of the crystalline domains in the direction perpendicular to R over larger distances (up to 100 nm at 217°C) should ensure a more efficient transport. Therefore, the increase in film crystallinity with TR explains in part the increase of µ ┴ . Conversely, it is the highly regular semi-crystalline lamellar morphology that hampers charge transport in the direction of the rubbing. It is worth to note that this situation is different from the case of spin-coated or cast films from solution that consist of solution grown nanofibrilar crystals that do not have extended amorphous zones around their crystalline cores. 47 Moreover, it must also be reminded that charge transport in rubbed polymer layers measured in bottom-gate bottomcontact configuration is always found to be lower as compared to that measured in topgate and bottom-contact geometry. 48 As a test, we have probed also the transport on the top surface of a rubbed film for TR= 171°C. To this aim, the rubbed P3HT film was prepared on NaPSS and floated on distilled water and deposited on an OFET substrate (patterned SiO2 BG-BC substrates) in such a way that the polymer/air interface would now face the SiO2 substrate. Values of µ//=6.6 x10 -2 cm 2 /V . s and µ ┴ =1.8 x10 -2 cm 2 /V . s were obtained (see Figure S5). This result shows that transport at the SiO2/P3HT and Air/P3HT interfaces are different. A possible reason for this result is that the structure of the films are different at both interfaces, especially in terms of crystallinity. For spin coated films, it is well known that the structure of the P3HT film at the buried interface with the substrate can be significantly different from that in the bulk. 49,50 It can be anticipated that the P3HT chains located at the SiO2 interface may have more difficulties to align and crystallize than those chains located at the film interface directly in contact with the rubbing cloth. Moreover, it must also be recalled that the charge mobilities of rubbed PBTTT and p(NDI2OD-T2) films prior to annealing were always rather low because of the structural damage in the films caused upon rubbing. 23,28 Usually, in all these systems, post-rubbing annealing was necessary to induce a substantial increase of the charge mobilities by 1-2 orders of magnitude as compared to the as-rubbed films. In the case of P3HT, it is observed that post-rubbing annealing at temperatures above 100°C induces a substantial loss of in-plane orientation, which was not observed for the more rigid PBTTT or p(NDI2OD-T2).

Conclusions.

High-T rubbing is a unique method that allows to fine tune the lamellar period in semicrystalline films of SCPs such as P3HT by adjusting the rubbing temperature TR. This is possible since the nucleation of crystalline domains, often difficult for such rigid polymers, is induced by mechanical rubbing at a sufficiently high temperature that allows P3HT to crystallize and form a regular lamellar semi-crystalline morphology. The periodicity of the lamellar semi-crystalline structure, l, scales with the rubbing temperature such as  l 1 (T m 0  T R ) with Tm 0 =301°C. A rather clear correlation is observed between the exciton band width W and the average crystal size lc since lc is limiting the conjugation length in the films (extent of planarized chain segments).

Regarding charge transport, the anisotropy of charge mobility (//)/(  ) is shown to decrease with TR. The mobility parallel to the chains, //, does not substantially increase with the overall crystallinity . This relative constancy is explained by the presence of amorphous interlamellar zones that hamper charge transport along the rubbing direction whatever the value of TR in the range 144°C-217°C. The existence of only tie chains linking successive crystalline domains seems not sufficient to efficiently channel the charges through amorphous interlamellar zones. In strong contrast, the hole mobility perpendicular to the chain direction,   , is more clearly correlated to both the crystallinity in the samples and the proportion of edge-on crystals in the films.

Preliminary results were obtained on other polyalkylthiophenes e.g. poly(3butylthiophene) as well as low bandgap polymers such as (F-PCPDTBT). They indicate that the methodology followed herein is very general and can be used to elaborate thin films with periodic semi-crystalline structures with high crystallinity, tunable crystal dimensions and orientation. These aspects are essential to clarify the processingstructure-property nexus of conjugated semi-crystalline polymers.

Experimental section.

a. Materials and sample preparation.

The poly(3-hexylthiophene) (P3HT) is purchased from Rieke (RMI-001E, batch number BS21-44). This batch has a regioregularity of 97%, M w =48 kg/mol and PDI=1.64 (see Figure S2 for the GPC analysis). For TEM and UV-vis studies, all P3HT films are prepared by doctor blading a 5wt% solution in ortho-dichlorobenzene (o-DCB) on clean glass slides (Roth) maintained at 170°C. Cleaning of the glass substrates is described in the literature. 51 For DSC studies, the clean glass slides are first coated with a thin film of 10 wt % NaPSS aqueous solution (poly(sodium 4-styrenesulfonate) from Sigma Aldrich, average M w ~ 10 6 g/mol) by spin-coating (3000 rpm for 45 s and 200 rpm/s). The P3HT films are then doctor-bladed on top of the NaPSS sacrificial layer using a 10 wt% solution in o-DCB and then rubbed. The rubbed P3HT films are slowly immersed in water to dissolve NaPSS. The floated P3HT films are collected and dried overnight under primary vacuum. Finally several rubbed films (total weight of 5-6 mg) are fit inside inox pans. Mechanical rubbing of P3HT films was performed following the methodology described in our previous work. 25,27,28 In brief, a microfiber cloth is applied at a pressure of 2.3 -3.0 bar on the P3HT films. The so-called rubbing length is fixed at ca. 50 cm, and three rubbing cycles are used. To avoid chemical degradation of the films in ambient during high temperature rubbing, the rubbing was performed in a glove box (Plas Labs, Inc.) with p(O 2 )< 0.01%.

Prior to rubbing, the film was allowed to stabilize for 1-2 min at the desired temperature. A careful calibration of the surface temperature of both silicon substrates and glass substrates on the rubbing machine was performed with a platinum RTD resistance in order to determine possible biases between the setting temperature and the real temperature on the sample surface during rubbing. All values of T R given hereafter correspond to the real temperatures measured on the samples. OFET characterization: Bottom-gate bottom-contact field-effect transistors (FETs) were elaborated on pre-patterned test structures (Fraunhofer) whose source and drain contacts were composed of a 30 nm thick gold layer on top of a 10 nm thick Indium Tin Oxide (ITO) layer. A 230 nm thick silicon oxide was used as gate dielectric and n-doped silicon crystal as gate electrode. The channel length and channel width are L=20 µm and W= 10 mm, respectively. These electrode patterns were oriented along two directions on the substrates at 90° relative orientation so that charge transport could be measured both parallel and perpendicular to the rubbing direction. The transistor substrates were cleaned by sonication in acetone and isopropanol at 45°C for 15 min in each solvent. After drying under nitrogen, the substrates were subsequently exposed to an ultra-violet ozone atmosphere for 15 min.

No surface functionalization of the SiO 2 with OTS or HMDS was performed because it was found to alter the efficiency of the rubbing process (films are partly removed from the modified SiO 2 substrates upon rubbing). Polymer films of ~ 50 nm thickness were spincoated from 5wt% solutions in o-DCB (1250 rpm for 120 s and then 2000 rpm for 60 s). The polymer solutions were prepared by dissolution at 80°C for 4 hrs under continuous stirring.

After deposition, the samples were left under vacuum (<10 -6 mbar) overnight to remove residual solvent traces. All polymer solutions and films were prepared in a nitrogen atmosphere.

After rubbing of the films, the electronic characterization of the OFETs was carried out in a nitrogen atmosphere using a Keithley semiconductor parametric test system. The field-effect mobilities (µ FET ) were determined from the current-voltage transfer characteristics in the saturation regime using the following equation 52 :

  sat   I Dsat V G         2  2L WC i (1)
where I Dsat is the source-drain current, V g is the gate voltage, and C i is the capacitance per unit area of the gate dielectric.

The mobility values were measured for both the saturation and the linear regimes. Both mobilities showed the same trends as a function of the rubbing temperature. For the low rubbing temperature (below 100°C) devices, we have observed an important contact resistance. In such case, charge transport was probed for several channel lengths (20, 10 and 5 µm) and corrected value of mobilities were extracted following the procedures described in the literature. 52 As contact resistance has more impact at low voltage and might affect the extraction of hole mobilities, only hole mobilities in saturation regime are discussed herein.

Figure1.

  Figure1. Polarized UV-Vis spectra of oriented P3HT films (Mw=50 kDa) rubbed at

  Figure 1.c depicts the dependence of the dichroic ratio DR at 610 nm (full squares) and of the 3D order parameter (full grey circles) defined as (DR-1)/(DR+2) as a function of the rubbing temperature.

5

 5

Figure 2 .

 2 Figure 2. (a-d) TEM BF images of the lamellar morphologies in oriented P3HT films

Figure 3 .

 3 Figure 3. Evolution of the ED diffraction patterns in rubbed P3HT films as a function of

Figure 4 .

 4 Figure 4. Statistical analysis of the stem length (lc) extracted from the HR-TEM images of

Figure 5

 5 Figure5shows clear trends concerning the overall shape, the peak positions and the

Figure 5 .

 5 Figure 5. First heating DSC traces for P3HT rubbed films at different rubbing

Figure 6 .

 6 Figure 6. Evolution of the melting enthalpy ∆Hm (full triangles) extracted from the 1 st

Figure 7 .

 7 Figure 7. a) Polarized UV-vis absorption spectra of oriented P3HT films prepared by

Figure 7 .

 7 b depicts the variation of W versus average stem length lc in the crystals. The fact that W first decreases with TR indicates that the conjugation length is limited by the average stem length lc in the crystalline domains.

Figure 8 .

 8 Figure 8. a) Evolution of hole mobility in bottom-gate bottom-contact OFETs made of

Figure 9 .

 9 Figure 9. Schematic illustration of the structural evolution in rubbed P3HT films as a

b.

  Sample characterization.UV-Vis spectroscopy: Polarized UV-vis absorption spectroscopy was performed using a Varian Carry 5000 UV-VIS-NIR spectrometer with polarized incident light.TEM analysis:A thin amorphous carbon film is evaporated on the P3HT rubbed films using an Auto 306 evaporator (Edwards). Then, samples are removed from the glass substrate by floating the films in a 5 wt% aqueous HF solution and recovered on TEM copper grids. TEM was performed in bright field, high resolution and diffraction modes using a CM12 Philips microscope equipped with a MVIII (Soft Imaging System) Charge Coupled Device camera. Specific conditions for HR-TEM and low dose diffraction are given elsewhere.36,37 DSC measurements: Differential scanning calorimetry (DSC) analyses were performed under argon on a DSC manufactured by Setaram. The heating/cooling rates are set to 15°C/min. The melting enthalpies were extracted from the 1 st heating cycle using the Pyris software (11.0 version). The error bars on the melting enthalpies are estimated from the contribution of the cold crystallization enthalpy since it generates an additional contribution to the true melting enthalpy of the rubbed films.

2- 3

 3 devices were used to measure mobilities and charge anisotropy for each rubbing temperature. The reported values of mobilities are the mean arithmetic values and the error bars are calculated as the standard deviations of the obtained values. Acknowledgments. Bernard Lotz is gratefully acknowledged for fruitful discussions and careful reading of the manuscript. C. Blanck and M. Schmutz are gratefully acknowledged for technical support in TEM. Chheng Ngov is acknowledged for performing the GPC analysis and C. Saettel for DSC measurements. We are extremely gratefull to the MaCEPV team at ICUBE (N. Zimmermann, P. Lévèque and T. Heiser) for technical support in charge transport measurements, privileged access to the glove box plateform and fruitfull discussions on charge transport measurements. Support from the IRTG Soft Matter and the European community (Rhin Solar Interreg project C25), the Université de Strasbourg, the Investissements d'avenir (IDEX) and the Fédération de recherche Matériaux et Nanosciences Alsace are gratefully acknowledged.

TR l (nm) ΔH (J/g)  DSC ( %) a lc (DSC) (nm) lc (HR-TEM) (nm)

							 HRTEM
							( %)
	144°C	13 ± 1	8.5 ± 2.5	26± 8	3.3 ±2.0	3.5 ± 1.2	25±17
	171°C	16 ± 1.5	11 ± 3	33± 13	5.3 ± 3.0	7.5 ± 1.5	47±15
	202°C	20 ± 1.5	16 ± 0.5	49 ± 7	9.7 ± 2.0	-	-
	217°C	25 ± 2	22 ± 1	66 ± 9	15.3 ± 3.6	14.2 ± 3.0	56±15

Table 1 collects the melting enthalpies obtained by integration of the DSC signals over the appropriate temperature ranges as well as the melting temperatures at the peak maximum (see experimental section). Table 1. Structural data on the semi-crystalline structure of high-T rubbed P3HT films.

Lamellar periods (l) extracted from BF TEM, melting enthalpy ∆H, crystallinity  DSC and HRTEM , average stem length lc extracted from DSC and TEM.

a The crystallinity  DSC is calculated by assuming a melting enthalpy for a perfectly crystalline P3HT sample of 33 J/g following reference 40. lc (DSC) is extracted from the values of l and assuming that lc (DSC)=l.  HRTEM is calculated from the ratio lc/l.