Tarek Chouaki
email: tarek.chouaki@irt-systemx.fr

Laura Mariana

Reyes Madrigal
email: mariana.reyes@centralesupelec.fr

Sebastian Hörl
email: sebastian.horl@irt-systemx.fr

ASSESSING THE IMPACT OF MONETARY INCENTIVES FOR WALKING USING AGENT-BASED MOBILITY SIMULATIONS AND DISCRETE MODE CHOICE MODELS

Keywords: pedestrian mobility, modal shift, agent-base simulations, discrete mode choice, active mobility, sustainable mobility

Sustainable and active urban mobility options, such as walking, represent a significant opportunity for achieving environmentally friendly and healthier transportation in the Paris Region. Despite the well-known benefits of walking on mental and physical health, there is a need to substantiate the potential gains that could be brought by supporting the development of walking as a transport mode in the eyes of public authorities at different governmental levels. Our research aims to analyze and model the potential impacts of economic incentives on walking behavior in the Paris Region. We do so by addressing the research problem of how these strategies can effectively encourage individuals to choose walking as a mode of transportation. Also, we look at how the modal shift would impact the use of Public Transport (PT), walking, bike, and private car. We propose to tackle the topic through a quantitative modeling exercise where the impact of financial incentives for walking is assessed in detail by using agent-based modeling and simulations of 36 different incentive scenarios. In our simulations, travelers' behavior is modeled and considered individually, and a mode choice model is used to approximate real-life user decision-making. Such a model takes into account different components of a trip, such as duration and cost. In this work, a representative simulation of the Île de France area and the underlying mode choice model are extended to test the incentive policies for walking. Various incentive scenarios are studied, and, by integrating the incentives in the mode choice model, we can assess each scenario's impact on user decisions. This study sheds light on potential strategies that decision-makers and other stakeholders in the region's ecosystem could take to achieve multisectoral sustainable goals using economic incentives for walking to encourage more sustainable mobility.

INTRODUCTION

Transport decarbonization is one of the main goals of governments and societies aiming to tackle the climate crisis resulting from the transgression of planetary boundaries. The European Commission has focused on developing policies to ensure achieving and maintaining the quality of life and a well-being economy while respecting the planetary boundaries. [START_REF] Rockström | A safe operating space for humanity[END_REF] forewarned about the impacts of social and economic systems on the outstepping of these boundaries that restrict the "safe operating space for humanity". In complex urban ecosystems, mobility is one of the proxies for individual, social, and economic activities enabling human development and well-being. However, it also represents one of the primary sources of pollutant emissions impacting the health of living beings and the natural environment. Therefore, identifying potential pathways towards sustainable mobility and addressing the barriers to encouraging decarbonized transportation is a way to tackle some of the existing challenges of complex sociotechnical systems [START_REF] Baltazar | Towards the design of sustainable mobility systems: objectives and barriers from the French local authorities' perspective[END_REF]. Active modes, such as walking and biking, represent a driver towards transport decarbonization and an opportunity to address diverse multisectoral challenges in relevant social and economic sectors such as transportation, health, and land use.

Transitioning towards more sustainable mobility

Sustainable mobility transitions require targeted strategies considering the specificities of territories, government echelons, and complex ecosystems of actors such as the ones involved in urban mobility. Therefore, the shifts necessary to attain more sustainable mobility practices depend on a mix of individual, social, physical, and economic conditions, as described in [START_REF]Chapter 1 Introduction to Transitions Towards Sustainable Mobility[END_REF]. Addressing and encouraging pedestrian mobility as a lever for sustainability requires a system's perspective taking into account the cultural aspects of the social dimension. (4) identified the multiple cultural elements behind the potential incentives and penalties that need to be considered to have an effective impact in promoting modal shifts and motivating new mobility practices (E.g., social connotation or judgment of people needing to walk, or from the stakeholder perspective, walking as an evident mode that does not require investment nor much extra attention and that does not bring a significant Return on Investment).

Appraising Walking

Walking is considered the "stem cell of mobility" [START_REF] Amar | directeur de la prospective à la RATP -Vidéo Dailymotion[END_REF]. It is also an essential element supporting the achievement of local, regional metropolitan and national policies and goals. Walking should mobilize transversal cooperation of different levels of government and actors, shaping policies appraising centrality and proximity as illustrated in the 15-minute city concept [START_REF] Allam | The 15-minute city offers a new framework for sustainability, liveability, and health[END_REF]. Appraising centrality and increasing the attractiveness of this model could represent a lever to encourage people to walk and cycle, increasing the distances traveled in these modes while at the same time reducing the use of individual motor vehicles. The link between the built environment and the social relationships and exchanges (that are practices happening in public spaces, enabled by walking sometimes) was identified and discussed in [START_REF] Cervero | Travel choices in pedestrian versus automobile oriented neighborhoods[END_REF] and in [START_REF] Giles-Corti | Increasing walking[END_REF]. In this sense, (9) also contributed by proving there is a positive correlation between the "comfort of walking and recreational well-being, happiness, and life satisfaction", based on findings in [START_REF] Kwon | Neighborhood Physical Environments, Recreational Wellbeing, and Psychological Health[END_REF]. Nevertheless, walking tends to be left out as a critical piece of the mobility system since the servitization of walking is potentially undesirable and seems hardly achievable [START_REF] Madrigal | Pedestrian mobility in Mobility as a Service (MaaS): sustainable value potential and policy implications in the Paris region case[END_REF]). Another reason why walking is more than relevant to achieve sustainability is health as the present and diverse urban-related lifestyles have a big impact on health.

For example, the super processed food available for consumption mostly in urban cores, and the way we move or don't move at all (sedentariness) on a daily basis. The lack of physical activity appears to be the cause of at least 7.2% of all-cause deaths and 7.6% of CVDs related deaths worldwide [START_REF] Katzmarzyk | Physical inactivity and non-communicable disease burden in low-income, middle-income and high-income countries[END_REF]. Just in 2017, in Île de France, circulatory diseases were one of the first causes of death, provoking around 254 deaths for every 100,000 inhabitants [START_REF] Insee | Causes de décès en 2017[END_REF]. This problem did not go unnoticed since, at a national level in France, the Public Health Code (Article L1172-1) integrates the possibility for general practitioners to propose adapted physical activity medical prescriptions (fr. Activité physique adapté, APA). This prescription is given for three to six months and provides individuals with the opportunity to adopt healthier habits by including physical activities in their daily routines and having medical supervision and advice to do so.

Incentives for Behavior Change

One of the main barriers to encouraging walking is the lack of a straightforward industry behind it [START_REF] Motion | How walking is undervalued in transport w/Bronwen Thornton, ???? 15[END_REF]. Unlike the bicycle, walking requires no other vehicle than one's own feet. This research explores economic incentives, which seem to have more impact when applied in parallel with other non-economic incentives, as described in (15). Policies aiming to incentivize virtuous behavior, such as walking, can be classified according to their type of interventions, and expected functions.

The functions of these policies can be multiple, as illustrated by [START_REF] Xiao | Shifting towards healthier transport: carrots or sticks? Systematic review and meta-analysis of population-level interventions[END_REF]. The authors considered functions linked to skills, finances, access, aesthetics, safety, convenience, space, and awareness.

All of which can have gain or loss effects according to the objectives and implementation strategies. [START_REF] Kane | Economic Incentives for Preventive Care. No. 101[END_REF] discuss the concept of "economic incentives," which encompasses a broad range of actions aimed at motivating individuals. These incentives can take various forms: "cash payments, lotteries, coupons for discounted or free goods and services, gifts, free or reduced-price medical services, and the chance to elude disincentives". [START_REF] Komiya | Effectiveness of Financial Incentives for a Pedometer-Based Walking Promotion Program[END_REF] explored the effectiveness of financial incentives for a pedometer-based walking promotion program among almost 17 000 individuals aged 40-75 years in the city of Takaishi, Japan, between 2016-2018. The authors set particular focus on the link between health-related costs and economic incentives based on the daily step count.

The main results displayed a correlation between the participation in the study and the reduction of health expenses in a year within the sample of Takaishi inhabitants: "The average medical costs per year was JPY 85,525.8 for the walking group and JPY 152,602.8 for the control group." "In fact, there was a difference of 67,077 yen in the average medical cost per person per year between the walking and control groups. With 1,923 walking group participants, the total medical cost reduction was predicted to be at least 12,898,904 yen (around 83 000 C). Similarly, in Australia, a study conducted by Victoria Walks in Melbourne, found that investing in walking yields significant benefits in terms of decongestion, environmental improvements, and health. The study found that for every dollar invested in walking initiatives in infrastructure or communication campaigns, approximately 13 dollars return in benefits [START_REF] Badawi | The economic case for investment in walking[END_REF].

BACKGROUND

In this work, we propose a novel approach to assessing the impact of financial incentives. Our approach relies on the use of agent-based simulation of mobility. Such a simulation individually considers every traveller (called agents), with related activities and trips. Global phenomena such as congestion emerge from local interactions between the agents. Using a behavioural model for agent decisions, the mobility-related decisions of travellers can be dynamic and depend on the quality of each alternative. This allows us to assess the impacts of a change on the mobility offer side on traveller decisions. We address this by testing the impacts that monetary incentives for walking could have on mobility in the Paris region and by responding to the following research question:

How can walking be incentivized to enable behavior change towards more sustainable mobility?

To do so, we focus on walking and delve into the potential financing schemes for incentives for pedestrian mobility as well as the global effects in terms of modal shifts and mobility practices.

France's Active Mobility Context

At a national level, in France, around 18 million people commute (home to work) by means of their private car, disregarding the distance traveled. Factually, 60% of employed people travel less than 5 km using their private vehicle. In Île de France, even for short trips, cars represent not the first, but an omnipresent mobility option in the decisional panel of individuals. In contrast, only 8% travel by active modes for their daily commute trips, and 2% walk [START_REF]La voiture reste majoritaire pour les déplacements domicile-travail, même pour de courtes distances[END_REF]. Also, in the Paris region, walking represents 40% of the trips made in a day, and in the case of the city of Paris, the numbers go up to more than 50%. Whether it is to encourage more people to walk or to provide better tools to people that are already walking (sometimes constrained to do so), the encouragement of walking has been identified to be of great relevance. Additionally, speaking of walking is also speaking about equity and accessibility. For example, in 2008, people with severely reduced mobility represented 12% of the population in the region, according to the Handicap-santé survey. Moreover, the ageing of the population also touches on the issue of accessibility. In the Paris region, 14,7% of the population is 65 years and older, and the representation of this group of age is projected to continue to augment.

METHODS

Simulation Model

In our work, we use the MATSim simulation framework [START_REF] Horni | The Multi-Agent Transport Simulation MATSim[END_REF]. MATSim is a fully open-source tool in constant evolution with an extended community supporting it.

The main input for an agent-based mobility simulation, besides the road network, is the mobility demand. In MATSim this is referred to as the population. Each traveller in MATSim is modelled as a separate agent. MATSim is activity-based in the sense that each agent has a sequence of activities to perform throughout the simulated period (typically one day). These activities are located in space and in time, consequently an agent needs to travel in order to perform the activities.

For each trip between two consecutive activities, the agents can use one of the modes available in the simulation. The activities and the travel routes between them constitute the agent plan.

Alongside the network and the population, other inputs can be supplied to MATSim according to the user's needs. MATSim is built in a modular manner which allowed the community to contribute with various extensions adding features to the tool. It is possible to simulate Public Transport (PT) systems by supplying a MATSim transit schedule specifying the stops, lines and departure times. A tool for converting a PT schedule in the GTFS format to a MATSim transit schedule is provided alongside MATSim.

The simulation consists in running all the agent plans, i.e. travelling between activities using the indicated modes and following the indicated routes. Some travel modes (car, PT, MoD) involve using a vehicle that travels throughout the links of the network while trips of other modes are simply teleported because they are assumed to not generate any congestion (walk and bike).

MATSim's key feature is certainly the replanning step and the iterative manner in which simulations take place. This allows agents to change their plans according to observed performance in previous iterations in order to build better plans on the individual level. Consequently, the changes in agent plans at the end of the simulation reflect the impact of the mobility offer on the user choices.

The performance of an agent plan depends on other agents' plans. For instance, the travel time of a car trip depends on the congestion on the route which in turn depends on the number of travellers on the route. In order to prevent oscillation effects in the plans, not all agents should perform replanning at every iteration. Consequently, a certain proportion (usually 5%) of the population is randomly selected at the beginning of every iteration for replanning. The other agents carry on with the same plans. Consequently, several iterations are needed to reach system equilibrium.

An approach for agent plans replanning that relies on Discrete Mode Choice (DMC) models has been proposed into MATSim Hörl et al. [START_REF] Hörl | Pairing discrete mode choice models and agentbased transport simulation with MATSim[END_REF]. This approach exclusively focuses on chosing the transport modes for the trips. When an agent is selected for replanning, its journey through the simulation is divided in tours that start and end at a home activity. E.g. a sequence home → school → shop → leisure→ home → leisure → home is divided into two tours: home → school → shop → leisure→ home and home → leisure → home. Afterwards, and for each tour, all the mode sequence alternatives are considered. A first filtering is performed to filter-out the alternatives that violate the pre-evaluation constraints (e.g. taking car without possessing a license). Then, utilities are computed for each tour alternative as the sum of utilities of its trips as illustrated in Figure ??. The utility of a trip depends on the considered mode but generally involves computing the trip route and estimating travel time, wait time and cost. Each mode m is then associated with a utility function U m (χ) where χ denotes the trip that is evaluated. Each utility function is a weighted sum of the relevent trip components and the mode-specific constant. A second filtering takes place to rule-out tour candidates that violate post-evaluation constraints (e.g. utility below a certain threshold or a PT trip route that only consists in walking). Among the remaining candidates, one is chosen using a selection method based on the estimated utility. The most often used method is the Multinomial Logit selection Train [START_REF] Train | Discrete choice methods with simulation[END_REF].

Using the DMC model approach described above, calibration is made easier by focusing only on the transport modes and filtering out "bad" plans beforehand, only acceptable plans are simulated. This reduces the number of iterations that is needed to reach the equilibrium.

For our study, we rely on a well-established methodology for the generation of a synthetic population for the Île-de-France. First introduced in ??, the tool is openly available online and relies on various socio-economic data. The openness of the data and the approach make the simulations fully reproducible and extensible by the research community. At a 100% sampling scale, the resulting population consists of more than 5 million households with 11 million persons and 46 million individual daily activities. The parameters of the discrete mode choice model that is used are calibrated so that a simulation with the real-life mobility offer reproduces the same high-level use mode choices.

Implementing monetary incentives in the DMC model

In this work, the DMC model has been extended to support the incentive scenarios that are considered. We note τ the incentive amount per kilometer. The incentives are integrated in the utilities of incentivized trips using the same utilitarian value of money, noted as β cost that is already used in U car and U pt to take into account the costs of car and public transport trips (β cost < 0). More precisely, the utility function for trips with modes walk, PT, and car have been extended:

The utility function of walked trips U walk (χ) is extended with a term representing the incentive money that the traveler would receive if the trip is performed. It is computed on the basis of the distance to walk in kilometers χ distance and τ:

U ′ walk (χ) = U walk (χ) -β cost .τ.χ distance (1)
With β cost < 0 and τ > 0, subtracting the extra term integrates the incentives positively in the utility

(U walk (χ) ≤ U ′ walk (χ))
The utility function of public transport trips U pt (χ) is extended with a term similar to the previous one. Except that the considered distance is the distance that is walked by the user along the trip as an access to, egress from and transfer between public transports.

U ′ pt (χ) = U pt (χ) -β cost .τ.χ walkedDistance (2)
E.g., with the τ = 0.5C/km, if the trip consists of a 1km walk to a bus station, then taking the bus until bus station A, then walking 200 meters for train station B then taking the until station C then walking 1km to the final destination, the incentive amount is 1.1 C. This new term opposes the base cost of the public transport trip.

Finally, the utility function of car trips U car (χ) is extended with a term reflecting the extra cost for travelling with cars due to financing the penalties.

U ′ car (χ) = U car (χ) + β cost .τ i .χ distance (3)
The extra cost per kilometer τ i is updated at the end of each iteration i by dividing the total amount of paid incentives on the total distance driven by cars during that iteration. With τ i ≤ 0, the extra term has a negative impact on the utility (U car (χ) ≥ U ′ car (χ)) and adds up with initial cost of the car trip. This term is activated only when the "Polluter Pays" principle Is followed.

During the simulation, the impacts of the incentives is achieved gradually as only a fraction of the synthetic population (5%) is allowed to perform mode choice and potentially make changes on their mobility plans. This ensure smooth transitions and convergence to an equilibrium.

EXPERIMENT

We describe in this section the incentive scenarios that are investigated in this work.

In this study, We consider three dimensions to the monetary incentives for walking. The first is the incentive amount in C/km that constitutes the basis on which the incentive received by the traveller for a trip is computed. 6 incentive amounts were investigated in this study: 0.1, 0.2, 0.5, 1, 1.5 and 2 C/km. This value corresponds to the τ parameter defined above.

The second dimension is what we call the incentive policy, it defines which walked trips are incentivized. Three incentive policies are investigated: (i) incentivizing only fully walked trips, with no interaction with another mode. When performing simulations with this policy, the expression presented in Equation 1 is used. This policy is labelled W. (ii) Incentivizing only walks that are part of a public transport trip, where the user walks to, from and between public transport stations. This policy, labelled PT, is enabled in the simulation by the experession presented in Equation 2. (iii) Incentivizing both fully walked trips and walks related to public transports.

This policy is labelled WPT and its simulations are performed by enabling both the expressions described in Equations 1 and 2.

Finally, the financing scheme behind providing the incentives is considered. In this work, we distinguish between two schemes: (i) subsidies coming from local authorities, labelled S and (ii) applying the "polluter pays" principle under which the cost of the incentives is reflected on car users as an extra cost per kilometer driven. Simulating this scheme is done by enabling the expression presented in Equation 3 for computing the utilities of car trips. This scheme is labelles as PP

The combination of these incentive dimensions (6 incentive amounts, two incentive policies and two financing schemes) produces a set 36 incentive scenarios. Each scenario is labelled with When the incentive amount is itself an axis on which measures are shown, this part is omitted in the label. The [policy] part reflects the walks that have been incentivized. The policy incentivizing only purely walked trips is noted W, the one incentivizing only walks from/to public transport is noted PT and the one incentivizing all walks is noted WPT. The last part indicates the scheme that is used to finance the incentives: S denotes scenarios in which the incentives are supported through subsidies and PP denotes scenarios in which the incentives are reflected on car drivers, I.e., polluter pays. For example, the label 1-WPT-S refers to the incentive scenario where all walks are incentivized with an amount of 1C/km and where the incentives are financed through subsidies. The following of this section is structured in this manner: (i) a focus is given to the reaction of the DMC model to the incentives, (ii) the effect of the incentives on the modal shares is outline, (iii) a detailed analysis of the impact of incentives on walking is performed, (iv) the implications on GHG emissions are investigated and (v) the cost of the incentives is outlined (both on local authorities and private car users for "polluter pays" strategies). In the presented results, the KPI values observed in the simulations are scaled back up according to the simulated population sample.

Stability of the mode choice model with the incentives for walk

Before diving into the KPIs themselves, it is necessary to make sure that the DMC model remains stable when the incentives are used. I.e., the traveler behavior reaches an equilibrium, and the total value of incentives converges. Special attention needs to be paid to the "Polluter Pays" effects. As Figure 1 shows the evolution of the total amount of paid incentives during simulation of various incentive scenarios. In each setting, this amount converges smoothly during the simulations and doesn't show oscillations. The same smoothness can be observed in the evolution of mode shares during a simulation of the "1-WPT-PP" incentive scenario (see Figure 2). This is encouraging for the following of this studies and the use of agent-based simulations and DMC models for the investigation of monetary incentives in general.

Impacts on modal shares

Figure 3 shows the shares of each mode across the simulated incentive scenarios and incentive amounts. In general, the incentive strategies that implement the "polluter pays" component are more effective for discouraging the use of private cars than their counterparts. Moreover, the incentives for walking towards/from public transports produce a more significant modal shift than the incentives for walking as a sole mode. Moreover, and as expected, the greater the amount of the incentives per kilometer, the more the effects of different strategies differ. These differences can already be noticed with amounts as low as 0.2C/km. With an incentive amount of 1C/km, incentivizing only fully walked trips only reduces the share of car trips to 34.39% from the initial 35.07%. Its "polluter pays" equivalent achieves a 32.12% of car trips. This is nearly the same effect as the one of the strategy incentivizing only PT- When the incentive amount is increased to 1.5 C/km, the share of car trips decreases almost linearly if the "polluter pays" feature is not used (down to 31% with the WPT-S). However, if the "polluter pays' component is activated, the share of car trips reaches 29.88% if only fully walked trips are concerned, 22.75% if only PT-related walks are concerned by the incentives, and a critical value of 2.16% if all walks are incentivized. This shows that both the amount and target of the incentives can greatly influence the travelling decisions of travelers.

Regarding the use of PT, as expected, the incentive strategies targeting PT-related walks have an effect on the modal share of PT. When incentivizing walked trips only while not activating the "Polluter pays" component, the shares of PT trips slowly decreases as the incentive amount increases. However, with "Polluter pays", PT gains travelers even though the incentive does not directly encourage this mode. This can be explained by the extra cost of using cars that encourages travelers to switch to public transports. This can be seen in Figure 28 where the shares of Public Transport trips according to trip distance are compared across the "No incentive", 1-W-S and 1-W-PP scenarios. The extra cost on the use of car majorly allows to shift long trips to public transport.

Figure 27 Shares of each mode across each of the simulated incentive scenarios

As for walking as a main mode of travel, incentivizing only such trips produces the highest shares for this mode regardless of the use of "polluter pays" or not. However, under 1.5 C/km of incentive, while the incentive of PT-related walks only lowers the part of fully walked trips.

Its "polluter pays" counterpart is able to encourage this mode. Finally, for the bike mode, even though it is not directly concerned by any of the incentive strategies, its use is greatly impacted. In most of the simulated incentive strategies, the share of bike trips lowers as the incentive amount increases. In some cases, however with high incentive amounts (PT-PP and WPT-PP), the use of bikes increases.

A focus on the impact of incentives on walked distances

Figure 29 shows the walked distances (both total and average per person) observed during simulations with all the incentive strategies and the incentive amounts considered in this study. Interestingly, incentivizing walks only from/to public transports results in more walking than incentivizing only fully walked trips. This is essentially thanks to the ability of such incentives to cause a modal shift for long trips where car can be replaced by public transports thus causing new intermediary walks. Without any incentive, an average daily walked distance per person of 1.74km/person.day is observed. With an amount of 1C/km, the W-S incentive strategy increases this average to 1.80km/person.day, the PT-S strategy to 1.83km/person.day and the WPT-S strategy to 1.88km/person.day. The largest impacting incentive feature is however the "Polluter pays" component. All incentive policies that include this component generate more walked distance than all the policies that do not. Activating the "Polluter pays" component increases the average daily person walked distance to 1.88km/person.day, 1.95km/person.day and 2.26km/person.day for the W-PP, PT-PP, and WPT-PP strategies respectively. Figure 29 Total and average per person walked distances observed during simulations of the incentive scenarios.

Figure 30 shows the distribution of daily walked distances in the simulated populations with the 1-WPT-S and 1-WPT-PP incentive scenarios, each compared to the No incentive scenario. We note that the incentives allow to push the bottom of the distribution (people who walk very little distances throughout the day) to greater distances.

Impact of the incentives on CO2 emissions

Agent-based mobility simulations allow a fully disaggregated view of the mobility behaviors taking place during the simulation. These can be aggregated as desired and combined with other data to obtain more KPIs. One example is the estimation of emissions in the simulation. Figure 31 gives an overview of estimated emissions of CO2 equivalent (combines CO2, methane CH4, and nitrous oxide N2O) per passenger per kilometer (kg/pkm) as estimated by the ADEME for various transportation modes (ADEME, 2023). These values were also used in Deliverable 2.4 of the Anthropolis Chair (Gall, Chouaki, Vallet, 2023).

Among the simulation outputs, we find the mode that was used for each trip of each agent of the simulation as well as the length of the route taken during the trip. Furthermore, if PT is used, the details on the chain of public transport sub-trips that have been performed can be found, including the type of PT (train, subway, bus. . . ). This allows to retrieve the passenger kilometers per each mode, which can then be multiplied by the emission values per mode to estimate the total emissions of CO2 equivalents for each simulation.

Figure 32 shows the CO2 emissions prevented thanks to each of the studied incentive policies in comparison to the "No incentive" setting. The impact incentives on emissions is analogous to their impact on walked distances. Incentivizing only fully walked trips saves less emissions than incentivizing only PT-related walks with 33 tons of saved emissions with the 1-W-S scenario against 408 tons with the 1-PT-S scenario and 432 tons with the 1-WPT-S scenario. Moreover, "polluter pays" strategies are able to save much more emissions. The previously mentioned strategies are able to save 619, 1162 and 2417 tons respectively if the incentives are reflected on car strategy. This analysis allows to put in perspective the effectiveness of the incentives in regard to their cost. The latter is detailed in the following subsection.

Cost implications of incentive strategies

The assessment of the impact of monetary incentives for walking cannot be performed without looking at the cost of supporting such incentives. Our simulation approach allows us to estimate the impact of incentives on user decisions, thus enabling to retrieve the total amounts of incentive given to agents in the simulations. Figure 33 shows the total daily incentive amounts paid according to the incentive strategy (and the incentive amount per kilometer). With the strategies that do not use the "polluter pays" component, the total amount of incentives is linear in function of the incentive amount per kilometer, the 1-W-S scenario results in a total of 10.1M C/day, the

DISCUSSION

The first result of this study is the ability of agent-based simulations and DMC models to enable the impact assessment of monetary incentives related to mobility behaviours. In this work, the proposed assessment methodology is applied in the investigation of monetary incentives for walking. A wide range of incentive scenarios can be implemented and tested within such models. The incentives are taken into account in the choice model alongside other components such as travel time and the interplay between the components is considered in the process. The traveler's decisions reach an equilibrium that reflects the impact of the introduced incentives. This is also the case when in the presence of a feedback loop between the incentives and other components that are directly dependent on them as illustrated through the "Polluter Pays" financing scheme.

Regarding the methodology, many development pathways can be envisioned. The current state of the DMC implementation does not explicitly forbid very long walks, since the utility of such trips decreases with the distance making them highly unlikely. However with the incentives, this can no longer be the case according to the amount per kilometer. This can result in very long walks that are highly unlikely. Extending the DMC model is then necessary to explicitly prevent these alternatives. Moreover, the simulation considers that the whole network offers the same walking potential. This diverges from real-life observations where the layout of the public space heavily impacts its walkability 1 . More efforts ought to be put in this aspect to achieve more realistic simulations. Finally, the mode choice parameters used in this work are the same for all individuals in the population, resulting in all travelers reacting similarly to the incentives. Using a DMC model that is calibrated specifically for different groups of travellers would allow to more precisely assess the impacts that monetary incentives for walking would have (e.g, if the utilitarian value of money is different for car owners and non-owners).

In this work, a wide range of incentive scenarios are tested. Each incentive scenario being characterized by an amount per kilometer, the walks that are targeted and whether or not they are supported by an extra cost inflicted on car drivers, an exhaustive study investigation is performed by testing all possible combinations. However, more complex incentive policies ought to be studied:

• In this work, only walking is incentivized and bike trips are left out. However, from a policy perspective, active modes are more likely to be incentivized altogether. This will be addressed in future studies.

• All the considered incentive policies apply to walks according to the main mode of the trips during which they occur (walk or public transport). In the future incentives that apply only to walks with certain purposes will be tested (e,g. home-work trips).

• Besides targeting specific trip purposes, incentives can also be applied only during specific times of the day. For instance, with the objective on reducing the load on public transport during peak-times, an incentive for fully walked trips can be implemented within that time period to encourage travellers performing short trips to shift from public transports to walking.

• It is supposed in this work that the incentive amount received by a traveller is a linear function to the walked distance. Whereas this assumptions already allows to investigate incentive policies and observe their impacts, more complex, and realistic, methods for computing received incentives can be integrated in the DMC model. Such methods do not need to necessarily apply on the trip level, but can span the whole day (e,g. grant incentives up to 1.5C/day only if a person walked at least 500m during the day).

• Two financing schemes are investigated in this study, the first supposes that the incentives are provided by subsidies while they are completely reflected on car users in the second.

While the latter shows to be more effective for encouraging a modal shift towards walking and public transports, it often comes at prohibitive extra costs for using cars. Exploring intermediate schemes where only a fraction of the incentives cost is reflected on car users can reveal configurations where the advantages are preserved while mitigating the drawbacks.

The use of agent-based mobility simulations that consider the whole mobility system as finely modelled entities allows us to precisely measure the impact of incentives across various dimensions and on different levels. Generally, the KPIs considered here and the levels at which they are presented can be highly adapted according to the vision and objective of an actor or the other. For instance, if the incentives are financed by municipalities, the impact assessment can be performed distinctively across areas for a better vision on the effect of incentives.

An interesting measure is the distribution of daily person walked distances. It is shown in this work that the incentives allow to push this distribution from the lower values, greatly reducing the number of people that do not walk at all or only a short distance throughout the day. The analyses of the impact on walked distances can be pushed further to estimate the savings made in the health sector (e,g. social security) thanks to an increased health condition over the population. This can then be included in the estimation of the economic impact of incentives alongside the value of saved GHG emissions. Moreover, the socio-economic impact can be evaluated more exhaustively by employing specific methods. A cost benefit analysis methodology previously proposed for on-demand autonomous vehicles that rely on simulation results can be extended and adapted to the context of monetary incentives [START_REF] Carreyre | On-demand Autonomous Vehicles in Berlin: A Cost Benefit Analysis[END_REF].

CONCLUSION

To our knowledge, our work is the first quantitative investigation examining monetary incentive policies for walking, under an agent-based modelling and simulation approach. Our approach is illustrated in the context of Île-de-France using open-source tools simulation tools fed with a synthetic population that is built from open data. Moreover, the incentives studies here are presented in details, including how they are integrated in the DMC model. This research and the presented results are consequently fully reproducible and extensible.

Various incentive scenarios were investigated, with variatons on three dimensions: the amount per kilometer, the types of walks that are targeted and the financing schemes. An extensive study has then been performed by performing simulations with all possible variations of the values considered in each dimension. The impacts of the incentives have been assessed on mobilitycentered aspects (mode shares and walked distances), environmental aspects (GHG emissions) and on the economic aspects (cost of the incentives).

The results show the potential of approaches relying on agent-based simulations and discrete mode choice models for the investigation of monetary incentives. The mode choice model allows the travellers to react to the incentives and the simulation allows to reflect the impact of the incentives and the implied new travel decisions on other aspects of the mobility, which than feed back to the mode choice model. The situation described at the end of the simulation then represents an equilibrium state.

Our research presents a high analysis potential and significant extensibility potential. Many development pathways are identified on various aspects of this research. Further developments ought to improve the underlying mode choice model for investigating monetary incentives for walk (e,g. mitigating the possibility of very long walks). Moreover, the studied incentive policies can be extended to consider strategies that target certain trips more specifically, with incentive amounts that are not necessarily linear to the walked distance. Finally, the results obtained with the "polluter pays" financing scheme encourages the investigation of intermediate schemes where only a part of the cost of the incentives is reflected on car users. These pathways will be explored in future works.

[

  amount]-[policy]-[scheme] with each part labelled as described above. E,g. an incentive scenario with an amount of 1 C/km, with the WPT policy and the PP financing scheme is labelled 1-WPT-PPRESULTSSimulations of the Île-de-France area with a population scale of 1% have been performed with each if the 36 described incentive scenarios plus no incentive at all for baseline. The population scale is lowered in order to save running times since the number of individual simulated scenarios in this study is relatively high. One simulation on this scale requires around 4 hours and 30 minutes of machine power. The different policy strategies aimed at providing a vision of the potential impacts of diverse policies in terms of incentive amounts provided, or the type of trip being incentivized.Additionally, the results include the impacts of the two different financing schemes: polluter pays and subsidies.The KPIs presented in the previous section have been measured from the simulations and are depicted below. In the graphics, the incentive scenarios are labeled with [amount] + [policy] + [financing scheme]. The [amount] part reflects the incentive amount in C/km (e.g., 1 C/km).

FIGURE 1

 1 FIGURE 1 Evolution of the total paid incentive during simulations of various incentive strategies

FIGURE 2

 2 FIGURE 2 Evolution of mode shares during a simulation with the 1-WPT-PP incentive scenario

FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6

 3456 FIGURE 3 Observed mode shares in simulations of various incentive scenarios

FIGURE 8

 8 FIGURE 8 Saved CO2 equivalents emissions and their corresponding monetary value in each of the simulated incentive scenarios

TABLE 1

 1 Extra cost for car users to supporting the polluter pays incentivesWith the implementation of the "polluter pays" scheme, the total amount of incentives increases and is not linear in function of the amount per kilometer. This is due to the fact that when the incentive amount increases, so does the extra cost for car users. With 1 C/km, using the "polluter pays" components renders a total of 10.31MC/day with the 1-W-PP strategy (2.37C/person.day), 10.67M C/day with the 1-PT-PP strategy (2.42C/person.day) and 24.18MC/day with the 1-WPT-PP strategy (2.99C/day). These incentives being reflected on the users of cars as an extra cost, it is necessary to investigate the impact of incentive strategies on car drivers. Table10shows the extra cost in C/km necessary to cover the incentives given under each of the studied strategies and the

	1-PT-S scenario

https://www.drieat.ile-de-france.developpement-durable.gouv.fr/IMG/pdf/mep_4__marchabilite_web.pdf


Maurizio Mastropasqua Talamo

Thomas Cauchy

Flavia Pop
email: flavia.pop@univ-angers.fr

Narcis Avarvari
email: narcis.avarvari@univ-angers.fr

Tuning the photophysical and chiroptical properties of [4]helicenediketopyrrolopyrroles

Keywords: chirality, diketopyrrolopyrrole, (thia)helicenes, circular dichroism, photophysics

Synthesis and functionalization of diketopyrrolo [3,4-c]pyrrole (DPP) derivatives containing chiral groups able to induce a strong chiral perturbation of the DPP core is still a challenging task. We report in this work the straightforward preparation of four bis([4]helicene)-DPP and bis([4]thiahelicene)-DPP dyes upon the condensation of 2-CN-[4](thia)helicene precursors, followed by their N-alkylation by nucleophilic substitution (compounds 9-11) or by a Mitsunobu type strategy (compound 12). The compound 12, which contains sec-phenylethyl groups attached to the nitrogen atoms, has been obtained as (R,R) and (S,S) enantiomers. The four DPP-helicenes are luminescent in solution, while the N-benzyl (10) and N-sec-phenethyl (12) are emissive in the solid state as well. The chiroptical properties of compound 12 in solution and in the solid state indicate a strong chiral perturbation provided by the stereogenic centres, in spite of the stereodynamic nature of the [4]helicene flanking units.

INTRODUCTION

The 3,6-diaryl derivatives of the 2,5-dihydropyrrolo [3,4-c]pyrrole-1,4-dione, commonly described as diketopyrrolopyrroles (DPPs), are known as outstanding fluorescent dyes and brilliant pigments. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] The planar, rigid, and conjugated bilactam core of DPPs bridging two aromatic units accounts for remarkable optoelectronic properties such as intense UV-visible absorption with high fluorescence quantum yields, as well as a strong tendency to solid-state organization through π-stacking interactions. [START_REF] Kuwabara | Solid-state structure and optical properties of highly fluorescent diketopyrrolopyrrole derivatives synthesized by cross-coupling reaction[END_REF][START_REF] Jin | Synthesis of novel diketopyrrolopyrrolebased luminophores showing crystallization-induced emission enhancement properties[END_REF][START_REF] Naik | Influence of Side-Chain on Structural Order and Photophysical Properties in Thiophene Based Diketopyrrolopyrroles: A Systematic Study[END_REF][START_REF] Pop | Solid state supramolecular structure of diketopyrrolopyrrole chromophores: correlating stacking geometry with visible light absorption[END_REF][START_REF] Saes | The Effect of α-Branched Side Chains on the Structural and Opto-Electronic Properties of Poly(Diketopyrrolopyrrole-alt-Terthiophene)[END_REF][START_REF] Saes | Tuning the Optical Characteristics of Diketopyrrolopyrrole Molecules in the Solid State by Alkyl Side Chains[END_REF] Owing to these features different DPP derivatives have been employed as active materials in a number of optoelectronic applications such as semiconducting layers in transistors, [START_REF] Li | High mobility diketopyrrolopyrrole (DPP)-based organic semiconductor materials for organic thin film transistors and photovoltaics[END_REF][START_REF] Liu | Developments of Diketopyrrolopyrrole-Dye-Based Organic Semiconductors for a Wide Range of Applications in Electronics[END_REF] energy harvesting [START_REF] Heath-Apostolopoulos | Using high-throughput virtual screening to explore the optoelectronic property space of organic dyes; finding diketopyrrolopyrrole dyes for dye-sensitized water splitting and solar cells[END_REF][START_REF] Tang | Design of Diketopyrrolopyrrole (DPP)-Based Small Molecules for Organic-Solar-Cell Applications[END_REF] and storage, [START_REF] Xu | Functional thiophenediketopyrrolopyrrole-based polymer derivatives as organic anode materials for lithiumion[END_REF][START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] fluorescent probes, [START_REF] Praveen | Self-Assembled Extended π-Systems for Sensing and Security Applications[END_REF][START_REF] Auwalu | Diketopyrrolopyrrole Fluorescent Probes, Photophysical and Biological Applications[END_REF] bioimaging [START_REF] Li | Diketopyrrolopyrrole-based fluorescent probes for detection and bioimaging: Current progresses and perspectives[END_REF][START_REF] Wang | Mannose-functionalized diketopyrrolopyrrole as AIE-active probes for lectin detection and cancer cell imaging[END_REF][START_REF] Ftouni | Water-soluble diketopyrrolopyrrole derivatives for twophoton excited fluorescence microscopy[END_REF] and theranostics. [START_REF] Zhang | Diketopyrrolopyrrole derivativesbased NIR-II fluorophores for theranostics[END_REF] A recent trend in the development of new DPP dyes consists in the introduction of elements of chirality into the molecular structure, in order to enrich the optoelectronic properties with chiroptical activity. [START_REF] Dhbaibi | Exciton coupling in diketopyrrolopyrrole-helicene derivatives leads to red and near-infrared circularly polarized luminescence[END_REF][START_REF] Gao | Axial chiral binaphthalenediketopyrrolopyrrole dyads as efficient far-red to near-infrared circularly polarized luminescent emitters[END_REF] For instance, chiral DPP have recently received increasing attention as circularly polarized luminescence (CPL) emitters, an emerging class of luminophores with possible application into future innovative technologies ranging from cryptography, quantum photonics, three-dimensional imaging, chiral probes, stereoscopic and/or anti-glare displays with enhanced external efficiency. [START_REF] Han | High-Performance Circularly Polarized Light-Sensing Near-Infrared Organic Phototransistors for Optoelectronic Cryptographic Primitives[END_REF][START_REF] Deng | Circularly polarized luminescence from organic micro-/nano-structures[END_REF][START_REF] Hao | Circularly Polarized Light Triggers Biosensing Based on Chiral Assemblies[END_REF][START_REF] Song | Highly Efficient Circularly Polarized Electroluminescence from Aggregation-Induced Emission Luminogens with Amplified Chirality and Delayed Fluorescence[END_REF][START_REF] Han | Recent Progress on Circularly Polarized Luminescent Materials for Organic Optoelectronic Devices[END_REF] The synthesis of DPP derivatives typically relies on a double condensation reaction between aromatic nitriles and succinic esters in the presence of tertiary alkoxides, that results in the formation of the conjugated bicyclic bilactam scaffold flanked by aromatic units, with different electron-rich character. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] Unhindered and/or electron poor aromatic nitriles generally give DPPs with higher yields, yet a great variety of bis-aryl DPP are known, including phenyl, thienyl, furyl, pyridyl, and benzofuryls derivatives. [START_REF] Bao | Diketopyrrolopyrrole (DPP)-Based Materials and Its Applications: A Review[END_REF][START_REF] Purc | The impact of interplay between electronic and steric effects on the synthesis and the linear and non-linear optical properties of diketopyrrolopyrrole bearing benzofuran moieties[END_REF] The DPP lactam functions obtained through the succinic method are of secondary type and susceptible to establishing extensive hydrogen bonding which prevents solubility in most of the solvents. For this reason, DPPs are thereafter often subjected to N-functionalization, in order to ensure satisfactory solubility for processing or further functionalization reactions. For this purpose, N-alkyl chains are commonly introduced via a bimolecular nucleophilic substitution reaction between the corresponding alkyl halide and the deprotonated lactams. [START_REF] Pop | Towards more sustainable synthesis of diketopyrrolopyrroles[END_REF] Recently, other types of N-derivatization have also been developed, allowing for the introduction of aryl, [START_REF] Gutkowski | N-Arylation of Diketopyrrolopyrroles with Aryl Triflates[END_REF][START_REF] Jiang | New Synthetic Approaches to N-Aryl and π-Expanded Diketopyrrolopyrroles as New Building Blocks for Organic Optoelectronic Materials[END_REF] cleavable tert-butoxycarbonyl, [START_REF] Punzi | 1,2,3-Triazole-Diketopyrrolopyrrole Derivatives with Tunable Solubility and Intermolecular Interactions[END_REF][START_REF] Rooney | Suzuki-Miyaura cross-coupling of latent pigments in water/toluene emulsion under aerobic atmosphere[END_REF][START_REF] Mula | Hydrogen Bonding as a Supramolecular Tool for Robust OFET Devices[END_REF] and, especially, chiral α-branched benzyl-type groups. [START_REF] Talamo | Straightforward N-alkylation of diketopyrrolopyrroles through the Mitsunobu reaction with benzyl, α-branched, and chiral alcohols[END_REF] In order to develop chiral DPP derivatives, stereogenic functions can thus either be introduced at the N-position as chiral substituents, or by carefully choosing stereogenic aromatic flanking groups. Accordingly, DPPs N-functionalized with chiral chains such as dihydrocitronellyl [START_REF] Albano | Aggregation Modes of Chiral Diketopyrrolo[3,4-c]pyrrole Dyes in Solution and Thin Films[END_REF] and caproamides of chiral amines [START_REF] Militzer | Impact of Chirality on Hydrogen-Bonded Supramolecular Assemblies and Photoconductivity of Diketopyrrolopyrrole Derivatives[END_REF] have been reported and described as CD (circular dichroism) active upon aggregation, which indicates adoption of preferential chiral conformations and increased chiral supramolecular organization. However, these derivatives seem to be nonemissive under aggregation, so that CD activity is not accompanied by measurable CPL. Conversely, stereogenic features can be introduced at the flanking positions as aromatic groups endowed with axial chirality or decorated with functions containing elements of point chirality. [START_REF] Dhbaibi | Exciton coupling in diketopyrrolopyrrole-helicene derivatives leads to red and near-infrared circularly polarized luminescence[END_REF][START_REF] Gao | Axial chiral binaphthalenediketopyrrolopyrrole dyads as efficient far-red to near-infrared circularly polarized luminescent emitters[END_REF][START_REF] Hume | Self-Assembly of Chiral-at-End Diketopyrrolopyrroles: Symmetry Dependent Solution and Film Optical Activity and Photovoltaic Performance[END_REF] Enantiopure binaphthyl groups, for instance, have been used as peripheral substituents on a bis(thien-2-yl) DPP derivative resulting in a CPL active fluorophore reaching glum dissymmetry factors of 5.8*10 -4 in dichloromethane solutions. [START_REF] Gao | Axial chiral binaphthalenediketopyrrolopyrrole dyads as efficient far-red to near-infrared circularly polarized luminescent emitters[END_REF] Similar glum dissymmetry factors (up to 9*10 -4 in dichloromethane solutions) have been obtained thanks to a mechanism of chiral exciton coupling for a dyad of achiral diketopyrrolopyrrole (DPP) fluorophores covalently bonded through ethynyl bridges to an enantiopure [6]carbohelicene. [START_REF] Dhbaibi | Exciton coupling in diketopyrrolopyrrole-helicene derivatives leads to red and near-infrared circularly polarized luminescence[END_REF] However, in both these latter two cases the stereogenic motifs (binaphthyls and helicenes) are likely too distant from the DPP core to contribute directly with their chiral sets of -electrons to the chiroptical properties of the overall chromophores, but only by means of through-space chiral perturbation (in binaphtyl-DPP derivatives) or by inducing reciprocal chromophore arrangement (in DPP dyads). Under this premise, we speculate that the capabilities of helicenes as strong chiroptical inducers, remain underexplored in the domain of DPP-based CPL emitters. For these reasons, in our work we have the purpose to investigate the synthetic viability of the direct connection of helicenes with the DPP core through sp 2 -sp 2 bonds, and the chiroptical properties of the resulting compounds. In order to do so, we attempted the direct synthesis of the DPP scaffold through classical condensation reactions between succinic esters and aromatic nitriles, but with the unprecedented use of cyano-helicenes as nitrile derivatives. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] All the while, we considered also the use of bulky N-substituents with the goal of reducing the extent of the aggregation caused quenching (ACQ). In particular, N-functionalization with chiral secphenethyl groups turned out to be beneficial towards enhanced chiroptical properties in the presence of stereodynamic and non-resolvable [4]helicenes [START_REF] Ouyang | Chiral multifunctional molecules based on organometallic helicenes: Recent advances[END_REF] as aromatic flanking groups.

MATERIALS AND METHODS

General

Chart 1: Molecular structure of the cyano-helicenes employed in this work.

All commercially available reagents and solvents were used as received unless otherwise noted. Dry tetrahydrofuran was directly used from the purification machines. Chromatography purifications were performed on silica gel Sorbent Technologies Silica Gel (60 Å, 65 x 250 mesh) and thin layer chromatography (TLC) was carried out using aluminum sheets precoated with silica gel 60 (EMD 40-60 mm, 230-400 mesh with 254 nm dye). All reactions were carried out in Schlenk tubes under argon atmosphere. NMR spectra were acquired on a Bruker Avance DRX 300 and 500 spectrometers operating at 300 and 500 MHz for 1 H and 75 and 125 MHz for [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] C, respectively, at room temperature in CDCl3 solutions. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] H and [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] C NMR spectra were referenced to the residual protonated solvent ( 1 H) or the solvent itself ( 13 C). All chemical shifts are expressed in parts per million (ppm) downfield from external tetramethylsilane (TMS), using the solvent residual signal as an internal standard and the coupling constant values (J) are reported in Hertz (Hz). The following abbreviations have been used: s, singlet; d, doublet; dd, doublet of doublets; dd, doublet of doublets of doublets; t, triplet; m, multiplet (Figures S1-S17). Mass spectrometry MALDI-TOF MS and HRMS analyses were recorded on JEOL JMS3000 (MALDI/TOF-TOF) spectrometer. In all cases the used matrix was DCTB trans-2-[3-(4-t-butylphenyl)-2-methyl-2-propenylidene]malononitrile.

Experimental procedures

Synthesis of 5-(2-(naphthalen-2-yl)vinyl)thiophene-2-carbonitrile (3)

In a Schlenk tube filled with argon, (naphthalen-2-ylmethyl)triphenylphosphonium bromide [START_REF] Martin | Reactivity and Mechanistic Issues in the Photocyclization of Dihalostyryl-Naphthalenes towards Halo-[4]helicenes: A Transposition on a Mallory Theme[END_REF] (1.000 g, 2.1 mmol) was dissolved in dry THF (50 mL). While stirring at -78 °C, n-BuLi (1.6 M in hexane, 1.36 mL, 2.17 mmol) was added dropwise to the solution, which was then let to reach rt over 30 min. The deep red/orange solution was cooled again at -78 °C and the 5formylthiophene-2-carbonitrile (0.284 g, 2.1 mmol) was added. The mixture was stirred overnight eventually reaching rt. The mixture was passed through a pad of celite and the solvent evaporated. The crude mixture was purified by column chromatography on silica gel with petroleum ether / dichloromethane 7:3 as the eluent, affording 0.520 g (98% yield) of 3 as white crystals of both E and Z isomers.

Z isomer: 1 H NMR (300 MHz, CDCl3) δ = 7.94 -7.82 (m, 4H), 7.61 -7.53 (m, 2H), 7.42 (dd, J = 8.4, 1.7 Hz, 1H), 7.40 (d, J = 3.9 Hz, 1H), 6.98 (d, J = 11.0 Hz, 1H), 6.97 (d, J = 4.4 Hz, 1H), 6.78 (d, J = 11.9 Hz, 1H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF]

Synthesis of phenanthro[3,4-b]thiophene-2-carbonitrile (4)

In a 1L photochemical reactor, 3 (0.450 g, 1.72 mmol) was dissolved in toluene (650 mL) and argon was bubbled through the mixture for about 10 min. Iodine (0.437 g, 1.72 mmol) and propylene oxide (6.0 mL, 86.1 mmol) were added, and the mixture was stirred overnight under irradiation from a 150W UV lamp. The mixture was then concentrated under vacuum, washed with a saturated aqueous solution of NaS2O3, dried over MgSO4, and finally the solvent removed under reduced pressure. The resulting crude was purified by column chromatography on silica gel with petroleum ether / dichloromethane 9:1 as the eluent, affording 0.440 g (99% yield) of 4 as a white solid. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF]

Synthesis of 5-(2-(benzo[c]phenanthren-2-yl)vinyl)thiophene-2-carbonitrile (5)

In a Schlenk tube filled with argon, (benzo[c]phenanthren-2-ylmethyl)triphenylphosphonium bromide [START_REF] Tinnemans | Synthesis and spectroscopic properties of 1,4diarylbutenynes[END_REF] (1.300 g, 2.23 mmol) was dissolved in dry THF (50 mL). While stirring at -78 °C, n-BuLi (1.6M in hexane, 1.39 mL, 2.23 mmol) was added dropwise to the solution, which was then let to reach rt over 30 min. The deep red/orange solution was cooled again at -78 °C and the 5formylthiophene-2-carbonitrile (0.306 g, 2.23 mmol) was added. The mixture was stirred overnight eventually reaching rt. The mixture was passed through a pad of celite and the solvent evaporated. The crude mixture was purified by column chromatography on silica gel with 5% ethyl acetate in petroleum ether as the eluent, affording 0.788 g (98% yield) of 5 as white crystals of both E and Z isomers. .75 (ddd, J = 8.5, 6.9, 1.6 Hz, 1H), 7.67 (ddd, J = 7.9, 7.0, 1.1 Hz, 1H), 7.53 (d, J = 3.9 Hz, 1H), 7.33 -7.28 (m, 2H), 7.08 (d, J = 3.9 Hz, 1H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] C NMR (76 MHz, CDCl3) δ = 150. 16, 138.26, 133.77, 133.74, 133.55, 133.32, 131.55, 130.66, 130.31, 129.36, 128.86, 128.17, 127.98, 127.79, 127.49, 127.18, 126.95, 126.58, 126.23, 125.69, 122.99, 120.26, 114.70, 107.28 ppm. HRMS (DCTB, M+) calcd for C25H15NS + 361.09274; found 361.09197. [1',2':5,6]phenanthro [3,4-b]thiophene-2-carbonitrile (6) In a 1L photochemical reactor, 5 (0.300 g, 0.83 mmol) was dissolved in toluene (650mL) and argon was bubbled through the mixture for about 10 min. Iodine (0.211 g, 0.83 mmol) and propylene oxide (2.9 mL, 41.5 mmol) were added, and the mixture was stirred overnight under irradiation from a 150W UV lamp. The mixture was then concentrated under vacuum, washed with a saturated aqueous solution of NaS2O3, dried over MgSO4, and finally the solvent removed under reduced pressure. The resulting crude was purified by column chromatography on silica gel with petroleum ether / ethyl acetate 95:5 as the eluent, affording 0.198 g (67% yield) of 6 as a white solid. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] H NMR (300 MHz, CDCl3) δ = 8.06 (d, J = 8.6 Hz, 1H), 8.02 -7.91 (m, 7H), 7.70 (d, J = 8.5 Hz, 1H), 7.41 (ddd, J = 7.8, 6.9, 1.0 Hz, 1H), 7.38 (dd, J = 7.0, 1.3 Hz, 1H), 7.11 (d, J = 0.4 Hz, 1H), 6.92 (ddd, J = 8.4, 7.0, 1.3 Hz, 1H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] [3,4-c]pyrrole-1,4-dione (7) In a three-neck flask, sodium metal (0.171 g, 7.42 mmol) was dissolved under argon atmosphere in refluxing tert-amyl alcohol (8 mL) with the help of few grains of FeCl3. Once all the sodium was completely dissolved, the temperature was lowered to 50 °C and 1 (0.470g, 1.86 mmol) dissolved in 4 mL of toluene was added to the stirred mixture. The temperature was raised to 130°C and di-tert-amyl succinate (0.959 g, 3.71 mmol) dissolved in tert-amyl alcohol (4 mL) was added dropwise over 18 h, letting the reaction to proceed overnight. The temperature was then lowered to 65 °C, 1 mL acetic acid was injected, and the mixture brought to reflux for 5 min before being finally cooled to rt. The resulting mixture was poured into 100 mL of MeOH. The precipitate was collected by filtration, washed with MeOH and Et2O, affording 0.192 g (35% yield) of 7 as a dark red powder which was used without further purification. [3,4-b]thiophen-2-yl)-2,5-dihydropyrrolo [3,4-c]pyrrole-1,4-dione (8) In a three-neck flask, sodium metal (0.237 g, 10.32 mmol) was dissolved under argon atmosphere in refluxing tert-amyl alcohol (10 mL) with the help of few grains of FeCl3. Once all the sodium was completely dissolved, the temperature was lowered to 50 °C and 4 (0.670 g, 2.58 mmol) dissolved in 5 mL of toluene was added to the stirred mixture. The temperature was raised to 130°C and di-tert-amyl succinate [START_REF] Humphreys | Solid state structure and properties of phenyl diketopyrrolopyrrole derivatives[END_REF] (1.335 g, 5.17 mmol) dissolved in tert-amyl alcohol (5 mL) was added dropwise over 18 h, letting the reaction to proceed overnight. The temperature was then lowered to 65 °C, 1 mL acetic acid was injected, and the mixture brought to reflux for 5 min before being finally cooled to rt. The resulting mixture was poured into 150 mL of MeOH. The precipitate was collected by filtration, washed with MeOH and Et2O, affording 0.400 g (52% yield) of 8 as a dark purple powder which was used without further purification.

Synthesis of naphtho

Synthesis of 3,6-bis(benzo[c]phenanthren-2-yl)-2,5-dihydropyrrolo

Synthesis of 3,6-bis(phenanthro

Synthesis of 3,6-bis(benzo[c]phenanthren-2-yl)-2,5-dimethyl-2,5-dihydropyrrolo[3,4-c]pyrrole-1,4dione (9)

Under argon atmosphere, 7 (0.160 g, 0.3 mmol) was dissolved in dry DMF (15 mL) with K2CO3 (0.188 g, 1.1 mmol), and stirred at 100°C for 30 min. The temperature was lowered to 60 °C, iodomethane (70 µL, 1.1 mmol) was injected, and the mixture stirred for 3h at 100°C. Once cooled back to rt, the mixture was poured into 150 mL of water, and the resulting precipitate was collected by filtration and washed with few mL of cold MeOH. The compound was purified by column chromatography on silica gel with dichloromethane as the eluent, affording 0.160 g (95% yield) of 9 as a dark red solid. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] H NMR (300 MHz, CDCl3) δ = 9.54 (s, 2H), 9.34 (d, J = 8.7 Hz, 2H), 8.11 (d, J = 0.9 Hz, 4H), 8.01 (dd, J = 7.9, 1.3 Hz, 2H), 7.93 (s, 4H), 7.93 (d, J = 8.5 Hz, 2H), 7.83 (d, J = 8.5 Hz, 2H), 7.78 (ddd, J = 8.3, 7.0, 1.3 Hz, 2H), 7.65 (ddd, J = 7.9, 7.0, 1.0 Hz, 2H), 3.50 (s, 6H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF] [3,4-c]pyrrole-1,4dione (10) Under argon atmosphere, 7 (0.070 g, 0.12 mmol) was dissolved in dry DMF (5 mL) with K2CO3 (0.164 g, 1.2 mmol), and stirred at 100 °C for 30 min. The temperature was lowered to 60 °C, benzyl bromide 140 µL, 1.2 mmol) was injected, and the mixture stirred for 3h at 100 °C. Once cooled back to rt, the mixture was poured into 50 mL of water, and the resulting precipitate was collected by filtration and washed with few mL of cold MeOH. The compound was purified by column chromatography on silica gel with dichloromethane as the eluent, affording 0.055 g (60% yield) of 10 as a dark red solid. [3,4-b]thiophen-2-yl)-2,5-dihydropyrrolo [3,4-c]pyrrole-1,4-dione (11) Under argon atmosphere, 8 (0.03 g, 0.05mmol) was dissolved in dry DMSO (5.0 mL) with K2CO3 (0.028 g, 0.2 mmol), and stirred at 140 °C for 45 min. The temperature was lowered to 60 °C, 1bromobutane (30 µL, 0.3 mmol) was injected, and the mixture refluxed for 5 h. Once cooled back to rt, the mixture was poured into 50 mL of water, and the resulting precipitate was collected by filtration and washed with few mL of cold MeOH. The compound was purified by column chromatography on silica gel with dichloromethane as the eluent, affording 0.008 g (22 % yield) of 11 as a dark purple solid. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] H NMR (499 MHz, CDCl3) δ = 10.52 (s, 2H), 9.69 (d, J = 8.5 Hz, 2H), 8.07 (d, J = 8.5 Hz, 2H), 8.02 (d, J = 8.0 Hz, 2H), 7.96 -7.92 (m, 4H), 7.90 (d, J = 8.6 Hz, 2H), 7.87 (d, J = 8.7 Hz, 2H), 7.72 (dd, J = 7.3 Hz, 2H), 4.37 -4.32 (m, 4H), 1.94 (tt, J = 7.5 Hz, 4H), 1.63 -1.54 (m, 4H), 0.88 (t, J = 7.5 Hz, 6H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF]

Synthesis of 3,6-bis(benzo

[c]phenanthren-2-yl)-2,5-dibenzyl-2,5-dihydropyrrolo

Synthesis of 2,5-dibutyl-3,6-bis(phenanthro

Synthesis of 3,6-bis(benzo[c]phenanthren-2-yl)-2,5-bis(1-phenylethyl)-2,5-dihydropyrrolo[3,4c]pyrrole-1,4-dione (12)

Under argon atmosphere, tributylphosphine (750µL, 3 mmol) was dissolved in dry THF (30mL) and the mixture cooled at 0 °C, then DIAD (600 µL, 3 mmol) was added dropwise resulting in a colourless solution. In a separate Schlenk tube, under argon atmosphere, 7 (0.010 g, 0.06 mmol) was dispersed in dry THF (3 mL) and the mixture cooled at 0 °C. 3.2 mL of the first solution containing the Bu3P/DIAD complex were added dropwise to the second solution resulting in a bright purple solution. At this point, (S)-1-phenyl-ethanol (37 µL, 0.3 mmol) dissolved in THF (1mL) was injected dropwise to the mixture over 2h. The mixture was then allowed to reach rt and kept under stirring overnight. The mixture was concentred under vacuum, diluted into CH2Cl2 and washed with 1M HCl, then water. The organic layer was dried over MgSO4 and the solvent removed under reduced pressure. The compound was purified by column chromatography on silica gel with petroleum ether / dichloromethane 2:8 as the eluent, affording 0.015 g (66% yield) of 12 as a red solid. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] H NMR (300 MHz, CDCl3) δ = 9.49 (s, 2H), 9.36 (d, J = 8.6 Hz, 2H), 8.09 (d, J = 8.4 Hz, 2H), 8.01 (dd, J = 7.9, 0.7 Hz, 2H), 7.95 (d, J = 7.1 Hz, 2H), 7.94 (s, 4H), 7.84 (d, J = 8.5 Hz, 2H), 7.76 (dd, J = 8.4, 1.4 Hz, 2H), 7.60 (t, J = 7.2 Hz, 2H), 7.41 (ddd, J = 7.1, 1.2 Hz, 2H), 7.37 -7.22 (m, 10H), 5.43 (q, J = 7.2 Hz, 2H), 1.99 (d, J = 7.1 Hz, 6H) ppm. [START_REF] Samuel | Ionic Charge Storage in Diketopyrrolopyrrole-Based Redox-Active Conjugated Polymers[END_REF]

CD and UV Measurements

CD and UV-Vis-NIR absorption spectra were recorded on a Jasco J-1500 CD spectrophotometer equipped with standard PMT detector (for the spectral range 180-800 nm) or InGaAs detector (800-1600 nm). All spectra were recorded at 20 °C in the transmission mode.

RESULTS AND DISCUSSION

Synthesis of DPP-helicenes

Aromatic nitriles are the key intermediates in the synthesis of DPP derivatives via the succinic method, with phenyl and thienyl derivatives being some of the most employed. [START_REF] Grzybowski | Diketopyrrolopyrroles: Synthesis, Reactivity, and Optical Properties[END_REF] The nature of the first aromatic ring connected to the bilactam core of the DPP is known to deeply impact the morphology and the spectroscopic properties of the resulting dye. Also, due to the lower steric hindrance of five-membered rings with respect to phenyl rings, cyanothiophenes usually give higher yields in the DPP synthesis. Moving from these premises, in order to include helicene moieties directly connected to the bilactam core of DPP, a series of helicenes with a terminal benzonitrile or a thienonitrile ring, including the 2-cyano-carbo [4]helicene (1) [START_REF] Kos | Oxidative Photocyclization of Aromatic Schiff Bases in Synthesis of Phenanthridines and Other Aza-PAHs[END_REF] , the 2cyanocarbo- [6]helicene (2), [START_REF] Moussa | Chiroptical Properties of Carbo[6]Helicene Derivatives Bearing Extended π-Conjugated Cyano Substituents[END_REF] the 2-cyano-thia [4]helicene (4), and the 2-cyano [6]thiahelicene (6), were prepared via a well-known two-steps procedure for sequential ortho-annulation. The compounds 1, [START_REF] Kos | Oxidative Photocyclization of Aromatic Schiff Bases in Synthesis of Phenanthridines and Other Aza-PAHs[END_REF] and 2 [START_REF] Moussa | Chiroptical Properties of Carbo[6]Helicene Derivatives Bearing Extended π-Conjugated Cyano Substituents[END_REF] were synthesized according to previously reported procedures.

Similarly, the thieno-fused compounds 4 and 6 were prepared starting from phosphonium salts: NaphCH2PPh3Br and H4CH2PPh3Br were first olefinated with formylthiophene-2carbonitrile under Wittig conditions, and then the resulting mixtures of E/Z diarylethenes were subjected to oxidative photocyclization in the Mallory conditions, [START_REF] Martin | Reactivity and Mechanistic Issues in the Photocyclization of Dihalostyryl-Naphthalenes towards Halo-[4]helicenes: A Transposition on a Mallory Theme[END_REF][START_REF] Mallory | Photochemistry of Stilbenes. III. Some Aspects of the Mechanism of Photocyclization to Phenanthrenes[END_REF] yielding the cyanothiahelicenes 4 and 6, respectively (Scheme 1). However, the subsequent condensation of these derivatives with succinic esters failed when performed in classical conditions, namely in sodium tert-amoxide/tert-amyl alcohol solutions. Indeed, this reaction tends to give lower yields as the electron-donating character and the steric hindrance increase within the aromatic reagent. Moreover, the cyano-helicenes showed poor solubility in tert-amyl alcohol (boiling point: 102°C). We therefore modified the protocol by dissolving the cyano-helicenes in hot toluene, and injecting the resulting solution into the hot reaction mixture, before starting the dropwise addition of the succinate ester. When cyanohelicenes 1 and 4 were used, a colour change from light brown to purple was observed few minutes after succinate addition, indicating the DPP formation. Conversely, cyano-helicenes 2 and 6 did not react, but were recovered almost quantitatively (Scheme 2). Under the assumption that toluene does not take part into the reaction mechanism due to its relatively high pka value, we presume that the increased reactivity of 1 and 4 under these conditions is to be ascribed to a better solubilization as well as to an increased reflux temperature (boiling point of toluene: 111 °C).

Scheme 2: Synthetic route to DPP-helicenes 7 and 8 via an optimized succinic method for DPP synthesis. The cyanohelicenes 2 and 6 did not react and were recovered almost quantitatively after work-up.

The lack of reactivity of 2 and 6 remains unexplained, and it is not clear if it has a steric or electronic origin, yet it seems to agree with the observed reduced reactivity of aromatic nitriles in reactions involving anionic nucleophiles, as the aromatic system becomes larger. [START_REF] Beldjoudi | Multifunctional Dithiadiazolyl Radicals: Fluorescence, Electroluminescence, and Photoconducting Behavior in Pyren-1 ′ -yldithiadiazolyl[END_REF] Due to the stereodynamic properties of [4]-helicenes, [START_REF] Ouyang | Chiral multifunctional molecules based on organometallic helicenes: Recent advances[END_REF] these derivatives required further modifications to become chiral. Achiral counterparts were synthesized by classical N-alkylation with alkyl or benzyl chains, for comparison. In details, the DPP 7 was alkylated with methyl groups and benzyl groups, yielding the dyes 9 and 10 respectively. Conversely, the DPP 8 gave the soluble derivative 11 upon N-alkylation with longer chains only, such as n-butyl chains (Scheme 3). Following our recently developed method for N-alkylation of DPP with chains bearing stereocenters at the alpha-position, [START_REF] Talamo | Straightforward N-alkylation of diketopyrrolopyrroles through the Mitsunobu reaction with benzyl, α-branched, and chiral alcohols[END_REF] we modified the DPP 7 with stereodefined 1-phenyl-ethyl chains, aiming at an effective chiral perturbation in compounds 12 (Scheme 4). The spectroscopic, chiroptical, and electrochemical properties of the resulting molecules were characterised.

Scheme 4: Enantioselective N-functionalization of DPP 7 via Mitsunobu reaction with enantiopure sec-phenethyl alcohols. As Walden inversion occurs during this type of reaction, the R,R enantiomer is from (S)-1-phenyl-ethanol, and vice versa.

Photophysical and chiroptical characterization

Helicene-DPPs 9, 10 and 12 in 10 -5 M chloroform solutions, show unresolved absorption bands peaking at 504 nm, 496 nm, and 494 nm, respectively. The resulting fluorescence spectra, measured under excitation at the wavelength of maximum absorption, exhibit large Stoke shifts (65 nm, 76 nm, and 58 nm respectively) and unresolved band structure. The large Stoke shifts indicate a significant flexibility of the chromophore scaffold that is able to dissipate a large part of the excitation energy via vibrational coupling. On the other hand, the thiahelicene-DPP 11 exhibited both absorption and emission spectra with evident vibronic structuration, and a relatively small Stoke shift of 15 nm, suggesting a more rigid molecular structure. Also, the intense bathochromic shift affecting the compound 11 compared to the carbohelicene-DPPs, of more than 100 nm, is coherent with a more planar conformation and a more efficient conjugation between the DPP core and the helicene (Figure 1). The two enantiomers (R,R) and (S,S) of the compound 12 in 10 -4 M THF solutions exhibited detectable mirror image circular dichroism (CD) activity, all over the UV-visible absorption region, which indicates that the chromophore is efficiently perturbed by the presence of the αchiral N-substituent. In THF, the low energy band at 475 nm corresponds to a gabs of +1.5*10 -4 , while the high energy bands peaking at 281 nm reach gabs of -2.5*10 -4 , for the RR enantiomer. In order to assess the impact of molecular chirality on the formation of stereodefinite aggregates and/or stereodefinite conformations stabilised upon aggregation, CD spectroscopy was performed on solutions of 12 in a series of binary mixtures of good and bad solvents, such as THF/H2O and CHCl3/MeOH. [START_REF] Resta | Consequences of Chirality on the Aggregation Behavior of Poly[2-methoxy-5-(2′-ethylhexyloxy)-pphenylenevinylene] (MEH-PPV)[END_REF][START_REF] Omar | Impact of chirality on the aggregation modes of l-phenylalanine-and d-glucose-decorated phenylene-thiophene oligomers[END_REF] It resulted that while the CD signature does not significantly evolve upon changing THF with a THF/water mixture in a 1:9 ratio (a bathochromic shift of 15 nm is observed only, Figure 2a), in CHCl3/MeOH mixtures, a slight evolution of the CD spectra is observed while increasing the methanol fraction: in pure chloroform the low energy band at 475 nm corresponds to a gabs of +1.7*10 -4 , for the RR enantiomer, and gradually increase up to +3.3*10 -4 in pure methanol, along with a slight bathochromic shift of 6 nm. Similarly, the band at 277 nm passes from a gabs of -1.1*10 -4 to -2.4*10 -4 , for the RR enantiomer, when the solvents changes from 100% chloroform to 100% methanol. Moreover, a signal peaking at 299 nm emerge upon increasing methanol fraction, going from negligible gabs in 100% chloroform up to -2.7*10 -4 in 100% methanol, for the RR enantiomer (Figure 2b). Films of (R,R)-12 and (S,S)-12 were prepared by spin coating 10 -3 M THF solutions onto glass slides (0.1 mL, 1000 rpm, 90 s), in order to study the solid state chiroptical properties of the resulting materials. The maximum absorption is red-shifted of around 15 nm with respect to solutions and the corresponding CD spectra show two large bands one with positive ellipticity at low energies, and negative at high energies, for the RR enantiomer. Upon thermal annealing (1h, 165 °C) the CD signals almost doubled in intensity, and the high energy band showed a marked evolution into a structured system (Figure 3a). In all the cases, the observed ECD is dominated by the intrinsic isotropic circular dichroism of molecular/supramolecular origin, since rotations around the optical axis or 180° flips of the sample did not produce any considerable variations in the ECD response. Interestingly, compounds 10 and 12 are emissive in the solid state as well (Fig. S18 and Fig. 3b), very likely thanks to the presence of the steric bulk benzyl and phenethyl groups which prevents the quenching due to - stacking between the DPP cores.

In conclusion, the synthetic strategy we adopted here for the chiral functionalization of the DPP core proves its efficiency, as the presence of stereogenic centres on the N-substituents in the position induces a chiral perturbation of the rest of the molecule, in spite of the dynamic chirality of the [4]helicene units, which is visible in the CD spectra in solution, in aggregates and in the thin films.

CONCLUSION

In summary, the synthesis of DPP-helicenes, with direct covalent link between the bilactam core and the helicene units, has been attempted for a series of four 2-cyano- [4] and [6](thia)helicenes. Only the corresponding bis- [4](thia)helicene-DPP 7 and 8 could be obtained and then engaged in N-alkylation reactions either by classical SN2 reaction or by the Mitsunobu strategy. The latter allowed the preparation of the enantiopure compounds (S,S)-12 and (R,R)-12 containing -stereogenic centers, while the former afforded the achiral compounds 9-11.

All the newly prepared DPP derivatives are luminescent in solution, while compounds 10 and 12 are emissive in the solid state as well. Particularly interesting are the chiroptical properties of the chiral DPP 12, which shows strong CD activity in solution and in the solid state, demonstrating that the presence of the N-phenethyl groups ensures a chiral perturbation of the entire molecule, in spite of the stereodynamic nature of the [4]helicene units. Further endeavour in this direction is devoted to the investigations of the CPL properties of such chiral DPP derivatives and to the understanding of their CD activity.

Z isomer 1 H

 1 NMR (300 MHz, CDCl3) δ = 9.04 (s, 1H), 8.84 (d, J = 8.4 Hz, 1H), 8.09 -7.99 (m, 2H), 7.95 -7.80 (m, 4H), 7.63 -7.55 (m, 3H), 7.40 (d, J = 2.5 Hz, 1H), 7.09 (d, J = 11.6 Hz, 1H), 7.00 (d, J = 2.5 Hz, 1H), 6.78 (s, J = 12.0 Hz, 1H) ppm. E isomer 1 H NMR (300 MHz, CDCl3) δ = 9.09 (s, 1H), 9.08 (d, J = 8.1 Hz, 1H), 8.05 (dd, J = 7.9, 1.5 Hz, 1H), 7.99 (d, J = 8.4 Hz, 1H), 7.92 (d, J = 8.5 Hz, 1H), 7.86 (d, J = 15.5 Hz, 1H), 7.83 (d, J = 15.6 Hz, 1H), 7.83 (d, J = 8.5 Hz, 1H), 7.78 (dd, J = 8.4, 1.5 Hz, 1H), 7

1 H

 1 NMR (300 MHz, CDCl3) δ = 9.53 (s, 2H), 9.26 (d, J = 9.0 Hz, 2H), 8.09 (d, J = 8.4 Hz, 2H), 8.00 (d, J = 9.3 Hz, 2H), 7.95 (d, J = 7.8 Hz, 2H), 7.94 (s, 4H), 7.84 (d, J = 8.6 Hz, 4H), 7.59 (ddd, J = 7.2, 1.4 Hz, 4H), 7.53 (ddd, J = 8.4, 7.1, 1.6 Hz, 2H), 7.23 -7.17 (m, 10H), 5.04 (s, 4H) ppm. HRMS (DCTB, M+) calcd for C56H36N2O2 + 768.27757; found 768.27713.

Scheme 1 :

 1 Scheme 1: Synthetic route to compounds 4 and 6, starting from (naphthalen-2-ylmethyl)triphenylphosphonium bromide (NaphCH2PPh3Br), and (benzo[c]phenanthren-2-ylmethyl)triphenylphosphonium bromide (H4CH2PPh3Br) respectively.

Scheme 3 :

 3 Scheme 3: N-alkylation of DPP-helicenes 7 and 8 via SN2 reaction with alkyl bromides, yielding the compounds 9, 10, and 11.

11 in 10 - 5 M12 in 10 - 5 MFigure 1 :

 1051051 Figure 1: Normalized absorption (dotted lines) and emission (solid lines) spectra of compounds 9 (a), 10 (b), 11 (c), and 12(d), in 10 -5 M chloroform solutions. The ε reported in each panel correspond to the molar extinction coefficient at the wavelength of maximum absorption, 𝝀 𝒎𝒂𝒙 𝒂𝒃𝒔 . The fluorescence spectra are measured under excitation at , 𝝀 𝒆𝒙𝒄 = , 𝝀 𝒎𝒂𝒙 𝒂𝒃𝒔 , on diluted solutions with absorbance of 0.1 in 1 cm wide cells, and the wavelength of maximum emission, 𝝀 𝒎𝒂𝒙 𝒆𝒎 is reported in each panel.

Figure 2 :

 2 Figure 2: Circular dichroism spectra of the RR and SS enantiomers of compound 12, in different solutions: a) each enantiomer is dissolved into THF (solid lines) or a mixture of THF/water (dotted lines) at a concentration of 10 -4 M; b) the RR enantiomer is dissolved at concentration of 10 -5 M in a series of chloroform/methanol mixtures with CHCl3/MeoH ratio of 10:0 (purple line), 7:3 (dark blue line), 4:6 (blue line), 1:9 (cyan line), 0:10 (green line). The average ε of the enantiomeric pair is shown in both panel as underlying gray area.

Figure 3 :

 3 Figure 3: a) circular dichroism spectra of the RR and SS enantiomers of compound 12, in dropcasted films, before (solid lines) and after (dotted lines) thermal annealing at 165°C for 1h (the normalized absorbance is shown as underlying gray area); b) photoluminescence spectrum (red line) of compound 12 in dropcasted film on glass, under excitation at 𝝀 𝒆𝒙𝒄 = 508 nm (the emission has a peak at 𝝀 𝒎𝒂𝒙 𝒆𝒎 = 573 nm, and the absolute fluorescence quantum yield is measured as 10%).

  H NMR (300 MHz, CDCl3) δ = 8.95 (s, 1H), 8.80 -8.75 (m, 1H), 7.98 (dd, J = 7.2, 2.2 Hz, 1H), 7.90 (s, 2H), 7.84 (d, J = 8.7 Hz, 1H), 7.78 (d, J = 8.7 Hz, 1H), 7.75 -7.63 (m, 2H) ppm. 13 C NMR (76 MHz, CDCl3) δ = 142.53, 136.38, 133.26, 133.12, 130.85, 129.71, 129.62, 129.14, 127.80, 127.22, 127.02, 127.01, 126.89, 125.91, 120.64, 115.00, 109.15 ppm. HRMS (DCTB, M+) calcd for C17H9NS + 259.04510; found 259.04502.

  C NMR (76 MHz, CDCl3) δ = 140.45, 137.27, 133.99, 133.19, 132.28, 132.03, 130.91, 129.80, 128.97, 128.58, 128.57, 128.34, 127.50, 127.41, 127.18, 127.07, 126.94, 126.47, 126.20, 125.52, 124.15, 120.90, 114.60, 106.34 ppm.

  C NMR (76 MHz, CDCl3) δ = 162.97, 149.06, 134.79, 133.66, 131.51, 130.12, 130.09, 129.49, 129.19, 129.17, 129.14, 128.60, 128.57, 128.30, 127.92, 127.10, 126.72, 126.47, 125.87, 125.77, 110.06, 29.89 ppm. HRMS (DCTB, M+) calcd for C44H28N2O2 + 616.21344; found 616.21453.

  C NMR (126 MHz, CDCl3) δ = 164.93, 145.93, 143.88, 137.02, 134.24, 132.24, 132.23, 131.96, 131.89, 131.74, 131.42, 130.75, 130.54, 130.50, 130.34, 130.11, 129.94, 123.88, 102.90, 49.14, 32.79, 24.75, 16.88 ppm. HRMS (DCTB, M+) calcd for C46H36N2O2S2 + 712.22217; found 712.22127.

  C NMR (76 MHz, CDCl3) δ = 163.19, 149.85, 141.43, 134.72, 133.50, 131.47, 130.34, 130.12, 129.86, 129.14, 129.06, 128.84, 128.62, 128.37, 127.90, 127.28, 127.24, 127.03, 126.88, 126.63, 126.35, 125.77, 125.23, 111.22, 53.75, 18.64.

	HRMS (DCTB, M+) calcd for C58H40N2O2 + 796.30710; found 796.30843.

ACKNOWLEDGMENTS

The authors thank the CNRS, the University of Angers and the RFI Regional project LUMOMAT (grant to M.M.T., project HEROES). Ingrid Freuze (University of Angers) is gratefully acknowledged for MS characterization,

DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding authors upon reasonable request.