Sarah Touhami
email: stouhami@laplace.univ-tlse.fr

Amal Zeaiter
email: amal.zeaiter@ensma.fr

Matthieu Fénot
email: matthieu.fenot@ensma.fr

Yvan Lefevre
email: lefevre@laplace.univ-tlse.fr

Jean-François Llibre
email: jean-francois.llibre@laplace.univ-tlse.fr

Etienne Videcoq
email: etienne.videcoq@ensma.fr

Electro-thermal Models and Design Approach for High Specific Power Electric Motor for Hybrid Aircraft

Keywords: Lumped Parameter Thermal Model, cooling system, target setting tool, permanent magnet synchronous motor

This paper presents electro-thermal models for sizing the electric motors with their cooling system for Hybrid Aircraft Propulsion. A design approach is proposed to reach high specific powers. An electric motor is sized using tools based on loadability concepts. Its performances are validated by Finite Element Analysis. Cooling system is sized based on adapted hydraulic calculations and temperatures are verified using Lumped Parameter Thermal Model.

INTRODUCTION

Hybrid aircraft propulsion coupling gas turbines (or turbojet engines) and electric motors is thought to be an interesting way to reduce fuel consumption and CO2 emissions. To keep as low as possible the weight of hybrid aircraft propulsion chain [START_REF]Power trip: HASTECS energizes the path to hybrid-powered flight[END_REF], mechanical, electrical and magnetic loads linked to the materials used in electric motor must be increased [START_REF] Pyrhönen | Design of rotating electrical machines[END_REF]. Nevertheless, higher loads lead to higher losses and lower efficiency of electric motor. Losses increase results in higher temperature in the motor. Since the properties of some materials used in electric motor are sensitive to temperature, an adequate choice of loads should be done to reach high specific power. In addition, extraction and evacuation of the high heat generation due to losses in small zones are serious issues. This requires using complex and specific high performance cooling system while considering its integration in the environment of the aircraft. If several studies [START_REF] Nategh | Evaluation of Impregnation Materials for Thermal Management of Liquid-Cooled Electric Machines[END_REF][START_REF] Assaad | Thermal Design Optimization of Electric Machines Using a Global Sensitivity Analysis[END_REF][START_REF] Pyrhönen | Heat-transfer improvements in an axial-flux permanent-magnet synchronous machine[END_REF][START_REF] Galea | A Thermal Improvement Technique for the Phase Windings of Electrical Machines[END_REF][START_REF] Madonna | Improved Thermal Management and Analysis for Stator End-Windings of Electrical Machines[END_REF][START_REF] Putra | Electric motor thermal management system using L-shaped flat heat pipes[END_REF][START_REF] Tighe | Assessment of cooling methods for increased power density in electrical machines[END_REF] have already dealt with thermal modeling of electric motors, very few have taken into account all the cooling system components including heat exchanger size and design, hydraulic circuit, and pump characteristics in particular in such a restrictive aircraft environment. This paper presents electro-thermal models developed to design the high specific power electric motor with its cooling system based on a pertinent choice of technologies. A Target Setting Tool (TST) model is developed to assess the technological choices. Then, a Surface Mounted-Permanent Magnet Synchronous Motor (SM-PMSM) model is set up to size accurately the electric motor. These electromagnetic models are validated by Finite Element Analysis. Based on the sizes and characteristics of the electric motor, a Lumped Parameter Thermal Model (LPTM) that takes into account the cooling system, the hydraulic circuits and the heat exchanger with the environment, assesses the motor dynamic thermal behavior considering aircraft mission and its surrounding external conditions during the flight. A strong interaction between these models is performed to minimize the total weight of the electric motor including its cooling system and maximize its overall specific power. Section 2 is devoted to loads of an electric motor. Issues and limitations of increasing specific power of electric motor are detailed in Section 3. In section 4, the electro-thermal models for sizing electric motor with its cooling system are described. Section 5 focuses on sizing the aircraft propulsion electric motor with its cooling system, and eventually several technological solutions are listed in Section 6 for further improvement of specific power of the designed electric motor.

LOADS OF AN ELECTRIC MOTOR

Loadability concepts have been developed from the experience of electric machine designers [START_REF] Pyrhönen | Design of rotating electrical machines[END_REF]. They characterize the performances and the technological levels of the motor. Magnetic load characterizes the magnetic flux density in airgap Bm allowed by the soft and hard magnetic materials. Electric load indicates the surface current density in airgap Km allowed by the insulation materials and the cooling technology. The combination of electric load and magnetic load indicates the allowed tangential stress in airgap σt. Table 1 gives an idea of the allowed values of electromagnetic loads and their limits (minimum, average and maximum) for low rotational speed non-salient synchronous machine according to cooling technology. Theses allowed values are given considering only Joule losses. Mechanical load characterizes the rotational speed Ω allowed by mechanical properties of rotor materials.

ISSUES AND LIMITATIONS OF INSCREASING SPECIFIC POWER OF ELECTRIC MOTOR

WITH ITS COOLING SYSTEM In electric motors, tangential stress level in airgap quantifies the electromagnetic torque as expressed in Equation 1. Increasing rotational speed allows decreasing rotor volume and thus its weight. Simultaneously, it leads to increase iron, Joule and mechanical losses (cf. Equations 2 to 5) and thus temperatures. Usually, thermal lifetime of insulation materials is reduced by half for every increasing of 10°C above its thermal class as shown in Equation 6. Polarization Br and coercive field Hc of hard magnet decrease as temperature increases (cf. Equation 7). Increasing electric load may lead also to irreversibly demagnetization risk of hard magnetic materials. Most of insulation materials used in electric motors are thermally very bad conductors. The evacuation of the heat generated due to losses through winding insulation is the main limitation for increasing specific power of electric motors.

𝑇 𝑒𝑚 = 𝑃 𝑒𝑚 Ω = 𝐾 𝑚 𝐵 𝑚 𝑉 𝑟 = 2𝜎 𝑡 𝑉 𝑟 (1)
where Pem and Tem are the electromagnetic power and torque, Ω is the rotational speed, Vr is the rotor volume, k, α and β are the coefficients of iron losses, γ is the coefficient of windage losses, R is the resistance function of resistivity ρcu (T) and rotational speed, Pi is the iron losses, Pj is the Joule losses, Pw is the windage losses, Pf is the friction losses.

𝑡 life = 𝐺 exp(𝐻/𝑇) (6)
{ 𝐵 𝑟 = 𝐵 𝑟20°( 1 + 𝛼 𝐵 100 (𝑇 -20°)) 𝐻 𝑐 = 𝐻 𝑐20°( 1 + 𝛼 𝐻 100 (𝑇 -20°)) (7)
where 𝑡 life is thermal life time of the insulator, 𝐺 and 𝐻 are insulator constants and T is the temperature. 𝐵 𝑟20° and 𝐻 𝑐20° are respectively polarization and coercive field at 20°C, and 𝛼 𝐵 < 0 and 𝛼 𝐻 < 0 are temperature constants in (%/°C).

ELECTRO-THERMAL MODELS AND SIZING APPROACH OF ELECTRIC MOTOR WITH ITS COOLING SYSTEM

Assessment of electric motor technologies: Target Setting Tool

Target Setting Tool "TST" is an assessment tool of electric motor technologies. It uses the loadability concepts and the analytical model of ideal sinewave synchronous motor [START_REF] Lefevre | Performance assessment tool based on loadability concepts[END_REF][START_REF] Touhami | Joint design of Halbach Segmented Array and Distributed Stator Winding[END_REF][START_REF] Collin | Design of Electric Machine Taking into Account the Partial Discharges Phenomena for Future Hybrid Propelled Aircrafts[END_REF]. TST assesses the specific power of electric motor from chosen loads linked to materials and from geometrical choices. Indeed, this tool helps to identify the most promising technological levels allowing achieving targeted specific power. Moreover, it allows making a quick tradeoff on specific power from very few data. TST takes as inputs:

-Specification: Mechanical power -Loads: magnetic, mechanical, electrical and thermal -Geometrical and material choices TST gives as outputs:

-The main sizes of radial flux non-salient electric motor (cf. Figure 1) -Approximate weight -Approximate losses -Approximate specific power of electric motor Equations 8 to 12 express the calculation of main sizes implemented in TST.

𝑅 = √ 𝜆𝑃 𝑒𝑚 4𝜋Ω𝜎 𝑡 3 ( 8
)
𝐿 𝑚 = 2𝑅 𝜆 (9)
ℎ 𝑦 = 𝑅𝐵 𝑚 𝑝𝐵 𝑦 ( 10
)
ℎ 𝑠 = 𝜋𝐴 𝑟𝑚𝑠 𝑘 𝑓𝑖𝑙𝑙 𝑗 𝑟𝑚𝑠 (𝜋- 2𝐵 𝑚 𝐵 𝑡 ) ( 11
)
𝑅 𝑜𝑢𝑡 = 𝑅 + ℎ 𝑦 + ℎ 𝑠 ( 12
)
Where R is the inner stator radius, Rout is the outer stator radius, Lm is the active length, λ is the shape coefficient, p is the pole pairs, By is the flux density in stator yoke with hy as height, Bt is the flux density in stator tooth with, kfill is the fill factor.

ℎ 𝑟𝑦 = 𝐵 𝑦 𝐵 𝑦𝑟 ℎ 𝑦 ( 13
)
𝑅 𝑠ℎ = 𝑅 -𝑒 𝑝𝑚 -ℎ 𝑟𝑦 ( 14
)
𝑙 𝑡 = 4𝐵 𝑚 𝑅 𝐵 𝑡 𝑁 𝑠 (15)
𝑙 𝑠 = 2𝜋𝑅 𝑁 𝑠 -𝑙 𝑡 (16)
where 𝐵 𝑦𝑟 is the flux density in rotor and 𝑁 𝑠 is the number of slots. It consists in creating a nodal network for a given system (the electric motor in this case) by discretizing it into finite volumes Vi. Each volume of this network is represented by a node and by some characteristics: mainly thermal capacities, heat sources, densities and thermal conductivities. Connections between nodes are set to define heat transfer occurring between volumes of these nodes. Through these conductance components, heat paths are made. They determine heat fluxes inside the motor resulting from conduction, convection or radiation heat transfer modes. In our case, according to [START_REF] Boglietti | Evaluation of radiation thermal resistances in industrial motors[END_REF], radiation phenomenon has been neglected. Based on series of coupled equations including Newton's law of cooling for convection heat transfer and Fourier's law for conduction heat transfer in addition to the mass transport term of advection for fluid nodes, the system model can be elaborated. These equations and assumptions allow writing the thermal energy balance as a first order linear differential equation of temperature Ti to which the boundary conditions were integrated. It is represented as in Equation 17.

𝐶 𝑖 𝑑𝑇 𝑖 𝑑𝑡 = ∑ 𝐺 𝑖𝑗 (𝑇 𝑗 -𝑇 𝑖 ) + 𝑄 𝑖 j,𝑖≠𝑗 (17)
Where Ci [J/K] is the heat capacity, Gij [W/K] is the thermal conductance connecting nodes i to j which is the ratio of heat flux Φij [W] (from i to j) to the temperature difference between (i and j) ∆Tij LPTM is simulated on MATLAB software and can be adapted to the motor dimensions to allow predicting motor temperatures.

Sizing of Cooling System

The cooling system of the electric motor designed to achieve high specific power densities consists in liquid forced cooling. In the stator, it is similar to that of Totally Enclosed Water Cooled (TEWC) machines. Sizing a liquid cooling circuit relies mainly on hydraulic calculations based on thermal requirements. Such calculations allow the estimation of the pumping power needed for the liquid circulation in motor channels and heat exchanger. They are performed correspondingly to the heat dissipation in the motor, and are useful to determine the cooling system weight that should be added to the bare motor weight to find the value of the specific power density. In order to carry out the design study of the complete cooling system of the machine, it would be convenient to begin with choosing the coolant and then setting its main thermal and physical parameters, and finally finding the heat transfer coefficients representing exchange of thermal energy between the fluid and the channel. These coefficients are determined based on Equations 18-21, that imply the calculation of dimensionless numbers (Nusselt, Prandtl and Reynolds numbers) for specified liquid channel geometry (mainly channel hydraulic diameter Dh)

𝑁𝑢 𝐷 ℎ = 𝑓 8 (𝑅𝑒 𝐷 ℎ -1000)𝑃𝑟 1+12.7√ 𝑓 8 (𝑃𝑟 2/3 -1) (18)
𝑃𝑟 = 𝑐 𝑝 𝜇 𝜆 𝑓𝑙𝑢𝑖𝑑 (19)
𝑅𝑒 𝐷 ℎ = 𝜌𝑢𝐷 ℎ 𝜇 ( 20
)
𝑁𝑢 𝐷 ℎ = ℎ𝐷 ℎ 𝜆 𝑓𝑙𝑢𝑖𝑑 (21)
Then, the hydraulic losses are determined using Equations 22-25 to find the pump head.

 Major losses:

𝐻 𝑀 = 𝐾 𝑝𝑖𝑝𝑒 𝑉 𝑝𝑖𝑝𝑒 2 2𝑔 (22)
 Major losses coefficient:

𝐾 𝑝𝑖𝑝𝑒 = 𝑓 𝑝𝑖𝑝𝑒 𝐿 𝑝𝑖𝑝𝑒 𝑑 𝑝𝑖𝑝𝑒,𝑖𝑛𝑡 (23)
 Friction coefficient:

𝑓 𝑝𝑖𝑝𝑒 = 1 [ln( 𝑘 3.7𝑑 𝑝𝑖𝑝𝑒,𝑖𝑛𝑡 ) +( 5.74 𝑅𝑒 𝑝𝑖𝑝𝑒 ) 0.9 ] 2 (24)
Where dpipe,int is the internal diameter of the pipe, Lpipe is the total pipe length, g is the gravitational acceleration, and k is the channel roughness coefficient.

 Minor losses:

𝐻 𝑚 = 𝐾 𝐿 𝑉 𝑝𝑖𝑝𝑒 2 2𝑔 (25)
Minor losses coefficient KL depends on the included hydraulic components, their geometries and the flow type. Hydraulic components might be elbows, tees, valves, and others. Nomographs and tables in this case provide the coefficients of these components.

Finally, pump power is computed based on pump head and liquid flow rate considering the pump efficiency ηpump as in Equations 26-29.

 Pump head:

𝐻 𝑝𝑢𝑚𝑝 = 𝐻 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 + 𝐻 𝑠𝑡𝑎𝑡𝑖𝑐 (26)  Dynamic head:

𝐻 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 = 𝐻 𝑚 + 𝐻 𝑀 (27)  Static head: 𝐻 𝑠𝑡𝑎𝑡𝑖𝑐 = 0 (28)  Pump power: 𝑃 𝑝𝑢𝑚𝑝 = 𝑞𝑔𝜌 𝑓𝑙𝑢𝑖𝑑 𝜂 𝑝𝑢𝑚𝑝 𝐻 𝑝𝑢𝑚𝑝 (29)
With data obtained from this procedure, all components weights are determined based on their properties and to find pump weight some catalogs are needed.

Sizing approach

Sizing both the electric motor and its cooling system in order to reach high specific power is complex to carry out, given that several inputs are needed. For this purpose, a sizing approach using the electro-thermal models are proposed to overtake this existing complexity. To avoid exceeding the thermal limits of electric motors, a thermal constraint is introduced in the sizing procedure. This constraint is based on current density product which depends only on the effectiveness of cooling system. Then an equivalent current density product 𝐴𝑗 𝑒𝑞 is calculated to take into account all losses:

< 𝐴𝑗 𝑒𝑞 >= 𝑃 𝑖 +𝑃 𝑗 +𝑃 𝑤 +𝑃 𝑓 2𝜋𝑅𝐿 𝑚 𝜌 𝑐𝑢 (𝑇)𝑘 𝑡𝑏 ( 30
)
Where ktb is the end-winding coefficient. Ajeq should be lower than the permitted values (cf. Table 1) according to the chosen cooling method. Figure 3 shows the sizing procedure.

It consists of six steps:

 Step 1: assess the electric motor technologies required to reach high specific power using TST.  Step 2: size surface mounted permanent magnet synchronous motor using SM-PMSM tool.  Step 3: check thermal constraint according to cooling method chosen in step 1.

 Step 4: assess the temperature inside electric motor.  Step 5: size cooling system.  Step 6: assess the total weight.

SIZING OF HIGH SPECIFIC POWER ELECTRIC MOTOR WITH ITS COOLING SYSTEM 5.1. Specification and aeronautical propulsion environment

The mechanical power and rotational speed of one propeller of Hybrid Electric Aircraft is presented in Figure 4.

Sizing point of electric motor is chosen in the Take-off phase, assuming that it should provide the highest power 1 . Electric motor and its cooling system are sized to reach specific power of 5kW/kg with efficiency higher than 96% in the Take-off flight phase.

Figure 3: Interaction between Electro-thermal models for sizing high specific electric motor with its cooling system

1 For confidentiality reason, exact power value will not be provided

High specific power electric motor sizing

To reach a specific power of 5kW/kg some choices in the technological levels of materials and the cooling method are made in the electro-thermal models:  Using Vacoflux 48 with thickness of 0.35mm for stator and rotor yokes given that it has the highest flux density in electrical sheets and lower specific iron losses as shown in Figure 5;  Using SmCo permanent magnet given that it is less sensitive to the temperature than NdFeB permanent magnet as illustrated in Figure 6;  Halbach segmented permanent magnet to ensure sinewave airgap flux density as presented in Figure 7. In addition, axial segmentation of PM reduces eddy current losses;  Using insulation materials with 220°C thermal class;  Using twisted strands (cf. Figure 8) in order to reduce Joule losses resulting in less skin and proximity effects;  Using external cooling technology for stator and inner cooling technology for shaft given that no partial discharge are allowed in winding as shown in Figure 9. The assessed loads, materials and geometrical choices using TST to achieve targeted specific power are summarized in Table 2. Table 3 summarizes the main sizes, estimated losses and weight of electric motor given by TST. Parameters of winding and rotor configurations chosen for SM-PMSM are given in Table 4. Sizes, weight and losses of surface mounted permanent magnet synchronous motor are grouped in Table 5. Losses and equivalent current density product profiles for operating at maximum torque are illustrated in Figure 10. Sizing using TST and SM-PMSM is validated using Finite Element Analysis as presented in Figure 11. Table 2: Loads, materials and geometrical choices assessed using TST to achieve targeted specific power Rotor yoke height "hry"

[mm] 29.72

Shaft radius "Rsh"

[mm] 50.98

Motor length

[mm] 538.6

End winding coefficient (according to winding configuration) "ktb" -1.69

Weight of SM-PMSM (without frame)

[kg] 236.5

Losses

--Joule losses "Pj"

[W] 7213

Iron losses "Pi"

[W] 3621

Total windage losses "Pw"

[W] 1837

Friction losses "Pf"

[W] 670

Thermal constraint: <Ajeq> (without armature reaction)

[A².m -3 ] 1.521×10 12

Specific power of SM-PMSM

[kW.kg -1 ] 6.03

Table 5: Sizes, weight and losses given by SM-PMSM Tool

Cooling system design

Considering the motor design parameters obtained, and its losses profiles, a thermal nodal network have been defined to represent the motor and the cooling system (Figure 12). In the motor structure and along the shaft axis, there are three identical radial sections to assess the evolution of motor and liquid temperatures in different machine zones, according to the fluid flow direction. Shaft and frame are assigned some axial and radial nodes connected to cooling medium, in turn represented by fluid nodes. The radial section and connections in the motor structure are detailed in [START_REF] Zeaiter | Thermal Sensitivity Analysis of a High Power Density Electric Motor for Aeronautical Application[END_REF]. The cooling system is based on a liquid water-glycol circuit. The water-glycol coolant extracts the heat flux produced in the motor by circulating in an annular channel around the stator and in an axial channel at the center of rotor shaft. Then the liquid is conducted into the heat exchanger allowing the evacuation of the heat into the outside air around the plane. Figure 12 shows nodes' locations 1 to 57 with axial and motor-end connections. In a practical approach, the heat exchanger in this case is a pipe embedded at the surface of a cold plate corresponding to the nacelle containing the motor. This nacelle has a total surface of 2.3 m² and the pipe diameter equals 4.5 cm with 1 mm of thickness. In the thermal model, a set of parameters and hypotheses are used for channels' characterization. The adopted parameters of the stator and shaft channels in the motor are given in Table 6.

The total flow rate of the coolant circulation and the coolant properties are used in order to determine the hydraulic losses and the pump power according to Equations 22-29. Some additional properties are needed for calculations including physical and geometrical characteristics of the pipe and plate. These properties include components thicknesses and material choices. They depend on the flow rate, coolant pressure, application and the provider's options. A group of these parameters is found in Table 7 for applied calculations, where the value of the pipe and channels roughness is: k=3.10 -4 . The total weight can now be determined as the sum of the weights of motor, pipe, heat exchanger, coolant and pumping system, considering a pump efficiency of around 60% (η=0.6).

Zone

In Parker Pump and Motor Division [16] an adequate pump is chosen for this application weighing no more than 14 kg. An example of adequate pump properties are given in Table 8. Coolant weight depends on the coolant choice. For water-glycol, the estimated liquid in channels and heat exchanger weighs around 31 kg. Resulting temperatures evolution in motor are depicted in Figure 13 according to the mission profile given in Figure 4. It shows the positions of the nodes and the conductance connections. In this figure, T coolant outlet is the outlet cooling temperature of the coolant (node 53), T stator corresponds to node 12.

Pump

T teeth is the temperature at node 35. Stator windings hottest point (T windings) is at the middle section and is given at node 34. The rear-end nodes of the motor have higher temperatures than front motor side, so the highest temperature of end-windings is given at node 13 (T end-windings in the figure). Finally, rotor temperatures, T pm of permanent magnet and T rotor of iron structure, are given at nodes 14 and 15.

Temperatures at the end-winding hot-spot zone remain below the thermal limits with the adopted cooling techniques for the chosen winding impregnation thermal class.

TECHNOLOGICAL SOLUTIONS TO EXCEED TARGETED SPECIFIC POWER

Several technological solutions have been proposed. They allow to double achieved specific power. Some of them are under research and some of them are marketed such as:  High energy and high temperature Grain Boundary Diffusion (GBD) Neodymium Iron Boron permanent magnet "GBD NdFeB".  Inorganic insulation materials (class 240°C). Using inorganic insulation materials allow increasing current density and frequency levels.  Carbon fiber sleeves with high permissible stresses allow peripheral speeds higher than 150m/s.  Very thin electrical sheets to reduce Iron losses. Their thickness down to 50µm.  Litz wires to reduce winding losses at very high frequency.  Bring the liquid coolant closer to the winding using small pipe embedded at the periphery of the windings.

CONCLUSION

The electro-thermal models developed in this paper are devoted for sizing high specific power electric motor with its cooling system. Target Setting Tool is used to assess the technologies and to make quick trade off on specific power. SM-PMSM Tool is used to calculate accurately the sizes and the losses of the electric motor. LPTM nodal network for electric motor and its associated cooling system is used to predict motor temperatures. In this model the cooling system design is integrated. Details on sizing of the cooling system hydraulic circuit are presented. Calculations are applied on the conceived high specific power electric motor in the frame of a hybridelectric propulsion.

Figure 1 :

 1 Figure 1: Main sizes given by TST

Figure 2 :

 2 Figure 2: Sizes given by SM-PMSM Tool 4.3. Lumped Parameter Thermal Model The thermal model is created based on Lumped Parameter Thermal Modeling (LPTM) method.It consists in creating a nodal network for a given system (the electric motor in this case) by discretizing it into finite volumes Vi. Each volume of this network is represented by a node and by some characteristics: mainly thermal capacities, heat sources, densities and thermal conductivities. Connections between nodes are set to define heat transfer occurring between volumes of these nodes. Through these conductance components, heat paths are made. They determine heat fluxes inside the motor resulting from conduction, convection or radiation heat transfer modes. In our case, according to[START_REF] Boglietti | Evaluation of radiation thermal resistances in industrial motors[END_REF], radiation phenomenon has been neglected. Based on series of coupled equations including Newton's law of cooling for convection heat transfer and Fourier's law for conduction heat transfer in addition to the mass transport term of advection for fluid nodes, the system model can be elaborated. These equations and assumptions allow writing the thermal energy balance as a first order linear differential equation of temperature Ti to which the boundary conditions were integrated. It is represented as in Equation17.

  [K] inducing this heat: 𝐺 𝑖𝑗 = 𝛷 𝑖𝑗 /𝛥𝑇 𝑖𝑗 . 𝑄 ̇𝑖 [W] is the total heat production in volume Vi. The thermal conductance expressions used in this model according to the heat transfer mode are as follows:  𝐺 𝑖𝑗 𝑐𝑜𝑛𝑑,𝑎𝑥𝑖𝑎𝑙 = 𝜆 𝑆 𝑖𝑗 𝐿 𝑖𝑗 for axial conduction  𝐺 𝑖𝑗 𝑐𝑜𝑛𝑑,radial = 2𝜋 𝜆 𝐻 𝑧 𝑙𝑛 (𝑟 𝑗 /𝑟 𝑖 ) for radial conduction  𝐺 𝑆 𝑖 𝑐𝑜𝑛𝑣 = ℎ 𝑆 𝑖 for convection  𝐺 𝑖𝑗 𝑓 = 𝑚̇ 𝑐 𝑝 for fluidic transport heat transfer Where λ is the thermal conductivity of the medium [W/(mK)], Sij is the surface of heat transfer between volumes represented by nodes i and j [m 2 ], Lij is the distance between nodes i and j [m], Hz is the height of the cylindrical object [m], Si is the surface of exposition to convection [m 2 ], 𝑚̇ is the fluid flow rate [kg/s], cp is the specific heat [J/(kg K)].

Figure 4 .

 4 Figure 4. Mechanical power and rotational speed of propeller vs time

Figure 5 :Figure 6 :

 56 Figure 5: Comparison between electrical steels

Figure 7 :Figure 8 :Figure 9 :

 789 Figure 7: (a) Halbach segmented permanent magnet, (b) Airgap flux density

Figure 10 :

 10 Figure 10: Losses profiles vs time

Figure 11 :

 11 Figure 11: Electromagnetic torque validation

Figure 12 :

 12 Figure 12: Axial and ortho-radial sections of half SM-PMSM electric motor including its cooling system with LPTM nodes locations, and axial and motor-end connections.

Figure 13 :

 13 Figure 13: Temperature evolution during flight mission in the designed high specific power electric motor.

  12

Table 1 :

 1 (*) is the current density, (**) is the linear surface current density permitted values of electromagnetic loads for non-salient synchronous machine according to cooling technology[START_REF] Pyrhönen | Design of rotating electrical machines[END_REF]

Table 3 :

 3 Main sizes, weight and specific power of electric motor given by TST

	Main Sizes	Unit	Value
	Stator yoke height "hs"	[mm]	34.29
	Teeth and slot heights "ht"	[mm]	36.11
	Inner stator radius "R"	[mm]	91.23
	Airgap thickness	[mm]	1.53
	Active length "Lm"	[mm]	317.33
	Assessed electric motor weight	[kg]	206
	(without frame)
	Assessed losses
	Joule losses "Pj"	[W]	5961
	Iron losses "Pi"	[W]	3621
	Total windage losses "Pw"	[W]	1461
	Friction losses "Pf"	[W]	278
	Winding configuration
	Number of phases "q"	-	3
	Number of slots "Ns"	-	24
	Rotor configuration
	Polarization of PM (SmCo)	[T]	1.16
	Flux density in rotor yoke "Byr"	[T]	1.4

Table 4 :

 4 Winding and rotor configurations chosen in SM-PMSM Tool

	Sizes	Unit	Value
	Tooth width "lt"	[mm]	10.58
	Slot width "ls"	[mm]	13.48
	Airgap thickness	[mm]	1.53
	Permanent magnet thickness "epm"	[mm]	9.00

Table 6 :

 6 Parameters for cooling system circuit.

			Unit	Stator Shaft
	Coolant		-	Water-Glycol
	Coolant density ρ	[kg.m -3 ]	1065
	Coolant conductivity λfluid thermal	[W.m -1 K -1 ]	0.3937
	Coolant specific heat cp	[J.kg -1 .K -1 ]	3361
	Coolant viscosity µ	dynamic	[kg.m -1 .s -1 ]	2.2564×10 -3
	Hydraulic diameter Dh	[mm]	45	16
	Flow rate q		[m 3 .s -1 ] 4.2×10 -3 10 -4
	Convection coefficient	[W.m -2 K -1 ] 3900	1000
	Component	Unit	Pipe Plate
	Material	-	Aluminum
	Material density ρ	[kg.m -3 ]		2699
	Material thermal	[W.m -1 .K -1 ]	200
	conductivity λ
	Material specific heat cp	[J.kg -1 .K -1 ]	900
	Thickness		[mm]	1	3
	Weight		[kg]	3.25 25

Table 7 :

 7 Pipe and plate properties-Heat Exchanger.

Table 8 :

 8 Pump properties from [16].

	Normal Operating Pressure	[bars]	206
	Maximum Speed	[rpm]	3646
	Length	[cm]	26.16
	Height	[cm]	21.84
	Width	[cm]	17.27
	Weight	[kg]	14

ACKNOWLEDGEMENT

This project has received funding from the Clean Sky 2 Joint Undertaking under the European Union's Horizon 2020 research and innovation program under grant agreement No 715483.


A Guzik

M Gronowski

M Turowski
email: mturowski@protonmail.com

Jean-Claude Guillemin

R Kolos

J.-C Guillemin

R Kołos

Photoisomerization of IC 3 N. An experimental and theoretical study

Keywords: photochemistry, cyanoacetylenes, matrix isolation, IR spectroscopy, computational chemistry

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The direct motivation for this study stems from a larger project devoted to the photochemistry of small alkynylcarbonitriles. In particular, former investigations on J o u r n a l P r e -p r o o f cryogenically isolated, UV-irradiated HC3N and HC5N have shown the wealth of photoproduced isomers, some of which being highly energetic and feature unusual chemical bonding. [START_REF] Kołos | Matrix-Isolated Products of Cyanoacetylene Dissociation[END_REF][START_REF] Coupeaud | Photochemical Synthesis of the Cyanodiacetylene HC5N: A Cryogenic Matrix Experiment[END_REF][START_REF] Coupeaud | Spectroscopy of Cyanodiacetylene in Solid Argon and the Photochemical Generation of Isocyanodiacetylene[END_REF] Isomerization could be anticipated also for IC3N. Moreover, it was of interest to check whether photolyzed IC3N could be an efficient source of C3N -, opening the way towards better characterization of this anion (HC3N and HC5N photolyses yielded C3N -and C5N -, respectively, but in small amounts).

Kloster-Jensen et al. published on the location of IR and UV absorption bands of IC3N, [START_REF] Kloster-Jensen | Unsaturated Hydrogen-Free Halogeno Cyano Compounds. I. Synthesis and Properties of Iodocyanoacetylene[END_REF] as well as on the electric dipole moment (4.59 D) of this nitrile, inferred from microwave spectra. Its Raman spectroscopy has also been studied. [START_REF] Klaboe | Raman Spectra and Revised Vibrational Assignments of Some Halogeno Cyanoacetylenes[END_REF][START_REF] Nolin | Vibrational Spectra of Crystalline HCCN, DCCCN, ClCCCN, BrCCCN, and ICCCN[END_REF] Linearity of the molecule was confirmed with Xray diffraction measurements. [START_REF] Borgen | Mutual Arrangement of Iodo-Cyano-Acetylene Molecules in the Solid[END_REF] Bieri et al. and Kuhn et al. measured the photoelectron spectra. [START_REF] Bieri | Electronic States of Substituted Haloacetylene and Cyanoacetylene Radical Cations[END_REF][START_REF] Kuhn | Photoelectron-Photon Coincidence Studies of the A ̃ and B ̃ excited Electronic States of X-C≡C-C≡N + , X = CH3, CD3, Cl, Br, I[END_REF] To our knowledge, no photochemical studies of IC3N have ever been reported.

Experimental and computational methods

IC3N was synthesized on a preparative scale by the method of Kloster-Jensen, involving the reaction of HC3N with I2/KI alkaline solution. [START_REF] Kloster-Jensen | Unsaturated Hydrogen-Free Halogeno Cyano Compounds. I. Synthesis and Properties of Iodocyanoacetylene[END_REF] The product was characterized by 13 C NMR spectroscopy: 13 C NMR ((CD3)2CO, 100 MHz)  22.4 (s, C-I), 67.8 (s, C-CN); 106.1 (s, CN).

The chemical shift of the sp carbon next to the iodine atom, observed at high-field, is characteristic of iodoalkynes. Traces of HC3N could not be completely removed by freeze-pumpthaw cycles.

Gaseous IC3N was mixed with Ar (Multax s.c.) in ratios ranging from 1:600 to 1:1100, in a vacuum manifold equipped with capacitance manometers (MKS Instruments). Mixtures were deposited at a rate of about 2 mmol/h onto a CsI substrate window, the latter attached to the cold finger of an Air Products Displex DE-202S cryostat. In photochemical experiments, the window was continuously VUV-irradiated (see below) throughout the sample deposition. The window was held either at 15-17 K or, exclusively during VUV irradiations, at 19 K. For electronic spectroscopy measurements, gaseous IC3N (0.13 Torr at room temperature) was mixed with 100 Torr of argon in a 10-cm glass cuvette equipped with quartz windows. Spectra were recorded in the 205-700 nm range with a resolution of 1.0 nm, using a Shimadzu UV-3100 instrument. A Nicolet Magna 560 FTIR spectrometer was used for IR absorption measurements in the 4000 -400 cm -1 range with a resolution of 0.5 cm -1 .

J o u r n a l P r e -p r o o f

For far-UV photolysis experiments, a microwave-driven Kr discharge lamp (Opthos Instrument Comp.) was attached to the vacuum shroud of the cryostat, about 5 cm from the sample substrate. The lamp, operated at 20 W, had a broadband spectral characteristic (127-160 nm) with a maximum near 145 nm; the emitted beam was not focused. The slightly elevated deposition temperature (19 K) was applied to boost the photochemical processes. The Becke's three-parameter hybrid exchange functional including the correlation functional of Lee, Yang, and Parr (B3LYP) was selected for the majority of DFT calculations. 10 11 The Dunning's correlation-consistent polarized valence triple-zeta basis set, 12 augmented by s, p, d, and f functions (aug-cc-pVTZ) was used for N and C, while for the I atom a basis set with pseudopotentials (hereafter: PP) was employed. 13 Geometric structures, energies, and harmonic frequencies were calculated for IC3N, its isomers, and several other potential photolysis products. The harmonic frequencies were scaled with a factor of 0.96 to correct for anharmonicity and for other inherent deficiencies of the DFT approach. 14,15 Transition states were localized on the electronic ground state potential energy surface (PES) using the Berny algorithm. 16 Their nature was verified by inspection of vibrational frequencies (exactly one imaginary frequency was expected). Further IRC (intrinsic reaction coordinate) calculations indicated the geometries of species linked by a given transition state. 17 In order to describe the mechanism of a photo-induced reaction, knowledge of excited PESs is crucial. Both triplet and singlet excited electronic state energies were calculated using the time-dependent DFT (TD-DFT) version. [18][19][20] The Tamm-Dancoff approximation was applied, as it was reported to perform well for numerically unstable cases and was found to provide reliable singlet-triplet separations. [START_REF] Chantzis | Is the Tamm-Dancoff Approximation Reliable for the Calculation of Absorption and Fluorescence Band Shapes?[END_REF][START_REF] Wang | Improving the TDDFT Calculation of Low-Lying Excited States for Polycyclic Aromatic Hydrocarbons Using the Tamm-Dancoff Approximation[END_REF][START_REF] Richard | Time-Dependent Density-Functional Description of the 1La State in Polycyclic Aromatic Hydrocarbons: Charge-Transfer Character in Disguise?[END_REF][START_REF] Hsu | Excitation Energies from Time-Dependent Density Functional Theory for Linear Polyene Oligomers: Butadiene to Decapentaene[END_REF][START_REF] Cordova | Troubleshooting Time-Dependent Density-Functional Theory for Photochemical Applications: Oxirane[END_REF] Excited-state PES landscapes were approximated using vertical excitations for a series of geometries obtained with ground-state IRC calculations.

The geometries of selected lowest excited states of IC3N and IC2NC were optimized with the B3PW91 functional and the same basis sets as for the ground state. B3PW91 (differing from B3LYP by a PW91 non-local correlation term) [START_REF] Perdew | Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Erratum: Atoms, Molecules, Solids, and Surfaces: Applications of the Generalized Gradient Approximation for Exchange and Correlation[END_REF][START_REF] Perdew | Generalized Gradient Approximation for the Exchange-Correlation Hole of a Many-Electron System[END_REF] has already been successfully used to describe some excited electronic states of cyanoacetylene family molecules, including HC9N, [START_REF] Szczepaniak | Cryogenic Photochemical Synthesis and Electronic J o u r n a l P r e -p r o o f Spectroscopy of Cyanotetracetylene[END_REF] CH3-C3N, [START_REF] Lamarre | Excited Electronic Structure of Methylcyanoacetylene Probed by VUV Fourier-Transform Absorption Spectroscopy[END_REF] and CH3-C5N. [START_REF] Turowski | Electronic Spectroscopy of Methylcyanodiacetylene (CH3C5N)[END_REF] We verified the reliability of B3PW91-derived vertical excitation energies by applying also the CAM-B3LYP functional [START_REF] Yanai | A New Hybrid Exchange-Correlation Functional Using the Coulomb-Attenuating Method (CAM-B3LYP)[END_REF] with large basis sets (aug-cc-pVQZ for C and N, and aug-cc-pVQZ-PP for the I atom). 12,[START_REF] Peterson | Systematically Convergent Basis Sets with Relativistic Pseudopotentials. II. Small-Core Pseudopotentials and Correlation Consistent Basis Sets for the Post-d Group 16-18 Elements[END_REF] J o u r n a l P r e -p r o o f Second order perturbation theory (VPT2) was used to predict anharmonic vibrational frequencies and intensities for fundamental, [START_REF] Barone | Vibrational Zero-Point Energies and Thermodynamic Functions beyond the Harmonic Approximation[END_REF][START_REF] Barone | Anharmonic Vibrational Properties by a Fully Automated Second-Order Perturbative Approach[END_REF][START_REF] Bloino | A Second-Order Perturbation Theory Route to Vibrational Averages and Transition Properties of Molecules: General Formulation and Application to Infrared and Vibrational Circular Dichroism Spectroscopies[END_REF] overtone, and combination bands, at the B3LYP level of theory. All DFT calculations were carried out using the Gaussian 09 Rev. E. 01 set of programs. 37 The vibrational self-consistent field (VSCF) 38,[START_REF] Rauhut | A Combined Variational and Perturbational Study on the Vibrational Spectrum of P2F4[END_REF] and correlation-corrected vibrational self-consistent field (VMP2) [START_REF] Rauhut | A Combined Variational and Perturbational Study on the Vibrational Spectrum of P2F4[END_REF][START_REF] Christiansen | Perturbation Theory for Vibrational Wave Functions[END_REF] methods were also used to compute anharmonic fundamental frequencies using a frozen-core version of CCSD(T) (coupled-cluster singles and doubles with perturbative treatment of triples). [START_REF] Hampel | A Comparison of the Efficiency and Accuracy of the Quadratic Configuration Interaction (QCISD), Coupled Cluster (CCSD), and Brueckner Coupled Cluster (BCCD) Methods[END_REF][START_REF] Deegan | Perturbative Corrections to Account for Triple Excitations in Closed and Open Shell Coupled Cluster Theories[END_REF][START_REF] Pople | Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies[END_REF][START_REF] Raghavachari | A Fifth-Order Perturbation Comparison of Electron Correlation Theories[END_REF][START_REF] Bartlett | Non-Iterative Fifth-Order Triple and Quadruple Excitation Energy Corrections in Correlated Methods[END_REF][START_REF] Stanton | Why CCSD(T) Works: A Different Perspective[END_REF] These two different approaches, VSCF and VMP2, were chosen to check for consistency of the resulting frequencies (variational VSCF computations are not as sensitive to resonance-related artifacts as those carried out with the perturbation methods VMP2 and VPT2. An efficient approach was used in VSCF and VMP2 calculations to generate potential energy surfaces around the equilibrium structures. [START_REF] Rauhut | Accurate Calculation of Anharmonic Vibrational Frequencies of Medium Sized Molecules Using Local Coupled Cluster Methods[END_REF][48][START_REF] Neff | Toward Large Scale Vibrational Configuration Interaction Calculations[END_REF] Fundamental harmonic frequencies were numerically derived, [START_REF] Rauhut | Impact of Local Approximations on MP2 Vibrational Frequencies[END_REF][START_REF] Hrenar | Impact of Local and Density Fitting Approximations on Harmonic Vibrational Frequencies[END_REF] for the previously optimized [START_REF] Eckert | Ab Initio Geometry Optimization for Large Molecules[END_REF] structures. One-and two-body terms were included. For CCSD(T) computations, Dunning's correlation-consistent polarized valence triple-zeta basis set (cc-pVTZ) 12 was selected for N and C, while a basis set with pseudopotentials (cc-pVTZ-PP) 13 was used for the I atom. All ab initio calculations of anharmonic vibrational frequencies were performed with the Molpro 2012.1 software. [START_REF] Werner | A General-Purpose Quantum Chemistry Program Package[END_REF][START_REF] Werner | Version 2012.1, a Package of Ab Initio Programs[END_REF] Computational results were visualized using ChemCraft. [START_REF]Chemcraft -Graphical program for visualization of quantum chemistry computations[END_REF]

Results and discussion

Electronic spectroscopy

Table 1 contains vertical electronic excitation energies and the respective oscillator strengths computed by CAM-B3LYP/aug-cc-pVQZ for IC3N. Optimization of excited-state structures starting from a linear geometry using B3PW91/aug-cc-pVTZ failed for most states or led to imaginary frequencies. This suggested a non-linearity of these states. Indeed, our search for the equilibrium geometry of the lowest excited singlet (S1) and triplet (T1) revealed the bent structures (Figs. S1 andS2). Similar computations were performed for IC2NC, a likely photochemical product arising from UV irradiation of IC3N (see Table S1 and Figs. S1-S2 of the Supplementary material). The predicted 0-0 (i.e. vibrationless) energies of S1-S0 excitations are 3.3 eV and 3.2 eV (TD-B3PW91/aug-cc-pVTZ) for IC3N and IC2NC, respectively.

J o u r n a l P r e -p r o o f

A UV-Vis spectrum of gaseous IC3N is presented in Fig. 1. The molecule is a strong absorber.

One can discern a structure resembling that previously reported, namely the bands at 222, 233, 245 and 262 nm, measured by Kloster-Jensen et al. in a cyclohexane solution. [START_REF] Kloster-Jensen | Unsaturated Hydrogen-Free Halogeno Cyano Compounds. II. Synthesis and General Properties of Bromocyanoacetylene[END_REF] The band pattern is similar to the one known for HC3N, [START_REF] Bruston | UV Spectroscopy of Titan's Atmosphere, Planetary Organic Chemistry, and Prebiological Synthesis[END_REF][58][START_REF] Job | The Electronic Spectrum of Cyanoacetylene: Part II. Analysis of the 2300-Å System[END_REF] but IC3N bands are distinctly broader. [START_REF] Lamarre | Excited Electronic Structure of Methylcyanoacetylene Probed by VUV Fourier-Transform Absorption Spectroscopy[END_REF] The spectrum shows clear maxima at 44 400, 41 400, 39 300, and 36 600 and cm -1 (225, 242, 254, and 273).

According to the predictions of Table 1, there are three closely spaced electronic states around 250 nm. While at least one of these is responsible for the said (presumably vibronic) bands, no reliable assignments can currently be proposed.

J o u r n a l P r e -p r o o f IR spectroscopy

An IR absorption spectrum of IC3N in Ar obtained for a sample deposited without photolysis (see Fig. 2) served as a reference for comparison with a photo-processed matrix. Fundamental vibrational bands have been identified based on data published (Table 2). [START_REF] Nolin | Vibrational Spectra of Crystalline HCCN, DCCCN, ClCCCN, BrCCCN, and ICCCN[END_REF][START_REF]NIST Chemistry WebBook[END_REF] A high S/N ratio allowed assignment of new combination bands and of several spectral features belonging to 13 C and 15 N isotopologues of IC3N present at their natural abundance (see Tables S2-S3 and the insets of Fig. 2); this was assisted with DFT predictions of isotopic shifts. Furthermore, it was possible to identify, for the first time, various combination and overtone vibrational bands of the molecule (Table 2). Several weak, unassigned bands may either be due to more complicated combinations of IC3N vibrational modes or to impurities.

J o u r n a l P r e -p r o o f

Theoretically considered IC3N photolysis products IC3N is a halogenated analogue of the extensively studied molecule HC3N. UV irradiation of the latter in inert cryogenic matrixes leads to HCCNC, HCNCC, and CCCNH. [START_REF] Kołos | Matrix-Isolated Products of Cyanoacetylene Dissociation[END_REF][START_REF] Khriachtchev | Insertion of Noble Gas Atoms into Cyanoacetylene: An Ab Initio and Matrix Isolation Study[END_REF][START_REF] Guennoun | UV Photoisomerisation of Cyano and Dicyanoacetylene: The First Identification of CCNCH and CCCNCN Isomers -Matrix Isolation, Infrared and Ab Initio Study[END_REF][START_REF] Kołos | The Infrared Spectroscopy of HNCCC: Matrix Isolation and Density Functional Theory Study[END_REF] We computed the electronic energies, structures, and vibrational IR absorption parameters of the 3 analogous isomers bearing iodine in place of hydrogen (Fig. 3). The ensuing relative energy values and molecular geometries turn out to be similar to those characterizing the HC3N family of isomers.

pVTZ (aug-cc-pVTZ-PP for I atom). See Table S5 for the computed ionization energy and electron affinity values.

Table S5 of the Supplementary material presents ionization energies predicted for the four considered isomeric variants of IC3N. What follows from these results is that none of the respective cations should be expected to appear out of IC3N irradiated with the presently applied far-UV lamp ( > 127 nm). Neither was any obvious source of electrons, leading to the corresponding anions, available in our experiment. Nevertheless, Table S5 provides also the J o u r n a l P r e -p r o o f electron affinities, as these, together with the structural parameters given in Fig. S3, might be useful in the interpretation of future experiments. The calculated ionization energy of IC3N (989 kJ/mol) is a good match to the value found experimentally, i.e. 974.5 kJ/mol (10.1 eV or 123 nm). [START_REF] Kuhn | Photoelectron-Photon Coincidence Studies of the A ̃ and B ̃ excited Electronic States of X-C≡C-C≡N + , X = CH3, CD3, Cl, Br, I[END_REF] Our theoretical treatment of permanent dissociation processes was limited here to the consideration of net thermodynamic effects confined to the ground-state potential energy surface.

Reaction endothermicities were compared to the amount of supplied energy (equivalent to λ > 127 nm). What follows is that one cannot rule out the dissociation of IC3N into either I+C3N, ICN+C2 or IC2+CN, while the heterolytic formation of ionic pairs, e.g. I + + C3N -, is not likely (Table S6). This simplistic approach does not allow us to conclude on the actual feasibility of the said homolytic cleavages, as it neglects the involvement of excited electronic states, possible energy barriers, and, of importance in cryogenic matrices, the cage effect. 68 The latter often curbs any durable separation of photofragments, giving preference to the stoichiometry-preserving molecular rearrangements.

Additionally, the possible formation of noble gas compounds IArC3N and IC2ArCN has been computationally examined. The respective theoretical predictions are provided in Fig. S4 and Table S7 of Supplementary materials (present experiments gave no supportive evidence for these species).

Photolysis results and discussion

Far-UV photolysis of Ar matrix-isolated IC3N led to the appearance of new bands in the IR absorption spectrum (see Fig. 4). The evolution of these was monitored over the course of the experiment. Thermal cycling (annealing) steps, involving the sample warm-up to approx. 22 K for about 6 minutes, followed by re-cooling to 15 K, was performed after the irradiation. In the case of IC3N, the observed IR band intensity pattern was correctly reproduced by our DFT calculations (see Table 2). We assume a similar reliability of this theoretical approach applied to other closed-shell IC3N-stoichiometry species.

J o u r n a l P r e -p r o o f

Data gathered in Table 3 concern the identification of IC2NC. A prominent IR absorption feature at 2050.2 cm -1 can be identified as 2. It is predicted for this isomer as the strongest one. The second strongest band, the one due to 6 bending, is expected at around 270 cm -1 , well beyond our available spectral range. The 3 stretching is predicted as 2 orders of magnitude less intense in IR than 2. Band strength data, collected throughout the photolysis, were helpful in the search for this weak feature. Correlations of integrated intensities, involving the postulated 2 band and J o u r n a l P r e -p r o o f the 3 candidate bands at 1054.5 cm -1 (Fig. 5a) and 1039.5 cm -1 (Fig. 5b) were analyzed.

Considering the extent of error bars, Fig. 5a shows (unlike Fig. 5b) quite a probable linear correlation. Common origin of the spectral features located at 2050.2 cm -1 and 1054.5 cm -1 is additionally suggested by their similar resistance to annealing (in contrast to the 1039.5 cm -1 band, slightly decreasing upon thermal treatment). Noteworthy, a broad hump centered at 1040 cm -1 is much too strong to be due to the 3 mode; its integrated intensity is almost the same as for the 2050.2 cm -1 band. In view of the above considerations, the sharp 1054.5 cm -1 feature is interpreted here as the 3 band of IC2NC.

J o u r n a l P r e -p r o o f

J o u r n a l P r e -p r o o f

The predicted frequency of the 5 bending vibration of IC2NC formally falls within the spectral range of the instrument used, although a S/N decrease near 400 cm -1 prevented detection of the respective absorption. On the other hand, the IR spectrum is crowded with absorption features around the predicted IC2NC 1 frequency. The anticipated separation of 1 and 2 is about 200 cm -1 at DFT and 220 cm -1 at CCSD(T) levels of theory. One can therefore expect to find the 1 band of IC2NC at around 2260 ± 20 cm -1 . Theory describes it as even weaker than 3, and comparable in intensity to the bands of 13 C-isotopomers of the parent species, located in the same region (cf. Fig. 2). Without further studies, involving isotopically labeled precursor species or the application of Raman spectroscopy (indeed, the expected Raman activity and IR absorption intensity patterns significantly differ one from the other; see Table 3), it is impossible to assign any specific band to the 1 mode of IC2NC.

We have carried out a theoretical study on the IC3N  IC2NC reaction, starting from the groundstate rearrangement, analyzed within the IRC scheme. Energies of the lowest excited singlet and triplet states were derived assuming vertical excitations from discreet IRC-obtained ground-state structures along the reaction coordinate. The result is depicted in Fig. 6. The computed groundstate activation energy (including zero-point energy contributions) amounts to 267 kJ/mol, a value similar to that reported for the analogous isomerization of HC3N (272 kJ/mol). [START_REF] Yang | Global Analysis of Reaction Pathways on the Potential Energy Surface of Cyanoacetylene by the Scaled Hypersphere Search Method[END_REF] This is well below the energies of any excited electronic state of IC3N. When the parent molecule absorbs a vacuum-UV photon from a Kr lamp, the reaction may proceed by overcoming the barrier in an excited singlet state, with a possible crossing to the lowest triplet-state surface. As demonstrated in Fig. 5c, spectral features observed at 2172.5 cm -1 and 1934.8 cm -1 are well correlated throughout the photolysis time. It was at first tempting to consider the C3N -anion as their possible common carrier. However, rather than a single 2172.5 cm -1 feature, the reported spectrum of C3N -coming from HC3N photolysis in solid Ar revealed a Fermi-resonance doublet manifesting as two bands located at 2173.0 and 2178.0 cm -1 . [START_REF] Kołos | Matrix Isolation IR Spectroscopic and Ab Initio Studies of C3Nand Related Species[END_REF][START_REF] Turowski | The C3N -Anion: First Detection of Its Electronic Luminescence in Rare Gas Solids[END_REF] Secondly, a mismatch of about 10 cm -1 between 1934.8 cm -1 and the frequency of another HC3N-derived anion band, 1944.0 cm -1 , is large, even considering some differences in local microenvironments (matrix cages) inherent to IC3N and HC3N experiments. Finally, the intensity ratio of 2172.5 cm -1 and 1934.8 cm -1 bands differs greatly from that reported for the two strongest C3N -IR absorption features produced upon the photolysis of HC3N. The currently observed ratio matches decently, however, what is predicted for the ICNC2 isomer, as do the frequencies of the two bands (see Table 4). In J o u r n a l P r e -p r o o f view of the above, and considering that a similar rearrangement, HC3N  HCNC2, has been observed for cyanoacetylene, we assign the said bands to ICNC2.

J o u r n a l P r e -p r o o f

According to our computations, UV photons available in this experiment are energetic enough (their spectrum extending from 9.76 eV to near-IR) to overcome all energy barriers separating IC3N from ICNC2. The initial step most likely involves IC3N  IC2NC isomerization, described above (Fig. 6). The path then proceeds (Fig. 7a) via a cyclic isomer. The latter species appears with a large excess of energy, which likely facilitates an efficient conversion towards ICNC2 (Fig. 7b). While the exact identity of the involved potential energy surfaces is not known, the path may lead either through singlet or triplet states of the participating molecules.

J o u r n a l P r e -p r o o f

J o u r n a l P r e -p r o o f

Conclusions

There is experimental evidence, backed with theoretical predictions, for the formation of chain species IC2NC and ICNC2 upon far-UV photolysis of iodocyanoacetylene isolated in solid argon.

The two isomeric species have not, to our knowledge, been observed before. IR-spectroscopic description of the parent IC3N molecule has been appended with the assignment of additional combination bands. Several fundamental IR transitions of 13 C-and 15 N-isotopologues of IC3N, present in their natural abundances, were identified. No IC3N-related ions, in particular no C3N -, have been detected in the course of these experiments.

Declaration of interests

☐ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. a States designated as the linear ones, irrespective of their equilibrium geometries, to ease the comparison with other cyanoacetylene family molecules.

J o u r n a l P r e -p r o o f b Basis set cc-pVTZ with cc-pVTZ-PP for I atom.

c DFT frequencies scaled by 0.96 (see Table S8 in the Supplementary material for the predicted overtone and combination bands).

d Harmonic approximation.

J o u r n a l P r e -p r o o f a Basis set aug-cc-pVTZ with aug-cc-pVTZ-PP for I atom.

b Basis set cc-pVTZ with cc-pVTZ-PP for I atom.

c DFT frequencies scaled with 0.96 (see Table S9 in the Supplementary material for the list of calculated overtone and combination bands).

J o u r n a l P r e -p r o o f

Figure 1 .

 1 Figure 1. UV-Vis absorption spectrum of IC3N, as measured for a gas-phase sample. Bars indicate the predicted location and oscillator strength of vertical electronic transitions, derived with TD-CAM-B3LYP/aug-cc-pVQZ.

Figure 2 .

 2 Figure 2. IR absorption spectrum of IC3N in solid Ar at 15 K. Asterisked bands arise from incomplete compensation of CsI substrate absorption.

  The most stable is the nitrile IC3N, the isonitrile IC2NC being more energetic by about 137 kJ/mol. Much less stable are two other chain structures: C3NI and C2NCI. No bound Y-shaped carbene structure C2(I)CN, analogous to the cyanovinylidene molecule,[START_REF] Goldberg | Experimental Evidence for the Existence of Cyanovinylidene :C:C(H)CN. Gas-Phase Characterization of a Possible Interstellar Molecule[END_REF][START_REF] Hu | An Observable Unsaturated Carbene and a Possible Interstellar Molecule[END_REF][START_REF] Kołos | Prospects for the Detection of Interstellar Cyanovinylidene[END_REF] has been found in our B3LYP study, but CAM-B3LYP computations suggest the presence of a corresponding shallow potential energy minimum. IR spectroscopic parameters predicted for the lowest-energy IC3N molecules can be found further in the text and in the Tables S3 -S5 of the Supplementary material.

Figure 3 .

 3 Figure 3. Relative ZPE-corrected electronic energies and structures (Å, deg) of the selected IC3N isomers (NBO charges are given for each atom), as derived with B3LYP/aug-cc-

Figure 4 .

 4 Figure 4. Bands of isomers in the IR absorption spectrum of VUV-photolyzed ( > 127 nm) IC3N isolated in solid Ar (upper trace). Bottom trace shows the spectrum of a nonirradiated sample. Absorbance scales are arbitrary.

Figure 5 .

 5 Figure 5. Correlation of the measured integrated optical density values for selected pairs of IR bands relevant to the identification of IC2NC (a, b) and ICNC2 (c), arising in the course of far-UV photolysis of IC3N isolated in solid argon. Red lines represent leastsquares linear fits.

Figure 6 .

 6 Figure 6. Ground-and selected excited-state cross-sections of IC3N potential energy surfaces depicting the isomerization towards IC2NC. The reaction coordinate comes from ground-state IRC calculations at the B3LYP/aug-cc-pVTZ (aug-cc-pVTZ-PP for I atom) level of theory. Molecular geometries corresponding to the two energy minima and a transition state are shown. Excited state energies were derived by TD-DFT calculations, departing from the respective ground-state geometries.

Figure 7 .

 7 Figure 7. Ground-and selected excited-state cross-sections of IC3N potential energy surfaces depicting a 2-step (panels a and b) isomerization path from IC2NC to ICNC2. The reaction coordinate comes from ground-state IRC calculations at the B3LYP/aug-cc-pVTZ (aug-cc-pVTZ-PP for I atom) level of theory. Molecular geometries corresponding to the energy minima and transition states are shown. Excited state energies were derived by TD-DFT calculations departing from the respective ground-state geometries.

( 10 )

 10 Becke, A. D. Density-functional Thermochemistry. IV. A New Dynamical Correlation Functional and Implications for Exact-exchange Mixing. J. Chem. Phys. 1996, 104 (3), 1040-1046. https://doi.org/10.1063/1.470829. (11) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-EnergyFormula into a Functional of the Electron Density. Phys.Rev. B 1988, 37 (2), 785-789. https://doi.org/10.1103/PhysRevB.37.785. (12) Kendall, R. A.; Dunning Jr, T. H.; Harrison, R. J. Electron Affinities of the First-row Atoms Revisited. Systematic Basis Sets and Wave Functions. J. Chem. Phys. 1992, 96 (9), 6796-6806. https://doi.org/10.1063/1.462569. (13) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110 (51), 13877-13883. https://doi.org/10.1021/jp065887l. (14) Andersson, M. P.; Uvdal, P. New Scale Factors for Harmonic Vibrational Frequencies Using the B3LYP Density Functional Method with the Triple-ζ Basis Set 6-311+G(d,p). J. Phys. Chem. A 2005, 109 (12), 2937-2941. https://doi.org/10.1021/jp045733a. (15) Merrick, J. P.; Moran, D.; Radom, L. An Evaluation of Harmonic Vibrational Frequency Scale Factors. J. Phys. Chem. A 2007, 111 (45), 11683-11700. https://doi.org/10.1021/jp073974n. (16) Li, X.; Frisch, M. J. Energy-Represented Direct Inversion in the Iterative Subspace within a Hybrid Geometry Optimization Method. J. Chem. Theory Comput. 2006, 2 (3), 835-839. https://doi.org/10.1021/ct050275a. (17) Fukui, K. The Path of Chemical Reactions -the IRC Approach. Acc. Chem. Res. 1981, 14 (12), 363-368. https://doi.org/10.1021/ar00072a001. (18) Bauernschmitt, R.; Ahlrichs, R. Treatment of Electronic Excitations within the Adiabatic Approximation of Time Dependent Density Functional Theory. Chem. Phys. Lett. 1996, 256 (4), 454-464. https://doi.org/10.1016/0009-2614(96)00440-X.

( 19 )

 19 Casida, M. E.; Jamorski, C.; Casida, K. C.; Salahub, D. R. Molecular Excitation Energies to High-Lying Bound States from Time-Dependent Density-Functional Response Theory: Characterization and Correction of the Time-Dependent Local Density Approximation Ionization Threshold. J. Chem. Phys. 1998, 108 (11), 4439-4449. https://doi.org/10.1063/1.475855.

J o u r

  n a l P r e -p r o o f

J o u r n a l P r e -p r o o f 29 Table 3 .

 293 Comparison of theoretically predicted and experimental IR absorption data for IC2NC.

Table 1 . Vertical excitation energies and oscillator strengths for electronic transitions of IC3N, as computed with CAM-B3LYP/aug-cc-pVQZ. State a

 1

		Vertical
		energy	f
		eV (nm)
	A 1 Σ -	4.95 (251)	0
	B 1 Δ	5.07 (245)	0
	C 1 Δ	5.11 (243)	0
	D 1 Π	6.90 (180)	0.07
	E 1 Σ +	7.10 (175)	1.3

Table 2 . Comparison of computed and experimental IR absorption data for IC3N.

 2 Ref. 6, values from Raman spectra if IR data not available, sh -shoulder band.

		B3LYP a	CCSD(T) b	Experimental frequency, cm -1
		IR	aharm, cm -1
		int.			Re
	Mode, symmetry 1, σ 2, σ 3, σ 4, σ 5, π 6, π 7, π J o u r n a l P r e -p r o o f harm , c scal ed, cm -1 harm. , km/ mol (relat ive int.) Ram ahar Iharm/ har IC3N, an activi ty d m, cm -1 km mol -1 m, gas e IC3N:Ar VS VM cm -1 (solid) f CF P2 226 2 174 (100) 1381 232 1 161 23 16 227 6 227 3 2270 (2262) 2266.4 212 6 21 (12) 80 218 5 15 21 55 211 8 211 5 2131 (21130 2123.1 983 1 (0.6) 1084 994 0.19 10 00 988 100 9 1031 (1037) 1031.1 347 0 645 359 0.01 35 6 353 353 364 (349) out of range 517 4 (2.3) 1.5 532 5 49 4 498 498 496 (483) 493.9+4 94.9 309 24 (14) 341 327 15 30 3 308 304 309 (323,32 2sh) out of range 108 0 271 114 1.0 11 0 124 116 (118,13 4) out of range	l. int . Ar 10 0 13 0. 8 5. 2
	2+4+6 or 1+27+6	278 1		2753.8	0. 1
		271		2717.9	0.

a Basis sets aug-cc-pVTZ for C and N atoms, aug-cc-pVTZ-I-PP for iodine.

b Non-augmented versions of the basis sets used in DFT calculations were applied.

c Harmonic frequencies scaled by 0.96 (see Table

S4

in the Supplementary material for an extended list of calculated overtone and combination bands). d Harmonic approximation. e Ref. 60.

f g Ref. 61.

Table 4 . Comparison of the theoretically predicted and experimental IR absorption data for ICNC2.

 4

	Computations

Acknowledgments

J.-C.G. thanks the Program PCMI (INSU-CNRS) and the Centre National d'Etudes Spatiales (CNES) for funding. Authors wish to thank Thomas Custer for valuable suggestions and comments on the manuscript. J o u r n a l P r e -p r o o f