Melya Boukheddimi

Rohan Budhiraja

Philippe Souères

Bruno Watier

Anthropomorphic Gait Generation using Differential Dynamic Programming with a Reduced Number of Cost Criteria

Bipedal gait is the natural means of human locomotion. Nonetheless, it is still unclear how the central nervous system coordinates the whole-body segments for gait generation. We address this question based on the wellknown hypothesis that the human motion is the result of an optimization process. We consider a reduced set of criteria taken from the observation of human walking and the study of the related literature, which seem to be optimized during the human gait. Differential Dynamic Programming is applied on these criteria with a 3D whole-body skeletal model involving 42 degrees of freedom to generate walking motions. Nine different skeletal models and gaits reconstructed from motion capture data are used to this end. The simulated walking motions are then analyzed and compared to the human reference to show the quality of the gait generation process. The interest of this optimization approach for human-like motion generation is finally discussed.

I. INTRODUCTION

A. Research significance

Walking is an inherent part of human locomotion. Yet, infants acquire this ability after approximately 18 months of trial and error, going through walking on all fours. This learning process leads to a unique walking pattern characterizing each individual like a fingerprint. However, in contrast to fingerprints, learned walking patterns are not fixed once and for all, but may change according to externals variables such as accidents, pathologies or age. The centralnervous system adjusts the gait whatever the alterations [START_REF] Latash | The bliss (not the problem) of motor abundance (not redundancy)[END_REF], to allow walking in the best possible way [START_REF] Viel | La marche humaine, la course et le saut: biomécanique, explorations, normes et dysfonctionnements[END_REF]. With more than 200 Degrees of Freedom (DoFs) the human body is obviously a highly redundant system for the walking task. Hence, the issue that arises is: "what is foremost optimized by the central-nervous system in order to coordinate the entire body and generate a human gait".

B. Related works

To answer this question, active research has been conducted and different approaches were implemented. Most of them consider simplified models of poly-articulated bodies for modeling the system with rigid segments and joints. In addition some studies use a musculoskeletal model to generate gait. Inverse Kinematics was applied in [START_REF] Rajagopal | Full-body musculoskeletal model for muscle-driven simulation of human gait[END_REF] using motion capture (MoCap) data and muscular activations as This work was partially supported by the European project RoboCom++, and by the French National Research agency (ANR), through the projects ANR-HOBIS (18CE27-0010) and ANR-COBOT (18CE10 -0003). 1 LAAS-CNRS, Université de Toulouse, CNRS, UPS, France 7 Avenue du Colonel Roche, F-31400 Toulouse, France.

2 LAAS-CNRS, 7 Avenue du Colonel Roche, F-31400 Toulouse, France. * corresponding author: mboukhed@laas.fr input. In [START_REF] Delp | Opensim: Open-source software to create and analyze dynamic simulations of movement[END_REF] a dynamic abnormal walking was produced using muscular control with OpenSim. A neuromusculoskeletal model was used in [START_REF] Hase | Human gait simulation with a neuromusculoskeletal model and evolutionary computation[END_REF] with kinematics and in vivo dynamic data to generate human-like walking and running.

In [START_REF] Song | A neural circuitry that emphasizes spinal feedback generates diverse behaviours of human locomotion[END_REF] a neuro-physiological control of the low-level spinal was considered to simulate locomotion. With the aim of reproducing realistic human gaits, a lot of contributions were also proposed in the 3D animation community. For instance a real-time complex controller was proposed in [START_REF] Coros | Generalized biped walking control[END_REF] to simulate different kinds of human walking. In [START_REF] Yin | Simbicon: Simple biped locomotion control[END_REF] the control framework "SYMBICON" was designed to generate bipedal walking without using MoCap data. Based on this framework, [START_REF] Wang | Optimizing locomotion controllers using biologically-based actuators and objectives[END_REF] presented an optimization controller robust to the environment uncertainties, which provided realistic gait simulations. A predictive human-like walking pattern was generated in [START_REF] Dorn | Predictive simulation generates human adaptations during loaded and inclined walking[END_REF] using a muscle-driven dynamic model with an energy optimization controller. A dynamic walking was obtained in [START_REF] De Lasa | Feature-Based Locomotion Controllers[END_REF] using a hierarchical tasks framework robust to the model modifications. Optimal control methods were also widely used to generate anthropomorphic gaits. One approach is to apply optimal control with direct collocation [START_REF] Diehl | Numerical optimal control (preliminary and incomplete draft[END_REF]. For example, in [START_REF] Ackermann | Optimality principles for model-based prediction of human gait[END_REF] gaits were generated with "tiredness and effort-like" costs optimization. Whereas in [START_REF] Dorschky | Estimation of gait kinematics and kinetics from inertial sensor data using optimal control of musculoskeletal models[END_REF] the kinetics and kinematics of the gait were calculated from raw inertial sensor data and dynamic gait simulations by applying one global optimization on three cost functions.

Other approaches used direct multiple-shooting to simulate walking. A predictive pattern of pathological gait applied to children was proposed in [START_REF] Sreenivasa | Optimal control based stiffness identification of an ankle-foot orthosis using a predictive walking model[END_REF]. In [START_REF] Felis | Synthesis of full-body 3-d human gait using optimal control methods[END_REF], a half gait cycle was generated using a multiple optimization function approach. It was later implemented using MUSCOD II [START_REF] Kuhl | Muscod-ii users' manual[END_REF] and validated by comparing the obtained gait with MoCap data. In [START_REF] Clever | Inverse optimal control based identification of optimality criteria in whole-body human walking on level ground[END_REF] direct inverse optimal control was used to identify the cost functions minimized by humans during walking by identifying the weights applied to a set of chosen criteria.

C. Contribution of the paper

In this work we propose to generate human-like walking gait from optimization in accordance with [START_REF] Todorov | Optimal control methods suitable for biomechanical systems[END_REF]. We use direct optimal control with multiple-shooting to simulate human-like locomotion with multiple contacts while coping with the redundancy of a 42 DoFs model. Our objective is to demonstrate that human-like walking can be closely reproduced by optimizing a small number of key costs functions. Based on the biomechanical literature and the observations of the human gait throughout experimental analysis [START_REF] Boukheddimi | Human-like gait generation from a reduced set of tasks using the hierarchical control framework from robotics[END_REF], an appropriate reduced set of optimization criteria is identified. A specific optimization method, Differential Dynamic Programming (DDP), is used to simulate the gait from the minimization of the identified criteria. Nine different models and gait patterns scaled on nine different subjects are used to test our hypothesis. Thus, Nine different simulations of gait are obtained by optimizing over the same objective criteria. Results are validated by comparing the simulated gaits profile with the human references reconstructed from MoCap considering both the kinematics and the dynamics.

D. Structure of the paper

The paper is organized as follows. Model and data are presented in Sec II. Sec III describes the decomposition of the human gait cycle. Sec IV exposes the optimal control (OC) problem of whole-body locomotion, and introduces the OC solver CROCODDYL. The application to gait generation is detailed in Sec V. Sec VI presents the simulation results and provides a comparison with the human reference. Finally the relevance of the approach is discussed in Sec VII.

II. HUMAN MOTION RECONSTRUCTION

A reconstruction of human gaits was conducted for nine volunteers, in order to construct a human reference for analyzing the human likeness of the simulated gaits.

A. The data

Experimental data were extracted from [START_REF] Carpentier | On the centre of mass motion in human walking[END_REF], they were conducted in agreement with the standards of the Declaration of Helsinki (revision 2013), and formal accordance of the ethics evaluation by the ethic committee of INSERM , Paris, France (IORG0003254, FWA00005831). The volunteers were nine healthy men, (age: 24.2 ± 2.3yrs, height: 1.74 ± 0.09 m, mass: 71.0 ± 9.0 kg) performing at least 3 trials of normal walking. One randomly chosen trial was used for each participant. The experimental framework was equipped with 13 infrared cameras sampling at 200 Hz (Vicon, Oxford Metrics, UK). The markers set was positioned in accordance with Wu guidelines [START_REF] Wu | Isb recommendation on definitions of joint coordinate system of various joints for the reporting of human joint motionpart i: ankle, hip, and spine[END_REF] [23] and the International Society of Biomechanics recommendations.

B. The model

The whole-body skeletal model proposed by [START_REF] Maldonado | Whole-body musculoskeletal model v1[END_REF] was considered for this study as it was proven to be sufficient to reproduce the main features of human walking [START_REF] Boukheddimi | Human-like gait generation from a reduced set of tasks using the hierarchical control framework from robotics[END_REF] or parkour jumps [START_REF] Maldonado | Angular momentum regulation strategies for highly dynamic landing in Parkour[END_REF]. It is a 3D whole-body skeletal dynamic model involving 42 DoFs and 19 segments. This model was scaled respectively to the height and weight of each subject using the open-source software OpenSim. Therefore nine different models were obtained and used to generate nine different gaits.

C. Reconstruction of the human reference

An Inverse Kinematics (IK) process was conducted with the model corresponding to each subject with OpenSim [START_REF] Hamner | Muscle contributions to propulsion and support during running[END_REF]. The IK process aims to compute the generalized coordinates (i.e., the body configuration) that fit at best the position of the model with the experimental position of the markers at each time step. The generalized coordinates were obtained by solving a least squares problem. The resolution is based on a general quadratic programming (QP) solver [START_REF] Delp | Opensim: Open-source software to create and analyze dynamic simulations of movement[END_REF]. The generalized coordinates obtained by solving the minimization problem will be referred to as the "human reference coordinates". They will be used in Sec VI to compare the joint angles extracted from the obtained gait simulations.

III. GAIT MODELING

In this section, we discuss the different contact phases that make up the human gait cycle.

A. Gait cycle decomposition

The complete anthropomorphic gait cycle is defined by two steps: left foot swinging (with right foot support) and right foot swinging (with left foot support). Each step was divided into 4 phases, according to the contact changes. Here the phases are defined only for the right foot support step; the left foot support step can be deduced by symmetry. Based on the literature of human gait dynamics, these phases are defined as shown in Fig. 2. The phases for the left foot are:

• Swinging heel of the left foot: begins when the heel of the left foot starts moving upward, and ends when the toes of the left foot take off, the left foot being no more in contact with the ground. • Flexing of the left foot: begins when the left foot stops being in contact with the ground, and ends when the heel of the right foot loses its contact. • Landing heel of the left foot: begins at the end of the previous phase and ends when the heel of the left foot lands on the ground. • Landing toes of the left foot: begins when the heel of the left foot strikes the ground, the toes of the left foot moving downward, and ends when the left foot is fully in contact (6D) with the ground. Afterwards, the next step starts with the swinging of the right foot.

B. Features of the human gait

Based on the biomechanical definition of the human gait and the related literature, the following features arise:

• The foot contact placements have to be specified to ensure the dynamic feasibility of the human gait cycle. • During the contact changes, the three dimensional position of the center of mass (COM) of the whole-body is crucial. Notably to maintain the position of the upper part of the body at a reasonable height [START_REF] Carpentier | On the centre of mass motion in human walking[END_REF]. • Flexions of the swinging knee occur when the walker tries to avoid the ground or an obstacle close to the ground with the swinging foot [START_REF] Byrne | Swing phase kinetics and kinematics of knee replacement patients during obstacle avoidance[END_REF].

• Minimizing the torque is necessary to maintain a human-like torque at the joints [START_REF] Xiang | Optimization-based prediction of asymmetric human gait[END_REF]. • The velocity of the swinging foot is reduced just before landing to reduce the impact with the ground [START_REF] Kim | Modeling of heel strike transients during running[END_REF]. These features of the human gait and the stated cycle decomposition will be used in Sec V for simulating the gait.

IV. HUMAN GAIT EXPRESSED AS AN OPTIMIZATION PROBLEM

A. Multi-body Dynamics

The dynamics of a poly-articulated system of rigid bodies involving K contacts is given by the Euler-Lagrange equations of movement (1):

M(q) q + b(q, q) = S τ + K ∑ k=1 J k (q) λ k (1)
where,

• q is the configuration vector which includes the joint angles and the free-flyer coordinates. • M(q) is the inertia matrix.

• b(q, q) contains the nonlinear and gravity forces.

• S is a matrix which selects the actuated components.

• τ are the internal joint torques.

• K is the number of contacts.

• J k (q) is the Jacobian matrix for the k th contact.

• λ k is the vector of contact forces of the k th contact. See [START_REF] Featherstone | Rigid Body Dynamics Algorithms[END_REF] for more details.

B. Rigid Contact Constraints

During walking the body is always in contact with the ground with one or both feet. Contacts can be expressed as a kinematic constraint on the equation of movement [START_REF] Latash | The bliss (not the problem) of motor abundance (not redundancy)[END_REF]. For the k th body the rigid contact constraint is expressed as follows:

J k q + Jk q = 0 ∀k ∈ 1 • • • K (2)
Note that since our dynamics lies in the acceleration space the rigid contact constraint is represented as a second order kinematic constraint on the contact placement. Combining the equation of motion [START_REF] Latash | The bliss (not the problem) of motor abundance (not redundancy)[END_REF] with the contact constraints (2) the multi-contact body dynamics can be rewritten as:

M J c J c 0 q -λ c = S τ -b -Jc q (3)
where 1 ,

J c = J 0 • • • J k • • • J K and λ c = λ 0 • • • λ k • • • λ K
This redefined dynamics is the same as the one obtained by applying the Gauss principle of least constraints on the motion of a multi-body system with contact constraints [START_REF] Wieber | Holonomy and nonholonomy in the dynamics of articulated motion[END_REF]. If we consider the Karush-Kahn-Tucker optimality conditions on the Gauss's principle, we obtain (3) [START_REF] Budhiraja | Differential Dynamic Programming for Multi-Phase Rigid Contact Dynamics[END_REF].

C. Optimization for motion generation: Crocoddyl Solver

Consider the problem of generating a human-like gait using the dynamics defined in Sec IV-A and IV-B. To this end a multi-phase optimization problem is defined, each phase being governed by (3) under a specific set of contact. The fixed contacts and the gait modeling was discussed in Sec III. The optimization problem is formulated as2 : minimize q, q,τ S ∑ s=1 t s +∆t s t s l s (q, q, τ) dt

subject to q ∈ Q (4a) q ∈ V (4b) τ ∈ T (4c) q, q = f (q, q, τ) (4d)
where,

• s = 1 • • • S is used to describe the contact phases which define the human walking gait, as discussed in Sec III. • l s is the cost function for the contact phase s.

• f is a reduced formulation of the contact constrained dynamics (3). • Q, V , T are the admissible sets for q, q, τ (defined by the biological limits of the human joint). To solve this optimization problem we use a Shooting Method. These methods provide a way of solving boundary value problems with simple path constraints (such as (4)). Shooting methods are popular since they are fast to solve compared to other available methods [START_REF] Diehl | Numerical optimal control (preliminary and incomplete draft[END_REF]. Among Shooting methods, Differential Dynamic Programming (DDP) is a good way of handling this optimization problem. DDP allows us to truly exploit the sparsity introduced by the Markovian nature of the dynamics in (3) in a highly iterative manner. In this work, we use the framework Crocoddyl [START_REF] Mastalli | Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control[END_REF] to solve the above optimization problem. Crocoddyl is a DDP-based library [START_REF] Budhiraja | Differential Dynamic Programming for Multi-Phase Rigid Contact Dynamics[END_REF], which is open-Source, memory efficient and uses fast dynamics and derivative algorithms provided by Pinocchio [START_REF] Carpentier | The Pinocchio C++ library -A fast and flexible implementation of rigid body dynamics algorithms and their analytical derivatives[END_REF]. Moreover, Crocoddyl proposes a variant of DDP, called FDDP (Feasibility DDP) [START_REF] Mansard | Feasibility-prone differential dynamic programming is ddp a multiple shooting algorithm?[END_REF], which avoids the numerical limitations of single-shooting in DDP and allows warm starting the problem from an infeasible state. In this research, we use the FDDP method to solve the discretized version of our optimization problem (4).

V. GAIT SIMULATION

Relying on the observations made in Sec III-B and according to the decomposition of the gait cycle stated in Sec III-A, we define an optimization problem that covers each step. Solving this optimization problem leads to compute the optimal trajectories of the state x = (q, q), and the optimal control u = τ. Moreover, our formulation (3) leads to compute the contact forces λ k as a function of x and u.

In order to solve our optimization problem numerically with Crocoddyl, the problem is first discretized over N subintervals (evenly distributed or not) of [0, T ]. In each subinterval n, the control trajectory u n is constrained to be in the span of a given finite trajectory basis, and is fixed to a constant value. The values of x n are obtained by integrating numerically the dynamics (3) using an Implicit Euler scheme [START_REF] Press | Numerical recipes : the art of scientific computing[END_REF]. In Crocoddyl, we define a separate dynamics and cost model (collectively called an action model) for each node of the descritization interval, the optimization problem is created as a list of action models in a series. Based on the list of features of the human gait listed in Sec III-B different costs Φ n are designed for the optimization problem. Each cost is weighted differently by a coefficient α n ∈ R. The final objective function for an action model is written as:

l s = N ∑ n=1 α n Φ n (q, q, τ), (5)
with the following costs and weights, t s denoting the final time of each phase, and t f inal the final time of each half cycle of the gait.

• CoM Cost: During a contact phase, the CoM trajectory c(t) tracks the final CoM position for each phase c re f (t s ).

Φ 1 = c(t) -c re f (t s ) 2 2
, α 1 = 17 × 10 3 • Feet Cost: During a contact phase, the swinging foot position trajectory (r h (t) for the heel or r t (t) for the toes) tracks the final foot placement for each phase.

Φ 2 = r h (t) -r re f h (t s ) 2 2 , α 2 = 1 × 10 3 • Ground Avoidance:
The swinging foot needs to maintain a clearance from the ground. This is implemented by a quadratic barrier on the z position of the foot. Φ 6 = q(t)q re f (t s ) 2 2 , α 6 = 0.1 Just for the final node of a half cycle of gait at t f inal , a higher weight α = 10 is used for the posture task. The Fig. 3. Flexion-extension of the right hip weights α i for this optimization problem were determined experimentally. Their were adjusted in order to obtain the better kinematic results, which were assessed by comparing them to the joint rotations obtained from MoCap. Additionally to this kinematic benchmarking, the joint torques were also checked and the costs Φ 5 were tuned with the aim to obtain human-like joints torques values. The obtained results are validated in the next section by comparing them to the human references coming from MoCap, using the following biomechanical criteria:

Φ 3 = minimum{r z h (t) -r z h (t s ), 0} 2 2 , α 3 = 50 × 10
• Range Of Motion (ROM) of the joint rotations.

• Mean and standard deviation.

• Student test (α = 0.05), with his test of significance.

• Shapiro-Wilk test of normality (α = 0.05).

VI. RESULTS AND COMPARISON

A. Results

Nine anthropomorphic gait were generated, each one with its own scaled model and gait pattern. These simulations were obtained by solving the same optimization problem defined in Sec V and III for each gait cycle. Some sequences of snapshots of complete gait-cycles are presented in Fig. 1. Relevant human-like gait behaviors arise from these simulations. Indeed, the generated movements show a human-like roll of the swinging foot on the ground, and a natural flexion of both the knees and the hip. Regarding the upper part of the body including the neck and the head, a good tracking of the human walking pattern with natural back and forth motions of the arms can be observed. Additionally to these visual and qualitative observations, a statistical analysis is provided in the next section.

B. Comparison

This section summarizes the study that was conducted to compare the simulated gaits obtained from the resolution of the OC problem and the reference human movement. We compute the mean and standard deviation of joint rotations over one gait cycle for the nine subjects. Fig. 3 to Fig. 8 show the simulated and the reference gaits for the right lower limbs, i.e the hip, the knee and the ankle. For all the obtained movements the results indicate that big parts of the motion are significantly identical to the reference movements. Table I presents, for the simulated gait and the human reference, the mean of the ROM for the joint rotations of the lower limbs with their differences. The Student test is conducted and the obtained joint rotations which are significantly identical to the references are highlighted in this table. The ROM for the simulated joint rotations are significantly identical to the human reference for the ankle, the abduction -adduction and the external-internal rotation of the hip for both left and right sides, and for the flexionextension of the left hip. Regarding this comparison, the results show that the joint rotations of the simulated gaits closely follow the joint rotations pattern and values of the human references. Moreover, for the nine subjects, the mean and standard deviation of the joint torques of the right lower limbs, obtained in simulation over one gait cycle, are represented in Fig. 9 to 12. It can be noticed that the simulated joint torques remain within the physiological limits: mostly between -1 and 1 Nm.Kg -1 , with maximum values ±4 Nm.Kg -1 . However, these joint torques are not following a human-like profile along the gait cycle, as described in [START_REF] Viel | La marche humaine, la course et le saut: biomécanique, explorations, normes et dysfonctionnements[END_REF].

VII. CONCLUDING DISCUSSION

The analysis of the simulated walking movement presented in Sec VI supports the hypothesis stated in (Sec I-C), namely that the anthropomorphic gait can be reproduced from the optimization of a small number of adequately chosen criteria. In our approach only 8 phases were used to reconstruct the full gait cycle, while only discrete values at the end of each phase were given to the optimizer, without requiring any reference trajectories. By comparison, a half gait cycle required 5 phases to be simulated in [START_REF] Felis | Synthesis of full-body 3-d human gait using optimal control methods[END_REF]. Having a low number of phases makes the method more general and easier to implement as the quantity of data required to specify the motion is reduced. Concerning the dynamics, the only considered optimization criterion is the torque minimization which provides a way of regularizing the optimization problem. As a result we observed that the torques values remain within the physiological limits of the human movement all along the gait cycle. In our previous work [START_REF] Boukheddimi | Human-like gait generation from a reduced set of tasks using the hierarchical control framework from robotics[END_REF], in which the task-hierarchy framework was used with a kinematic model, it was necessary to give the highest priority to the foot tracking task. Here, as the full body dynamics is considered, a good quality of the trajectories is obtained by putting a higher weight on the CoM cost than on the foot cost. This difference reflects the key role of the CoM regulation in dynamical systems. The proposed method based on DDP allows the minimization process to be handled for at least one complete gait cycle while preserving a good quality of the optimized movement including the execution of the human-like features all along the simulation. The strength of DDP lies in its ability to solve the problem in a highly iterative and fast manner. However, in order to produce quick results, DDP compromises in its ability to consider constraints on the optimization (unlike previous works which used Non-Linear Programming solvers like MUSCOD-II [START_REF] Kuhl | Muscod-ii users' manual[END_REF]). While the ability to consider constraints is definitely a plus, as shown by [START_REF] Clever | Inverse optimal control based identification of optimality criteria in whole-body human walking on level ground[END_REF], we found that we can by-pass the constraints by using penalty methods on DDP. Moreover, the additional computational speed offered by DDP opens new avenues in which to carry our research. While speed of computation is more relevant in control of systems, the fast results by DDP give us the ability to transition smoothly from the realm of biomechanics to that of robotics. Thus, this work could possibly be extended to apply our biomechanical analysis in hardware system, in order to generate realistic humanlike movements in real time. Finally, though the generated gaits show some important anthropomorphic features of the human walking, we believe that the following propositions provide interesting directions for further improving our results: (1) Adding a cost for the contact forces to the optimization problem could lead to better movements, and be suitable for dynamic validation in a physics engine. (2) A sufficient flexion of the swinging knee was obtained by the Ground Clearance criterion. Removing this cost results in a stiff-knee with an insufficient flexion. This problem could be alleviated by adding instead a cost for the CoM to follow the Spring-Load Inverted Pendulum dynamics. (3) Since we did not try to constraint directly the knee, the maximal extension of this joint, especially during stance phase, was not reached in the simulations. A dynamic cost based on the correlation between the contact forces during the impact and the extension of the knee could be considered in future works. [START_REF] Delp | Opensim: Open-source software to create and analyze dynamic simulations of movement[END_REF] The weights in the optimization problem were so far determined empirically. An inverse optimal control method could be used to compute this weights (as it was formulated in [START_REF] Panchea | Human Arm Motion Analysis Based on the Inverse Optimization Approach[END_REF]). This is indeed a research for the future.

Fig. 1 .

 1 Fig. 1. Examples of human-like gaits obtained with Differential Dynamic Programming.

Fig. 2 .

 2 Fig. 2. Decomposition of the gait cycle. RF: right foot, LF: left foot. 3D: Three-dimensional contact. 6D: contact in translation and rotation. Red line: 3D, purple line: 6D.

2 2 , α 4 = 1 × 10 5 •

 2415 Torque minimization: Minimization of the joint torques for realistic dynamic movements. Φ 5 = τ(t)2 2 , α 5 = 1 × 10 -3 • Posture regularization: This cost deals with the redundancy of multi-body dynamics, giving as input only the final reference posture for each phase.

Fig. 4 .

 4 Fig. 4. Abduction -adduction of the right hip

Fig. 8 .Fig. 9 .

 89 Fig. 8. Plantarflexion-dorsiflexion of the right ankle

Fig. 10 .

 10 Fig. 10. Mean and standard deviation of the joint torques of the flexionextension of the right knee.

Fig. 11 .

 11 Fig. 11.Mean and standard deviation of the joint torques of the plantarflexion-dorsiflexion of the right ankle.

Fig. 12 .

 12 Fig. 12. Mean and standard deviation of the joint torques of the eversioninversion of the right ankle.

3 •

 3 Minimization of the toes velocity: (ṙ(toes) t f inal ) just before the impact of the swinging foot (applicable only on the toes and on the last node of a half cycle of gait) Φ 4 = ṙ(toes) t f inal

TABLE I THE

 I MEANS OF THE ROM FOR THE JOINT ROTATIONS (DEGREES). ‡ SIGNIFICANTLY IDENTICAL (α = 0.05). R : RIGHT, L : LEFT.

	Joint Rotations	ROM	ROM	ROM
		Simulation	Reference	Difference
	HIP R Flex/Exte	59	54	5
	HIP R Abdu/Aduc	23	24	1 ‡
	HIP R Axial rotation	12	16	4 ‡
	Knee R Flex/Exte	51	67	16
	Ankle R Dors/Plan	36	34	2 ‡
	Ankle R Ever/Inve	30	27	3 ‡
	Hip L Flex/Exte	62	57	5 ‡
	Hip L Abdu/Aduc	26	26	0 ‡
	Hip L Axial rotation	13	16	3 ‡
	Knee L Flex/Exte	48	66	18
	Ankle L Dors/Plan	35	35	0 ‡
	Ankle L Ever/Inve	29	29	0 ‡

When considering the rigid contact constraint (2) in the contact constrained dynamics (3), terms defined by Baumgarte Stabilization[START_REF] Baumgarte | Stabilization of constraints and integrals of motion in dynamical systems[END_REF] are often included to improve numerical behaviour of integration.

[START_REF] Viel | La marche humaine, la course et le saut: biomécanique, explorations, normes et dysfonctionnements[END_REF] q, q, q, τ are functions of t. We drop the dependence here for clarity.


Abbas Hodroj
email: abbas.hodroj@inpg.fr

Odette Chaix-Pluchery

Marc Audier

Ulrich Gottlieb

Jean-Luc Deschanvres

Thermal annealing of amorphous Ti-Si-O thin films

Keywords: Ti-Si-O thin films, Aerosol CVD, Multilayered microstructure, Mictamict

Ti-Si-O thin films were deposited using an aerosol chemical vapor deposition process at atmospheric pressure. The film structure and microstructure were analysed using several techniques before and after thermal annealing. Diffraction results indicate that the films remain X-ray amorphous after annealing whereas Fourier transform infrared spectroscopy gives evidence of a phase segregation between amorphous SiO 2 and well crystallized anatase TiO 2 .

Crystallization of anatase TiO 2 is also clearly shown in the Raman spectra. Transmission electron microscopy analysis indicates that anatase TiO 2 nanograins are embedded in a SiO 2 matrix in an alternated SiO 2 /TiO 2 multilayer structure.

I. INTRODUCTION

Mixed titania-silica (TiO 2 -SiO 2 ) amorphous films cover a wide range of achievable refractive index because of the large difference of the refractive index of the two compounds. This property is useful for the preparation of several optical devices (antireflective coatings [START_REF] Ouellette | Experimental studies of inhomogeneous coatings for optical applications[END_REF] , passive [START_REF] Sorek | Sol-gel glass waveguides prepared at low temperature[END_REF] or active [START_REF] Orignac | Fabrication and characterization of sol-gel planar waveguides doped with rare-earth ions[END_REF] waveguides, notch filter [START_REF] Fabes | Porosity and composition effects in sol-gel derived interference filters[END_REF] ). The mixed TiO 2 -SiO 2 thin films can also be used as dielectric materials due to a high dielectric constant, a high breakdown field and a low leakage current. [START_REF] Brassard | High-k titanium silicate thin films grown by reactive magnetron sputtering for complementary metal-oxide-semiconductor applications[END_REF] These films have been deposited by various physical methods such as electron beam evaporation [START_REF] Sankur | Crystallisation and diffusion in composite TiO 2 -SiO 2 thin film[END_REF] , sputtering [START_REF] Brassard | High-k titanium silicate thin films grown by reactive magnetron sputtering for complementary metal-oxide-semiconductor applications[END_REF][START_REF] Giauque | Thermal stability of amorphous thin films: Ti 3 Si 1 O 8 vs. TiO 2 and mictamict compounds[END_REF] , pulsed laser deposition [START_REF] Sarkar | High-k titanium silicate dielectric thin films grown by pulsed laser deposition[END_REF] and chemical methods such as sol gel [START_REF] Jiwei | Characterization and optical propagation loss of sol-gel derived TiO 2 /SiO 2 films[END_REF][START_REF] Langlet | Handbook of Sol-Gel Science and Technology: Processing Characterization and Applications[END_REF][START_REF] Song | Structure and photoluminescence properties of sol-gel TiO 2 -SiO 2 films[END_REF] and chemical vapour deposition (CVD) with low-pressure systems [START_REF] Smith | CVD of Ti x Si 1-x O 2 Films: Precursor Chemistry Impacts Film Composition[END_REF][START_REF] Lee | The deposition behaviour of SiO 2 -TiO 2 thin film by metalorganic chemical vapour deposition method[END_REF] or with assisted process (ultraviolet (UV) [START_REF] Fang | FTIR and XPS investigation of Er-doped SiO 2 -TiO 2 films[END_REF] or plasma [START_REF] Larouche | Microstructure of plasma-deposited SiO 2 /TiO 2 optical films[END_REF] ). In a previous paper, we reported a new process to obtain Ti-Si-O films by an aerosol CVD process at atmospheric pressure [START_REF] Hodroj | Growth of amorphous Ti-Si-O thin films by aerosol chemical vapor deposition process at atmospheric pressure[END_REF] . The as-deposited films are amorphous and the relative proportions of TiO 2 and SiO 2 are controlled in function of the deposition conditions.

As previously mentioned, mixed Ti-Si-O thin films have a larger number of applications in the amorphous state. These films are also obtained as composite materials with crystallized titania embedded in silica matrix. Machida et al. [START_REF] Machida | The effect of SiO 2 addition in super-hydrophilic property of TiO 2 photocatalyst[END_REF] reported that the addition of SiO 2 into a TiO 2 film yields optimum photoinduced superhydrophilicity. Such films with crystallized TiO 2 grains can be also obtained from amorphous Ti-Si-O films by thermal annealing.

Since TiO 2 and SiO 2 are immiscible [START_REF] Best | A Raman study of TiO 2 -SiO 2 glasses prepared by sol-gel processes[END_REF] , any crystallization in the mixed films implies segregation or exodiffusion of Ti. The segregation phenomenon is well reported by Sankur et al. [START_REF] Sankur | Crystallisation and diffusion in composite TiO 2 -SiO 2 thin film[END_REF] : in codeposited TiO 2 -SiO 2 films, TiO 2 crystallizes in anatase structure between 600 and 900°C and in rutile phase between 900 and 1100°C. The crystallization temperature as well as the crystal size depend on the initial composition of the film. The segregation mechanism is controlled by the Ti diffusion in the film.

In this paper we study the influence of thermal annealing under different gas atmospheres on the structure and microstructure of mixed TiO 2 -SiO 2 films deposited by aerosol CVD.

II. EXPERIMENTAL

The Ti-Si-O thin films of about 100 nm thickness were deposited on Si (100) substrate using an atmospheric aerosol CVD reactor. A precursor solution was transformed in an aerosol by ultrasonic spraying and, after transport, it was deposited by pyrolysis on a heated substrate [START_REF] Labeau | Thin films of highresistivity zinc oxide produced by a modified CVD method[END_REF] . Titanium tetrabutoxide and di-acetoxi di-butoxisilane were used as precursors, butanol-1 as solvent and acetic acid and acetylacetone as adducts. More details on this experimental process are reported in Refs. 16 and 20. Thermal transformations of two types of films were studied: films deposited at 550°C with a TiO 2 /SiO 2 atomic ratio of 40/60 (A) with a density of 2.56 g/cm [START_REF] Orignac | Fabrication and characterization of sol-gel planar waveguides doped with rare-earth ions[END_REF] and films deposited at 500°C with a TiO 2 /SiO 2 atomic ratio of 56/44 (B) with a density of 2.61 g/cm [START_REF] Orignac | Fabrication and characterization of sol-gel planar waveguides doped with rare-earth ions[END_REF] . The film composition and density were obtained from X-ray Photoelectron Spectroscopy (XPS) and electron probe microanalysis. Pure TiO 2 and SiO 2 reference films were grown using the same process.

Annealing treatments were performed at different temperatures ranging from 700°C to 950°C for 1 to 12 hours in air or argon atmosphere.

X-ray diffraction (XRD) data were obtained on a q/2q Siemens D500 (Bruker-AXS, Marne la Vallée, France) powder diffractometer (Cu K a1 l=0.15406 nm) or on a Siemens D500 (Bruker-AXS) powder diffractometer (Fe K a1 l=0.19374 nm) at grazing incidence angle of 3°. Fourier transform infrared spectroscopy (FTIR) measurements were performed in transmission geometry using a "BioRad" spectrometer. Raman spectra were collected using a Jobin Yvon/Horiba LabRam spectrometer (Villeneuve d'Asq, France) equipped with a liquid nitrogen cooled chargecoupled device (CCD) detector. Experiments were conducted in the micro-Raman mode at room temperature in a backscattering geometry. The 514.5 nm line of an Ar + laser was focused to a spot size smaller than 1 µm. The incidence laser power measured at the sample surface was close to 7 mW. Cross sections of Ti-Si-O thin film specimens were characterized by Transmission Electron Microscopy (TEM) using a high resolution JEOL 2010 (Tokyo, Japan). Observations were made on small fragments, obtained by scraping the thin film surfaces, deposited on copper grids coated with a carbon film.

III. RESULTS AND DISCUSSION

XRD diagrams of both types of films (atomic ratio TiO 2 /SiO 2 = 40/60 and 56/44) obtained either in a classical q/2q configuration or with grazing incidence showed no Bragg reflections.

Either an amorphous or a nanocrystalline state below the X-ray coherence length can explain such diagrams.

FTIR absorption spectra of amorphous SiO 2 , anatase TiO 2 and mixed A films before and after annealing for 1 hour at 950°C under air are shown in Fig. 1. The pure SiO 2 spectrum (Fig. 1a) presents absorption bands at 450 and 1075 cm -1 attributed to Si-O-Si asymmetric rocking and stretching vibrations, respectively [START_REF] Brassard | High-k titanium silicate thin films grown by reactive magnetron sputtering for complementary metal-oxide-semiconductor applications[END_REF] . Absorption bands observed at 435 and 260 cm -1 in the case of pure TiO 2 (Fig. 1b) are characteristic of the TiO 2 anatase crystal structure [START_REF] Gonzalez | Infrared reflectivity and lattice fundamentals in anatase TiO 2[END_REF][START_REF] Busca | FT Raman and FTIR studies of titania and metatitanate powders[END_REF] . For the asdeposited A film spectrum (Fig. 1c), the broad absorption band at around 440 cm -1 may result from a mixture of both Si-O-Si and Ti-O bands; the bands at 930 and 1050 cm -1 come from Ti-O-Si and Si-O-Si bonding, respectively [START_REF] Brassard | High-k titanium silicate thin films grown by reactive magnetron sputtering for complementary metal-oxide-semiconductor applications[END_REF] . After annealing (Fig. 1d), the Si-O-Si band is slightly shifted to ~ 1060 cm -1 and its intensity increases whereas the Ti-O-Si band nearly disappears. Despite a quite noisy signal, the absorption band around 440 cm -1 seems to split in two lines, at 430 cm -1 (Ti-O stretching) [START_REF] Fang | FTIR and XPS investigation of Er-doped SiO 2 -TiO 2 films[END_REF] and ~ 450 cm -1 (Si-O-Si asymmetric rocking). Moreover, a band is noticed at 266 cm -1 as in the pure TiO Figure 2 shows the evolution of the Raman spectra of A and B mixed films before and after several thermal annealings at 700°C, 800°C and 950°C for 1 hour under air. Spectra of pure SiO 2 and pure TiO 2 films are also shown. It is to be noticed that the pure SiO 2 /Si spectrum is identical to the Si substrate spectrum (not shown in the figure). The pure TiO 2 film spectrum contains three lines at 143, 395 and 638 cm -1 which are characteristic of the TiO 2 anatase phase and assigned to E g , B 1g and E g modes, respectively [START_REF] Busca | FT Raman and FTIR studies of titania and metatitanate powders[END_REF] .

The spectra of as-deposited mixed TiO 2 -SiO 2 films do not differ from that of the Si substrate nor from the SiO 2 /Si one, which is in agreement with an amorphous state and with the fact that TiO 2 -SiO 2 composite films are known to stay amorphous as long as the SiO 2 atomic content exceeds 15% [START_REF] Sanders | Glassy optical coatings by multisource evaporation[END_REF] . After annealing at 700°C a small and broad band can be noticed at ~ 151 cm -1 for both films; its intensity is slightly stronger in B film. This band is assigned to the low wavenumber anatase E g mode and is a sign of the beginning of TiO 2 crystallization [START_REF] Chang | Thermo-Raman Studies on Anatase and Rutile[END_REF] . When the annealing temperature is raised to 800°C, the E g line gets better defined and shifts slowly to smaller wavenumbers. After annealing at 950°C, the spectra of both films show a well-defined E g line at ~ 143 cm -1 in B film and ~ 146 cm -1 in A film, as well as two other lines characteristic of the TiO 2 anatase phase. Whatever the annealing temperature, the Raman lines of the TiO 2 anatase phase in films with higher TiO 2 content are always sharper and slightly shifted towards lower wavenumbers in comparison with those with lower TiO 2 content.

Let us now discuss the two possible origins of the shift of the TiO 2 E g mode from 151 to 143/146 cm -1 induced by the thermal treatment: a size effect or a stress effect. The increase of the annealing temperature improves the crystalline state of TiO 2 and usually causes an increase of the TiO 2 grain size. The Raman spectrum of TiO 2 nanoparticles has been extensively studied due to the unusual broadening and shifts of the Raman lines with decreasing particle size and because the intense E g line appears as the most sensitive line to reveal size effects. The shift towards low wavenumbers actually indicates an increase in particle size, as reported in several papers [START_REF] Choi | Size effects in the Raman spectra of TiO 2 nanoparticles[END_REF][START_REF] Kelly | Raman Spectroscopy as a Morphological Probe for TiO 2 Aerogels[END_REF] . The second possible origin of such a shift could be a compressive stress effect of the SiO 2 matrix on the TiO 2 nanograins. The TiO 2 spectra of the films annealed at 950°C would thus reveal a stress relaxation of the TiO 2 particles, complete in the B film as observed by the similarity between its Raman spectrum and the reference anatase spectrum, and partial in A. This can be explained by a higher compressive stress of the matrix on the TiO 2 crystallites, which are smaller in A film.

Indeed, it is reported that an increase in TiO 2 content in TiO 2 -SiO 2 codeposited films involves an increase in TiO 2 crystal size [START_REF] Sankur | Crystallisation and diffusion in composite TiO 2 -SiO 2 thin film[END_REF] . Our Raman results do not allow elimination of one of the two hypotheses since both size and stress effects are related each other; we will see in the following section that TEM observations rather suggest that the stress effect is dominant.

Bright field transmission electron micrographs of mixed A film cross sections and corresponding selected area electron diffraction patterns are reported in Fig. 3. The film thickness indicated on each bright field image was determined with respect to 111 lattice fringes observed on Si substrates (i.e., d 111 = 3.134 Å). For the as-deposited sample (Fig. 3a), an amorphous SiO 2 layer of about 1.5 nm in between the thin film and the Si substrate can be identified by its average Z contrast lower than that of the amorphous Ti-Si-O film. Let us note that the film exhibits a speckled contrast which, along with being an effect of the transfer function of the microscope, could partly result from an unmixing of amorphous states. The corresponding electron diffraction pattern (Fig. 3b) is composed of the reflections of the Si substrate oriented along a [110] zone axis and of a broad diffuse ring centered at about 1.8 Å -1 . After annealing at 950°C under air for 1 hour, crystalline particles of anatase TiO 2 of less than 10 nm size and embedded in a SiO 2 matrix are observed (Figs. 3c and3d). The anatase structure is unambiguously identified from a comparison between the diffracting rings observed on the corresponding electron diffraction pattern (Fig. 3d) and a simulation of the anatase diagram. Curiously, the TiO 2 particles appear to be arranged in a multilayered structure parallel to the (001) surface of the silicon substrate. Six strata of TiO 2 particles can be observed in this case. Because of the annealing treatment under air, an important oxidation of the Si substrate has occurred giving rise to an increase of the SiO 2 interface layer thickness (up to 45 nm), probably by ionic oxygen and electronic diffusion. This thick SiO 2 layer can explain the intensity increase of the Si-O-Si band at ~ 1075 cm -1 observed in the corresponding FTIR spectrum (Fig. 1d).

Such an oxidation effect can be avoided by using argon instead of air during the annealing treatment (Fig. 3e). In this case, however, smaller crystalline TiO 2 particles of less than 5 nm size are formed. A multilayered microstructure is also observed but with more strata of TiO 2 particles (11 or 12 strata). The identification of the anatase structure shown in

IV. CONCLUSIONS

Complementary techniques were used to study the influence of thermal annealing on the structure and microstructure of 100 nm thick TiO 2 -SiO 2 films deposited by aerosol CVD at atmospheric pressure.

Although the films remain X-ray amorphous at annealing temperatures as high as 950°C,

  2 anatase spectrum. Similar spectra have been obtained for mixed B films, only band intensities are different. These results could be explained by phase segregation, i.e. a partial (or total) separation of the TiO 2 and SiO 2 phases; TiO 2 crystallizes in anatase structure whereas SiO 2 remains amorphous. The intensity increase of the band at 1075 cm -1 after annealing can occur because the FTIR spectra have been obtained in transmission configuration where SiO 2 signal is provided by both the TiO 2 -SiO 2 film and SiO 2 formed during annealing on the backside of the substrate.

  Fig. 3f corresponds to a selected area of a plane view of the thin film. After a second annealing at 950°C for 11 hours, only a few changes are observed (Figs. 3g and 3h); the average size of TiO 2 has slightly increased of about 15 % and, as observed in the thicker part of the cross section, the number of strata of TiO 2 particles has reduced to six. The formation of these alternated TiO 2 -SiO 2 multilayers or strata in Ti-Si-O thin films after annealing can result from the regular Ti diffusion in the mixed films in order to obtain stress relaxation, as observed in Raman spectra. The number of TiO 2 strata varies between six and twelve, depending on the initial film thickness, on the grain size and the gas atmosphere during annealing. All these results related to mixed TiO 2 -SiO 2 thin films prepared by aerosol CVD agree with those reported in literature for films obtained by other deposition techniques. Song et al 11 prepared TiO 2 -SiO 2 films by sol-gel from starting solution with Si/Ti ratio equal to 1/1. After thermal treatment at temperatures up to 950°C, they observed anatase TiO 2 nanocrystallites embedded in a SiO 2 -rich matrix. Our Raman results show that the incorporation of SiO 2 in a TiO 2 film raises the crystallization temperature of the TiO 2 anatase phase as reported by Giauque et al 7 et by Sankur et al 6 on mixed TiO 2 -SiO 2 films prepared by reactive magnetron sputtering and electron beam evaporation, respectively.

FTIR 5 Figure captions Fig. 1 :

 5captions1 Figure captions

Fig. 2 :

 2 Fig. 2: Raman spectra of amorphous SiO 2 film, anatase TiO 2 film, mixed TiO 2 -SiO 2 films with atomic ratios TiO 2 /SiO 2 = 40/60 (A) and 56/44 (B) as-deposited and annealed at 700°C, 800°C and 950°C for 1 hour under air.

Fig. 3 :

 3 Fig. 3: Bright field transmission electron micrographs and selected area diffraction patterns of a mixed TiO 2 -SiO 2 film (A: atomic ratio TiO 2 /SiO 2 = 40/60) (a, b) as-deposited, (c, d) annealed for 1 hour at 950°C under air, (e, f) annealed for 1 hour at 950°C under argon, (g) annealed for 12 hours at 950°C under argon. The insets in (a), (c) and (e) correspond to high resolution images of the Si/film interface. A multilayer microstructuring is shown in (h).

  Fig.1

Fig. 3

 3 Fig. 3

ACKNOWLEDGMENTS

This work was supported by the European Community in the framework of the Network of Excellence FAME (Functional Advanced Materials and Engineering of hybrids and ceramics).

We thank also Dr. Jens Kreisel (LMGP, Grenoble, France) for his helpful remarks.

and 10 nm size, and 6 and 12 layers, respectively, for films annealed at 950°C for 1 hour. In agreement with Raman results, such a multilayered structure may favour a stress relaxation in the films. All these results indicate that TiO 2 -SiO 2 films belong to the quasi binary Mictamict alloys (mictamict: mictos-amictos in Greek, means miscible-immiscible) [START_REF] Giauque | Thermal stability of amorphous thin films: Ti 3 Si 1 O 8 vs. TiO 2 and mictamict compounds[END_REF] .


Marion Pitorre

Guillaume Bastiat

Le Pham

Jean-Pierre Benoît

The

The same nucleoside crosslinking agent to develop hydrogel and organogel platforms

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

The same nucleoside crosslinking agent to develop hydrogel and organogel platforms Marion Pitorre 1,2 , Guillaume Bastiat 1,2 , Le Thuy Trang Pham 1,2 and Jean-Pierre Benoit 1,2 1 LUNAM, MINT, Angers, France ; 2 INSERM, U1066, Angers

• Gels are attractive pharmaceutical systems to develop local administration and/or drug sustained release therapy. • Nanoparticle-loaded gels combine the gel advantages with the nanoparticle properties: stealthiness, targeting site, decreased toxicity and protection of the encapsulated drug from degradation. • Previously, the formulation of gemcitabine-loaded lipid nanocapsules (LNCs) formed an unexpected and spontaneous gelling [1]. • This hydrogel was due to H-bond interactions between gemcitabine moieties exposed at the LNC surface.

• The subcutaneous administration of this hydrogel in mice showed a sustained release of LNCs along with a progressive accumulation in lymph nodes, and allowed to combat mediastinal metastases issued from an orthotopic non-small-cell lung cancer model [2].

We decided to develop the same platform without the use of gemcitabine (highly toxic component), replacing it by an endogenous molecule with similar properties.

Contact

marion.pitorre@univ-angers.fr guillaume.bastiat@univ-angers.fr jean-pierre.benoit@univ-angers.fr

Conclusion

Cyt-C16 is a very promising crosslinking agent to obtain two gel platforms with opposite properties. The LNC-based hydrogel could allow sustained release of lipophilic drug loaded nanocarriers after subcutaneous administration. Whereas, sustained release of hydrophilic components could be obtained from the organogel.

Cyt-C16 was also able to form an organogel. The molecule was simply solubilized in an oil phase at high temperature and a gel was formed after cooling. Viscoelastic properties of the organogel were enhanced with increasing Cyt-C16 concentration (Kinexus® rheometer, Malvern Instruments S.A,). (mean ± sd; n=3)

• Rheological properties

A gel form could be obtained at a Cyt-C16 concentration of 1 or 2.5% (w/w Labrafac®) and LNC concentration higher than 0.2 g/mL, for LNC sizes from 50 to 100 nm. For all the gels, phase transition temperatures were higher than the body temperature (> 70°C) (Kinexus® rheometer, Malvern Instruments S.A). (mean ± sd; n=3)

• Cytotoxicity

Cell mortality study on a macrophage cell line (derived from THP-1 cell line) confirmed the safety of Cyt-C16, comparing LNCs with and without Cyt-C16. (48h incubation, 37°C, MTT test, mean ± sd, n=3) An administration with a syringe does not alter the gel state of the formulation. Inclusion of urea, sodium chloride and ethanol (60 mol for 1 mol Cyt-C16) in the formulation to inhibit physical association, did not change the rheological properties of the hydrogel. An hydrogel resulted from H-bond interactions between LNCs, forming a network in water similar to a tridimensional pearl necklace structure.

Organogel

was due to interactions between Cyt-C16, forming fiber network in oil. LNC 50 nm Cyt-C16 2.5%

LNC 100 nm Cyt-C16 2.5%

  in vitro release of LNCs from hydrogel study was performed in artificial extracellular matrix (pH 7.4) at 37°C over 3 days. LNCs were labelled with nile red dye and followed by fluorescence.(2.5% w/w Labrafac®, mean ± sd; n=3)


Marion Pitorre

Karolina Frankova

Jérôme Bejaud

Le Pham

Jean-Pierre Benoit

Guillaume Bastiat
email: guillaume.bastiat@univ-angers.fr

Jérôme Béjaud

Le Thuy

Trang Pham

a new generation of implants to control drug sustained releases

INTRODUCTION

New drug delivery systems were designed as nanoparticle-loaded hydrogels. These attractive pharmaceutical systems combine the gel advantages: local administration and/or a drug sustained release, and nanoparticle properties: stealthiness, targeting and decreased toxicity. Nevertheless, even using biodegradable polymer to design the gel matrix, implants can always be found at the injection site long time after administration. This research focuses on the development of lipid nanocapsule (LNCs)-based hydrogels without the use of polymer, and the drug release profiles from the hydrogel and their modulation correlated to hydrogel characteristics.

CONCLUSION

New generation of nanoparticle-loaded hydrogels: LNC-based, polymerfree hydrogels is promising as implants for health application. Once the LNC release is completed, no gel matrix remains at the injection site, minimizing the additional toxicity due to the persistence of polymeric implant. Drug sustained release profiles can be controlled by the mechanical properties of the hydrogels and will be tailor-made, depending on the therapeutic strategies.

ACKNOWLEDGMENTS

Authors wish to acknowledge European Community (Project NICHE), and charitable associations LIGUE contre le Cancer and Fondation ARC pour la recherche sur le cancer for providing financial support for this work.

SYNTHESIS OF CROSS-LINKING AGENTS

The two aliphatic-modified cytidine and gemcitabine exhibit amphiphilic properties, at oil/water interface. They are positioned at the surface of lipid nanocapsules (LNCs), formulated using a phase inversion process.

Hydrogels of LNCs

RELEASE PROFILES Drop tensiometer (Teclis Scientific) n = 3, mean  SD

In the hydrogel, lipophilic drugs were encapsulated in LNCs and hydrophilic ones were loaded in medium around the LNC network. The LNC (and lipophilic drug) release profiles are controlled by mechanical properties of the hydrogels (slower release profiles correlated with higher mechanical properties). There is no correlation between hydrophilic drug release profiles and hydrogel viscoelastic properties (due to drug diffusion). Whatever the hydrogel characteristics, total LNC release profiles were achieved and hydrogels were totally solubilized leading to LNC suspensions.


Claire Gazaille

Marthe Akiki

Joël Eyer

Guillaume Bastiat

Quantification of peptide adsorption on lipid nanocapsules without prior purification or separation process

Better NFL adsorption with negatively charged LNCs.

Results consistent with the positive charge of NFL. 7 Hypothesis : electrostatic interactions between NFL and LNCs.

LNC formulation 5,6

To quantify the encapsulation rates of active agents (drug, protein, etc.) in nanoparticles, the separation of non-loaded agents from the loaded ones is often reported in literature, using dialysis or centrifugal filters. 1,2 However, these techniques are more and more questioned, and the low quality of the separation could lead to over or underestimated data. 3,4 To avoid the biases, a method was developed to quantify free peptide proportions without prior separation step from peptide adsorbed at the nanoparticle surface, using NFL-TBS.40-63 (NFL) and lipid nanocapsules (LNCs) as peptide and nanoparticle models, respectively.

Influence of LNC charge on NFL adsorption 4. Influence of LNC composition on NFL adsorption

Influence of LNC size on NFL adsorption

When the LNC surface increases, NFL adsorption is enhanced.

Thanks to a size exclusion method, the separation between nanoparticles and active agent and their quantification are performed simultaneously. This single step is a real benefit for analysis accuracy and robustness, minimizing the biases compared to sequential steps for separation and quantification. In this particular case, the best combinations of concentrations/types of LNCs and NFL were determined to achieve a total NFL adsorption at LNC surface. This technique could be a promising tool to characterize other nanoparticle/active agent interactions.

Interaction inhibition between NFL and LNCs

Inhibition of NFL adsorption at LNC surface when NaCl and urea are present.

Proof of electrostatic interactions and hydrogen bonds between LNCs and NFL.

Figure 1 .

 1 Figure 1. Chromatogram showing the retention times of LNCs (3.5 minutes) and NFL (7.7 minutes) on size exclusion column.

•

  Oil : Labrafac® • Surfactants : Span® 80, Kolliphor® • De-ionised water • NaCl NFL and Span® 80 at LNC surface.

Figure 3 .

 3 Figure 3. Influence of Span® 80 composition of LNCs on NFL adsorption. LNCs were used at 0.975 mg/mL and NFL at 0.1 mg/mL. The LNC size corresponds to 50 nm. (Mann-Whitney test ; ** p < 0.01 ; ns p > 0.05 ; n = 4-5 ; mean ± SD).

Figure 4 .

 4 Figure 4. Influence of LNC size on NFL adsorption. LNCs were used at 0.975 mg/mL and NFL at 0.1 mg/mL. (Mann-Whitney test ; * p < 0.05 ; ns p > 0.05 ; n = 4-5 ; mean ± SD)

Figure 5 .Figure 2 .

 52 Figure 5. Inhibition of interactions between NFL and LNCs in presence of NaCl and urea. LNCs were used at 9.75 mg/mL and NFL at 0.1 mg/mL. The LNC size corresponds to 50 nm. (n = 3 ; mean ± SD)

Acknowledgments


David Rondeau
email: david.rondeau@univ-rennes1.fr

Yves Gimbert

Karoly Vekey

Laszlo Drahos

Mathieu Turbiez

Pierre Frère

Jean Roncali

Károly Vékey

Laszlo Dráhos

Mass Spectrometry Evidence for Self-Rigidification of π-Conjugated Oligomers Containing 3,4-Ethylenedioxythiophene (EDOT) Groups using RRKM Theory and Internal Energy Calibration

Keywords: Conjugated systems, oligothiophenes, RRKM, MIKES, unimolecular dissociations

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

Introduction

Owing to a unique combination of moderate band gap, stability and structural versatility, thiophene-based pi-conjugated systems have been a focus of considerable fundamental and technological interest for almost four decades. [START_REF] Roncali | Conjugated poly(thiophenes): synthesis, functionalization, and applications[END_REF] In this context, the control of the energy levels of frontier orbitals and hence of the band gap of the corresponding materials represent key issues for the potential applications of these materials in organic (opto)electronics and photovoltaics. [START_REF] Roncali | Molecular Engineering of the Band Gap of π-Conjugated Systems: Facing Technological Applications[END_REF][START_REF] Cheng | Synthesis of Conjugated Polymers for Organic Solar Cell Applications[END_REF] The design and synthesis of low band gap thiophene-based conjugated systems has been developed along different approaches such as the increase of the quinoid character of the thiophene ring, the synthesis of systems containing alternating electronreleasing and electron-withdrawing groups, or the planarization and rigidification of the conjugated backbone by covalent or non-covalent intramolecular interactions . [START_REF] Roncali | Molecular Engineering of the Band Gap of π-Conjugated Systems: Facing Technological Applications[END_REF] Besides being the monomer of the well-known poly(3,4-ethylendioxythiophene) (PEDOT) initially developed by Bayer. [START_REF] Groenendaal | Poly(3,4ethylenedioxythiophene) and Its Derivatives: Past, Present, and Future[END_REF] EDOT is also an interesting building block which combines strong electron-donor properties with the ability to planarize and rigidify the π-conjugated systems in which it is inserted by means of intramolecular non-covalent sulfur-oxygen interactions. [START_REF] Turbiez | Mixed p-conjugated oligomers of thiophene and 3,4-ethylenedioxythiophene (EDOT)[END_REF][START_REF] Raimundo | Push-pull chromophores based on 2,2′bi(3,4-ethylenedioxythiophene) (BEDOT) π-conjugating spacer[END_REF][START_REF] Roncali | 3,4-Ethylenedioxythiophene (EDOT) as a versatile building block for advanced functional π-conjugated systems[END_REF][START_REF] Turbiez | Design of organic semiconductors: tuning the electronic properties of pi-conjugated oligothiophenes with the 3,4-ethylenedioxythiophene (EDOT) building block[END_REF] These phenomena have been investigated in detail on series of hybrid conjugated oligomers based on various combinations of thiophene (T) and EDOT (E) moieties. [START_REF] Turbiez | Design of organic semiconductors: tuning the electronic properties of pi-conjugated oligothiophenes with the 3,4-ethylenedioxythiophene (EDOT) building block[END_REF] An interesting case is given by the comparison of quaterthiophenes ETTE and TEET (Scheme 1). In fact, whereas TEET is fully rigidified by four intramolecular S…O interactions, for ETTE only the two ET pairs are rigidified by a single S…O interaction while a free rotation is possible around the central T-T single bond (Scheme 1). Scheme 1: Chemical structures of ETTE and TEET rigidified by non-covalent sulfur-oxygen interactions (dashed lines).

The crystallographic structure of these two compounds has been reported and their electronic properties have been investigated by UV-Vis absorption spectroscopy and cyclic voltammetry. The results provide a coherent picture showing that moving the two E units from the outer to the inner positions leads to a more rigid structure as confirmed by X-ray data and by the exaltation of the vibrational fine structure of the absorption spectrum. On the other hand, the CV of the two compounds show that this structural modification leads to a negative shift of the first oxidation potential with a large increase of the difference between the first and second anodic peak potential (from 270 to 440 mV). These results indicate a better electron delocalization in the radical cation in TEET but a strong increase of the coulombic repulsion between positive charges in the dication state (Figure 1). 8 To summarize, the major role of EDOT in the self-rigidification and planarization of πconjugated systems is well-established, and namely the influence of its position on the oligomer physico-chemical properties as highlighted by the measurements performed from the TEET and ETTE isomers. [START_REF] Turbiez | Mixed p-conjugated oligomers of thiophene and 3,4-ethylenedioxythiophene (EDOT)[END_REF][START_REF] Raimundo | Push-pull chromophores based on 2,2′bi(3,4-ethylenedioxythiophene) (BEDOT) π-conjugating spacer[END_REF][START_REF] Roncali | 3,4-Ethylenedioxythiophene (EDOT) as a versatile building block for advanced functional π-conjugated systems[END_REF][START_REF] Turbiez | Design of organic semiconductors: tuning the electronic properties of pi-conjugated oligothiophenes with the 3,4-ethylenedioxythiophene (EDOT) building block[END_REF] However, whereas this behaviour has been widely demonstrated for neutral species, experimental evidences for the occurrence of such effects on radical cations are still lacking.

Mass spectrometry can provide a suitable tool for studying the intrinsic behaviour of such charged species through the ion unimolecular dissociation reactions. The structural identification performed for validating the synthesis of the ETTE and TEET compounds has previously shown that their low resolution mass spectra recorded using electron impact (EI) ionization, exhibit the same fragment ions m/z 418 and m/z 390. In these ion source mass spectra, the m/z 390 ion intensity is greater than that of the m/z 418 in the case of the ETTE radical cation fragmentation whereas the opposite result is obtained for TEET. In the theory of mass spectra, the ion intensities are related to their dissociation kinetics. [START_REF] Lafferty | Interpretation of Mass Spectra[END_REF] As a result, we assume that the difference in ion intensity ratios is a function of the vibration mode of each of the two fragmenting oligomers ETTE and TEET. The aim of this paper is then to account for the difference in planarization of these π-conjugated systems. For highlighting this property we have simulated the behaviour of these ions that dissociate in the second field free region (FFR2) of a designed magnetic mass spectrometer using the MassKinetics Software. [START_REF] Drahos | MassKinetics: a theoretical model of mass spectra incorporating physical processes, reaction kinetics and mathematical descriptions[END_REF]

Theory

In mass spectrometry, the ion decay due to dissociation processes depends on the fragmentation reaction rate ( , int ( ) i j k E ) of an ion i at a given internal energy (E int ) producing a fragment ion j. The value of , int ( )

i j k E
can be calculated using the RRKM formalism developed in the context of the transition state theory (TST) such as: [START_REF] Marcus | The Kinetics of the Recombination of Methyl Radicals and Iodine Atoms[END_REF][START_REF] Rosenstock | Absolute Rate Theory for Isolated Systems and the Mass Spectra of Polyatomic Molecules[END_REF] (

) ‡ int 0 , int int ( ) ( ) σ ρ - = i j N E E k E h E (1)
where, σ is the reaction degeneracy, h is Planck's constant, E 0 is the reaction critical energy,

N ‡ (E int -E 0 )
is the sum-of-states at the transition state (TS) from 0 to E int -E 0 and ρ(E int ) is the density of states of the dissociating ion at an energy level equal to E int . The evaluation of the sum and density of states is usually done by a direct count using the Beyer-Swinehart algorithm with the harmonic oscillator model applied with internal rotations approximated by low-frequency vibrations. [START_REF] Beyer | Algorithm 448: Number of Multiply-restricted Partitions[END_REF] The frequency file of an ion in its ground state is usually obtained from quantum chemical calculations. To evaluate the vibration frequency file of the activated complex at the TS, a frequency value close to the vibration mode corresponding to the reaction coordinate (CR) is removed and five other frequencies are scaled to obtain a value of the well-known Arrhenius pre-exponential (A pe ) factor. [START_REF] Vékey | Internal Energy Effects in Mass Spectrometry[END_REF] This one is considered as a convenient parameter for describing the differences between the vibrational frequencies of the reacting ion and the TS. [START_REF] Baer | Statistical Rice-Ramsperger-Kassel-Marcus quasiequilibrium theory calculations in mass spectrometry[END_REF] The A pe factor is related to the vibrational activation entropy difference ( o r m S Δ á ). [START_REF] Baer | Unimolecular Reaction Dynamics: Theory and Experiments[END_REF][START_REF] Holmes | Proton Affinities of Primary Alkanols: An Appraisal of the Kinetic Method[END_REF] An A pe value of the order of 10 14 characterizes dissociation reactions where few oscillation modes disappear between the reactant ion and the TS. [START_REF] Robinson | Unimolecular reactions[END_REF] Conversely, ~ 10 10 A pe values are in agreement with unimolecular dissociation reactions where a fragmenting ion is less ordered at its ground state than at the TS. [START_REF] Robinson | Unimolecular reactions[END_REF] For an ion taken at a given E int that dissociates via two competitive channels, the relative daughter ion intensities are related to the relative magnitudes of the reaction rate constants , int ( ) i j k E characterizing the ion dissociation process j. In the case of the studied oligomers ETTE and TEET where i is related to the m/z 446 parent ion and j either to the m/z 418 or 390 daughter ion, one can state that the ratios of the rate constants and the daughter ion intensities (I j ) are such that: 2). At a given E int , the fragment ion intensities of the each isomer oligomer are related to the ratios of the dissociation rate constants that roughly depends on the A pe (i → j) factor and the fragmentation critical energy E 0 (i → j) characterizing each dissociation processes. Such an assumption is valuable because the deposited energy during the ionization process at 70 eV of the ionizing electron kinetic energy is considered as reproducible for these two isomers that fragment through the same dissociation mechanism. [START_REF] Cooks | Metastable ions[END_REF] As a result, if E 0 (i → j) is evaluated from theoretical calculations and by assuming that the TS of the reaction leading to the isobaric ions have the same vibrational properties whatever for the ETTE or TEET dissociating ion, then the measured differences in term of ion intensities depend only of the relative planarization of the reacting ion at its ground state.

( ) ( )
m z m z m z m z m z m z I k E k E I ∝ (
The Mass Kinetics algorithm generates theoretical mass spectra from simulated mass spectrometric processes. It is a general framework that allows for calculating dissociation reaction rates, transition probabilities between different ion states and the abundances of the ions moving through different parts of a mass spectrometer whose geometry and acting parameters are modelised. [START_REF] Drahos | MassKinetics: a theoretical model of mass spectra incorporating physical processes, reaction kinetics and mathematical descriptions[END_REF] In MassKinetics the ions are characterized by their internal and kinetic energies that's define the 'state' of a given ion. The MassKinetics modelling was namely applied to the internal energy distribution P(E int ) evaluation of ions emitted in electrospray ionization sources interfaced with different mass spectrometers, [START_REF] Naban-Maillet | Internal energy distribution in electrospray ionization[END_REF][START_REF] Pak | Internal energy distribution of peptides in electrospray ionization : ESI and collision-induced dissociation spectra calculation[END_REF][START_REF] Rondeau | Non-thermal internal energy distribution of ions observed in an electrospray source interfaced with a sector mass spectrometer[END_REF][START_REF] Ichou | Collision cell pressure effect on CID spectra pattern using triple quadrupole instruments: a RRKM modeling[END_REF][START_REF] Rondeau | Internal energy distribution in electrospray ionization: towards the evaluation of a thermal-like distribution from the multiple-collision model[END_REF] ion-molecule reaction studies in the application field of the collision activated reaction experiments (CAR) [START_REF] Gatineau | Experimental bond dissociation energies of benzylpyridinium thermometer ions determined by threshold-CID and RRKM modeling[END_REF] and kinetic energy release determination (KERD) of metastable ions fragmenting in sector mass spectrometer. [START_REF] Gömöry | Kinetic Energy Release of Protonated Methanol Clusters Using the Low-Temperature Fast-Atom Bombardment: Experiment and Theory Combined[END_REF][START_REF] Drahos | Theoretical calculation of isotope effects, kinetic energy release and effective temperatures for alkylamines[END_REF] For the present work, the ion intensity theoretical ratios (see equation 2) have been compared

with the measurements performed from Mass-analyzed Ion Kinetic Energy Spectrometry (MIKES) experiments. The considered adjusting parameter was the A pe factor since the E 0 values are inspired from literature data. The calibration in E int of such experiments has been performed by a preliminary study that allows us to evaluate the internal energy distribution P(E int ) of reacting ions by using the well-known reactivity of the butylbenzene radical cation.

The latter is considered as a thermometer ion for calibrating the internal energy deposited in compounds ionized under EI at 70 eV electro, kinetic energy. [START_REF] Nacson | Energy transfer in collisional activation. Energy dependence of the fragmentation of n-alkylbenzene molecular ions[END_REF][START_REF] Baer | Dissociation Dynamics of n-Butylbenzene Ions: The Competitive Production of m/z 91 and 92 Fragment Ions[END_REF][START_REF] Dawson | Low-energy collision-activated dissociation of n-butylbenzene. Effect of the electron energy used during parent ion formation[END_REF][START_REF] Plomley | The Consecutive Fragmentation of n-Butylbenzene in a Quadrupole Ion Trap[END_REF][START_REF] Muntean | Modeling Kinetic Shifts for Tight Transition States in Threshold Collision-Induced Dissociation. Case Study: Phenol Cation[END_REF]

Materials and Methods

Chemical

The two oligomers have been synthesized by Stille coupling reactions as already described. [START_REF] Turbiez | Design of organic semiconductors: tuning the electronic properties of pi-conjugated oligothiophenes with the 3,4-ethylenedioxythiophene (EDOT) building block[END_REF] Thus, ETTE was obtained in 78 % yield by reacting a slight excess of stannic derivative of EDOT onto 5,5'-dibromo-2,2-bithiophene. For TEET, an excess of 2-bromothiophene was coupled to the bisstannic derivative of bis-EDOT leading to the target molecule in 50% yield.

Chemical quantum calculation

All calculations were performed using the Gaussian 09 software package. i Optimization of geometries, frequency and single point energy calculations were done using the B3LYP functional ii with the basis set 6-31G** iii Table 1.

Species

Frequencies (cm -1 ) ETTE +.

Table 1: Frequency file obtained from theoretical

Mass Spectrometry

Experiments were performed on a JMS-700 double-focusing (B/E) mass spectrometer with reversed geometry (JEOL, Akishima, Tokyo, Japan). The analytes were introduced in the ion source via a direct inlet probe equipped with a cooling water device that keeps the sample temperature at a constant value. Calibration compound (PFK) was introduced into the mass spectrometer ion source via the standard sample inlet device. Ions are produced by Electronic Impact (EI) ionization in positive ion mode with a 300 µA ionizing current and a 70 eV ionizing energy. Depending on the experiment, the source temperature was kept at 200 °C or 300 °C. Low-resolution full-scan mass spectra (typically R = 1000 at 10% valley) were obtained by scanning the magnetic field over a wide range of mass-to-charge ratios while keeping constant the electric field for an accelerating voltage (V acc ) value of 10 kV. Elemental composition of the ions was checked by high resolution measurements (typically R = 10000 at 10% valley) using an electric field scan method with PFK ions as internal standard. In this case, the accelerating voltage (V acc ) and the electric field are scanned while the magnetic field is being kept constant. Metastable ion (MI) spectra were obtained by the MIKES experiments where the dissociations take place in the second field-free region (FFR2), i.e. after the magnetic sector and before the electric sector. The molecular ion (M +. ) produced from analysed compounds, was selected using the magnetic sector and the product ions were analysed by scanning the electric filed while the magnetic field is kept constant for a V acc value fixed at 10 kV. For the measurement of the survival yields (SY) and the ratios of the daughter ion amounts, the MIKE spectra were collected by averaging the signals measured on each set of ten MIKE scans. Each MIKE spectrum was treated by the SigmaPlot™ Software in order to express the number of ions via the calculion of the area under the detected peak.

Note that for all the measurements related to the metastable ion formation, the voltage values of the different part of the ionization chamber were maintained at constant values, i.e. the voltage of the ion accelerating refinement, the repeller lens, the first and the second focus lenses and the deflector lens. The determination of ion survival yields (SY) was performed using the well-known equation (3) such as:

1 P n i P i I SY I F + + + = = + ∑ (3)
, where in the case of the butylbenzene full scan mass spectra, P I + is the intensity of the m/z 134 parent ion, and

1 n i i F + = ∑
is the sum of the two fragment ions at m/z 92 and 91.

Mass spectra modelling

Theoretical survival yields and ion abundance ratios were calculated using the MassKinetics software (ver. 1.17), available at http://proteomics.ttk.mta.hu/masskinetics/. The simulations performed by MassKinetics use internal and kinetic energy distribution functions together with the probabilities that describe transition between different states of an ion. For the present study, the considered changes in kinetic and internal energies of the ions in the gas phase are due to acceleration in electromagnetic fields and energy partitioning in chemical reactions.

In the case of the butylbenzene ion fragmentation, the ρ(E int ) and N ‡ (E int -E 0 ) (see equation 1) have been evaluated from the frequency models of the ground and the transition states proposed by Muntean and Armentrout ; the σ and E 0 values of the m/z 134 → m/z 91 and m/z 134 → m/z 92 reactions are also considered from the same paper. [START_REF] Muntean | Modeling Kinetic Shifts for Tight Transition States in Threshold Collision-Induced Dissociation. Case Study: Phenol Cation[END_REF] In the case of the TEET and ETTE radical ions the values of σ and E 0 will be further indicated in the text (vide infra).

For evaluating the ρ(E int ) term of theses radical cations in their ground state, the vibrational frequency values were obtained from theoretical calculations at a B3LYP/6-31+G** level of theory (vide supra). For evaluating the TS frequency file of the m/z 446→ m/z 418 and m/z 446→ m/z 390 reactions, a frequency of value typically close to 1200 cm -1 is removed and five other frequencies are scaled to obtain the expected A pe value. It must be mentioned that in this frequency range encompassing the 1000 to 3000 cm -1 value, the influence of the magnitude of the removed vibration on the RRKM calculation results can be considered as very low. The Mean Thermal Energies at 473 K (

( )

Therm 473K E

) of the ETTE and TEET radical cations that correspond to the source temperature can be calculated from the frequency files of the Table 1 by using the Equation 4 such as:

( )

Therm 1 473K e 1 i B s i h k T i h E ν ν ⎛ ⎞ ⎜ ⎟ = ⎝ ⎠ = - ∑ (4)
In equation 4, k B is Boltzmann's constant, T is the temperature and v i is the frequency value of a vibration mode i considered among the s oscillators of the radical cation. From this ( )

Therm 473K E is of 1.392 eV and 1.396 eV for ETTE +. and TEET +. , respectively. This two close values indicate that the frequency levels of these two radical cations at their ground state, do not account a priori for the relative rigidifications of so-called S…O interactions.

This is thus rather the magnitudes of A pe (i → j) that will evidence the relative planarization of

Results and discussion

Calibration in internal energy of ions produced in the EI source experiments

The ratios of the intensities of the m/z 91 and 92 fragment ions produced from the two competitive reactions of the butylbenzene molecular ion and the survival yield of the m/z 134 parent ion, have been calculated by the MassKinetics software and compared to the experimental values measured from the EI mass spectra (see Table 2). The fitting parameter between experiment and simulation is the initial internal energy distribution of the ionized compounds. This distribution associates two components. One of them is the thermal energy of the molecule (P(E Therm )) vaporized in the EI source under a 473 K or a 573 K temperature and the other takes into account the deposited energy during the ionization process (P(E Ionization )). The latter is a Gaussian like distribution that does not depend of the source temperature. The thermal component is based on the ergodicity principle assuming that the thermally excited states of all the vibrational modes can be reached with the same probability leading to the expression: 5). The internal energy deposited during the interaction of a gaseous molecule with an electron beam at a 70 eV kinetic energy can be expressed from a Gaussian like function such as:

( ) ( ) int int Therm int int 0 exp ( ) exp B B E E k T P E E E k T ρ ρ ∞ - ⎛ ⎞ ⋅ ⎜ ⎟ ⎝ ⎠ = - ⎛ ⎞ ⋅ ⎜ ⎟ ⎝ ⎠ ∫ (
( ) 6), where w and X c are the so-called width and position terms, respectively. The initial internal energy distribution (P(E int )) of a butylbenzene radical cation is the result of the contribution of the two distributions Therm ( ) P E and ( )

2 1 2 Ionization 1 2 c E X w P E e w π - ⎛ ⎞ -⎜ ⎟ ⎝ ⎠ = (
Ionization P E
. In this study, the best fit between experiment and theory (see Table 2) has been obtained for T = 473 K (see Equation 5) and w = 5.5 eV and X c = 3.5 eV (see Equation 6). The contribution of these two components in the total internal energy distribution (P(E int )) is illustrated in Figure 2. This initial internal energy distribution (P(E int )) was considered for the rest of the study as a calibration in internal energy of the ionization source. the more that it can be used to calibrate internal energy of the EI-MIKE spectra for that a fragmentation that occurs in the second field free region of the mass spectrometer. In our case, a ratio between the intensities of the m/z 91 and 92 has been evaluated as being greatly favorable to the formation of the later in agreement with that was documented. [START_REF] Vékey | Internal Energy Effects in Mass Spectrometry[END_REF] Behavior οf π-conjugated oligomers containing 3 The low-resolution full scan mass spectra recorded for the two studied compounds at several low electron kinetic energies (namely at 12 and 15 eV), have indicated roughly the same appearance potentials for the m/z 390 than for the m/z 418 ion for the TEET and ETTE radical cations. This behaviour is in agreement with metastable decompositions that are due to competitive unimolecular reactions rather than consecutive dissociations. From these data and the results of the literature, the fragmentation reactions of the m/z 446 molecular ion of the ETTE and the TEET compounds yielding the m/z 418 and 390 daughter ions, can be described as reported in Schemes 2 and 3, respectively. The relative formation enthalpies of the structures 1a-1c and 2a-2c are regrouped in Table 4 for the two studied series ETTE and TEET. The dissociation pathways b) depicted in the Schemes 2 or 3 describe a retro-Diels Alder (RDA) mechanism for the m/z 446 → m/z 418 transition (with reaction degeneracy σ = 2). [START_REF] Beno | The C7H10 Potential Energy Landscape: Concerted Transition States and Diradical Intermediates for the Retro-Diels-Alder Reaction and [1,3] Sigmatropic Shifts of Norbornene[END_REF][START_REF] Ovcharenko | Mass-spectrometric differentiation of diexo-and diendo-fused isomers of norbornane/ene-condensed 2-thiouracil and 1,3-thiazino[3,2-a]pyrimidine derivatives: stereoselectivity of retro-diels-alder fragmentations under EI and CI conditions[END_REF] The quinoid form of the structure 1c and 2c related to the m/z 418 ions produced from the dissociations of ETTE (see Scheme 2) and TEET (see Scheme 3), respectively, suggests that these daughter ions can be characterized by roughly the same vibration modes. In this context, the S…O interactions are not at the origin of the planarization of such a quinoid form. The endothermic reactions observed in mass spectrometry involve an activated complex at the TS characterized by a structure closer to the products than the reactant. The vibration modes in the TS are close to that of the m/z 418 daughter ion. This leads to consider a very influence of the S…O interactions on the rigidification of the activated complex at the TS in the case of a RDA process. This is then the vibration modes of the m/z 446 parent ion that will govern in a large extend the magnitude of the rate constant for this fragmentation reaction underwent by the ETTE and TEET radical cations. Considering the dissociating ion at its ground state, the vibration frequency values and namely those that are characteristics of the internal rotations along the central bond of ETTE or TEET, will be influenced by the selfrigidification of the system in its non-quinoid form, and thus by the number of S…O interactions (see the dashed grey lines in Schemes 2 and 3), i.e. two and four for ETTE and TEET, respectively. A defined TS can be associated to the dissociation pathways b) (with σ = 2) (see Schemes 2 and 3) in agreement with the mechanisms proposed for such a RDA process suggesting then to consider a reverse reaction energy for this fragmentation. [START_REF] Beno | The C7H10 Potential Energy Landscape: Concerted Transition States and Diradical Intermediates for the Retro-Diels-Alder Reaction and [1,3] Sigmatropic Shifts of Norbornene[END_REF][START_REF] Ovcharenko | Mass-spectrometric differentiation of diexo-and diendo-fused isomers of norbornane/ene-condensed 2-thiouracil and 1,3-thiazino[3,2-a]pyrimidine derivatives: stereoselectivity of retro-diels-alder fragmentations under EI and CI conditions[END_REF] The E 0 (m/z 446 → m/z 418) values are then greater than that calculated from the ΔΔH f values of the so-called states "1c + CO" and "2c + CO" in Table 4. This reverse critical energy has thus been considered in this work (vide infra).

Experimental

For the formation of the m/z 390 daughter ion, the dissociation pathways a) (with σ = 4) (see eV in magnitude for a reaction occurring via a RDA mechanism. This is not in agreement with literature data suggesting that the critical energy of such reaction should not be greater than about 2 eV. [START_REF] Beno | The C7H10 Potential Energy Landscape: Concerted Transition States and Diradical Intermediates for the Retro-Diels-Alder Reaction and [1,3] Sigmatropic Shifts of Norbornene[END_REF][START_REF] Ovcharenko | Mass-spectrometric differentiation of diexo-and diendo-fused isomers of norbornane/ene-condensed 2-thiouracil and 1,3-thiazino[3,2-a]pyrimidine derivatives: stereoselectivity of retro-diels-alder fragmentations under EI and CI conditions[END_REF] Despite this, if one considers that reverse critical energies of a RDA reaction of about 0.3 to 0.5 eV, then the 1.77 eV value of energy level defined by the structure 1b and the CO molecule (see The data regrouped in Table 5 show that A pe (m/z 446 → m/z 418) for the fragmentation of ETTE +. is greatly lower than that of the TEET +. dissociation in the case of the RDA process.

Schemes

Figure 1 .

 1 Figure 1. Cyclic voltammograms of ETTE and TEET in 0.10 M Bu 4 NPF 6 /DCM, scan rate 100 mV s -1 (reprinted with permission from Ref 8).

the

  ETTE and TEET ions at their ground state. Two mass spectrometer geometries have been modelised for accounting for the mass spectrometric experiments with MassKinetics. For the full scan mass spectrometry experiments the following sequence was used: (1) gaseous molecule initially considered with thermal internal and kinetic energy distributions evaluated either at 473 K or at 573 K; (2) a Gaussian deposited energy function considered to account for the energy transfer during the ionization process; (3) acceleration under a 10 kV potential difference (flight length: 1.6 cm); (4) ion selection followed by detection (field-free flight from the source to the detector with 1.9656 m flight length). For a MIKES experiment, the following events have been built up as followed: (1) to (3) are identical as described above; (4) field-free flight (from the acceleration lens to the beginning of the FFR2 with a 0.966 m flight length); (5) Ion selection (m/z 446); (6) field-free flight (through the FFR2 with a 0.449 m flight length); (7) ion selection by scanning the electric analyser followed by detection (field-free flight from the end of the FFR2 to the detector with 0.55 m flight length).

Figure 2 :

 2 Figure 2: Contribution of the thermal (P(E Therm )) (dotted line) and ionization energy distribution (P(E Ionization )) (solid line) to the initial distribution of the butyl benzene molecularion produced in the EI source of the JMS 700 sector mass spectrometer (dashed line). Note that for a better reading of the figure, the maximum of the P(E Therm ) curve has been equalized with that of the P(E Ionization ) distribution.

Figure 3 :

 3 Figure 3: MIKE spectra of the molecular ion (m/z 446) of the ETTE (a) and TEET (b) compounds.

Figure 3

 3 Figure3shows that the ratios between the intensities of the m/z 418 and 390 fragment ions yielded from metastable decompositions are reversed as a function of the fragmenting ion.

Scheme 2 :Scheme 3 :

 23 Scheme 2: Proposed dissociation mechanisms of the ETTE radical cation (m/z 446) to account for competitive metastable decompositions involving either a direct cleavage sequence (pathway a) or a retro-Diels Alder process (pathway b)

  calculated using MassKinetics for different A pe (m/z 446 → m/z 418) values. In this calculation, the values of E 0 (m/z 446 → m/z 390) mentioned above, have been taken into account for the ETTE and TEET ions with A pe (m/z 446 → m/z 390) = 10 14 . For the values of E 0 (m/z 446 → m/z 418), five reverse critical energy values have been considered from 0.2 to 1 eV. The results of this simulation are reported in Figures 4 and 5 for the reactivity of the ETTE and TEET radical cations, respectively.

Figure 4 :

 4 Figure 4: Ion intensity ratios (I (m/z 390) /I (m/z 418) ) calculated by the MassKinetics software in an simulated EI-MIKES experiments modelling the dissociation pathways of the ETTE radical cation (see Scheme 2). The data are plotted as a function of the critical energy E 0 (m/z 446 → m/z 418) for different A pe (m/z 446 → m/z 418) values of the RDA process (¿: 10 8 , ¢: 10 10 , p:10 12 and Í:10 14 sec -1 ). Note that in this simulation E 0 (m/z 446 → m/z 390) = 2.56 eV (see

Figure 5 :

 5 Figure 5: Ion intensity ratios (I (m/z 390) /I (m/z 418) ) calculated by the MassKinetics software in an simulated EI-MIKES experiments modelling the dissociation pathways of the TEET radical cation (see Scheme 3). The data are plotted as a function of the critical energy E 0 (m/z 446 → m/z 418) for different A pe (m/z 446 → m/z 418) values of the RDA (¿: 10 8 , ¢: 10 10 , p:10 12 and Í:10 14 sec -1 ). Note that in this simulation E 0 (m/z 446 → m/z 390) = 2.08 eV (see Table 4) and A pe (m/z 446 → m/z 390) = 10 14 (see text). The grey horizontal straight line plotted in the Figure indicates the value of the experimental ion intensity ratio.

4 ,Scheme 4 :

 44 Scheme 4: Illustration of the influence of the S…O interactions in the relative rigidifications of the ETTE and TEET radical cations at their ground state towards their transition state

Table 2 :

 2 Measured and simulated data related to intensity ratios of fragment ions and SY values of the butylbenzene radical cation obtained from experimental and theoretical EI full scan mass spectra.

	Data	Theoretical data

Table 3 .

 3

	446	446
	418
	390
	390
	418
	m /z	m /z

Table 3 :

 3 Results of Exact Mass Measurements Performed from High Resolution Full ScanMass Spectra of ETTE and TEET compounds ionized under electronic impact (EI).

Table 4 :

 4 Becke3LYP/6-31G**Energetics of the dissociation pathways a) and b) depicted in

	Schemes 2 and 3 for the fragmentation reactions of the ETTE (1a) and TEET (2a) radical
	cations.
		Absolutes energies		Relatives enthalpy
	Structure	(E) a	State	(ΔΔH f ) b
	Ethen (C 2 H 4 )	-78.542683
	Carbon monoxide (CO)	-113.304423
	1a	-2663.638555	1a	0
	1b	-2471.697421	1b + C 2 H 4 + CO	2.56 c
	1c	-2585.030935	1c + CO	1.77 c
	2a	-2663.643976	2a	0
	2b	-2585.048	2b + C 2 H 4 + CO	2.08 d
	2c	-2471.720478	2c + CO	1.45 d

a E values in hartrees including corrections for zero point vibrational energy. b ΔΔH f values in eV considering thermal corrections at 298 K. c values in eV relative to ΔH f (1a). d values in eV relative to ΔH f (2a).

  2 and 3), describe series of direct bond cleavages. One can postulate that the overall process can be kinetically characterized by a Log(A pe ) value close to 14. The lack of welldefined structures at the TS's indicated by this value, leads to consider the ΔΔH f values of the

	so-called states "1b + C 2 H 4 + CO" and "2b + C 2 H 4 + CO" (see Table 4) as the reaction
	critical energies E 0 (m/z 446 → m/z 390) for ETTE and TEET transitions, respectively.
	In agreement with that has been stated above through the Equation 2, the values of the

Table 4 )

 4 and A pe (m/z 446 → m/z 390) = 10 14 (see text). The grey horizontal straight line plotted in the Figure indicates the value of the experimental ion intensity ratio.

		5.00
		4.50
		4.00
		3.50
	Ion Intensity ratio	2.00 2.50 3.00
		1.50
		1.00
		0.50
		0.00
		1.8	1.9	2	2.1	2.2	2.3	2.4	2.5	2.6	2.7	2.8
						Critical Energy (eV)

Table 4

 4 describing the ETTE radical cation behavior. By focusing on the TEET radical cation fragmentation, one can state that the same range of reverse critical energy values increase the E 0 (m/z 446 → m/z 418) value for from 1.45 eV (see Table4) to 1.75 and 2.25 eV. In this case, the Figure5shows that the best fit between the modeling and the experiment is obtained with A pe (m/z 446 → m/z 418) values ranging from 10 12 to 10[START_REF] Baer | Unimolecular Reaction Dynamics: Theory and Experiments[END_REF] . By proposing that a 0.4 eV reverse critical energy leading to E 0 (m/z 446 → m/z 418) values of 2.17 and 1.85 eV for the ETTE and TEET radical cations, respectively, a refinement of the fit between calculation and experiment allows to propose the Log(A pe ) values reported in Table5.

		2.00
		1.80
		1.60
		1.40
	Ion Intensty ratio	0.80 1.00 1.20
		0.60
		0.40
		0.20
		0.00
		1.45	1.55	1.65	1.75	1.85	1.95	2.05	2.15	2.25
						Critical Energy (eV)

) will be increased from 2.07 to 2.27 eV. Even though this E 0 (m/z 446 → m/z 418) values exceeds 2 eV, the orders of magnitude of 10 10 and 10 12 for the A pe (m/z 446 → m/z 418) parameter are better in agreement with the experimental data

Table 5 :

 5 Molecular parameters of metastable dissociations of the two oligothiophenes containing EDOT groups leading to adjust the values of the ratio I (m/z 390) /I (m/z 418) calculated by MassKinetics (see the last column in the Table) with the data obtained from the MIKES

experiments (see Figure

2

)