S Moubarak

M T Pham

T Pajdla

T Redarce

Design and Modeling of an Upper Extremity Exoskeleton

Keywords: Upper extremity exoskeleton, medical robotics, rehabilitation

This paper presents the design and modeling results of an upper extremity exoskeleton mounted on a wheel chair. This new device is dedicated to regular and efficient rehabilitation training for weak and injured people without the continuous presence of a therapist. The exoskeleton being a wearable robotic device attached to the human arm, the user provides information signals to the controller in order to generate the appropriate control signals for different training strategies and paradigms. This upper extremity exoskeleton covers four basic degrees of freedom of the shoulder and the elbow joints with three additional adaptability degrees of freedom in order to match the arm anatomy of different users.

I. INTRODUCTION

Elderly people, stroke victims, hemiplegic subjects, paralyzed and spinal cord injured persons suffer from many forms of handicaps for locomotion because of the decline of their physical and muscular strength. Robotic assistance and rehabilitative training have recently become more common, and thus, commercial robotic devices and orthosis are already available and increasingly needed to assist, facilitate and accelerate the training and the recovery of weak and injured people.

Several studies have been carried out on robotic medical training and assistance. For lower limbs, these works not only concentrated on the therapeutic applications of the robotic devices, but also on the development of lower extremity exoskeletons for the augmentation of the load carrying capability and the endurance of the user [1]. However, for the upper limbs, most researchers have paid increasing attention to develop upper extremity exoskeletons for medical assistance and rehabilitation training [2]- [START_REF] Denève | Développement et commande d'un robot pour la rééducation des membres supérieurs[END_REF].

This paper deals with the development and the modeling of an upper extremity exoskeleton mounted on a wheel chair (Fig. 1). Our objectives are to provide an efficient rehabilitative training and physiotherapy for the patient's arm, as well as the possibility for the therapist to apply different training strategies with a variable assistance degree depending on the state of the user and the injury level. Furthermore, this device enables the patient to have a consistent training without the continuous assistance of the therapist; therefore, the latter can work on many patients simultaneously and the total cost of the therapy can be reduced.

The paper is organized as follows: Section 2 deals with the human arm anatomy. Section 3 describes the different components of our prototype. Section 4 presents the kinematic and dynamic modeling of the exoskeleton. Finally, a brief conclusion highlights the ongoing works but also the perspectives of this project. The shoulder and elbow gather 5 bones of the upper limb: the clavicle, the scapula, the humerus, the ulna and the radius [START_REF] Denève | Développement et commande d'un robot pour la rééducation des membres supérieurs[END_REF] (Fig. 2).

Fig. 2 The shoulder and elbow bones

From a biomechanical point of view, the human anatomy can be represented as a set of rigid bodies connected by joints. In robotic rehabilitation, biomechanical models can be used for the design as well as the control of the prototype to simplify the interaction mechanism between the human and the robot. Mechanical analyses are carried out to validate the kinematic structure of the robot and its actuators dimensions.

Biomechanical models of the upper limb are also used for evaluation and diagnosis, in order to control the forces and the couples generated by the upper limb movements during a robotic assisted rehabilitation session. Fig. 3 The four basic degrees of freedom of the arm The human arm has three complex articulations; the shoulder, the elbow and the wrist. Our prototype, being dedicated to the shoulder and elbow rehabilitation training, covers three shoulder degrees of freedom (DoFs) (abduction / adduction, flexion / extension and internal / external rotation) and one elbow DoF (flexion / extension) (Fig. 3). Table 1 gives the average range of the shoulder and the elbow joints of the human arm [START_REF] Denève | Développement et commande d'un robot pour la rééducation des membres supérieurs[END_REF].

Table 1 Human arm characteristics

III. A NEW UPPER EXTREMITY EXOSKELETON

This section describes the three prototype's components: -The mechanical structure -The actuators and the force sensors -The control system

The prototype has 4 motorized degrees of freedom; the shoulder abduction / adduction, flexion / extension and internal / external rotation as well as the elbow flexion / extension motion. The shoulder height, the shoulder width and the arm length can be adapted to fit with different body sizes for different users. An arm holder and a wrist holder with 8 integrated force sensors are sending information signals to the controller in order to estimate the state of the user and his motion intentions. Each motor is connected to a drive and can be controlled either by torque or by velocity.

The 4 drives, the force sensors and the adaptability motors are connected to a Dspace card and continuously exchanging information and control signals. Different control schemes can be created and applied using Matlab / Simulink and Dspace -Control Desk interface.

III.1-Mechanical structure:

The main purpose of an exoskeleton is not only to provide efficient motion assistance to the human limbs, but also to guarantee the safety and the comfort of the user. That is why matching the human body anatomy is one of the most important criteria for an exoskeleton design. The mechanical structure of our prototype (Fig. 4) mainly consists of three links and four revolute joints covering the basic degrees of freedom of the human arm. The motion range of the robot's joints is limited to provide a wide risk-free workspace for the user. The arm is attached to the exoskeleton by external arm and wrist holders with pressure adjustable internal pneumatic holders. The rotation motion is transmitted from the motor axes to the joint axes by rigid and compact spiro-conical gear systems. The prototype is relatively lightweight (10 Kg) with a high ratio of DoFs / weight (Fig. 5). The four active DoFs of the prototype are motorized by brushless motors with high torque and relatively small dimensions. The motor torques are amplified by the reducers and the gear systems, to give final output torques of 63 Nm for the shoulder abduction / adduction, 52.5 Nm for the shoulder flexion / extension, 17.1 Nm for the shoulder internal / external rotation, and 13.5 Nm for the elbow flexion / extension motion.

The prototype must be adaptable so it can be used by different patients with different body sizes. The shoulder height, the shoulder width and the arm length can be varied using three DC motors to fit with the users' body dimensions.

The control of the prototype with different training strategies is mainly based on the information feedback signals from the user and the exoskeleton. The motor encoders' feedbacks provide a real time estimation of the position and the velocity of the joints and can be used as feedback information for the kinematic and dynamic models. However, to control an exoskeleton for medical and rehabilitation applications, we need to estimate the state of the user, his interactions with the robot and sometimes we need to predict his motion intentions in order to apply the appropriate robotic assistance. One solution consists in using force sensors. Therefore, depending on the training strategy, we can guide the patient's arm in the correct displacement or modify the exoskeleton's motion to assist him in his desired motion. Fig. 6 The arm holder with the force sensors In our prototype, 4 force sensors are applied in each arm holder. Each sensor can measure any force in the 0 -125 N interval. The sensors are surrounding the arm and the wrist at 90° on from the other, detecting almost all the possible interactions between the user and the robot (Fig. 6).

III.3-Control system:

All brushless motors are equipped with high resolution magnetic encoders for position feedback measurements. Each motor is connected to a drive with a sampling frequency of 5 KHz. The 4 drives, the 3 adaptability DC motors and the 8 force sensors are connected to the same electronic interface card.

The electronic card exchanges information and control signals with a Dspace controller analyzing all the feedback information and sending the appropriate control signals to the system depending on the training strategy. At this stage, different control schemes and therapy modes are created and applied to the system using Matlab / Simulink software and Controldesk interface.

The complete electrical setup diagram of the system is shown in Fig. 7. Fig. 7 The electrical setup

IV. MODELING OF THE EXOSKELETON

In order to achieve a compliant controller for the exoskeleton, the kinematic and dynamic models of the structure must be calculated and identification experiments must be carried out to get a better estimation of the dynamic and friction parameters of the robot, and therefore, improve the theoretical models.

IV.1-Geometric and inertial parameters:

The mechanical structure of our prototype mainly consists of three links and four joints. The geometric parameters of the robot have been calculated using the Denavit-Hartenberg notations.

The theoretical inertial parameters, used in the dynamic modeling have been calculated based on a complete CATIA model of the prototype.

IV.1-Kinematic and dynamic models:

The following models have been calculated using SYMORO+ software (Symbolic Modeling of Robots) and simulated with Matlab/Simulink interface [START_REF] Khalil | Modélisation, identification et commande des robots[END_REF]:

-The direct kinematic model (DKM) Identification experiments are being carried out in order to improve the theoretical estimations of the inertial and the friction parameters of the exoskeleton.

- The direct and inverse kinematic, differential kinematic and dynamic models of our prototype have been created based on the Denavit-Hartenberg notations, calculated using SYMORO+ software, simulated and validated with Matlab/Simulink interface.

Another aspect of this work concerns the control strategy. The force sensors feedback will be used in order to estimate the state and the motion intentions of the user; and create efficient training strategies and therapy modes for a better and faster recovery.

REFERENCES -The inverse dynamic model (IDM)

The simulation diagram of the kinematic and dynamic models is shown in fig. 8.

A motion generator (MG) creates, for each joint, a 5 th degree displacement between two given positions, in a given time, starting and ending with a null acceleration. q , and represent the joint position, velocity and acceleration vectors created by the motion generator.

q q X , X and represent the final link position and velocity vectors and the joints torque vector calculated by the direct models.

Q , and Q represent the joint position, velocity and acceleration vectors calculated by the inverse models. An important criterion for comfortable rehabilitation training is the efficient gravity compensation of the prototype so that the user can move his arm freely without feeling the mass of the robot. The static component of the inverse dynamic model is applied on the prototype and 90% of the gravity effect of the exoskeleton has been compensated successfully.

Q

q q q X X Q Q Q q q q

Fig. 1

 1 Fig. 1 The upper extremity exoskeleton

Fig. 4

 4 Fig. 4 The mechanical structure of the exoskeleton

Fig. 5

 5 Fig. 5 The gear systems and the arm holders of the exoskeleton

  The inverse kinematic model (IKM) -The direct differential kinematic model (DDKM) -The inverse differential kinematic model (IDKM) -The direct dynamic model (DDM) V. CONCLUSION AND FURTHER WORKS This paper introduces the design and modeling results of an upper extremity exoskeleton mounted on a wheel chair. The key objective of this device is to help users with disabled upper limbs to practice their daily living activities by providing different training levels and therapy modes. It can accelerate the muscle strength development and the recovery of post-stroke and spinal cord injured persons, as well as accident victims and elderly people.

ACKNOWLEDGMENT

  This work was supported by EC project MEST-CT-2005-021024 WARTHE.

Fig. 8

 8 Fig. 8 The modeling and simulation diagram

  4. R. Song, K.Y. Tong, X.L. Hu, S.F. Tsang, and L. Li, "The therapeutic effects of myoelectrically controlled robotic system for persons after stroke-A pilot study ", 28th IEEE EMBS International conference, New York city, USA, August-September 2006, pp.3504-3511.

Design and Modeling of an Upper Extremity Exoskeleton


Sylvie Marcos
email: marcos@lss.supelec.fr

RANGE RECURSIVE SPACE TIME ADAPTIVE PROCESSING (STAP) FOR MIMO AIRBORNE RADAR

This paper presents a range recursive algorithm for the space time adaptive processing (STAP) of multi input multi output (MIMO) airborne radar signals involved in clutter rejection for the detection of slowly moving ground targets. The MIMO aspect comes from the fact that the transmitter consists of an array of spaced elements sending non coherent waveforms and that the receiver is a conventional array used for spatial clutter rejection. The transposition of the STAP algorithms from the single input multi output (SIMO) systems to the MIMO ones has been claimed to theoretically improve performance in clutter resolution and rejection. However, even if this transposition is conceptually easy, in practice, the convergence and the complexity of the MIMO-STAP algorithms are higher than for SIMO models. After reconsidering the advantages and drawbacks of the extended MIMO-STAP, namely the the sample matrix inversion (SMI) and eigencanceller (EC), algorithms, we propose the fast approximated power iteration (FAPI) range recursive algorithm as an alternative to resolve the convergence and complexity problems 1.

INTRODUCTION

Space time adaptive processing (STAP) of airborne radar signals received on an array of antennas consists in constructing for each range and in each look direction a Doppler filter capable of rejecting ground clutter in order to detect a possible slow moving target [START_REF] Guerci | Space-time adaptive processing[END_REF][2] [START_REF] Ward | Space-time adaptive processing for airborne radar[END_REF]. In conventional STAP, the target and the ground are illuminated by a known waveform coming from a single omnidirectional transmitter antenna localized (monostatic configuration) or not (bistatic) on the same platform as the receiver antenna array. It has been recently shown that multiple-input multipleoutput (MIMO) antenna systems have the potential to improve the performance of communication and radar systems over single-input multiple-output (SIMO) systems [START_REF] Fishler | MIMO radar: an idea whose time has come[END_REF][5] [START_REF] Rabideau | Ubiquitous MIMO MIMO multifunction digital array radar[END_REF]. Concerning STAP, it has been claimed that the clutter rejection and consequently target detection may be improved by considering, instead of a single omnidirectional transmitter antenna, an array with spaced antenna elements sending non coherent (possibly orthogonal) waveforms. After their reflection on the ground and the eventual target they can then be extracted at the receiver by a matched filters bank [START_REF] Bliss | MIMO radar and imaging: degrees of freedom and resolution[END_REF][8] [START_REF] Chen | MIMO radar spacetime adaptive processing using prolate spheroidal wave functions[END_REF]. Indeed, it has been shown that for certain configurations and geometries of radar antenna arrays at the transmitter and the receivers, the transposition of STAP algorithms, well established in the literature, from SIMO to MIMO yields as if STAP would be applied to a SIMO system with a virtual array of larger size (equal to the product of the numbers of transmitter and receiver elements) thus involving a higher resolution of the clutter spectrum [START_REF] Chen | MIMO radar spacetime adaptive processing using prolate spheroidal wave functions[END_REF]. However this improvement is obtained at the price of an increased computational load and a slower convergence of the algorithms. In this paper we will first explain the transposition of the sample matrix inversion (SMI) [START_REF] Van Trees | Optimum array processing[END_REF] and the eigencanceller (EC) [START_REF] Haimovich | Eigenanalysis-based space-time adaptive radar: performance analysis[END_REF] based STAP algorithms from SIMO to MIMO radar systems and we will discuss the actual advantages and drawbacks of the MIMO extension. We will then propose a MIMO extension of a range recursive STAP algorithm showing that it can reach the performance of the EC algorithm, namely the same convergence advantage over the SMI, related to the rank of the clutter covariance matrix, with a drastically reduced computational complexity. The paper is organised as follows. Next section is devoted to the presentation of the MIMO signal model received at the receiver for the STAP approach. Section 3 will shortly recall the SMI and EC STAP algorithms in order to detail the actual advantages and drawbacks of their extension to the MIMO case. In section 4, the extension of the fast approximated power iteration (FAPI) range recursive STAP algorithm [START_REF] Badeau | Fast approximated power iteration subspace tracking[END_REF] [START_REF] Belkacemi | Fast iterative subspace algorithms for airborne STAP radar[END_REF] to MIMO STAP will be presented and its advantages over the EC algorithm will be established. The previous discussion and results will be supported by simulations in section 5. Section 6 is the conclusion.

SIGNAL MODEL

Consider the simplified MIMO narrowband airborne radar system of Figure 1 1 with transmitting and receiving antennas arranged in two collocated uniform linear arrays (ULA) of M and N elements, respectively [START_REF] Chen | MIMO radar spacetime adaptive processing using prolate spheroidal wave functions[END_REF]. The system transmits simultaneously M linearly independent (orthogonal) waveform baseband pulses ) (τ m Φ , denoting time within a radar pulse interval of length T . The transmitted signals of the m-th antenna corresponding to the l-th pulse interval among L pulses in a coherent processing interval (CPI) can be expressed as τ

) ( 2 ) ( ) ( τ + π τ = τ + lT f j m m e E lT s

Φ

where m=1, 2,…, M, f is the carrier frequency and E is the transmitted energy of the pulse. The signals after their reflection on a target or on a ground clutter patch in direction can be extracted on each receiver by M matched filters. The transmitter and the receiver are assumed close enough and on the same platform so that they share the same angle . The radar platform is flying at altitude h with a velocity vector v assumed collinear with the x-axis radar and of amplitude v. This configuration is referred to as the side looking (SL) configuration. We here assume a non ambiguous clutter and the absence of jammer and internal clutter motion (ICM). Because of the orthogonality of the transmitted waveforms, the extracted signal at the output of the m-th

matched
+ + = ) 2 ) 2 ( (sin , , 2 Tl v m d n d vTl j t t l m n t T R t e ρ x + + + θ λ π = ∑ - = + + θ λ π = 1 0 ) 2 ( sin , , , , 2 c T R i c N i m d n d vTl j i c c l m n e ρ x
where , and , are the looking direction and the amplitude of the reflected signals associated with the target and the i-th clutter patch, respectively. is the number of clutter patches at a given range, is the target speed relative to the platform, and are the transmitting and receiving antennas spacing respectively, and λ is the wave- length. is a white Gaussian noise component. Let us define the normalized spatial and Doppler frequencies such as

t θ t ρ i c θ , i c ρ , c N t v R d T d n l m n x , , λ θ d f t R t S sin , = , λ θ d f i c R i S , , sin = , λ v θ v T f t t t D ) sin ( 2 , + = and λ θ Tv f i c i D , , sin 2 =
, for the target and the i-th clutter patch, respectively. In order to avoid spatial aliasing, is assumed and

2 / λ d R = R T d d = γ and R d vT β 2 =
are defined. With these notations the target and clutter components of the extracted signals can be rewritten as

l f j m n f j t t l m n t D t S e e ρ x , , 2 ) ( 2 , , π γ + π = ∑ - = + + π = 1 0 ) ( 2 , , , , c i S N i βl γm n f j i c c l m n e ρ x
There is thus a total of NML extracted signals at the receiver output during a CPI and for a given range, which can be viewed as the signals which would be received on a virtual array of NM antennas in a SIMO radar system whereas only N+M physical antennas exist. By stacking the MNL MIMO STAP signals in a MNL dimensional vector x yields

n c t x x x x + + = (1) with (2) ) ( ) ( ) ( , , , t S T t S R t D t t f f f ρ a a b x ⊗ ⊗ = (3) ∑ = ⊗ ⊗ = c N i i S T i S R i D i c c f f f ρ 1 , , , , ) ( ) ( )
p f j D p D e f b β π = 2 ) ( p f j S p R S e f a π = 2 , ) ( p f j S p T S e f a γ π = 2 , ) (
Let us recall that in the case of SIMO, the target and clutter components would reduce to the following expressions

) ( ) ( , , t S R t D t t f f ρ a b x ⊗ = ∑ = ⊗ = c N i i S R i D i c c f f ρ 1 , , , ) ( ) ( a b x
where and would be vectors of dimension NL.

THE MIMO SMI AND EC ALGORITHMS

The aim of STAP is to mitigate the effects of ground clutter in order to detect an eventual slowly moving target. This is performed by a two dimensional filtering of the received data followed by a detector. The optimal STAP weight vector maximizing the signal to noise plus interference ratio (SINR) [START_REF] Van Trees | Optimum array processing[END_REF] is given by (4)

t opt x R w 1 - α =
where α is a scalar constant which does not affect the SINR and R is the clutter plus noise covariance matrix

(5) ] ) )( [( E H n c n c x x x x R + + =
The output of the filter is .

x w r

H opt

=

The extension from the SIMO to the MIMO system is trivial, matrix R and weight vector being of dimension MNLxMNL and MNLx1 in the latter case instead of NLxNL and NLx1 in the first case, respectively. opt w It is well known that the localization of sources by an antenna array is improved when the number of receiving elements of the array increases. In the case of MIMO STAP, a better estimation of the clutter spectrum is thus expected yielding a better rejection of it when constructing the weight vector (4). Indeed, in this case, it has been seen that the number of elements is virtually MN for a number of physical elements of N+M instead of N in the case of SIMO. However this is only true in the theoretical (optimal) case.

In practice, neither R or are known.

) (k x 0 k ∑ ≠ = - + + = K k k k n c n c K k k k k k 0 1 H 1 1 0 )) ( ) ( ))( ( ) ( ( ) ( ˆx x x x R (6)
The target component is replaced by a steering vector of the form ) , (

t x ) ( ) ( ) ( ) , ( S T S R D S D f f f f f γ ⊗ ⊗ =
S D f f (7) ) , ( ) ( ) , , (
1 0 0 S D S D SMI f f k f f k v R w - =
Note that a weight vector is computed for each range cell and each couple of Doppler and spatial frequencies. It is known in the STAP literature [START_REF] Reed | Rapid convergence rate in adaptive arrays[END_REF] that the "convergence" of the SMI defined as the number of snapshots necessary to achieve a SINR loss performance of 3 dB compared to the optimal STAP in the absence of clutter, is twice the dimension of the received vector. It follows that the convergence for the SIMO and the MIMO cases is obtained for K=2NL and K=2NML snapshots, respectively. In the same way, the larger the size of the covariance matrix, the more complex the computational load required for the inversion in [START_REF] Bliss | MIMO radar and imaging: degrees of freedom and resolution[END_REF]. It follows that and are necessary to compute the SMI weight vectors in the MIMO and SIMO cases, respectively. The theoretical interest of the MIMO system becomes thus limited in practice.

)

) (( 3 MNL O ) ) (( 3

NL O

An alternative approach proposed in the literature for reducing the convergence is based on rank reduction. For example, the eigencanceller (EC) method consists in computing the STAP weight vector as follows (

)

) , ( ) , , ( 0
S D H c c S D EC f f f f k v U U I w - = (8)
Indeed, the clutter covariance matrix being rank deficient the clutter plus noise covariance matrix R can be eigendecom- posed as follows (9)

H n n n H c c c U U U Λ U R 2 σ + =
In practice, this eigendecomposition is obtained from the estimated covariance matrix (6) yielding a convergence as above defined of K=2r where r is the rank of the clutter covariance matrix. It has been shown in [START_REF] Ward | Space-time adaptive processing for airborne radar[END_REF], and the references inside, and in [START_REF] Chen | MIMO radar spacetime adaptive processing using prolate spheroidal wave functions[END_REF] that the rank in the SIMO and the MIMO cases is approximately

) 1 ( - + = L β N r SIMO and ) 1 ( ) 1 ( - + - γ + = L β M N r MIMO
in the absence of jammers. It is thus worth noting that the convergence speed is no longer proportional to the product of the number of transmitting and receiving elements but a linear combination of them. Moreover it is also worth noting that if you compare a SIMO antenna array of N'=MN physical elements you can find a MIMO system of N and M physical receiving and transmitting elements, so that by choosing adequately γ ( N < γ ) the rank is smaller than the rank of the corresponding SIMO. It then follows that with the EC approach, the MIMO STAP system can converge faster than its SIMO counterpart. This was not the case for the SMI algorithm.

MIMO r ' SIMO r

From the computational complexity point of view the EC STAP algorithm encounters the same drawbacks as the SMI algorithm, it is to say that it is increased by a multiplicative factor of because of the eigendecomposition of the clutter plus noise covariance matrix. It is why in the following section we propose a range recursive EC-based STAP algorithm. It takes benefit of the abovementioned rank reduction property and consequently convergences faster than the SMI and has a computational load of only and for the SIMO and the MIMO cases, respectively.

)

) (( 3 M O ) (NL O ) (MNL O 4.

RANGE RECURSIVE FAPI ALGORITHM

Here we propose to use a range recursive subspace-based algorithm in order to construct the STAP filter.

Traditionally used in spectral analysis and antenna processing as time-recursive adaptive algorithms [START_REF] Badeau | Fast approximated power iteration subspace tracking[END_REF], adaptive recursive subspace-based algorithms such as FAPI have been more recently used in STAP for airborne radar [START_REF] Belkacemi | Fast iterative subspace algorithms for airborne STAP radar[END_REF] 2 . In this case of STAP, the recursion relates to the distance instead of time.

The classical subspace tracking algorithm on which FAPI is established considers the following scalar function [START_REF] Yang | Projection Approximation Subspace Tracking[END_REF] ⎟

⎠ ⎞ ⎜ ⎝ ⎛ - = 2 ) ( x WW x W H E J
where x is the observed data vector of covariance matrix R and W is the matrix argument. This cost function possesses just a global minimum [START_REF] Yang | Projection Approximation Subspace Tracking[END_REF] which is attainted only if

Q U W c =
where is the clutter subspace basis defined in [START_REF] Chen | MIMO radar spacetime adaptive processing using prolate spheroidal wave functions[END_REF] and Q is a unitary matrix. The original algorithm which considered this abovementioned criterion is the projection approximateon subspace tracking (PAST) algorithm [START_REF] Yang | Projection Approximation Subspace Tracking[END_REF] replacing the expectation by an exponentially weighted sum and supposing an approximation of the clutter subspace

( c U ) ( ) 1 ( i i W W ≈ -
where i was time in the original version of PAST and that we transpose to range in the proposed STAP version). Thus a basis of the clutter subspace is obtained as the solution of the unconstrained minimization problem:

2 1 ) ( ) 1 ( ) ( ) ( )) ( ( i i k i k J H k i i k x W W x W - - β = ∑ = -
where x(i) is the observed data vector at range i and W(k) is the estimated interference (clutter plus noise) subspace basis at range k and β a forgetting factor,

1 0 < < β
. This exponentially least square problem is solved by a recursive computa-tion. We here are more interested by the FAPI algorithm [START_REF] Belkacemi | Fast iterative subspace algorithms for airborne STAP radar[END_REF] which is based on the previous approach with a less restrictive approximation: the projection on the clutter subspace at range is approximated by the projection on the clutter subspace at range .

i 1 - i H H i i i i ) 1 ( ) 1 ( ) ( ) ( - - ≈ W W W W
The obtained subspace is found to be orthonormalized. The details of this algorithm are given in table 1. The corresponding STAP filter computed for each snapshot is obtained through

(10) ) , ( ) ) ( ) ( ( ) ( S D H FAPI f f k k k v W W I w - =
In table 1, the input x(k) is x defined in (1) at range k.

SIMULATION RESULTS

In this section, we compare the performance of our proposed FAPI method, the SMI and EC in the MIMO context of N=12 receiving elements, M=3 transmitting elements and L=10 pulses, β =1 and γ =10 or 2. The performance meas- ure is here defined as the signal to interference plus noise ratio loss (SINR loss) defined as the ratio of the SINR to the SNR (without clutter)

Rw w v w

H S D H loss NML f f SINR 2 2
) , ( σ = [START_REF] Haimovich | Eigenanalysis-based space-time adaptive radar: performance analysis[END_REF] where w is the weight vector of the clutter rejection filter calculated according to each algorithm [START_REF] Bliss | MIMO radar and imaging: degrees of freedom and resolution[END_REF], [START_REF] Mecca | MIMO radar space-time adaptive processing for multipath clutter mitigation[END_REF] or [START_REF] Van Trees | Optimum array processing[END_REF]. For the simulations, a pulsed Doppler airborne monostatic radar composed of a uniform linear array in a side looking configuration is considered. The operating frequency of the radar is 450 MHz with a PRF of 600 kHz. The radar bandwidth is 4.5 MHz. The platform is assumed to move with a constant velocity of 100 m.s -1 at the altitude of 9km. The clutter to noise ratio (CNR) is assumed equal to 30 dB. The SINR loss is plotted for =0 as a function of the normalized Doppler frequency . the EC and FAPI, are capable of converging with at least 90 snapshots. This is observed in Figure 2. Let us note that FAPI algorithm performs similarly to EC algorithm (with a drastically reduced complexity). Figure 3 exhibits the results concerning the MIMO case with transmitting and receiving antenna arrays of M=3 and N=12 physical elements, respectively. K=120 snapshots are used as in the previous case and γ =10. We can see that the re- sults are comparable to those of the SIMO case (Figure 1). It is to say that the MIMO STAP behaves with a total of only M+N=15 physical elements as a SIMO STAP system with a virtual array of N'=36 receiving elements. Note that in this case the rank is 41 = MIMO r , smaller than that of the corresponding SIMO system. In Figure 4, the performance of the SIMO and MIMO versions of the EC and FAPI algorithms are compared in the same conditions that those of Figures 2 and3 except that K=60 snapshots and γ =2. In this case, the rank for the SIMO case is still equal to 45 while for the MIMO case it is reduced to =25. It is why we can observe that there are enough snapshots for MIMO EC and MIMO FAPI to converge (a little bit more than twice the rank, it is to say, at least 50 snapshots) while there are not enough snapshots for the SIMO EC and FAPI algorithms (where at least 90 snapshots are required).

MIMO r

CONCLUSION

This paper proposes the FAPI STAP algorithm as an alternative to the EC STAP algorithm in the context of MIMO radar systems for clutter rejection and target detection. Indeed, while being a reduced rank subspace based technique as the EC algorithm, it requires much less training snapshots to converge than the SMI method. Contrarily to the EC it also has a low computational cost which is a linear function of the dimension of the virtual received signal vector. Note that the FAPI STAP algorithm for the MIMO context could be used to track clutter range non stationarities. As a perspective, the case of non localized transmitter and receiver as well as non orthogonal waveform pulses could also be of interest.

  receiving and transmitting spatial steering vectors of dimensions L, N and M, respectively.

⊗

  denotes the Kronecker product. The p-th components of the steering vectors are , and , with p=0,…,L-1, p=0, …, N-1 and p=0, …, M-1, respectively.

  candidate couple of Doppler and spatial frequencies . The suboptimal sample matrix inversion (SMI) STAP weight vector then consists in[START_REF] Guerci | Space-time adaptive processing[END_REF][START_REF] Klemm | Principles of space-time adaptive processing[END_REF][START_REF] Ward | Space-time adaptive processing for airborne radar[END_REF]

Figure 2

 2 Figure2exhibits the results concerning the SIMO case with a single transmitting antenna (M'=1) and a receiving an-

Figure 1 -Figure 2 -Φ 1 Figure 3 -Figure 4 -

 12134 Figure 1-Simplified scheme of a MIMO radar system

  γ

For simplifications, the scheme and the corresponding model assume that the target, the ground clutter and the antenna array are coplanar. In fact the problem is 3D and in our simulations, each look direction is of course parameterized by both elevation and azimuth angles.

Range or time recursive subspace-based algorithms are not only devoted to subspace tracking in case of non stationarity but also to converge towards a stationary optimal or suboptimal solution with a smaller computational complexity than their block counterparts.


M Beauvais
email: muriel.beauvais@saint-gobain.com

B Piezel

F Hamidi

M Villalobos

C Da Silva

E Martin

D Dalmas

E Barthel

Film Formation Mechanism in Glass Lubrication by Polymer Latex Dispersions

Keywords: glass, lubrication, SnO 2, roughness, surface chemistry, polymer

The stabilization of organic coatings by tin dioxide resulting in glass bottle lubrication was investigated on flat glass. The anchoring function of SnO 2 was assessed for a mixture of polyethylene and polymethylmethacrylate. Friction tests in air confirm the SnO 2 anchoring property with the maintaining of the lubricant effect due to the polymer over large sliding distances. The persistence of the polymethylmethacrylate stretching band ν C=O on significant sliding distances in infrared microscopy experiments shows that the polymer coating stabilization results from the strong adhesion of the polymer on SnO 2 . The impact of roughness and surface chemistry on the stabilization of the polymer coating was tested. The suppression of the lubricant effect by surface chemistry alteration or by roughness modification of SnO 2 suggests that roughness and surface chemistry of SnO 2 are both necessary for lubrication.

Introduction

Surface flaws generated by sliding contacts between glass bottles on production lines and transport affect both their mechanical strength and visual aspect. To improve their scratch resistance and prevent surface damage, glass bottles are subjected to two successive surface treatments. The first one, called "hotend coating", is a vapour phase deposition at atmospheric pressure of a thin oxide film while bottles are at elevated temperature in the range 520-650 °C. The oxide coating maintains the high pristine strength of glass [1,2]. Tin dioxide is currently used industrially for its high transparency to visible light and high hardness and is deposited from organometallic precursors such as tin tetrachloride (SnCl 4 ) [3,4] or monobutyltintrichloride (n-C 4 H 9 SnCl 3 ) [5][6][7][8][9]. The second one, called "cold-end coating", consists in a spray deposition of an organic water-based formulation (polyethylene, waxes, oleic acid …) at bottle temperatures between 80 °C and 160 °C [10,11]. The organic layer is stabilized by the oxide resulting in lubrication and surface damage prevention [1,4,11]. The metal oxide film is reported to act as an anchor or primer for the organic coating to the glass surface container [1,12]. There are two possible explanations to organic layer stabilization. The anchoring function of the primer would originate from its ability to increase the bond strength of organic coatings to the glass. This assumption is based on an overview by Smay [13] about the nature and strength of interactions between organic adsorbates and glass surfaces or oxides. The author concludes about the existence of stronger Brönsted acid sites and strong Lewis acid sites due to the metallic cations which explain why they interact with polar and nonpolar organic molecules more strongly than sodalime silica glasses. The stronger acid-base interactions between the primer and the polymer also result from the cation polarisability of oxides. Glass surfaces interact strongly with organic molecules only if they possess highly polar functional groups.

The more covalent character of tin dioxide determined by surface energy measurements of bare soda-lime silica glass and SnO 2 -coated glass supports this assumption [14]. Microextraction experiments of cold-end coatings such as modified polyethylene from SnO 2 -coated glass containers suggest that the organic layer is firmly anchored to the primer, but the existence of a polymer-SnO 2 interface chemistry is not evidenced [11].

Many efforts have been made to optimize the scratch resistance or the internal bursting pressure of glass bottles. Optimal mechanical properties are mainly reported as a function of a combination of tin dioxide thickness and quantity of deposited polymer [1,4,10,15]. However, the glass surface is roughened by the tin dioxide deposit [16,17], and the anchoring function of the primer would also be mechanical in nature as suggested by Pantano et al. [16]. Moreover, a rise of the primer roughness leads to an increased deposition of polymer and the oxide morphology also changes with its thickness [15,18].

From these observations and results, the roles of surface chemistry, roughness and morphology in the anchoring function of the primer remain unclear.

The purpose of this work is to understand why the SnO 2 primer is able to anchor the organic layer: are the morphology and roughness of the primer responsible or does the organic layer-oxide interface chemistry play a role? Moreover, concerning the role of roughness in lubrication, could glass without primer also be able to act as an anchor for the polymer coating with an appropriate roughness?

The present paper is divided in two main parts. The first one is devoted to the evaluation of the anchoring function of the primer for the polymer coating. The primer is a rough tin dioxide deposited on flat glass by chemical vapour deposition (CVD) and the polymer is a mixture of polyethylene (PE) with a dispersion of polymethylmethacrylate (PMMA) spheres. Such a coated glass is considered as a reference in this study. The scratch resistance of the SnO 2 -coated glass is quantified through friction tests in air on a reciprocating ball-on-plate tribometer and is compared to that without primer after the polymer deposition. To understand the stabilization phenomenon of the organic layer by the primer, wear tracks resulting from friction on polymer-coated glass and polymer-SnO 2 coated glass were analyzed by infrared microscopy to follow the presence of the polymer. The wear tracks were also characterized by Nomarski optical microscopy and atomic force microscopy (AFM) in air to investigate the impact of the primer on the evolution of the polymer morphology due to the compressive and shear stresses. The second part is dedicated to the role of surface chemistry and roughness of the primer in the organic layer stabilization. The postulated mechanical anchoring of the polymer by the primer due to an increase in the surface roughness after the primer deposition on glass is evaluated with smoother tin dioxides deposited on flat glass as well as with a flat glass whose surface is roughened by a silica coating deposition. To suppress the strong acid-base interactions between the primer and the polymer, a thin silicon nitride layer is deposited on the rough CVD SnO 2 while preserving the original roughness of the primer. The scratch resistance of such coated glasses is quantified and compared to that of the rough primer after the polymer deposition.

The study shows that the enhanced scratch resistance of the polymer-coated SnO 2 -CVD film on glass is due to the strong adhesion of the polymer to the primer, as revealed by the persistence of the PMMA stretching band ν C=O over large sliding distances. Good wetting results in well dispersed PMMA spheres on the surface and the strong adhesion leads to the formation of a continuous organic film under the mechanical stress by coalescence of flattened spheres. Moreover, the results suggest that the roughness and the surface chemistry of the primer are both necessary to the glass bottle lubrication. The large plastic deformation of PMMA spheres results from the combination of the surface roughness sharpness and shear due to strong adhesion.

Experimental

Methods

Friction experiments

Friction tests were performed on a reciprocating ball-on-plate tribometer (Plint T79) with a fused silica sphere as the ball specimen in ambient air. All experiments were carried out with an initial Hertz mean pressure Pm close to 450 MPa (i.e. a normal load F N of 9 N and a mean diameter of the ball specimen of 5.5 mm). Under these conditions, the theoretical contact width is 155 µm. Sliding velocity and length were fixed at 1 mm/s and 8 mm respectively. The ball specimens were made from silica rods (Won Ik Quartz) by melting the extremity with a blowtorch until a molten droplet of glass formed. Silica spheres were cleaned in an ultrasonic bath using four successive sequences of 15 min, respectively in detergent, distilled water, acetone and absolute ethanol and irradiated for 1 h by a UV-Ozone flow. Friction tests were carried out immediately after the silica ball cleaning and the polymer deposition on flat glasses to minimize surfaces contamination. The friction force F T between counterparts was averaged over each cycle (1 cycle corresponds to a cumulative sliding distance of 16 mm, i.e. one back and forth carried out by the silica sphere).

Each experiment was repeated at different locations on the surface (at least four) with a new silica ball. The mean value of the friction coefficient µ, defined as the ratio F T /F N , is reported as a function of the cumulated sliding distance of the ball specimen in a test.

Surface imaging and roughness characterization

The coatings morphology was examined prior to friction tests with a Digital Instruments Nanoscope III atomic force microscope in air. Surfaces were scanned in tapping mode at a resolution of 512×512 pixels, with a silicon nitride tip having an estimate stiffness of 0.06 N.m -1 . The RMS roughness R rms of inorganic coatings was calculated from AFM images analysis using the Nanoscope III software. For each coating, R rms was averaged from three different measurements over scanned areas of 1 µm 2 . AFM in tapping mode was also used to follow the impact of the CVD primer on the evolution of the organic coating morphology due to compressive and shear stresses. Scans were performed at different locations in wear tracks as a function of the cumulated sliding distance of the ball specimen in the test. Only half of each track from the edge to the center was characterized owing to the symmetric distribution of pressure in the contact as predicted by Hertz for a static ball-on-flat elastic contact [START_REF] Johnson | Contact Mechanics[END_REF]. Scans were conducted in such a way that half tracks were completely imaged.

The coatings morphology was also examined by scanning electron microscopy (SEM) (inorganic coating) and by differential interference contrast microscopy (Nomarki optical microscopy)(organic coatings and wear tracks).

Infrared microscopy

Wear tracks on polymer-coated SnO 2 CVD films and polymer-coated glass were analyzed by infrared microscopy to follow the presence of polymer on surface.

The carbonyl stretching band of PMMA (ν C=O ) centered at 1729 cm -1 and the stretching bands of PE (ν CH2 ) at 2920 cm -1 and 2850 cm -1 were selected. Their intensity was reproducible at different locations on the undamaged coatings and thus could be compared to the ν C=O and ν CH2 intensities detected in wear tracks. These comparative measurements made it possible to follow the variation of the amount of polymer due to the mechanical stress. Measurements were performed at two different locations in each track, as a function of the cumulated sliding distance. Such a technique couples a conventional optical microscope to a Nexus spectrometer in reflexion mode. The optical visualisation of surfaces after wear and the use of a mask having a rectangular slit to only select wear tracks provided infrared absorption data from an area of 120 µm x 850 µm. Spectra were taken at a resolution of 4 cm -1 for 512 scans with unpolarized light.

Polymer deposition

Prior to polymer deposition, the coated glasses were cleaned in an ultrasonic bath using two successive sequences of 10 min, respectively in absolute ethanol and distilled water. The glass without primer was irradiated for 1 h by a UV-Ozone flow after cleaning in the ultrasonic bath. The organic layer was deposited on the glass plates by dip-coating in laboratory, using a withdrawal speed of 50 mm/min. This procedure avoids the heterogeneous polymer distribution observed on the surface when sprayed in the factory. The organic deposition was followed by a heat treatment at 120 °C for 10 min to match with the industrial d eposit temperatures on bottles.

Materials

Polymer emulsion

A diluted dispersion of PMMA spheres and PE in water was chosen. Such a polymer mixture is commonly used in cold-end treatment of glass bottles. The size distribution of PMMA spheres in the emulsion is narrow and centered around 100 nm, as determined by dynamic light scattering.

Substrates for the polymer coating

Different substrates for polymer deposition were used. The film thickness was evaluated by X-ray reflectometry or SEM. Designation and characterizations are as follows: (see Table 1 for justification)

(1) Glass: commercial flat soda-lime silica glass having the same Na 2 O content as in the bottle glass.

(2) R-SnO 2 : CVD of tin dioxide SnO 2 on (1), performed on site on a production line of glass bottles at a homogeneous glass surface temperature of 570 °C with the same deposition parameters used for glass bottles. The coating is crystallized [START_REF] Choe | [END_REF] and has a thickness of a few tens of nanometres, in the range of the usual SnO 2 CVD film thicknesses on glass bottles [10].

To modulate the roughness and surface chemistry of the substrate for the polymer coating, reactive d.c. magnetron sputtering of amorphous inorganic coatings were carried out in the laboratory. The substrate holder temperature was maintained at 25 °C during the deposition. These inorganic coa tings consisted in:

(3) S-SnO 2 : tin dioxide on (1), with a thickness of 5 nm.

(4) r-SnO 2 : same as (3) followed by annealing at 570 °C durin g 5 h for crystallisation [START_REF] Choe | [END_REF].

(5) R-SiO 2 : silica on (1), with a thickness of 475 nm.

(6) R-Si 3 N 4 : silicon nitride on (2), having a thickness of 5 nm.

Morphology and roughness of substrates for the polymer coating.

R rms roughnesses are reported in Table 1.

(1) Glass: typical defects of float glass surface (rings) are present and randomly distributed [17]. Their height does not exceed 0.8 nm and controls the R rms roughness.

(2) R-SnO 2 : the glass surface has been roughened by the SnO 2 CVD deposit, in agreement with the observations of Pantano et al. [16,17]. The coating is rough and structured due to discrete facetted grains whose average size is close to 27 nm (Fig. 1a-b). The discrete facetted oxide grains lead to the sharp variation of heights of the AFM section profile (Fig. 1c). The film is also characterized by empty volumes or holes (black features) which are randomly distributed (Fig. 1a). Hole depth is of the same order of magnitude as the coating thickness, i.e. a few tens of nanometres.

These features are also present on SnO 2 -coated glass bottles [16,21]. They are created by the dissolution of the sodium chloride crystals formed during the deposition [21,22], when bottles are annealed and cold-end coated. (3) S-SnO 2 : the sputtering of a thin tin dioxide layer on glass results in a smooth primer which has no particular structure but the ring defects of glass are still visible owing to the small oxide coating thickness (Fig. 2a-b). Their height does not exceed 0.8 nm (Fig. 2c) and the rings control the coating roughness. (4) r-SnO 2 : annealing of the sputtered SnO 2 film on glass has roughened the surface (Fig. 3a) and formed grains with some distribution (18 nm -39 nm) (Fig. 3b-c). The ring defects of glass are still visible (Fig. 3a). The AFM section profile does not evidence sharp variation of heights indicating that grains are not facetted as in the case of the CVD film (Fig. 3c). (5) R-SiO 2 : the sputtering of a silica layer on glass has roughened its surface. Silica coated glass is characterized by a thin structure due to small grains having a diameter which can be as large as a few tens of nanometres. The grains are gathered in clusters which are not well defined (Fig. 4a-c).

(b) (c)

Results and discussion

Organic layer stabilization by tin dioxide

A first step was to assess the anchoring function of the tin dioxide for the polymer coating. The scratch resistance of R-SnO 2 and glass without primer are compared after the polymer deposition.

Morphology of polymer on R-SnO 2 and glass

At the AFM scale, the morphology of polymer coatings is only described by the dispersion of the PMMA spheres on surfaces. PMMA spheres are mainly individual and rather well distributed on R-SnO 2 (Fig. 6a), while forming large clusters of variable sizes on glass (Fig. 6b).

Friction behaviour of polymer on R-SnO 2 and glass

Fig. 7 compares the friction behaviour of glass and R-SnO 2 after the polymer deposition. The polymer layer has a lubricant effect on both substrates: the friction averaged on the first cycle is low (µ = 0.07 for glass and µ = 0.11 for R-SnO 2 )

compared to the friction between silica and glass (µ ≈ 0.6-0.7) or SnO 2 (µ ≈ 0.55-0.6). However, this lubricant effect disappears almost instantaneously on glass as confirmed by the substrate damage within 2 cycles (i.e. 32 mm). A steep rise in friction is recorded and a friction coefficient of 0.6 is quickly achieved.

The lubricant effect is dramatically stabilized when the SnO 2 primer is present.

Before substrate damage, the friction of the polymer-coated R-SnO 2 evolves in two stages. The first one is characterized by a low friction (µ ≤ 0.1). The second stage is described by a progressive increase in friction (0.1 ≤ µ ≤ 0.2) ending with a sudden jump in friction accompanied by damage (substrate cracking) when µ exceeds 0.3.

The cumulated sliding distance to substrate damage quantifies the scratch resistance of the coated glasses.

Wear track analysis

Infrared microscopy results

To understand the stabilization phenomenon of the organic layer by the primer, the evolution of the amount of the polymer due to the mechanical stress was investigated on polymer-coated R-SnO 2 and polymer-coated glass before substrate damage. Infrared spectra from wear tracks obtained after short friction tests duration (one pass, 1 and 2 cycles) on polymer-coated glass are reported in Fig. 8. The intensity of ν CH2 and ν C=O can increase or significantly be reduced from one point to the other in the track after one pass, but these bands are no longer detected after 1 cycle wherever the location in the track. A similar trend is observed when the friction test is repeated at different locations on the coating.

In the presence of tin dioxide, the evolution of ν CH2 is difficult to follow as the signal to noise ratio recorded before friction is weaker than the one recorded on glass (not shown). Therefore, infrared results were only focused on the evolution of the carbonyl band intensity of PMMA, i.e. within the first 2 cycles and when µ has reached a given value in each stage of the friction evolution. As shown in Fig. 9, the ν C=O intensity remains stable within the first 2 cycles and the stretching band is detected as long as µ does not exceed 0.2.

Nomarski optical microscopy and AFM results

Initial stage of friction: onset of wear on glass

A heterogeneous build up of polymer is observed after one pass on the polymer-coated glass. Aggregates with sizes as large as 20 µm have formed (Fig. 10a). Their sizes are larger than those formed during the deposit and are made of flattened PMMA spheres which have coalesced (Fig. 11a). The heterogeneous distribution of the polymer in the contact as well as the large dispersion in the aggregate sizes clarifies the infrared results after one pass, i.e. the decrease or the increase in the ν C=O intensity at different locations in the track. There is a strong variation of the amount of polymer at different locations in the wear track and the size of the rectangular slit in the mask used to select areas is not large enough to average these variations. After 1 cycle, the density of clusters as well as their size decreases, and the polymer is only evidenced by AFM after 2 cycles. At this stage which precedes glass damage, polymer fragments are aligned in the sliding direction covering about half of the wear track (Fig. 11c). The polymer alignment starts in the center of the track where the pressure is maximal [START_REF] Johnson | Contact Mechanics[END_REF].

Initial stage of friction: onset of lubrication on R-SnO 2

After one pass on the polymer-coated R-SnO 2 , aggregates have not formed (Fig. 10b) as on glass but infrared microscopy confirms the presence of the polymer which masks the tin oxide grain boundaries (Fig. 11b). AFM observation and infrared results suggest that the polymer forms a continuous film compared to the clusters built up on glass. The film starts to coalesce in the center of the track and already covers about half of the track after one pass. After 2 cycles, the film becomes more homogeneous. Regions which were free of PMMA are gradually covered by the polymer, suggesting a large plastic deformation of the film. When µ has reached a stable value in the first stage of the friction evolution, the film is still present in the track, as confirmed by infrared results and homogeneously distributed. The film is very smooth, as evidenced by the flat section (Fig. 11e) and has expanded towards edges to cover the whole track.

Discussion

Without primer, the fast disappearance of the carbonyl stretching band of PMMA and the CH 2 stretching bands of PE in infrared microscopy evidences a weak adhesion of the polymer on glass. This induces a high mobility of the polymer under the mechanical stress. Large aggregates are built up and are quickly removed from the contact, resulting in the absence of scratch resistance. On the other hand, the persistence of the PMMA stretching band ν C=O over large sliding distances on tin dioxide-coated glass highlights a strong adhesion of the organic layer on the primer.

The mobility of the polymer is then considerably reduced and a continuous film is formed under the mechanical stress. This leads to a significant scratch resistance of the coated glass. Glass and R-SnO 2 have both acidic surface OH groups which are effective sites for organic adsorbates [23]. However, the strength of Brönsted acidity of hydroxyl groups is increased by the metallic cation, the presence of which enhances the O-H bond polarisation as well as results in strong Lewis acid sites [13].

Therefore, the basic carbonyl oxygen in the ester groups of PMMA can coordinate by H-bonding with the acid sites more strongly on tin dioxide than on glass [24]. In the specific case of the non polar PE which is reported to adhere weakly on glass [13], its C-C double bonds may coordinate with the Lewis sites. However, according to the slow decrease in the ν C=O intensity, the strong adhesion of the organic coating on R-SnO 2 does not prevent its progressive wear. Moreover, the presence of some polymer in the contact is not excluded when the ν C=O band is no longer detected at µ = 0.2. This assumption is based on the optical observation that cracks only initiate at a higher value of friction (µ > 0.3). Friction tests also pointed out that R-SnO 2 without polymer has no scratch resistance (not shown). From wear track analysis and imaging, it is then concluded that before damage, the tribological behaviour of the polymer-coated R-SnO 2 can be ascribed to the progressive wear of the organic film leading first to a silica-polymer contact (first stage, µ ≤ 0.1) and then to a contact between silica and SnO 2 with some patches of polymer film (second stage, 0.1 ≤ µ ≤ 0.2 and µ > 0.3). Damage occurs when there is no longer enough polymer in the contact to protect the oxide (µ > 0.3). The friction value observed in the first stage is higher than those observed for polyethylene-based coating dispersions in dual coatings (µ ≈ 0.03) [1]. This result may be explained by the addition of PMMA which is used for a suitable label adhesion [25][26][27]. The suggestion about the nature of the contact in the second stage is supported by the observation of lower friction values on hot-end coated glass bottles [1,28] or SnO 2 -coated flat glass when surfaces are contaminated with organic residues [28,29]. The high friction recorded for the silica-SnO 2 contact without surface contaminants (µ ≈ 0.55-0.6) is considerably reduced due to their lubricant effect [30][31][32].

Respective roles of roughness and surface chemistry of tin dioxide in the organic layer stabilization

The deposition of a crystallized tin dioxide film on glass has roughened the surface, modified the surface chemistry as well as the surface morphology. In order to identify the parameters which are responsible for the stabilization of the polymer layer, the effect of roughness and surface chemistry was assessed on flat glass with different coatings. The polymer aggregates on S-SnO 2 and R-SiO 2 . Clusters are of large variable size on S-SnO 2 , as in the case of glass and smaller on R-SiO 2 . The good wetting of the polymer previously observed on R-SnO 2 is similar on R-Si 3 N 4 and r-SnO 2 . A large dispersion in shape and cluster sizes is only noticed for S-SnO 2 , the surface of which has topographical and/or chemical heterogeneities (rings) unlike R-SiO 2 , R-Si 3 N 4 and r-SnO 2 . The variable size and shape of aggregates on the smoothest tin dioxide may be due to a pinning effect by these surface defects which can influence the polymer wetting [33][34][35].

Morphology of polymer on S-

Friction behaviour of polymer on S-SnO 2 , r-SnO 2 , R-SiO 2 and R-Si 3 N 4

The friction behaviour of R-SiO 2 and R-Si 3 N 4 is reported in Fig. 7, and Fig. 12 compares the friction results for S-SnO 2 and r-SnO 2 , after polymer deposition.

Whatever the coated glass, the friction averaged on the first cycle is low compared to the friction between silica and glass or SnO 2 (cf. 3.1.2). R-SiO 2 behaves like glass.

Friction on R-Si 3 N 4 evolves as R-SnO 2 , but each stage is associated with higher friction values (first stage with µ ≤ 0.18 and second stage with 0.18 ≤ µ ≤ 0.

Discussion

The suppression of the strong acid-base interactions between CVD SnO 2 films and the polymer by a silicon nitride deposit has instantaneously inhibited the anchoring function of SnO 2 . These results suggest that the polymer-oxide interface plays a role in the stabilization of the organic layer, insofar as the R rms roughness of the surface was preserved. Glass roughening by a silica layer has no impact on the polymer anchoring, but the polymer stabilization by a rougher glass is not excluded.

S-SnO 2 and r-SnO 2 are both able to anchor the polymer on surface, but the scratch resistance is improved when the tin dioxide roughness increases, suggesting that the primer roughness also contributes to the stabilization of the polymer layer. The highest scratch resistance is obtained on the roughest tin dioxide and this trend agrees well with the suggestion of Pantano et al. [16] about the mechanical anchoring function of the primer for organic coatings. Moreover CVD SnO 2 films differ from the smoother primers by their sharpened roughness. Therefore, two possible parameters can control the large plastic deformation of PMMA spheres leading to the lubricating film, i.e. the sharpness of SnO 2 roughness and shear due to the strong adhesion of the polymer on the primer. A schematic view of the film formation mechanism is presented in Fig. 13. Such a cooperative effect has been also reported in the case of electrically conductive polymers deposited on oxidized metals such as titanium oxides [36]. The weak adhesion of polymer noticed on the pure metal is strongly enhanced after the metal pre-oxidation which simultaneously induces a change in surface chemistry as well as an increase in the roughness of the surface.

Conclusion

The stabilization of organic coatings by CVD SnO

Fig. 1 .

 1 Fig. 1. R-SnO 2 morphology (a) SEM image: holes are present in the coating (cf. arrow) (b-c) AFM image (0.25 µm 2 ) and corresponding section profile.

Fig. 2 .

 2 Fig. 2. S-SnO 2 morphology (a) SEM image of a tilted section of 15°: ring defects of glass are visible (cf. arrow) (b-c) AFM image (0.25 µm 2 ) and corresponding section profile.

Fig. 3 .

 3 Fig. 3. r-SnO 2 morphology (a) SEM image of a tilted section of 15°: ring defects of glass are still visible (cf. arrow) (b-c) AFM image (0.25 µm 2 ) and corresponding section profile.

Fig. 4 .( 6 ) R-Si 3 N 4 :Fig. 5 .

 46345 Fig. 4. R-SiO 2 morphology (a) SEM image of a tilted section of 15° (b -c) AFM image (0.25 µm 2 ) and corresponding section profile.

Fig. 6 .

 6 Fig. 6. AFM image (25 µm 2 ) of organic coating on (a) R-SnO 2 and (b) glass.

Fig. 7 .

 7 Fig. 7. Evolution of µ with the cumulated sliding distance when the polymer is deposited on (--•--) glass, (-⊡-) R-SiO 2 , (-◊-) R-Si 3 N 4 , (-⊖-) R-SnO 2 . µ averaged on the first cycle is: 0.12 for R-SiO 2 , and 0.18 for R-Si 3 N 4 .

Fig. 8 .

 8 Fig. 8. Reflection infrared spectra from the polymer-coated glass before friction and from the wear tracks as a function of the cumulated sliding distance. (A) before friction (B) after one pass (8 mm) at the 1 st location in the track (B) after one pass at the 2 nd location in the track (C) after 1 cycle (16 mm) at the 1 st or 2 nd location in the track (D) after 2 cycles (32 mm) at the 1 st or 2 nd location in the track. Measurements at two different locations in the track are different after one pass (1 st and 2 nd point) and become similar after 1 and 2 cycles (1 st or 2 nd point).

Fig. 9 .

 9 Fig. 9. Evolution of the normalized ν C=O intensity with the cumulated sliding distance when the polymer is deposited on (-•-) glass, and (-○-) R-SnO 2 (left vertical axis). Evolution of µ with the cumulated sliding distance when the polymer is deposited on (--•--) glass and (-⊖-) R-SnO 2 (right vertical axis).

Fig. 10 .Fig. 11 .

 1011 Fig. 10. Optical image of the wear track after one pass on (a) polymer-coated glass and (b) polymer-coated R-SnO 2 .

  SnO 2 , r-SnO 2 , R-SiO 2 and R-Si 3 N 4

  3). The general trend of friction on S-SnO 2 and r-SnO 2 is similar: the friction averaged on the first cycle remains stable on a given sliding distance and ends with a steep increase in µ. Optical examination of wear tracks shows that the polymer does not protect R-SiO 2 and R-Si 3 N 4 as both substrates are damaged after one pass.Damage begins at the center of the track on R-SiO 2 similarly to glass and cracks initiate on R-Si 3 N 4 as observed in the case of R-SnO 2 . Unlike R-SiO 2 and R-Si 3 N 4 , the polymer has a lubricant effect on S-SnO 2 and r-SnO 2 which disappears when µ exceeds 0.3, as confirmed by cracks initiation. In spite of the large scratch resistance dispersion on both coated glasses, the lubricant effect is stabilized over larger cumulated sliding distances on r-SnO 2 . The scratch resistance can double on r-SnO 2 as compared with the highest scratch resistance recorded on S-SnO 2 .

Fig. 12 .

 12 Fig. 12. Evolution of µ with the cumulated sliding distance when the polymer is deposited on (--○--) S -SnO 2 , (-□-) r-SnO 2 and (-⊖-) R-SnO 2 . µ averaged on the first cycle is: 0.06 for S-SnO 2 and 0.09 for r-SnO 2 .

Fig. 13 .

 13 Fig. 13. Schematic view of the polymer film formation mechanism under friction (a) PMMA spheres dispersion on the SnO 2 primer, the roughness of which is due to facetted grains (b) spheres flattening and coalescence of flattened spheres under the compressive and shear stresses leading to a lubricating film which coexists with some patches of film (c-d) expansion of the film to cover the whole contact: the film becomes smoother.

  2 films (primer) resulting in glass bottle lubrication was investigated on flat glass with a mixture of PE and PMMA spheres. Friction tests in air on bare glass and with the primer confirm that the stabilization of the polymer over large sliding distances is only achieved in presence of SnO 2 . The study evidences the strong adhesion of the polymer on SnO 2 through the persistence of the PMMA stretching band ν C=O on significant sliding distances, leading to the build up of a continuous film. Weak adhesion on bare glass results in fast disappearance of ν C=O and the build up of large aggregates which are quickly removed from the contact. The film and aggregates are formed by coalescence of squashed PMMA spheres. The role of roughness and surface chemistry in the anchoring function of the CVD SnO 2 films was tested. The surface chemistry alteration and glass roughening suppress the lubricant effect. By modulating the primer roughness, it was demonstrated that the scratch resistance is highly correlated to this roughness. The study shows that the interplay between roughness and surface chemistry of SnO 2 is necessary for stabilization of the polymer into a lubricating film.

Table 1 :

 1 R rms roughness of substrates for the polymer coating. In the presentation, the roughest coatings are denoted R (R for Rough): R-Si 3 N 4 , R-SnO 2 and R-SiO 2 , the

smoothest coating is denoted S (S for Smooth); S-SnO 2 and the intermediate primer roughness between S-SnO 2 and R-SnO 2 is denoted r (r for rough).

Acknowledgements

The authors thank Saint-Gobain Recherche for the interactive discussions and financial support.