Henri Gouin
email: henri.gouin@univ.u-3mrs.fr

Kolumban Hutter

The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

Keywords: contact angle, contact line, hysteresis

), we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.

Introduction

In [START_REF] Gouin | The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines[END_REF], henceforth referred to as part 1, we proposed a model of non-Newtonian fluids for slow movements in the immediate vicinity of the contact line that is formed at the interface of two immiscible fluids and a solid. Fluid interfaces are modelled by differentiable manifolds endowed with constant capillary energy. Solid surfaces are also regarded as differentiable manifolds endowed with a position dependant surface energy (we only consider the case of surfaces without surfactant). The kinematics of slow isothermal movements close to the contact line, revisited in the framework of continuum mechanics, required the adherence condition to be relaxed at the contact line. The velocity field is discontinuous at the contact line and generates a concept of line friction but viscous dissipation remains bounded. Simple observations associated with the motion of two fluids in contact with a solid wall reveal the following behaviour: depending upon whether the fluid on the wall advances or retreats, a variable contact angle is observed. The value of this apparent dynamic contact angle, also called simplyYoung's angle, depends upon the contact line celerity. These observations resolve distances which are not shorter than a few microns.

The most notable unanswered problem is connected with the equation controlling the macroscopic motion of the contact line and the justification of contact-angle hysteresis when the fluid is advancing or receding on a solid wall.

To verify the accuracy of the model proposed in part 1 and, particularly to justify the Young-Dupré equation for the apparent dynamic contact angle associated with the notion of line friction, a simple academic example is considered for which the equations of motion together with the boundary conditions can be integrated in a suitable approximation. This is the case of a thin cylinder containing an incompressible fluid separated from air by a meniscus. The apparatus is a capillary test-tube with rotation of symmetry.

In our example, we assume that the solid wall of the tube is endowed with a fluid-solid surface energy which oscillates periodically with small variations with very short wave length relative to the length of the tube 1 . The fact that we have chosen oscillations superposed on a slowly varying function may be justified by the possibility to solve the equations of motion analytically. More general forms could also be considered. For suitable dimensionless numbers corresponding to slow movements, the equations of motion of the liquid and conditions on interfaces take simplified forms. The two-fluid interface can then be modelled as a spherical cap. It turns out that the microscopic motion of the contact system is governed by a simple differential equation. This equation is analytically decoupled from those of the liquid motion. When the irregularities of the liquid-wall-surface energy vary over a length that is vanishingly small relative to the size of the capillary tube, the solution of the microscopic motion tends to a limit which is the solution of a new differential equation. This differential equation of the macroscopic or homogenized motion is not the limit of the microscopic equation. The liquid in the capillary tube is controlled by a piston. We deduce the motion of the two-fluid interface and we study the behaviour of the apparent dynamic contact angle for the advance and retreat of the contact line. In so doing a hysteresis phenomenon appears. The deduced results are compared with those obtained in the literature with methods of statistical physics and experimental measurements.

The capillary tube apparatus

The apparatus is a cylindrical tube of radius a with a vertical symmetry axis 0 k. A liquid of volume V 0 fills the cylinder above a position determined by a piston. In accordance with the hypotheses and notations of part 1, the liquid is in contact with air through an interface Σ 2t ; the constant air-liquid-surface energy is σ 2 ≡ σ AB . In the motion, air is considered as incompressible. The wall of the cylinder (piston included) is denoted by Σ 1t . The wall is inhomogeneous and the surface energy σ 1 ≡ σ AS -σ BS (difference between the superficial energies of solid-liquid and solid-air) depends on the geometrical position on Σ 1t . The value σ 1 is assumed to be rotationally invariant. The contact line is the curve Γ t connecting the two interfaces Σ 1t and Σ 2t . Due to the axi-symmetric geometry, its representation in fig.

1 is a point P of which the position is given by the abscissa z; the point J of the piston, the position of which is given by the abscissa L, is a function of time commanded by an operator. On the interval JI of the wall, the surface energy σ 1 is assumed to be constant with the value σ 10 . We consider the case when the surface energy σ 1 on the interval IP of the wall is such that

σ 1 = σ 10 ( 1 -k sin z ε a ), (1)
where 0 < ε ≪ 1 is a small dimensionless parameter, | k |< 1 and k σ 10 is positive.

Let us note that for sufficiently small ε, the average value of σ 1 on any

h P θ Σ t2 I J a i k 0 y L z ε V o

Piston

Figure 1: Circular cylinder with vertical axis filled with a liquid of volume V 0 held in position by a piston having cap form. The part of the cylinder wall with the constant surface energy σ 10 is colored in grey; the part of the cylinder wall with the non-uniform surface energy σ 1 is hachured (see main text). Referred to the orthonormal axis 0 i k , z denotes the position of the contact line, L = L(t) determines the position of the piston (z = y ε + L).

The meniscus at the upper free surface is rotational symmetric; the apparent dynamic contact angle between the meniscus and the wall is denoted by θ; h is the height of the meniscus.

unspecified macroscopic set of the wall tends to σ 10 when ε tends to zero.

In relation [START_REF] Abeyaratne | Proceedings of the Symposium on the Mechanics of Phase Transformations and Shape Memory alloys[END_REF] the interfacial energy σ 1 is built by two terms. The second is f ε = -k σ 10 sin z/(ε a) . The distribution f ε converges to zero when ε tends to zero and its virtual work on Σ t1 is null 2 . We understand that the 2 Let us calculate the value of the distribution gε = sin (z/ε) when ε → 0, (ε > 0). For associated force has an action only on the contact line Γ t . It is proposed to study the motion of the contact line, i.e. to determine the value of the position z(t) as a function of time. To this end, it is necessary to study the liquid motion.

any function φ ∈ C ∞ [R, R] with compact support, < gε, φ >= +∞ -∞ sin (x/ε) φ(x) dx = ε +∞ -∞ sin v φ(εv) dv = -ε [ cos v φ(εv) ] +∞ -∞ + ε 2 +∞ -∞ cos v φ ′ (εv) dv. The first term [cos v φ(εv)] +∞ -∞ = 0 and |< gε, φ >| ≤ ε 2 +∞ -∞ | φ ′ (εv) | dv = ε +∞ -∞ | φ ′ (x) | dx . From +∞ -∞ | φ ′ (x) | dx < ∞, we obtain lim

Equations of motion and boundary conditions

In part 1, we proposed the equations of motion and boundary conditions of a capillary motion of two fluids in contact with a solid wall. The equations of motion are

ρa i + p ,i = φ i + Q j i,j
, where φ denotes the volumetric force, ρ the density, a the acceleration vector, Q the (non-Newtonian) viscous stress tensor and p the pressure. At the solid wall, adherence conditions are required except at the contact line. On the meniscus Σ t2 , the boundary condition is

2σ AB R m n 2i = (Q j Ai -Q j Bi ) n 2j + (p B -p A ) n 2i , (2)
where the indices A and B refer to the fluids L A and L B , n 2 is the unit vector of Σ t2 external to L B , and R -1 m is the mean curvature of Σ t2 . The boundary conditions on Σ t1 introduce an additional unknown scalar expressing the action of the solid wall on the fluids (see Eq. [START_REF] Concus | Static menisci in a vertical right cylinder[END_REF], in part 1). The only pertinent parameter in the vicinity of the contact line is the apparent dynamic contact angle, formulated as an implicit function of the contact line celerity (see Section 5, in part 1); the intrinsic contact angle (see Eq. [START_REF] Dussan | On identifying the appropriate boundary conditions at a moving contact-line: an experimental investigation[END_REF], in part 1) does no longer appear in our continuum mechanics point of view. Consequently, we denote simply by θ the apparent dynamic contact angle and, in the following, we refer to it as the Young angle. The dynamic Young-Dupré equation on the contact line is

σ 2 cos θ + σ 1 + ν u = 0 ( 3
)
where ν is the line friction and u the contact line celerity. The functional representation of ν and its value were studied for a plane two-dimensional motion in part 1 and can be extended to an axi-symmetric motion. The line friction depends on the apparent dynamic contact angle (see Eq. ( 27) in part 1), and is positive. It is the problem of the meniscus that determines the moving boundary including the contact line. To this end, a complete picturing of the fluid-fluid interface is necessary. In fact, the geometry of the meniscus is a consequence of the flow of the two fluids in the vicinity of the meniscus and this flow is a functional of pertinent dimensionless parameters. Without wanting to redo what many authors have previously done, it is useful to recall the main results known in the literature. Many papers are concerned with the shape of the meniscus near the contact line in capillary tubes. West, [START_REF] West | On the resistance to the motion of a thread of mercury in a glass tube[END_REF], was among the first to study this problem.

Concus, [START_REF] Concus | Static menisci in a vertical right cylinder[END_REF], presented an analysis of the static meniscus in a right cylinder. Analysis using the Navier-Stokes equations and comparing results with experiments of advancing interfaces in cylinders were undertaken by Hoffman, [START_REF] Hoffman | A study of the advancing interface. Interface-shape in liquid-gas systems[END_REF], Legait and Sourieau, [START_REF] Legait | Effects of geometry on a advancing contact angle in fine capillaries[END_REF], Finlow, Kota and Bose, [START_REF] Finlow | Investigations of wetting hydrodynamics using numerical simulations[END_REF], Ramé and Garoff, [START_REF] Ramé | Microscopic and macroscopic dynamic interface shapes and the interpretation of dynamic contact angles[END_REF]. Zhou and Sheng, [START_REF] Zhou | Dynamics of immiscible fluid displacement in a capillary[END_REF], analyzed the link between macroscopic behaviour of the displacement of immiscible fluids in a capillary tube and the microscopic parameters governing the dynamics of the moving contact line; Thompson and Robbins, [START_REF] Thompson | To slip or not to slip[END_REF], performed molecular dynamics simulations in the hydrodynamics of the contact line; Dussan, Ramé and Garoff, [START_REF] Dussan | On identifying the appropriate boundary conditions at a moving contact-line: an experimental investigation[END_REF], Decker et al, [START_REF] Decker | Physics of contact angle measurement[END_REF], gave considerations on the contact angle measurements; Voinov, [START_REF] Voinov | Motion of line of contact of three-phases on a solid: thermodynamics and asymptotic theory[END_REF], proposed a thermodynamics approach to the motion of the contact line. In all these papers, the following dimensionless numbers are of significance,

Reynolds number R e = ρ a | u | µ 0 , capillary number C a = µ 0 | u | σ 2 , Weber number W e = ∆ρ u 2 a σ 2 , Bond number B = ∆ρ ga 2 σ 2 ,
where ∆ρ is the density difference between the two fluids, g is the acceleration due to gravity and µ 0 is the viscosity in the liquid bulk. A vertical capillary system treated with an asymptotic simplification was undertaken by Pukhnachev, [START_REF] Pukhnachev | Thermocapillary convection under low gravity[END_REF], and Baiocci and Pukhnachev, [START_REF] Baiocci | Problems with one-sided constraints for Navier-Stokes equations and the dynamic contact angle[END_REF]. Their study involves Navier-Stokes fluids paired with an imposed apparent dynamic contact angle as an additional condition at the points of contact between the free boundary and the solid wall. The problem of the dissipative function becoming infinite near the contact line is avoided by introducing a slip length at the solid wall. It appears that for two-dimensional or axi-symmetric motions, when the capillary number tends to zero, the free interface tends uniformly to the equilibrium position. Moreover, to minimize the effect of gravity on the meniscus shape, the capillary tube radii are generally of order less than 1 mm. A quantitative assessment of relative effects of gravity and capillary forces can be made on the basis of the Bond number. In Foister, [START_REF] Foister | The kinetics of displacement wetting in liquid/liquid/solid systems[END_REF], it is experimentally and theoretically proved that the capillary effects dominate over gravity for all systems when B < 1. Likewise, the relative importance of inertial and capillary effects can be characterized by the Weber number. In all experimental systems, when W e < 10 -3 , inertial effects did not significantly affect the three phase boundary motion.

In 1980, Lowndes, [START_REF] Lowndes | The numerical simulation of the steady movement of a fluid meniscus in a capillary tube[END_REF], performed numerical calculations of the steady motion of the fluid meniscus in a capillary tube. He showed that when R e < 10 -2 , the meniscus formed by an incompressible Newtonian fluid can be determined by using the creeping flow approximation. In this case, our proposed non-Newtonian model has the same streamlines as the Navier-Stokes model, [START_REF] Gouin | The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines[END_REF]. The method used by Lowndes considers a slip length less than 10 Angströms near the contact line. This length is of the same order as the distance from the contact line where the fluid is no longer Newtonian. Comparisons between the calculated and observed contact angles are in accordance with the experiments of Huh and Mason, [START_REF] Huh | Effects of surface roughness on wetting (theoritical)[END_REF]; conclusions agree with those in part 1. In the partial wetting case, when

C a < 10 -2 , a Young's angle in the interval [ π 6 , 5π 6
] verifies Eq. [START_REF] Baiocci | Problems with one-sided constraints for Navier-Stokes equations and the dynamic contact angle[END_REF].

In what follows, we wish to simplify the formidable mathematical problem and describe the dynamics of the air-liquid interface by a suitable approximation with as few parameters as possible. The fluids are considered to be Newtonian except in a close (molecular) vicinity of the contact line, [START_REF] Gouin | The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines[END_REF].

Boundary condition on the meniscus is the classical equation ( 2). For slow movements, when R e < 10 -2 , C a < 10 -2 , W e < 10 -3 and B < 1, the capillary flow is axi-symmetric, and the shape of the surface Σ t2 at a given time t is described as a spherical cap where the angle with Σ t1 is the apparent dynamic contact angle. At 20 • Celsius, for water, in c.g.s. units, ρ = 1, µ 0 = 0.01 and for an airwater interface σ 2 = 72. When a = 0.1, the above conditions on R e , C a , W e and B are largely verified with a velocity u of some centimeters per hour. Similar results are obtained for glycerol (ρ = 1.26, µ 0 = 11.8 and σ 2 = 63) with a velocity u less than a meter per hour. In the developments of section 4 below, these conditions are assumed to be fulfilled.

The motion of the contact line

Let us present some analytical formulae related to the geometry of the contact line, see fig. 1.

The volume of the spherical cap with height h and span 2a is

V = πh 6 (h 2 + 3a 2 ), where h ∈ [-a, a].
The volume of the liquid in the cylindrical tube is constant, so

V 0 = πa 2 y ε + πh 6 (h 2 + 3a 2 )
is constant. Let l 0 be such that πa 2 l 0 = V 0 . Then,

y ε -l 0 = - h 6a 2 (h 2 + 3a 2 ) and tan ( π 4 - θ 2 ) = - h a . ( 4
) If λ = h/a where λ ∈ [-1, 1], then cos θ = - 2λ (1 + λ 2 ) . (5)
Eqs. ( 4), ( 5) establish the connections between y ε and h and between y ε and θ. From y ε = z -L and taking Eq. ( 4) into account, we deduce

z = l 0 + L - h 6a 2 (h 2 + 3a 2 ) ≡ l 0 + L - a 6 λ (λ 2 + 3). ( 6
)
For a given value of t and for λ belonging to [-1, 1], z is a decreasing function of λ with values in the interval [ l 0 + L -2a/3, l 0 + L + 2a/3 ]. With u = dz/dt and the above expressions, the dynamic Young-Dupré Eq.

(3) yields

ν dz dt = 2 λ (1 + λ 2 ) σ 2 -σ 1 ,
where ν is also a function of z through the Young angle θ. Taking Eq. ( 1) into account, we obtain

ν dz dt = f (z, t) + K sin z ε a with f (z, t) = 2 λ (1 + λ 2 )
σ 2 -σ 10 and K = k σ 10 .

(7) Remarks: The surface of the spherical cap is π (h 2 +a 2 ). The capillary energy of the total system per unit length of the circumference of the capillary is W e ; so,

2πaW e = πσ 2 (h 2 + a 2 ) + 2πa z L σ 1 dz, Relation (1) implies, W e = σ 2 ( h 2 2a + a 2 ) + z L σ 10 dz - z z I kσ 10 sin z εa dz,
where z I denotes the abscissa of the point I (see fig. 1). Consequently,

W e = W 0 + W 1 + C te with W 0 = σ 2 h 2 2a + σ 10 (z -L), W 1 = k σ 10 ε a cos z εa , (8)
and

C te = σ 2 a/2 -k σ 10 ε a cos (z I /εa) is an additional constant.
By taking relation ( 6) into account, we obtain

∂h ∂z = - 2a 2 h 2 + a 2 and ∂W 0 ∂z = -f (z, t), ∂W 1 ∂z = -k σ 10 sin z εa .
Eq. ( 7) can now be written in the form

ν dz dt = - ∂W e ∂z (9)
which is an equation for a unidimensional motion of a mechanism with linear friction where the effects of inertia (associated with the second derivative d 2 z/dt 2 ) are absent. In subsection 4.1, we will see that the behaviour of the solutions of Eq. ( 9), when the parameter ε is vanishingly small, is completely different from what happens when the effects of inertia are present in a dynamics equation.

Asymptotic analysis of the motion of the contact line

The differential equation ( 9) yields the motion of the contact line. The behaviour of the solutions when ε tends to zero has already been studied in the literature within the framework of a problem associated with shape memory alloys (Abeyaratne, Chu and James, [START_REF] Abeyaratne | Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy[END_REF]).

Note that Eq. ( 7) implies ∂f /∂z (z, t) = (4σ 2 /a) (λ 2 -1)/(λ 2 + 1) 3 ; for t given and λ ∈ [-1, 1] , f (z, t) is a decreasing function of z. We consider the case associated with an average surface tension σ 10 of partial wetting corresponding to an average Young angle θ m such that,

σ 2 cos θ m + σ 10 = 0.
Consequently, the inequality, | σ 10 /σ 2 | < 1, is verified. Since σ 2 is positive, this relation is equivalent to the inequalities

σ 2 + σ 10 > 0 and σ 2 -σ 10 > 0. ( 10
)
The equation of the contact line motion is only valid for partial wetting, nevertheless, we obtain the following limit relations associated with the limit values of λ: Eq. ( 5) expresses the connection between λ and θ; analytically, for λ = -1, cos θ = 1 and the Young angle θ = 0. Eq. ( 6) expresses the connection between λ and z; for λ = -1, z = l 0 + L + 2a/3, for which Eq. ( 7) implies, f (z, t) = -σ 10 -σ 2 .

In the same way, for λ = 1, the Young angle θ = π and z = l 0 + L -2a/3, for which f (z, t) = -σ 10 + σ 2 .

Consequently, under conditions [START_REF] Dussan | On identifying the appropriate boundary conditions at a moving contact-line: an experimental investigation[END_REF], for K ≡ k σ 10 sufficiently small, the differential equation ( 7) fulfills exactly the conditions of the asymptotic theorem presented in the Appendix. Thus, it is possible to deduce the behaviour of the solutions from Eq. ( 7) when ε tends to 0. Our aim is not to discuss the general solution of Eq. ( 7) when L(t) is an arbitrary function of t. We only consider two significant cases encountered in experiments (Raphael and de Gennes [START_REF] Raphael | Dynamics of wetting with nonideal surfaces. The single defect problem[END_REF]), namely (i) piston at rest and (ii) piston in uniform motion (L(t) = v 0 t).

With y ε ≡ z -L(t) ≡ l 0 -(a/6)λ(λ 2 + 3), let us define the function F by

F (y ε ) ≡ f (z, t) ≡ 2 λ (1 + λ 2 ) σ 2 -σ 10 ≡ -σ 2 cos θ -σ 10 . (11)
Then, y ε satisfies the relation

ν dy ε dt + ν v 0 = F (y ε ) + K sin z ε a ,
where y ε (0) = y 0 and ν is a function of y ε . Now, straightforward adaptation of the asymptotic theorem in this simple case yields the macroscopic behaviour of the contact line: When ε → 0, y ε (t) converges uniformly to y(t) ∈ C 1 [ℜ + ] and satisfies the differential equation

ν(y) dy dt = G(y) , (12)
where y(0) = y 0 , ν is now a function of y in place of y ε and

G(y) =                [F 2 (y) -K 2 ] 1 2 -νv 0 , if y < y -, -νv 0 , if y -< y < y + , (13)
-[F 2 (y) -K 2 ] 1 2 -νv 0 , if y + < y .
y -and y + are constants verifying the relations

F (y -) = K and F (y + ) = -K .
Now, we study the two main classes of the dynamical systems (Penn and Miller, [START_REF] Penn | A study of primary cause of contact angle hysteresis on some polymeric solids[END_REF]): those in which the interface is in non-equilibrium and moves to an equilibrium, and the others in which the advancing interface is driven on the solid wall of the cylinder with a constant velocity.

(i) Piston at rest

In this subsection, the piston is fixed (v 0 = 0 and we take z ≡ y ε ). In Eq. ( 8), the potential W 0 is now independent of t and a convex function such as that shown in fig. 2. The differential equation corresponding to the asymptotic behaviour of Eq. ( 9) when ε → 0 is expressible in terms of the potential W s as follows

∂W s ∂y = -G(y) ,
where G(y) is defined in [START_REF] Gouin | The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines[END_REF]. When K is sufficiently small, the driving force G(y) has square root singularities (see [START_REF] Gouin | The wetting problem of fluids on solid surfaces. Part 1: the dynamics of contact lines[END_REF] with v 0 = 0). The functions W 0 and W s are convex, but W s is not the limit of W e when ε → 0 (as W 0 is). When changing the scales -i.e. when ε tends to zero -W s cannot be regarded as the limit of the sum of separate energies associated with the mean energy W 0 and the energy of the perturbation W e -W 0 . This shows that by changing the scale we lose the additivity property of the energy for the solution of the limit differential equation: W s is not the potential energy limit. However, a physical interpretation of the previous limit behaviour can be given. When ε → 0, the potential W e admits on [y - ε , y + ε ] a large number of local minima whose respective distances converge to zero with ε. For any initial position y 0 ∈ [y - ε , y + ε ] the closest local minimum is reached in an infinite time. When ε tends to zero, any initial position y 0 of the interval [y - ε , y + ε ] is located between two local minima whose gap tends to zero with ε. On a macroscopic scale the local minima find themselves together with Figure 2: Traces of the three potentials W e , W 0 , W s when the piston is at rest. In suitable units, we can take the values a = 1, K = 0.005, σ 10 = -0.5, σ 2 = 1. The curves are centered around z = z m associated with θ m = Arccos 0.5 (coordinate z is defined up to an additive constant). The potentials W 0 , W e and W s have been shifted up or down for better visibility (since potentials are defined up to an additive constant). Note that W 0 is the limit of W e when ε tends to 0, but this is not so for W s which is fundamentally different: tangent lines at the limiting points z -and z + are parallel to the z-axis and the function G(z) = -∂W s /∂z is of square root type at these points.

the initial value which becomes a position of equilibrium. Note that the angle θ A (0), given by the value λ, drawn from Eqs. ( 5), ( 6), corresponds to the y - ε -position. In the same way, an angle θ R (0) corresponds to the y + εposition. In fact K ≡ k σ 10 is positive and, consequently, θ A (0) and θ R (0) are solutions of the relations

cos θ R (0) = -σ 10 + k σ 10 σ 2 and cos θ A (0) = -σ 10 -k σ 10 σ 2 . ( 14
) Then, θ R (0) < θ m < θ A (0) . An angle θ ∈ [θ R (0), θ A (0)] corresponds to an initial position y 0 ∈ [y - ε , y + ε ]. This is not so for y 0 / ∈ [y - ε , y + ε ]
. Indeed, in this case, the second member G(y)

of the asymptotic equation of motion ( 12) of the contact line, constitutes a non zero attractive force toward the points y - ε and y + ε . The points y - ε and y + ε are now reached in finite time due to the explicit convergence of the solutions of Eq. ( 12) (see Appendix for the computation of these times). The position y - ε (resp. y + ε ) is the position of equilibrium associated with y 0 < y - ε (resp. y 0 > y + ε ) to which angle θ A (0) (resp. θ R (0)) corresponds. This static case indicates that the Young angle θ is included in the interval [θ R (0), θ A (0)]. The final value of θ, denoted by θ f , depends on the initial position y 0 of y and, consequently, on the initial value θ 0 of θ. We obtain the asymptotic behaviour

             θ 0 ∈ ( θ R (0), θ A (0) ) =⇒ θ f = θ 0 , θ 0 ≤ θ R (0) =⇒ θ f = θ R (0) , θ 0 ≥ θ A (0) =⇒ θ f = θ A (0) . (15)

(ii) Piston in uniform motion

When v 0 = 0, it is easy to prove that for all initial conditions y 0 , a constant solution to Eq. ( 12) is reached in a finite time. In the Appendix, an order of magnitude of this time is calculated. We obtain u = v 0 .

When the piston advances, v 0 = u > 0 and when the piston retreats, v 0 = u < 0. The constant solutions of Eq. ( 12) are given by

F 2 (y) -k 2 σ 2 10 -ν 2 u 2 = 0 .
Taking into account the definition of F in relation [START_REF] Finlow | Investigations of wetting hydrodynamics using numerical simulations[END_REF], the value of the advancing angle θ A (u) is

θ A (u) = Arccos -σ 10 -k 2 σ 2 10 + ν 2 u 2 σ 2 . ( 16
) 1
The same arguments yield the value of the retreating angle θ R (u)

θ R (u) = Arccos -σ 10 + k 2 σ 2 10 + ν 2 u 2 σ 2 , (16) 2
and we deduce the inequalities

θ R (u) < θ R (0) < θ m < θ A (0) < θ A (u) .
The Young angle θ is a function of the contact-line celerity u in an universal form. In fact, the line friction ν depends on θ but ν/ν 0 , (where ν 0 is a constant friction value) belongs to the interval [1, 1.7] when θ ∈ [30 • , 150 • ] (see part 1). A simple approximation of ( 16) consists to consider ν as a constant (for example an average value of the line friction like 1.35 ν 0 ). With such an approximation, graphs for θ A (u) and θ B (u) are associated with the three values σ 10 /σ 2 ≡ -cos θ m , k/σ 2 , ν/σ 2 . The different forms of graphs are presented in fig. 3. They are drawn from θ = 0 • to θ = 180 • although our model is no longer valid for these limit values.

Comparison between results, experimental data and other models obtained in the literature

We propose a model of hysteresis of the contact system at the interface liquid-fluid-solid with the aid of which experimental results can be interpreted. Moreover, we find that the behaviour matches that obtained by kinetic molecular arguments in the literature.

The dynamic line tension behaviour

The differential equation ( 7) is equivalent to Eq. ( 3) in the form

ν dz dt = -σ 2 cos θ -σ 1 .
Following the expression for the solid-surface energy, the emerging equation admits a macroscopic behaviour expressed by the differential equation [START_REF] Foister | The kinetics of displacement wetting in liquid/liquid/solid systems[END_REF]. When the piston is at rest, the macroscopic contact-line motion is governed by the equation (see Eq. ( 12)):

ν dz dt = ± [(σ 2 cos θ + σ 10 ) 2 -k 2 σ 2 10 ] 1 2 , (17)
where the sign + or -depends on the direction of the line motion and k σ 10 ≡ max | σ 1 -σ 10 | is the maximum of the fluctuations in the fluidsolid energy with respect to its average value σ 1 .

The average value of the surface tension is τ = σ 2 cos θ + σ 10 . It has the dimension of a force per unit length. If τ m = -kσ 10 represents the value of τ at θ = θ A (0) (see relation ( 14)), when the angle θ is close to θ A (0), we obtain

ν dz dt = (τ 2 -τ 2 m ) 1 2 ≈ √ 2 τ m (τ -τ m ) 1 2 . ( 18
)
When the Young angles are small, on expanding θ to order 2, we obtain

θ 2 -θ 2 A (0) ≡ β 0 (τ -τ m ) , (19)
where β 0 is a suitable constant.

The results are extendable to the case of a piston in advancing motion. Eq. ( 17) remains unchanged, but the dynamic angle of contact is such that

(σ 2 cos θ + σ 10 ) 2 -k 2 σ 2 10 -ν 2 u 2 = 0 . Noting that τ u = -(σ 2 cos θ + σ 10 ) 2 -ν 2 u 2 , the previous results are un- changed but | τ u |<| τ m |.
When the contact line retreats, it is easy to present similar calculations and to obtain analogous results.

These results are similar to those obtained in the literature by molecular statistics or single defects (Ruckenstein and Dunn, [START_REF] Ruckenstein | Slip velocity during wetting of solids[END_REF]). For example, Eq. ( 18) and Eq. ( 19) and an analysis of their consequences are also presented in Raphael and de Gennes, [START_REF] Raphael | Dynamics of wetting with nonideal surfaces. The single defect problem[END_REF], Joanny and Robbins, [START_REF] Joanny | Motion of a contact line on a heterogeneous surface[END_REF].

Limit velocities of the contact line

Limit velocities for advancing and retreating contact lines have been experimentally found and described in detail (Hoffmann, [START_REF] Hoffman | A study of the advancing interface. Interface-shape in liquid-gas systems[END_REF], Dussan, [START_REF] Dussan | On the spreading of liquids on solid surfaces: static and dynamic contact-lines[END_REF], Blake and Ruschak, [START_REF] Blake | A maximum speed of wetting[END_REF], Chen, Ramé and Garoff, [START_REF] Chen | The velocity field near moving contact line[END_REF], Decker et al, [START_REF] Decker | Physics of contact angle measurement[END_REF]). These velocities are generally outside the domain of validity of Eq. ( 3). Nevertheless, we formally extend our calculations to the case θ ∈ (0, π), and the asymptotic behaviour obtained in subsection 4.1 makes it possible to calculate the limit velocities! Of course, this extension corresponds to the fact that the forms of the graphs of θ as a function of u presented in fig. 3 are similar to experimental graphs proposed in the literature. Indeed, the advancing Young angle must be smaller than π. The celerity of the contact line is u π and the associated line friction ν π . Relation ( 16) 1 yields

ν π u π = (σ 2 -σ 10 ) 2 -k 2 σ 2 10 . (20)
In the same way the retreating Young angle must be larger than 0. The celerity of the contact line is now u 0 and the associated line friction ν 0 . Relation (16) 2 yields

ν 0 u 0 = -(σ 2 + σ 10 ) 2 -k 2 σ 2 10 . (21)
Notice that the velocities u 0 and u π do not have the same absolute value. With this crude approximation, when the line friction is chosen with a constant value ν, knowledge of σ 2 , σ 10 = σ 1 , u 0 and u π allows us to determine K = k σ 10 and ν.

In the Appendix, it is proved that the representation (1) for the surface energy is only a convenient way to consider calculations with surface heterogeneities. The representation is extendable to any periodic function with variations on short intervals with respect to macroscopic sizes. Consequently, the previous results make it possible to investigate the surface quality and line friction by simple measurements.

Connection between the dynamic contact angle, the line celerity and the line friction

The purpose of this paragraph is to show by comparison with simple experiments that our model leads to qualitative and perhaps some quantitative coincidental behaviours of the contact system with experimental evidence. The simplest way is to consider the surface inhomogeneity given by our model represented by relation [START_REF] Abeyaratne | Proceedings of the Symposium on the Mechanics of Phase Transformations and Shape Memory alloys[END_REF]. The values of σ 10 , σ 2 and k, allow us to draw the graphs of the applications given by ( 16) 1 and ( 16) 2 , (see fig. 3).

Only the ratio σ 10 /σ 2 and the value of k are important.

We present in fig. 4 experimental layouts drawn in the literature for an advancing motion of the contact line (Zhou and Sheng, [START_REF] Zhou | Dynamics of immiscible fluid displacement in a capillary[END_REF]). The similarity of the theoretical graph and the experimental data is striking. Nevertheless, we must note that the experimental data in the literature is always presented in logarithmic scales. This comparison makes it possible to obtain numerical values for the line friction ν (as an average) and the limit velocities u 0 and u π . We use the experimental results for liquid flows in contact with air in capillary tubes. Results do not take any explicit account of the inhomogeneity of the tube walls. In the model suggested by relation ( 1), the solid surface inhomogeneity is represented by the factor k. In fact, k ≪ 1, and in relations ( 20) and ( 21) the term k 2 σ 2 10 is neglected in comparison to the terms (σ 2 -σ 10 ) 2 and (σ 2 + σ 10 ) 2 . In order to be in agreement with the experimental conditions, we suppose the diameter of the tube to be about 1 mm. We deduce the numerical relations between the celerities C a and u for two liquids. These expressions are given in c.g.s. units. For water we obtain u = 7200 C a and for glycerol u = 4.2 C a . The experimental curves yield limit velocities of the contact line. In various measurements they represent values for C a and range between 10 -2 and 10 -1 . For an air-glycerol interface, these values correspond to the limit celerity u π with a value between 0.042 cm s -1 and 0.42 cm s -1 , and for an air-water interface the limit celerity u π lies between 72 cm s -1 and 720 cm s -1 . They are widely out of the range of validity of our model, but for a wonder, they are in good agreement with experimental results! For glycerol and a limit celerity of 0.42 cm s -1 and for a static wetting angle θ A (0) of about 50 • , we obtain a line friction of about 240 Poise. For water and a limit celerity of 100 cm s -1 , the line friction is about one Poise. Let us note that the case of water is obviously less realistic than the case of glycerol. These values of the line friction are of the same order of magnitude as those obtained with relation [START_REF] Ruckenstein | Slip velocity during wetting of solids[END_REF] in part 1. 12 from Zhou and Sheng, [START_REF] Zhou | Dynamics of immiscible fluid displacement in a capillary[END_REF]). Solid curves are calculated with [START_REF] Huh | Effects of surface roughness on wetting (theoritical)[END_REF] 1 . The solid surfaces are assumed to be sufficiently smooth for the hysteresis to be small. It is easy to adjust the values of σ 10 , σ 2 and ν to fit the experimental data given by points.

Conclusion

We proposed in this paper a dynamic model of slow movements of the contact system between two fluids and a solid surface. Comparison between our results and recent experiments or behaviour inferred from statistical physics shows good agreement on the qualitative level and, more unexpectedly, on the quantitative side. The most significant innovation in this paper is the introduction of the notion of line friction. This term is essential to the construction of the model. The line friction depends on the Young angle, but an order of magnitude for its average value can be obtained by using experimental measurements in the literature.

The Young-Dupré relation (3) takes the inhomogeneity on the solid surface into account. It describes the microscopic behaviour of the Young angle. The inhomogeneity is distributed at distances between a few tens to some hundred Angströms. This distance is that of the operating ranges of intermolecular forces which command the surface energies. At the lower part of this scale, energies are homogenized and these distances on a macroscopic scale are no longer significant. The shape of the surface is prescribed on larger scales.

The results are independent of the radius of the tube. Indeed, the hysteresis behaviour solely depends on the physico-chemical properties of the solid surface. The universal form of the hysteresis loop makes it possible to discuss the general case independently of any particular apparatus. Relations ( 20) and ( 21) can be written without difficulty using the inhomogeneity of the solid surface in a form different from Eq. ( 1). Not all the efforts on the contact line have the same effects: the one associated with the rapid oscillations of the surface energy of the wall, (Ksin (z/εa)), produces a work that tends to zero when the wave length of the oscillations tends to zero. This effort appears in the macroscopic expression of the contact line motion represented by Eq. ( 12). It is noteworthy that the weak differences between the potentials W 0 and W e have huge implications. This may seem surprising at first sight. It is due to the fact that the contact line is massless and consequently its motion equation is not in the same form as for material systems. Some authors model contact lines as lines with matter (Slattery, [START_REF] Slattery | Interfacial transport phenomena[END_REF]); nevertheless, the inertial force associated with the mass of the line is generally of an order smaller than the magnitude of the force due to the line friction.

Finally we note that jumps on the inhomogeneity are considered by Jansons, [START_REF] Jansons | Moving contact lines at a non-zero capillary number[END_REF]. A shift factor is proposed by Hoffman, [START_REF] Hoffman | A study of the advancing interface. Interface-shape in liquid-gas systems[END_REF], correcting the relation between u and θ. These considerations appear unnecessary in our model where movements are slow and θ is the apparent dynamic contact angle. Furthermore, the experimental literature notes the influence of evaporation on the relaxation time for approaching the apparent dynamic contact angle (Penn and Miller, [START_REF] Penn | A study of primary cause of contact angle hysteresis on some polymeric solids[END_REF]). Similar inferences are drawn for equipments which are subjected to vibrations (Marmur,[START_REF] Marmur | Equilibrium contact angles: theory and measurement[END_REF]). The relaxation time of the apparent dynamic contact angle is obtained by phenomenological methods (Hoffman, [START_REF] Hoffman | A study of the advancing interface. Interface-shape in liquid-gas systems[END_REF], Penn and Miller, [START_REF] Penn | A study of primary cause of contact angle hysteresis on some polymeric solids[END_REF]). It corresponds to the calculations carried out in the Appendix. Lastly, other models for high-speed motions of the contact line using a notion of dynamic surface energy are also considered in the literature: Shikhmurzaev, [28], Blake, Bracke and Shikhmurzaev, [START_REF] Blake | Experimental evidence of nonlocal hydrodynamic influence on the dynamic contact angle[END_REF]. Their study is outside the scope of our slow movement model.

The theorem, proved for ν(z) = constant, is extended without difficulty for ν(z) belonging to [α, β] where 0 < α < β < ∞ 3 .

Let us give an elementary proof of the fundamental theorem. For a complete demonstration using Young measures, we refer to Abeyaratne, Chu and James, [START_REF] Abeyaratne | Proceedings of the Symposium on the Mechanics of Phase Transformations and Shape Memory alloys[END_REF], [START_REF] Abeyaratne | Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy[END_REF]. We just consider the case ν = constant (ν = 1 with a convenient unit) and f independent of t. For the variable z belonging to a compact interval, the segment [-1, 1] is considered. The hypothesis ∂f /∂z < 0 corresponds to strict convexity of W 0 ∂W 0 /∂z = -f (z) . For a given ε, consider z 0 ∈ [-1, 1] as the initial value of the solution z ε (t) of Eq. (A1). The critical points of Eq. (A1) are the roots of

f (z) + K sin z ε = 0 .
The roots belong to the interval [z -, z + ]. Let us consider the case for which z 0 is smaller than z -; when T is sufficiently small, it is the same for z ε (t) with t ∈ [0, T ]. Let us calculate the limit values t according to position z when ε tends to zero. For ε ≪ 1, the function sin (z/ε) oscillates rapidly between -1 and 1. Let z 0,ε be the value immediately above or equal to z 0 such that sin (z 0,ε /ε) = -1 and let z 1,ε be the value immediately below or equal to z ε (t) such that sin (z 1,ε /ε) = 1. Then, In the same way, for z 0 above z + we obtain,

ż = -f (z) 2 -K 2 .
When z 0 belongs to the interval [z -, z + ], it is easily seen that there exists a critical point z ε of Eq. (A1) such that | z ε -z 0 |< b ε where b is a positive constant depending only on K and f . The solution of Eq. (A1) tends in a monotonous way towards z ε . Consequently, for t belonging to [0, +∞[, z ε (t) converges uniformly to z 0 when ε tends to zero. The macroscopic law associated to z 0 belonging to [z -, z + ] is ż = 0.

General oscillations

We consider the superimposed effect of an arbitrary smooth periodic function P (z/ε) in place of sin (z/ε). We can assume without loss of generality that P (z/ε) has a zero average, (in other cases, we add a constant to f ). The amplitude of P gives the placement of the flat region as in figure 2:

-max P ≤ f (z, t) ≤ -min P With the same hypotheses as in the theorem we define z -(t) and z + (t) such that f (z -(t), t) = -min P and f (z + (t), t) = -max P ; so the flat region remains [z -(t), z + (t)].

In the special case when f is independent of t, the calculation is developed in the same way as previously. The results are unaltered with -min P in place of K and -max P in place of -K.

The complete proof of this extension is given in Abeyaratne, Chu and James, [START_REF] Abeyaratne | Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy[END_REF].

Relaxation time associated with Eq. (A3)

We consider the case when g is explicitly independent of t and ν is constant. For z 0 < z -, let

χ = ν z - z 0 du f (u) 2 -K 2 .
For z 0 near z -, f (u) + K ∼ 2 K and f (u) -K ∼ (u -z -)f ′ (z -). Then, f (u) 2 -K 2 ∼ 2 K(u -z -)f ′ (z -) and

χ ∼ ν 2 -K f ′ (z -) z --z 0 .
The χ-value yields the magnitude of the relaxation time necessary to obtain the final position of the contact line.

Figure 3 :

 3 Figure 3: Values of the Young angle as functions of the celerity u of the contact line. We plot different formal cases associated with relations (16) 1 and (16) 2 and convenient values of σ 10 , σ 2 , k, ν. In panel (a), k = 0 and the Young angle θ m is 90 • . In panels (b), (c) and (d), k = 0 and the Young angle θ m has values 90 • , 120 • or 60 • . In cases (b), (c) and (d), we note a hysteresis phenemenon due to the discontinuity of θ for u = 0. The unit of the u-axis depends on the fluids.

Figure 4 :

 4 Figure 4: Apparent dynamic contact angle plotted as a function of C a = µ 0 u/σ 2 . The C a -axis is based on a logarithmic scale. Panels (a) and (b) are associated with the data of J.P. Stokes et al. (ref. 13 from Zhou and Sheng, [32]). Panels (c) and (d) are associated with the data of G.M. Femigier and P. Jenffer (ref.12 from Zhou and Sheng,[START_REF] Zhou | Dynamics of immiscible fluid displacement in a capillary[END_REF]). Solid curves are calculated with (16) 1 . The solid surfaces are assumed to be sufficiently smooth for the hysteresis to be small. It is easy to adjust the values of σ 10 , σ 2 and ν to fit the experimental data given by points.

s 2 , 3 2 , εpπ + ε π 2 ] 2 -

 23222 Let us divide the interval [z 0,ε , z 1,ε ] in intervals of length επ. Then, (z 1,ε -z 0,ε )/(επ) At each interval [z 0,ε + pεπ, z 0,ε + (p + 1)επ] the change of variables s = sin If ξ = z ν(ς)dς, ξ is a strictly increasing function of z corresponding to a bounded change of length scale depending on the considered point and f1(ξ, t) = f (z, t) is a decreasing function of ξ.where λ = ε arcsin s and λ ∈ [εpπ -ε π . Because f is continuous, this expression has the same limit when ε tends to zero as1 π z) + Ks) √ 1 -s 2 dz .When ε tends to zero, this expression converges to Because f (z) 2 ≥ K 2 , the change of variables s = sin α yields K 2 = t ,which implies ż = f (z) 2 -K 2 .

Surface energies of solid walls with many small wiggles, arising from small-scale microstructural changes, appear often in scientific problems; for example, phase transformations, protein folding and friction problems (Abeyaratne, Chu and James,[START_REF] Abeyaratne | Kinetics of materials with wiggly energies: theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy[END_REF]). The scale of microstructural changes is a microscopic one and consequently is of an order smaller than the length of the tube.

Acknowledgments

The author would like to express his gratitude to Professor Hutter and the anonymous referees for helpful suggestions during the review process.

(we present the same differential equation as Eq. ( 7), but f may be a more general function than listed in [START_REF] Concus | Static menisci in a vertical right cylinder[END_REF], and a = 1 corresponds to the choice of a convenient unit of length).

The following hypotheses are assumed:

• K and ε (ε ≪ 1) are two strictly positive constants;

• f is continuously differentiable for any z ∈ ℜ, and for any t ∈ ℜ + , ∂f /∂z < 0 ; • There exist z -and z + belonging to C 1 (ℜ) such that for any

• ν is a strictly positive continuous function of z.

Remarks:

The fact that for t fixed, f (z, t) is a decreasing function on [0, +∞), implies z -< z + . Differential equation (A1) yields a single solution z ε (t) defined in ℜ + with z ε (0) = z 0 , (the differentiable equation fulfills the conditions of uniqueness of the Cauchy problem (Hartman,[START_REF] Hartman | Ordinary differential equations[END_REF])). We obtain the fundamental result that gives the behaviour of z ε (t) when ε tends to 0 from the following theorem

Asymptotic theorem

When ε tends to 0, z ε (t) converges uniformly to z(t) belonging to C 1 [ℜ + ] and satisfying the differential equation

where z(0) = z 0 and

if z + (t) < z .


Mr Clément Sire

Bertrand Mr

Georgeot

Emmanuel Mr

Trizac

Mr Peter Holdsworth

Ens Lyon

Patrizia Mrs

Vignolo

Marc Mr

Knecht

Mr Éric

François Mr

Université Demangeot

Sabatier Paul

Virginie Mrs

Mahdi

Alexis Mr

Université Valentin

Bart Mr

Van Tiggelen

evaluation by the experts committee, the composition of which is specified below.

 Introduction History and geographical location of the unit

The unit, located on the Paul Sabatier -Toulouse 3 campus, was officially created in 2003. It originates from a team of theoretical physicists which arrived in 1992 as a part of the Laboratoire de Physique et Chimie Quantique, in an effort to promote fundamental physics in Toulouse. The graft was particularly successful, so that it now forms a separate joint Université Paul Sabatier (UPS) -CNRS unit ('Unité Mixte de Recherche'). It belongs to the IRSAMC (Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes) federation, together with three other units. Two of these share the same premises (building 3R1).

Management team

The present director is Mr Clément SIRE, assisted by Mrs Malika BENTOUR (secretary) and Mrs Sandrine LE MAGOAROU (on a 50 % part-time position, in charge of computer aspects).

HCERES nomenclature

ST2 -Physics.

Brief description of activities

The fields of study pertain to condensed matter and statistical physics in the broad sense. The range of topics investigated at LPT is impressive for a unit of this size, from strongly correlated quantum systems to irradiation processes in clusters, including quantum coherence, mesoscopic physics, soft condensed matter, non-equilibrium and disordered systems. Several lines of research are directly relevant to closely related disciplines such as biology, mathematics, chemistry, astrophysics, computer sciences and social sciences.

Unit workforce

The research staff consists of twelve CNRS researchers and nine faculty members. It is organized in four groups, assessed separately in section 3: 2  Overall assessment of the unit

Global assessment of the unit

After a very positive round of evaluation conducted in 2009, the LPT has gained even more momentum, maintaining a first rate scientific production, appointing junior staff of excellent level, and securing funds from multiple sources with remarkable success. The research conducted is original, diverse and of excellent pedigree, highly visible and recognized. It is embedded in a convincing network of collaborations. This provides the grounds for a vigorous and sound outreach activity, knowledge dissemination and valorisation. The unit, furthermore is managed in an exemplary fashion, consequently it enjoys an excellent academic reputation and appeal. It ranks highly among theory laboratories in France and competes among the top 10 % at the international level. Twenty-two years after the initial transplant in Toulouse, the LPT has evolved into an outstanding research and teaching organization, constituting an ongoing success story.

Strengths and opportunities in relation to the context

The experts committee has identified a number of strong points and opportunities, starting with the high level of scientific expertise of the staff. The lab shows a healthy age distribution, improved gender characteristics, and in spite of the disparity in size of the different groups, the activity for all is well balanced in terms of community service in the broad sense, and contract management. Praiseworthy are also:

the collective dynamics within the unit, which is highly positive;

the skilful and sterling management, be it on scientific or on administrative affairs;

the success in outreach, knowledge dissemination, transferred knowledge;

the supporting staff, highly efficient and appreciated;

the commendably successful effort to establish collaborations with experimentalists, and outside physics;

the interactions with IRSAMC federation, a convincing and efficient agora, common to four physics/chemistry units, which endows them with an impact and visibility at the local scale, that they would not reach with the same efficiency otherwise.

Weaknesses and threats related to the context

Although no clear weaknesses have been identified in the course of the evaluation, a number of potential threats can be outlined, some of them being rather generic:

the unit has significantly grown in size in recent years. It awaits appropriate support in terms of office space.

Congestion looms;

there are concerned on the lacuna-rich projection of fundamental unit's activities, such as the LPT, onto the regional, national and European strategies for research. This worry echoes recent ANR trend for 'low energy' theoretical physics activities, which, if not hostile, is at least unfavourable;

the experts committee deplores the decrease of funding opportunities at doctoral level;

compared to structures of a similar size and range of activities, LPT presents a notably weak administrative support in terms of numbers;

career perspectives of supporting staff are thwarted. The experts committee encourages the unit to pursue sustained efforts towards the promotions of the managing secretary, and, at the level of IRSAMC federation, of the engineer in charge of computers, for instance encouraging and supporting the supervision of students.

As emphasized above, this pair is of remarkable quality, providing invaluable assistance.

Recommendations

Several issues deserve attention:

the activity in the realm of biophysics and soft matter has witnessed critical weakening in the last two years. It is currently carried by teaching staff only. Reinforcing this domain of activity seems a priority, and a CNRS position would be highly desirable here;

two professors have recently left, for personal reasons. Their scientific performances, during their stays at the LPT, were rather exceptional. The experts committee thus hopes that the recent professor position opening, submitted by the unit, will meet benevolence from the governing bodies. The proposed scientific profile is large, and promises a strong competition at the best international level;

a convergent need has emerged in two groups, to benefit from the support of a computer scientist, in charge of optimization and development. What it at stake is not computer or hardware assistance, duly and competently covered already. Given the heavy and advanced computational nature of numerous LPT's research projects -several millions of CPU hours are used yearly at facilities such as IDRIS/GENCI, or the local excellent CALMIP -, such an opening, at 'Ingénieur de Recherche' level, is fully justified, and endorsed by the experts committee. Loss of competitiveness is to be feared otherwise. A hiring of this kind has proven invaluable in other units of a similar size and it is evident that all four groups would enormously benefit from interaction with such a person. The experts committee anticipates a rewarding return on investment, not only for the range of activity where numerical efficiency is the keystone, but also for the whole lab;

as in other institutions, the situation of faculty members ('enseignants-chercheurs') is fragile, and often impeded by a heavy teaching load, to which unofficial but time consuming chores must be added. This work force within LPT, of exceptional quality, would benefit from a partial transfer of duties to CNRS staff. Such an evolution, which requires that the University accepts CNRS volunteers for teaching duty, would be a significant progress;

finally, LPT took the lead on the 'École des Sciences Avancées de Luchon', an endeavour to enhance interdisciplinary exchange between different sciences. It is of interest for a large number of researchers in the Midi-Pyrénées region, with a potential for matching the most notable realizations of the kind. It aims at providing the site with a structure for hosting schools and conferences, thereby contributing to the academic reputation and appeal of the entire Toulouse scientific scene. The experts committee enthusiastically supports this initiative, which merits proper funding. To this end, it is recommended that the School governing body and Scientific Council match, in their diversity, the proposed thematic breadth of the project.

Unit workforce Number as at 30/06/2014 Number as at 01/01/2016 N1: Permanent professors and similar

	positions	9	9
	N2: Permanent researchers from Institutions and similar positions	12	13
	N3: Other permanent staff (without research duties)	1.5	1.5
	N4: Other professors (Emeritus Professor, on-contract Professor, etc.)
	N5: Other researchers (Emeritus Research Director, Postdoctoral students, visitors, etc.)	6
	N6: Other contractual staff (without research duties)
	TOTAL N1 to N6	28.5	23.5
	Unit workforce	Number as at 30/06/2014	Number as at 01/01/2016
	Doctoral students	14
	Theses defended	14
	Postdoctoral students having spent at least 12 months in the unit	16
	Number of Research Supervisor Qualifications (HDR) taken	3
	1. Strongly Correlated Fermions (headed by Mr Didier POILBLANC); Qualified research supervisors (with an HDR) or similar positions	12	>12
	2. Quantum Coherence (headed by Mr Dima SHEPELYANSKY);
	3. Statistical Physics of Complex Systems (headed by Mr Nicolas DESTAINVILLE);
	4. Finite Fermionic Systems and Clusters (headed by Mr Éric SURAUD).


History and geographical location of the federative structure and its member research units and brief description of its activities FR 3425 also known as iRTSV (Institut de Recherche en Technologies et Sciences pour le Vivant) is one of the eight CEA Institutes in the CEA's Life Sciences department. For the next contrat, the name will be changed into BioScience and Biotechnology Institute of Grenoble, with B 2 IG as an acronym. It is currently organized in four laboratories plus one research group in Neurosciences. iRTSV has been running for at least one contract under the supervision of Dr Jérôme Garin. The lab units participating to this Fédération de Recherches are all situated in Grenoble but scattered in several separate buildings. The four major contract operators are:

i) The CBM Lab (Chemistry and Biology of Metals, UMR 5249 CEA CNRS UJF). Its domain of expertise is to study metal in biolgy, with a special interest in the structure and spectroscopic properties of metalloproteins, regulation of biological systems using metal ions, bio-inspired chemistry involving metal systems, particularly in the fields of human health and energy.

ii) The PCV lab (Cellular and Plant Physiology, UMR 5168, CEA, CNRS, UJF). PCV studies plant cell functions with emphasis on chloroplast proteomics metabolism and regulation, flowering and actin networks.

iii) The BCI lab (Biology of Cancer and Infection, U 1036, CEA INSERM, UJF, CNRS). BCI studies the molecular mechanisms involved in cancer and infection with the aim to develop medically relevant applications for detection and treatment.

iv) The BGE lab (Large Scale Biology, U 1038, CEA, INSERM, UJF). BGE aims at producing large scale data using approaches in genomics, proteomics, imaging and medium throughput screening assays in order to feed system biology.

Together with the smaller research team GPC, overall iRTSV comprises a staff of more than 350 persons including 220 tenured jobs (100 of those at CEA). This Fédération de Recherche is housed in CEA facilities except the GPC team. Other institutional partners are CNRS, INSERM and UJF. iRTSV represents a strong entity in biology in Grenoble. Locally it interacts with two Labex structures (GRAL and ARCANE) and also with the major research structures present in Grenoble, namely IBS, INaC, CHU, IAB, etc. The activity of FR 3425 is facilitated by the existence of four large platforms, a computer center, mouse and plant facilities. These platforms are shared and operated by iRTSV.

Management team

iRTSV has a director (Mr Jérôme GARIN) and a deputy director (Mr François PARCY). They are assisted by a team composed by the directors and deputy directors of the four participating laboratories. They convene twice a month and additionally hold a steering committee together with representatives of the funding bodies once a year.

Specific workforce allocated to the federative structure

Twenty staff members are currently listed as employees of iRTSV. Five CNRS employees are affiliated to iRTSV but indeed work for BGE. Since this lab is not associated with CNRS, the administrative solution was to consider them as iRTSV staff. Although the director and deputy director are listed as "affectés en propre or primarily affiliated", they nevertheless also belonged to their respective research labs (as director and group leader) at least during the current contract. This leaves 13 staff members primarily affiliated to iRTSV. They are all CEA employees and all involved in management (Human Resources, Finances, European and International Connections, Scientific Communication, Working Security Conditions). Overall, a close scrutiny of this list indicates that CEA has chosen to organize administratively this sector of biology in Grenoble in the form of a Fédération de Recherches (it is actually listed on the front page of the report as Structure Fédérative which is a bit confusing). It does not seem that platform staff members are directly linked to iRTSV but rather to the individual partner labs.

2  Overall assessment of the federative structure Global assessment of the federative structure

The labs involved in iRTSV have had an excellent scientific productivity in the last contract. It seems that in each lab the quality of scientific production has improved significantly compared to the earlier contract. They indicate that this is related to their capacity to equip, manage and renew scientific material of high quality in the platforms of the Structure Fédérative. This is essentially what is expected from a Federation de Recherches. More specifically, they have produced a large number of high quality papers in journals of high impact factor, but even more revealing with already a relatively large number of citations. The fields covered include first an integrated study of proteins in a large diversity of organisms (e.g. photosynthetic, human). This has relied very much on proteomics, metabolomics and also on cooperation with IBS for the structural part. Also cellular imaging and large scale genomics are extensively used together with modelling for getting into systems biology. This first part of the project intersects to a large extent with the two Labexes GRAL and ARCANE. A second part of the overall project is a large step into nanotechnologies in the framework of the innovation campus GIANT. Research performed in the labs of iRTSV has already generated some nanomaterials of interest in particular based on actin polymerization and also metal containing bio-inspired catalysts with possible applications in chemistry, energy (hydrogen generation) or photosynthesis. Accordingly, several patents have been deposited in the domain of biotechnology and a start-up NMR Bio (in collaboration between IBS and CBM) is foreseen in 2015. The Structure Fédérative iRTSV has had clearly the merit to bring together several important individual actors of the biological field in Grenoble but also chemists interested in bio-inspired materials. It has also favored the creation and maintenance of platforms of high scientific and technological standards particularly in proteomics and imaging and this has benefited to the whole community and beyond. Care was taken to maintain a good communication between iRTSV, the local Labexes and more generally with the Giant program. Examining the achievements of the partners of iRTSV leads to conclude that several of them have reached true international status with many invitations in international congresses but also notably ERC grants to a couple junior scientists and a series of valued international grants and prizes.

Strengths and opportunities related to the context

Provided that iRTSV can maintain its funding (an achievement difficult to make in the present context, see below), the future of the Grenoble consortium might indeed be very bright. On the one hand they have been able so far to stabilize their permanent staff (29 departures for 29 arrivals in the contract), but also they have attracted high caliber scientists either locally or from other French Institutes or more rarely internationally. The present situation of the platforms is good, they possess in general recent equipments (sometimes maintenance is even still valid from the purchase contract). The training in iRTSV labs has been efficient with the presence of an average of 50 doctoral and 60 post-doctoral students. Several of those have eventually returned to Grenoble on permanent positions. In the last contract iRTSV has organized at least five scientific meetings, with at least one in association with the Labex GRAL. The research program proposed for the next contract is innovative and daring. Based on results obtained in the present contract they propose to develop new bio-inspired materials at the nanometer scale. In particular they want to construct de novo new metalloenzymes, to model the cytoskeleton, to use the capacity of 3D organoids to differentiate into tumour-like acini in order to study the tumoral process, just to name a few of these projects. Many of them also deal with the creation of new biomaterials. Large scale biology and systems biology will be extended to several of the topics studied previously in the partner labs. It seems that the researchers of iRTSV have demonstrated their capacity to move into this new frontier.

Weaknesses and threats related to the context In a French system which is forever changing its organization, it will be essential for iRTSV to maintain its status and originality. What about the relations with the Grenoble Labexes and GIANT? Will those structures slowly substitute to the Federations de Recherche? One worrying point which is underlined in the report is that the present funding of iRTSV is insufficient. This is due to the fact that iRTSV is a CEA operated structure and CEA is presently not in a financial shape which would allow it to support the Federation de Recherches at an adequate level. On the bright side, CEA probably needs to keep its 8 Structures Fédératives in order to manage the different labs that it hosts and probably the financial gain provided by concentrating the administrative staff is still of interest. It is also important to create a critical mass in biology, able to interact at a sufficient level with the other constituting bodies of the CEA center in Grenoble. Considering the huge recent development in physics, nanotechnologies, etc. it is absolutely mandatory to put together the whole biology of this campus in such a Fédération, in order to keep it in a favorable position for the discipline.

Recommendations

In the present difficult financial context it would be wise for iRTSV to diversify its funding and try to attract private funds in order to stabilize its financial status. The project based on the construction of new biomaterials at the nanoscale should very much help in this respect. Another aspect also mentioned in the report is the scattering of the labs of iRTSV and the existence of a building construction and renovation program. Given the age of some of the buildings housing the labs of iRTSV, this should also be a priority.

Federation


A Merlen
email: merlen@univ-tln.fr

| C Pardanaud

| S Coussan

| C Panagiotopoulos

| O Grauby

Carmen M Ruiz

Formation of cyanide compounds during preparation of gold surfaces evidenced by surface-enhanced Raman spectroscopy

Keywords: cyanide compounds, gold, surface-enhanced Raman spectroscopy

We report surface-enhanced Raman spectroscopy (SERS) measurements on nanostructured gold surfaces prepared using a primary vacuum sputtering technique. Even if no molecules have been deposited on the metallic surface, a clear Raman signal is observed. A very intense and sharp peak around 2,100 cm -1 together with low-wavenumber modes are visible. The comparison between the experimental spectra and those obtained using density functional theory calculations confirms that these new modes are associated with the cyanide compound Au(CN) 2 -. This proves the high sensitivity of SERS for the chemical analysis of metallic surfaces. It also shows that the pollution should be carefully taken into account in SERS analysis. We also demonstrate that high power laser illumination transforms these toxic compounds into carbon species; this method can be used to clean SERS substrates.

| INTRODUCTION

Surface-enhanced Raman spectroscopy (SERS) is an analytical method based on classical Raman spectroscopy associated with optical nano-antenna. [START_REF] Etchegoin | Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects[END_REF] It combines the advantage of Raman spectroscopy, a vibrational spectroscopy with a very low cross section, with the high sensitivity of enhanced optical processes. For most SERS studies, optical nano-antenna is based on metallic nanostructures with strong plasmonics resonances. It is well established that if the wavelength of the optical excitation corresponds to a plasmonic resonance of the metallic nanostructures, a strong enhanced electromagnetic (EM) field is produced in the near field of the antenna. The places where the EM field is enhanced are called hot spots. If a molecule is localized in such a hot spot, which usually occurs for those with a strong chemical affinity for metallic surfaces, its Raman cross section can be increased by several orders of magnitude. This is the basic principle of SERS. The process is so efficient that single-molecule detection with SERS has been reported. [START_REF] Ruan | [END_REF][3][4] In addition, SERS offers several advantages: It is a fast, (acquisition time takes typically a few seconds, a couple of minutes if the signal intensity is low) easy, and nondestructive analysis tool. As a consequence, SERS is now currently used in a large field of applications, notably for the detection of pollutant. [5,6] For instance, for the analysis of ambient air composition, Mosier-Boss and Lieberman [7] have used an SERS sensor based on silver chemically functionalized substrates mounted on a thermoelectric cooler to detect volatile organic compounds. With their method, they successfully detected various compounds such as chlorinated solvents, aromatic compounds, and methyl t-butylether. Thus, SERS appears as a privileged tool to study air pollution.

Usually, the protocol to perform SERS is divided in 3 steps: (1) preparation of the metallic (usually gold or silver but any metals with plasmonic resonances in the visible can be used) nanostructured substrate, (2) deposition of the molecule on the SERS substrate (most of the time, this process is done by immersion in a low concentration solution followed by a thorough rinsing to remove molecules in excess, and (3) Raman measurement is performed using a classical Raman spectrometer. Surprisingly, even if SERS is regarded as an extremely efficient and sensitive process, most of SERS studies are performed under ambient air conditions. This experimental procedure has two major drawbacks. First, the metal can be oxidized losing its optical properties. This is particularly true for silver: It is well known that silver SERS substrates must be used immediately after preparation otherwise the chemical degradation of its surface will cause a rapid decrease of the SERS signal. [8] This problem can be avoided using gold, which is more chemically stable compared with silver. Second, in ambient conditions, the substrate can be easily polluted by molecules present in the air. Nevertheless, in most cases, molecules studied by SERS have a strong chemical affinity for metallic surfaces and their adsorption removes the possible contaminants. At the end, the SERS signal corresponds to the Raman signature of the molecule, except for specific modes associated with the interaction between the molecule and the metal.

Nevertheless, the question of the SERS signal of the nanostructured metallic surface when no molecules is deposited remains open. In such conditions, polluting molecules should still be present, and indeed, it can be found in scientific forums on the internet discussions about Raman modes observed on blank gold surfaces. [START_REF] Etchegoin | Principles of Surface-Enhanced Raman Spectroscopy and Related Plasmonic Effects[END_REF] The origin of such spectral signatures remains unclear and may overlap with compounds of interest while analysis.

In this study, we have performed SERS measurements on a blank gold SERS substrate. Surprisingly, we have observed Raman signature of cyanide compounds. It proves the adsorption on the gold surface of chemical species.

| METHODS

Gold nanostructured surfaces were prepared using metallic sputtering under primary vacuum (10 -1 Pa). We used a Jeol Fine Coat ion sputter JFC-1100 with a voltage of 1.3 kV. The deposition rate was set at 10 nm/min. Before sputtering, the glass slides were washed with alcohol and we have systematically used gloves to avoid any contamination. A typical picture of a glass side after gold deposition can be seen in Figure 1. Its typical color is between blue and purple.

Raman experiments were performed using a Horiba Jobin Yvon HR800 Raman spectrometer associated with a 600-lines/mm array. This device gives a spectral resolution better than 0.5 cm -1 . SERS measurements were performed with a laser power of 0.1 mW for the 633-nm excitation and 0.35 mW for the 514 nm. The laser spot was focused on the sample surface using a 100× objective (NA: 0.9). The scattered light was collected through the same objective in a backscattering geometry. Time acquisition was optimized to ensure a high signal to noise ratio and was typically a few minutes.

DFT calculations were performed using Gaussian09 suit of programs. [9] They were carried out in the DFT formalism. We used the B3LYP functional and D95V basis set for C and N, whereas LANL2DZ one was used for Au atoms. Au, C, and N atoms of Au(CN) 2 molecule were kept free to move whereas those of Au layer were blocked in a monolayer structure, in order, in a first rough approximation, to mimic Au surface. The aim of this protocol was to check Au(CN) 2 bending ability.

| RESULTS AND DISCUSSION

Figure 1 depicts a typical Raman spectrum of a blank SERS sample. As no molecules have been normally deposited on the gold surface, we should not observe any Raman modes. Surprisingly, this is obviously not the case: With the 633-nm excitation, four modes are visible. A very intense mode is observed at 2,135 cm -1 , two low-wavenumber modes with a similar intensity are observed at 300 and 388 cm -1 , and a last mode is visible at 130 cm -1 in the shoulder of the Rayleigh scattering (evidenced in the inset of Figure 1). It must be said that we have observed a remarkable stability and homogeneity of this Raman signature all over the sample. We performed measurements on the same sample 4 months later, and the signal was still the same. This point is remarkable as, for SERS measurements (in particular in the case of singlemolecule detection), strong fluctuations of the Raman signal are usually observed. [10] This is not the case here; the signal is remarkably stable. In addition, we performed this measurement using two Raman spectrometers in different laboratories, and the signal was still the same.

To be sure that we really have an SERS effect, we performed Raman measurements using a different excitation wavelength: 514 nm instead of 633 nm. It is established that the EM enhancement of an SERS substrate is strongly related to its plasmonic properties: It is much higher when the excitation wavelength is close to the plasmonic resonance. [11] For gold substrates prepared with our protocol, the resonance is much closer to 633 than 514 nm, which is confirmed by optical absorption measurements (not shown). As a consequence, the EM enhancement should be much higher at 633 nm compared with 514 nm. As can be seen, comparing both excitation wavelengths in Figure 1, this is exactly what we observed: At 514 nm, the Raman signal, even if it is still present, has a very low intensity. Low-wavenumber modes are not visible anymore, and only the 2,130 cm -1 peak is still present. This result demonstrates that Raman signal is really coming from an SERS effect. It must be noticed that we also observe a rather strong background with the 514-nm excitation, this probably comes from the luminescence of gold nanostructures. [12] The question now is the identification of the chemical species responsible for this SERS signal. Bulk gold has no Raman signal, and the unidentified modes cannot be associated with the vibrational signature of this metal. In the particular case of gold nanoparticles, acoustic modes can be observed at very low wavenumber (typically 35 cm -1 for nanoparticles of 3.2 nm diameter, and the wavenumber downshifts if the diameter increases). [13] This suggests that these modes are coming from a molecule present at the surface of the metal.

There is a very large number of different kind of molecules in the air, each one having a typical vibrational signature. If all molecules are indeed adsorbed, we should observe a Raman spectrum with a very large number of modes. Obviously this is not the case here: only four sharp modes are observed. We can reasonably assume that these modes are the vibrational signature of a limited number of various molecules.

The most abundant gases present in the air are dioxygen (O 2 ) and nitrogen (N 2 ). The Raman spectrum of O 2 has a typical band at 1,550 cm -1, [14] not present in our experimental data. N 2 has a band at 2,330 cm -1 , neither observed. [15] Therefore, it appears clearly that these two gases are not responsible of the modes observed on the gold surface. As there is no spectral signature between 1100 and 1800 cm -1 , it is clear that these modes do not come from carbon soot potentially present in the atmosphere. [16] In addition, it is clearly established that a molecule can give rise to an intense SERS signal only if it has a strong affinity for the metallic surface. As gold has a rather low chemical reactivity, the number of chemical functional groups that can strongly adsorb on its surface is limited. The most commonly used functional group that can react with a gold surface is the thiol function (-SH). This kind of molecules is extensively used as probe molecules in SERS measurements. [17] In this case, some Raman bands at typically 200-300 cm -1 appear and are associated with the Au-S stretching mode. [18,19] In our measurements, we do not observe such modes. In addition, it is also well known that the molecules with a thiol functional group have strong odors (they are used as additives in the domestic gas to facilitate its detection) and their presence in the air (even in a very low amount) can be easily detected by the experimentalists themselves. It was not the case during our experiments. We can therefore safely assume that the reported modes cannot be associated with thiol molecules. The other functional groups with an affinity for gold potentially present in the air are those with a nitrogen atom. These various compounds with nitrogen atoms can react with the gold surface to form specific molecules. It has already been shown that the CN functional group can react with gold and the SERS signature of cyanide compounds has already been extensively studied, [20][21][22][23] in particular the dicyanoaurate Au(CN) 2 -molecules. [24][25][26] In Figure 2, we compare the DFT calculations of this molecule with our experimental Raman measurements. DFT calculations have been performed with two configurations: first, the free Au(CN) 2 -molecule and, second, with the same molecule in interaction with a gold surface. It appears clearly that the molecule remains linear when it is free whereas it is bended when it bends when interacting with the gold surface. This point has already been reported [25] and is confirmed by our calculations. In this study, Jacobs et al. have also reported the transformation of dicyanoaurate ions to tetracyanoaurate ions Au(CN) 4 -.

We have here not observed the low-wavenumber modes associated with this new compound (notably the mode around 500 cm -1 ); therefore, the transformation does not occur in our measurements. Independent of the dicyanoaurate configuration, we observe a remarkable agreement between the calculations and the experimental spectra. The intense mode around 2,100 cm -1 is notably present for both configurations, even if it is associated with a doublet with the molecule in interaction with a gold surface. The experimental peak at 2,100 cm -1 is too broad to determine if it is composed of a doublet or a single mode. The main differences between the two configurations are for the low-wavenumber modes. For the free molecule, only one mode is observed, which can be associated with the experimental mode at 300 cm -1 . For the molecule in interaction with the gold surface, two modes are observed in the low-wavenumber region: one at 130 cm -1 and the other around 390 cm -1 . Some much weaker modes are also present in the calculations, but their intensities are too weak to give an observable mode. Thus, with DFT calculations of Au(CN) 2

-molecules free or in interaction with a gold surface, it is possible to identify all the experimental Raman modes. The fact that we observe both modes from the free and in interaction molecule suggest that we have different sites of adsorption on the gold surface. This is not surprising as the crystallinity of the gold nanostructures prepared using our protocol is rather poor and they offer a large variety of such adsorption sites. The different modes observed and calculated are reported in Table 1. The Raman signal thus originates from this cyanide molecule adsorbed on the hot spots of our SERS substrate. The high EM enhancement makes them detectable by Raman spectroscopy even if they are present in a very low amount.

The presence of cyanide compounds on gold surfaces could be useful: A recent study performed by Kim et al. [27] have demonstrated that cyanide SERS substrates could be used to detect organic volatile compounds and metal ions. To do so, they proposed to exploit the susceptibility of the CN stretching wavenumber of cyanide on Au (around 2100 cm -1 ). As this mode is spontaneously present in the SERS substrates (and very stable in time), our method could greatly facilitate their protocol. Nevertheless, as these molecules are highly toxic, for other applications of nanostructured gold surfaces, it is highly desirable to reduce their amount. To do so, we performed maximum laser power illumination (10 mW with the 633-nm excitation) of the sample during a few seconds. In Figure 3, we compare the SERS spectrum before and after this illumination. It is obvious that the Raman signal is notably affected. The intensity of 300, 388, and 2135 cm -1 modes has considerably decreased, and new modes between 1100 and 1,800 cm -1 are visible. These new modes are associated with the D and G bands of carbon species. [28] These features suggest that the cyanide molecules present at the gold surface have been partly degraded in carbon by the high power laser illumination. The catalytic activity of gold nanoparticles could also promote this reaction. [29] This method is thus efficient to reduce the amount of cyanide molecules on the surface. We have also performed SERS measurements using argon atmosphere and the Raman signature from the cyanide molecules rapidly decreased between 100 and 200°C confirming that they can be easily removed from the surface.

The next question is the origin of the cyanide compounds. As these molecules are not present in the air, we can reasonably assume that they are formed during the sputtering process. It is clear that the use of a primary vacuum does not prevent the presence of organic molecules in the chamber that could react during the sputtering process to form the contaminant molecules on the gold surface.

We performed identical measurements using a different gold evaporator device (EDWARDS Auto 306, pressure: 3.6 10 -6 mbar, deposition rate: 0.12 nm/s). A typical Raman spectrum of this new sample can be seen in Figure 4.

Obviously, the SERS signal is totally different. None of the previously observed modes are present, indicating that cyanide compounds are not present anymore. This result confirms that cyanide compounds are formed during the sputtering process and not as a pollution coming from ambient air, otherwise the signal should be the same whatever the method used for the preparation of the gold surface.

Three modes are now observed: a first one at 1375 cm -1 , potentially associated with aromatic azo functions, a second one at 1560 cm -1 , also associated with nitrogen groups, and a broad one, between 2840 and 2960 cm -1 usually associated with C-H functions. The presence of theses modes suggests that once again, nitrogen-and carbo-based molecules are present on the gold surface. In a similar way to the previous sample, if the gold surface is submitted to a high power laser illumination, the molecules are transformed into carbon species and the D and G bands are observed (spectrum 514 here). This result proves that this method can be efficiently used to clean an SERS substrate independently of the organic species present at its surface.

In this study, we have demonstrated using SERS that organic molecules with nitrogen functions are formed during sputtering of gold under primary vacuum. For some specific conditions, these molecules can be cyanide compounds. The presence of such molecules should be systematically taken into account for the surface analysis of gold prepared using such protocols. We have also shown that an optical treatment can be used to transform these potentially toxic molecules in carbon species. This study proves the high sensitivity of SERS for the analysis of metallic surfaces.

FIGURE 1

 1 FIGURE 1 Typical Raman spectra of blank surface-enhanced Raman spectroscopy surface (633-and 514-nm excitation) [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 2

 2 FIGURE 2 Comparison between experimental data and density functional theory (DFT) calculations [Colour figure can be viewed at wileyonlinelibrary.com]

FIGURE 3

 3 FIGURE 3Comparison between the Raman spectrum of the gold surface before and after high power laser illumination. Both spectra have been recorded in the same experimental conditions with the 633-nm excitation

FIGURE 4 TABLE 1

 41 FIGURE 4 Surface-enhanced Raman spectroscopy spectrum of a different gold surface

https://www.researchgate.net/post/What_is_the_peak_at_around_2100_ cm-1_on_a_clean_gold_surface_due_to

ACKNOWLEDGEMENT

The authors would like to thank Petra Hansen (Institute of Energy and Climate Research of Jülich, Germany) for complementary measurements.

ORCID

A. Merlen http://orcid.org/0000-0002-8453-299X