J Le Rouzic

P Delobelle
email: patrick.delobelle@univ-fcomte.fr

P Vairac

B Cretin

Comparison of three different scales techniques for the dynamic mechanical characterization of two polymers (PDMS and SU8)

Keywords: , 81-05, Lg: Polymers and plastics, 83, 60, Bc: Linear viscoelasticity

In this article the dynamic mechanical characterization of PDMS and SU8 resin using dynamic mechanical analysis, nanoindentation and the scanning microdeformation microscope have been presented. The methods are hereby explained, extended for viscoelastic behaviours, and their compatibility underlined. The storage and loss moduli of these polymers over a wide range of frequencies (from 0.01 Hz to some kHz) have been measured. These techniques are shown fairly matching and the two different viscoelastic behaviours of these two polymers have been exhibited. Indeed, PDMS shows moduli which still increase at 5 kHz whereas SU8 ones decrease much sooner. From a material point of view, the Havriliak and Negami model to estimate instantaneous, relaxed moduli and time constant of these materials has been identified.

-Introduction

.

. Yet, direct measurements at high frequencies are far less studied in the literature of materials.

In this paper, three techniques of dynamic mechanical characterization working at different scales have been used. A Dynamic Mechanical Analysis (DMA) is a technique working at macro scale by tensile tests. The Scanning Microdeformation Microscope (SMM) [12,13] is a type of AC-force microscope, a non destructive system which allows quantitative measurements of elastic properties at micro scale. At last, nanoindentation tests which can characterize materials at nano or micro scale and for quasi-static or dynamic loadings have been carried out.

We decided to characterize two polymers by measuring their complex Young's moduli for a wide range of frequencies to exhibit their viscoelastic properties. We chose two very different organic materials often used in MEMS applications, PDMS and SU8 resin.

PolyDiMethylSiloxane (PDMS) is a silicon-based elastomer. Mechanical properties of this very versatile material vary with preparation conditions. Young's moduli values can actually fluctuate in the range of 0.1 MPa to some tens of MPa depending on its preparation [14,15,16,17]. It exhibits an important viscoelastic behaviour. The other material we decided to characterize is a SU8 resin film. This resin is a polymer based on epoxies which is used for photolithography and MEMS applications and has a Young modulus in the range 3-6 GPa associated with a low viscoelastic behaviour [18].

Bulk samples have been designed to allow DMA measurements and to verify the compatibility of these techniques. To our knowledge such a comparison on viscoelastic materials has not been yet reported in the literature. This is the principal aim of this study performed on these two very different polymers. The material point of view will be briefly analyzed at the end of this paper.

-Materials and experimental procedures

Materials

Polydimethylsiloxane (PDMS) has become the most popular building material used in a variety of low-cost acqueous microfluidic devices aimed in particular at single use for biological or medical diagnostics. In order to have low power consumption, many groups use this material for the manufacture of mobile part (often membrane, bridge,…) in active systems such as microvalves and micropumps. Therefore the characterization of the dynamic mechanical properties of PDMS is of great interest. To realize the PDMS samples, the Sylgard 184 PDMS Kit manufactured by Dow Corning Corporation and composed by a prepolymer and a curing agent has been used. The samples were made by the same method. The prepolymer and curing agent in ratio 10:1 were mixed with an Ultra Turax homogenizer for 30s. The solution was poured into a Petri dish up to a thickness of about 3-4 mm and degassed in a desiccator by application of vacuum for 15 mn with a cycle of 2 mn at 0.5 m Torr. The solution was then cured in an oven at 65°C for 4 h following the recommendations from Dow Corning. PDMS was demolded and cut to make rectangular specimens. Different samples have been tested. Specimen 1 was tested thanks to the three different techniques for aging times t v of about 1500 hours and 11 000 h at constant temperature T ≈ 20-22° C in a closed Petri dish and without light exposure. Specimen 2 is a very old sample which has been aging for a long time (t v > 3 years) at room temperature (20 to 30 °C), without any particular precaution and whose preparation conditions are not exactly the same as those previously presented for specimen 1. Thus, these two PDMS samples must be considered as two different materials.

The SU8 resin is a negative epoxy type photoresit which has been developed by IBM (Watson Research Center). This polymer is a good material for MEMS applications. Two different samples have been tested. Specimen 1, tested with the three techniques, is a film of 0.13 mm thick obtained by spin-coating liquid SU8 resin (for 30 s at 5000 rpm/s) on a glass substrate.

Before the deposition a deshydratation base of 1 h at 200°C has been realized. The final step, after deposition, is a curing of 5 mn at 120 °C. The obtained film was removed from the glass substrate and then cut to make the different samples, one sample for each technique. Specimen 2 is a film of 50 µm thick deposited on <100> silicon substrate by spin-coating liquid resin (for 120 s at 500 rpm/s). A first soft-bake deshydration of 1 h at 50 °C followed by a hard-bake of 15 h at 90 °C have been performed. Due to the small thickness of these films, only nanoindentation and SMM procedures have been carried out.

Dynamic Mechanical Analysis (DMA)

DMA measures with frequencies in the range of 10 -2 -100 Hz were performed on a commercial BOSE Electroforce 3200 machine, at room temperature for the three different materials and at T = 23, 0, -20, -40, -60°C for the PDMS sample 1. Thus, for this specimen the time-temperature equivalence has been analyzed over a large domain of frequency; 10 -2 < f < 10 5 Hz.

For PDMS and SU8 resin (specimen 1) samples, gage lengths of the specimens were about 30 mm and 36 mm for a cross section of about 13 x 3-4 mm 2 and 10.2 x 0.13 mm 2 respectively. A control on the position with a peak to peak amplitude of 0.5 mm (corresponding to a strain of ± 7.6.10 -3 ) for a preload strain of 9.1.10 -3 was realized. Thus the samples were always in tension even at the low point of the cycles. According to the ASTM Standard Guide for Dynamic Testing the software calculates the phase angle φ between the imposed displacement and the measured force and uses the specimen shape to convert the stiffness and the phase information to provide the values of E', the storage modulus, E", the loss modulus and tan(φ), the tangent of the phase angle. Moreover, for the specimens 1 (PDMS and SU8), the evolution of E' and E" with the aging time t v has been studied between 3 to about 1300 hours.

2.3

The Scanning Microdeformation Microscope (SMM)

Presentation of the microscope

The SMM is a type of AC-force contact microscope. The sensor is a micromechanical resonator (Fig. 1) composed of a silicon cantilever with a small sharp sapphire tip at the end. The cantilever is glued onto a piezoelectric bimorph transducer at the other end. The transducer excites the vibration of the tip-sample system. The tip remains in contact with the sample and vibrates at some kHz with an amplitude of some nanometres. Amplitude and phase of the cantilever vibration are measured with a high sensitivity heterodyne interferometer [19,20]. The synoptic of the SMM is presented in Fig. 2.

The signal at the probe output is averaged with the double-phase lock-in amplifier and the amplitude and the phase of the cantilever displacement are recorded by the computer. Moreover, a modulated laser diode is used in a deflectometer to control the static force applied on the sample thanks to the second lock-in (and the third one can be used for a transmission mode operation). This microscope is an effective tool to record images of surfaces and subsurfaces with heterogeneous local elasticity or to characterize elastic properties of a material.

In the framework of this study, it has been used to measure Young's moduli. So we put the tip in contact with the sample and an additional static force is applied by vertically displacing the clamped end of the cantilever is applied. Then the excitation frequency is scanned. The resonant frequency depends on the static force applied via the contact stiffness. Actually, by measuring this resonant frequency, local contact stiffness can be estimated and then, with a well-suited model, the local Young's modulus is extracted. Other ultrasonic non-invasive methods like atomic force acoustic microscope (AFAM), ultrasonic force microscopy (UFM) or AFM spectroscopy with heterodyne interferometer can make such a characterization on the nanometre scale but with less accuracy because the contact model must take into account additional forces at this scale [1,2,3,7].

Model

A continuous model (Fig. 3) has been used [START_REF] Vairac | [END_REF][START_REF] Variac | Scanning Microdeformation Microscopy : Subsurface Imaging and Measurement of Elastic Constants at Mesoscopic Scale[END_REF] to obtain Young's moduli values of tested samples from the measured contact resonant frequencies. The cantilever is represented as a beam interacting with the sample through two springs ' N k and T k . The piezoelectric bimorph transducer action on the cantilever has been modelled as a simple mass m p and a spring k p . A Hertz contact has been considered to obtain the expression of the contact stiffness, ' N k :

' *2 / 3 1/ 3 N 0 k E (6 RF ) = (1)
However, for polymers, a dynamic Hertz contact is needed to consider the frequency dependence of the Young's modulus [START_REF] Mahaffy | [END_REF]23], thus :

* ' 1/ 3 1 N 0 *1/ 3 0 E k (6 RF ) E = (2)
Where

(E E ). ≈

To extract the Young's modulus value from the contact resonant frequency f 0 , the linear differential equation for the vibration of the beam with boundary conditions has been solved

[21] :

4 2 c 4 2 y y E I S 0 x t ∂ ∂ + ρ = ∂ ∂ (3)
, where E c is the Young's modulus, I the area moment of inertia, ρ the volume density and S the cross section of the cantilever.

In this study a simple spring-mass approximation has been introduced to take into account the damping and to determine the complex Young's modulus like Arinéro et al. [24] did for an AFM. First, the relation between f 0 and ' N k is obtained:

' N c 0 eff k k 1 f 2 m + = π (4)
where k c is the beam stiffness. The linear differential equation describing the response of an oscillator, with m eff the effective mass of cantilever and tip, x % the complex value of the response, ω 0 the cantilever-tip-sample system's resonance angular frequency and λ the damping coefficient is:

2 2 0 0 2 eff F x x 2 x exp(i t) t m t ∂ ∂ + λ + ω = ω ∂ ∂ % % % (5)
with:

0 x X exp(i t) exp(i ). = ω φ % So, 0 eff 0 2 2 0 F / m X exp(i ) ( ) 2i φ = ω -ω + ωλ (6)
Introducing the resonance frequency of the system f 0 and the 3 dB half-bandwidth f 1 , given by f 0 = ω 0 /2π and f 1 = λ/2π, the expression of the complex contact dynamic stiffness can be obtained: 7).

2 2 2 2 0 CCD eff 0 1 0 F k m (4 (f f ) 8i f f ) X exp(i ) = = π - + π φ (
By taking the imaginary part, and as f is close to f 0 , the " N k stiffness is obtained:

" 2 N eff 0 1 k 8m f f = π (8)
Introducing the complex effective Young modulus * x E :

* '* "* x E E iE = + (9)
and writing the expression of the complex stiffness as [START_REF] Haddad | Viscoelasticity of Engineering Materials[END_REF] :

' " N N N k k ik = + (10)
with a static Hertz contact :

" "*2 / 3 1/ 3 N 0 k E (6RF ) = (11),
and thanks to Eqs. ( 4), ( 8) and ( 11), the expression of E "* is given by:

' 3 / 2 "* N c 1 3 / 2 1/ 2 0 0 (2(k k )f ) E f (6RF ) + = (12)
This relation will be used for the SU8 resin as * * 1 0

E E ≈ .
For a dynamic contact:

"* " 1/ 3 1 N 0 *1/ 3 0 E k (6RF ) E = (13)
Thanks to Eqs. ( 4), ( 8) and ( 13), the following expression of "* 1 E has been obtained:

' *1/ 3 "* N c 1 0 1/ 3 0 0 2(k k )f E E f (6RF ) + = (14)
This relation will be used for the PDMS elastomer.

At last, it is interesting to note that the relations on the components of the complex Young's modulus determined with the hypothesis of static (st) (Eq. 1) or dynamic (dyn) (Eq. 2) Hertz contact are such that :

'* '* 2 / 3 *1/ 3 "* "* 2 / 3 *1/ 3 dyn st 0 dyn st 0 E (E ) E and E (E ) E = = (15)
.

It is thus possible to write:

1/ 3 * (i)* (i)* 0 st dyn (i)* st E E E (1 ) E         = α + -α           (16)
with (i) = ( ' or " ), α = 1 for a non viscous material and α = 0 for a viscoelastic material.

Experimental conditions

Two different cantilevers have been used for the characterization of these two materials. Thanks to a previous study on the sensitivity of the SMM [23], we chose 2 different cantilevers which are optmized for PDMS and SU8 resin. Actually, we showed that the cantilever stiffness must be chosen close to the contact stiffness to have the best sensitivity. As cantilever stiffness depends on the inverse of the cube of the length, a length of 7 mm for PDMS and 4.5 mm for the SU8 which is harder have been chosen. The width and the thickness of the beam are 400 µm and 150 µm respectively. The tip has a cylindrical base and a conical end as shown in Fig. 1.

The sharp end of the tip is spherical. For the beam with a length of 7 mm, the tip length l is 697 µm, its mass m = 0.23 µg and its curvature radius R = 45 µm. For the one with a length of 4.5 mm, l = 976 µm, m = 0.45 µg and R = 20 µm. The static applied force F 0 was 0.15 mN for the PDMS and 0.5 mN for the SU8 resin. The frequency domain of the SMM with these cantilevers corresponds to some kHz. As an example, Fig. 4 gives the first resonance mode of the two PDMS samples (specimens 1 and 2). On each sample about 5 to 7 measurements have been performed and the final result is the mean of the values. The shift frequency difference between these two specimens, due to their different modulus, is about 350 Hz. Note that the SMM has already been tested on standard hard materials like silicon and silica [START_REF] Vairac | [END_REF][START_REF] Variac | Scanning Microdeformation Microscopy : Subsurface Imaging and Measurement of Elastic Constants at Mesoscopic Scale[END_REF][START_REF] Vairac | [END_REF] and a precision of nearly 5 % have been determined with the used model.

With these experimental conditions the polymers are loaded in their linear viscoelastic regime.

Actually, PDMS remains linear until deformations of 60 % [17] and 5 % for SU8 resin [18]. For a spherical tip like SMM ones, deformation of the contact area is ε = 0.2a/R [START_REF]Tabor D The hardness of metals[END_REF], where a is the contact area radius and R the tip radius. With the tips we have used, a < 5 µm and R > 20 µm, thus ε < 5 %.

Nanoindentation tests

Model

The Berkovich's indentations were performed with a Nanoindenter II S (NanoInstruments). The hardness H b and the Young's modulus E * are deduced using the classical static procedure or the continuous stiffness method (CSM) described as follows. One of the most commonly used methods for analysing nanoindentation data is the Oliver and Pharr one [8], which expands on earlier ideas developed by Loubet et al. [START_REF] Loubet | [END_REF] and Doerner and Nix [29]. This analysis has often been applied to polymer characterization, for example [18], [30] and [31], even if the true contact area is underestimated due to the pushing up of the material around the indenter. In this case the Young's modulus is slightly overestimated. However, in our method described below the Young's modulus has been estimated for an indentation depth close to zero (Eq. ( 32)) and thus the pile up effect may be considered as negligible.

In the Oliver and Pharr method, the hardness H b and the reduced modulus E * are derived from :

max b F H A = (17) and 2 2 * s i s * s i unloading 1 1 dF 2 1 S E A with dh E E E -ν -ν η   = = = +   π   (18)
In these equations, F max is the maximum indentation load, A the projected area of the elastic contact, S s the unloading stiffness measured at different maximum depths of penetration h for the classical method (quasi-static method), or continuously with the CSM technique (at a frequency f = 45 Hz). η = 1.034 for a Berkovich's tip. E s and ν s are the Young's modulus and the Poisson's ratio of the specimen and E i , ν i the same parameters for the indenter. The expression of the projected contact area A for a Berkovich indenter is given by the following formula:

4 2 1/ n c c n c n 1 A(h ) 24.56 h (a h ) = = + Σ (19)
The second term in Eq. ( 19), evaluated using fused silica as a reference material, takes into account the geometrical deviations due to the tip rounding. Presently, this term is negligible due to the large penetration depths. The displacement h c is given by:

max c s F h h S = -ε (20)
in the case of the classical method. S s is calculated by analytical differentiating of the experimental unloading curve:

m f F D(h h ) = - (21)
and evaluating the derivative at the peak load F max . h f is the remanent penetration depth and m ≈ 2 for a Berkovich indenter. For the CSM method, the displacement h c is given by:

c s F h h S = -ε (22)
where S s and F are the unloading stiffness and the force recorded along the displacement of the indenter, respectively. So, with this method, hardness and Young's modulus can be determined as a function of the penetration depth h. In ( 20) and ( 22), ε = 0.72 which corresponds to a conical indenter. In the CSM method a small harmonic load oscillation is superimposed to the static one and if the tested material presents a viscoelastic character it is then possible to deduce its complex modulus [32]. If the dynamic loading is given by:

0 F F exp(i t) = ω (23)
the deformation response of the material is :

0 h h exp(i t) exp(i ) ∆ = ∆ ω φ ( 24
)
where φ is the phase lag due to viscous dissipation, as in Eqs. ( 5) and ( 6) for the SMM technique. The components of the complex modulus E * can be calculated according to:

'* d E S cos( ) 2 A π = φ η ( 25
) "* d E S sin( ) 2 A π = φ η (26)
with S d = F 0 /∆h 0 and thus tan(φ) = E "* /E '* .

In the present case, for polymer application, E i >> E s (Eq. 18) and then, *

2 s s E E /(1 ) = -ν as in
SMM experiments. Now, if S i , S f and S s are the stiffness of the indentation cell, of the load frame and of the sample respectively, the total stiffness S 0 is :

1 0 i s f 1 1 S S S S -   = + +     (27)
In our case S f >> S s , then:

0 s i S S S = + (28)
Combining Eqs. ( 18) and ( 19), we obtain :

η = = = π -ν (29).
This relation supposes that the surface of the sample is precisely detected without initial penetration (S s >> S i ≈ 44 N/m). This is the case for metallic materials and hard polymers such as the SU8 resin. However, with PDMS, S s < S i and thus when the contact is detected the indenter has penetrated into the sample. In this study we determined the contact with the sample for different fixed stiffnesses S 0 , such that S 0 > S i > S s , that is to say for a certain penetration depth h 0 function of S 0 . In this case, the measured Young's modulus E mes is given by:

s mes mes S E 2µh = ( 30
)
where h mes is the measured indentation depth penetration.

Due to the quasi-elastic indentation response of the PDMS samples, h f ≈ 0 and m = 2 in Eq. ( 21), and thanks to the relations ( 19) and ( 20), it's easily shown that:

c i i h h with 1 = α α < (31)
Note that the coefficient α i is not the same in quasi-static or dynamic methods. As the measured indentation depth for a given contact stiffness S 0 is h mes = h -h 0 , combining Eqs. ( 29), ( 30) and (31) the relation ( 32) is obtained:

0 0 mes s s mes h (S ) E E E h = + (32)
Thus the representation E mes = f(1/h mes )s 0 must be linear ; the intersection with the Y axis gives the value of the true Young's modulus E s and the slope of the straight line allows to determine E s h 0 (S 0 ) which is an increasing function of the initial stiffness S 0 .

In fact, when h mes >> h 0 , E mes = E s . Thanks to these representations the E s values for quasi-static condition or for dynamic loading (f = 45 Hz) can be determined.

In the CSM technique the loss tangent is defined as:

0 2 0 E" tan( ) E ' S m λ ω φ = = -ω (33)
where S 0 is given by the relation [START_REF] Loubet | [END_REF] at the considered frequency, λ 0 is the sum of the damping coefficient of the apparatus and the one of the contact, m is the mass of the moving part of the indenter. The measured tan(φ) is false as λ 0 and S 0 are functions of the initial indentation depth h 0 . The true value of the loss tangent corresponds to those at h = h 0 + h mes = 0. Plotting the measured values of tan(φ) as a function of (h 0 + h mes ), the intersection with the Y axis should give the true value of this parameter. The initial depth penetration h 0 can be calculated from the experimental representation of Eq. ( 32); the slope gives the product h 0 E s and knowing E s previously determined, we calculate the h 0 value. This way will be used to determine the tan(φ) value of the PDMS samples and thus the loss modulus E" (Eq. ( 33)). For the SU8 resin, the contact is precisely detected, thus h 0 = 0 and the tan(φ) value given by the standard procedure is considered as accurate.

Experimental conditions

Nanoindentation tests were performed using a Nanoindenter II S . As previously mentioned the study was conducted following the classical (quasi-static) and CSM (dynamic at f = 45 Hz) procedures. For each tested sample and for each initial stiffness S 0 , the measurement sequence consists on 5 indents with a 50 µm space between them with a maximum penetration depth of h max ≅ 4 µm. The penetration speed was not constant but increased with depth from 2 to 45 nm.s -1 with 8 steps such that

(1/ h)(dh / dt) ε = &
is approximately constant and equal to 2.10 -2 s -1 .

The stiffness of the indentation cell S i is 44 N/m and the values of the imposed initial stiffness are in the range 53 < S 0 < 94 N/m. For the quasi-static method, four unloadings (to 90 % of the total loading) were performed at about h max ≈ 1, 2, 3 and 4 µm and 50 % of the unloading curves are considered to calculate the contact stiffness of the samples S S as previously presented. For the CSM procedure, the indenter vibrates at a frequency of 45 Hz for an amplitude of 1-2 nm during the indenter penetration 2 1

( 2.10 s )

-- ε ≈ & .
As an example, Fig. 5 shows, for the PDMS sample 1, the evolution of the measured Young's modulus E mes obtained with the two methods as a function of the measured indentation depth h mes and for different values of S 0 . As expected by Eq. ( 32), E mes decreases with h mes . According to Eq. ( 32), Fig. 6 gives the representations of E mes as a function of 1/h mes , for the same conditions as those presented in Fig. 5. These representations are linear and lead to determine E st = 1.7 MPa, E dyn = 2.6 MPa for the classical and CSM methods respectively. Note that, for the same value of S 0 , the slopes of these representations are different, depending on the performed method. Indeed, this is due to the different value of α i in Eq. ( 31) for quasi-static or dynamic loadings. Thanks to Eq. ( 32) and knowing E s we can evaluate the indentation depth h 0 corresponding to the initial stiffness S 0 . For instance, in the case of the sample 1, if (S 0 -S i ) ≈ 25 N/m, h 0 ≈ 4 µm.

In the case of the SU8 films the maximum penetration depth has been fixed at h max =3 µm and the contact between the surface of the sample and the indenter tip is easily detectable. Thus, the measured values of the Young's modulus and of the hardness are constant overall the indentation depth.

-Experimental results

The three techniques work at different scales and at different frequencies. As previously shown, they enable us to check the viscoelastic properties of these polymers. Actually, storage and loss moduli of polymers change depending on the frequency. We recorded the measures of E' and E"

for the two specimens of PDMS and for the two SU8 resin films.

Case of the PDMS samples

We took ν = 0.48 for the Poisson's ratio of the PDMS (hyperelastic material). The values of E' for the two PDMS samples are plotted in Fig. 7 as a function of the working frequency and for the three experimental techniques. Note that for the SMM value, f is the first contact resonance frequency equal to 4,18 KHz. The measures given by the DMA and the nanoindentation methods are in a fairly good agreement. The SMM ones even if it is two decades further show a possible continuity. Static moduli * 0 E for the two samples are respectively 1.7 and 2.9 MPa. As it will be shown, this difference is principally due to the different preparation conditions and weakly to the aging time. Storage modulus increases with the frequency for the two samples, which is typical of a viscoelastic material. For these two materials the values given by the SMM at nearly 4 kHz are 3.4 and 5.5 MPa (Fig. 7). In the Fig. 8 the loss modulus is plotted as the function of the working frequency. At 0.01 Hz the values are very low, near zero, but sharply increase with the working frequency. Results between DMA and SMM show the same behaviour for E" than for E'. Typically, for polymers, E" increases before reaching a maximum and then decreases with the working frequency. The SMM values of E" at 4 kHz for the two specimens are about 1 and 1.6 MPa.

E' and E" are of the same order of magnitude which means that for this range of frequencies the material is very viscoelastic. This behaviour is quantified by the parameter tan(φ) = E"/E' as shown in Fig. 9. The values estimated with the CSM nanoindentation procedure are in good agreement with those obtained by the DMA analysis. The SMM values also show a possible continuity. The tan(φ) parameter is an increasing function of the frequency, as expected, and the SMM values are close to 0.28 for f ≈ 4 kHz. It should then decrease for higher frequencies, the maximum value should be obtained at a frequency of about 10 6 Hz. From a material point of view, it is interesting to note that the values of the tan(φ) parameter are the same for the two tested specimens, indicating that this parameter seems insensitive to the elaboration conditions and the aging time as it will be shown later.

To

( ) ( ) (i) 0 (i) (i) (i) (i) 1 o T / T T / T (i) o o 0 2 C (T T ) E (T, f ) E T , a f with Ln a and (i) (' or ") C T T - - = = = + - ( 34
)
In the representations drawn in Figs. 11 and12, the reference temperature is T = 23°C and the values of the parameters (i)

(i) 1 2
C and C ( C) ° are equally reported in these figures. E' and E" continuously increase with the equivalent frequency (10 -2 < f < 10 5 Hz) from 2 to 7.5 MPa and 0.02 to 1.6 MPa respectively. Figure 13 gives the evolution of the parameter tan(φ) = E"/E' as a function of the equivalent frequency.

New nanoindentation and SMM tests have been performed on this aged specimen (t v = 11 000 h) and the results are plotted in Fig. 11, 12, 13. As for the previous results (Figs . 7, 8, 9), nanoindentation measures (quasi-static and dynamic) perfectly match those given by the DMA. an increasing of 14 % on the values of the Young's modulus components when t v increases from 1460 h to 11 000 h (Fig. 10), the values of the previous measurements (f 0 = 4,16 KHz) have also been reported in these figures. They are in the neighbourhood of the master curves.

From a material point of view, it is interesting to note that the values of the tan(φ) parameter obtained with these three different techniques on the two specimens are identical, thus insensitive to the aging time and the elaboration conditions. The values measured with the SMM technique (tan(φ) ≅ 0.27) are slightly higher than those evaluated with the DMA timetemperature equivalence, tan(φ) ≅ 0.21, for the same frequency domain. Indeed, the E" values are slightly overestimated with the SMM method. This observation tends to show that, if g(t ,

ElC) is a function of the aging time t ν and the elaboration conditions ElC, the complex modulus should be given by :

* '* "* E g(t , ElC)(E iE ) ν = + (35)
As a conclusion, our measures given by the three different techniques working at different scales lead to characterize the PDMS material over a wide range of frequencies (10 -2 -10 4 Hz), but with a certain discrepancy due to the difference in the working frequency of these three methods. However, the measures show the compatibility and the complementary of these characterization systems. We quantitatively saw the evolution of storage and loss moduli of these bulk PDMS samples. Indeed, the measured values are in a fairly good agreement with the results reported by Mata et al. [15], Roure et al. [16] and Schneider et al. [17], ie : E' = 1.9 MPa without climate test and for quasi-static measurements.

Case of the SU8 resin

The same measures on the SU8 resin film have been carried out. For this material we took a

Poisson's ratio of ν = 0.29. For the two specimens the evolution of the storage modulus E' with the frequency has been plotted in Fig. 14. This time, the three techniques do not perfectly match.

Actually for sample 1, at 0.01 Hz the DMA value is about 2.9 GPa (2 different measures)

whereas the nanoindentation value is about 4.5 GPa. Moreover, for these two techniques the storage modulus slightly increases with the frequency in the studied range. The SMM value at 23 kHz (first resonance frequency) confirms the indentation modulus values with a nearly equal value of 4.2 GPa. As previously mentioned, the value of the order of 4.5 GPa is in agreement with the results given in the overall literature E' ≈ 4 to 6 GPa. The low values obtained by DMA technique are certainly due to the too small thickness of the tested specimen (0.13 mm) and the small preload strain (≈ 9.10 -3 ) allowing to a certain inhomogeneity in the strain field across the specimen section. The artefacts due to the instrument compliance effects observed on rigid specimens are also not neglectible. So in the typical curve of the storage modulus of a polymer, the maximum of slope has already been passed and the modulus is quite constant. The same evolution can be expected for the loss modulus in this range of frequencies. In Fig. 15 a loss modulus which decreases with the frequency can be observed. The nanoindentation value is a slightly greater than the DMA one. The SMM value at 23 kHz is lower and confirms the global decreasing of the loss modulus. It can be noted that the loss modulus if far lower than the storage one (20-80 MPa versus 4-4.5 GPa). Thus, the SU8 resin presents a very weak viscoelastic behaviour, far less than the PDMS one.

The tan(φ) has also been plotted in Fig. 16. The maximum has been passed (f ≅ 10 -2 Hz) and this parameter decreases with the frequency. Of course, the values are much lower than for the PDMS and the maximum value is close to 0.025. It is important to observe that the three techniques perfectly match. DMA and nanoindentation values are the same at 45 Hz and the SMM value prolongs the decrease of the curve. In fact with DMA technique, the error due to the small thickness of the film (or other causes) has the same effect on the determination of E' and E" and disappears on the loss tangent which is equal to the ratio E"/E'.

Nanoindention and SMM measurements have been performed on the same sample (specimen 1)

but for an aging time at room temperature of about 13000 h. Contrary to the PDMS samples, no noticeable evolution outside of the method accuracies has been pointed out.

For the SU8 film deposited on the Si substrate (specimen 2), the nanoindentation and the SMM techniques perfectly match (Fig. 14) and the determined values of the storage modulus are 5.57 ± 0.15 GPa and 5.6 ± 0.3 GPa, respectively. These values are higher than those measured on specimen 1, but close to those reported by Al-Halhouli et al. [18], i.

-Phenomenological modeling

From a material point of view and for viscoelastic materials as polymers, the crucial problem in vibration experiments concerns the accurate determination of the viscoelastic parameters over a broad range of frequency. So, in the case of sinusoidal deformation, the complex modulus can be written as [START_REF] Cunat | [END_REF] :

n n * i r i j j j 1 j 1 j 1 E E (E E ) p with p 1 1 i = = = + - = ∑ ∑ + ωτ (36)
where E i and E r are the instantaneous and relaxed Young's moduli, respectively. The parameters τ j are the different relaxation times and p j is a ponderation coefficient for each relaxation time. It is very difficult to determine the values of the parameters p , τ j and their number n. From a phenomenological point of view, to overcome this difficulty the empirical model of Havriliak and Negami [35] (H-N model) is considered, which combines the advantages of the modelling of Cole et al. [36] and Davidson et al. [37]. In this model, the complex modulus is given by:

* i r i 1 E E (E E ) (1 (i ) ) α β = + - + ωτ (37)
Thus, storage and loss moduli are respectively given by:

( ) i r i / 2 2 cos( ) E ' E (E E ) 1 2
α - α   ωτ απ φ =     + ωτ απ   ( 40
)
where τ is a single parameter with time dimension and α, β two empirical parameters.

Note that if α = β = 1, the equation ( 37 38), ( 39), ( 40) and the results drawn on these figures. The identified values of the parameters are listed in Table 1. Note that these values correspond to the working range of frequencies and cannot be used for very higher frequencies.

The simulations are fairly good especially considering on the one hand the three different experimental techniques that have been used and on the other hand the wide range of frequency which has been analysed. Notice the very great difference between the time parameter of the PDMS and the SU8 resin's one; the PDMS is very viscous (tan(φ) ≈ 0.21 at f = 10 4 Hz) contrary to the SU8 resin (tan(φ) ≈ 0.005 at f = 10 4 Hz for sample 1). The same trend is observed on the ratio between the instantaneous and the relaxed moduli, E i /E r : E i /E r ≈ 17 for the PDMS and only ≈1.12-1.25 for the SU8 resin. Note that from an experimental point of view, the timetemperature equivalence experiments performed on PDMS samples with E r = 2 MPa give E(f)/E r ≅ 7.5 at f = 10 7 Hz (this study) and from [38] with E r ≈ 50 MPa give E(f)/E r ≈ 10 at f = 10 11 Hz. These results corroborate the value E i /E r ≈ 17 presently determined for f → ∞.

-Conclusion

  compare in a more quantitative manner the results obtained by the DMA and the SMM techniques, DMA experiments at low temperatures (T = 0, -20, -40, -60°C) on specimen 1 have been carried out. The frequency range is 0.01 to 50 Hz and thus, thanks to the time-temperature equivalence, a large domain of frequency can be analyzed; 10 -2 < f(Hz) < 10 7 . However, for the specimen 1, between the first experiments previously presented (Figs.7, 8, 9) for a relatively short aging time (t v = 1460 h) and these new measures (t v = 11 000 h, Figs. 11-12-13), the material has evolved over a very long time at room temperature. The effect of aging time has been analyzed thanks to the DMA technique and figure10shows the increasing of the normalized storage modulus E(t v )/E'(4h) (E'/(t v ) measured at an aging time t v over the modulus measured just after the elaboration of the material, E'(4h)) as a function of the aging time t v and for three frequencies. So, between these two experiments, the storage modulus (and also the loss modulus) has grown of about 14 %. The William-Landel and Ferry model has been applied to calculate the storage and loss moduli master curves as shown in Figs.11 and 12respectively. In this model, for a fixed reference temperature T o , the translation parameter T / T o a of the frequencies, is given by:

ForE = 2

 2 the SMM experiments, a new cantilever whose characteristics are: length 6,5 mm, width 400 µm, thickness 80 µm, l = 697 µm, m = 0.44 µg and R = 45 µm, has been used. The first resonance mode with an applied static force of 0.15 mN is f o = 2,65 KHz, which corresponds to E' = 4.39 MPa ( * o MPa in Eqs. (2) or (15)). The value of the lost modulus determined from the half-bandwidth f 1 of the resonance peak is E" = 1,19 MPa, thus tan(φ) = 0.27. These different values are plotted in Figures 11, 12, 13 and are in a fairly good agreement with the time-temperature equivalent curves. Taking into account the aging of the specimen, resulting in

  e.: 5.2 GPa. The values of the loss modulus and the tangent of the phase lag are plotted in Figs. 15 and 16. As for the specimen 1 these two parameters decrease with the frequency, but the values are slightly lower than those determined on the previous sample, i.e.: E '' = 40 MPa (at 45 Hz) and E '' = 8.4 MPa (at 13 KHz) for the nanoindentation and the SMM procedures, respectively. These observations, increasing of E' and decreasing of E'' compared to the values obtained on sample 1, are certainly due to the long bake during 15 h at 90 °C performed on this specimen. Note that the Berkovich hardnesses H b of these different polymers are about, H b = 0.33 ± 0.05 MPa and 0.55 ± MPa for the two PDMS samples (specimens 1 and 2 respectively) and H b = 330± 20 MPa and H b =362± 13 MPa for the two SU8 films (specimens 1 and 2). This last value is in fairly good agreement with the one given by Al-Halhouli et al.[18] (H b ≈ 430 MPa).

  ) with a single relaxation time is obtained. The different experimental curves of Figs. 11, 12 and 13 for the PDMS and Figs. 14, 15 and 16 for the SU8 resin have been fitted by equations (

Fig. 1 :Fig. 2 :

 12 Fig. 1 : Vibrating sensor of the SMM. Fig. 2 : Principle of the SMM microscope.

Fig. 3 :

 3 Fig. 3 : Model to describe the behaviour of the SMM.

Fig. 4 :Fig. 5 :

 45 Fig. 4 : Experimental spectra of amplitude of vibration (1 st mode) as a function of frequency in contact with the two different PDMS samples for a static force of 150 µN and for a driving voltage of the bimorph of 1V. Fig. 5 : Evolution of the measured indentation modulus E mes as a function of the measured depth penetration h mes for PDMS sample 1 (t v = 1460 hours) and different contact stiffness S 0 . The results are obtained with quasi-static and CSM methods.

Fig. 6 :

 6 Fig.6: Determination of E st (static measurement) and E dyn (dynamic measurement) according to Eq. (32) : E mes as a function of 1/h mes .

Fig. 7 :Fig. 8 :

 78 Fig. 7 : Storage modulus of PDMS samples measured by nanoindentation, DMA and SMM techniques as a function of the working frequency. Simulation with the H-N model.Fig. 8 : Loss modulus of PDMS samples measured by nanoindentation, DMA and SMM techniques as a function of the working frequency. Simulation with the H-N model.

Fig. 9 :Fig. 10 :

 910 Fig. 9 : tan(φ) parameter of PDMS samples determined by the three different techniques. Simulation with the H-N model.Fig. 10 : Evolution of the storage modulus of sample 1(E'(t v )/E'(4h)) as a function of the aging time t v .

Fig. 11 :Fig. 12 :

 1112 Fig. 11 : Storage modulus of PDMS sample 1 (t v = 11 000 h) measured by nanoindentation, DMA time-temperature equivalence and SMM techniques as a function of the working frequency. Simulation with the H-N model.Fig. 12 : Loss modulus of PDMS sample 1 (t v = 11 000 h) measured by nanoindentation, DMA time-temperature equivalence and SMM techniques as a function of the working frequency. Simulation with the H-N model.

Fig. 13 :

 13 Fig. 13 : tan(φ) parameter of the PDMS sample. Simulation with the H-N model.

Fig. 14 :

 14 Fig. 14 : Storage modulus of SU8 resin samples measured with the three techniques as a function of the working frequency. Simulations with the H-N model.

Fig. 15 :

 15 Fig. 15 : Loss modulus of SU8 resin samples measured with the three techniques as a function of the working frequency. Simulations with the H-N model.

Fig. 16 :

 16 Fig.16: tan(φ) parameter of the two SU8 resin samples determined by the three techniques.Simulations with the H-N model.

Fig: 1 Fig: 2 Fig: 3 Fig: 4 0Fig: 16

 123416 Fig:1

Table 1

 1

		: Parameters values of equation (38) (39) and (40)
	Specimen	t ν	α	β	τ(s) E r (MPa) E i (MPa)	F(Hz)
	PDMS (Spec. 1)	1460 h	0.236	1	2 10 -9	1.65	29.6	10 -2 -10 6
	PDMS (Spec. 1)	11 000 h	0.236	1	2.10 -9	1.9	34	10 -2 -10 6
	PDMS (Spec. 2)	>25000 h 0.236	1	2.10 -9	2.6	44	10 -2 -10 6
	SU8 (Spec. 1)	~ 1000 h	0.4	0.38	40	3600	4500	10 -2 -10 5
		~14000h
	SU8 (Spec. 2)	~1000 h	0.4	1	0.5	5000	5600	10-10 5

Acknowledgments

The authors thank the city of Besançon for supporting this project. The authors acknowledge V.

Placet for his assistance for the DMA experiments.

In this article the efficiency of the three mechanical characterization methods has been pointed out. The results of the three different scales techniques (macro, micro and nanoscale) fairly match. The two very different viscoelastic behaviours of PDMS and SU8 resin for the same frequency range have been quantified. Their storage, loss moduli and tan(φ) from 0.01 Hz to some kHz have been measured. Satisfying global behaviours according to the models and good agreement between measured values and literature ones have been obtained. In conclusion, these three complementary experimental techniques and the developed methods can be used as powerful metrology tools for the mechanical characterization at very small scale of viscoelastic materials. To our knowledge, such a comparison of these three experimental methods applied on viscoelastic materials has not been reported in the literature and highlights the potentialities of these techniques for polymer applications.

Note that as multiple modes were measurable by SMM method (4 modes detected on the SU8 resin), we started to develop a suitable identification procedure to recover both the Young's modulus at different frequencies and the Poisson ratio from SMM measurements.


Lucy A Parker
email: lparker@umh.es

Blanca Lumbreras

Ildefonso Hernández-Aguado

Health information and advocacy for 'Health in All Policies': A research agenda

Keywords: Population health, policies, advocacy

Placing health in the agendas of all policy-makers remains a challenge. Finding new ways to boost Health in All Policies (HiAP) should be a continuous process. Currently, health information initiatives gather core health statistics, indicators related to health care, along with individual level risk factors such as smoking or obesity. However, there is a lack of identifiable information showing the effect of non primary health policies on population health. We propose a research agenda focused in three related areas that would frame health information in such a way that the implications for decision makers from non-health sectors are clear: a) research in order to provide solid and quantitative evidence linking the social and environmental determinants of health with their ultimate health outcomes; b) research that shows and quantifies the effect of policies and specific interventions on these determinants; and, c) the development of policy linked indicators which provide a quantitative estimate of the health that would be gained (or disease burden that could be avoided) by adoption of a specific policy.

Introduction

It is well recognised that relevant factors which ultimately contribute to health lie out with the domain of the health service. Nevertheless, encouraging non-health sectors to accept responsibility for health and be aware of the health consequences of their actions has proven to be challenging. Recognising health effects of non-health policies may prove useful not only in avoiding the adoption of detrimental policies but in advocating for the adoption of certain policies. Consider, for example, a policy aimed at reducing traffic congestion, and the ancillary health benefits linked to the reduction in air pollution, [START_REF] Bell | Ancillary health benefits of improved air quality resulting from climate change mitigation[END_REF] or through encouraging active commuting to school [START_REF] Davison | Children´s active commuting to school: current knowledge and future directions[END_REF] or the workplace. [START_REF] Hamer | Active commuting and cardiovascular risk: A meta-analytic review[END_REF] 'Healthy public policies' were originally called for in the 1986 Ottawa Charter for Health Promotion, [4] and these concerns were revisited in the 2006 Health in All Policies (HiAP) [START_REF] Ståhl | Health in All Policies, prospects and potentials[END_REF] proposal from the European Union Finnish presidency. In 20 years of experience, there have been several attempts to promote the interconnection between health and other spheres of society, among the most successful the healthy cities movement. [START_REF]Healthy Cities around the world: an overview of the Healthy Cities movement in the six WHO regions[END_REF] Nevertheless the extent to which health concerns are currently integrated into non-health policies is far from complete and finding new and innovative ways to promote HiAP should be a continuous process.

We propose here that among the barriers to progress is the shortage of indicators which clearly illustrate the connection between key health problems and non-health sectors. Health information should be framed in a way that the policy implications are clear and the parties that should be held accountable are identified. We acknowledge that there is a vast myriad of competing interests which actually influence policy decisions, and that these political determinants of policy evaluation may play an important role in identifying what constitutes a policy consequence and in defining accountability. Furthermore, the link between scientific evidence and the development of public health policies is complex, as has been considered from diverse points of view. [START_REF] Briss | Science and public health policy makers[END_REF][START_REF] Davis | Translating research findings into health policy[END_REF][START_REF] Nutmeam | What influences the transfer of research into health policy and practice? Observations from England and Australia[END_REF][START_REF] Petticrew | Evidence for public health policy on inequalities: 1: the reality according to policymakers[END_REF] Its analysis, however, is beyond the scope of this paper which focuses in exploring what information would be useful in the process of shaping non-health policies that are relevant to health, and how best to provide this information to policy makers and the public at large. We discuss the potential for more policy-relevant health indicators, which, as tools for advocacy, could help to bring health considerations into the aims and priorities of policy makers from all sectors.

Currently, there is a great wealth of health statistics available and the actors involved in their collection are wide ranging. These include inter-governmental agencies such as the WHO, OECD or UNICEF; national governments in their annual health reports, and public or private agencies reporting specific indicators of interest, at regional, national or local level.

Furthermore, the academic field of health metrics is increasingly playing a more important role. [START_REF] Horton | A new initiative for health monitoring, tracking and evaluation[END_REF] With this myriad of efforts, we hold that data is not scarce but that a gap exists between the information on hand and the data framed and delivered to policy-makers. In what may be referred to as the information age, it is not uncommon for important health statistics to become lost in the competition for limited information space.

Here, we present a proposal of where research efforts might best be focussed: a) research in order to provide solid and quantitative evidence linking the social and environmental determinants of health with their ultimate health outcomes; b) research that shows and quantifies the effect of policies and specific interventions on these determinants; and, c) the development of policy linked indicators which provide a quantitative estimate of health that would be gained (or disease burden that could be avoided) by adoption of a specific policy. The objective is to frame health information in a way that is applicable to the context of non-health policy-makers, and can be used as a tool for advocating health considerations in all policies.

The proposed agenda is directed at, but not limited to, researchers and funding agencies in an effort to stimulate the production of this type of information. In addition, it is intended Currently most health information initiatives are heavily focussed on core health statistics (such as life expectancy or morbidity statistics), indicators of health care provision and health systems accessibility, along with individual level risk factors such as alcohol or tobacco consumption or body weight. [START_REF] Hernández-Aguado | Intelligence for health governance: Innovation in the monitoring of health and well-being[END_REF] There is no doubt that core health statistics are essential, but the absence or scarcity of information on distal or medial health determinants in current proposals of sets of indicators will jeopardise the evaluation of policies that address social and environmental determinants of health.

Most current health indicators are difficult to link to any specific policies and for some health indicators it may take years for any discernable changes to occur after policy implementation.

Measuring the social or environmental determinants of health may be more appropriate to monitor non-health policies because they are more sensitive to change in short to medium term.

For example, planting trees or increasing city green zones may have various health related benefits, such as reducing childhood asthma, [START_REF] Lovasi | Children living in areas with more street trees have lower prevalence of asthma[END_REF] improving mental health [START_REF] Sugiyama | Associations of neighbourhood greenness with physical and mental health: do walking, social coherence and local social interaction explain the relationships?[END_REF] or those secondary effects brought on by increasing exercise among the population. [START_REF] Kaczynski | Environmental correlates of physical activity: a review of evidence about parks and recreation[END_REF] Reiterating these potential health benefits and indicating the proportion of the population living in tree dense areas may be a more appealing approach to encourage city planners to act on behalf of the health of the population. Notably there are some initiatives which incorporate advances in population health research and consider diverse health determinants. The Swedish Public Health Policy has among its objectives ensuring 'participation and influence in society'. [START_REF] Agren | Sweden's new public health policy. National public health objectives for Sweden[END_REF] Indicators chosen to monitor this objective include employment, gender inequality and turn-out in municipal elections, [START_REF] Lundgren | Indicators for Monitoring the New Swedish Public Health Policy[END_REF] all of which involve actors from outside the health sector.

In order to encourage such initiatives, it is necessary to gather solid, quantitative information linking the social and environmental determinants of health with their ultimate health outcomes and illustrate how these determinants can be affected by policies or interventions. The regular reporting of key determinants as indicators of public health should fuel a healthy and dynamic debate about social and environmental issues and help raise public health in the agenda of policy-makers from all sectors.

Avoidable burden of disease by policy

We also suggest an innovative approach to reframe health information in a way that makes it useful for policy makers. The launch of the Global Burden of Disease project [START_REF] Ezzati | Selected major risk factors and global and regional burden of disease[END_REF][START_REF] Lopez | Global and regional burden of disease and risk factors, 2001: systematic analysis of population health data[END_REF] saw a major advance in population attributable risk revealing that a large proportion of global health can be attributed to a relatively small number of factors. Although a major innovation in the identification of important health risks, the information provided is limited because it provides no insight into the processes involved in reducing the identified risks. Moreover, the initiative is predominantly focused on individual risk factors and so far distal determinants of population health, including policies, are omitted.

We propose that current models of comparative risk assessment should be expanded and linked to policies, to estimate the disease burden that could be avoided by adoption of a certain policy ('avoidable burden of disease by policy'). [START_REF] Hernández-Aguado | Intelligence for health governance: Innovation in the monitoring of health and well-being[END_REF] Similarly, HIA could be applied in a more proactive way, not only in the appraisal of potential policies, but from researchers and public health professionals to assess the health consequences of inaction or omitted policies. [START_REF] Kreiger | Assessing health impact assessment: multidisciplinary and international perspectives[END_REF] The final statement of this type of HIA could be transformed into indicators of 'avoidable burden of disease by policy', presenting a variety of outcomes, such as deaths, hospital intakes, disease cases, that could be averted by a particular policy action.

Development of indicators linked to policy is grounded on the availability of information provided by research on health determinants as previously proposed. For instance, we need information of the quantitative effect that a specific traffic policy has on pollution and the precise effect that these changes in pollution levels have on mortality and morbidity. Only then we can develop an indicator of health gain through policy or burden avoided by policy. For example an HIA carried out to assess the public health benefits of reducing air pollution in the Barcelona metropolitan area found reducing current levels of air pollution to the WHO standards would result in approximately 3,500 fewer deaths annually. [START_REF] Künzli | The Public Health Benefits from Reducing Air Pollution in the Barcelona Metropolitan Area. Barcelona: Centre recerca en epidemiologia ambiental[END_REF] By linking this with a specific policy aimed to reduce air pollution it would be possible to estimate the number of deaths avoided annually by the implementation of the policy. Furthermore, some non primary health policies such as educational policies have diverse effects on health, at different time periods, some of which develop throughout the whole life course. [START_REF] Huisman | Educational inequalities in cause-specific mortality in middle-aged and older men and women in eight western European populations[END_REF][START_REF] Steenland | All-cause and cause-specific death rates by educational status for two million people in two American Cancer Society cohorts, 1959-1996[END_REF].We acknowledge the challenge this poses for developing policy linked indicators. Nevertheless, research efforts aimed at deciphering the causal pathways by which social or environmental factors affect health and their complex interactions through out ones life course is progressing [START_REF] Mechanic | Population health: Challenges for science and society[END_REF][START_REF] Kuh | Life course epidemiology[END_REF] and could allow at least approximations to frame this information as policy linked indicators and then boost HiAP.

The strength of this approach is that the indicators can be adapted to any level of decision making. It can provide information specific to the context of the decision-maker, be it for the introduction of a community program or for a national policy change. In such, the decisionmaker would be provided with an estimate of the disease burden avoided, or health gained in his/her population by implementing the policy in question. Furthermore this type of calculation can be carried out at regular intervals, and may provide timely indicators for taking advantage of windows of opportunity for policy change. We think that their potential for advocacy is extensive.

Funding:

This work was supported by CIBER en Epidemiología y Salud Pública (CIBERESP) in Spain.

The funding sources had no role in the design, conduct, or reporting of the study or in the decision to submit the manuscript for publication.

to persuade policy officials to solicit more policy specific health indicators for decision making and policy appraisal.

Social and environmental health indicators

Research on the social and environmental determinants of health is fundamental for promoting health in all policies. Firm evidence on the different pathways by which policies affect health is a requisite for health impact assessment (HIA) [START_REF]Health impact assessment: main concepts and suggested approach[END_REF] and would be an essential step for the production of policy-linked indicators discussed later. HIA calls for the explicit consideration of health in the evaluation of all policies and programmes, and has been proposed as an opportune approach to promote HiAP. [START_REF] Kemm | Health impact assessment and health in all policies[END_REF] The procedures and methods of HIA are universally applicable, and as such can be applied to proposals from any sector in order to minimize detrimental effects and maximize benefits on population health. [START_REF] Kemm | Health impact assessment: a tool for healthy public policy[END_REF] The systematic integration of the approach as part of the rules and procedures involved in policy appraisal is debated and currently the level of implementation across Europe varies. [START_REF] Quigley | Evaluation as a key part of health impact assessment: the English experience[END_REF][START_REF] Policies | The effectiveness of Health Impact Assessment. Scope and limitations of supporting decision-making in Europe[END_REF] Although institutionalisation of HIA may restrict the scope for political advocacy by requiring impartiality of the HIA practitioner, the provision of a sound evidence base for evaluating health impacts would be greatly welcomed. [START_REF] Veerman | Health Impact Assessment and advocacy: a challenging combination[END_REF] Appropriate application of HIA relies on solid, quantitative data on causal relationships between the determinants affected by the specific policy and health. [START_REF] Mindell | Enhancing the evidence base for health impact assessment[END_REF][START_REF] Kreiger | Assessing health impact assessment: multidisciplinary and international perspectives[END_REF] Identifying and monitoring health determinants that are the target of non-health policies yet have an established effect on health will encourage stakeholders to see the relevance of health in their policies, and could allow them to track policy performance though improved indicators.

Competing interests: None.


Powles Jw

Amir Shroufi
email: amir.shroufi@doctors.org.uk

Adherence and chemoprevention in major cardiovascular disease: A simulation study of the benefits of additional use of statins

Background

In everyday practice, adherence with preventive medications for cardiovascular disease (CVD) is lower than in clinical trials and appears to decline to around 50% by around 5 years.

The UK body for the evaluation of health technologies, NICE, currently recommends that persons with a greater than 20% 10 year risk of incident cardiovascular disease receive statins.

Methods

Publications on adherence with statin medication in clinical trials and in normal practice were systematically reviewed.

We used data on CVD-free members of a large Southern Hemisphere cohort study to simulate the expected benefits of contrasting strategies to increase the use of statins.

Risks of incident CVD and CVD death were estimated using the equations of Anderson et al.

Results

A strategy to enhance statin adherence among cohort members meeting NICE statin prescribing guidelines resulted in about twice as large a reduction in the aggregate risk of CVD death as did a strategy to lower treatment thresholds.

Conclusions

The benefits from increased spend on statin medication will be much greater if it results from enhanced adherence rather than from a lowering of the medication threshold.

* Adherence assumed to be unrelated to absolute risk among those eligible for statins †Eligible for treatment if 10 year risk ≥20% ‡ Eligible if 10 year risk ≥ 15.5% § The number of adherent individuals could not be made exactly equal due to stochastic nature of simulation.

Introduction

The 3-hydroxy-3-methylglutarate coenzyme A reductase inhibitors (statins) are the only class of drug widely used for the purpose of cholesterol lowering. A recent metaanalysis of 164 placebo controlled trials suggested that statin use was associated with an average reduction of LDL cholesterol concentration of around 1.8mmol/l.

Reductions in the incidence of IHD and stroke were estimated to be as high as 60% and 17% respectively. [START_REF] Law | Quantifying effect of statins on low density lipoprotein cholesterol, ischaemic heart disease, and stroke: systematic review and meta-analysis[END_REF] Such gains are unlikely to be achieved in treated populations however because sustained adherence with statins in the community is generally low. [START_REF] Eagle | Adherence to evidence-based therapies after discharge for acute coronary syndromes: an ongoing prospective, observational study[END_REF][START_REF] Wei | Adherence to statin treatment and readmission of patients after myocardial infarction: a six year follow up study[END_REF][START_REF] Bouchard | Impact of adherence to statins on coronary artery disease in primary prevention[END_REF][START_REF] Lachaine | Persistence and adherence to cholesterol lowering agents: evidence from Regie de l'Assurance Maladie du Quebec data[END_REF][START_REF] Poluzzi | Adherence to chronic cardiovascular therapies: persistence over the years and dose coverage[END_REF][START_REF] Blackburn | Adherence to statins, beta-blockers and angiotensin-converting enzyme inhibitors following a first cardiovascular event: a retrospective cohort study[END_REF][START_REF] Benner | Association between short-term effectiveness of statins and long-term adherence to lipid-lowering therapy[END_REF] In principle there are 2 ways of extending the population benefits from increased statin use; one is to lower the treatment threshold, the other is to enhance adherence among those already eligible for treatment. Although means of increasing adherence over the long term are not reliably known, it remains of interest to estimate the potential benefits.

In the UK the National Institute for Clinical Excellence (NICE) now recommends that those with a 20% or greater 10 year risk of incident cardiovascular disease (CVD) receive statins. [START_REF]Modification of Cardiovascular risk assessment and the modification of blood lipids for the primary and secondary prevention of cardiovascular disease[END_REF] Only the adherent among the eligible will gain substantial benefit, yet the non-adherent are likely to be at greater risk.

Discussion hitherto has focussed on increasing the population benefits of statins by lowering the thresholds for treatment. Here we consider, as an alternative, improving adherence among subjects meeting existing eligibility criteria.

Methods

Review of literature on levels of adherence to statin medication

We identified studies using the key words statins, adherence, compliance and concordance, searching Pub-Med. We included only large well conducted randomised control trials of statins for the primary and secondary prevention of CVD and studies whose primary aim was to measure adherence with statins for the primary or secondary prevention of CVD in the community setting. We included RCTs which were frequently cited by other studies as providing evidence of statin effectiveness and were adequately randomised and controlled, and provided analysis by intention to treat. Only studies of adherence in the community setting with a clear study design were included.We initially sought to include only studies which used a common operational definition of adherence although this criterion was relaxed in order to increase the number of studies included. No restrictions were placed on the year of the study or the duration of follow up used by the study authors.

Adherence observed within randomised control trials of statin use are shown in table 1. Studies of adherence in the community setting are shown in table 2. 1

The data summarised in Tables 1 and2, including the observed declines in adherence with time suggest that an assumed average adherence with medication over 10 years of around 50% is reasonable.

Simulation of proposed scenarios using cohort study data

The were smokers. Recruitment occurred between 1990 and 1994. [START_REF] Giles | Nutrition and lifestyle: opportunities for cancer prevention[END_REF] This study population was suitable for estimating the benefits of cardiovascular preventive strategies because the data set contained all necessary data on participants that was required to derive a risk score using the Framingham equations, and few subjects had existing CVD.

From the source population, 2485 subjects were excluded due to having existing CVD and a further 388 subjects were excluded due to missing data leaving 38,268 individuals. Data on CVD risk factors for each of these individuals were transferred into an Excel spreadsheet.

We used the equations of Anderson et al [START_REF] Anderson | Cardiovascular disease risk profiles[END_REF] (based on the experience of the Framingham cohort) to estimate 10 year risk of CVD onset and death using age, sex, systolic blood pressure, smoking status, diabetes status and total serum cholesterol concentration. The risk equation for calculating 10 year risk of CVD death, written as Excel code is included as a supplementary on line file.

Having used this method to estimate risk scores for each cohort member we went on to estimate how competing assumptions with respect to statin adherence and the risk threshold used to determine eligibility for therapy would alter the population level benefits from statin therapy. This was achieved by constructing 3 scenarios -a baseline scenario implementing the current NICE guidelines for statin use, an enhanced compliance scenario and a lowered threshold scenario. Individuals assigned to be adherent with statins were assumed to experience a 20% reduction in their serum total cholesterol concentration. This was chosen as a representative rounded value consistent with clinical trials data. (see Table 1). Adherence is here defined as taking ≥80% of the prescribed monthly dose of medication. Adherence was assumed to be unrelated to the magnitude of risk among those deemed eligible for therapy.

In the baseline scenario, only subjects exceeding the NICE risk threshold received statins and adherence was hypothetically assumed to be maintained at 50%.

The details of the alternative scenarios we compare with this baseline scenario are: a) Enhanced adherence scenario. This assumes an instantaneous and sustained increase by 50% (from 50% to 75%).

b) Lowered prescribing threshold scenario, where the threshold is adjusted downward sufficiently to result in an increase in statin consumption equivalent to that under scenario a). This was achieved at a 10 year risk threshold of approximately 15.5%.

Assignment of adherence

Adherent individuals were assigned at random using a random number generator within Excel.

Results

Adherence with statin therapy in clinical trials (Table 1) tends to be much higher than in everyday practice (Table 2). The shorter follow up in the latter studies makes them likely underestimators of the difference in the longer term.

The distribution of 10 year risk of CVD (among those free of CVD at baseline) among members of the source study population are shown in Supplementary Figure 1. The distribution is positively skewed.

[Supplementary Figure 1 Predicted outcomes over 10 years under the three scenarios are given in Table 3.

1 1

In the baseline scenario, among those without existing CVD and not assigned to statins, 5390 onsets of CVD and 710 CVD deaths would be expected over 10 years.

Twenty-four percent (9,279/38,268) of the source population had an estimated 10 year risk of CVD ≥20%, and were eligible for therapy under the NICE guidelines. Fifty percent (4563) of these are assigned to be adherent to statin therapy and among them, an estimated 174 CVD onsets and 70 CVD deaths were averted.

In the lowered treatment threshold scenario, 6991 were assigned to be adherent resulting in an estimated additional 70 CVD onsets and 18 CVD deaths being averted.

In the enhanced adherence scenario, 6971 individuals were assigned to be adherent to statin medication, resulting in an additional 91 CVD onsets and 37 CVD deaths being averted.

The enhanced adherence scenario, in comparison with the lowered threshold scenario, shows a modest gain in averting CVD onsets but a, proportionally, much larger gain in averting CVD deaths -roughly, a doubling. This implies that the incremental cost effectiveness would also be approximately double.

Sensitivity analyses

We examined how robust our results were to the specified increase in adherence, the proposed reduction in cholesterol from using statins and the assumed baseline level of adherence. We found the relative benefit of the increased adherence scenario remained largely unchanged for plausible alternative values of these variables.

Discussion

Relative to a baseline based on current NICE guidance, twice as many CVD deaths would be prevented by a 50% improvement in adherence (from 50 to 75%) under current prescribing guidelines, than by relaxing those guidelines to an extent that would result in a similar increase in statin consumption.

It is not surprising that a strategy that concentrates on enhancing treatment among high risk individuals yields bigger benefits than a strategy of extending prescribing to lower risk individuals. However, the magnitude of the difference is notable and it serves to emphasise the need to find more effective means to increase adherenceespecially over the long term Although we have not estimated cost effectiveness of any particular strategy, our results indicate that if adherence could be improved by the magnitude specified here at a cost not greater than that of extended prescribing it should be more cost effective.

This excludes actual medication costs, and reduced waste associated with improved adherence should further improve the cost effectiveness profile of this strategy.

Recent Cochrane reviews conducted in this area suggest that measures such as telephone reminders, self-monitoring mechanisms, and improved patient information may increase short term adherence but the long term effectiveness of such measures is unknown. [START_REF] Haynes | Interventions for enhancing medication adherence[END_REF][START_REF] Schedlbauer | Interventions to improve adherence to lipid lowering medication[END_REF] Our estimates of absolute benefit should be viewed cautiously given the simplifying assumptions employed. We have made no attempt to account for poly-pharmacy or for the fact that in practice many individuals above risk thresholds would remain unidentified.

The Framingham equations, used here, have been criticised for overestimating CVD risk, and so overestimate numbers eligible for therapy [START_REF] Neuhauser | A comparison of Framingham and SCORE-based cardiovascular risk estimates in participants of the German National Health Interview and Examination Survey[END_REF]. Nevertheless they are recommended by NICE. [START_REF]Statins for the prevention of cardiovascular events in patients at increased risk of developing cardiovascular disease or those with established cardiovascular disease[END_REF] Although they may overestimate absolute risk, the effects of this on our estimates of relative benefit should be more modest. While some studies have suggested that Framingham overestimates risk by proportionally similar amounts across risk strata [START_REF] Brindle | Predictive accuracy of the Framingham coronary risk score in British men: prospective cohort study[END_REF] others have suggested that the overestimation of risk was greatest in lower risk populations. [START_REF] Menotti | Comparison of the Framingham risk functionbased coronary chart with risk function from an Italian population study[END_REF] Were Framingham to overestimate risk more among low risk strata of the cohort used here, then this may lead to an overestimation of benefit from the wider prescribing scenario, in which a greater number at lower risk are treated.

We have used a Southern hemisphere cohort with a low prevalence of smoking;

absolute benefits of cholesterol lowering should be higher in higher risk populations with higher smoking prevalence. Mean systolic blood pressures and serum cholesterol concentrations are similar to the values for 45 to 64 year olds in the 2003

Health Survey for England. [START_REF]Health survey for England[END_REF] The relatively modest benefit of the 2 strategies in absolute terms is a result of their application to a relatively low risk population for the purposes of primary prevention.

We have assumed that adherence is unrelated to risk. However, even with a placebo, poor adherence appears to be associated with increased risk of death, [START_REF] Simpson | A meta-analysis of the association between adherence to drug therapy and mortality[END_REF] along with higher age, low mood, [START_REF] Kulkarni | Long-term adherence with cardiovascular drug regimens[END_REF] low socioeconomic status, [START_REF] Kopjar | Adherence with statin therapy in secondary prevention of coronary heart disease in veterans administration male population[END_REF] smoking, [START_REF] Horwitz | Treatment adherence and risk of death after a myocardial infarction[END_REF] hypertension and number of concurrent medications [START_REF] Benner | Association between short-term effectiveness of statins and long-term adherence to lipid-lowering therapy[END_REF] If risk among the nonadherent is higher than among the adherent, our estimates of the relative benefit from enhanced adherence will be underestimates.

Although many CVD risk factors follow an approximately normal distribution, overall CVD risk is positively skewed (see figure 1). This is a consequence of the multiplicative way in which CVD risk factors combine to determine overall risk. Our finding, that potential gains are greater when efforts are concentrated on the top tail of the distribution of overall risk, is not incompatible with Rose's observations that strategies which focus on the top tails of risk factor distributions, considered one at a time, fail to identify most of those with high overall risk. [START_REF] Rose | Sick Individuals and Sick Populations[END_REF]

Conclusions

Failure to take account of adherence levels that are typically achieved in practice can lead to an overestimation of the potential benefits from chemopreventive strategies. It may also inadvertently result in policies for the use of statins that fail to maximise benefits from their use.

More work is needed on the best ways to enhance long term adherence.

Implications for policy and practice

• Long term adherence to statin medication is likely to be around 50%.

• Improving adherence among the highest risk individuals will avert substantially more CVD deaths than would equivalent increases in prescribing directed at those at lower risk.

• Effective interventions to improve long term adherence with medication are urgently needed.

about here] Supplementary Figure 1 :

 1 Distribution of 10 year of CVD within simulation cohort; risk scores estimated using Framingham equations provided by Anderson et al 18 for 38,264 individuals without existing CVD*

Table 1 : Adherence observed during principal RCT of statins for primary and secondary prevention of cardiovascular disease

 1

	Trial	Author, year	Definition of	Ascertainment Mean lowering of	Primary or secondary	Mean age	Observation	Adherence at
			adherence		serum cholesterol	prevention		period	end of period
					concentration
	AFCAPS/ texCAPS	JAMA, 1998	≥75%	Pill-counts	19%	Primary prevention	58	5.2 years	99%
	[10]
	EXCEL [11]	Shear et al,	≥75% medication	Self report	Not stated	Secondary prevention	54	4 years	99%
		1992	taken
	CARE [12]	Sacks et al,	Continuation of	Not-stated	20%	Secondary prevention	59	Median 5 years	94%
		1996	therapy
	4-S [13]	Conroy et al,	Continuation of	Not stated	26%	Secondary prevention	58	Median 5.4 years	90%
		1998	therapy
	Heart Protection	Farmer et al,	≥80% medication	Pill-counts	17%	Secondary prevention	64	Median 5 years	82%
	Study [14]	2003	taken
	LIPID [15]	N Eng J Med,	Continuation of	Not-stated	18%	Secondary prevention	62	6.1 years	81%
		1998	therapy
	WOSCOPS [16]	Shepherd et al,	≥75%	Pill-counts	20%	Primary prevention	55	Mean 4.9 years	70%
		1995

Table 2 : Studies of statin adherence in the community setting*

 2

	Authors, year	Study design	Operational definition of	Method of ascertainment	Primary or secondary	Mean	Observation	Adherence at end
			adherence		prevention	Participant age	period	of period
	Kim A. Eagle et al,	cohort study	Continuation of therapy	Structured telephone	Secondary prevention	65	6 months	87%
	2004 [2]			interview
	L Wei et al, 2002 [3] cohort study	≥80% medication	Pharmacy records	Secondary prevention	67	2.4 years	64%
			availability
	Marie Bouchard et al,	Nested case control	≥90% prescriptions filled	Data retrieved from health	Primary prevention	63	1 year	62%
	2007 [4]	study		care database
	Jean Lachaine et al,	Retrospective	≥80% medication	Pharmacy records	Primary and secondary	58	2 years	58%
	2006 [5]	cohort study	availability		prevention
	Elizabeth Poluzzi et	Retrospective	300/365 minimum daily	Health Authority database	Primary and secondary	≥40	3 years	52%
	al, 2007 [6]	cohort study	doses received		prevention
	David F Blackburn l,	Retrospective	≥80% prescriptions filled	Pharmacy records	Secondary prevention	58	5 years	49%
	2005 [7]	cohort study
	Benner et al 2005 [8] Retrospective	Continuation of therapy	Pharmacy records	Primary and secondary	60	3 years	21%
		cohort study			prevention

* Studies of those with new and existing prescriptions for Statin medication for primary or secondary prevention outside the clinical trial setting.

  Melbourne Collaborative Cohort Study was a prospective study of 41 141 people

	(17 049 men), with a mean age of 55 at baseline. (range 25-75) Mean values for
	systolic blood pressure and total serum cholesterol concentration were 137mmHg
	(SD=1.05) and 5.5mmol/l (SD1.05) 3.8% of cohort participants had diabetes and 11%

Table 3 : Number of incident cardiovascular disease and vascular deaths predicted over 10 years in hypothetical scenarios, according to adherence with statin medication and the treatment threshold for prescribing. Estimates derived using risk prediction equations based on Framingham data and provided by Anderson et al. [18]

 3

	N=38,264	Untreated	Baseline scenario		Enhanced adherence	Lowered prescribing
			Adherence=50%*	†	counterfactual scenario	threshold counterfactual
	(Those among cohort of 41,141with no existing				Adherence=75%*	†	scenario Adherence=50%*	‡
	CVD)
	Number adherent to statin therapy	0	4563		6971		6991	§
			(11.9% of population)	(18.2% of population)	(18.3% of population)
	Predicted incident cardiovascular disease over 10 years	5390 (13.1% of source	5215 (13.6% of source	5124 (13.4% of source	5145 (13.5% of source
		population)	population)	population)	population)
	Additional incident cardiovascular disease averted	-	-		91		70
	(above baseline)
	Predicted cardiovascular deaths over 10 years	710	640		603		622
	Cardiovascular deaths averted	-	70		107		88
	Additional cardiovascular deaths averted (above	-	-		37		18
	baseline)				(53% improvement from	(25% improvement from
					baseline)		baseline)

Table 4 : Sensitivity analyses with alternative assumptions regarding adherence and cholesterol lowering

 4

	Deaths averted in	Deaths averted in
	enhanced adherence	lowered treatment
	scenario	threshold scenario

Acknowledgements: Material upon which article is based was presented orally at the October 2007 EUPHA conference, Helsinki.

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Adherent individuals were assumed to experience an instantaneous and sustained reduction of 20% in their serum cholesterol concentration and their Framingham risk score was recalculated to reflect this. Risk in non adherent individuals was a function of their baseline risk factor values.

Conflict of interest statement:

The authors declare that there are no competing interests.