Erik Geissler
email: e.geissler@orange.fr

Dynamic Light Scattering in Gels and Solutions

Dynamic light scattering (DLS) is a rich source of information in investigations of the frequency response of soft materials. Most commonly, however, it is underemployed, mainly for determining the size of suspended particles or macromolecules in solution. This article emphasizes some of the other aspects of the technique, how it acts as a frequency discriminator between mechanisms of differing relaxation rates, and how it can be used to determine directly the thermodynamic properties not only of simple solutions, but also of polymer gels and inhomogeneous solutions, as well as their large-scale structure. The method is illustrated with several detailed examples.

§1. INTRODUCTION

Since its beginnings in the 1970s, [START_REF] Pike | Photon Correlation and Light-Beating Spectroscopy[END_REF][START_REF] Berne | Dynamic Light Scattering[END_REF] dynamic light scattering has become the standard laboratory method for measuring the size of particles in suspension, or more precisely their hydrodynamic radius R H . The technique became a practical possibility after intense coherent monochromatic light sources, i.e., lasers, were developed in the previous decade.

Unlike incoherent light, where each separate atom in the source emits independently with random phase, the wave front of the electric field advancing from a coherent light source remains in phase over a large spatial distance. This property is illustrated by the characteristic speckle pattern generated when a coherent light beam passes through an inhomogeneous medium, such as slightly sanded glass or a sheet of semi-crystalline polymer, in which the different crystallites composing the film in the beam each scatter light strongly in the forward direction. As the roughness of the glass surface or the crystallites in the film are located randomly, the electric fields that they re-emit interfere with each other, additively at some angles, producing a bright spot in the far field, and cancelling each other at other angles, yielding zero light intensity. Figure 1 shows a typical speckle pattern projected on a screen by a laser beam passing through a thin sheet of polyethylene. The resulting pattern of dark and bright spots is not random. It encodes information about the distribution of inhomogeneities in the medium. A suitably placed converging lens on the axis of the beam will reconstitute the image of the film. The speckle intensity pattern I(q)= E(q)E*(q) of Fig. 1 exemplifies the reciprocal space q, where the electric field is E(q) ∝ 𝜌(𝒓) 𝑒 !!𝒒.𝒓 𝑑𝒓 (1) and ρ(r) is the distribution of inhomogeneities in the film, r being the position of the scattering particles. E*(q) is the complex conjugate of E(q). Here, the transfer wave vector q is the difference between the wave vectors of the scattered and incident light, with amplitude |q|=q=(4πn/λ)sin(θ/2)

(2) n being the refractive index of the medium, λ the wavelength of the light and θ the angle of scattering with respect to the incident beam. The electric field E(q) is thus the Fourier transform of the distribution of inhomogeneities in the film. Since q is an inverse length, the counter-intuitive character of reciprocal space lies in the fact that small objects in real space r are detected at large q, and vice-versa. A corollary of this relationship is that if the incident beam on the film is divergent, then displacing the film perpendicularly to the beam causes the speckle pattern to move in the same direction. If, on the contrary, the incident beam is convergent, then the apparent movement of the speckle pattern is in the opposite direction. This property is sometimes used in store window advertisements to alert passers-by to their need for corrective eyewear. In that arrangement coherent light illuminates a continuously moving semi-transparent screen, in such a way that the image received on the retina of a myopic or hypermetropic individual appears to move respectively up or down, while for a person with corrected eyesight the image merely fluctuates with no perceptible overall movement.

If now, instead of a medium in which the inhomogeneities are static, the coherent light passes through a dilute suspension of latex beads, then, as before, each bead re-radiates light in all directions. The difference here is that the scattering particles are not fixed: the suspended latex beads move freely, and the intensity of the speckles fluctuates constantly. Usually the changes are so fast that the naked eye, which cannot detect rapid fluctuations, perceives only an average intensity at each angle. With an electronic detector such as a photomultiplier or a light sensitive diode, however, the rapid fluctuations can be recorded.

As the particles are driven by thermal excitation, their concentration c fluctuates in time and space within the sample, and is subject to the diffusion equation

!" !" = 𝐷∇ ! 𝑐 (3)
where D, the coefficient of translational diffusion of the particles, is defined by the Stokes Einstein relation

D = kT/(6πηR H ) (4)
in which k is Boltzmann's constant, T the absolute temperature, η the viscosity of the solvent and, as already stated, R H is the hydrodynamic radius of the particles. The scattering pattern generated by these concentration fluctuations is mapped by the transfer wave vector q defined in Eq. 2. In terms of the reciprocal space of the scattering pattern, for a concentration fluctuation of initial amplitude Δc(0), Eq. 3 yields the following time dependence

∆𝑐 𝒒, 𝑡 = 𝑐(𝒒, 𝑡) -< 𝑐 >= ∆𝑐(0) 𝑒 !!! ! ! ( 5
)
where <c> is the time average concentration of the particles in the suspension. These concentration fluctuations are accompanied by local changes in the refractive index of the medium, and hence fluctuations in the intensity of the scattered light I(q,t).

In standard DLS instruments, the laser source is polarised vertically, with the detector moving in the horizontal plane. This means that the observed transfer wave vector q is defined only by the scalars n, λ and θ in Eq. 2, and is therefore a scalar itself. In the analysis that follows, therefore, the vector notation can be dropped. Measurement of the time dependence of the concentration fluctuations Δc(q,t), or rather of the fluctuations in the intensity of the scattered light I(q,t), together with Eq. 4, thus offers the means of measuring the hydrodynamic radius R H of the particles in suspension. The approach adopted here is inspired by the seminal work of Joosten, McCarthy and Pusey. [START_REF] Joosten | Dynamic and static light scattering by aqueous polyacrylamide gels[END_REF] §2. STATIC LIGHT SCATTERING Before entering into the details of DLS, it is worth remembering that light scattering observations were being performed well before the development of lasers. [START_REF] Stein | A Light Scattering Investigation of Cellulose Acetate[END_REF][START_REF] Debye | A Photoelectric Instrument for Light Scattering Measurements and a Differential Refractometer[END_REF][START_REF] Speiser | A Light Scattering Photometer for Determining High Molecular Weights[END_REF] For such measurements the only requirement is for a monochromatic light source, for example the blue line of the mercury arc spectrum. [START_REF] Zimm | Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions[END_REF] Since the electric field scattered by a concentration fluctuation is proportional to Δc, the intensity of the scattered light scattered is proportional to Δc 2 . However, the mean square amplitude of concentration fluctuations in a solution at equilibrium is governed by the general relationship <Δc 2 >= kTc 2 /(c∂Π/∂c) (6) where Π is the osmotic pressure of the solution, and c∂Π/∂c is known as the osmotic modulus. [START_REF] Landau | Statistical Physics[END_REF] For simplicity at this point we assume an arrangement whereby a beam of monochromatic light of wavelength λ is directed through a medium of refractive index n that contains a dilute suspension of small beads or molecules of radius R with refractive index n 1 . If the ratio R/λ <<1, then the light scattered by the particles obeys the Rayleigh condition, according to which the intensity scattered at all angles is simply proportional to <Δc 2 >. The intensity of the scattered light <I(q, t)> must however first be corrected for the angular variation of the scattering volume. With cylindrical samples, since the volume of sample probed by the detector varies as 1/sinθ, the observed intensity must accordingly be corrected by the factor sinθ. Secondly, the measurement should be calibrated against a standard sample under identical conditions, for which the Rayleigh ratio ΔR θ standard is known. A commonly employed standard light scattering sample is toluene, the Rayleigh ratio of which at λ = 632.8 nm is ΔR toluene =1.34 10 -5 cm -1 . [START_REF] Wu | Correlations between the Rayleigh ratio and the wavelength for toluene and benzene[END_REF] Upon application of these corrections, the constant of proportionality K between <I(q)> and <Δc 2 > then appears as <I(q)> = K <Δc 2 > = KkTc/(∂Π/∂c) [START_REF] Zimm | Apparatus and Methods for Measurement and Interpretation of the Angular Variation of Light Scattering; Preliminary Results on Polystyrene Solutions[END_REF] where K is defined as

K = (2π) 2 n 2 (dn/dc) 2 /λ 4 (8)
In Eqs 6 and 7, Π is the osmotic pressure exerted by the beads or molecules in the solution. The refractive index increment dn/dc, expressing the dependence of the refractive index of the solution on the concentration of suspended particles, can be calculated through the Clausius-Mossotti relation [START_REF] Born | Principles of Optics[END_REF], or even better, measured directly.

In the case of a dilute suspension of small particles, the osmotic pressure Π is simply proportional to the number of particles per unit volume, or

Π = kTc/M (9)
M being the mass of the suspended particles. The intensity of the light scattered intensity thus becomes <I(q)> = K cM [START_REF] Born | Principles of Optics[END_REF] The above expressions summarize the information to be derived for the ideal model of a dilute suspension of small beads in the absence of mutual interactions.

Solutions, however, are not in general ideal: the solute particles interact, either repelling or attracting each other. This is usually accounted for by expressing the osmotic pressure in terms of its virial coefficients, thus

Π = kT(c/M + A 2 c 2 + A 3 c 3 ) (11
) In a 'good' solvent, that is, when the solvent molecules are more strongly attracted to the solute particles than the solute particles are to each other, the second virial coefficient A 2 is positive. In a poor solvent, by contrast, A 2 is negative, which means that the solubility of the particles is limited. The third virial coefficient A 3 is generally interpreted as a measure of three-body interactions. [START_REF] De Gennes | Scaling Concepts in Polymer Physics[END_REF] A second important consideration is that particles that scatter light are not always very much smaller than the wavelength of the light, λ. When their radius is comparable with, or larger than λ, then the intensity in Eq. ( 7) is no longer independent of the scattering angle θ. The intensity <I(q)> becomes <I(q)>= <I(0)> P(q) S(q) (12) where P(q) is the particle form factor, which depends on the shape of the particle, and S(q) is the structure factor, which depends on the disposition of the particles and their concentration. When the particles are distant from each other and randomly distributed, S(q)=1. At sufficiently small values of q, P(q) reduces to a general form that is independent of shape

P(q) = 1/(1+ q 2 R G 2 /3) (13
) where R G is the radius of gyration of the particle, defined by

𝑅 ! ! = ! ! ! ! ! ! 𝒅𝒓 ! ! ! ! !𝒓 (14)
R being the outer limit of the particle and ρ(r) the density of matter at distance r from the centre. For uniform spherical particles of outer radius R, R G = (3/5) 1/2 R. Another, frequently useful, way of expressing P(q) at small q is the Guinier expression

P(q) =exp(-q 2 R G 2 /3) (15)
From Eq. 7, and with the assumption that the third virial term is negligibly small, it follows that the normalised intensity of the scattered light can be expressed in the form Kc/<I(q

)> = (1/M)[1+(qR G ) 2 /3] + 2A 2 c ( 16
)
A plot of the quantity Kc/<I(q)> as a function both of c and of q 2 (Zimm plot, c.f. §5, Fig. 4), in which R G 2 and A 2 are evaluated simultaneously for all data points, and in which both c and q 2 are extrapolated to zero, yields the value of the mass 𝑀 of the solute molecules, as well as their radius of gyration R G . [START_REF] Zimm | The Scattering of Light and the Radial Distribution Function of High Polymer Solutions[END_REF] The molar mass M derived by this technique is the weight average molar mass, M w . Apart from the special case of monodisperse distributions, M w > M n , where M n is the number average molar mass that is obtained by osmotic pressure measurements through Eq. 11. §3. PHOTON CORRELATION Most light scattering instruments operate with a laser with vertically polarised light. This greatly simplifies the interpretation of measurements performed in the plane perpendicular to the polarisation. Although dynamic light scattering can be performed with incoherent visible or X-ray light sources, [START_REF] Jakeman | Intensity fluctuation lightscattering spectroscopy using a conventional light source Optics[END_REF][START_REF] Sutton | Observation of speckle by diffraction with X-rays[END_REF] the coherent light from lasers greatly facilitates the task. It offers the means to measure the time dependence of the motion of the suspended particles and thus to distinguish between different modes of particle movement. In a DLS experiment the light intensity I(q,t) scattered from the incident laser beam by the concentration fluctuations arrives as a sequence of photons with a fluctuating rate at the detector, where they are transformed into a train of electronic pulses. On being fed into a digital correlator, these generate an intensity correlation function G(τ) = <I(q,t+τ) I(q,t)>/<I(q,t)> 2 (17) where the values of G(τ) are accumulated in successive channels corresponding to each value of the delay time τ. In Eq. 17 the angular brackets < > mean an average of the time t over the duration of the observation. The correlator also measures the average scattered intensity <I(q,t)>= <I(q,0)>.

A basic characteristic of the concentration fluctuations Δc(q,t is) that at each value of q the fluctuations are independent of those of its neighbours. It follows that if the light falling on the detector comes from more than one independent coherence area q then the fluctuations tend to cancel, and the amplitude of G(τ) is correspondingly reduced. This is expressed through the Siegert relation between the intensity correlation function G(τ) and the corresponding field correlation function

g(τ) G(τ) = 1 + β |g(τ)| 2 (18)
where the optical coherence factor β ≤1, is approximately inversely proportional to the number of coherence areas probed by the detector. The instrumental factor β is defined not by the sample but exclusively by the optical arrangement between the sample and the detector, e.g., aligned pinholes, or an optical fibre. In principle, if a single mode optical fibre is used, then β=1. The actual value of β of the instrument is ascertained simply by measuring the correlation function G(τ) of the light scattered by a dilute suspension of small latex beads. In this case the intensity correlation function becomes by virtue of Eq. 5

G(τ) = 1 + β exp(-2Dq 2 τ) (19
) This expression allows the diffusion coefficient D and hence the corresponding bead radius R H to be evaluated using Eq. 4. In many situations, however, for example when the suspended particles are not identical, or several relaxation processes are present, G(τ) -1 has multi-exponential character.

Meanwhile, the amplitude of the intensity fluctuations, measured independently by the correlator, is <I(q,t)> =<I(q,0)> Dynamic light scattering thus provides information not only on the hydrodynamic radius of particles suspended in solution, but equally importantly, through Eq. 16, their mass, their radius of gyration R G , in addition to the second virial coefficient A 2 . In the case of solutions of overlapping macromolecules, it yields the hydrodynamic correlation length ξ H of the fluctuations in the medium, and more generally, when the measurements are extrapolated to q=0, the osmotic modulus c∂Π/∂c of a polymer solution at any concentration. §4. EXPERIMENTAL CONSIDERATIONS We now discuss some of the properties that are desirable in a DLS instrument to obtain reliable information from a sample. Since on any instrument the light scattering measurements are likely to be performed on a wide variety of specimens, the instrument should be able to respond to a broad range of situations. Certain samples, for example, such as polymer solutions, and even more so solutions or gels close to a phase transition, can be disturbed by the heat absorbed from the laser beam. [START_REF] Jamie | Thermal and collective diffusion in polymer solutions: a small angle light scattering study[END_REF] The DLS instrument should therefore be able to work at low power, and also allow for reproducible attenuation of the intensity of the incident laser beam, with no deviation of its position. For this reason it can be advantageous to use a low power He-Ne laser working at 632.8 nm as the light source. While the quantum efficiency of conventional photomultiplier tubes is low for radiation at this wavelength (5-10%), this is not true of avalanche diodes -their quantum efficiency is close to 70%, and they can be selected for low noise.

Experimentally, evaluation of the diffusion coefficient D and the osmotic modulus c∂Π/∂c from a DLS measurement requires an instrument with the following characteristics: 1) A refractive index matching bath, usually containing toluene, to reduce reflections and flare from the light beam at the entry and exit points of the sample holder.

2) Precise temperature control system for the sample.

3) Digital read-out of the contents of the delay channels to permit user-defined analysis of the intensity correlation function. 4) A memory channel to store the total scattered light intensity measured by the detector, and its average count rate CR. 5) To protect the detector and avoid correlator overload, a variable beam attenuator that maintains the position of the laser beam in the sample at each attenuator setting. 6) A beam splitter to monitor the instantaneous intensity of the laser input as a function of the attenuation selected, and a memory to record the resulting average beam monitor count MON. 7) A digital record of the elapsed time of the experimental measurement.

While it is desirable to measure in situ the transmission T R of the sample, with slightly inhomogeneous solutions or gels, such samples can spread or deviate the beam and make the measurements unreliable. In that case the sample transmission can be measured separately in a spectrophotometer with light of the same wavelength as the laser used in the DLS instrument.

We discuss the configuration in which the sample is held in a cylindrical cell and the light scattering intensity is measured in a horizontal plane perpendicular to the polarization of the incident light. To transform <I(q)>, recorded as a count rate CR, into a physically meaningful value, the instrument must be calibrated. For this, a standard light scattering sample, such as pure toluene, is itself first measured over a range of scattering angles, generally in the range 30º≤ θ ≤ 150º. The constancy of the product CR tol (θ)×sinθ over the whole range is an indication that stray light scattered from reflections within the index matching vat is negligible. Both the intensity of the dynamically scattered light <I d (t)> and <I tol (θ)> must be corrected for the electronic dark current noise of the detector. Here the subscript tol refers to toluene.

The resulting intensity of the sample is then normalized according to

<Ι d (t)> = ΔR tol ×CR sample ×MON tol /[CR tol ×MON sample ] (20)
We recall that this expression is independent of the value of the coherence factor β in Eq. 18. §5. GELS AND INHOMOGENEOUS SAMPLES Light scattering measurements are straightforward when the sample to be investigated is a simple and transparent solution or a dilute suspension of uniform particles. When, on the contrary, the sample is either a gel or a solution containing a mixture of rapidly diffusing particles and much larger, slowly moving particles, then the total instantaneous scattered intensity I(t) received by the detector at angle θ is the following product

I(t) = (E s (t)+E d (t))(E s *(t)+E d *(t)) = [E s (t).E s *(t)+E d (t).E d *(t)]+[E s (t).E d *(t)+E d *(t).E s (t)] = I s (t)+I d (t)+[E s (t).E d *(t)+E s *(t).E d (t)] (21)
where E s (t) is the (vertically polarized) electric field scattered by the static or quasistatic particles at angle θ, and E d (t) that by the rapidly fluctuating particles. As stated earlier, the asterisk in Eq. [START_REF] Kloster | Dynamics of a Polymer Solution in a Rigid Matrix[END_REF] However, although the time average of the cross term is zero, its effect on the intensity correlation function G(τ) in Eq. 17 can be substantial. In hydrogels such as polyacrylamide, in which the structural inhomogeneities, such as the clusters of crosslinks that give rise to I s (t) are stationary, I s (t) is therefore constant. In such gels it is the mobility of the network chains between the cross-links, which generate the osmotic swelling pressure in the gel, that give rise to I d (t). In this case the amplitude of I s (t) is constant, which enabled Joosten et al. [START_REF] Joosten | Dynamic and static light scattering by aqueous polyacrylamide gels[END_REF] to conclude that <I s 2 (t)> = <I s (t)> 2 [START_REF] Provencher | CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[END_REF] and consequently the total intensity correlation function of the scattered light reduces to

G(τ) = <I(t)I(t+τ)>/<I(t)> 2 = {<I d > 2 (1+βg 2 (τ))+<I s > 2 +2<I d ><I s >+2β<I d ><I s >g(τ)}/<I(t)> 2 (24)
On setting X as the ratio of the dynamic to the total scattering intensity, we have

X = <I d >/(<I d >+<I s >)
The intensity correlation function G(τ) then reduces to

G(τ)-1 = β[2X(1-X) g(τ)+X 2 g 2 (τ)] (25) Since g(0)=1, it follows that X= 1-{1-[G(0)-1]/β} 1/2 (26)
From this result Joosten et al. [START_REF] Joosten | Dynamic and static light scattering by aqueous polyacrylamide gels[END_REF] demonstrated that the value of g(τ) can then be calculated simply for each value of τ using the expression

g(τ) = {-(1-X)+[(1-X) 2 +(G(τ)-1)/β] 1/2 }/X (27)
Analysis of g(τ) as a function of the transfer wave number q can then yield the diffusion coefficient D either of mobile particles trapped inside the lattice of a stiff gel, or, in the case of gels in which the lattice chains themselves are mobile, the collective diffusion coefficient D c = Γq 2 of the solvent in the gel, where Γ is the relaxation rate of g(τ). [START_REF] Tanaka | Spectrum of light scattered from a viscoelastic gel[END_REF] In the latter case, by analogy with Eq.4 D c = kT/(6πηξ H ) (28) Here η is the viscosity of the solvent and ξ H the hydrodynamic correlation length of the gel. D c describes the rate of swelling or drying of a gel when it is exposed to a change in its external conditions. [START_REF] De Gennes | Scaling Concepts in Polymer Physics[END_REF] Remarkably, the overwhelming attention of the literature on DLS in gels concentrates on the hydrodynamic properties of the relaxation rates Γ and on D c , rather than on the intensity of the scattered light. [START_REF] Tanaka | Spectrum of light scattered from a viscoelastic gel[END_REF][START_REF] Pusey | Dynamic light scattering by non-ergodic media[END_REF][START_REF] Feng | Dynamic Light Scattering by Permanent Gels: Heterodyne and Nonergodic Medium Methods of Data Evaluation[END_REF][START_REF] Shibayama | Swelling/Shrinking and Dynamic Light Scattering Studies on Chemically Cross-Linked Poly(vinyl alcohol) Gels in the Presence of Borate Ions1[END_REF] Figures 2 and3 illustrate how DLS can be used to investigate the intensity of light scattered by gels that possess a static large-scale structure (i.e., with constant I s (t)), but contain either large mobile molecules or mobile network chains. [START_REF] Rochas | Measurement of Dynamic Light Scattering Intensity in Gels[END_REF] The intense static speckle structure (red curve) comes principally from the static structure and corresponds to the intensity variations similar to those shown in Fig. 1. Unlike the scattering pattern from the dry polyethylene sample, however, the network chains in polyacrylamide hydrogels are free to fluctuate locally, exerting an osmotic pressure Π that keeps the gel swollen. Open blue circles are the corresponding intensity of the dynamic signal calculated from Eq. 26, from which the osmotic modulus is calculated via Eq. 7.

In Fig. 2 it is notable that the line of minimum intensities of the total scattered light (represented by the horizontal dashed line) is not, as it should be, the same as that of the dynamic light scattering intensity, [START_REF] Joosten | Dynamic and static light scattering by aqueous polyacrylamide gels[END_REF] but instead lies above it. The discrepancy is due to depolarized light coming either from the intermediate scale static architecture of the gel or from multiple scattering. As the electric field of depolarised light is orthogonal to that of the vertically polarised scattered light, it cannot participate in the heterodyne mechanism, but merely adds a constant background intensity. This effect, particularly notable when X is close to unity, is reduced by placing a vertical polariser before the detector. Although the swelling pressure is constant throughout the gel, apparent deviations of <I d > from what should be a constant value are visible in Fig. 2. These are the consequence of larger scale defects in the sample, which reduce the value of the transmission T R at certain angles θ. To avoid such anomalies, measurements from nearby positions should be compared.

Figure 3 illustrates how the field correlation function g(τ) calculated from Eq. 27 for a polyacrylamide hydrogel is independent of the brilliance of the particular speckle at which the measurement is made. [START_REF] Rochas | Measurement of Dynamic Light Scattering Intensity in Gels[END_REF] The large difference in the corresponding intensity correlation functions G(τ)-1 is shown in the inset in this figure. Measurements made with an argon ion laser working at λ=488 nm. Upon multiplication by the scattering intensity factor K=4.48 10 -7 mole cm 2 /g 2 , the intercept of the extrapolated lines (c=0, q 2 =0) with the ordinate axis at c/<I d (q=0,t)> = 4.125 g cm -2 , yields the inverse of the weight average molecular weight M W = 540 kDa. The slopes of the lines at constant c (almost horizontal in this figure) give for the radius of gyration R G =23.1 nm, while those at constant q 2 (steep lines) yield the interaction parameter A 2 =2.5 10 -4 cm 3 mole g -2 . In this figure q 0 = (4πn/λ)sin(θ/2), with θ = 150º. Solid and empty symbols designate successive values of c. Figure 4 is an example of the DLS response of another gel system, an agarose hydrogel with rigid chains containing mobile dextran molecules. [START_REF] Kloster | Dynamics of a Polymer Solution in a Rigid Matrix[END_REF] It shows how the molecular weight of the trapped molecules can be determined by means of this technique. The results are displayed in this figure using a Zimm plot, described in Eq. 16 for the more common case of dilute solutions of macromolecules. In this figure the product c/<I d (t)> is plotted as a function of q 2 + Bc, where the constant B is chosen to make the image span a scale similar to that of q 2 . The least squares straight line fits at constant c and constant q are each extrapolated to c=0 and q=0 to yield 1/KM w , where K is the contrast factor in Eq. 16. The slopes of the lines respectively define the second virial coefficient A 2 and the radius of gyration R G . §6. SOFT GELS AND INHOMOGENEOUS SOLUTIONS

In contrast to the above procedure, an interesting approach in which laser light scattering is used to evaluate simultaneously the osmotic modulus as well as the static architecture of a polydimethyl siloxane gel swollen in benzene and in toluene was reported [START_REF] Soni | Light Scattering Studies of Poly(dimethylsiloxane) Solutions and Swollen Networks Macromolecules[END_REF]. In this study, instead of recording the light scattered from a single coherence area, the detector aperture is opened to accept a large number of speckles, thus generating an ensemble average of the light scattered by the sample. [START_REF] Pusey | Dynamic light scattering by non-ergodic media[END_REF] This is equivalent to the standard static light scattering procedure with an incoherent source. While this choice of configuration loses the time dependence of the response and hence cannot discriminate between fast and slow modes, the authors were nevertheless able to verify a specific theoretical model for the soft gel studied. Other observations, based on exhaustive investigations of the statistical distribution of the speckles, have been reported in hydrogels [START_REF] Pusey | Dynamic light scattering by non-ergodic media[END_REF][START_REF] Feng | Dynamic Light Scattering by Permanent Gels: Heterodyne and Nonergodic Medium Methods of Data Evaluation[END_REF][START_REF] Shibayama | Swelling/Shrinking and Dynamic Light Scattering Studies on Chemically Cross-Linked Poly(vinyl alcohol) Gels in the Presence of Borate Ions1[END_REF]. These lengthy studies, although yielding relative values of the scattered intensity, nevertheless did not evaluate the osmotic moduli of the gels.

With soft gels, where the elastic modulus G is small, heating effects from the incident laser beam can perturb the network structure, making it difficult for the resulting static intensity I s (t) to remain constant during the measurement, and thereby to satisfy the condition <I s 2 (t)> = <I s (t)> 2 . Even without external heating effects network fluctuations still tend to occur, and the correlation function Eq. 25 then becomes

G(τ)-1 = β[2X(1-X) g(τ)+X 2 g 2 (τ) + (1-X) 2 f 2 (τ)] (29)
where f(τ) is the field correlation function of the light scattered by the more slowly moving network structure.

When the relaxation rate of the field correlation function g(τ) of the osmotic fluctuations is much greater than that of the network structure, f(τ), it becomes possible under certain conditions to discriminate between them. However, the value of X remains poorly defined and it is therefore important that over the experimental accumulation time the network structure fluctuations explore a statistically significant number of configurations to satisfy the condition f(τ ->∞)=0. If this is not the case it is possible in principle to rotate the sample at a rate much slower than the fast relaxation decay g(τ). A custom designed electric motor for this purpose could for example prove preferable to tedious step-by-step ensemble averaging. The decomposition of the full correlation function could then be performed in principle by using a Laplace transform procedure such as CONTIN [START_REF] Provencher | CONTIN: A general purpose constrained regularization program for inverting noisy linear algebraic and integral equations[END_REF], bearing in mind that the more slowly relaxing mechanism heterodynes the faster relaxation process. This is the situation of inhomogeneous solutions. Without further information, however, Eq. 29, unlike Eq. 25, does not allow an analytical solution. Again, an inverse Laplace transform approach could in principle be used to resolve the different components of Eq. 29. If, however, the two processes have clearly distinct relaxation rates, such as for example in semi-dilute solutions of polyelectrolyte, where the fast relaxation process characterises a "breathing" mode in which the solvent and the polymer exchange positions, and the slow mode describes the motion of large, slowly moving associations of polymers diffusing through the solution, then manual separation of the two modes becomes possible. For example, the last term on the right hand side of Eq. 29 can often be replaced by an approximation that represents the size distribution of the polymer associations diffusing in the solution. Figure 5 illustrates this second approach in an aqueous solution of chondroitin sulphate, using a stretched exponential expression of the form exp[-(2Γ s τ) µ ] to describe the last term, in which the exponent µ<1. [START_REF] Horkay | Chondroitin Sulfate in Solution: Effects of Mono-and Divalent Salts[END_REF] Figure 5 calls for several comments. First, [G(τ)-1]/β does not reach the theoretical value 1 at small τ. This discrepancy is not, as implicitly and incorrectly assumed in reference 24, the consequence of static scattering from the liquid sample, but is due to depolarised scattered light. (No polariser was placed before the detector in this part of the measurements.) As already noted, depolarised light, which acts as an incoherent source, merely adds to the total scattering intensity. In this case, where it amounts less than 2.5% of the total, it affects <I d > and <I s > equally and therefore does not affect the ratio X. It is therefore reasonable to re-normalise the amplitude of the response [G(0)-1]/β to 1. The best fit to the amplitude of stretched exponential term then yields (1-X) 2 =0.897. Secondly, while at delay times τ longer than the characteristic relaxation time of the slowly varying reference intensity I s (t) the amplitude of its electric field E s (t) is no longer correlated with that of the osmotic contribution E d (t), the phases of the two electric fields nevertheless remain synchronous and E s (t) continues to heterodyne. This means that the intensity correlation function [G(τ)-1]/β continues to build up at all delay times τ as before, and the quantity X 2 in Eq. 29 remains unchanged. In Fig. 5 it can also be seen that at delay times τ greater than 1 s the value of [G(τ)-1]/β still displays incompletely averaged noise owing to the short experimental acquisition time (200s).

The above analysis allows us to evaluate the collective diffusion coefficient D c = Γ/q 2 of the polyelectrolyte solution and the intensity <I d (t)> of the osmotic mode in this sample, and compare these values with those previously cited in reference 24. At θ=150º, with λ=632.8 nm, q 2 =6.608 10 10 cm -2 . The slope of the exponential decay in the inset of Fig. 5, therefore yields D c =1.06 10 -6 cm 2 s -1 , agreeing, within experimental error, with that previously quoted for this sample, 1.09 10 -6 cm 2 s -1 . From Eq. 28 we can now calculate the value of the hydrodynamic correlation length of the corresponding osmotic fluctuations in this sample, namely ξ H = 2.3 nm (30) The Rayleigh condition for light scattering for small particles that the ratio ξ H /λ <<1 is thus largely satisfied. It follows that the light scattered by the osmotic fluctuations is independent of angle θ.

The intensity of the light scattered by the fast osmotic fluctuations is then, from Eq. 20

<I d (t)> = X sinθ CR sample Ι tol /MON sample (31)
where CR sample =297238 counts/s and MON sample =335200 counts/s. Here I tol is the normalised expression I tol =ΔR tol CR tol /MON tol This yields the value <I d (t)> = 2.13 10 -3 m -1 (32) in acceptable agreement with that found in reference 24 for this sample, namely (2.03±0.12) ×10 -3 m -1 . Unlike the situation described in Figure 4, where R G , although small, is not very much smaller than λ, in the present case, extrapolation of the measurements to q=0 is therefore unnecessary. The present findings therefore remain consistent with the previously stated value of the osmotic modulus, namely κ os =(2.52±0.15) 10 5 Pa.

We are now in a position to discuss the slow mode f 2 (τ) in Figure 5. Large scale domains or clusters have long been observed in polyelectrolyte solutions and are a subject of controversy. [START_REF] Gan | Enhanced low-angle scattering from moderately concentrated solutions of atactic polystyrene and its relation to physical gelation[END_REF][START_REF] Sedlák | The ionic strength dependence of the structure and dynamics of polyelectrolyte solutions as seen by light scattering: The slow mode dilemma[END_REF][START_REF] Borsali | Small-angle neutron scattering and dynamic light scattering from a polyelectrolyte solution[END_REF][START_REF] Ermi | Domain Structures in Low Ionic Strength Polyelectrolyte Solutions[END_REF][START_REF] Sedlák | Real-time monitoring of the origination of multimacroion domains in a polyelectrolyte solution[END_REF] Although in reference 24 the structure of the clusters in the polyelectrolyte chondritin sulphate solutions was not investigated, the stretched exponential form found for f(τ) implies that the particles participating in the slow motion possess a broad size distribution. This view is reinforced by Figure 6, which shows the intensity of the slowly varying component <I s (q,t)>, normalised by the polymer concentration, and plotted in the double logarithmic representation log[<I s (q,t)>/c] vs log(q). It is notable that the data for the different concentrations lie on a closely similar curve, indicating that in this overlapping coil regime the intensity of this feature is essentially proportional to the polyelectrolyte concentration. Furthermore, in this representation, the data obey a simple power law, which means that in the q range explored no length scale R G is detectable. In particular, the absence of curvature at low q signifies that R G is considerably in excess of 100 nm. Owing to the inverse relationship between the scattered intensity and the osmotic modulus (Eq. 7), this finding means that the osmotic contribution coming from the slow mode <I s (q=0> is several orders of magnitude smaller than that of the polyelectrolyte breathing mode, which overwhelmingly dominates the osmotic pressure. Interestingly, although the DLS data of Fig. 6 extend to values of q appreciably lower than those attained by the small angle neutron scattering measurements in ref. [START_REF] Horkay | Chondroitin Sulfate in Solution: Effects of Mono-and Divalent Salts[END_REF], the observed power law slope, -3.0, faithfully reproduces that of the neutrons. They even extend well below the static light scattering measurements of reference [START_REF] Ermi | Domain Structures in Low Ionic Strength Polyelectrolyte Solutions[END_REF] in solutions of poly(N-methyl-2-vinylpyridinium chloride)., where, unlike here, a pronounced shoulder was detected at low q. §7 CONCLUSION DLS is a rich source of thermodynamic information not only from dilute polymer solutions or particles in suspension, but also from gels or inhomogeneous solutions. The examples selected here illustrate how DLS is substantially more powerful than just a means of measuring the rate of decay of the intensity correlation functions. They illustrate in particular the outstanding advantage that DLS possesses over traditional static light scattering: it offers a means of discriminating between different relaxation modes, and hence of measuring directly both the intensity and the osmotic modulus of each component. §8. ACKNOWLEDGMENTS The author acknowledges his deep debt and gratitude to numerous colleagues for many enlightening discussions, and particularly to the late Anne-Marie Hecht (Université Grenoble Alpes), to Ferenc Horkay (National Institutes of Health) and to Mark Sutton (McGill University) with whom he has benefitted from many fruitful discussions and collaborations.

Figure 1 .

 1 Figure 1. Static speckle pattern from laser light passing though a thin sheet of low density polyethylene. Vertical bar is shadow of beam stop to remove the direct laser beam.

Figure 2 .

 2 Figure 2.Total light scattering intensity <I(t)> measured in kHz as a function of angle θ in steps of 0.01 degree in a 0.1g/cm 3 polyacrylamide gel.[START_REF] Rochas | Measurement of Dynamic Light Scattering Intensity in Gels[END_REF] The intense static speckle structure (red curve) comes principally from the static structure and corresponds to the intensity variations similar to those shown in Fig.1. Unlike the scattering pattern from the dry polyethylene sample, however, the network chains in polyacrylamide hydrogels are free to fluctuate locally, exerting an osmotic pressure Π that keeps the gel swollen. Open blue circles are the corresponding intensity of the dynamic signal calculated from Eq. 26, from which the osmotic modulus is calculated via Eq. 7.

Figure 3 .

 3 Figure 3. Field correlation function g(τ) calculated from Eq. 27 for two neighbouring positions in the speckle pattern for the polyacrylamide gel having different ratios X of the dynamic to the total intensity. Inset: the corresponding intensity correlation functions G(τ)-1.[20]

Figure 4 .

 4 Figure 4. Zimm plot of dynamic light scattering intensity from a 5% agarose hydrogel containing solutions of dextran molecules of nominal molecular mass 500 kDa at four concentrations between c = 0.00065 g/cm 3 and 0.005 g/cm 3 .[21]Measurements made with an argon ion laser working at λ=488 nm. Upon multiplication by the scattering intensity factor K=4.48 10 -7 mole cm 2 /g 2 , the intercept of the extrapolated lines (c=0, q 2 =0) with the ordinate axis at c/<I d (q=0,t)> = 4.125 g cm -2 , yields the inverse of the weight average molecular weight M W = 540 kDa. The slopes of the lines at constant c (almost horizontal in this figure) give for the radius of gyration R G =23.1 nm, while those at constant q 2 (steep lines) yield the interaction parameter A 2 =2.5 10 -4 cm 3 mole g -2 . In this figure q 0 = (4πn/λ)sin(θ/2), with θ = 150º. Solid and empty symbols designate successive values of c.

Figure 5 .

 5 Figure 5. DLS intensity correlation function [G(τ)-1]/β, where β=0.97, obtained from a 10% chondroitin sulphate solution containing 100 mM NaCl, measured at θ = 150°.[24] Continuous blue line is the expression (1-X) 2 exp[-(2Γ s τ) µ ] in the best fit to Eq. 29. Inset: field correlation function g(τ) of the rapid component, calculated from Eq. 27 (after normalisation of [G(τ=0)-1]/β to 1 -see text), using the difference signal [G(τ)-1]/β -(1-X) 2 f 2 (τ)], with (1-X) 2 =0.897, i.e., X=0.0528.

Figure 6 .

 6 Figure 6. Double logarithmic representation of the slowly varying intensity component <I s (q,t)> in chondroitin sulphate solutions at different concentrations c. In this figure <I s (q,t)> is normalised by c, expressed as a weight fraction.


domain: chim spi

text:
Ali Maziz

Cedric Plesse

Caroline Soyer

Eric Cattan

Fredeŕic Vidal

Top-down Approach for the Direct Synthesis, Patterning, and Operation of Artificial Micromuscles on Flexible Substrates

Keywords: semi-IPN, conducting polymer, microactuator, flexible substrate, electrochemical microdevices

Recent progress in the field of microsystems on flexible substrates raises the need for alternatives to the stiffness of classical actuation technologies. This paper reports a top-down process to microfabricate soft conducting polymer actuators on substrates on which they ultimately operate. The bending microactuators were fabricated by sequentially stacking layers using a layer polymerization by layer polymerization of conducting polymer electrodes and a solid polymer electrolyte. Standalone microbeams thinner than 10 μm were fabricated on SU-8 substrates associated with a bottom gold electrical contact. The operation of microactuators was demonstrated in air and at low voltage (±4 V).

E lectronic conducting polymers (ECPs) are promising candidates for the development of artificial muscles. When immersed in an electrolytic solution, these materials can convert low voltage stimulations into volume or shape changes through redox reactions. [START_REF] Baughman | Conducting Polymer Artificial Muscle[END_REF][START_REF] Smela | Conjugated Polymer Actuatorsfor Biomedical Applications[END_REF] E. Smela et al. demonstrated the potential of these actuators using microfabrication 20 years ago. [START_REF] Smela | Microfabrication of PPy Microactuators and other Conjugated Polymer Devices[END_REF][START_REF] Jager | Polypyrrole Microactuators[END_REF][START_REF] Jager | Microfabricating Conjugated Polymer Actuators[END_REF] These microactuators operated only in a liquid electrolyte and could suffer from delamination problems.

To operate outside an electrolyte, two ECP electrodes are usually synthesized simultaneously on both faces of membrane, a so-called solid polymer electrolyte (SPE) which acts as an "ion reservoir" (Figure 1A). [START_REF] Otero | Artificial Muscles with Tactile Sensitivity[END_REF] Under low applied voltage, inverse volume variation occurs in both electrodes and leads to reversible bending deformations. The delamination issues were then overcome using either a commercial porous or synthesized membranes as SPE. [START_REF] Wu | Fast Trilayer Polypyrrole Bending Actuators for High Speed Applications[END_REF] Despite this progress, the fabrication of open-air actuation devices was only recently demonstrated on a microscale. [START_REF] Alici | Conducting Polymer Microactuators Operating in Air[END_REF][START_REF] Khaldi | Conducting Interpenetrating Polymer Network Sized to Fabricate Microactuators[END_REF][START_REF] Gaihre | Synthesis and Performance Evaluation of Thin Film PPy-PVDF Multilayer Electroactive Polymer Actuators[END_REF][START_REF] Maziz | Demonstrating kHz Frequency Actuation for Conducting Polymer Microactuators[END_REF] However, their fabrication process was directly inspired by their macroscopic equivalent. Manual handling is required, which limits further scaling down (less than 10 μm thick) and makes it difficult and time-consuming to create many devices in parallel.

Other possible manufacturing methods such as layer-by-layer casting or inkjet printing, nowadays used in organic electronics, are not suitable for ECP microactuators since they require the use of soluble materials or a colloidal dispersion. Although the best candidates for ECP-based actuators (polypyrrole (PPy) and poly(3,4-ethylenedioxythiophene) (PEDOT)) are not normally soluble in any solvent, their soluble or colloidal dispersion versions (PPy-(2-ethylhexyl)sulfosuccinate PPy-DEHS, PEDOT-polystyrenesulfonic acid PEDOT-PSS) do not attain the same level of performance.

A global rethink of the fabrication process is therefore required to achieve the real integration of ECP-based microactuators and allow further development in microrobotics, for example.

To achieve this goal, we report on a new and versatile method of synthesis that is fully compatible with microsystems technologies, to design and operate ECP micromuscles in open air on a soft substrate (Figure 1B). The ECP/SPE/ECP trilayers were first obtained by successively polymerizing layers on top of each other, followed by a final intralayer cross-linking and interlayer cobonding (Figure 2A). The first and last layers were obtained using vapor phase polymerization (VPP) of 3,4ethylenedioxythiophene (EDOT) and the intermediate SPE layer was synthesized as a semi-interpenetrating polymer network (semi-IPN) combining a poly(ethylene oxide) PEO network as the SPE and nitrile butadiene rubber (NBR) for mechanical strength. [START_REF] Klempner | Interpenetrating Polymer Networks[END_REF][START_REF] Vidal | Long-Life Air Working Conducting Semi-IPN/Ionic Liquid Based Actuator[END_REF] The additional subtlety of the process derives from the presence of methacrylate cross-linkers in each synthesized layer allowing the final cobonding and preventing de facto any delamination issues. Finally, the compatibility of these novel electroactive materials with conventional micropatterning methods will be demonstrated. Furthermore, the process allowed direct integration of electrical connections for the first time, leading to the direct operation of microactuators on flexible substrates.

The first thin layer of ECP is described in detail below because of the specific chemistry used and its importance in the final structure. Active research is currently underway on the synthesis of ECP layers using VPP, in particular to obtain highly conductive layers. [START_REF] Winther-Jensen | Vapor Phase Polymerization Of Pyrrole And Thiophene using Iron(III) Sulfonates as Oxidizing Agents[END_REF][START_REF] Winther-Jensen | Base Inhibited Oxidative Polymerization of 3,4-ethylenedioxythiophene with Iron-(III)Tosylate[END_REF][START_REF] Fabretto | Polymeric Material with Metal-Like Conductivity for Next Generation Organic Electronic Devices[END_REF] However, no work has yet been reported on the use of polar monomers as additives in the synthesis of such ECP layers. The presence of polyethylene glycol methacrylate derivatives (MPEG) is a key element here because these will act as PEO network precursors to ensure adhesion between the layers of the final micromuscles. VPP of EDOT was therefore studied first. It was performed by means of direct chemical oxidation using the commercially available Baytron C Iron(III) tosylate Fe(Tos) 3 (40% by weight in butanol), because this oxidant is known to produce highly conducting PEDOT films. [START_REF] Fabretto | Polymeric Material with Metal-Like Conductivity for Next Generation Organic Electronic Devices[END_REF] To this solution was added 10 wt % poly(ethylene glycol)methyl ether methacrylate (PEGM) (5%) and poly(ethylene glycol)dimethacrylate (PEGDM) (5%) as a monomer and cross-linker, respectively. The oxidant mixture was spin-coated on a poly(vinyl alcohol) (PVA)-coated silicon substrate, which was then placed in a gas-phase polymerization chamber together with a vessel containing EDOT (see Figure S1). The polymerization chamber was then sealed in a vacuum at 40 °C to speed up the process. After this EDOT vapor phase polymerization step, PEDOT-MPEG layers, i.e., PEDOT electrodes containing PEG-based monomers were obtained. The MPEG can therefore be either (i) directly rinsed with methanol, (ii) polymerized by free-radical polymerization before the washing step, leading to PEDOT-PEO composite electrodes, or (iii) left as it is in the PEDOT for subsequent trilayer fabrication.

When MPEG was rinsed directly, the electrical conductivity of the PEDOT layer was measured in order to assess the quality of the electrodes (Figure 2C). The conductivity showed a maximum of around 400 S cm -1 for EDOT VPP times shorter than 60 min, and then decreasing gradually to 100 S cm -1 as the polymerization time increased to 150 min. Indeed, a longer polymerization time may result in higher structural disorder in the polymer. This eventually leads to a 3D conduction pathway that reduces charge transport and results in higher resistance on the upper polymer surface, as observed in the case of PEDOT. [START_REF] Ugur | Low-Dimensional Conduction Mechanisms in Highly Conductive and Transparent Conjugated Polymers[END_REF] Concomitantly, PEDOT film thicknesses increased from 0.64 to 1.1 μm( Figure 2D).

Interestingly, although a conductivity of 391 S cm -1 was obtained for 30 min of polymerization in the presence of 10 wt % MPEG, it only reached 22 S cm -1 for a PEDOT layer synthesized without MPEG (see Figure S2). This result can be explained by recent work showing that the addition of a glycolbased surfactant to the Fe(Tos) 3 solution has a positive effect on the synthesis of highly conducting PEDOT. [START_REF] Zuber | Improved PEDOT Conductivity via Suppression of Crystallite Formation in Fe(III)-Tosylate During Vapor Phase Polymerization[END_REF][START_REF] Fabretto | High Conductivity PEDOT Resulting from Glycol/Oxidant Complex and Glycol/Polymer Intercalation during Vacuum Vapour Phase Polymerisation[END_REF] Indeed, the use of such glycol-based surfactant/oxidant media reduces the number of defects along the conjugated backbone of the polymer by suppressing Fe(Tos) 3 oxidant crystallization, as well as controlling the polymerization rate.

The influence of in situ free radical polymerization of MPEG on the resulting PEDOT layer was also characterized. For that purpose, a free radical initiator was introduced into the oxidant solution with the MPEG before EDOT VPP. The selected initiator was dicyclohexylperoxydicarbonate (DCPD) (3 wt % vs. MPEG). After EDOT VPP times of 30 and 120 min, MPEG was polymerized at 50 °C for 4 h and then for 2 h at 80 °C, leading to an interpenetrated PEO network within the PEDOT film. Polymerization of MPEG resulted in so-called PEDOT-PEO electrodes that were thicker than the corresponding PEDOT without MPEG (Table 1). However, the polymerization of MPEG also led to a significant decrease in electronic conductivity, i.e., from 391 without polymerization to 75 S cm -1 after polymerization for the PEDOT layer obtained after 30 min of EDOT VPP. The sample obtained after 120 min VPP polymerization displayed the same behavior (from 192 to 51 S cm -1 )( Table 1). This negative effect can be explained by the loosening of the PEDOT packing by the cross-linked PEO polymer, [START_REF] Shaplov | Truly Solid State Electrochromic Devices Constructed from Polymeric Ionic Liquids as Solid Electrolytes and Electrodes Formulated by Vapor Phase Polymerization of 3,4-ethylenedioxythiophene[END_REF] but can also be related to the partial degradation of PEDOT during polymerization. Indeed, previous studies have shown that oxygen radicals can induce PEDOT degradation. [START_REF] Verge | Thermal Ageing of Poly-(ethylene oxide)/Poly(3,4-ethylenedioxythiophene) Semi-IPNs[END_REF] In this study, MPEG free radical copolymerization involved homolytic decomposition of the DCPD initiator to produce alkoxy radicals. Oxygen radicals can thus react with PEDOT leading to the partial rupture of the conjugation in the backbone, hence the loss of electroactivity even though it remains relatively high and sufficient for actuator implementation. Next, the complete trilayer structure can be synthesized directly on the substrate. The solid polymer electrolyte layer, which will subsequently act as an "ion reservoir" for the device, was then deposited on top of a PEDOT layer containing nonpolymerized MPEG monomers. The solid polymer electrolyte is based on a semi-IPN architecture (Figure 2A) and combines the ion transport properties of a PEO network and the mechanical properties of a linear NBR. The PEO/NBR 50/ 50 (w/w) semi-IPN was obtained as described in the experimental section and elsewhere. [START_REF] Maziz | Demonstrating kHz Frequency Actuation for Conducting Polymer Microactuators[END_REF] Briefly, all the semi-IPN precursors, i.e., MPEG and NBR, as well as the free radical initiator DCPD, were solubilized in cyclohexanone, a high boiling point solvent. The reactive mixture was spin-coated on the bottom PEDOT-MPEG layer. The two layers were then preprocessed in a vacuum at 50 °C for 45 min to initiate the formation of the PEO network present in each layer and to ensure good mutual adhesion by the polymerizing monomers at the interface. However, complete conversion of methacrylate functions must be avoided to allow the final covalent linking between the semi-IPN layer and the next PEDOT layer (see Figure S4). Finally, the second VPP PEDOT-MPEG layer can be synthesized on the bilayer in the same way as the first conducting layer. Annealing for 4 h at 50 °C and 2 h at 80 °Cin a vacuum was carried out to polymerize the methacrylate within the layers but also at the interfaces. The cobonded trilayer was then washed several times in 1-Butanol. The trilayer morphology of the resulting structure was confirmed by scanning electron microscopy (Figure 2B). Energy-dispersive X-ray spectroscopy (EDS) mapping was used to distinguish the sulfur content in PEDOT and shows that the conducting PEDOT-PEO electrodes and PEO-NBR semi-IPN electrolyte layers are connected seamlessly, thereby facilitating intra-and interlayer ion transport, which is essential for the correct operation of an electrochemical device. Conventional microfabrication techniques were then used to design trilayer in parallel devices. Material patterning was performed by means of photolithography and reactive ion etching (RIE) (Figure 3A). The positive photoresist SPR220-7 μm was spin-coated to be used as an etching mask. Dry etching was then performed using RIE (more details are available in the Supporting Information). [START_REF] Khaldi | Conducting Interpenetrating Polymer Network Sized to Fabricate Microactuators[END_REF][START_REF] Maziz | Demonstrating kHz Frequency Actuation for Conducting Polymer Microactuators[END_REF] A high etch rate (1.3 μm min -1 ) and good selectivity (1.85) were obtained using the 90/10 O 2 / CF 4 gas ratio (Figure 3B). In these conditions, as illustrated in Figure 3C, D, microfabrication of trilayer microstructures can be performed with precise control of the geometry, size and shape. The proof of concept presented in Figure 3E contains 500 ECP elements with diameters ranging from 500 to 5 μm and lengths from 3000 to 50 μm. In other words, large-scale batch fabrication of precisely defined ECP-based microelectrochemical devices can be performed directly on a Si substrate.

The last step in demonstrating actuation of ECP micromuscles on flexible substrates was to fabricate and pattern such structures, as described earlier, on top of a specifically designed wafer. Figure 4A illustrates the process sequences. Considering that microbeams must be produced in standalone form with integrated electrical contacts, a specific process must be set up. Thus, a locally UV-exposed/cross-linked epoxy-based photoresist SU-8 was chosen as the flexible substrate and will act as the fulcrum for microbeam actuators (Figure 4A.2). Base gold electrodes were then patterned on top of the cross-linked SU-8 layer to form stable electrical connections for flexion producing muscles (Figure 4A.3. Because of solubilization of the noncross-linked SU-8 photoresist during the development of the gold electrodes, a PVA sacrificial layer was used to fill the remaining 90 μm deep cavity (Figure 4A.4). The structure was ready to be coated with a PEDOT/PEO-NBR/PEDOT trilayer and then patterned as described previously (Figure 4A.5, 6 and Figure 4B). Finally, the PVA sacrificial layer was dissolved in water to release the microbeams locally (Figure 4A.7) (more details are available in the Supporting Information). The ions required for the redox process of the conducting polymer electrodes were then incorporated through a swelling step, turning these microstructures into electroactive micromuscles. N,N-ethylmethylimidazolium bis(trifluoromethanesulfonyl)imide (EMITFSI) ionic liquid was chosen as the electrolyte. Standalone electroactive polymer microbeams were then obtained: the base of the device rests on an SU-8 flexible surface with gold electrodes integrated on the base (Figure 4C. A micromechanical gold tip was positioned on top of the trilayer to make the second electrical connection. A demonstration of air-operation of the micromuscles directly on SU-8 is presented. The microdevices were characterized by their maximum performances, i.e., maximum displacement, expressed in terms of free strain, and maximum output force. The free strain as a function of the electrical stimulation frequency under ±4.0 V square wave potential is shown in Figure 4D. Bending toward the anode can be observed during actuation indicating a volume contraction during oxidation. This behavior indicates that cation motion is the main driving mechanism in this material as it has been shown on macro devices. [START_REF] Festin | Robust Solid Polymer Electrolyte for Conducting IPN Actuators[END_REF] Thus, the electrodes switch from an expanded reduced state to a contracted oxidized one. In the low frequency region (0.05-0.2 Hz), the microbeams show a maximal free strain of 0.13%, corresponding to a peak-to-peak displacement of 127 μm ± 6 μm for a 650 μm long beam. At such low frequencies, the two electroactive PEDOT layers are fully oxidized and reduced, leading to maximum charge transfer and then to maximum bending displacement. For frequencies up to 10 Hz, the microactuator showed a linear decrease in mechanical response. This indicates that less and less PEDOT undergoes the redox process and is then involved in the actuation as the frequency increases. Nonetheless, at 1 Hz, the microbeams still present significant mechanical amplitude of 0.03%. Figure 4E shows both the tip displacement and output force as a function of time measured for 20 repeated cycles at 1 Hz. Interestingly, this micromuscle produces a fast mechanical response with a free displacement of 32 μm and a maximum output force of 0.75 μN.

To summarize, this work proposes a novel and versatile approach to fabricate, pattern, and operate solid-state electro- chemical micromuscles directly on flexible surfaces through processes fully compatible with microsystems. The cobonded trilayer structures are fabricated by innovative sequential layer stacking. The two PEDOT electrodes were obtained by vapor phase polymerization and the intermediate SPE layer as a PEO-NBR semi-interpenetrating polymer network. These materials have been successfully patterned using photolithography and RIE techniques and are easily scalable for the simultaneous batch-production of microdevices with hundreds of electromechanical structures. We have demonstrated that they can be directly synthesized on an SU-8 flexible substrate with integrated electrical connections. Under low voltage, the resulting microbeams have a strain of up to 0.13% and output forces just under 1 μN. To the best of our knowledge, this is the first time that electrochemical micromuscles operating in air have been manufactured on a flexible substrate, eliminating risky multistage processing typically reflected in the literature to date. Further studies are still in progress and are focused on the actuation speed and on the size dependence of the actuator responses. These results open up new prospects for the accurate and cost-effective production of fully flexible microelectromechanical systems. Moreover, such an approach could be easily extended to a more general procedure by varying the choice of functional materials and their synthesis conditions. Indeed, numerous other electrochemical microdevices such as sensors, optoelectrical devices, supercapacitors, or microbatteries with a trilayer structure could be designed, leading to new prospects for flexible microsystems.

ASSOCIATED CONTENT Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.5b09577.

Description of the material, experimental data about the effect of MPEG on PEDOT electrical conductivity, experimental details about the top-down fabrication of standalone trilayer microactuators, additional scanning electron microscopy images (PDF)

Figure 1 .

 1 Figure 1. (A) Working principle of open-air macroscopic artificial muscles based on conducting polymers. (B) General structure of the integrated micromuscles on flexible substrate.

Figure 2 .

 2 Figure 2. (A) On-substrate fabrication process of the PEO-NBR-PEDOT conducting semi-IPN. (B) SEM image of nonswollen trilayer structure and (B′) corresponding EDS picture with sulfur atom cartography (red). (C) Influences of polymerization time on electrical conductivity and (D) on film thickness of PEDOT film synthesized in the presence of 10 wt % of MPEG.

Figure 3 .

 3 Figure 3. (A) Dry etching process of trilayer actuators on silicon substrate. (B) Etching rates and selectivity of PEDOT, PEDOT-PEO, PEO-NBR semi IPN, and PEDOT-PEO-NBR conducting semi IPNs in plasma of 90/10 O 2 /CF 4 at 300 W and 200 mTorr. (C) SEM image of trilayer microstructures and (D) the corresponding zoom-in SEM image. (E) Image of the trilayer microstructures on PVA-coated 2 in. Si substrate. The inset show the trilayer coated substrate before microfabrication.

Figure 4 .

 4 Figure 4. (A) Top-down fabrication process of trilayer microactuators on flexible substrate, (B) images of microactuators after batch microfabrication, (C) standalone microactuator on SU-8 substrate, (D) free strain as a function of frequency of the microactuator (Lwh: 650 μm × 100 μm × 10 μm) under ±4 V square wave potential, (E) tip displacement and output force versus time at 0.2 Hz.

Table 1 .

 1 Influence of MPEG Free Radical Copolymerization on PEDOT Properties

	thickness (μm)	electrical conductivity (S cm -1 )

*

Washing with methanol leads to the extraction of MPEG from the PEDOT film.

ACKNOWLEDGMENTS

The authors thank the ANR for its financial support (Grant ANR-09-BLAN-0110) and the European Network on Artificial Muscles (ESNAM). This work was partly supported by the French RENATECH network.

AUTHOR INFORMATION

Corresponding Author E-mail: eric.cattan@univ-valenciennes.fr.

Notes

The authors declare no competing financial interest.


Ngoc Tan Nguyen

Mirza Saquib Sarwar

Claire Preston

Aziliz Le Goff

Cédric Plesse

Frédéric Vidal

Eric Cattan

John D W Madden
email: jmadden@ece.ubc.ca

Transparent stretchable capacitive touch sensor grid using ionic liquid electrodes

Low cost soft, flexible and stretchable sensors are being explored that can be applied to virtually any surface, and promise to enable tactile sensing on robots, prosthetics, skin and stretchable displays. Previous work has shown that capacitive sensors that are both stretchable and transparent can be created by using ionically conductive hydrogel electrodes. In this study, the electrodes are interpen-etrating polymer networks swollen with ionic liquid, enabling high transparency and stretchability, without evaporation. The interpenetrating network is synthesized from poly(ethylene oxide) and nitrile butadiene rubber. Electrodes are patterned using femtosecond laser machining, creating stretchable electrodes. These were encapsulated in a polydimethylsiloxane substrate, producing a 95% transparent sensor (450 nm). A 4x4 tactile array shows the ability to sense proximity and multi-touch, as well as be robust to variations in environmental temperature (from 4 • C to 72 • C). Temperature change has a large effect on the resistance of the electrodes -an effect that could be used to measure device temperature. In addition, the sensor is able to detect proximity and touch while on skin, when covered by a layer of fabric or during stretch.

Introduction

Transparent and stretchable touch sensors have attracted attention as they could be used to provide sensory feedback in applications ranging from common handheld consumer electronics to advanced robotics and even prosthetics. These applications involve frequent human computer interactions combining touch overlaid on a visual display [START_REF] Koo | Flexible and stretchable smart display: Materials, fabrication, device design, and system integration[END_REF], stretch and/or bend and preferably stability in the face of changing temperature [START_REF] Kim | Stretchable silicon nanoribbon electronics for skin prosthesis[END_REF]. In addition, it may be useful to enable human machine interaction through a layer of material such as clothes. Two main approaches are capacitive and resistive sensing.

Various methods have been attempted to develop transparent and stretchable electrodes. They can be classified into three categories: geometric design of less stretchable materials, composite materials of conducting nanomaterials with stretchable elastomeric polymers, and the synthesis of intrinsically conducting polymers that are highly stretchable. In the first group, the stretchability of the electrodes can be achieved by patterning inorganic conductive materials like metals in a serpentine-like architecture [START_REF] Kim | Stretchable, transparent graphene interconnects for arrays of microscale inorganic light emitting diodes on rubber substrates[END_REF][START_REF] Yang | Indium Tin Oxide (ITO) serpentine ribbons on soft substrates stretched beyond 100%[END_REF][START_REF] Han | Fast plasmonic laser nanowelding for a Cu-nanowire percolation network for flexible transparent conductors and stretchable electronics[END_REF][START_REF] Liu | Carbon nanotube yarns with high tensile strength made by a twisting and shrinking method[END_REF], or depositing thin layers of silver nanowires (AgNW)s, carbon nanotubes (CNT)s or graphene [START_REF] Cai | Carbon nanotube flexible and stretchable electronics[END_REF][START_REF] Xu | Wavy ribbons of carbon nanotubes for stretchable conductors[END_REF] on elastomeric substrates that can be extended when the substrate underneath is stretched -or by pre-straining substrates [START_REF] Zhang | Experimental and theoretical studies of serpentine microstructures bonded to prestrained elastomers for stretchable electronics[END_REF]. A second route to obtain transparent and stretchable electrodes is the employment of nanocomposite materials such as AgNWs or CNTs mixed with elastomeric polymers such as PDMS or polyurethaneurea [START_REF] Lipomi | Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes[END_REF][START_REF] Chen | High-performance transparent and stretchable all-solid supercapacitors based on highly aligned carbon nanotube sheets[END_REF][START_REF] Kim | Silver nanowire network embedded in polydimethylsiloxane as stretchable, transparent, and conductive substrates[END_REF]. The third approach uses conducting polymers [START_REF] Vosgueritchian | Highly conductive and transparent PEDOT:PSS films with a fluorosurfactant for stretchable and flexible transparent electrodes[END_REF][START_REF] Li | Stretchable and conductive polymer films prepared by solution blending[END_REF] which are solution-process-able and pattern-able, to attain highly stretchable electrodes. In all these approaches, conductive materials must be kept very thin in order to maintain transparency. There is a challenge in combining soft stretchable materials and with stiff conductors. Even the conducting polymers are quite stiff and can only be stretched slowly. Nevertheless, devices fabricated using these stretchable conductor technologies have shown the ability to either detect touch [START_REF] Someya | Flexible pressure sensor matrix with organic field-effect transistors for artificial skin applications[END_REF][START_REF] Hu | Elastomeric transparent capacitive sensors based on an interpenetrating composite of silver nanowires and polyurethane[END_REF][START_REF] Mirza Saquib Sarwar | Transparent and conformal 'piezoionic' touch sensor[END_REF], stretch [START_REF] Han | Fast plasmonic laser nanowelding for a Cu-nanowire percolation network for flexible transparent conductors and stretchable electronics[END_REF][START_REF] Liu | Carbon nanotube yarns with high tensile strength made by a twisting and shrinking method[END_REF][START_REF] Lipomi | Skin-like pressure and strain sensors based on transparent elastic films of carbon nanotubes[END_REF][START_REF] Pang | A flexible and highly sensitive strain-gauge sensor using reversible interlocking of nanofibres[END_REF], bending [START_REF] Park | Stretchable energy-harvesting tactile electronic skin capable of differentiating multiple mechanical stimuli modes[END_REF], or all three -but without the ability to distinguish between them [START_REF] Sun | Ionic skin[END_REF].

A fourth approach is to use ionic conductors. Ionic conductors can be both highly stretchable (by as much as 21x when tough hydrogels are employed) and extremely transparent (95%) [START_REF] Keplinger | Stretchable, transparent, ionic conductors[END_REF]. The carriers -ions -have very low mobilities, and so are only suitable for applications involving small currents. Fortunately, capacitive sensors use only very low currents. These conductors are transparent because, unlike electrons and holes, they are so massive that they hardly move at visible light frequencies. They have been employed as stretchable electrodes in pressure sensors, electric-field driven actuators [START_REF] Sun | Ionic skin[END_REF], and resistive touch sensors [START_REF] Kim | Highly stretchable, transparent ionic touch panel[END_REF]. In our previous work [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF], we demonstrated the use of a hydrogel electrode to perform proximity sensing, just as is done on most touch screens. A form of projected capacitance called mutual capacitance is used, in which field lines projected beyond the surface of the device couple with a finger or other approaching objects. The array detects a touch, and multi-touch, but is relatively insensitive to stretch and bend. A disadvantage of the approach is susceptibility to evaporation -which can be reduced by adding hygroscopic salts, but at the expense of conductivity [START_REF] Floch | Wearable and washable conductors for active textiles[END_REF] and, in turn, practical array size [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF].

Building on this work, we demonstrate a mutual capacitancebased sensor that uses a semi-interpenetrating network (semi-IPN) polymer containing ionic liquid (IL) as electrodes. Advantages of this material combination include the ability to withstand high temperatures (180 • C in the case of ionic liquid used [START_REF] Goujon | Flexible solid polymer electrolytes based on nitrile butadiene rubber/poly(ethylene oxide) interpenetrating polymer networks containing either LiTFSI or EMITFSI[END_REF]), stretchability (140% [START_REF] Mecerreyes | Applications of Ionic Liquids in Polymer Science and Technology[END_REF]) and absence of evaporation. Among different types of semiIPNs, such as poly(ethylene oxide)/ hydroxytelechelic polybutadiene [START_REF] Plesse | Poly(ethylene oxide)/polybutadiene based IPNs synthesis and characterization[END_REF], poly(ethylene oxide)/ polytetrahydrofurane [START_REF] Plesse | Polyethylene oxide-polytetrahydrofurane-PEDOT conducting interpenetrating polymer networks for high speed actuators[END_REF], poly(ethylene oxide)/ nitrile butadiene rubber (PEO/NBR) [START_REF] Marwanta | Improved ionic conductivity of nitrile rubber/ionic liquid composites[END_REF][START_REF] Ichino | New concept for polymer electrolyte: Dual-phase polymer electrolyte[END_REF], NBR/PEO semiIPN shows quite good ionic conductivity (up to 0.13 S/m), high strain at break (150%) [START_REF] Nicolas | Robust solid polymer electrolyte for conducting IPN actuators[END_REF], and a small Young's modulus (330 kPa) [START_REF] Tan | Nonlinear dynamic modeling of ultrathin conducting polymer actuators including inertial effects[END_REF]. In addition, the material shows good temperature stability. The ionic liquid incorporated into the semiIPN (1-Ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide: EMITFSI) has a decomposition temperature of 307 • C [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF], while the semiIPN itself can be stable up to 180 • C [START_REF] Nicolas | Robust solid polymer electrolyte for conducting IPN actuators[END_REF]. These features, in addition to a high transparency, render the material suitable for a stretchable and transparent electrode.

In this paper we demonstrate transparency; proximity, touch and multi touch sensing with and without bending and stretching; and mechanical durability. The sensor array is designed to sense the approach and presence of a finger, which will cause a decrease in measured capacitance. Other grounded objects or objects with a large capacitance, such as other parts of the body or metal wires connected to ground, will also reduce capacitance as they approach. The array is relatively insensitive to pressure, stretch and bend. Novel aspects are the stability of its ionically conductive electrodes, which do not evaporate, and the investigation of temperature sensitivity of the measurement, showing how the use of lower frequency excitation can be used to eliminate temperature dependence, and how high frequency measurements might be used to measure temperature.

Fabrication

The fabrication of the sensor is based on a simple spin coating method. SemiIPN electrodes are first spin coated and the laser machined. Successive spin coating of dielectric elastomer layers that sandwich the two electrode layers creates the full structure.

Fabrication of semiIPN electrodes

The semiIPN is composed of a PEO ionically conductive phase, interpenetrated with elastomer NBR, which provides good elastic properties -with the resulting semiIPN being swollen with EMITSFI ionic liquid, which provides ion charge carriers. The EMITFSI, and the PEO are much more transparent in comparison to the NBR, which has a light yellow color. Here, since we expect a highly transparent stretchable semiIPN electrode, the ratio of NBR to PEO in the semiIPN structure was reduced relative to previous work on actuators [START_REF] Nguyen | Ultrathin electrochemically driven conducting polymer actuators: fabrication and electrochemomechanical characterization[END_REF] to minimize the yellowish color -while also maintaining the high stretchability.

The fabrication process of semiIPN described in [START_REF] Nguyen | Ultrathin electrochemically driven conducting polymer actuators: fabrication and electrochemomechanical characterization[END_REF] is briefly summarized as follow: the NBR solution (16 wt% NBR and 84 wt% cyclohexanone) was mixed with PEO precursors (75 wt% PEGM and 25 wt% PEGDM), where the ratio between the NBR and PEO is varied from 20% to 50%. A free radical initiator DCPD (3 wt% of PEO precursors) was then added to the mixture, stirred for 15 min, and degassed. A homogeneous mixture was obtained and spin-coated (600 rpm, 300 rpm s -1 , 30 s) on top of a silicon wafer. The polymerization was carried out under continuous supply of N 2 at 50 • C for 4 h to enable the formation of the PEO network.

The resulting semiIPN membrane was then swollen in EMITFSI for 3 days to allow it to reach the maximum swelling state. Finally, the sample was patterned by a femtosecond laser (Oxford Lasers, UV fundamental wavelength: 1064 nm, pulse length: 400 fs, spot size: 10 µm, galvanometric mirror resolution: 1 µm, maximum power 2 W) with patterning conditions of 10% power, 1 mm/s cutting speed, and 10 cut such that passes and electrodes were obtained.

Fabrication of sensor

The sensor fabrication process is mainly based on a highly reproducible precision coating technique combined with the fast femtosecond laser patterning method, as shown in Fig. 1a. In general, this fabrication includes three-step process where the first PDMS was spin-coated on a glass wafer following the first four semiIPN stripes containing disc electrodes. After the second PDMS dielectric layer was deposited, the second set of electrodes was laid down in a perpendicular direction to the previous set of electrodes. Finally, the third PDMS layer was deposited on these electrodes and spin-coated (details about the fabrication process can be found in S1).

Note that the spin coating method offers an easy means to tune the thickness of PDMS layer. The total thickness of the sensor was demonstrated to vary from approximately 300 µm to 1.5 mm by changing the spin coating speed. However, here we decided to conduct the characterization on a thick sensor (the total thickness: 550 ± 60 µm) as our readout circuit is restricted to values of capacitance < 4 pF.

Readout circuit

A capacitance to digital converter (CDC, AD7746) is used to measure the capacitance. The CDC estimates capacitance based on how much charge is transferred over 1/32,000th of a second. If the resistance of the circuit is significant -as in some of the measurements described below -the apparent capacitance is underestimated. In order to read the array, the signals are multiplexed (two MAX 4518, one each for the row and column electrodes). The output is directed to a microcontroller (ATmega 2560 8-bit). I2C protocol is used for the communication between the capacitance-to-digital-converters and the microcontroller and the data is read via a serial port. The marked rows and columns are described in Fig. 1b, and the complete system consists of the sensor and circuit is shown in Fig. 1c. The complete 4 x 4 matrix of 16 taxels is sampled at 3 Hz.

Characterization

Transparency

An investigation on the transmittance through the fabricated sensor in the wavelength range of 400 nm-800 nm was performed using a Perkin-Elmer Lambda 800 UV-VIS spectrophotometer (semiIPN transparency optimization is described in S2.). As shown in Fig. 2a, the lowest optical transmittance here is 92% at a wavelength of 400 nm. In comparison to other PDMS based stretchable electrodes, such as silver nanowires/PDMS [START_REF] Weili | Intrinsically stretchable transparent electrodes based on silver-nanowirecrosslinked-polyacrylate composites[END_REF] and aligned CNT ribbon/PDMS [START_REF] Zhang | Polymer-embedded carbon nanotube ribbons for stretchable conductors[END_REF] having a transmittance of 80%-90% and 60%, respectively, the 95% of transmittance at 450 nm meets the standards needed for high quality displays. There is nonetheless some quality loss due to the imperfectly flat surface of the material, as can be seen from the slight distortion of the inset image -where edges of the electrodes can be seen.

Temperature sensitivity

Temperature dependence of sensitivity complicates sensor readings since temperature needs to be known. Some recent work has investigated temperature sensing in stretchable arrays thanks to variation of metal resistance [START_REF] Dossi | An electrochemical gas sensor based on paper supported room temperature ionic liquids[END_REF][START_REF] Maziz | Demonstrating kHz frequency actuation for conducting polymer microactuators[END_REF] under temperature changes. Here we explore the effect of temperature on our sensor response. When sampling at 32 kHz, there is a significant change in capacitance with temperature. We show that this can be eliminated by reducing the input measurement frequency to 10 kHz. As will be discussed, the reason that we see temperature effects on capacitance is because the resistance of the ionic liquid changes with temperature, which the capacitive sensing chip confuses with changes in capacitance. The change in ionic liquid resistance with temperature provides the ability to measure temperature, which may be desirable in prosthetic or robotic applications, for safety purposes for example, or to identify human touch. It may also be useful in medical sensor arrays.

In our stretchable transparent sensor, we instead use the conductivity variation of ionic liquid upon temperature change. The first aim is to see whether exposure to temperature has an effect on the sensor readings once the sensor is returned to ambient conditions. The sensor was cooled to -4 • C using a refrigerator, and then heated to 100 • C using an oven, to see if exposure to a range of temperatures would change the response. Functionality was tested after the array returned to ambient temperature (23 • C). No change in behavior was seen.

In a second set of experiments, the capacitance evolution of the sensor was recorded while temperature changed from 4 • C to 72 • C (Fig. 2c). The capacitance of a taxel was measured (the 3,3 taxel near to the corner furthest from the connectors, where the effect of electrode resistance is large due to the long trace length). Between 8 • C to 55 • C, the capacitance value linearly increases from 0.5 pF to 1.99 pF at a rate of 3.4% / • C. It reaches a plateau when the temperature continues to increase up to 72 • C.

In the capacitance measuring chip, capacitance is estimated from charge accumulated in about 16 µs. If there is significant resistance in the circuit, represented by the resistances of the traces in Fig. 2b, this can slow the accumulation of charge, resulting in the underestimation of capacitance. Resistivity of ionic liquids is know to be a strong function of temperature [START_REF] Mecerreyes | Applications of Ionic Liquids in Polymer Science and Technology[END_REF][START_REF] Cheng | Stretchable electronic skin based on silver nanowire composite fiber electrodes for sensing pressure, proximity, and multidirectional strain[END_REF], dropping as temperature increases. The increasing conductivity with temperature of semiIPN containing ionic liquids also shows a fast drop with increasing temperature [START_REF] Cotton | A multifunctional capacitive sensor for stretchable electronic skins[END_REF]. Fig. 2c shows an apparent increase in capacitance of the sensor element with increasing temperature, which is consistent with the resistance hypothesis.

To further test this hypothesis, we measured capacitance and resistance over a range of frequencies. Considering the taxel (3,3), resistances of column 3 (top electrode), R T , and row 3 (bottom electrode), R B , respectively, as shown in Fig. 2b. Together with the coupling capacitance C TR between the two electrodes, an (R T + R B )C TR time constant will be associated with this taxel. The data in Fig. 2d shows the measured capacitance value of taxel (3,3) as a function of temperature at frequencies of 10 kHz, 20 kHz, 40 kHz, and 100 kHz, obtained using an HP/AGILENT 4275A Multi-Frequency LCR Meter. When the excitation frequency is at 10 kHz, the capacitance remains constant as the temperature is varied from 25 • C to 70 • C. A stronger dependence of the capacitance on temperature is observed as the excitation frequency is increased. Fig. 2e shows that, as expected, the resistance drops as temperature increases. Practically, it also suggests that a low measurement frequency is appropriate for eliminating the temperature dependence of conductivity. The flat response at 10 kHz (Fig. 2d) suggests that resistance is no longer limiting estimation of the full capacitance. At this frequency, for the given values of resistance and capacitance, the sensor can operate effectively over a wide temperature range. The time constant, based on the resistance and capacitance estimate using the LCR meter measurement, is 6 µs, much shorter than the 1/(2π f) = 16µs. The key to effective touch measurement is to measure at sufficiently low frequencies where the capacitance dominates the impedance [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF]. Interestingly, by making measurements of impedance at high frequency, it should be possible to measure temperature.

Proximity, touch, and multi-touch sensing

In order to test proximity and touch response, the sensor is laid down on a flat surface and connected to the readout circuit. The sensor is able to detect the proximity when the finger moves within 2 cm of the surface, which is consistent with previous work on the same electrode geometry [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF] and other work using a stretchable crossed grid of silver nanowire electrodes [START_REF] Yao | Wearable multifunctional sensors using printed stretchable conductors made of silver nanowires[END_REF]. Fig. 3a shows the setup with a finger hovering above taxel [START_REF] Kim | Stretchable, transparent graphene interconnects for arrays of microscale inorganic light emitting diodes on rubber substrates[END_REF][START_REF] Kim | Stretchable, transparent graphene interconnects for arrays of microscale inorganic light emitting diodes on rubber substrates[END_REF]

at a distance of approximately 2 mm. The corresponding change in capacitance ∆C

Co (where ∆C is the difference between the reduced capacitance due to the proximity and the steady state capacitance C 0 ) is plotted in the 3D bar plot in Fig. 3b, which shows a drop of 6%. It is observed that the position of the finger in plane can be easily interpreted from this data.

In the case of touching of a finger (Fig. 3c) a similar decrease in capacitance is observed but at higher magnitude (12%) as seen in Fig. 3d. Finger hover and contact with the surface are distinguished by the magnitude of drop in capacitance, as seen in Fig. 3e. This changing percentage capacitance is comparable to other stretchable capacitive touch sensors of similar electrode spacing that use thin gold films [START_REF] Choi | Stretchable, transparent, and stretch-unresponsive capacitive touch sensor array with selectively patterned silver nanowires/reduced graphene oxide electrodes[END_REF], silver nanowires [START_REF] Li | Elastic capacitive tactile array pressure sensor system[END_REF], and silver nanowires/reduced graphene oxide [START_REF] Armani | Re-configurable fluid circuits by PDMS elastomer micromachining[END_REF] as electrodes, where a finger touch induces a 25%, ∼18%, and 22% changing capacitance, respectively. These stretchable sensors are not transparent.

Similar to commercial touch screens, the sensor is able to recognize the multi-touch of the fingers (shown in Fig. 3f,g), where the locations of touch of three fingers are detected. The response time of the sensor is limited by the sampling rate of sensing circuit and the time to scan through the 4×4 matrix. Each taxel is sampled every 0.33 s. This sampling rate is slower than in a typical commercial touch screen, indicating that it should be possible to make this less than 10 ms by using less precise but faster electronics.

There is some cross-talk between adjacent taxels, as seen in Fig. 3d, which is expected given the proximity effects. One method of determining the center of touch is to compute the probability distribution, as is used in commercial device, leading to super-resolution -higher than that offered by the taxel spacing. The crosstalk may also be reduced by either (i) grounding all electrodes except the ones under test [START_REF] Belanger | Hemocompatibility, biocompatibility, inflammatory and in vivo studies of primary reference materials low-density polyethylene and polydimethylsiloxane: a review[END_REF] instead of leaving them floating or (ii) adding another grounded conducting electrode underneath the sensor to reduce the effect of fringing field, but at the cost of losing proximity detection range. 4a, the induced strain on the electrodes is 3.7%, resulting in a maximum change in capacitance of 5% -similar to proximity signal, but lower than touch. Fig. 4c is a demonstration of the sensor's ability to detect a touch while being rolled. In this case the sensor is only rolled to a radius of curvature of 6 mm in order to avoid contact between two taxels or of the hand with the taxels while folding. Upon the bending, the capacitance values are decreased (< 4%) (Fig. 4b) due to interfering fringe fields. The sensor architecture, which contains pairs of loop and disc and thin top and bottom electrodes equally spaced to the neutral axis, ensures a high immunity from the bending effect [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF]. A touch on the sensor while it is bent produces a peak with ∼15% decrease in capacitance value (Fig. 4d), making the touch clearly distinguishable from bending.

Touch sensing while bending and stretching

In Fig. 4e, f, the ability to detect a touch is demonstrated while the bottom half of the sensor is stretched. Fig. 4e shows the setup where the sensor is stretched by 30%, and is touched. A stretch excitation induces a linear decrease in capacitances of all the taxels in the bottom half by approximately 5% (Fig. 4f). The likely reason for this decrease is that the resistances of the electrodes being stretched are increased, resulting in a reduction of the apparent measured capacitances. At this stretched state, the sensor is still be able to detect a finger touch, inducing 12% of change in capacitance, as shown in Fig. 4f. An investigation on pressure sensitivity of the sensor is described in supplemental S3, showing that pressure results in a local increase in capacitance, and that this change is small for large applied forces (14 N) and stresses (100 kPa). The effects of bending and stretch are small and more distributed in space than the effect of touch. This should make it possible to develop an algorithm that distinguishes touch from bend and stretch. Identifying proximity will be more challenging under conditions of active deformation, but may be possible based on the localization of the response.

Sensor applied on the skin and through fabric, and mechanical durability of the sensor

The sensor is composed mainly of PDMS, which has a low elastic modulus (360-870 kPa) [START_REF] Zahid | Optical properties study of silicone polymer PDMS substrate surfaces modified by plasma treatment[END_REF], good biocompatibility, and high conformability to the skin. As shown in Fig. 5a, the sensor is being touched while placed on an arm. The arm acts as a large, grounded object, reducing all values of capacitance in the array by almost 20%. Fig. 5b demonstrates the sensor response upon touching while it is on the arm. In this case the base capacitance value, C o , has been reset to the new background set by the presence of the skin. The touch is clearly visible.

For robotics applications involving interactions with humans, it may be desirable that the robots touch and 'feel' the presence of a human through clothing. Clothing has only a secondary effect on capacitance since it is not conductive and the dielectric constant is small. This sensor has the capability of detecting a touch through a layer of fabric, as shown in Fig. 5c,d. The corresponding change, ∆C C 0 , is 10% upon contact between the finger and the two fabric layers made of 0.75 mm thick cotton (Fig. 5d). The fabric layer allows the fringe field to go through, however distances the finger from sensor surface. The penetrating field enables proximity and localization of the touch through cloth.

As an initial test of robustness against delamination, 500,000 tensile cycles at an amplitude of 10% were applied, showing no perceptible loss of sensitivity, as described in Supplement S4. The sensor array has also not changed in performance over the 30 months since it was initially fabricated, suggesting that the ionic liquid is being effectively contained.

The semiIPN itself can be stretched by more than 100% without any significant degradation [START_REF] Mecerreyes | Applications of Ionic Liquids in Polymer Science and Technology[END_REF]. Therefore, the stretchability of the sensor is limited only by the smaller elongation of the PDMS used here. The stretchability of the sensor can be further improved if the PDMS is replaced by other types of rubbers, such as Ecoflex R ⃝ . The PDMS does have the advantage of high transparency [START_REF] Sarwar | Bend, stretch, and touch: Locating a finger on an actively deformed transparent sensor array[END_REF].

Conclusion

A capacitive sensor, composed of ionic liquid swollen semiIPN, forming the electrodes, and PDMS dielectric layers, was fabricated using a simple process and low cost materials. The array can sense proximity and touch by a finger while placed on a flat surface, human skin, or when covered by layers of fabric. The effect of touch is clearly visible even when the sensor is bent or stretched. In addition, the sensor is transparent (95% at 450 nm), is resilient under repeated tensile strain, can withstand exposure to temperatures between -4 and 100 • C without loss of performance, and shows good shelf life. A sensitivity to temperature of 3.4%/ • C was discovered, whose origin is the resistance change of the ionic liquid with temperature. This sensitivity is eliminated by measuring capacitance at a lower frequency, where capacitance dominates the impedance (10 kHz). The temperature dependence of resistance could be used in a temperature sensor.

Fig. 1 .

 1 Fig. 1. (a) Layer by layer fabrication process of an artificial skin sensor and its structure, (b) Rows and columns of the electrodes, and (c) The sensor connected to the readout circuit.

Fig. 2 .

 2 Fig. 2. (a) The optical transmittance versus wavelength plot for the resulting sensor with the 40%/60% ratio of NBR/PEO and the total thickness of 550 µm (the insert figure is a prototype of the artificial skin sensor), (b) An equivalent circuit model of taxel (3,) being measured, (c) Absolute capacitance value C TR of the taxel (3, 3) (measured by circuit board) and relative capacitance (red) as a function of the temperature, (d) Temperature dependence of the absolute measured capacitance values (measured by multi-frequencies LCR meter) and (e) calculated resistances of taxel (3, 3) at sinusoidal excitation frequencies of 10 kHz, 20 kHz, 40 kHz, 100 kHz.

Fig. 3 .

 3 Fig. 3. (a) A proximity sensed while the finger approaches the sensor, and (b) the resulting decrease in capacitance of 8% due to this proximity. (c) Sensor being touched, and (d) the taxel touched showing a decrease in capacitance of 13%. (e) The capacitance value decreases upon proximity and touch, (f) Three fingers touch the sensor simultaneously, and (g) the change in capacitance with peaks showing the locations of touch.

Fig.

  Fig. 4a, b demonstrate the change in capacitance that results when the sensor array is folded. At a radius of curvature of

Fig. 4 .

 4 Fig. 4. (a) The sensor being folded, (b) Resulting a small change in capacitance value, (c) The sensor being touched while being bent, (d) A change in capacitance showing its ability to sense in bent state, (e) The sensor being stretched up to 30% strain and touched while stretched, and (f) The capacitances of the stretched taxels (columns 3 and 4) decrease, and the finger touch causes a further clearly visible decrease at 3, 3.

Fig. 5 .

 5 Fig. 5. (a) The sensor being touched while placed on the arm, and (b) the change in capacitance showing the ability to sense touch when on the arm. (c) and (d) Ability to sense the touch while being covered by fabric.

Acknowledgments

This work was partly supported by the French Government through the National Research Agency (ANR) under program RE-NATECH, and by the Natural Sciences and Engineering Research Council of Canada (NSERC) through a Discovery Grant.

Appendix A. Supplementary data

Supplementary material related to this article can be found online at https://doi.org/10.1016/j.eml.2019.100574.