Etienne Caillosse

Mohamed Zaier

Mariam Mezghani

Samar Hajjar-Garreau

Loïc Vidal

Daniel Lougnot

Lavinia Balan
email: lavinia.balan@cnrs-orleans.fr

Photo-Induced Self-Assembly of Silver Nanoparticles for Rapid Generation of First and Second Surface Mirrors

Keywords: Silver mirrors, photo-induced synthesis, silver nanoparticles layers, reflective coating, nanostructured material

ABSTRACT:

Interesting mirror-like, highly reflective and conductive silver films have been successfully generated directly on a glass slide using a simple and fast photo-induced approach. A waterbased photosensitive formulation containing the silver precursor and a photo-generator of free radicals was used. It was applied like paint and exposed to UV light for a few seconds, in the absence of any additional reducing agents and without further treatment of any kind. This approach allowed ultrathin films of silver nanoparticles to be generated in situ (AgNPs) on the back side of the glass substrate. The particles are homogeneously auto-assembled onto the glass surface and the glass/silver diopter exhibits a high reflective character. With such an experimental arrangement, reflective surfaces are obtained: in contact with the glass slide, which is called the second surface mirror, and on the air side, which is called the first surface mirror. Quite interestingly, these reflective and conductive thin films exhibit strong natural adhesion on the glass substrate without the need for enhancing treatments (sensitization or activation) to improve the adhesion of the silver layer to the glass, as usual with silver glass mirrors. The influence of several chemical and photonic parameters has been examined in order to optimize the final optical and electrical properties of these silver films.

■ INTRODUCTION

Nowadays, mirrors of all types are part of most people's daily lives, from smart coated windows and bathroom equipment, car rear-view mirrors, optical instruments (microscopes and telescopes) to laser reading systems such as compact disc players and barcode scanners, and so on. These mirrors are commonly referred to as front or second surface mirrors depending on the position of the reflective metal layer on the front or rear side of the glass substrate [START_REF] Ennaceri | Optical Properties of Front and Second Surface Silver-Based and Molybdenum-Based Mirrors[END_REF]. In fact, glass is an ideal material to be coated with a reflective metal top layer to create a mirror. It offers an optimal combination of thermal, mechanical and optical properties that provide protection against degradation factors and aggressive external conditions. In addition, it helps preserving the optical image and ensures the dimensional stability of the mirror even under severe conditions (high temperature, humidity, sun exposure) as long as it is not exposed to extreme environments [START_REF] García-Segura | Durability studies of solar reflectors: A review[END_REF].

In recent years, the use of metal nanoparticles (MNPs) in advanced applications has attracted considerable attention from the scientific community because of their tunable optical properties.

They have also stimulated a major research effort due to a large number of new and potentially promising applications in a wide range of fields such as photonics, opto and microelectronics, SERS detection, solar concentrators/reflectors or light filters [START_REF] Shenashen | Morphological Control, and Properties of Silver Nanoparticles in Potential Applications[END_REF]. In order to tailor them to these new types of applications, a great deal of research has been devoted, in particular, to the synthesis and manipulation of metal nanoparticles with a view to generating nano-or microlayers on a variety of substrates. In addition, they are also finding an increasing place in the manufacture of mirrors for arts, design and architecture of buildings. For example, nanoparticles are being used to customize the appearance of buildings or to make their air-conditioning systems more efficient and less energy-intensive by deflecting heat during high summer months.

To achieve this, characteristics such as reflectivity, thermal and electrical conductivity or the durability of thin metal deposits become priorities. Hence the interest of many researchers in the study and development of new synthesis approaches (physical, chemical, photochemical...) of metallic nanolayers on glass or other substrates.

Chemical methods are the most commonly used to synthesize thin layers of silver or gold MNPs with a mirror-like appearance. Traditionally, the Tollens reaction (or other methods based on the same principle) is used for this purpose. By adding a small amount of a reducing sugar (i.e. glucose) to the Tollens reagent (a solution containing silver nitrate, sodium hydroxide and aqueous ammonia), silver is formed, which is deposited as a mirror-like coating inside the reaction vessel [START_REF] Liebig | Uber die Produkte der Oxydation des Alkohols[END_REF][START_REF] Yin | Synthesis and characterization of stable aqueous dispersions of silver nanoparticles through the Tollens process[END_REF][START_REF] Qu | Novel Silver Nanostructures from Silver Mirror Reaction on Reactive Substrates[END_REF][START_REF] Wang | High sensitivity fibre surface plasmon resonance sensor based on silver mirror reaction[END_REF]. This method is still of current use in the manufacture of common household mirrors.

Lili He et al. used a chemical method in which a commercial aqueous suspension of citratecoated silver nanoparticles (AgNPs) was gently poured into a mediator vessel that contained a mixture of water and an immiscible non-polar solvent. At the water/solvent interface the AgNPs/citrate assemblies are destabilized and NPs spontaneously self-assembled to form nanothick scales of silver, which settled by gravity at the bottom of the container. They were then collected, air-dried and deposited on a slide to form a mirror [START_REF] Qu | A facile solvent mediated self-assembly silver nanoparticle mirror substrate for quantitatively improved surface enhanced Raman scattering[END_REF]. Another chemical method consists of reducing metal ions with a Lewis base in an aprotic solvent. Thus Ag(+) can be reduced to Ag(0) by F(-) in a mixture of MeCN/DMSO to form silver mirrors on the inner surface of the reaction vessels. However, this method is only valid in aprotic solvents and requires an additional washing step to remove excess reagents [START_REF] Maity | Fluoride-Induced Reduction of Ag(I) Leading to Formation of Silver Mirrors and Luminescent Ag Nanoparticles[END_REF]. In any case, the various chemical approaches most often come up against problems related to the toxicity of the reagents, solvents or stabilizers used and the delicate handling and post-treatment of the by-products.

Among the physical methods used to produce MNPs films, the Physical Vapor Deposition (PVD) approach is one of the best known; it has the advantage of not requiring solvents, but it uses heavy machinery and involves significant energy consumption [START_REF] Perrenot | Sulphur corrosion effect on the electrical performance of silver films elaborated by physical vapor deposition[END_REF]. Ghidelli et al. used an ex-situ synthesis of gold nanoparticles by pulsed laser deposition (PLD) to develop nanostructured Au films with tailored optical properties in a pure Ar background gas [START_REF] Ghidelli | Engineering plasmonic nanostructured surfaces by pulsed laser deposition[END_REF].

However, this method requires severe deposition conditions such as high background pressures, high number of laser shots (500 shots) and high temperature of post-deposition annealing treatments up to 650°C. Moreover, other complex physical methods such as ion sputtering, pulsed laser ablation, e-beam deposition, spark discharge generation and spray pyrolysis could be used for generating thin films of MNPs [START_REF] Nakata | Particle dynamics during nanoparticle synthesis by laser ablation in a background gas[END_REF][START_REF] Weber | Application of Aerosol Techniques to Study the Catalytic Formation of Methane on Gasborne Nickel Nanoparticles[END_REF][START_REF] Fryauf | Silver Film Surface Modification by Ion Bombardment Decreases Surface Plasmon Resonance Absorption[END_REF][START_REF] Kim | Size monodisperse metal nanoparticles via hydrogen-free spray pyrolysis[END_REF]. However, all of these physical methods require a rigorous control of many technical parameters (voltage, initial and working chamber pressure, spraying speed, rapid thermal annealing time (RTA), temperature, degree of supersaturation, etc.).

Recently, our research group has introduced a novel photo-induced synthesis approach that allows the creation of nascent AgNPs and coat or mark a variety of material surfaces with metal NPs. This UV photoreduction process has made it possible, to directly functionalize plastic food packaging or other substrates and has allowed effective control of the shapes and sizes of the generated NPs to obtain specific plasmonic silver layers or biocide coatings [START_REF] Mustatea | A photochemical approach designed to improve the coating of nanoscale silver films onto food plastic wrappings intended to control bacterial hazards[END_REF][START_REF] Zaier | Tuning the morphology of silver nanostructures photochemically coated on glass substrates: an effective approach to large-scale functional surfaces[END_REF].

Moreover, in previous works, we introduced an innovative and totally photo-chemical approach which allows the photo-crosslinking of a acrylate formulation and simultaneously the photo-reduction of the metal precursor; the ester functions of the polymer act also as a stabilizers for these NPs. Hence, the innovation lies in the specific nano-assembly of the NPs in the form of an in-depth concentration gradient in the acrylate polymer matrix that endows the as synthesized metal/polymers nanocomposite coating with valuable optical properties and a mirror-like appearance [START_REF] Zaier | Generating Highly Reflective and Conductive Metal Layers through a Light-Assisted Synthesis and Assembling of Silver Nanoparticles in a Polymer Matrix[END_REF][START_REF] Schejn | Photo-Induced Design of Reflective Metallized Gold@polymer Coatings with Tuned Architecture[END_REF].

In the present paper, we introduce an innovative and greener alternative that breaks with everything we have done before. It still consists in using a photo-induced process but this time without any stabilizer or polymer matrix. The mirrors are made up solely of a submicrometrically thick metal layer of self-aligned silver NPs. For this purpose, the implementation of a one-step one-pot process and non-toxic reagents was a priority. Mirrors were obtained by depositing a water-based photosensitive formulation directly onto the substrate to be silvered and illuminating the sample for a few seconds with a standard continuous UV source. The as-synthesized AgNPs layers appear as highly reflective mirrors with effective electrical properties. To our knowledge, this photo-induced approach to obtaining first and second surface mirrors has never been reported in the literature.

The notion of first and second surface mirrors is purely conventional; it refers to the configuration of the mirror and its support in relation to the observer: first surface mirror when the reflecting surface is seen in front of the support by the observer and second surface mirror when it is seen through the support (transparent). Each of these types of mirrors has specific advantages that determine their fields of application. The great advantage of the process described in this publication is that it allows the manufacture of either second surface mirrors or specimens with two reflective surfaces (first surface + second surface mirrors) and this only depending on the thickness of the formulation and the photonic conditions of its implementation.

In addition, in order to obtain highly reflective layers with the lowest possible thickness (and thus save the maximum amount of silver precursor used), special attention has been paid to some particular aspects of the in situ generation of AgNPs, such as their spatial organization, homogeneity of their size and compactness of thin films.

■ MATERIALS AND METHODS

Materials. 2-hydroxy-2-methylpropiophenone used as a generator of primary free radicals was obtained from BASF. Silver nitrate (AgNO3) purity > 99%, diiodomethane and various solvents (ethanol, distillate water and acetonitrile) were from Sigma-Aldrich and used as received.

The samples were prepared on borosilicate microscope glass slides purchased from Roth.

Before use, they have been treated to remove all traces of organic contamination. For this purpose, the 25*30 mm glass slides were soaked in sodium hydroxide solution N/10 (4 g/L) for about 10 minutes, then rinsed with abundant demineralized water and dried under air flow.

Instruments. Photochemical reactions were performed with a standard continuous UV LLC source from Heraeus Noblelight America equipped with an H bulb. This device provided a fluence of up to 2 W/cm 2 in the 200 to 600 nm window. Unless otherwise stated, the value used in this study was 800 mW/cm 2 .

Reflectance measurements were carried out using a Thermo Fisher Scientific Evolution 200 UV-visible spectrophotometer with a 60 mm w/Spectralon® integrating sphere. The interrogating beam hit the sample under a 8° incidence and a Teflon slide was used as a reference. In this configuration, the measured value was the total reflectivity, i.e. the sum of specular and diffuse reflection. In another configuration that uses another detector and bypasses the integrating sphere, this spectrophotometer was used to measure the transmittance of the samples. In general, reflectance and transmittance spectra are recorded between 300 and 1000 nm.

Transmission electron microscopy (TEM) studies were carried out using a Jeol ARM-200F microscope (Tokyo, Japan) operating at 200 kV. The scanning electron microscopy images were obtained with an FEI Quanta 400 scanning electron microscope (SEM).

Atomic Force Microscopy (AFM) characterizations were performed on a FlexAFM Nanosurf microscope operating in tapping mode under ambient conditions using an ACT tip (AppNano), with a scanning frequency of 1 Hz and a resolution of 256 x 256 pixels. This device has been used to determine the thickness of silver films. For this, one calculates the difference in the altitude distribution along a scan perpendicular to a scratch made on the film by a hard tip.

Height and roughness calculations were performed using the Gwydion freeware.

Samples were analyzed by X-ray photoelectron spectroscopy (XPS) on a VG Scienta (Uppsala, Sweden) SES 200-2 x-ray photoelectron spectrometer under ultra-high vacuum (P < 10-9 mbar).

The monochromatized AlKα source (1486.6 eV) was operated at a power of 420 W (30 mA and 14 kV). During acquisition, the pass energy was set to 100 eV for high-resolution and 500 eV for wide scan spectra. The deconvolution of the spectra into different components is performed with Gaussian (70%) -Lorentzian (30%) shaped peak or an asymmetry function in the case of Ag met using casaXPS software after having subtracted a Shirley-type background. The atomic percent is determine taking into account the transmission factor of the spectrometer, the inelastic mean free path, and the sensitivity factor of each atom.

■ RESULTS AND DISCUSSION

Photo-induced synthesis of assembled NPs silvered mirror. The sample preparation protocol used in this study is similar with that used in our previous works [START_REF] Gadelmawla | Roughness parameters[END_REF][START_REF] Qu | Facile Route to Silver Nanotubes[END_REF]. In a typical synthesis, about 10 mg of 2-hydroxy-2-methylpropiophenone (ca 0.5 % by weight) and about 100 mg of silver nitrate (ca 5 % by weight) were added to 2 mL of solvent and maintained for 60 minutes at room temperature under magnetic stirring to ensure complete dissolution. When the formulation was dropped onto the glass slide, the liquid film spontaneously spreads under the effect of its surface tension and low viscosity. However, in order to allow rapid and homogeneous and perfectly reproducible application of the formulation on the glass, an automatic bar coater was used for the deposition. For this, 4-5 drops (about 100 -125 µL) of the photosensitive formulation were carefully deposited on the microscope slide placed horizontally and various bar coater were used (24 µm, 12 µm and 6 µm) to control the thickness of the liquid layer. The sample was then exposed to irradiation by the light source for a variable time (typ. 20-40 seconds). Under these conditions, and with a 24 µm bar coater, the optical density associated with the absorption of the free radical generator was about 0.02 @ 365 nm, 0.07 @ 334 nm and 0.09 @313 nm. Figure 1 illustrates the successive steps of the photo-induced process and the formation of thin silver layers on a glass substrate. Table 1 shows the range of solvents used for the preparation of sensitive formulations and the corresponding exposure times to UV light. The UV-exposure time is determined by the reactivity of each formulation and is therefore specific to each solvent or solvent mixture used. The irradiation is stopped when the surface of the film is totally dried (cured). In addition, exposure times have been optimized based on the evaluation of the properties of the samples and their stability over time. Too short an exposure time does not allow the sample surface to dry making it unstable. Conversely, too long an exposure time leads to a deterioration (whitening) of the metal layer, probably due in part, to bigger aggregates formed and some oxidation of the metal surface. CN 32 Characterization of the AgNPs metalized layers.

The structure of the layer as seen from the open air surface. The resulting silver coatings (air side) were analyzed by atomic force microscopy (AFM) to determine the topography and morphology of the nanoparticles forming the thin metal film. This characterization was performed in tapping mode. For each sample, a scan size of 2 x 2 µm was set with a resolution of 256 * 256 pixels. Multiple scans, randomly located, were carried out on the surface of each sample, in order to scan it thoroughly. As can be seen in Figure 2, the spatial organization of the AgNPs remains uniform over the entire surface of the metal coating, with a roughness ranging from 7 to 100 nm, depending on the thickness of the film. The thickness of the silver coating measured by the scratch technique is typically in the range of 50 to 350 nm (see Figure S1). The roughness parameter Ra corresponds to the arithmetic mean of the absolute deviations from the mean altitude calculated over a line drawn along the length of the sample [START_REF] Gadelmawla | Roughness parameters[END_REF]. This roughness has an impact on the reflective properties of the silver film on the air side. It can be observed that the roughness depends on the thickness of the sample. Interestingly, with the two thinner samples (150 and 50 nm) this surface exhibits high reflectivity and is capable of forming the image of an object (see images Figure 2b andc). However, in the case of the thicker (and rougher) sample, the surface on the air side is only diffusely reflective and therefore cannot form an image (Figure 2a).

In order to perform analysis by transmission electron microscopy (TEM), a sample of the material of a thin reflective film of AgNPs was scrapped off from the glass substrate after synthesis. The recovered powder was dispersed in ethanol and a small drop was rapidly deposited on a TEM grid for analysis. As shown in Figures 3a andb, AgNPs exhibit a spherical shape with a diameter between 2 and 10 nm. In addition, analysis of a batch of about 100 AgNPs from a portion of the grid returned an average diameter of 5.8 ± 0.5 nm (see insert in Figure 3a).

The corresponding electron diffraction pattern of silver nanoparticles (boxed in the corner of Figure 3b) shows fringes corresponding to the 111, 200 and 220 planes of fcc silver [START_REF] Qu | Facile Route to Silver Nanotubes[END_REF]. Figures 3c andd present the atomic resolution chemical mapping of a silver sample. This mapping is obtained by scanning energy dispersive x-ray spectroscopy (SEDX). Figure 3c shows the nanoparticles against a background of carbon. The nanoparticles are well dispersed in the observed field with some agglomerates and a kind of spatial arrangement in a preferential direction seems to appear. Figure 3d shows the elemental mapping of silver (in violet) which

shows that the main element is silver. This result corresponds to the EDS analysis (Figure S2) which confirms the presence of silver as the very major element. We also observe in EDS analysis, some weak peaks of O and C which originate from the photolysis of the free radical generator and Si from the glass substrate (Figure S2). very intense binding energy double peak whose position corresponds to the spin-orbit splitting components Ag 3d 5/2 and Ag 3d 3/2 (Ag 3d 5/2 at 368.30 eV and Ag 3d 3/2 at 374.30 eV) (see Figure S3). This confirms the presence of Ag(0) as the major constituent in the film layer [START_REF] Ferraria | X-ray photoelectron spectroscopy: Silver salts revisited[END_REF]. No oxidized form of silver has been observed [START_REF] Rajasekharreddy | Qualitative assessment of silver and gold nanoparticle synthesis in various plants: a photobiological approach[END_REF]. Signals of the elements C, O and H, which correspond to photoproducts resulting from the photolysis of the free radical generator present in the initial liquid formulation, were also present in the wide scan survey spectrum (Figure S3). A weak signal corresponding to traces of N in metal films was also detected (Figure S4). The results recorded with a series of mirror samples obtained from a variety of formulations are summarized in Table S1. They clearly confirm that Ag(0) is always the most predominant element at the surface of the sample, regardless of the solvent used to prepare the photosensitive formulation.

The reflectivity of the glass/silver diopter. Reflectivity was evaluated directly on the asprepared samples, without any further processing. According to the terminology adopted in this contribution, the mirror created at the glass/silver interface is designed as the second surface mirror. Its reflectivity was measured through the supporting glass plate between 300 and 1000 nm as shown in Figure 5 on thick samples (ca 350 nm).

Usually, reflection spectrophotometers with a detection system based on an integrating sphere are designed to measure specular and diffuse reflection as a whole. As the equipment used operates in this way, a preliminary control was therefore made to ensure that in the samples studied, the contribution of diffuse reflection on the glass/silver diopter was negligible and thus the total reflection measured could be considered to correspond only to the specular component.

For this purpose, the following experiment was carried out: the beam of a green cw laser ( = 532 nm; beam diameter = 3 mm; divergence < 1.2 mrad) was directed onto the reflecting surface under an incidence of 5°. The distribution of light energy in a plane perpendicular to the direction of propagation of the reflected beam was measured after a travel of 50 then 100 cm using a beam analyser. Comparison of the results obtained for the five samples described in Table 1 with that corresponding to the interrogating beam itself after an identical travel does not reveal any significant difference. This confirms that the contribution of diffuse reflection on the glass/silver diopter can be disregarded in this batch of samples. Another issue related to the optical characteristics of these second surface mirrors deserves a brief comment. In fact, Fresnel reflection on the glass/air diopter of the support plate is well known to decrease with increasing wavelength; this feature is described by the Cauchy relationship [24]. Combining it together with the Fresnel relationship makes it possible to evaluate this spurious reflectivity under any incidence. Thus, all recorded reflectance spectra have been corrected to take into account this spurious reflection, the values of which are reported in Table S2.

As can be seen from Figure 4 and Table S3, several formulations led to very interesting results.

In particular, the three water-based systems have made it possible to generate second surface mirrors with a reflectance exceeding 80%. In the case where the reaction medium was H 2 O/CH 3 CN, the reflectance was about 94%, very close to that of optically polished solid silver [START_REF] Taneja | Size dependence of the optical spectrum in nanocrystalline silver[END_REF]. Interestingly, the reflectance fluctuation in a batch of 5 supposedly identical replicas was measured to be +/-5%. On the other hand, systems formulated in acetonitrile or pure ethanol, which lead to mirrors with reflectance of 50-60 %, seem less promising. In an attempt to interpret these experimental observations, large differences in the saturated vapor pressure of these three solvents can be put forward. The saturated vapor pressures of ethanol (6 kPa) and acetonitrile (10 kPa) are about twice and four times that of water (2.6 kPa), respectively. It is also important to keep in mind that the photo-induced process goes in line with a heating due both to the exothermicity of the photoreduction reaction of silver cations and most importantly, a degradation of the energy of the non-actinic photons into thermal energy. Thus, in parallel with the generation of native silver and the photoassisted creation of nanoparticles, the reaction medium evaporates. This phenomenon is therefore directly dependent on the saturated vapor pressure of the liquid phase. It could also be mentioned that the kinetic coupling between production of elementary nanoparticles and evaporation of the reaction medium is a key factor of the synthesis. While we have not yet rationalized this phenomenon, which is obviously a multi-parameter issue, the nature of the solvent has a decisive impact on the size and distribution of the NPs as already shown in our previous work [START_REF] Zaier | Tuning the morphology of silver nanostructures photochemically coated on glass substrates: an effective approach to large-scale functional surfaces[END_REF] and at least two characteristics of the solvent are important: its polarity and its saturation vapour pressure. The polarity is involved in controlling the reduction reaction of the metal precursor and in the stabilization process of metal seeds and the saturation vapour pressure determines the rate of evaporation of the solvent. Moreover, rapid evaporation interrupts reduction prematurely and leads to an assembly of NPs not compact enough to achieve high reflectance. Conversely, slow evaporation promotes coalescence of particles and the formation of large aggregates, leading to a diffusing surface.

Modelling these phenomena will require a description of the thermal conditions of the experiment (exothermicity of the chemical reaction, heating due to plasmon resonance and deposition of parasitic heat by the actinic source) which is a very complex matter. It will be examined in a future study.

In addition, the coalescence process of NPs greatly influences the intimate structure and the compactness of the metal layer formed in this way. From this, it can therefore be inferred that these phenomena must also have an indirect influence on the electrical conductivity of the silver layers and on the quality of their adhesion to the glass substrate. Moreover, different concentrations of Ag + have been tested and 5% is the optimized value of the silver concentration.

When the concentration of Ag + is lower (2 % for example), spaced NPs on the glass were obtained but no mirror aspect and when the concentration is higher, the mirrors are very inhomogeneous with a lot of aggregates.

In order to analyze how the thickness of silver layers impacts the reflectivity of second surface mirrors, a thorough study was carried out by gradually reducing the quantity of the photosensitive formulation with water based. Figure 5 shows the reflection spectra of a set of three samples obtained under the same experimental conditions with water formulations leading to thicknesses of 50, 150 and 350 nm. The characteristic of these spectra that catches the attention is their overall shape: they approximately deduce from each other by a geometrical affinity (from one thickness to another, the reflectance is multiplied by a constant factor over the whole spectrum). Such an observation suggests that what differentiates these three samples is the density i.e. the intimate structure of the metal layer. As thickness decreases, the stacking of nanoparticles becomes less compact so that the silver layer is no longer continuous. The evolution of the general shape of the reflection spectra as a function of the thickness of the layers is totally different from what has been reported by several research groups that have studied silver layers obtained by CPV (chemical vapor deposition) or have carried out theoretical calculations on this question [START_REF] Domaradzki | Investigations of optical and surface properties of Ag single thin film coating as semitransparent heat reflective mirror[END_REF]. Indeed, as the thickness decreases, the shape of the reflection spectrum is known to change. If the spectra deduce from each other by geometric affinity, it means that the observed effect is mostly due to the presence of more and more through-holes. The thickness of the layer certainly decreases a little, but at the same time it becomes more and more of a sort of strainer whose holes allow part of the incident light to pass through.

In order to further investigate the structure of semi-reflective layers -typically those with thicknesses in the order of 150 nm -the study of their properties was completed by recording their transmission spectrum (Figure 6). This makes it possible to draw up a balance of the light reflected (R %) and transmitted (T %) by these samples. It can then be seen that there must be a third component since the sum of R% + T% does not equal the totality of the incident light.

When this deficit is reported as absorbance [100 -(R% + T%)], one recognizes the typical absorption associated with the surface plasmon of large silver particles -a broad, almost symmetrical and unstructured absorption band with a maximum around 585 nm (Figure 6). Indeed, to explain the presence of this plasmon band, one must consider that the elementary particles that form the reflecting film are juxtaposed, in close contact, but only incompletely sintered and coalesced. As a result, the dielectric confinement at the origin of the plasmon resonance in isolated elementary nanoparticles is partly preserved. The reflectivity of the open air surface, i.e. first surface mirror. The AFM study of the surface topography on the open-air side revealed that for the thinnest layers (50 and 150 nm), the measured rugosities were well below wavelength (see Figure 2). Therefore, it can be expected that the reflection occurring at these surfaces would be mainly of the specular type. Conversely, the reflectivity of thick samples, whose roughness is generally greater than 100 nm, should be mainly diffuse reflection. Figure 7 presents the reflection spectra of the open-air surfaces of the thinner samples (50 and 150 nm) studied by AFM along with illustrations showing the images of an object provided by these reflective surfaces (Figure 2). It was observed that the thicker the sample, the higher the reflectivity of the open air-surface (Figure 7). The air-surface roughness depend on the AgNPs size distribution and the gaps between the particles (see figure 3a) if are not filled with smaller ones, lowering in this way the reflectance [START_REF] Yen | Highly Reflective Liquid Mirrors: Exploring the Effects of Localized Surface Plasmon Resonance and the Arrangement of Nanoparticles on Metal Liquid-like Films[END_REF]. However, as the thickness of the silver film increases, the roughness of the rear surface of the silver film also increases, to such an extent that the reflection from this surface ends up being only diffuse. This is effectively what happens with the thicker sample (350 nm), which for this reason, is no longer capable of forming a mirror image (see Figure 2a) [START_REF] Zheng | Identifying Key Factors towards Highly Reflective Silver Coatings[END_REF]. Electric resistivity of the silver layer. The resistivity of silvered layers was measured on the air-side with a two points Keithley 2000 device [START_REF] Khan | Structural and thermal studies of silver nanoparticles and electrical transport study of their thin films[END_REF]. Regardless of the formulations and UV exposure times used, the general trend is that the various samples tested exhibit low resistivity.

By way of illustration, resistivity data for 350 nm samples are collected in Table 2. It is clear that this measuring approach provides only a very rough assessment of the conductivity of thin silver films. It does, however, reveal very large differences of about two orders of magnitude in the batch under consideration. Among the samples studied, with one exception, the higher the reflectivity, the better the electrical conductivity. This observation seems consistent with the notion of compactness of the layer formed by the assembly of AgNPs mentioned above to explain the differences in reflectivity observed in the same batch. Nevertheless, the case of the sample prepared from a formulation based on acetonitrile is singular: it is at the same time, the least reflective and the most conductive. In any case, the conductivity property will have to be studied in greater depth using the much better adapted device known as the four-tip device.

Adhesion of the silver layer. Before considering possible practical applications of these second surface mirrors, it is necessary to ensure the quality of the adhesion of silver nano-layers on glass substrates. A test described by ASTM D3359 and ISO 2409 [START_REF] Zainab | Standard Test Methods for Measuring Adhesion by Tape Test 1[END_REF] is commonly used in the industrial world to evaluate the adhesion of coatings deposited on a variety of surfaces. It is known as the "Tape test". It consists in i) tracing a grid across the film to the substrate with a sharp razor blade, scalpel, knife or other cutting device, at a pitch of 1 mm with a spacing of 1 mm, ii) applying a 25 mm wide, pressure sensitive tape onto the pattern (typ. with an adhesive force of 8.75 N) and iii) peeling off the tape. The grid is then observed and the number of tiles torn off by the adhesive tape is recorded. Depending on the result, the adhesion is evaluated qualitatively on a scale of 0 to 5. A score of 0 corresponds to the absence of chipping and 5 corresponds to the removal of more than 70 % of the film by the tape. In our case, the adhesion evaluated on a set of about ten samples corresponds to a score of 0, indicating excellent adhesion of silver nanolayers to glass (Figure S5).

Although not yet clearly identified, the origin of this strong natural adhesion, two hypotheses can be put forward: i) most probably the first seeds are created on surface defects of the glass substrate which alone are capable of stabilizing them. And then the layer builds up from these hooking points; ii) photochemically generated primary radicals may also react with surface functions of the glass substrate or graft themselves onto this surface to create functions capable of strongly interacting with the silver seeds.

Wettability of the open air surface. In everyday applications of second surface mirrors (exterior, bathroom, car rear view mirror), it is necessary to protect the air side of the mirror against oxidation, corrosion or scratches. To do this, hard back coatings are generally applied to the AgNPs film. However, the choice of materials used in the formulation of these coatings is not obvious. The reason is that the wettability of this type of deeply corrugated surface at the submicrometer scale is often problematic. To access the apparent free energy of the air-side surface of silver mirrors, the static contact angles of water and diiodomethane on the surface of a sample with a silver layer thickness of ca 350 nm were determined. To do this, 2 µL drops of deionized water and then diiodomethane were deposited on the sample surface, using a microsyringe and the contact angle was measured using a video capture device. To calculate the surface energy, Fowkes' mathematical model was used here [START_REF] Mirzaeian | Surface characteristics of silver oxide thin film electrodes for supercapacitor applications[END_REF].

Figure 8 shows a contact angle of approximately 110° with water (Figure 8a) (the deposited drop remains stable and does not flatten over time) and about 34 ° with diiodomethane (Figure 8b). The calculated surface free energy is thus 43 ± 2 mN/m. This result is in line with the literature and is highly dependent on the roughness of the sample. Indeed, the more marked the surface roughness of a sample, the greater the contact angle with water. In the case under study, the Ra parameter was about 100 nm [START_REF] Zhou | Superhydrophobic surface created by the silver mirror reaction and its drag-reduction effect on water[END_REF]. These results indicate that the 350 nm silver film behaves like a very hydrophobic material. The same experience was then repeated on the samples with much thinner silver films, which exhibit a lower roughness of their open air surface (see Figure 2). All the experimental results are gathered in Figure 8c and Figure S6.

c)

Two models have been developed to explain the hydrophobicity of this type of highly uneven surface, the Cassie-Baxter model and the Wenzel model. The first considers that the roughness of the substrate and the small fraction of solid in contact with the liquid, combined with the micropockets of air trapped between the surface and the liquid, increase the contact angle.

Wenzel's model, on the contrary, explains that the liquid fills all the porosity of the surface, due to the roughness, increasing the contact surface area significantly, thus increasing the actual hydrophobicity. A simple way to decide on which model applies to the systems studied in this work is to deposit a drop of water on the surface and then tilt the support at an angle of 20°. If the drop slips off the support, Cassie-Baxter's law applies to the system in question; otherwise Wenzel's model applies [START_REF] Lafuma | Superhydrophobic states[END_REF].

In all of the systems studied throughout this work, the Wenzel model seems to apply systematically (Figure 9 and Figure S6). The surface energies evaluated must allow the coating intended to protect the mirrors to be applied without having to carry out special treatments usually required (passivation or adhesion promoter for primer and finishing paints).

■ CONCLUSION

This article reports on an original and very efficient photo-induced process for applying a silver mirror coating onto a glass substrate by using a simple water-based photosensitive formulation and UV light. After photo-induced synthesis, silver nanoparticles self-assembled to generate thin layers which can exhibit reflectivity up to 90 % with excellent adhesion to the glass substrate and behave as electrically conductive coatings. The process is carried out at room temperature, in the open air and is completed within a few seconds. By playing with chemical and photonic parameters, some improvements in the optical reflectivity and electrical

Figure 1 .

 1 Photosensitive formulationAg +

Figure 2 .

 2 Figure 2. 3D AFM images of the air-side surface of Ag nanoparticle films of different

Figure 3 .

 3 Figure 3. (Top) TEM images of the AgNPs film (thickness = 50 nm, 20 s UV exposure and

Figure 4 .

 4 Figure 4. a) Reflectivity of the silver films on the glass side as a function of the solvents used for

Figure 5 .

 5 Figure 5. Reflectivity of silver mirrors on the glass side with increasing thickness (50, 150, 350

Figure 6 .

 6 Figure 6. Reflection (R%), transmission (T%), reflection + transmission (R% + T%) and

Figure 7 .

 7 Figure 7. Reflectivity of the open air surface (rear surface) of the thinner silver mirrors

Figure 8 .

 8 Figure 8. Contact angles on an water 350 nm thick silver film a) water drop (insert 20° inclined

Table 1 .

 1 Photosensitive formulations with various solvents and the time exposure to UV light.

	Solvents	UV exposure (sec)
	100% H 2 O	40
	100% C 2 H 5 OH	24
	80% H 2 O + 20% C 2 H 5 OH	27
	100% CH 3 CN	36
	80% H 2 O + 20% CH 3

Table 2 .

 2 Resistivity data of 350 nm silver coatings as a function of the solvents used to prepare the sensitive formulation.

	Solvents	Resistivity (Ohm.cm)
	100 % H 2 O	10
	100 % C 2 H 5 OH	100
	100 % CH 3 CN	1.2
	80 % H 2 O + 20 % C 2 H 5 OH	20
	80 % H 2 O + 20 % CH 3 CN	4

■ ACKNOWLEDGMENTS

The authors express their thanks to the Agence Nationale de la Recherche (ANR) for financial support under contract ANR-16-CE08-0032-01 and SATT Conectus project MIRROR.

conductivity of silver nanolayers have been achieved. Several solvents or solvent mixtures (water, ethanol, acetonitrile) were also tested with which ultra-thin (50 and 150 nm) first and second surface mirrors were obtained.

The use of this innovative approach for the manufacture of first and second surface mirrors should open the door to numerous industrial applications; some of the most booming areas include printing of micro-electric circuits, advanced light reflectors, solar cells, thermal insulation or smart windows. The approach offers an easy, inexpensive and environmentally friendly process to generate large scale functionalized surfaces with highly reflective and conductive properties.

■ ASSOCIATED CONTENT

Supporting information

Supporting information is available: AFM characterizations, EDXS spectrum, XPS analysis, additional results of the reflectance, images of the "Tape Test", and images of the water drops on silver films.

■ AUTHOR INFORMATION

Corresponding Author *E-mail: lavinia.balan@cnrs-orleans.fr ORCID Lavinia Balan: 0000-0003-0144-401X Notes The authors declare no competing financial interest.


Juan Rosso
email: juan-pablo.rosso@imag.fr

Céline Coutrix
email: celine.coutrix@imag.fr

Matt Jones
email: matt.jones@swansea.ac.uk

Laurence Nigay
email: laurence.nigay@imag.fr

Simulating an Extendable Tangible Slider for Eyes-Free One-Handed Interaction on Mobile Devices

Keywords: Human-centered computing~Interaction techniques, Human-centered computing~Mobile devices Extendable slider, Mobility, Thumb interaction, Tangible interaction, Shape-changing interfaces

Sliders are widely used on mobile devices. Envisioning mobile devices that can dynamically deform to raise tangible controls from the screen surface, tangible sliders offer the benefit of eyesfree interaction. However, reaching for distant values with one hand is problematic: users namely need to change their handgrip, which is not comfortable. To overcome this problem, this paper sets out to experimentally study an extendable tangible slider to support one-handed clutching. The tangible slider's knob extends to maintain the thumb's movement within its comfortable area. We first built a low-fidelity prototype made of a knob long enough to allow clutching. This low-fidelity prototype significantly improves performance when reaching distant targets, as compared to a standard tangible slider. We then built a higher-fidelity prototype, introducing actuation and allowing for a shorter knob. When used for clutching, the knob moves back towards the users' thumb. Experimental results show that the motion of the actuated knob does not interrupt eyes-free interaction during manipulation. In comparison, a graphical extendable slider performed 0.9s slower due to the required visual attention. However, the results suggest that the motion of the actuated knob affects performance, as the higherfidelity prototype performed 0.6s slower than the low-fidelity prototype.

INTRODUCTION

Adjusting continuous parameters in an eyes-free manner is a common task. Users often need to define a parameter value within a large continuous interval. For instance, mobile audio engineers fixing the sound volume of a venue before a concert [START_REF] Kim | KnobSlider: Design of a Shape-Changing UI for Parameter Control[END_REF], scientists filtering data displayed on a wall-sized display [START_REF] Jansen | Tangible remote controllers for wall-size displays[END_REF], a person at home adjusting the TV sound volume while going to open the door. Current technologies fail to cover the users' demands when performing such tasks. On the one hand, standard remote controls offer discrete buttons, which can be tedious and/or difficult to operate. Repeatedly pressing a button for specifying a particular value is tiring [START_REF]Repetitive Strain Injury (RSI)[END_REF]. Maintaining a button pressed and releasing it when the target is reached requires high sensorimotor coordination [START_REF] Roald | Reaction time and movement time measured in a key-press and a key-release condition[END_REF]. On the other hand, solutions on smartphones and tablets provide graphical widgets used for continuous adjustment -e.g., sliders. However, these solutions lack tactile feedback, forcing the user to visually focus on the input device to operate it. This visual dependency prevents the users from eyes-free interaction, which is a feature desired by users of mobile devices [START_REF] Yi | Exploring user motivations for eyes-free interaction on mobile devices[END_REF].

Another problem related to interaction with mobile devices is the unreachability of some areas by the thumb when using only one hand. This is particularly problematic for large sized phones, which are difficult to use in a one-handed manner [START_REF] Chang | Understanding Users' Touch Behavior on Large Mobile Touch-Screens and Assisted Targeting by Tilting Gesture[END_REF]. This Figure 1. Clutching with an extendable tangible slider: (A) the user places her thumb on the slider knob and (B) begins to push upwards (direction of the blue arrow). (C) When this action is no longer comfortable the user is able to continue to adjust the controlled parameter (as visualized with the green landmark line) by carrying out a clutching action, drawing the thumb down to the comfortable starting position. (D) This is possible because the slider knob expands (yellow side) in the opposite direction.

problem has motivated several studies on the functional area of the thumb [START_REF] Bergstrom-Lehtovirta | Modeling the functional area of the thumb on mobile touchscreen surfaces[END_REF][START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF][START_REF] Karlson | Understanding One-Handed Use of Mobile Devices[END_REF]. When reaching outside the functional area of the thumb, users perform different types of hand movements in order to change their handgrip [START_REF] Chang | Understanding Users' Touch Behavior on Large Mobile Touch-Screens and Assisted Targeting by Tilting Gesture[END_REF][START_REF] Eardley | Investigating how the hand interacts with different mobile phones[END_REF][START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF]. These hand movements can lead to uncomfortable handgrips for the user.

Inspired by early attempts to provide eyes-free interaction through tangibility [START_REF] Hemmert | Dynamic knobs: shape change as a means of interaction on a mobile phone[END_REF][START_REF] Jansen | Tangible remote controllers for wall-size displays[END_REF][START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF], a study on interacting with mobile tangible controls, focused on shrinking the tangible control to avoid handgrip changes [START_REF] Rosso | Impact of mobile tangible slider design and its reachability on pointing performance[END_REF]. However, the study confirmed previous work [START_REF] Chapuis | Effects of motor scale, visual scale, and quantization on small target acquisition difficulty[END_REF] by showing the negative impact of small motor scale on performance.

A solution would be to use a tangible isometric device to control the direction and speed of movement within the comfortable area, rather than the position of the cursor. However, position control was found to offer a high degree of perceived usability as compared to rate control [START_REF] Woźniak | Limiting trial and error: introducing a systematic approach to designing clutching[END_REF]. As a consequence, in this paper we adopt another solution by considering an extendable slider capable of extending its knob length (Figure 1). The slider's knob increases its length in order to support thumb-clutching movements. When the knob is moved upwards, the knob deforms downwards while letting the slider's landmark move upwards (see Figure 1 A-B and C-D), and vice versa. Furthermore, clutching allows us to provide a large motor scale [START_REF] Chapuis | Effects of motor scale, visual scale, and quantization on small target acquisition difficulty[END_REF] while maintaining thumb's movements within its comfortable area. Users can then always manipulate the knob precisely, eyes-free, and comfortably -i.e., from the functional area of the thumb.

As a practical example of use, we consider the audio engineers' case presented in [START_REF] Kim | KnobSlider: Design of a Shape-Changing UI for Parameter Control[END_REF]. These professionals would benefit from our approach: mobility is key for audio engineers in order to check the sound at different locations around the venue. Moreover, eyes-free interaction is required to control audio parameters while looking at the stage. Finally, one-handed interaction is required while changing audio parameters -audio engineers communicate with musicians through a microphone or hand signals.

After showing how prior work on one-handed interaction contributed to our problem, we present our first user study: we measured the expected performance through a low-fidelity prototype having a very large knob. We then present our evaluation of a higher fidelity prototype that introduces actuated motion of the knob, before concluding.

RELATED WORK

In mobile situations, users most likely use one hand. An observational study, based on data from 780 people [START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF], revealed that there are three basic ways of how users hold their mobile phones while interacting with them: 49% interacted with the same hand that holds the phone, 36% interacted with one hand while holding the device with the other hand and 15% interacted with both hands.

The preference and dominance for one-handed interaction on mobile devices have motivated several studies on the functional area of the thumb. An empirical study by Karlson et al. [15] demonstrated that areas difficult to reach with the thumb provoke a significant slowdown (between 7% and 12%) in movement time.

Hand movements on mobile devices have been observed in situations where users reach for targets beyond the functional area of the thumb [START_REF] Chang | Understanding Users' Touch Behavior on Large Mobile Touch-Screens and Assisted Targeting by Tilting Gesture[END_REF][START_REF] Eardley | Investigating how the hand interacts with different mobile phones[END_REF][START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF]. When targets are near the functional area, two small movements have been identified: (1) fingers placed on the back of the device change position, and (2) the mobile device is tilted within the user's hand. We will refer to these movements as a handgrip change.

When handgrip changes are not sufficient to reach a target, a shifting of the device within the hand is observable [START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF]. We will refer to the shift of the device as a hand relocation.

Handgrip changes and hand relocations can be uncomfortable, unstable, and cause the falling of the device. The distinction between handgrip changes and hand relocations is important as they represent two distinct areas outside the functional area of the thumb [START_REF] Hoober | How Do Users Really Hold Mobile Devices?[END_REF]. However, the limits between these areas are not defined.

Accessing Targets Outside the Functional

Area: Graphical Interaction Graphical interaction techniques have been proposed by manufacturers to access targets outwith the functional area of the thumb, e.g., double-tapping the home button on iOS will bring the top half of the screen down to the thumb.

Researchers have further studied graphical interaction techniques, first leveraging the thumb. ThumbSpace [START_REF] Karlson | ThumbSpace: generalized one-handed input for touchscreen-based mobile devices[END_REF] generates a proxy view of a part of the screen within the functional area of the thumb. The proxy view facilitates the access to out-of-reach targets with the thumb. MagStick [START_REF] Roudaut | TapTap and MagStick: improving one-handed target acquisition on small touch-screens[END_REF] is a "magnetized" cursor allowing access to out-of-reach targets. It can be controlled from within the functional area of the thumb through a telescopic stick. Yu et al. [START_REF] Yu | Rapid selection of hard-to-access targets by thumb on mobile touch-screens[END_REF] presented two techniques: the first technique is similar to Thumbspace [START_REF] Karlson | ThumbSpace: generalized one-handed input for touchscreen-based mobile devices[END_REF] but initiated by one single swipe gesture from the thumb. The second technique makes use of a graphical circular widget that appears inside the functional area of the thumb. The widget is composed of four buttons, which allow the user to access "magnetized" elements near the corners of the screen.

Other graphical techniques consist of expanding the interaction space of the thumb by using the back of the device. Hakoda et al. [START_REF] Hakoda | Back-of-Device Interaction based on the Range of Motion of the Index Finger[END_REF] investigated the index finger's range on the back of the device while interacting with the thumb on the front. Löchtefeld et al. [START_REF] Löchtefeld | Evaluation of Hybrid Front-and Back-of-device Interaction on Mobile Devices[END_REF] presented a hybrid approach combining front-and back-of-device touch input. While the thumb is used to select reachable areas on the lower part of the display, the index finger is used on the back to reach the top left corner of the display.

Accessing Targets Outside the Functional

Area: Towards Tangible Interaction So far, all the studies related to the functional area of the thumb have been done for graphical interfaces. Yet, the benefits of tangibility for eyes-free interaction have been demonstrated for mobile devices, through tangible controls placed by the user on the display [START_REF] Jansen | Tangible remote controllers for wall-size displays[END_REF] and tangible controls emerging from a deformable display [START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF]. However, performance was not analyzed for one-handed interaction with such tangible controls [START_REF] Jansen | Tangible remote controllers for wall-size displays[END_REF][START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF]. Many continuous tangible controls can be considered for eyes-free mobile interaction. Scrolling wheels lack a landmark to provide observability of the parameter. Knobs can have a landmark, but the left/right adjustment is not easily mapped to min-max of a parameter, as different cultures can differ on the spatial representation of numbers [START_REF] Shaki | Reading habits for both words and numbers contribute to the snarc effect[END_REF]. The landmark is important when the user needs to acquire the current value (through vision or touch) after the task was interrupted. In this paper, we focus on linear controls, such as vertical sliders, since they are commonly used to control a variety of functionalitiese.g., sound, heat, light, TV channels, and data filtering. This allows us to ensure better adoption by providing retrocompatibility [START_REF] Cockburn | Supporting Novice to Expert Transitions in User Interfaces[END_REF].

In previous work we analyzed the impact that the slider's length and orientation have on performance when used with one hand [START_REF] Rosso | Impact of mobile tangible slider design and its reachability on pointing performance[END_REF]. We found that shrinking the slider's length to fit it within the thumb's comfortable area has a negative impact on performance in comparison with a long slider. This is in line with the results by Chapuis and Dragicevic about the impact of reducing the motor scale (i.e., reducing the target's size in the motor space) [START_REF] Chapuis | Effects of motor scale, visual scale, and quantization on small target acquisition difficulty[END_REF] on performance.

While we adopt a similar approach by considering an emergeable tangible slider for eyes-free interaction, our aim is to design and study an extendable tangible slider that allows thumb clutching in order to support a large motor scale while maintaining the thumb's movements within its comfortable area.

EXPERIMENT: BALANCING HANDGRIP CHANGES, HAND RELOCATIONS, AND CLUTCHING

We first explore the impact that thumb-clutching movements have on performance. For this, we compared thumb-clutching, performed on a large knob, with handgrip changes and hand relocations, caused by standard tangible sliders. A withinsubjects design was used with three independent variables: Knob, Distance, and Width.

The Knob is used on a mobile device to control a graphical cursor displayed on a distant screen. The Knob variable is composed of two conditions (see Figure 2):

Small (20mm×10mm×23mm): To reach a target near (resp. outside) the functional area, users have to change their handgrip (resp. relocate their hand, see Figure 2A-B). It resembles a standard tangible slider;

Large (150mm×10mm×23mm): To reach a target outside the functional area, users perform thumb-clutching within the area (see Figure 2C). This is meant as a low-fidelity prototype of an extendable slider.

The Distance variable refers to the distance between targets displayed on a distant screen. To explore targets that force handgrip changes and hand relocations, we chose the following values: First, 116mm between consecutive on-screen targets (i.e., 90mm in the control space on the mobile device) proved to force handgrip changes [START_REF] Rosso | Impact of mobile tangible slider design and its reachability on pointing performance[END_REF]. Second, 217mm between consecutive onscreen targets (i.e., 150mm in the control space on the mobile device) experimentally proved to force the relocation of the hand. Both distances fit within modern large-sized mobile phones [START_REF]Zenfone 2 Laser[END_REF].

The Width variable represents the target's width. In order to analyze performance from coarse to fine adjustment, two different widths were chosen: 7mm and 1.6mm.

The Distance×Width variables were fully crossed, defining the following task IDs = 4.2, 5, 6.3, 7, as computed in [START_REF] Soukoreff | Towards a Standard for Pointing Device Evaluation, Perspectives on 27 Years of Fitts[END_REF]. This confirmed our choice by giving medium and hard difficulty levels and avoiding the task being too difficult [START_REF] Soukoreff | Towards a Standard for Pointing Device Evaluation, Perspectives on 27 Years of Fitts[END_REF].

We then hypothesize that: H1: When pointing at closest targets, thumb-clutching (large knob) and handgrip changing (small knob) perform equally well.

H2: When pointing at farthest targets, thumb-clutching (large knob) outperforms hand relocations (small knob).

H3: When pointing at smallest targets, thumb-clutching (large knob) outperforms both handgrip changes and hand relocations (small knob).

Apparatus and Participants

A single body for the prototype (see Figure 2) was built with the following dimensions: 150mm (height) × 70mm (width) × 17mm (thickness), giving a total thickness of 40mm when using the knobs. An exploratory study [START_REF] Rosso | Deformable Tangible Slider for Eyes-Free One-Handed Thumb Interaction on Mobile Devices[END_REF] underlined the impact of the device's thickness on performance. In this study, we controlled the thickness of both knobs to be the same. The length and width were the ones of a commercial large phone [START_REF]Zenfone 2 Laser[END_REF] for a realistic grip. The prototype was built using a 3mm-thick lasercut medium-density fiberboard. A membrane potentiometer [START_REF] Sparkfun | SoftPot Membrane Potentiometer 200mm[END_REF] of 200mm length captures the position of the slider's cursor. The slider and the knobs were made with an Ultimaker 2+ 3D printer, using PLA as the filament. The potentiometer was connected to an Arduino Mega 2560 board. The board was connected via USB to a MacBook Pro running the experimental software, displayed on a 27-inch Thunderbolt screen (2560×1440, 109ppi).

Sixteen volunteers (between 23 and 34 years old, M=27.3, 11 males and 5 females) were recruited on campus. All were righthanded and owners of touchscreen phones. The average measured distance between participants' thumb and index finger with the open hand was 176mm (SD=12.1mm).

Task

The study requires participants to perform a distant pointing task, as in several previous studies e.g., [START_REF] Coutrix | Shape-Change for Zoomable TUIs: Opportunities and Limits of a Resizable Slider[END_REF][START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF][START_REF] Roudaut | TapTap and MagStick: improving one-handed target acquisition on small touch-screens[END_REF]. This abstract task allows representing of real-life tasks in which users adjust a distant parameter without looking at the mobile input device, e.g., browsing a list of channels displayed on the TV, fixing the sound volume while looking at a stage.

The experimental task (see Figure 3) consisted of the user controlling the input device without looking at it. The visual focus was on a screen placed at a distance of 1.60m. The mobile device controlled cursor of a graphical slider displayed on the distant screen. The graphical slider had a length of 232mm. The cursor, controlled by the user, was displayed as a white horizontal line (Figure 3). A visual feedback of the remaining distance (in red) from the user's cursor to the target (in green) is displayed along the slider. Participants were asked to point as fast as possible.

For validation, users were asked to maintain the cursor in the target area for 1s. This validation mechanism is used to avoid any additional error-prone actions [START_REF] Tory | Comparing physical, overlay, and touch screen parameter controls[END_REF]. The extra second was subtracted from the movement time before analysis. Overshoots (i.e., passing over a target -entering and leaving the target area) are used to indicate pointing accuracy [START_REF] Tory | Comparing physical, overlay, and touch screen parameter controls[END_REF]. After the task is completed successfully, a new target appears at a predefined Distance (116mm or 217mm) from the current location of the user's cursor.

Dependent Variables

Our main objective in this study was to determine the impact of thumb-clutching (large knob), handgrip changes and hand relocations (small knob) on performance. To this end, we recorded the movement time from the beginning of each task until the validation. In addition, we recorded the number of performed overshoots in order to study the accuracy of the hand movements (as done in [START_REF] Tory | Comparing physical, overlay, and touch screen parameter controls[END_REF]). Finally, as an indication of perceived usability of the tested knobs, we asked them to fill in a System Usability Scale (SUS) form [START_REF]System Usability Scale (SUS)[END_REF]. The actions of the participants were also video-recorded to study the required hand movements to operate the prototypes (i.e., handgrip changes and hand relocations for the small knob).

Procedure

Participants were first introduced to the prototype through a training phase in which they performed the tasks with the different combinations Knob × Distance × Width. During training, the order of presentation of the conditions was randomized. The training phase lasted 10 minutes on average. Afterwards, the trials started.

The tasks were performed in 2 blocks, one per Knob condition. Half of the participants started with the large knob and continued with the small one and vice versa for the other participants. Each block was divided into 4 sub-blocks representing the 4 Distance × Width combinations. The presentation order of the sub-blocks was randomized. For each sub-block, participants performed 17 repetitions of the task. The first repetition was not analyzed to avoid having results affected by the knob's position from the previous sub-block. A small break was allowed after each sub-block. After participants completed the task for the 2 blocks, they were given the SUS form to fill in.

A total of 2048 measures of movement time were collected, from 16 participants × 16 repetitions × 2 knobs × 2 distances between targets × 2 target's widths. This resulted in 256 measures for each Knob×Distance×Width condition.

Results

We used the geometric mean to estimate the center of the distribution of movement times [START_REF] Sauro | Average Task Times in Usability Tests: What to Report?[END_REF]. Trials were aggregated using the factors Knob, Distance, and Width for each participant. A Shapiro-Wilk test revealed that we could not assume the normality of the data (W = 0.9, p < 0.001). Thus, we applied an Aligned Rank Transformation on the data [START_REF] Wobbrock | The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only Anova Procedures[END_REF] and then ran repeated measures ANOVA on the aligned ranks to investigate possible interactions between factors.

A three-way ANOVA shows that Knob (F(1, 105) = 32.9, p < 0.0001), Distance (F(1, 105) = 191.9, p < 0.0001) and Width (F(1, 105) = 634.4, p < 0.0001) had a significant impact on movement time (Figure 4). An interaction between Width and Distance (F(1, 105) = 4.8, p < 0.05) proved to be significant. This confirms that the Width values were appropriate to distinguish between fine and coarse adjustment for the Distance values.

An interaction between Knob and Distance (F(1, 105) = 8.5, p < 0.01) proved to be significant. For the 217mm Distance condition, the large Knob performed faster for both 1.6mm and 7mm target's Width (+0.6s and +0.4s respectively) than the small Knob. A Tukey's post-hoc test revealed a significant difference between the large and small Knob conditions (t(105) = 5,7, p < 0.001, Cohen's d=0.5). For the 116mm Distance condition, the large Knob performed better (+0.4s) than the small Knob for a target's Width of 1.6mm. For the 7mm target's Width, the large and small Knobs performed equally. We illustrate this in Figure 4.

To explain the equal performance of the Knob conditions for the single 7mm×116mm condition, we used the video footage. We compared the amount of thumb-clutching and handgrip changes performed during the task. On average, 1 clutching movement on the large Knob was required (SD=0.4). Only 1 handgrip change was required on the small Knob. This suggests that when reaching large targets with a short distance between targets, a small knob perform equally well as a large knob.

Regarding the number of overshoots, on average, for large targets (7mm) and long distances (217mm), participants overshot two times (SD=0.02) with the large knob; and 4 times (SD=0.03) with the small knob. For large targets and short distances (116mm), participants overshot 3 times (SD=0.03) with the large knob; and 4 times (SD=0.04) with the small knob. For small targets (1.6mm) and long distances (217mm), participants overshot 13 times (SD=0.09) with the large knob; and 17 times (SD=0.13) with the small knob. For small targets and short distances, participants overshot 15 times (SD=0.13) with the large knob; and 12 times (SD=0.09) with the small knob. This suggests that thumb-clutching movements are slightly more precise than hand relocations and handgrip changes for: 1) large targets for both distances between targets, and 2) small targets and long distances. For small targets and short distances, handgrip changes are slightly more precise.

Contrastingly, SUS indicates that the small knob (69/100, 51% when normalized [START_REF]System Usability Scale (SUS)[END_REF]) is perceived slightly more usable than the large knob (65/100, 48%).

Discussion

In this section, we discuss the observed effects that had an impact on the performance of the hand movements engaged in the Knob conditions.

Short Distances: Thumb-clutching vs.

Handgrip Changes

For small targets (1.6mm) and large targets (7mm) near the functional area of the thumb (116mm), thumb-clutching movements done with the large knob outperform handgrip changes done with the small knob (+0.4s). Moreover, participants were also more precise with thumb-clutching. Participants overshot 9 times more on average with the small knob than with the large one. H1 is consequently discarded.

Long Distances: Thumb-clutching vs. Hand Relocations

Similarly to short distances, for small targets (1.6mm) outside the functional area of the thumb (217mm), thumb-clutching movements done with the large knob outperform hand relocations done with the small knob (+0.6s). Participants overshot 9 times more on average with the small knob than with the large knob. This result suggests again greater precision with the large knob than with the small knob. Regarding large targets (7mm), thumb-clutching outperformed hand relocations (+0.5s). This suggests that hand relocations are more time-consuming than a thumb-clutching. We argue that it is caused by the special care needed to relocate the hand without dropping the device: video footage shows that participants used all the fingers to displace the device.

Overall, hand relocations were slower and less precise than thumb-clutching when pointing outside the functional area of the thumb; supporting H2.

The aforementioned results on thumb-clutching movements support the results about clutching on relative pointing devices [START_REF] Nancel | Clutching Is Not (Necessarily) the Enemy[END_REF].

Small Targets

Thumb-clutching movements outperformed handgrip changes and hand relocations when reaching small targets (1.6mm) for both short (116mm) and long (217mm) distances. As explained before, thumb-clutching enabled participants to perform faster and more precise, thus to reduce overshoot; supporting H3.

Preference

Participants found the small knob slightly more usable, presumably due to the similar operability between the small knob and graphical sliders, and the familiarity with the latter. However, they also reported fatigue after using the small knob. This is confirmed by the video footage: participants were shaking their hands to relax their muscles during the breaks. Finally, participants indicated that the large knob was more comfortable to use since they only needed to move their thumbs.

EXPERIMENT WITH AN ACTUATED SLIDER

Thumb-clutching proved to perform well for targets at the border and far from the functional area of the thumb while offering a stable handgrip. However, in this solution the knob is long. Even on a future miniature prototype, the knob has to be long in order to allow clutching. Unfortunately, a large knob hinders portability of the solution.

We, therefore, explore a solution with a smaller knob. For this, we introduce actuation: we build a prototype that actuates the location of a small knob so that it moves back in the functional area of the thumb after clutching.

We experimentally evaluate this prototype. We were particularly interested in observing if the motion of the actuated knob disrupts the users from being eyes-free. In addition, we wanted to study the impact that the motion of the actuated knob has on the performance of thumb-clutching movements. Finally, we analyzed the perceived usability of such a device.

Actuated Prototype

The starting point is to automatically slide the knob of the slider back to the functional area of the thumb. The prototype is formed by: 1) a base composed of the slider's landmark and a FEETECH FS90R [START_REF] Feetech | Micro 360 Degrees Continuous Rotation Servo[END_REF] continuous rotation servomotor with a pinion on its top; and 2) a piece composed of a solid block, a rack, and a flat surface that serves as the slider's knob (see Figure 5). Its length is half (0.53) the length of the previous prototype.

The pinion-rack mechanism locks the movement between the base and the knob, hence, when the user pushes the knob upwards or downwards, the base moves in the same direction. This gives the sensation of directly pushing the slider's landmark. The mechanism also transforms the rotational movement of the servomotor to a bidirectional linear movement along the slider's axis. The rotation of the pinion makes the solid block slide within the base. This gives the users the feeling that the knob is long, or becoming longer upwards or downwards according to the current position of the landmark (see Figure 6). This allows the thumb to keep manipulating the slider within its comfortable area.

As on any slider, the landmark indicates the current position of the knob. We minimized the thickness to make it as portable and mobile as possible. The obtained thickness is then less than the prototype from the first study (20mm). The knob is 80mm long in order to remain within the thumb's comfortable area while reaching the extremes of the slider. The knob is 10mm wide as for any standard slider knob.

Comparative Experiment

We performed the same task as in the first experiment but with the actuated knob instead of the large knob. We considered two conditions for the actuated knob in order to study eyes-free interaction with it: one condition for which the participant could look at the mobile device to receive visual feedback and one condition with no possible visual feedback by covering the input device with an opaque plastic bag. We also compared these two conditions with an extendable graphical slider. The goal was to compare the performance of clutching when manipulating: 1) an actuated knob that requires no visual attention and, 2) a graphical extendable one that requires switching the visual attention from the mobile device to a distant display.

We thus considered a Technique variable composed of three conditions. The following three conditions allow participants to perform thumb-clutching movements within the functional area of the thumb with a stable handgrip:

Tangible slider with visual feedback (Tangible-Visual): Participants are free to look at the input device and obtain visual feedback from the physical landmark (see Figure 7A).

Tangible slider with no visual feedback (Tangible-Blinded): Same as Tangible-Visual but the tangible prototype is hidden, thus preventing visual feedback as in [START_REF] Lischke | Using Variable Movement Resistance Sliders for Remote Discrete Input[END_REF]. Participants were asked to operate the prototype inside an opaque plastic bag (see Figure 7B).

Graphical slider with visual feedback (Graphical-Visual): An extendable graphical slider that enables users to operate it in the same way as its tangible counterpart (see Figure 7C).

We discarded the condition with a graphical slider and no visual feedback after we ran a pilot study that showed that it was not possible to properly manipulate the graphical extendable slider without looking at the mobile device.

We consider the same Distance and Width conditions as in the first study for this experiment. Given these conditions, we hypothesize the following: H1: Eyes-free interaction with an actuated knob: manipulating an actuated knob will not result in a decrease of performance when users are not looking at the device. The automatic motion of the knob does not mean one has to look at the mobile input device.

H2: Manipulating an actuated knob versus switching visual attention: manipulating an actuated knob will not result in a decrease of performance compared to the equivalent graphical input method that requires switching visual attention between the mobile device and the screen.

Apparatus and Participants

The tangible slider was printed with the Ultimaker 3+ 3D printer with PLA filament. For the Graphical-Visual, an ASUS Zenfone 2 Laser (6-inch screen) smartphone [START_REF]Zenfone 2 Laser[END_REF] was used. We 3D printed a case for the smartphone in order to have the same thickness, equal to 20mm, between the tangible and graphical prototypes. We made use of the same experimental software and connection setup as in the first experiment to operate the tangible prototypes. For the graphical prototype, the communication with the experimental software was done through a Wi-Fi connection.

Seventeen volunteers (between 23 and 34 years old, M=26, 11 males and 6 females) were recruited on campus.

Task and Procedure

For this experiment, participants performed the same task and followed the same procedure as in the first experiment.

A total of 3264 measures of movement time were collected, from 17 participants × 16 repetitions × 3 techniques × 2 target's widths × 2 distances between targets. For each Technique × Width × Distance conditions, this resulted in 272 measures of movement time.

As in the first experiment, we recorded the movement time to complete the task and the number of performed overshoots for each Technique. We also video recorded the thumb movements and gaze of participants while operating the prototypes (as done in [START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF]): we analyzed gaze diversions and thumb movements during the automatic motion of the actuated knob.

Results

As in the first experiment, we used the geometric mean to aggregate movement time. The data was aggregated per participant and variables. A Shapiro-Wilk test revealed that we could not assume the normality of the data (W = 0.9, p < 0.01). Thus, we applied an Aligned Rank Transformation on the data [START_REF] Wobbrock | The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only Anova Procedures[END_REF].

A repeated measures three-way ANOVA showed a significant main effect of Technique (F(2, 176) = 62.7, p < 0.0001), Distance (F(1, 176) = 123.7, p < 0.0001) and Width (F(1, 176) = 118.7, p < 0.0001) on movement time. As in the previous experiment, the differences in movement time between small (1.6mm) and large targets (7mm) for the same distance confirm that the chosen conditions were appropriate for distinguishing between fine and coarse adjustment (see Figure 8).

An interaction between Technique and Distance (F(2, 176) = 9.5, p < 0.001) proved to be significant. For the 116mm Distance condition, the Graphical-Visual condition presents the highest movement time on both 1.6mm and 7mm target's width (3.5s and 3s respectively). A Tukey's post-hoc test revealed no significant difference between the Tangible-Visual and Tangible-Blinded conditions for both widths (t(80) = 5.5, p > 0.05, Cohen's d=0.4). Similarly, for the 217mm Distance condition, the Graphical-Visual condition presented the slowest performance (+1.1s from the tangible conditions) for both target's widths. A Tukey's posthoc test revealed no significant difference on performance between the Tangible-Visual and Tangible-Blinded conditions for both target's widths (t(80) = 5.5, p > 0.05, Cohen's d=0.2). These differences are observable in Figure 8 where the Tangible-Visual and Tangible-Blinded conditions have similar performance times. This suggests that, when operating tangible controls, having visual feedback from the input device is not critical for performance. On the contrary, visual attention was required to operate the Graphical-Visual condition.

Regarding the number of overshoots, on average, for short distances (116mm) and small targets (1.6mm), participants overshot 9.8 times (SD=0.07) with the Tangible-Visual condition, 14.7 times (SD=0.14) with the Tangible-Blinded condition, and 15 times (SD=0.08) with the Graphical-Visual. For large targets (7mm), participants overshot 6.4 times (SD=0.05) with the Tangible-Visual condition, 6.5 times (SD=0.05) with the Tangible-Blinded condition, and 7 times (SD=0.05) with the Graphical-Visual. This suggests that the tangible prototype is slightly more precise than the graphical one for small and large targets over short distances between targets.

For long distances (217mm) and small targets (1.6mm), participants overshot 21.7 times (SD=0.17) with the Tangible-Visual condition, 21.9 times (SD=0.15) with the Tangible-Blinded condition, and 14.3 times (SD=0.07) with the Graphical-Visual. For large targets (7mm), participants overshot 7.5 times (SD=0.06) with the Tangible-Visual condition, 10.4 times (SD=0.08) with the Tangible-Blinded condition, and 4.4 times (SD=0.03) with the Graphical-Visual. This suggests that the graphical prototype is more precise than the tangible one for small and large targets over long distances between targets.

The SUS scores indicate that participants found both graphical slider (72.1/100, 53% after normalization [START_REF]System Usability Scale (SUS)[END_REF]) and tangible slider (71.7/100, 52.7%) as equally usable.

DISCUSSION

In this section, we discuss the observed effects that had an impact on the performance of each technique.

Eyes-free Interaction With an Actuated

Tangible Knob

The Tangible-Visual condition performed equally well as the Tangible-Blinded condition for both short and long distances.

Based on the number of overshoots, the Tangible-Visual was slightly more precise than the Tangible-Blinded for small targets and short distances (-4 overshoots), and large targets and long distances (-3 overshoots). These results suggest that the motion of the actuated knob did not prevent participants from operating in an eyes-free manner, thus supporting H1.

On the contrary, the Graphical-Visual presented the worst performance. We explain the bad performance of the graphical solution by the number of time that participants looked down to reacquire the slider's knob. This effect has already been observed when operating graphical widgets [START_REF] Jansen | Tangible remote controllers for wall-size displays[END_REF][START_REF] Lischke | Using Variable Movement Resistance Sliders for Remote Discrete Input[END_REF][START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF]. We used video footage from the experiment to annotate each time participants gazed at the graphical slider on the input device. The result shows that participants looked down at the input device, on average, two times per repetition of the task; giving a total of 128 gaze deviations. We argue that the parabolic movement of the thumb [START_REF] Bergstrom-Lehtovirta | Modeling the functional area of the thumb on mobile touchscreen surfaces[END_REF] prevented participants from operating the slider in a vertical manner, thus leading participants to operate outside the slider area. Moreover, the lack of tangible feedback from the Graphical-Visual condition made difficult for users to land their thumb back into the slider graphical area when clutching. On the contrary, the tangible prototype under both visual conditions did not require visual attention to be operated.

Impact of the Motion of the Actuated

Tangible Knob on Performance

The motion of the actuated knob had an unexpected effect on interaction: participants stopped manipulating the slider while the knob was in motion. Video footage shows that, when performing thumb-clutching movements, 15 out of 17 participants waited for the knob to stop moving before landing their thumb. Since participants stopped manipulating the slider, we argue that the motion of the knob had an impact on performance. To confirm this, we compared the mean number of times the operating hand was idle when using the actuated slider with the large knob from the first experiment. We found that the mean number of idle time increased 35% for the 1.6mm Width condition and 64% for the 7mm Width condition in comparison with the same conditions from the first experiment. Although both conditions were not tested in the same experiment, we expected that the thinner body of the designed actuated knob (-20mm) would have implied an easier operation, thus better performance. However, this was not the case. We can then only speculate that the motion of the actuated slider had an impact on the performance of thumb-clutching movements. Despite the observed stops in movement provoked by the actuated knob and its resulting drop in performance (+0.6s) in comparison with the large knob from the first experiment, the tangible slider proved to outperform the graphical slider. This suggests that the switching of visual attention required by the graphical extendable slider had a bigger impact on performance than the motion of the actuated knob; supporting H2.

Preference

Both graphical and tangible sliders were found equally usable. We argue that despite the visual attention required by the graphical slider, its high score is due to the familiarity of the participants with tactile interfaces [START_REF] Maria Troiano | User-defined gestures for elastic, deformable displays[END_REF].

Regarding our tangible prototype, we argue that a higher fidelity version could have been perceived as more useful [START_REF] Robinson | Emergeables: Deformable Displays for Continuous Eyes-Free Mobile Interaction[END_REF]. Nevertheless, we consider our tangible prototype as being of medium fidelity since it supported good performance.

CONCLUSION

In this paper, we introduced thumb-clutching on tangible extendable sliders for eyes-free and one-handed interaction on mobile devices. We built two prototypes to test the viability and performance of thumb-clutching on tangible extendable sliders.

Our first low-fidelity prototype -a tangible slider with a very large knob -gave us insight into the manipulation and performance of an extendable slider and how it compares to a standard tangible slider. Experimental results show that clutching on this prototype improves performance when reaching for proximal and distant targets.

Our second higher-fidelity prototype -a tangible slider with an actuated knob -was compared to an extendable graphical slider. The results show that (1) the motion of the actuated knob did not disrupt participants from eyes-free interaction; (2) the switching of the visual attention required to operate the graphical extendable slider has a bigger impact on performance than the stops in manipulation during the automatic motion of the actuated knob.

Our results show the benefits of thumb-clutching on tangible extendable sliders for eyes-free and one-handed interaction in the context of remote displays. To address the limitations of the designed prototype we will in the future work test different directions for deforming the knob instead of moving it. For instance, the knob could extend by morphing out of the surface below the thumb; this would prevent the user from feeling the motion of the knob and therefore stopping the manipulation of the slider. Furthermore, we will investigate the challenge of combining the use of multiple extendable tangible sliders for the adjustment of different continuous parameters -e.g., controlling the RGB levels of a projector.

ACKNOWLEDGMENTS

This work was supported by the French National Research Agency (ANR-11-LABX-0025-01, ANR-11-EQPX-0002, ANR-15-CE23-0011-01), the EPSRC grant (EP/N013948/1), the Alexander von Humboldt Foundation, the German Research Foundation through projects C02 & C04 of SFB/TRR 161, and the German Federal Ministry of Education and Research as part of the project Be-greifen (grant no. 16SV7527). The prototypes have been partially made in MSTIC (http://fabmstic.liglab.fr/).

Figure 2 .

 2 Figure 2. The Knob conditions and the hand movements related to their operation: (A1) the small knob is pushed (direction of the blue arrow) with an initial handgrip. (A2) The fingers on the back of the device move (direction of the red arrow), thus changing the handgrip. (B1) the small knob is pushed (direction of the blue arrow) with an initial hand location. (B2) The hand is relocated (direction of the red arrow) when the thumb's limit is reached. (B3) The knob is pushed with the new hand location. (C1) The large knob is pushed (direction of the blue arrow) with an initial handgrip. (C2) Relocation of the thumb. (C3) The knob is pushed with the same handgrip.

Figure 3 .

 3 Figure 3. Screenshot of the experimental pointing task with a slider of 232mm/1121px, a target's width of 1.6mm/7px, and a distance of 217mm/1048px.

Figure 4 .

 4 Figure 4. Mean movement time for the 2 Knob conditions and for the 4 possible Distance × Width conditions (y-axis). Error bars show 95% confidence intervals.

Figure 7 .

 7 Figure 7. A participant trails under different conditions: (A) Tangible slider with visual feedback. (B) Tangible slider with no visual feedback. (C) Graphical slider with visual feedback.

Figure 6 .

 6 Figure 6. (A) The thumb pushes the knob (direction of the red arrow) until it reaches its maximum elongation. (B) The knob starts to move back (direction of the blue arrow) while the thumb clutches to a comfortable position. (C) The thumb is relocated within its comfortable area and ready to continue operating.

Figure 5 .

 5 Figure 5. Actuated slider: the rotational movement (green arrow) of the pinion (in red) is transferred to a bidirectional movement (red arrow) on the rack (in blue), provoking the solid block (in orange) slide through the base and thus, simulating the extension of the knob (in green). A physical landmark (in purple) represents the position of the specified value.

Figure 8 .

 8 Figure 8. Mean movement time for the 3 Technique conditions and for the 4 possible Distance × Width conditions (y-axis). Error bars show 95% confidence intervals.