Qingfeng Li
email: li@lp3.univ-mrs.fr

David Grojo

Anne-Patricia Alloncle

Philippe Delaporte

Dynamics of double-pulse laser printing of copper microstructures

Keywords:

Laser induced forward transfer process can be implemented in a double-pulse scheme where a solid thin film deposited on a transparent donor substrate is irradiated by two synchronized lasers. In a recently demonstrated methodology, a long pulse is first applied to melt the film and an appropriately delayed ultrashort laser pulse initiates material transfer in the liquid phase toward a receiver substrate. This provides a versatile method to print high-resolution (<2 µm) patterns with a long working distance (>40 µm). In this paper we focus on the study of the dynamical aspects associated with these printing performances. The temperature evolution of the thin copper film during irradiation with a quasi-continuous wave (QCW) pulse is calculated. By combining the calculations with time-resolved imaging experiments, we reveal the influence of the copper film temperature and molten metal diameter on the ejection dynamics. Characterization of the transferred materials shows that the delay between the two laser pulses is a control parameter for the shape and volume of the printed structures. This is finally exploited to demonstrate high-precision printing of different debris-free microstructures onto a Si receiver substrate set as far as 60 µm away from the donor film.

Introduction

Recently, the double-pulse laser-induced forward transfer (DP-LIFT) process has been successfully applied for generating liquid nano-jets from solid donor films and consequently transfer various materials (Cu, Au, Ag, Ni) on a receiving substrate with well-defined and debris-free depositions [START_REF] Li | Generating liquid nanojets from copper by dual laser irradiation for ultra-high resolution printing[END_REF][START_REF] Li | Laser-induced nano-jetting behaviors of liquid metals[END_REF]. However, due to the numerous mechanisms taking place during the double-pulse process, the physics behind this novel laser-induced jetting and deposition technique is not fully understood yet. LIFT related jetting phenomenon from low viscosity liquid donors has been extensively investigated by several groups, both experimentally [START_REF] Duocastella | Time-resolved imaging of the laser forward transfer of liquids[END_REF][START_REF] Boutopoulos | Laser-induced forward transfer of silver nanoparticle ink: time-resolved imaging of the jetting dynamics and correlation with the printing quality[END_REF][START_REF] Unger | Time-resolved imaging of hydrogel printing via laser-induced forward transfer[END_REF][START_REF] Biver | High-speed multi-jets printing using laser forward transfer: time-resolved study of the ejection dynamics[END_REF] and numerically [START_REF] Brown | Impulsively actuated jets from thin liquid films for high-resolution printing applications[END_REF][START_REF] Bourasseau | Calculation of the surface tension of liquid copper from atomistic Monte Carlo simulations To cite this version: calculation of the surface tension of liquid copper from atomistic Monte Carlo simulations[END_REF][START_REF] Pearson | Bubble interactions near a free surface[END_REF]. These studies point out that the jetting mechanism is initiated by an expanding cavitation bubble generated between the donor substrate and the liquid-free surface. However, in the DP-LIFT situation, the typical thickness of the donor film is below 1000 nm, and thus, such a cavitation bubble driving mechanism would require a strong downscaling of the bubble size and make it unlikely. Besides, laser-induced nano-jetting from ultra-thin (<100 nm) solid donor films has been reported and investigated experimentally [START_REF] Nakata | Solid-liquid-solid process for forming free-standing gold nanowhisker superlattice by interfering femtosecond laser irradiation[END_REF][START_REF] Zywietz | Generation and patterning of Si nanoparticles by femtosecond laser pulses[END_REF][START_REF] Korte | Formation of microbumps and nanojets on gold targets by femtosecond laser pulses[END_REF][START_REF] Moening | Formation of high-aspect-ratio protrusions on gold films by localized pulsed laser irradiation[END_REF][START_REF] Unger | Time-resolved studies of femtosecond-laser induced melt dynamics[END_REF][START_REF] Kuchmizhak | Plasmon-mediated enhancement of rhodamine 6G spontaneous emission on laser-spalled nanotextures[END_REF][START_REF] Wortmann | Experimental and theoretical investigation on fs-laser-induced nanostructure formation on thin gold films[END_REF] and theoretically [START_REF] Anisimov | Formation and crystallisation of a liquid jet in a film exposed to a tightly focused laser beam[END_REF][START_REF] Inogamov | Solitary nanostructures produced by ultrashort laser pulse[END_REF][START_REF] Inogamov | Jet formation in spallation of metal film from substrate under action of femtosecond laser pulse[END_REF]. In these experiments, an ultrashort pulse irradiates the thin film with a Gaussian beam profile which induces a Gaussian distributed pressure force in a film melted over its full thickness in the irradiated area. Under appropriate conditions, the molten film can detach from the substrate with the shape of a dome shell. Within this dome shell the normal component of the capillary force decelerates the normal velocity of the shell and the parallel component leads to the displacement of the shell material towards the center. Taken these effects all together, a jet starts to form when the reverse motion of the shell begins [START_REF] Anisimov | Formation and crystallisation of a liquid jet in a film exposed to a tightly focused laser beam[END_REF]. A difference with the DP-LIFT situation is the diameter of the melted area which is only 1 to 2 orders of magnitude larger than the dimension of the ultrafast laser spot used in these experiments. The much larger melted area achieved in DP-LIFT, makes less relevant the above-mentioned description based on a locally detached dome shell for this process, and such a dome has never been observed in this configuration. For these reasons, the dynamical aspect associated to DP-LIFT remains unclear and requires further investigations. Looking at the already performed DP-LIFT experiments [START_REF] Li | Generating liquid nanojets from copper by dual laser irradiation for ultra-high resolution printing[END_REF][START_REF] Li | Laser-induced nano-jetting behaviors of liquid metals[END_REF][START_REF] Narazaki | On-demand deposition of functional oxide microdots by double-pulse laser-induced dot transfer[END_REF][START_REF] Klini | Laser induced forward transfer of metals by temporally shaped femtosecond laser pulses[END_REF], even though they have demonstrated the unique features and liquid metal jetting behaviors, they have not been dedicated to study the specificities of the laser printing in this configuration. By comparing the calculated time-evolution of the film temperature initiated with the pre-pulse and the experimental observations of both the ejection dynamics and the printed structures, we intend here to investigate these aspects to improve the physical understanding of nano-jetting. This allows also finding new parameters to finely control the shape and the volume of the printed structures, and subsequently optimize the performance of DP-LIFT for digital micro-nano-printing.

Materials and methods

Experimental setup

The experimental arrangement implemented to investigate various aspects of the DP-LIFT process is depicted in Fig. 1(a). The laser source used to achieve the melting of the donor film is a quasi-continuous wave (QCW) laser (IPG Photonics YLR-150/1500-QCW-AC-Y14) emitting, at 1070-nm wavelength, pulses of variable duration from 50 µs to the continuous wave operation. Synchronized with the QCW laser irradiation, a femtosecond laser (Amplitude Systemes S-Pulse HP), delivers at 515 nm wavelength (second harmonic), pulses of 500 fs duration (FWHM) and focused at the center of the melted region to induce material ejections. Both beams enter collinearly through a long working distance 0.55NA (Mitutoyo M Plan Apo 50× ) objective lens. The measured beam diameters at half maximums (FWHM) at the copper-donor interface are respectively 1.6 µm for the femtosecond laser and 9.7 µm for the QCW laser. The power of both lasers is inde pendently adjusted using half-wave plate and polarizer combinations. The positioning of the two beams and the systematic inspection of the donor film is facilitated by a customized reflection microscopy arrangement (not shown here). Time-resolved shadowgraphs of material ejections are recorded using a CCD camera (QImaging QICAM) mounted on a customized microscopy arrangement based on a 50× super-long working distance microscope objective lens (Mitutoyo M Plan Apo SL NA = 0.4). Bright-field flash illumination is provided by a nanosecond flash lamp (High-Speed Photo-Systeme KL-M NANOLITE). The flash duration of 12 ns determines the temporal resolution of the acquisition system. A digital delay generator (Stanford Research Systems DG645) is used to precisely synchronize, with adjustable delay, the two laser pulses and the flash lamp to perform time-resolved shadowgraphy imaging. As illustrated in Fig. 1(b), the delay Δt between the initial time (t = 0) of the sequence and the femtosecond laser pulse can be arbitrarily adjusted by the delay generator. For each sequence, the flash light will illuminate the field-of-interest with a preset flash-to-LIFT delay τ to acquire with the camera a snapshot of the ejection event occurring at a delay τ after the fs pulse. In this paper, conditions corresponding to different Δt delays and various τ are investigated. For all the experiments presented in this paper, a 1-µm thick copper film with a 25 nm chromium interlayer (magnetron sputtering onto a 1-mm-thick glass substrate) is used as donor film.

QCW heating model

In DP-LIFT, the role of the irradiation by the first QCW pulse is to induce a local melting on the donor film. At fixed QCW power, when the second femtosecond pulse irradiates the heated donor film with different delays Δt, the donor film exhibits different temperatures below or above melting. For copper, as shown in Table 1, some of the physical properties of the film are significantly temperature-dependent [START_REF] Battezzati | The viscosity of liquid metals and alloys[END_REF][START_REF] Egry | Surface tension of liquid metals: results from measurements on ground and in space[END_REF][START_REF] Baba | Thermal conductivity measurement of molten copper using an electromagnetic levitator superimposed with a static magnetic field[END_REF][START_REF] Valencia | Thermophysical Properties[END_REF]. One can expect different behaviors depending on the hydrody

N C O R R E C T E D P R O O F Q. Li et al. Applied Surface Science xxx (2018) xxx-xxx
namic characteristics of the film such as the dynamic viscosity and the surface tension. Accordingly, it is worth investigating the ejection dynamics of liquid copper for different temperatures simply controlled by varying the delay between the two laser pulses. For the interpretation, the impact of the molten pool diameter (also varying) should also be taken into account as it will have an influence on the pressure distribution in the liquid film, which is known to play a key role in some ejection processes. For this reason, the space-time evolution of the film temperature under irradiation by the QCW pulse irradiation is first calculated.

The heating process of the donor by the QCW pulse is governed by the general heat equation: which gives the temperature T in the system in response to a heat source Q. The enthalpies of fusion and vaporization are incorporated by adding a Gaussian function to the heat capacity C p , centered at the equilibrium phase-change temperatures, exhibiting a width of . The density ρ and thermal conductivity k are temperature dependent [START_REF] Assael | Reference data for the density and viscosity of liquid copper and liquid tin[END_REF][START_REF] Cagran | Thermal Conductivity and Thermal Diffusivity of Liquid Copper[END_REF]. Thus, the heat equation which describes this process is numerically solved. The heat source Q corresponds to the absorption of the QCW laser energy, with a Gaussian profile along x direction, parallel to the film surface. According to the Beer-Lambert law and taking into account multiple internal reflections in the thin film the heat source is expressed as [START_REF] Li | Laser-induced nano-jetting behaviors of liquid metals[END_REF] where R represents the reflection coefficient, α the linear absorption coefficient, D the thickness of the thin film, ω 0 the beam waist and z the absorption direction. For all the experiments presented in this article, the QCW laser and the sequence is driven by an electrical square pulse of 400-µs duration. Its raising edge defines the initial time (t = 0 µs). The optical output power of the QCW laser pulse starts at t = 24 µs and is constant until it exponentially decays at t = 383 µs (see Fig. 1b), reaching zero at t = 400 µs. To fulfill the actual temporal evolution of the optical output, the QCW laser puls e intensity I 0 (t) is described by a piecewise function:

(3) where E p is the QCW pulse energy measured as 770 µJ ± 70 µJ in the experiments and τ qcw is the total pulse duration measured as 378 µs (from t = 24 µs to t = 400 µs).

Results and discussion

Ejections at different Cu temperatures

Using numerical simulations, the temperature evolution of the donor film under QCW pulse irradiation is calculated from t = 0 µs to t = 500 µs and presented in Fig. 2. More precisely, the time-evolution of the lateral temperature distribution is mapped out and shown in Fig. 2(a). The donor film thickness is small enough (1-µm) to consider the temperature to be uniform in the z-direction (whole thickness). The solid line plot on this graph shows the contour line for the melted region (temperature above the fusion point). To have an overview of the heat affected area after DP-LIFT, a SEM image of the corresponding processed area on the donor film is presented in Fig. 2(b). A light grey disk with diameter of ≈60 µm refers to the heat affected zone after the QCW laser irradiation and a dark grey disk with diameter ≈20 µm refers to the re-solidified material after melting. At the center of the molten pool, a vestige of surface pinching can be observed. This observation proves that a jet is initiated at the center of the QCW laser spot. As this central region also corresponds to the maximum temperature of the donor film, we plot its temporal evolution in Fig. 2(c). Referring to the temporal profile of the QCW pulse described in Eq. ( 2), the copper film temperature starts to rise at t = 24 µs and the central region reaches the melting point at t = 150 µs. From Fig. 2(c), we can see that the temperature raises up to its highest value of 1689 K at t = 383 µs before to drop sharply at t = 395 µs leading to the re-solidification of the film. In Fig. 2(d), the time-evolution of the molten pool diameter during this process is also presented. A similar evolution can be observed for this parameter. The molten pool starts to form at t = 150 µs and the maximum diameter 27.4 μm is reached at t = 383 μs. After that, the molten pool diameter decreases sharply and at t = 395 μs the molten pool has completely disappeared.

With the knowledge of the temperature of the copper donor film under the QCW pulse irradiation and the experimental observations of the ejection dynamics using the setup presented in Fig. 1, it becomes possible to investigate the impact of different molten pool temperatures and diameters on the ejection behaviors. We have performed DP-LIFT experiments for different QCW-to-fs delays Δt (see Fig. 1(b)) without the presence of a receiver substrate. As shown in Fig. 3, the time-resolved observations of the ejection events are captured with LIFT-to-flash delays τ of and . During the heating process, the femtosecond LIFT laser with the pulse energy of 2 µJ irradiates the middle of the heated zone with delay Δt with respect to the experimental initial moment (t = 0). The LIFT-to-flash delay τ was first set at 300 ns in order to illuminate the ejection before any droplet develops. As shown in Fig. 3(a), jetting seems to appear at Δt = 125 µs From Δt = 175 µsto 380 µs the length of the jet increases, because of higher ejection velocities, and then diminished rapidly until no significant jetting is observed after Δt = 388 µs. The second LIFT-to-flash delay τ was set at 600 ns in order to observe the ejection after the potential appearance of droplets. First, the shadowgraphy images acquired for this delay show that there is no evolution of the copper film motion between τ = 300 ns and τ = 600 ns for Δt delays shorter 155 µs or longer than 385 µs. There is no ejection occurring for these conditions. Even if a jet seems to be initiated at Δt = 155 µsand Δt = 386 µsone should note that it cannot escape from the donor surface. From Δt = 175 µs to 380 µs jets encounter different pinch-off processes and evolve into equilibrium spheres, complex oscillators or the so-called endpinching depending on the initial aspect ratio of the jets. It is interesting to mention that these observations are consistent with the theoretical prediction of Notz et al. [START_REF] Notz | Dynamics and breakup of a contracting liquid filament[END_REF], even though the jet radius is downscaled down to the micrometer scale in our experiments. To help in the interpretation of these mechanisms, the morphologies of the donor film surface after the DP-LIFT process are also presented in Fig. 3(c) for each experimental condition. By using the shadowgraphy images acquired at the two times, we have also calculated the average velocity of the ejection. This average velocity is plotted in the graph of Fig. 2(c) to highlight the correlation with temperature evolution of the donor film.

According to these investigations, a first conclusion is that the impact of the copper film temperature on the process does not lead to a binary response associated with melted or unmelted films. This parameter plays a significant role in the dynamics of the laser-induced jetting process. When the donor film is melted, as the temperature increases, the initial ejection velocity increases. As both optical (reflectivity) and hydrodynamics (surface tension and viscosity) parameters are temperature related, we have tried first to correlate the temperature evolution to the ejection velocity changes using an energy balance model treatment (see supplementary materials). However, the velocity

U N C O R R E C T E D P R O O F Q. Li et al. Applied Surface Science xxx (2018) xxx-xxx
variations that can be predicted by this approach are not as large as those observed in our experiments and plotted in Fig. 2(c). This is most probably caused by the influence of the molten pool size ignored in our calculations. To establish the correlation between the molten pool diameter and the ejection velocity, we plot in Fig. 2(e) the measured ejection velocities as a function of calculated molten pool diameters. From 15 µm to 25 µm the ejection velocities are proportional to the molten pool diameters. This is of significant technical importance as the time-evolution of the molten pool diameter during the DP-LIFT process allows us to access in principle a wide range of ejection regimes changing neither the laser parameters (energy, fluence, pulse duration, etc.) nor the donor thickness.

Ejection regimes 3.2.1. Bump-like deformations

With the space-time evolution of the film temperature provided in Fig. 2, we determined that in DP-LIFT configuration with femtosecond LIFT pulse arriving with delay Δt = 75 µs, the temperature of the donor film is high (>1100 K at QCW spot center) but still remains in its solid phase. Accordingly, as shown in Fig. 3(c) (75 µs), there is no flow motion occurring at the free surface and finally the femtosecond pulse induces a pressure simply leading to a bump-like deformation of the donor film. At continuously increasing delays up to Δt = 125 µs the temperature reaching about 1300 K near the melting point. For this condition, it can be seen in Fig. 3 that the femtosecond LIFT pulse produces a local expansion that can be observed at the early time (

) whereas this motion will be quickly stopped before . This will finally lead to a bump-like deformation with a higher aspect ratio on the donor film as shown in Fig. 3(c) (125 µs).

Dynamics below ejection threshold

As the donor temperature continuously increases with delay above 125 µs, local melting of the film starts to occur, and the liquid motion induced by the femtosecond pulse irradiation changes drastically the dynamical response of the film. It can be observed that from Δt = 125 µs to Δt = 155 µs the deformation velocity jumps from to . This is due to conditions for which the temperature of the copper film crosses the melting point (from 1303 K to 1368 K). For the same conditions, the molten pool diameter increases from 0 to 3.8 µm.

However, Figs. 2(c) and Fig. 3(a-b) show that, from Δt = 155 µs to 165 µs (see Fig. s1), even if the copper is molten and liquid ejection initially appears, the material does not escape from the free surface. The SEM image shown in Fig. 3(c) (155 µs) also confirms this behavior. In fact, this trapping can be explained by comparing the values of the kinetic energy and the surface energy, as the ejection can only occur if the kinetic energy of the expelled material exceeds the surface energy [START_REF] Brown | Impulsively actuated jets from thin liquid films for high-resolution printing applications[END_REF][START_REF] Pohl | Ejection regimes in picosecond laser-induced forward transfer of metals[END_REF]. The dimensionless Weber number We ej can be used to characterize this relation. It is given by the ratio:

(4)
The material escape threshold condition corresponds to We ej = 1 and that allows the calculation of a minimal required velocity V ej_min found at and matching remarkably well with the measured velocity at Δt = 175 µs(see Fig. 2(c)).

Dynamics above escape threshold

From Δt = 175 µs to Δt = 380 µs the average ejection velocity increases from to with a temperature increase from to and a molten pool diameter increase from 8.8 μm to 27.4 μm. It is worth to notice that, under those conditions, the average ejection velocity is proportional to the molten pool diameters. From SEM images presented in Fig. 3(c) one can also observe that there is no significant protrusion structures formed on the surface for these conditions. Only some ripples are observed. Shadowgraphy observations presented in Fig. 3(b) show that, the DP-LIFT generated jets pinch off at the surface for these conditions. Interestingly, these surface pinching and protrusion free features are different from most of the reported laser-induced nano-jetting phenomenon generated from ultra-thin metal films [START_REF] Nakata | Solid-liquid-solid process for forming free-standing gold nanowhisker superlattice by interfering femtosecond laser irradiation[END_REF][START_REF] Zywietz | Generation and patterning of Si nanoparticles by femtosecond laser pulses[END_REF][START_REF] Korte | Formation of microbumps and nanojets on gold targets by femtosecond laser pulses[END_REF][START_REF] Moening | Formation of high-aspect-ratio protrusions on gold films by localized pulsed laser irradiation[END_REF][START_REF] Unger | Time-resolved studies of femtosecond-laser induced melt dynamics[END_REF][START_REF] Kuchmizhak | Plasmon-mediated enhancement of rhodamine 6G spontaneous emission on laser-spalled nanotextures[END_REF][START_REF] Wortmann | Experimental and theoretical investigation on fs-laser-induced nanostructure formation on thin gold films[END_REF]. In those cases, the jetting process involved with the competition between inertia-capillary dynamics and crystallization, in which the jet elongates and breaks up into droplets due to the Plateau-Rayleigh instability and the formation of a neck occurs in the solidification zone between the crystalline and liquid parts of the jet [START_REF] Anisimov | Formation and crystallisation of a liquid jet in a film exposed to a tightly focused laser beam[END_REF].

Printed copper microstructures

Droplet arrays printed with different QCW-to-fs delays

According to the previous discussions, the ejection behavior depends on the QCW-to-fs delay. A direct benefit from this finding is that it allows us to perform pixel-to-pixel printing with controllable pixel shapes and sizes. By placing a silicon receiver substrate at 50 µs distance in front of the donor film, the ejected material can be readily collected. Then, by repeating the DP-LIFT process and controlling the motion of the receiver and donor substrates, 2D patterns with arbitrary designs can be printed on the receiver. As a first demonstration, we have printed three 6 × 6 matrices with a period of 30 μm for three different QCW-to-fs delays.

As shown in Fig. 4(a1), for a QCW-to-fs delay Δt = 195 µs, the ejection of the liquid copper have evolved into an equilibrium sphere at after a travel distance of µm. The corresponding average flying velocity is . Under this condition, due to the low initial aspect ratio, the droplet will keep its spherical shape once the equilibrium is established. Due to the short transfer distance of 50 µm, the air drag effect can be neglected and one can assume that the impact velocity on the receiver is directly V im = V f . When the droplet reaches the receiver, its diameter d is µm and the impact Weber number We im can be approximated as:

(5) Thus, as presented in Fig. 4(a4), when the droplet wets the receiver with such a small Weber number it can hardly spread and finally solidifies with a sphere [START_REF] Vandam | Experimental study of the impact of an ink-jet printed droplet on a solid substrate[END_REF]. In Fig. 4(a2) and (a3), the repeatability is demonstrated by the matrix printing. The average diameter of the printed droplets is measured as 2.40 μm with a deviation of ± 0.23 µm.

For Δt = 275 µs, as shown in Fig. 4(b1), the material is ejected as a jet which has travelled a distance of µm at . When this ejection reaches the receiver, the impact Weber number We im is approximately 13.7. Under these conditions, as presented in Fig. 4(b4), the printed droplet starts to spread on the receiver. Compared to the previous case, and the droplets exhibit discontinuities at the surface and contours. This feature indicates that the pinch-off of the jet must have started before the material reaches the receiver and the re-solidification stage. The consequence is that the quality of the printed pixels suffers from the merging of segmented droplets. In Fig. 4(b2) and (b3), a printed pixel matrix under these conditions is shown. The average diameter of the printed droplets is measured as 2.77 µm with a deviation of ± 0.12 µm. This corresponds to a feature size larger than the one of the previous case but with a similar repeatability.

For Δt = 375 µs, as shown in Fig. 4(c1), this long liquid jet starts to pinch-off followed by a so-called endpinching mechanism at for a travel distance of μm. When the ejected material reaches the receiver the impact Weber number We im is approximately 54.8. As presented in Fig. 4(c4), similarly to previous case, the corresponding printed droplets exhibit rough contours and discontinuities, but they

U N C O R R E C T E D P R O O F
are also somehow squeezed with a flatten shape. In Fig. 4(c2) and (c3), a printed pixel matrix is also shown, and the average diameter of the printed droplets is measured as 4.22 µm with a deviation of ± 0.48 µm.

High-aspect ratio copper microstructures

As presented in the last section, it is for the conditions with Δt = 275 µs that the printed droplets exhibit the best reproducibility. For this reason, we have chosen these printing conditions to demonstrate the ability of building microstructures in the third dimension by repeated DP-LIFT technique at the same location. In Fig. 5(b), we show the structure obtained after printing four droplets while the receiver is kept at the same location. The droplets are piled one by one on top of each other to finally form a with a height of μm without any debris around the structure. Despite the drawback of the inherent discontinuity of the structures formed by this mean, the ability to assemble droplets in the third dimension represents a critical step for technological considerations.

Conclusions

In conclusion, we have demonstrated laser-induced jetting from a copper film of 1-µm thickness using a dual laser approach and the associated ejection dynamics were investigated. The space-time temperature evolution of the donor film under illumination has been numerically calculated. By irradiating the heated film with identical femtosecond pulses at different delays, we have observed different ejection regimes. By comparison between the thermal simulations and time-resolved imaging of the material ejections, we conclude that the size of the melted region more than the copper film temperature plays an essential role in the jetting ejection dynamics. A technological benefit of these results is the possibility to achieve multi-scale printing without changing neither the laser parameters (energy, fluence, pulse duration, etc.) nor the donor thickness. Droplet matrices with pixel diameters from 2.40 ± 0.23 µm to 4.22 ± 0.48 µm and micro-column with a height of 13.6 µm are successfully printed without any debris. This shows the potential of this DP-LIFT approach for the development of a true-3D laser nano-micro-printing technology.

Fig. 1 .

 1 Fig. 1. (a) Sketch of the experimental setup for DP-LIFT. The femtosecond LIFT laser beam is represented in green and the QCW laser beam in red. Illumination flash light is shown by the blue color. (b) Time chart of events for synchronization of the DP-LIFT and time-resolved observations.

Fig. 2 .

 2 Fig. 2. Space-time characteristics of the copper film and ejections during the DP-LIFT process. (a) Time-evolution of the lateral temperature distribution of the donor copper film under QCW pulse irradiation. (b) SEM image of the film after the DP-LIFT process. (c) Time-evolution of the temperature evolution in the central region of the QCW beam and the measured ejection velocities as a function of LIFT time (synchronization of the fs pulse). The melting temperature of copper under atmospheric pressure is 1357.7 K and shown by a horizontal dash line on the graph. (d) Time-evolution of diameter of the molten film region. (e) Measured ejection velocities as a function of melting pool diameter.

Fig. 3 .

 3 Fig. 3. Shadowgraphy images of ejections at different LIFT times during the QCW irradiation, with LIFT-to-flash delays of 300 ns (a) and 600 ns (b), scale bars: 10 μm. (c) SEM image of remaining structures on the donor film after the DP-LIFT process at different LIFT times, scale bar: 2 μm.

Fig. 4 .

 4 Fig. 4. Ejection induced by DP-LIFT process and the printed pixel matrixes with QCW-to-fs delays of 195 µs (a); 275 µs (b) and 375 µs (c). In column 1, we present the ejection images corresponding to each condition. By placing a silicon receiver at 50 μm in front of the donor and performing DP-LIFT process with different QCW-to-fs delays, column 2, 3 and 4 show the printed results at different observation magnifications.

Fig. 5 .

 5 Fig. 5. By placing a silicon receiver at 50μm distance in front of the donor and repeated DP-LIFT processes with a QCW-to-fs delay of 275 μs, a 2.5D microstructures are formed. (a) Array of four individual droplets separated by an interval of 30 µm. (b) A micro-column formed by four droplets stacked on top of each other.

U

Table 1

 1 Thermal and hydrodynamic parameters of copper for different temperatures.

	Temperature [K]	Thermal conductivity [ ]	Heat capacity [ ]	Density [ ]	Viscosity [mPas]	Surface tension [ ]
	293 573 1400 1850	400 381 167 180	382 413 516 516	8960 8809 7907 7576	--3.74 2.14	--1280 1220

Appendix A. Supplementary material

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.apsusc.2018.12.052.


'I have no humour to marry' 1 : Representation of Conjugal Life in The Roaring Girl and its Reflections on Our Present Society

Barbora Šedivá, Charles University, Prague

In literary criticism, early modern English drama is extensively examined for its treatment of gender roles. Often involving powerful female characters, the plays written in this period contributed to the redefinition of social norms concerning gender in contemporary society.

According to Susan Zimmerman, a prominent scholar in the field of early modern culture, 'as a primary locus for the interrogation of subjectivity, the English Renaissance theatre would also have served as a medium for the release of transgressive erotic impulses' (Zimmerman, 2005: 34). Although this aspect of Renaissance writing has been the subject matter of many critical texts, most of these were concerned with the plays of a single author: William Shakespeare. As Zimmerman notes in the introduction to her analysis, Studies of the English Renaissance theatre, including many postmodern ones, have traditionally foregrounded the dramatic canon of Shakespeare. Notwithstanding the importance of Shakespeare to his time and ours, such a skew, particularly in cultural criticism, is badly in need of correction. Neither the social function of the theatre nor the production of eroticism within it can be anatomized in terms of the oeuvre and practices of a single playwright. (idem, 5) In support of Zimmerman's claim, this paper considers one of the other plays written in this period, worth noticing especially for its focus on gender roles.

Written between 1607 and 1610, The Roaring Girl by Thomas Middleton and Thomas Dekker contributes to the discussion concerning gender in several different ways. Dealing with the position of women in English society, the play has been argued to both reaffirm and transgress established social norms. Moll Cutpurse, the play's protagonist, is based on a real historical person, Mary Frith, an eccentric figure of a disreputable character. While a lot of critical attention has been given to the theme of female cross-dressing in the play 2 , there seems to be a proportional lack of interest in its treatment of the role of women in marital life.

Although the protagonist's preference for male attire has been perceived as the main source of the play's transgressive character, the representation of conjugal life provides an essential comment on gender roles, which contributes to the overall message of the play. Rather than a relationship based on love and mutual respect, marriage is depicted as an economic transaction governed by the exchange of money and personal interest. In her steady refusal to marry, Moll is expressing the need for independence but also, and most importantly, her resistance to the corrupted values associated with marital life in the society around her. Worth noting is the fact that a lot of the principles concerning marriage in Middleton and Dekker's piece are still perceived as valid today. It is the aim of the present study to examine the representation of conjugal life within the play and to consider its reflections on our present society. Consequently, in dealing with plays such as The Roaring Girl, we might not only learn about the role of women in the early modern period, but also trace the development of this role until the present day, and in this way to learn about ourselves. For a society like ours, facing various kinds of crises, one way of constructing a positive future is by understanding and re-establishing the essential unit of humankind: the couple.

In seventeenth-century England, marriage was considered of central importance, especially for women. As Phyllis Rackin asserts, it was 'the paradigm that governed the lives and defined the identities of Renaissance women' (Rackin, 1987: 30). In this sense, marriage was seen as the ultimate goal of every woman's life. According to The Lawe's Resolution of Women's Rights, published in 1632 and designed to help the female population accept their role in society, 'all [women] are understood either married or to be married' (Edgar, 1632: sig. B3 v ). While women were thus pressed into wedlock, the significance of marriage in Renaissance society is also testified by the presence of numerous advice manuals and conduct books dealing with marital obligations and proper household management. Such advice books were then very popular and widely read, especially among the middle classes. Mostly written by men, they propagated patriarchal ideals of conjugal life as the norm and reaffirmed patriarchal values at the same time.

One notable advice book, A Godly Form of Household Government [...] (1621) written by John Dod and Robert Cleaver, promotes the notion of marriage as a patriarchal type of government, with the husband as its sovereign ruler and the wife as an obedient subject.

According to this manual, the husband is to 'love his wife as his own flesh', 'to govern her in all duties that properly concern the state of marriage', and 'to use her in all due benevolence, honestly, soberly, and chastely' (Dod and Cleaver, 1621: sig. H2 v ). The wife, on the other hand, was exposed to a necessary subjection in all the duties concerning marriage and household care. The institution of marriage was thus compared to that of a realm, with the male part being the government and the female its subject.

It bears keeping in mind, however, that while conduct books such as this A Godly Form were one thing, reality was another. In fact, society was much more heterogeneous already at that time, and that is precisely what Middleton and Dekker's play reflects. While the publication of The Roaring Girl roughly coincides with that of Dod and Cleaver's manual, the notion of the sacred union between a man and a woman in the play is represented in vastly different terms. As mentioned above, the meaning of marriage within the play is presented in favour of a more economic understanding of the relationship, where women often take the leading position instead of their male counterparts. The pressure for women to marry was in any case thriving, both in society as well as within the play. Within certain contexts, it can be felt even today.

Although the main protagonist of The Roaring Girl avoids marriage in any way possible, this kind of union nevertheless plays an important role in the play, both in Moll's surroundings and in her own life. As Stephen Orgel argues, 'the historical Mary Frith, but as Middleton and Dekker present her in The Roaring Girl, [...] is powerfully concerned with matrimony, both as the object of wooing and as the enabling figure for other marriages' (Orgel, 2005: 15). In this sense, there seems to be a certain discrepancy between Moll's attitude to the institution of marriage in relation to herself, and with respect to other women around her, especially one of the maidens, Mary Fitz-Allard. Critics, including Jean Howard, note that 'seeing marriage as a straitjacket for herself, she [Moll] none the less promotes it for Mary Fitz-Allard and other women' (Howard, 2005: 37). In the course of the play, Moll becomes willingly involved in a strategic plan, the aim of which is to achieve the consent of a gentleman called Sir Alexander Wengrave for the marriage of his son Sebastian and Mary.

The question of Moll's readiness in promoting marriage for others while rejecting it for herself has been the subject matter of several critical studies dealing with this play.

In her essay examining the role of women in the marketplace in The Roaring Girl, Jo E. Miller claims that 'one of the most troubling things about this play is that Moll does not at first glance seem overtly to reject her society's vision of marriage as a male-dominated hierarchy, but rather opts out of it only for herself' (Miller, 1990: 12). For Miller, rather than being a transgressive figure, Moll is used as an instrument to reaffirm precisely those values that she appears to refuse. In spite of her dismissal of Moll as a conventional character, Miller nevertheless perceives the play as transgressive in that it makes its audience aware of the objectionable conventions concerning marital life that Moll is helping to re-establish. Along the same lines, Jane Baston argues that 'Moll is fitting into the traditional requirements of marriage rather than seeking to change them' (Baston, 1997: 328). Indeed, in several places throughout the play, Moll does appear to be reinforcing social conventions regarding the role of women in conjugal life rather than trying to do away with them. An example of such an attitude can be found in her conversation with Sebastian in Scene 4, where she claims that 'a wife, you know, ought to be obedient, but I fear me I am too headstrong to obey' (4.36-7).

However, while such a statement seems to be in accordance with the patriarchal notion of marriage, it does not yet mean that Moll identifies with it. Neither does it necessarily imply that she is pursuing the same kind of union for Sebastian and Mary.

Moll's seeming inconsistency in her approach to marriage might be resolved by the claim that there are, in fact, two kinds of marriages within the play: the ideal one and the actual one. While most of the married couples represent the debased, profit-driven, and ultimately unfaithful kind of union, what Moll seeks to achieve for Sebastian and Mary is precisely the opposite, uncorrupted, and ideal relationship, based on love and mutual respect.

As Jennifer Higginbotham asserts, Moll's objection to marriage is not to marriage per se, but the social reality of marital power relations in her world. Her speeches recognize the material constraints within which women function in her society, and Moll seeks to open up, rather than close down, options for other female characters (Higginbotham, 2013: 91).

Instead of reaffirming the convention that perceives marriage as a patriarchal union involving female subjugation, Moll promotes for her friends the kind of union in which both participants would be allowed to retain an equal share of power and independence. The wedlock of Sebastian and Mary is thus set into direct opposition to the already established marriages of the middle-classes couples within the play. According to Viviana Comensoli, 'the idealistic conclusion of the Sebastian-Mary action must be considered in relation to the dramatists' cynical treatment of marriage in the citizen-plot and its realistic treatment of conjugal malaise' (Comensoli, 1987: 251).

Therefore, if the play 'offers a biting critique of the institution of marriage', as Higginbotham insists (Higginbotham, 2013: 90), it is not to be searched for in the final union promoted by Moll, but rather within the lives of the couples already settled, whose affairs generate the play's subplot. It is precisely this deviation from the main marriage plot that distinguishes this particular play from other comedies of the early modern period. While The Roaring Girl departs from a similar situation to that in Shakespearian festive comedies -a young couple's pursuit of a happy marriage -in its moral implications it goes far beyond. It is an exceptional play, precisely because it attempts to answer the question of what happens after the happy endings in Shakespeare's comedies. As Howard argues, 'Shakespearean comedy, of course, rarely moved beyond the portrayal of courtship to engage the actuality of marriage' (Howard, 2005a: 136). In this sense, The Roaring Girl starts where the conventional comedy ends: in the life after the wedding, which might not always be the exact image of happiness.

As a typical city comedy, The Roaring Girl is thus much more realistic than most Shakespearean plays. In contrast to them, this play portrays a broad range of characters encompassing the whole social spectrum. In its focus on the lives of the ordinary citizens and their daily activities, the play employs what Ben Jonson has termed the 'deeds and language such as men do use', 3 as opposed to the dramatic adventures and elevated language of Shakespeare's characters. Its highly satirical tone, characteristic of city comedies, also contributes to the gender debate. In their portrayal of the lives of the merchant families, Middleton and Dekker depict the dissatisfactions of conjugal life that were considered taboo in most Elizabethan drama.

The subplot dealing with the merchant-class families commences in the 'marketplace scene' (scene 3), where the corrupted nature of conjugal life becomes exposed through the couples' moral failings in their behavior outside of marriage. While marital life is pushed into the background in this scene, new relations are uncovered between the married women and the single gallants, which reflect on the marital relations themselves. It is precisely in the economic environment of the market, that the commercial nature of human relationships among the characters is revealed. As Valerie Forman observes, 'at the same time that the marriage plot recedes, the merchant/gallant plots come into the foreground and the play negotiates social relations, and especially relations of desire, through the circulation of money and commodities' [START_REF] Forman | Marked Angels: Counterfeits, Commodities, and The Roaring Girl[END_REF](Forman, : 1531-2)-2). In this sense, the market becomes a space of both economic and sexual transactions. While the citizens' wives offer their goods to the passing gallants, their own bodies are on display for potential exchange. In her essay investigating the importance of space in the play, Kelly Stage observes, 'the play's intertwined dynamic of commercial practices and private practices', arguing that 'early Stuart popular literature often conflated the shopwoman's crying of her goods with the advertisement of her own body' (Stage, 2009: 420).

The marketplace run by the merchants' wives is thus far from neutral ground. The appearance of the wives in the public space of the market reflects the changing role of women in society. While women were historically confined to the domestic space of the household, the early modern period witnesses a general release of this stereotype. Within the play, the public and private spaces become intertwined. When their own house is turned into a shop, the wives find themselves somewhere in between the domestic and the public zone. Not only does the play observe these married women in public, it also assigns them a role in the business sphere that was often perceived as an exclusively male space. The merchant's wife thus becomes a potential threat to patriarchy precisely for her ability to move in the economic sphere and to be even more successful there than her husband. The fact that the wife can operate to some extent independently of her husband's income creates tension in the married couple.

This tension is further enhanced by the sexual implications of the woman's exposure to the public gaze. According to Mario DiGangi, the marketplace is 'an arena, much like the public theatre itself, in which female visibility could easily translate as sexual availability' (DiGangi, 2003: 147). This assumption is confirmed when the crooked relationships between the gallants and the wives become exposed. The marketplace within the play thus becomes the stage for marital infidelity and corruption.

Public visibility and sexuality in the marketplace go hand in hand with the economic status this setting offers. Just as the wife becomes economically independent from her husband, her erotic desire starts to develop on parallel lines. For a self-sufficient woman, marriage, as represented in the merchant subplot of The Roaring Girl, becomes highly frustrating and as a result she starts to search for other sources of fulfilment. Female economic independence was thus perceived as troublesome. Howard accurately describes this implication when she argues that the marriages in the play 'are not depicted as erotically fulfilling. There is the unmistakable implication that, like female play-goers, the publicly visible, economically useful urban wives were experienced by men as threatening figures' (Howard, 2005a: 137-8).

Already from the very beginning of the marketplace scene, economic metaphors are used for the expression of social relations. In this way, sexual innuendo in the dialogue becomes intertwined with business-related language, and the exchange of goods soon turns into a potential transaction of human bodies. While marriage has the function of a mere economic partnership, the citizens' wives feel the need to pursue their sexual fulfilment outside of wedlock. This is precisely where the play offers its critique of the contemporary conditions of conjugal life. A union that is supposed to be based on loyalty and chastity will not, in this case, prevent the married women from committing adultery. This is obvious already from Mistress Openwork's opening line: 'Gentlemen, what is't you lack? What is't you buy? See fine bands and ruffs, fine lawns, fine cambrics. What is't you lack, gentlemen, what is't you buy?' (3.1-3). Always ready to provide anything the gallants might need, Mistress Openwork would not hesitate to offer her own body if it was in the gentlemen's demand, something they might be lacking. According to DiGangi, 'when she introduces the market metaphor of "opening shop" to describe her attempts to "take" her husband sexually, Mistress Openwork blurs the distinction between the "chaste wife" and the "whore"' (DiGangi, 2003: 150). What follows her initial cry for attention is a conversation held between the two men she was addressing, full of double entendre, the function of which is to reveal the erotic subtext of the social relations operative in the market, as well as to make the audience laugh.

Another example of what Higginbotham calls an 'unruly woman' is Mistress Gallipot.

In her attempt to seduce one of the gentlemen, she herself becomes an object of the economic transaction, the purpose of which is the acquisition of money rather than erotic fulfilment.

Naively believing herself to be an object of Laxton's sexual desire, Mistress Gallipot is in fact turned into a mere tool in his strategic plan to obtain her husband's money. Laxton's manipulation of Mistress Gallipot is disclosed in one of his confessional asides: 'I put her off with opportunity still: by this light I hate her, but for means to keep me in fashion with gallants: for what I take from her, I spend upon other wenches, bear her in hand still; she has wit enough to rob her husband, and I ways enough to consume the money' (3.77-81).

In order to preserve Mistress Gallipot in her role of one who obtains money, Laxton constantly delays the sexual satisfaction that is promised in their economic exchange. Instead of expressing his gratitude for Mistress Gallipot's service, the gallant uses her husband's money in order to draw the attention of other women. With his belief that 'money is that aqua fortis that eats into many a maidenhead' (3.176-7), Laxton hopes to use Master Gallipot's money in order to buy Moll herself. However, in his presupposition that every woman can be bought with enough money, Laxton critically underestimates Moll's moral principles, which only results in driving her further away from himself. Moll's refusal to participate in the economic transaction of bodies testifies to her chastity and moral purity, but also results in her avoidance of marriage. As Miller asserts, Moll's 'unwillingness to enter the market of exchange must effectively exclude her from the celebration of exchange that constitutes marriage as her society knows it' (Miller, 1990: 22).

In the market scene, as well as in the rest of the play, the character of Moll is constantly contrasted with the married women. Since marriage is considered a social norm, Moll's deviation from this norm -or rather, her refusal of this norm -is perceived as one of the sources of her presumed madness. In this sense, marriage serves as a standard for women to be judged against. As The Lawe's Resolution of Women's Rights explains, a woman can either be already married or not yet so. According to Adrienne Eastwood, 'the social category of singleness has, until recently, been largely ignored by both literary critics and historians, who tended to group unmarried women with widows' (Eastwood, 2004: 10). It might be for this reason that Moll's refusal to be married is met with little or no understanding. Even if it were not for the practice of cross-dressing, society might still condemn her simply for the fact of her desired singleness. As Eastwood argues, 'her unmarried status allows her freedom, but not without the negative consequence of being considered a whore or a "monster" by some of the characters in the play' (ibidem).

Even though it is always Moll who is, because of her unconventional behaviour, dismissed by her surroundings as a whore, she is the one who steadily resists all kinds of temptation and corruption of character. Since the married women in the play could hardly aspire to become models of chastity, this position is instead taken up by Moll. Although she is not bound by any legal union as the others are, she nevertheless remains true to her moral principles. Whereas the middle-class women in the play are willing to sell their bodies for any amount of money, Moll will not be bought. In this way, Moll's unmarried status is always compared to the marital life considered the norm. As a result, there is a reversal of values between what is perceived as normal and what deviates from this norm. The presumably happy conjugal life therefore becomes associated with infidelity, immorality, and corruption, whereas the transgressive figure of Moll stands for righteousness, chastity, and virtue. The monstrous within the play is thus associated with the normative rather than with the queer.

Moll's independence is contrasted with the unhappy side of marriage, and her single status becomes the target for the married couples to express their anxieties stemming from the degraded nature of their own relationships.

More than four hundred years have gone by since the first publication of The Roaring Girl, and yet the figure of Moll Cutpurse might still serve as an example of a successful independent woman in social life. Although the position of women in society has advanced considerably since the English Renaissance, there are certain points in which the development appears to stagnate. It is especially the role of women in marital life that remains fairly conservative. The pressure for women to marry is prevalent in many cultures, and although female independence is acknowledged and accepted as a possibility, it is still often frowned upon, whereas marriage tends to be seen as the ultimate goal of every woman's life. Take, for example, a recent popular comedy movie conveniently entitled Man Up (2015) 4 , which tells the story of a single thirty-four-year-old woman, who is pressed by her surroundings to find herself a husband. While the movie never questions the desirability of marriage for that particular woman, the audience is manipulated into the belief that wedlock is the only possible solution for her (whereas the unmarried status of the man she eventually finds is seen as unproblematic).

Other aspects of The Roaring Girl also find reflection in today's world. Middleton and Dekker wisely chose to stage some of the most revealing scenes of the play in a marketplaceit is an environment where economic transactions took place, but also the kind of public sphere where women start to build their independence. Since then, the distribution of men and women in public spaces has changed considerably. Although complete equality in this area is still far in the future (sometimes even for understandable reasons), the presence of women in the public sphere is nowadays mostly unrestricted. If the marketplace and the public theatre were among the first spaces to open up to female visitors, the range of places to frequent is incomparably wider today. And yet, one can hardly speak of complete freedom of movement for women. The threat of assault or violation is so powerful in some places that many women feel discouraged from venturing out. These conditions are, of course, vastly different from those in which Moll had to fight for her independence, and yet her free movement is something to be envied by women both then and now.

Another instance of the persistent quality of The Roaring Girl's portrayal of gender roles lies in the economic nature of the conjugal bond itself. It is no secret that marriage was, and continues to be, a way of obtaining economic security. Similarly, it was also often used as a means of social mobility and to the acquisition of property. The link between marriage and money is so firmly embedded in our thinking that we rarely deem the union successful if it does not involve material improvement for the woman. If the improvement is too substantial, on the other hand, the bride is easily dismissed as a gold-digger. In this sense, Laxton's hypothesis that 'money is that aqua fortis that eats into many a maidenhead' is not far from the general premise held about women entering marriage even today.

In The Roaring Girl, we see several marriages that could be described as unsuccessful from this point of view. As soon as the woman becomes economically self-sufficient, the authority of her male counterpart starts to disintegrate. Such marriage, as Howard points out, is no longer erotically fulfilling. There is the straightforward implication that only an economically successful man might have done for an attractive husband. To argue that such an approach is predominant today would be, of course, a serious overstatement. Nevertheless, it is not uncommon to come across this perspective in certain contexts. Though it might not be appropriate to quote from an American rap song here, the environment surrounding this type of music would be precisely such a context, to name but one. The discrepancy in economic prosperity between men and women is thus still a hot topic when it comes to marriages. This goes hand in hand with the way women are perceived in the economic sphere.

Female independence and individual ambition are still considered a threat, especially in a conjugal bond. For the man, losing the status of breadwinner in the family is often felt to be a loss of masculinity itself, while ambitious women are perceived as overtly masculine. A suitable example is the case of Angela Merkel, the Chancellor of Germany, who is often caricatured in popular media as a man due to her self-confidence and powerful initiative.

However, even worse than being an ambitious wife is to be a resourceful single woman. Therefore, to be Moll Cutpurse today would not necessarily mean to wear men's clothes, but to behave as an independent economic person, or in other words, as a man. And such behaviour might be considered just as transgressive as Moll's cross-dressing was.

When comparing the situation concerning gender roles in marital life between the early modern period and today, one needs to keep in mind the extent of this subject as well as the impossibility of encompassing it as a whole in a study of this scope. Also, relying on a text such as The Roaring Girl as a single primary source may potentially lead to serious misconceptions and overgeneralizations. Nevertheless, Europe is said to be in a state of crisis.

In order for us to be able to face the present challenges, we need to make sure our society is transparent and can rely on its constituents. As a central unit of society, the married couple represents stability. For this reason, it needs to be a union in which both components feel comfortable, secure, and self-assured. To what extent this is the case today is debatable and highly individual. In any case, Moll's decision to avoid marriage as she saw it around her continues to be understandable and inspiring.