Cl Ément Patat

Franc ¸oise Baillot
email: francoise.baillot@coria.fr

Jean-Bernard Blaisot

Éric Domingues

Guillaume Vignat

Preethi Rajendram Soundararajan

Antoine Renaud

Daniel Durox

S Ébastien Candel
email: sebastien.candel@centralesupelec.fr

Swirling spray flames dynamical blow-out induced by transverse acoustic oscillations

Keywords: Flame blow-out, transverse acoustics, swirling spray flames

Recent experiments on a laboratory scale annular system comprising multiple injectors (namely, MICCA-Spray) indicate that combustion instabilities coupled with azimuthal modes may induce large amplitude oscillations, which under certain conditions, lead to blow-out of some of the flames established in the system, a phenomenon designated as dynamic blow-out (DBO). An attempt is made in the present investigation to reproduce this phenomenon in a linear array of injectors (namely, TACC-Spray), where the sound field is externally applied to flames established by injector units that are identical to those used in the annular combustor. The sound field is generated by driver units placed on the lateral sides of a rectangular cavity. The pressure level induced in TACC-Spray can reach a peak value of 1700 Pa in a frequency range extending from 680 to 780 Hz, which corresponds to the typical frequency of azimuthal instabilities observed in the annular system. A theoretical model based on dimensional analysis serves to guide the choice of operating conditions that may lead to the DBO phenomenon. Experiments carried out in TACC-Spray and MICCA-Spray are then used to determine the DBO boundary, define the conditions that need to be fulfilled to observe this phenomenon, and gather high-speed visualizations providing some insights on the mechanisms that induce blow-out.

Introduction

A considerable amount of research has concerned issues raised by combustion instability. Some of the recent efforts in combustion dynamics has concerned annular configurations that are typically found in aircraft engines and gas turbines. The experimental works [START_REF] Fanaca | Comparison of the Flow Field of a Swirl Stabilized Premixed Burner in a Annular and a Single Burner Combustion Chamber[END_REF][START_REF] Moeck | Thermoacoustic Instabilities in an Annular Rijke Tube[END_REF][START_REF] Worth | Self-excited circumferential instabilities in a model annular gas turbine combustor: Global flame dynamics[END_REF][START_REF] Worth | Modal dynamics of selfexcited azimuthal instabilities in an annular combustion chamber[END_REF][START_REF] Bourgouin | Ignition dynamics of an annular combustor equipped with multiple swirling injectors[END_REF][START_REF] Bourgouin | Selfsustained instabilities in an annular combustor coupled by azimuthal acoustic modes[END_REF][START_REF] Worth | Azimuthally forced flames in an annular combustor[END_REF][START_REF] Prieur | A hysteresis phenomenon leading to spinning or standing azimuthal instabilities in an annular combustor[END_REF][START_REF] Prieur | Strong Azimuthal Combustion Instabilities in a Spray Annular Chamber With Intermittent Partial Blow-Off[END_REF] have been accompanied by theoretical investigations [START_REF] Evesque | Spinning and azimuthally standing acoustic modes in annular combustors[END_REF][START_REF] Ghirardo | Azimuthal instabilities in annular combustors: standing and spinning modes[END_REF][START_REF] Noiray | On the dynamic nature of azimuthal thermoacoustic modes in annular gas turbine combustion chambers[END_REF][START_REF] Bauerheim | An analytical model for azimuthal thermoacoustic modes in an annular chamber fed by an annular plenum[END_REF][START_REF] Bauerheim | Symmetry breaking of azimuthal thermo-acoustic modes in annular cavities: a theoretical study[END_REF][START_REF] Ghirardo | Weakly nonlinear analysis of thermoacoustic instabilities in annular combustors[END_REF][START_REF] Bothien | Analysis of azimuthal thermo-acoustic modes in annular gas turbine combustion chambers[END_REF][START_REF] Laera | Flame Describing Function analysis of spinning and standing modes in an annular combustor and comparison with experiments[END_REF][START_REF] Moeck | Nonlinear thermoacoustic mode synchronization in annular combustors[END_REF] and by some remarkable large eddy simulations [START_REF] Wolf | Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers[END_REF][START_REF] Wolf | Acoustic and large eddy simulation studies of azimuthal modes in annular combustion chambers[END_REF]. Since the perimeter is usually the largest dimension in these combustor geometries, azimuthal modes feature the lowest eigenfrequencies, which fall in the range where combustion is most sensitive to disturbances. As a consequence, these systems are susceptible to instabilities coupled by azimuthal modes. If this happens in a real system, this may lead to serious consequences, including mechanical vibration, cyclic fatigue, enhanced heat fluxes to the combustor walls, and in extreme cases, mechanical degradation and possibly failure. There are also instances where the oscillation reaches an amplitude that can lead to flashback. Many of these issues are considered in research reported in recent reviews (see [START_REF] Candel | Combustion dynamics and control : progress and challenges[END_REF][START_REF] Huang | Dynamics and stability of lean-premixed swirl-stabilized combustion[END_REF][START_REF] O'connor | Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes[END_REF][START_REF] Poinsot | Prediction and control of combustion instabilities in real engines[END_REF]

on azimuthal instabilities).

A series of more recent experiments have been carried out in annular systems allowing investigations of instabilities coupled by azimuthal modes. Much of these data originates from two laboratory scale annular systems with optical access to the combustion region, one earlier located in Cambridge and later in NTNU [START_REF] Worth | Self-excited circumferential instabilities in a model annular gas turbine combustor: Global flame dynamics[END_REF][START_REF] Worth | Modal dynamics of selfexcited azimuthal instabilities in an annular combustion chamber[END_REF], while the other (MICCA-Spray) is operated at EM2C lab [START_REF] Bourgouin | Selfsustained instabilities in an annular combustor coupled by azimuthal acoustic modes[END_REF][START_REF] Prieur | A hysteresis phenomenon leading to spinning or standing azimuthal instabilities in an annular combustor[END_REF][START_REF] Prieur | Strong Azimuthal Combustion Instabilities in a Spray Annular Chamber With Intermittent Partial Blow-Off[END_REF][START_REF] Bourgouin | A new pattern of instability observed in an annular combustor: The slanted mode[END_REF][START_REF] Bourgouin | Characterization and modelling of a spinning thermoacoustic instability in an annular combustor equipped with multiple matrix injectors[END_REF]. These two facilities reproduce in an idealized fashion, the conditions that prevail in gas turbines and jet engines. The two systems comprise multiple injectors arranged in an annular chamber. While the first is essentially fed with premixed reactants (air and ethylene), MICCA-Spray may be operated with premixed air and propane or may be fed with liquid fuel (n-heptane or dodecane) that is injected in the form of sprays. Flame stabilization in the Cambridge-NTNU system is assured by central bluff bodies with a relatively low swirl number. In the MICCA-Spray device, most investigations have been carried out with swirling injectors fed by premixed reactants and more recently by liquid fuels atomized as a spray of droplets.

These experimental facilities have provided considerable insight on the processes driving and coupling azimuthal instabilities. Recent combustion instability experiments carried out in MICCA-Spray have revealed an intriguing phenomenon when the oscillation amplitude was taking large values, typically in excess of 2% to 3% of the chamber pressure [START_REF] Prieur | Strong Azimuthal Combustion Instabilities in a Spray Annular Chamber With Intermittent Partial Blow-Off[END_REF]. Under these conditions, some of the flames established in the annular combustor were extinguished, as illustrated in Fig. 1 for an acoustic pressure amplitude of 4000 Pa. Further analysis indicated that this partial blowout occurred in the vicinity of the pressure nodal line, where the transverse velocities associated with the azimuthal mode reach their maximum level inducing an intense sweeping motion. Under these conditions, the combustion process is disrupted, inducing the complete extinction of flames located in the neighborhood of the nodal line. The time duration of this phenomenon was found to encompass about 100 ms, corresponding to about 70 cycles of oscillation. After this blow-out, the amplitude of oscillation in the chamber diminishes and the flames are established again. The process may then be repeated, leading to a new partial blow-out. This phenomenon, designated in what follows as dynamical blowout (DBO) was the subject of a further investigation [START_REF] Vignat | High amplitude combustion instabilities in an annular combustor inducing pressure field deformation and flame blowoff[END_REF], and it was found that the flame extinction was accompanied by a notable distortion of the pressure field and simultaneously by an increase of the shift in the resonance frequency. It was also possible to estimate the velocity fluctuation amplitude corresponding to the initial flame extinction.

The objective of the present study is to pursue the analysis of the DBO by making use of a configuration designated as TACC-Spray, in which the acoustic modulations are imposed to the flame by external means. In essence, this consists in placing a linear array of swirl spray injectors in a rectangular system. A transverse acoustic mode is generated by driver units located on the lateral boundaries of this facility. The central flame of the injector array can then be placed at the pressure nodal line, corresponding to the maximum transverse acoustic velocity. It is then possible to augment the level of oscillation and examine the process leading to flame blow-out. One advantage of this procedure is that the acoustic level is fully controlled, thus facilitating the detailed investigation of the DBO. It is in particular possible to decouple the level of the acoustic mode and the combustion operational conditions, a feature that is not accessible in the annular combustor MICCA-Spray where the acoustic level is governed by the coupling between acoustics and combustion.

The idea of using linear arrays of injectors to represent a sector of an annular system is not new. This has already been exploited by O'Connor and Lieuwen [START_REF] Lieuwen | Disturbance field characteristics of a transversely excited burner[END_REF][START_REF] Lieuwen | Further characterization of the disturbance field in a transversely excited swirlstabilized flame[END_REF], by Wong and Steinberg [START_REF] Kwong | Effect of internozzle spacing on lean blow-off of a linear multinozzle combustor[END_REF] or by Lespinasse et al. [START_REF] Lespinasse | Responses of v-flames placed in an hf transverse acoustic field from a velocity to pressure antinode[END_REF][START_REF] Baillot | Response of a laminar premixed v-flame to a high-frequency transverse acoustic field[END_REF]. In these last references, a premixed "V" flame is placed in a transverse acoustic field. When placed at the pressure antinodal line, the flame is led to execute an axial motion. There are also nonlinear features with lateral ejections of fluid at the injector outlet [START_REF] Baillot | Response of a laminar premixed v-flame to a high-frequency transverse acoustic field[END_REF]. In the vicinity of the pressure nodal line, the flame is periodically swept in the transverse direction. If the injection unit comprises a swirler, helical perturbations result from the interaction of the transverse acoustic velocities with the shear regions and with the vortex breakdown process [START_REF] Lieuwen | Disturbance field characteristics of a transversely excited burner[END_REF][START_REF] Lieuwen | Further characterization of the disturbance field in a transversely excited swirlstabilized flame[END_REF]. Transverse waves acting on the upstream side of the injector unit may also induce a rotational motion of the flames at the injector outlets, associated to asymmetric velocity field perturbations in the injector nozzles [START_REF] Hauser | Influence of transversal acoustic excitation of the burner approach flow on the flame structure[END_REF]. The capacity of flames to maintain the combustion process under intense transverse velocities induced by an acoustic mode was investigated by Lespinasse et al. [START_REF] Lespinasse | Responses of v-flames placed in an hf transverse acoustic field from a velocity to pressure antinode[END_REF], where it is shown that premixed "V" flames placed at a pressure nodal line are more sensitive to blow-off than the same flames placed at a pressure antinodal line. These flames were stabilized on a cylindrical rod having a diameter d = 3 mm placed in a premixed flow at a bulk velocity U b = 2 ms -1 . Flame extinction was obtained, for example, at a pressure amplitude of 100 Pa at two resonance frequencies f 0 = 506 Hz and f 0 = 1012 Hz. The transverse velocity at the pressure node could be estimated to be about 0.2 ms -1 , corresponding to 10% of the bulk velocity. The response of a linear array of swirling spray flames centered on a pressure antinode of a 2T1L resonant mode was examined in the new facility TACC-Spray [START_REF] Baillot | Saturation phenomenon of swirling spray flames at pressure antinodes of a transvese acoustic field[END_REF], where the flames are stabilized without any bluff-body and without the help of side walls.

Further references dealing with combustion instabilities and coupling with transverse acoustic modes are reviewed in [START_REF] O'connor | Transverse combustion instabilities: Acoustic, fluid mechanic, and flame processes[END_REF]. It appears that there are no detailed investigations of the DBO process for swirling spray flames subjected to a Prepared using sagej.cls transverse acoustic field. The objective of the present work is to bring new insight into this process by combining well controlled experiments with a theoretical framework initially proposed in [START_REF] Prieur | Ignition dynamics in an annular combustor for liquid spray and premixed gaseous injection[END_REF] but modified in the present article. This article begins with a brief description of the experimental configuration. The blow-out process is examined in the framework of a theoretical model, which serves to guide the experimental investigation. Experiments indicate that flame blow-out is observed when the pressure amplitude reaches high levels and when the flame is located near the transverse velocity antinodal line. This point is examined in more detail for two mass flow rates of air.

Experimental set-up and diagnostics

The TACC-Spray set-up, shown in Fig. 2, comprises a rectangular chamber. The top of the chamber is surmounted by a convergent part which prevents the entrainment of surrounding air. Its exhaust is open to the atmosphere. An array of five injection units is mounted in the chamber backplane with a spacing that is equal to that used in the MICCA-Spray experiment. They are equipped with tangential swirlers of type 716, identical to those of MICCA-Spray (see [START_REF] Vignat | High amplitude combustion instabilities in an annular combustor inducing pressure field deformation and flame blowoff[END_REF] for further details about the swirler). The three central ones inject air and n-heptane while the two lateral ones supply only air, as they act as stabilizers of the lateral flames. This original arrangement allows to stabilize the lateral flames far from the side walls, which puts the central flame in an environment similar to that of MICCA-Spray at any location of the acoustic field. Two compression drivers Beyma CP850ND (marked as CD in Fig. 2) are fixed on the side walls, facing each other such that their common acoustic axis which passes through their centers is at 90 mm from the chamber backplane. They are characterized by a wide frequency range (0.5-20 kHz). The excitation signals are delivered by a Hameg HM8150 signal generator, an IMG Stageline frequency filter and a Peavey PV900 amplifier. Here, the acoustic pressure P is measured with a B&K type 4182 microphone placed at the central pressure antinode of the chamber.

The vertical side walls holding the driver units are placed on rails and the front walls are made of plates of height h c = 200 mm and different lengths, which allows to vary the chamber length l c and ensure acoustic resonance at a selected frequency f for a frequency in the range 680-780 Hz, corresponding to the DBO frequency range in MICCA-Spray. A transverse mode is generated in the rectangular chamber, with peak amplitude levels that may reach 1700 Pa. This is used to locate the pressure, velocity or intensity antinode so that it coincides with the central injector. Highspeed imaging of the OH* radical is performed at an acquisition rate of 10000 fps with a Phantom V2012 camera equipped with a Lambert HiCATT 25 intensifier, a UV-105 mm lens and a UG11 filter.

Theoretical framework

The general ideas that were followed in [START_REF] Prieur | Ignition dynamics in an annular combustor for liquid spray and premixed gaseous injection[END_REF] to derive a theoretical model for the DBO phenomenon are now used to guide the blow-out experiments in TACC-Spray. Blow-out takes place when the central injector is located at a pressure node of the resonant acoustic field, where the transverse velocity v x reaches maximum values. The data from MICCA-Spray indicate that DBO requires high amplitude oscillations. It is also found that the transverse velocity induced by the acoustic field displaces the flames in the transverse direction. This modifies the heat release rate in the flames located near the pressure nodal line where the transverse velocity reaches its maximum. In the initial model, the parameters influencing the blow-out were as follows : d, U b , τ c , v x , ω = 2πf , and the swirl number S. The conversion time τ c = τ m + τ v + τ ch includes a mixing time τ m , a vaporization time τ v and a chemical time τ ch . Mixing is essentially governed by turbulence, vaporization depends on the droplet diameters and clustering in the spray, while the chemical conversion is a function of the local equivalence ratio φ. Dimensional analysis indicates that there are four dimensionless groups that may be written as v x /U b , the relative velocity perturbation, v x /(ωd), the ratio of the transverse displacement to the injector outlet diameter, (τ c U b )/d, the ratio of the chemical conversion time to a mechanical time d/U b and S, the swirl number measuring the rate of rotation with respect to the axial flow velocity. The flame extinction is then formally governed by a criterion that may be cast in the form:

ψ 1 v x U b , v x ωd , τ c U b d , S > 0 (1)
It was initially considered that the relative transverse displacement amplitude v x /(ωd) was governing the flame extinction process. When this ratio is sufficiently large, the central recirculation zone which anchors the flame is significantly perturbed, destabilizing the flame and inducing blow-out. However, v x /ωd is dependent on v x /U b and the inverse of the Strouhal number St defined by St = ωd/U b . So, it may be interesting to replace the second dimensionless group by the Strouhal number. The influence of frequency on the process is then reflected by this important dimensionless number. The extinction condition may then be rewritten in the form:

v x U b > ψ 2 St, τ c U b d , S (2)
It is known that the parameter (τ c U b )/d that will be designated from here on by b, typically determines the stability of a combustion system. When this parameter is smaller than a critical value corresponding to static blowout, say b * of the order of one, the conversion time is shorter than the mechanical time and the flame is stabilized. When b exceeds b * , the flame is extinguished. This is equivalent to say that the Damköhler number should exceed a critical value for flame stabilization (i.e. Da > Da c ). The difference b * -b then measures the stability margin and may be used in place of the dimensionless group b. One may then separate the right hand side in expression [START_REF] Moeck | Thermoacoustic Instabilities in an Annular Rijke Tube[END_REF] in two parts, the first reflecting the state of rotation and flow response ψ 3 (S, St) while the second represents the stability margin in the form (b * -b) n . The dynamical blow-out criterion then takes the form:

v x U b > ψ 3 (S, St)(b * -b) n (3)
This criterion slightly differs from that proposed in [START_REF] Prieur | Ignition dynamics in an annular combustor for liquid spray and premixed gaseous injection[END_REF] in that it puts the accent on the transverse velocity disturbance and on the stability margin of the flame. The function ψ 3 portrays the swirling flow characterized by the swirl number S and its response to external modulations through a Strouhal number. For a fixed injector and a broadband receptivity to incident disturbances, one may consider that ψ 3 is a constant so that the criterion is essentially controlled by the stability margin (b * -b) n where n may be obtained from experiments. If the flame is close to blow-off, it may be easily perturbed by the external acoustic field. If the stability margin is greater, then the combustion process will be less easily perturbed. In the previous expression, b = U b τ c /d defines the stability of the flame and one may note that v x /U b has to be sufficiently large if the acoustic field is to play a role and induce flame blow-off. This analysis may be tested by changing the value of b to vary the stability margin of the flame. For a fixed injector geometry, this may be achieved by changing the bulk velocity U b or by changing the conversion time τ c . When τ c is increased, the stability margin is reduced. It is most convenient to augment the chemical time by operating under leaner conditions i.e. by reducing the equivalence ratio and operating near the lean blow-out limit. This is illustrated in Fig. 3.

Diagrams in Fig. 3 may be used to guide the exploration of the DBO phenomenon. The central idea is to explore flames that have a narrow margin with respect to the lean blow-out limit. The acoustic level is fixed and the equivalence ratio is progressively decreased until flame blow-out. This scheme is repeated for higher acoustic levels until the maximum achievable level is reached. The corresponding equivalence ratio φ lim is that which requires the highest achievable level of pressure oscillation, i.e. the highest level of transverse velocity fluctuation. Beyond that point, the system cannot provide a level of oscillation that will lead to blow-out. When this ratio reaches the lean blow-out limit, the flame is extinguished. The range of equivalence ratios between φLBO and a limit value φ lim may be explored and the level of transverse oscillation that leads to extinction may be determined. Beyond φ lim , the level of transverse velocity fluctuation exceeds the maximum achievable value and this range cannot be explored. These diagrams only consider lean operating conditions. Left: Low bulk velocity case. The flame is not very well anchored and extinction may be observed over an extended range of equivalence ratios limited by the maximum achievable level of transverse velocity fluctuation. Right: High bulk velocity case. Flame anchoring is improved and the maximum achievable level of relative transverse velocity oscillation is reduced. The range of equivalence ratios in which DBO may be observed is diminished.

Flame blow-out induced by high amplitude oscillations

It is now interesting to examine results of blow-out experiments carried out for two different mass flow rates of air. The corresponding blow-out boundaries are plotted in Fig. 4.

When the bulk velocity is low (U b = 17.8 m/s) corresponding to the blue line, the maximum level of fluctuation may reach a value of 32 %. The flame is also not very well anchored because atomization probably produces bigger droplets and the vaporization time is high, reducing the Damköhler number. In this case, transverse acoustic oscillations induce blow-out at equivalence ratios as high as 1.03. This situation corresponds to that shown schematically in Fig. 3 (left). When the bulk velocity is increased (U b = 26.7 m/s) atomization is improved, vaporization time is reduced and flame anchoring is enhanced. The achievable level of velocity fluctuation is reduced to about 20%. In this case, DBO is only observable in a more limited range of equivalence ratios, as shown schematically in Fig. 3 (right). Moreover, blow-out occurs at the same equivalence ratio without acoustics and for a relative velocity perturbation of 9%, which is not observed for the low bulk velocity.

The DBO process may now be examined by making use of high speed imaging of OH*. As shown in Fig. 5, the two lateral flames are still present a short time after blow-out of the central flame, which is thus the only one concerned by DBO. Since it is located at the velocity antinode, it experiences a transverse velocity modulation of stronger amplitude compared to the lateral flames. This indicates that DBO at the pressure nodal line observed in MICCA-Spray can be reproduced in TACC-Spray. A time analysis of the DBO process of the central flame in TACC-Spray is provided in Fig. 6, which shows a map of images extracted from a film recorded at 10000 frames per second. The blow-out requires about 21 ms corresponding to about 15 acoustic cycles at 760 Hz. During the DBO process, the flame is extinguished by its upper part, the OH*-intensity of which decreases from cycle no. 1 to cycle no. 5. At the same time, the flame is laterally displaced away from the axis of the injector (e.g., images of cycle no. 5) while its stabilization height from the burner is practically unmodified. This process is accompanied by the occasional reactivation of the stabilization point (e.g., in the beginning of cycle no. 6 and the end of cycle no. 10), but these puffs of OH*-intensity are not capable to reignite the entire flame, which leads to a complete blow-out in cycle no. 15. It is interesting to note that the duration of the process is of the order of ten times the residence time in the inner recirculation zone that anchors the flame. This region is progressively modified by the transverse velocity field and the flame foot displaced in the lateral direction is subjected to cooler gases and a reduced level of fuel that are less favorable to stabilization.

Conclusion

Experiments have been carried out in a system comprising an array of swirling injectors fed with liquid n-heptane and air placed in a rectangular configuration operating at atmospheric pressure. This configuration may be modulated by transverse acoustic modes generated by a set of driver units located on the lateral sides of the system. The pressure oscillation may reach peak values of the order of 1700 Pa peak (about 2% of the chamber pressure). Experiments reveal that these high acoustic levels induce a strong transverse motion in the neighborhood of the pressure nodal line. Experiments indicate that the combustion process markedly changes when the position of the central injector coincides with a pressure antinode or when it corresponds to a nodal line. In this latter case, when the pressure oscillation amplitude exceeds a certain threshold, the flame senses maximum transverse velocity fluctuations that produce a dynamical extinction. A mechanism is proposed for the flame extinction process that defines a critical value for the transverse velocity amplitude with respect to the injection velocity. The data reported in this article provide new insights on the dynamical blow-out that results from excessive levels of acoustic oscillation. The data can serve to guide modeling and simulation of interactions between acoustics and combustion.

Figure 1 .

 1 Figure 1. Dynamical blow-out in MICCA-Spray. Images show the progressive blow-out of the flames located near the pressure nodal line as the acoustic pressure amplitude grows up to 4000 Pa [27].

Figure 2 .

 2 Figure 2. (a) The TACC-Spray setup showing the injector array and lateral quartz window, (b) close-up view of the three flames, (c) transverse acoustic field inside the cavity and top view of the TACC-Spray setup. The central flame (injector B) is placed at a velocity antinode. The pressure fluctuation P is measured at the central pressure antinode.

Figure 3 .

 3 Figure 3. Dynamical flame blow-out conditions may be determined by changing the equivalence ratio to vary the stability margin.

Figure 4 .

 4 Figure 4. Flame blow-out boundary for two different regimes of operation. Swirler type: 716, n-heptane fuel. The blue symbols correspond to U b = 17.8 m/s, f = 760 Hz and the red symbols correspond to U b = 26.7 m/s, f = 755 Hz. Filled symbols indicate the maximum achievable level of P /(ρ0c0U b ).

Figure 5 .

 5 Figure 5. Images of the flames in TACC-Spray. Left: 0.25 s before blow-out; right: 0.03 s after blow-out of the central flame. U b = 17.8 m/s, φ = 0.96, f = 760 Hz, P /(ρ0c0U b ) = 0.24.

Figure 6 .

 6 Figure 6. Images of the flame blow-out process extracted from a high speed film recorded at 10000 fps for U b = 17.8 m/s, φ = 0.96, f = 760 Hz. The process is decomposed in 15 acoustic cycles (rows), and five images per cycle for the same phase angles (columns).

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Prepared using sagej.cls

Acknowledgements

This work was partially supported by project FASMIC (ANR16-CE22-0013) of the French National Research Agency (ANR), and by the European Union's Horizon 2020 research and innovation programme, "Annulight" with grant agreement no. 765998. The authors wish to thank RENADIAG for the technical support provided to this research.


Lazzaroni

Ph Leclere

V Cornet

M Surin

P Viville

J P Aime

R Lazzaroni

Dynamic atomic force microscopy analysis of polymer materials: Beyond imaging their surface morphology

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The development of nanotechnology implies a large effort to study and understand physical phenomena at the nanometer scale. Methods using local force probes provide important contributions to those studies, because the small size of the tip allows one to probe surfaces with excellent lateral and vertical resolution. Among those scanning microscopies, dynamical force techniques, i.e., using an oscillating tip, are particularly well adapted to soft samples such as polymers or biological systems. Among many applications of those techniques, one convincing illustration of their potential is the advance brought to microstructural studies of block copolymers by phase imaging in Tapping mode Atomic Force Microscopy [I-7).

In dynamical modes, two types of operation are possible: either the oscillating amplitude is fixed and the output signal is the resonance frequency (this is called the non-contact resonant force mode [8]), or the oscillation frequency is fixed and the variations of the amplitude and phase are recorded. This mode is commonly named tapping-mode (also known as intermittent contact mode [9]) and is the one that is considered in this study. Tapping-mode (TMAFM) is commonly used because of its ability to probe soft sampies, due to the minimization of sample damage during the scanning. Moreover, tapping-mode images can be of two different types: in one type, the image corresponds to the changes of the piezoactuator height necessary to maintain a fixed oscillation amplitude through a feedback loop (the height image); in the other type, the image contains the changes of the oscillator phase delay relative to the excitation signal (phase image). This additional imaging possibility has revealed in many cases a high sensitivity to variations of the local properties. A number of studies have shown the possibility to extract useful information from tapping-mode images of soft samples, especially with samples showing a particular contrast on the local scale, like blends of hard and soft materials [5,IO].

Nevertheless, important questions remain about the physical origin of the image contrast in tapping mode [11][12][13]. In many cases, the height images are considered to display topographic information, but it must be kept in mind that the local mechanical properties of the samples (i.e., the possibility that the tip slightly penetrates the surface) may also contribute to contrast in the height image. For the phase image, in the dominant repulsive regime, the phase shifts are related to the local mechanical properties. At this point, it is worth mentioning that, in order to maintain the tip in a well-defined oscillating behavior, the perturbation to the oscillator due to the contact with the surface is chosen to be small; in other words, the reduction of the free amplitude (the set-point) is only of a few percent. This method has two advantages: from an experimental point of view, this allows one to identify immediately hard and soft domains, the bright parts of the image corresponding to hard domains. From a theoretical point of view, this allows us to use simple approximations providing analytical solutions able to fit the experimental data [ 5,13].

Here, we propose a straightforward method, based on the analysis of approach retract curves, to provide an unambiguous quantitative measurement of the local mechanical response and/or topographic contribution(s), depending on the studied sample. Moreover, a step further in the understanding of the image contrast is proposed, via the analysis of the variation of the phase as a function of the tip surface distance. The fitting of the experimental data by an appropriate model provides a quantitative evaluation of the contribution of topography, adhesion, indentation and dissipation processes to the contrast. This approach is first applied to thin films of thermoplastic elastomer block copolymers, which are known to phase-separate into well-defined domains on the nanometer scale. The method is extended to other polymer systems, such as polymer blends and polymer nanocomposites.

Experimental Results

Thermoplastic Elastomers as Model Systems

A key point for soft materials is a proper interpretation of the observed contrast. In most cases one has to discriminate between the respective contributions of: (i) the actual topography and (ii) the difference in mechanical properties to the height images. Here, we review a straightforward and easy experimental method to evaluate the contribution of the local mechanical properties to the image contrast. Our approach is based on the reconstruction of height or phase image sections via a rapid analysis of approach-retract curves recorded along those section lines. As recently described (5), a comparison between recorded images and the set of approach-retract curves provides an easy way to discriminate between the topographic and mechanical contributions.

The model system is a thin film of a thermoplastic elastomer, i.e., a block copolymer in which the chemical structure of the sequences is designed in such a way that (i) phase separation of the sequences occurs, giving a well-defined spatial distribution of domains at the nanometer scale and (ii) the domains containing different sequences possess different mechanical properties (5,6). Here, the chemical composition has been selected to produce a lamellar morphology. In this case, AFM pictures of a PMMA-b-poly(alkylacrylate)-b PMMA film present an alternating array of rubbery and glassy lamellae, with a periodicity of27 nm, as shown in Figure I. The correspondence between the two sets of data (same behavior for the topographic section, not shown here) appears to be very good. This agreement means that for those copolymers, the contrast in the height image is related to different oscillator responses on the glassy and elastomer domains, with no discernible topographic contribution to the contrast. Therefore, the contrast is mostly due to changes in the sample local mechanical properties.

From tapping-mode images of block copolymers, it is not only possible to describe the morphology corresponding to the nanophase separation occurring between the specific domains but also to evaluate accurately the respective contributions of the topography and the mechanical properties. In this case, we can also propose that the phase contrast can be explained on the basis of the viscous forces acting against the tip motion during the indentation of the tip in the sample [13][14][15].

Applications to other polymer materials.

Biodegradable Polymer Blends. In this section, we extend the concept to polymer blends made of biodegradable and biocompatible components, namely PMMA and poly(e-caprolactone)(PCL). These blends are in current development for biomedical applications such as drug release systems or prostheses [ 16). Figure 2a illustrates the topographic image of a 7 5 :25 weight % PMMA/PCL blend as a thin film. From the section analysis (Figure 2b) and the bearing analysis (not shown here) of the topographic image, it appears that the dark areas, corresponding to the softer component (i.e., the PCL domains), are located approximatively 60 nm below the bright (mechanically harder) zones.

Approach-retract curves recorded on different domains on the polymer blend sample surface are markedly different: the slope of the amplitude/distance curve is 0.75 for the harder, glassy domains while it is smaller (0.60) on the softer domains, meaning that, for the same set-point, there is larger tip indentation in the softer domains. Using the same procedure as described for the block copolymer, we measure a difference of about 15 nm between the lowest points in the image section and the corresponding reconstruction (Figure 2b). Therefore, from these data (160 points), it appears that, in this case, an indentation of about 15 nm in the PCL softer domain has to be considered to fit the experimental data. Note that, at room temperature, the PCL is largely above its glass temperature transition (Tg= -60°C). Therefore, the 60 nm height difference recorded in the height images actually corresponds to a 15 nm indentation into PCL domains that are actually 45 nm below the level of the PMMA domains. This height difference probably originates from the film formation process from the solution of the two polymers in a common solvent. The topographic modulation can be explained by a different rate of solvent evaporation during the film drying process for the two phases [ 17). Conjugated polymers. We also applied this technique to conjugated organic semiconducting materials. Compared to inorganic materials, conjugated polymers have the advantages of easy control of the semiconducting properties through chemical modification, and ease of processing over large areas, leading to major potential cost savings in device manufacture. LEDs and transistors based on conjugated materials are now being actively developed for commercial applications. Generally, when conjugated oligomers or polymers are deposited fr om a molecularly dissolved solution on a substrate, like muscovite mica, HOPG or silicon wafers, they tend to form fibrils by self-assembling processes governed by Tt-stacking of the polymer chains [18][19][20]. In the present case, the conjugated oligomer is a made of about 20 units of indenofluorene (Figure 3). This polymer is a well-known efficient blue emitter for LED's. Upon annealing at 300°C (above the liquid crystal transition temperature of 270°C), the polymer reorganizes in such a way that the fibrillar morphology is no more present. Figure 4 illustrates the typical morphology observed by AFM after annealing. The analysis of the height image shows a difference of 18 run between the upper (brighter) layer and the lower (darker) layer. From the phase image (vertical grey scale 1.0 degree) there is no significant contrast between the two layers (only the contours of the cavities are visible). The length of the extended indenofluorene oligomer with 20 units is estimated to be around 18.S nm. This strongly suggests that the layers are made of molecules standing up perpendicularly to the substrate, as depicted in Figure 4c. The fact that the phase contrast between the different layers is very low means that the tip is probing the same material or at least material with the same mechanical properties. For this sample, approach retract curves are strictly identical whatever the location on the sample. This implies that the contrast observed on the height image is purely topographic.

'•'•'•'t'•'•'•'t'•'•'•' '•'•'•'•'•' •1 '" l{+ o '. no•+ ' + H '+ {n i•u •o t'n • • • o • o t toot' Ho (c)
Figure S illustrates the morphology adopted by ar conjugated oligomer based on six thiophene units substituted on one end by a short poly(ethylene oxide) segment (Figure Sc). These molecules are deposited on a freshly cleaved HOPG substrate. On the height image, we clearly see a molecular step (indicated by the arrow on Figure Sa). The thickness of brighter islands (indicated by an "A" on Figure Sa) is about 6.0 nm, which roughly corresponds to length of the fully extended molecule. The islands are thus two-dimensional assemblies in which the molecules are perpendicular to the substrate (or slightly tilted). This interpretation is fully confrrmed by the phase image, on which the islands show the same• phase lag (i.e., the same dark color). Small white spots are also visible (indicated by "C" on Figure Sb). STM analysis of the same sample indicates that this zone is actually the HOPG surface while the light gray zone ("B" on Figure Sb) is made of a mono layer of molecules lying flat. The phase of the oscillating tip is different enough when the tip is over the monolayer, or over an island, or over the HOPG, so that it is possible to understand the nature of the three distinct zones in the AFM image.

Nanocomposites. This work deals with the preparation and the surface characterization of biodegradable nanocomposites made of poly(e-caprolactone) (PCL) and Montmorillonite-type clay. Nanocomposites with different relative compositions of PCL and Montmorillonite, either natural or organo-modified by various alkylammonium cations, are prepared by melt intercalation and in situ intercalative polymerization [22,23]. The goal of this study is to characterize the dispersion of the clay layers in the PCL matrix, which is a critical parameter governing the final physical properties of the obtained nanocomposites. Figure 6a shows a TMAFM image of the sample, where flat elongated objects are dispersed in the matrix. On Figure 6b, we can clearly see that the approach curves on zone A and B are drastically different. On zone A, the slope is around 0.99 and is much larger than for zone B (slope = O.S2). A slope value close to unity is the typical signature of a very hard surface (see model curve on Figure 6b), because it corresponds to a situation where no tip indentation takes place. In contrast, a slope value significantly lower than I indicates that the tip indents the surface (hence, its oscillation amplitude decreases more slowly than on a hard surface). Thus, we can easily assign the two components from their mechanical responses [18): zone A is made of Montmorillonite layers while zone B is the PCL matrix. This example illustrates the usefulness of approach-retract curve analysis in the description of the surface morphology.

Conclusions

Here we described a simple and straightforward method (based on the analysis of approach-retract curves) to: (i) give a quantitative estimation of the topographic and the mechanical contribution to height and phase images; (ii) assign the various components in image of heterogeneous polymer materials. This technique has been successively used for pure topographic or pure mechanical contrast as well as for samples with a mixing of the two contributions to the height and phase AFM images.

5

 5

Figure 1 .

 1 Figure 1. Tapping-mode AFM images ( 1.0 x 1.0 µmz) of a PMMA-b poly(alkylacrylate)-b-PMMA . film: (a) Height image (b) Phase; Comparison of the image sections with the pro.files built from the approach-retract curves data [ 13 ]: ( c) Height image; (d) Phase image.

Figure 2 .

 2 Figure 2. (a) Tapping-mode AFM height image (8.0 x 8.0 µm2) of a PMMA-PCL co continuous polymer blend (75:25).film The vertical scale is 80 nm; (b) Image section and its reconstruction fr om approach-retract curve analysis. The solid line corresponds to the i mage section and the black dots are the reconstructed data.

Figure 3 .

 3 Figure 3. Chemical structure of oligo indenojluorene (n= 20-22).

Figure 4 .

 4 Figure 4. (a) Tapping-mode AFM height image (30.0 x 30.0 µm2 ) of an oligo indenojluorene thin deposit. The vertical scale is JOO nm; (b) Corresponding phase image. The vertical scale i s 1.0 degree; (c) Proposed mode/for the molecular organization within the film.

Figure 5 .Figure 6 .

 56 Figure 5. (a) Tapping-mode AFM height image (30.0 x 30.0 µm2) ofT6-(EOha thin deposit on HOPG from THF solMtion. The vertical scale i s 25 nm; (b) Corresponding phase image. The vertical scale is JO degree; (c) Chemical structure of the oligothiophene molecule.

Acknowledgements

The authors are grateful to J. D. Tong and R. Jerome (CERM, University of Liege, Belgium) for the synthesis of the triblock copolymers. Conjugated polymers were kindly provided by K. Millien ( MPl -P , Mainz, Germany) and W.J. Feast (IRC Durham, UK). Research in Mons is partially supported by the Belgian Science Policy Program "Pole d'Attraction Interuniversitaire en Chimie Supramoleculaire et Catalyse Supramoleculaire" (PAI 5/3), the European Commission and the Government of the Region Wallonne (Phasing Out Program). Research in Bordeaux is supported by the Conseil Regional d'Aquitaine. M.S. acknowledges the F.R.l.A.

(Belgium) for a doctoral scholarship.