Laser breakdown in alcohols and water induced by λ = 1064 nm nanosecond pulses

Chemical Physics Letters 500 (2010) 242–250

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Laser breakdown in alcohols and water induced by k = 1064 nm nanosecond pulses Tatiana Kovalchuk, Gregory Toker, Valery Bulatov, Israel Schechter ⇑ Schulich Faculty of Chemistry and the Grand Water Research Institute, Technion – Israel Institute of Technology, Haifa 32000, Israel

a r t i c l e

i n f o

Article history: Received 20 May 2010 In final form 29 September 2010 Available online 27 October 2010

a b s t r a c t Laser breakdown, induced by nanosecond pulses of 1064 nm wavelength, was studied in four alcohols and in water. The time dependent structure and physical properties of the breakdown were measured at high temporal and spatial resolutions, using Mach–Zehnder interferometry, shadow and Schlieren diagnostic techniques. The results indicate that just after the laser pulse the spark column has essentially discrete character and in all liquids it consists of a train of plasma micro-balls, triggered by microscopic inclusion particles. At longer times, namely in a few nanoseconds, micro-bubbles and associated microspherical shockwaves appear. These structures and their time-evolution were measured. Warmed channels were observed in the focal volume in all studied liquids. Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction Understanding the optical breakdown mechanism in liquids, formation of laser spark columns and their time evolution are of considerable importance to a variety of tasks. These include biomedical applications, plasma-mediated eye and biological tissues surgery [1,2], selective cell targeting with light-absorbing nanoparticles, chemical engineering and generation of micro/nano-particles. It is also relevant to numerous analytical applications based on laser plasma spectroscopy [3–6]. Laser induced breakdown mechanism in air and in solids is well established [7–12]. The hydrodynamic characteristics of laser induced breakdown in water, as well as in some other liquids, have also been studied [8,11–21]. At earlier works [13–15,22] the breakdown was analyzed at microsecond resolution, which was not sufficient for revealing the early stages of the breakdown mechanism. Better spatial and temporal resolution [23–25] down to the ns range allowed a better insight into the breakdown phenomenon; however, the discrete structure of the laser spark column was not observed. Discrete micro-spherical shockwaves were reported for the first time in liquids in [16]. Several numerical simulations have also been carried out. Such simulations and experimental data on plasma dynamics [24,26] and shock wave formation [24,27,28] succeeded in explaining the cavitation dynamics and the bubbles arising in water after the breakdown and observed for times longer than 1 ls [25,29]. It has been suggested that plasma formation in water is initiated by electrons generated by multiphoton absorption in the liquid itself or in persistent impurities [24,30,31].

In almost all Letters published in the last few decades the laser spark column in water was considered as a continuous object. The discrete structure and dynamics of laser spark columns in water have been recently revealed by applying shadow and Schlieren diagnostic techniques [32]. These high temporal and spatial resolution techniques allowed, for the first time, to determine the discrete structure of the breakdown in its earl stages. The laser spark in water was interferometrically imaged at its earlier moments of time. The results proved that the mechanism of breakdown in water is initiated by inclusion particles, and that the laser spark column has a discrete nature. It consists of numerous plasma balls, concentric bubbles and associated micro-spherical shock waves. That structure and its dynamics have been explained in terms of individual micro-explosions of inclusion particles located in the focal volume of a focusing lens. Such inclusion particles are always persistent in liquids (even filtered) and cannot be practically avoid. In this Letter the earlier stages (up to 1 ls) of optical breakdown in water and in some alcohols are investigated. Very little is known on this subject, and it is hoped that the comparison of the behavior in various liquids will further reveal the detail mechanism of the breakdown. The applied interferometry Mach–Zehnder technique posses both high spatial and temporal resolutions, as needed for studying the discrete microscopic structures of a laser spark column. The results fill the gap between the early times (ns) when the laser spark columns are of discrete nature, and the late times (ls) when the continuous behavior is mainly manifested. 2. Experimental 2.1. Instrumentation

⇑ Corresponding author. E-mail address: [email protected] (I. Schechter). 0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2010.09.076

The experimental set-up is presented in Figure 1. The plasma was initiated by a Nd:YAG laser (Continuum, Powerlite-8010,

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T. Kovalchuk et al. / Chemical Physics Letters 500 (2010) 242–250

Ar-ion laser

Mirror

Mirror

Laser 1

1064nm

Focusing lens Cuvette

Delay generator

Beam splitter cube

Collimator Film or CMOS camera

Mirror Aperture Beam diaphragm splitter

Laser 2

Laser breakdown volume

532nm

532nm filter

Mirror Beam Beam expanding splitter cube lens

Power meter

Figure 1. Experimental set-up.

US). Its fundamental harmonic pulses (k = 1064 nm, 6 ns) were focused by a singlet of the focal length of 75 mm into a quartz-windowed cuvette, where the liquid under study is located. No hot spots were observed in the focal volume. Since the numerical aperture NA  nD/(2f) = 0.08, the spherical aberrations do not remarkably change the focal spot radius of 35 lm. The maximal deviation from fitted Gaussian in the near field (<1 m) was 40%. The absorbed laser power in the alcohols as well as in water was not sufficient for bringing about self-focusing effects. This was confirmed by the interference imaging method. The output laser energy was varied in the range of eout = 20– 150 mJ. Taking into account the Fresnel reflections from the input window and the actual absorption in water (40%) and in ethanol (35%), the focal spot was illuminated with 60% and 65% of the output energy. In most measurements where eout = 70 mJ, the energy was not sufficient for self-focusing. In water the self-focusing was not observed up to 150 mJ. A second laser (2nd harmonic of a Nd:YAG, INDI, Spectra Physics, CA) was used for probing the cuvette in a direction perpendicular to the first laser beam. The probing laser was fired at controllable time delay after the first laser pulse. Both lasers were operated in the single-pulse mode and synchronized using an external pulse generator (BNC 555–8cG, Berkley Nucleonic Corp., Berkley, CA) with accuracy better than a 1–2 ns (measured by comparing the two pusses on a dual-beam oscilloscope). An argon-ion laser was used for alignment and adjustment of the optical components. Three different diagnostic techniques were applied for visualizing and measuring the breakdown region: shadow, Schlieren and interferometry. An optical scheme of shadow photographing was used for Schlieren measurements, by locating an adjustable optical knife in the back focal plane of the first objective lens of the collimator. In this series of experiments the dark field Schlieren technique was applied for visualizing vertical gradients of the refraction index (horizontal location of the optical knife). The laser spark columns were also studied by applying a Mach–Zehnder interferometric scheme. The interferometer consisted of two beam-splitting cubes and two flat mirrors. All three test approaches provide imaging with spatial resolution 610 lm, depending on the magnification coefficient. The optical collimation system, consisting of two objective lenses (ILOCA-Quinon, f = 50 mm and Jupiter-9, f = 85 mm), sharply focused the breakdown region onto the imaging detector. The detector was either a digital camera or a photo-film. The digital

camera (Alpha-900, Sony Corporation) was equipped with a CMOS sensor (24  36.9 mm size, 24.6 megapixels). In most experiments the camera worked in a binning mode with resolution of 1890  1260 pixels. The digital resolution of the frames was of the order of 4.5 lm/pixel. Photo-films were also applied (Kodak, T-MAX 100 with resolving power  100 lines/mm). The obtained pictures were digitized at the resolution of 2600  1900 pixels. 2.2. Chemicals Analytical grade ethanol was supplied by Frutarom LTD, Israel; butanol, UV-spectral grade and 1-heptanol, purity >99.5%, were supplied by Fluka Chemika, Germany; methanol, HPLC grade, was supplied by J.T. Baker, Germany. All compounds were used without further purification or filtering. Tap water, which meets the international standards [33], was used with no additional purification. Double distillated water (DDW) samples were prepared using NanoPure Analytical Deionization System type D4700 (Barnstead-Thermolyne Corp. Dubuque, IA). The size distributions of the persistent particulate material in the liquids were analyzed using a zeta potential particle seizer, Nicomp™380 ZLS (Particle Sizing System, Santa Barbara, CA). The particulate concentrations were measured using the method of scattering detection (since the actual concentrations were below the LOD of the Nicomp™380 ZLS Sizer). An Ar-Ion laser beam tested the liquid sample in a cuvette and scattered on the impurities. The light perpendicularly scattered was accurately imaged on the CMOS camera. The thus obtained pictures were analyzed and the number of scattering centers was calculated. 3. Results and discussion 3.1. Particulate size and concentration The size distribution of persistent particulates in double distillated water (DDW) was measured. It was bimodal with maxima at 115 nm and 1.4 lm. The particulate concentration, measured as described in the Experimental, was (2.5 ± 0.6)  104 cm3. The particulate concentration in the tap water was (1.2 ± 0.4)  106 cm3. (Due to the high level of concentration, the concentration measurement required a proper dilution in DDW). Filtration of tap water through Millipore filters of pore size 0.45 lm, reduced the particulate concentration to (1.2 ± 1.5) 

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105 cm3. Filtering through 0.22 lm pore-size filter further reduced the concentration to (2.8 ± 0.6)  104 cm3. The particulate concentration in the alcohols was comparable to those in DDW. The further filtration though 0.22 lm pore-size filters did not reduce the concentration. This fact indicates only that the size distribution is mainly below 0.22 lm. 3.2. The structure of a laser spark column Mach–Zehnder interferometry is one of the most informative optical diagnostic techniques. It allows studying the structure of a laser spark columns with spatial resolution of 610 lm. The results are a function of time delay, and this method provides ns temporal resolution. The shifts of the interference fringes and their sign allow calculating the local changes of the refraction index in the examined liquids. For example, the region compressed by a shockwave has positive change of the refraction index, which can be deduced from the corresponding sign of fringe shifts; the region warmed by the laser radiation has negative change of the refractive index. Positive and negative changes of the refraction index lead to the fringe shifts in the opposite directions, perpendicular to the fringes. Let us first define the basic features and the nomenclature, using a schematic picture (Figure 2): In the vicinity of the focal point and along the laser beam numerous plasma events are formed. All of them together are called the laser spark column. It consists of micro-plasma balls, micro-bubbles and a spherical shockwave (of a well defined front). During the laser radiation, warmed channel forms in the liquid along the laser beam. In some cases (in alcohols) the warmed channel results in a cylindrical shockwave, of a front propagating apart of the laser beam. In other cases (in water) a different kind of cylindrical shockwave evolves: at longer times the spherical shockwaves expand and interfere with each other. This situation also results in a cylindrical pattern, called interfering shockwave cylinder. The structure of the laser spark depends on the laser beam characteristics, on the liquid and on time. The discrete structure of a laser spark column is formed during a few ns after the heating laser pulse. The laser spark was examined up to 1 ls and we found it convenient to divide its time evolution into three major time intervals: the first stage (sd < 50 ns); the second time stage (50–200 ns) and the third stage (>200 ns). 3.2.1. First stage (<50 ns) As can be seen in Figure 3, just after the heating laser pulse, the spark column is filled with luminous micro-plasma balls of ca. 100 lm diameter. The luminous plasma balls can be observed up

Figure 2. Schematic structure of a general laser-spark column and nomenclature definitions.

Figure 3. Fragments of interferograms of laser spark columns at the first time stage: sd < 50 ns: (a) in water, time delay sd = 17 ns; (b) in ethanol, sd = 22 ns; (c) in butanol, sd = 10.5 ns. The laser pulse energy was 70 mJ. The laser beam was focused from right to left. The focal spot coincides with the picture’s left margin.

to 1 ls. Since the interferograms are focused on a photo film, the regions of luminous plasma balls are overexposed due to the intensive plasma radiation. Since the plasmas are created around inclusion particles, the initial sizes and characteristics of the micro-plasma balls within the plasma column depend on the nature of the suspended particulates and on their concentration. As has previously been reported, the size of the micro-plasma balls monotonically increases in the first ca 500 ns, in both water and alcohols [32]. The luminous micro-plasma balls arise due to avalanche ionization in the vapors of inclusion material and successive heating of the plasma due to the bremsstrahlung effect. It is suggested that the hot ionized material’s vapors create a spherical envelope of the liquid’s vapors over the inclusion, which forms the micro-bubble. This vapor envelope moves as a piston working on the surrounding liquid and generates a powerful micro-spherical shockwave in it. In order to support the mechanism of plasma triggered by inclusion particles, we measured the volume concentrations of plasma balls induced in both tap water and in ethanol. The concentration in water was of the order of 60  104 cm3 and in ethanol it was approximately 2  104 cm3. The results were compared to the measured concentration of inclusion particles in these liquids: in the case of tap water about 50% of inclusion particles took place in the breakdown process, while in ethanol the majority of the particles were associated to plasma events. The differences can be attributed to the specific size distributions and to the chemical nature of the suspended particulates in these liquids. Nevertheless, the large percentage of particles involved in the breakdown mechanism support the picture of the discrete nature of plasma generation in liquids. At about 20 ns the micro-spherical shockwaves are getting clearly visible in both tap water and ethanol in Figure 3a,b. However, while in water the size of the spherical shockwave fronts are remarkably larger than the size of micro-plasma balls, in ethanol the size of the spherical shockwave only slightly exceeds that of the luminous micro-plasma ball. Also the speed of the shockwaves (visible as coaxial rings) is larger in water (measured at the same time). This can be explained by the much lower compressibility of water compared with the alcohols. The compressibility of water reaches a minimum of 4.4  1010 Pa1, as to ethanol it is 11.0  1010 Pa1 [34]. Note that in Figure 3c the shockwaves in butanol are not observed at all. This is because this figure was acquired at an earlier time delay (10.5 ns), when the spherical shockwaves have been just formed and have not detached yet from the micro-plasma balls.

T. Kovalchuk et al. / Chemical Physics Letters 500 (2010) 242–250

3.2.2. Second time stage (50–200 ns) This stage is characterized by enhanced sizes of the micro-bubbles and the associated spherical shockwaves. This process is illustrated in Figure 4a, where micro-bubbles over exploding inclusion particles and the associated spherical shockwaves of enhanced diameters are visible. Note, that the micro-bubble sizes are larger than those of the luminous micro-plasma balls. At this time (ca 150 ns), the characteristic size of the spherical shockwaves is comparable to the distance between inclusion particles. This forms an interfering shockwave cylinder, which is clearly observed in Figure 4a. It is formed by overlapping neighboring spherical shockwaves, which results in a mixture of interferometric fringes of the cylindrical pattern. When the spherical shockwaves emerge in a cylindrical pattern, it is still a shockwave (delay times of 50–90 ns and Mach number >1). At later times it becomes a strong acoustic wave. Note that this interfering shockwave cylinder was previously reported as a continuous object. Simply, the experimental setups were not good enough for resolving the discrete structure of the laser spark column [8,18–21]. Our results provide an explanation of the earlier observations. 3.2.3. Third stage (>200 ns) The evolution of micro-bubbles and spherical shockwaves is shown in Figure 4b. At this time the size of the micro-bubbles is remarkably larger than the diameter of the luminous micro-plasma balls. Also the interfering shockwave cylinder becomes a cylindrical acoustic wave, which is clearly observed and its radius is much increased.

Ethanol, τd=152 ns

Micro plasma balls

0

0.2mm

a

245

The overall process is such that the laser induced plasmas are of a discrete nature in the first stage and at a later time the plasma structure changes from discrete to continuous. This happens when the numerous micro-spherical shockwaves expand and combine into a cylindrical shockwave. The formation of cylindrical shockwaves by merging of spherical shockwaves is a new concept. Cylindrical shockwaves have been previously reported. [22,35] However, in [22] the merging was missed due to a too long delay time, of ca 5.9 ls. In [35] that cylindrical shockwave was seen for continuous spark column, where the temperature close to the plasma exceeded the critical point of water. These are very different conditions, since we conclude from our interferometric measurements that the temperature rise is lower than 50 K. Under the experimental conditions described in [35] the discrete structure of the laser spark column in its early time (<100 ns) could not be observed, so the mechanism of the formation of the cylindrical shockwave could not be revealed. When studying the laser spark columns, one must realize that more than one mechanism might take place. This should depend on the actual experimental conditions: Plasma generation can be obtained by both sharp focusing conditions (e.g., using microobjectives or short focal length lenses) and by moderate focusing (e.g., using common lenses of long (50–100 mm) focal length. We also have to distinguish between plasmas induced in extremely pure liquids, which have been well filtered and in regular liquids, which consist of numerous suspended particulates. Under sharp focusing conditions, spherical shockwaves are expected, and not cylindrical. If the particulate concentration is very small such that not even a single particle is present in the focal volume, the mechanism of the breakdown might be different than that described in this Letter. Such situations require different analysis. However, under moderate focusing conditions in most cases there will be at least one particle in the interaction volume, and the mechanism presented here is valid. This is definitely true in tap water, where the concentration of inclusion particles is huge, and also in liquids exposed for a short time to ambient air. Our investigation shows that in most commercially available liquids of analytical grade, there are a few particles present in the focal volume of a singlet of f = 50–100 mm, and at least 1–2 breakdown events can be observed. Again, in special cases where the laser is focused in extremely pure liquids, the mechanism could be different. The existence of additional possible breakdown mechanisms is also supported by other reports where much shorter plasma luminescence file-times were observed [26,36]. 3.3. The mechanism of optical breakdown in alcohols

Micro bubbles

Ethanol, τd=333 ns

b

Figure 4. Fragments of interferograms of laser spark columns in ethanol. The laser pulse energy is 70 mJ. The laser beam is focused from right to left. The focal spot coincides with the picture’s left margin. (a) Delay of sd = 152 ns (second time range) (b) delay of sd = 333 ns (third time range). Dotted circles mark spherical shock wave fronts.

The structure details of the breakdown in the alcohols indicate a substantial similarity to breakdown characteristics in water, which have been recently reported [32]. The details reveal the following picture: the breakdown starts after absorbing the focused laser light by persistent solid particulates. The absorbed energy ablates the particulate’s surface and forms vapors. However, the expanding vapors are strongly restricted by the surrounding liquid. This results in a high vapor pressure, which supports avalanche ionization there. Multi-photon processes cause the appearance of the first electrons [37]. The electronic density in the vapors increases, which in turn increases the laser light absorption due the bremsstrahlung mechanism. The thus formed hot plasma quickly evaporates a spherical envelope of the liquid around it. The vaporization process has an explosive character. The spherical layer of the evaporated liquid acts as a piston and generates a powerful shockwave in the surrounding liquid, which propagates at high supersonic velocity. At the same time, a micro-bubble is created over the plasma ball. Later the walls of the micro-bubble

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expand along with velocity, which is much lower than the speed of the associated spherical shockwave. It is clear from the above that both the micro-bubble and the associated spherical shockwave evolve with time. In the following we investigate their dynamics. 3.4. Micro-bubble and associated spherical shockwave dynamics The radii of the micro-bubbles and of the surrounding spherical shockwaves in water and ethanol are presented as a function of time in Figure 5a. The results were calculated from a large series of interferograms, by measuring sizes of the micro-bubbles and the shockwaves at a series of time delays after the laser pulse. The data were averaged over numerous individual events occurring at many laser shots. The Mach numbers of the spherical shockwave fronts as a function of time are shown in Figure 5b, for both water and ethanol. The graphs indicate that the velocities of the expanding spherical shockwaves and of the micro-bubbles in water are remarkably higher than in ethanol [34]. This might be attributed to the higher compressibility of ethanol (and other tested alcohols) and to the lower speed of sound in this liquid (1.16 km/s in ethanol and 1.46 km/s in water). The lower compressibility of water may lead to higher pressure on the front of the shockwaves.

ter wa

Radius / µm

300

s ave w k hoc al s c i er sph

200

100

l ano eth

water ethanol

micro-bubbles

0 0

50

a

100

150

Time / ns

b

Mach number / M

6

4 water

2

ethanol

0 0

20

40

60

80

100

120

140

delay time / ns Figure 5. Experimental dependence of micro-bubbles and associated spherical shockwave radii in water and in ethanol as a function of time (a-top) and Mach number of spherical shockwaves as a function of time (b-botom). Solid lines: eye guiding smooth curves.

The asymptotic behavior of the spherical shockwaves and micro-bubbles can easily be observed in Figure 5a,b. At times longer than 50 ns, the velocities of the spherical shockwaves in both water and ethanol asymptotically approach the corresponding sound speeds. The micro-bubble walls reach asymptotic speeds of 90 m s1 in water and of 60 m s1 in ethanol. Similar kind of results has been previously reported [24], however, for different conditions: Figure 4 in [24], presents the speed of a bubble wall and shockwave in radial direction from the continuous complex of a single laser spark column. Note that the pressure in [24] was about 1 kbar only, while in our case it reaches the Mbar range. However, in our case the pressure is measured in a spherical shockwave around a separate inclusion particles, while in [24] the results are related to a continuous laser spark column. In our case, the data of Figure 5b indicate a pressure of 0.4 Mbar, for M  6.2 at the shortest time delays. In 35 ns the Mach number drops to M = 2, corresponding to a pressure of 20–25 kbar. The conclusion is that the micro-spherical shockwave from an inclusion is much more intensive than that from a plasma spark column. 3.5. Pressures and densities behind the micro-spherical shockwaves in water Laser radiation at k = 1064 nm is effectively absorbed by numerous inclusion particles in the focal volume in water. The explosive vaporization of water around an inclusion particle creates a powerful micro spherical shockwave, which effectively compresses the liquid. The pressures and the densities of the compressed liquid are time dependent and their estimation is of interest. Unfortunately, at short time delays the interference information is not available and cannot be used for calculating the pressures and densities. This limitation is due to the strong luminescence of the micro plasma balls and due to the extraordinary compression of a liquid. The latter results in large local fringe shifts, which cannot be resolved by interference techniques (the spatial resolution is insufficient). Nevertheless, the pressures behind the spherical shockwave front at short time delays can still be estimated from the shockwave velocities (showed in Figure 5). These estimations are based on previously calculated and tabulated data for water [38]. The results from Figure 5b indicate that the pressures at short time delays reach 0.4 Mbar for water and 0.25 Mbar for ethanol (compare to pressures of 1.2 kbar, previously obtained for continuous laser spark columns [24]). When the spherical shockwaves just starts to outdistance the micro-bubbles in water, the Mach number is Ms  5 and the corresponding estimated pressure is Ps  0.26 Mbar. At later time delays, in the range 10 < sd < 50 ns, the Mach number of the shockwaves in water drops to Ms  2.0, which corresponds to an estimated pressure of Ps  21.5 kbar. Let us now estimate the pressures behind the spherical shockwave front at longer time delays. This can be done using our interferometric data. The results could be of interest since up to now such data have not been published. It could be used for verifying breakdown models and for obtaining hydrodynamic parameters. At time delays longer than 50 ns, the pressure behind the shockwave front quickly dies. Now interference data can be used directly for characterizing the radial distribution of the liquid’s pressure between the micro-bubble and the associated shockwave front. The procedure for estimating this pressure is described in the following. The pressure behind a shockwave, Ps, is related to the change in the liquid density Dq, according the following expression [38]:

Ps ¼ q0 a20

Dq ; Dq þ q 0

ð1Þ

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where q0 = 1 g cm3 and n0 = 1.33 are the density and the refraction index of the undisturbed liquid (n0 – 1 = Kq0 [39]; K is the Gladston–Deil constant). a0 is the speed of sound in the liquid and Dq is the compression of the liquid behind the front of the shockwave. The Dq values are directly derived from the experimentally measured fringe shifts Dk, in the interferograms [39]:

Dq

q0

¼

kDk Lðn0  1Þ

ð2Þ

where: L is the traveling distance of the probing beam in the compressed layer of the liquid and k is the wavelength of the diagnostic light. The radial distributions of water densities behind the spherical shockwave fronts were evaluated, using Equations (1) and (2) for a series of times. In the following we present the results for 52 and 453 ns: The results for time delay of 52 ns are shown in Figure 6a,b. At this time the shockwave moves with supersonic speed Ms  1.39. The radial distribution of the density of water between the front of the shockwave and the micro-bubble is presented in Figure 6b. The change of the normalized density just behind the front of the shockwave was Dq/q0 = 0.14 and the corresponding pressure, according to Eq. (1), was Ps  5 kbar. The results at the longer time delay sd = 463 ns, when the shockwave propagates with a velocity close to the speed of sound a0, are shown in Figure 6d. At this time, the normalized density change just behind the front of the shockwave was Dq/q0 = 0.01 and the corresponding pressure was Ps  0.2 kbar.

3.6. Warmed channels in the alcohols and water Interference imaging allows for observing the effect of warming in the focal volume region. The temperature increase may be evaluated from general physical considerations and compared to the interference measurements. Let us first estimate the temperature increase from simple physical considerations: assume that the laser pulse energy ea, is absorbed in the liquid along its path according the Beer–Lambert law exp(az), where a is the extinction coefficient of a liquid at the irradiation wavelength (k = 1064 nm) and z – is the axis along the laser beam. The laser light is absorbed in a cylindrical volume of diameter P 2w0 (where 2w0 = 70 lm is the focal spot of the laser beam) and the cross-section S P p w02. The warming DT, can be evaluated from conservation of the energy:

DT 

a ea ¼ bT ES qc S

where q (g cm3) is a liquid density, c (J g1 K1) is the heat capacity and ES = ea/S (J cm2) is the pulse energy flux. Thus, the warming of a liquid in the focal volume is determined by the factor bT = a/(qc), which might be called the warming factor. The numerical values of the warming factors and other relevant parameters are presented in Table 1. Using Eq. (3) and taking into account the absorbed energy ea = 50 mJ, the calculated temperature rise in water is DT  47 K. In ethanol the calculated temperature rise is 82 K. Lower values were found in methanol, butanol and in heptanol. Note that both temperature and pressure-induced refractive index changes can be measured: the cylindrical shock wave moving in radial direction from the heated central region makes positive

c , 453ns

a, 52ns

0.012

0.16

b

0.008 Δρ / g cm

-3

-3

0.12 Δρ / g cm

ð3Þ

0.08 0.04

d

0.004 0.000 -0.004

0.00

-0.008 50 75 100 125 150 175 200 225 Radius / μm

100 200 300 400 500 600 700 800 Radius / µm

Figure 6. Fragments of interferograms of laser induced breakdown in water and the corresponding radial distributions of the water density change, located between bubble’s wall and the shockwave front. Time delays: (a,b) sd = 52 ns; (c,d) sd = 463 ns. Laser pulse energy: 63 mJ.

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Table 1 Termo-physical parameters of water and alcohols. Compound

Heat capacity c (J K1 g1)

Density [40,41] q (g cm3)

Refractive index [42] n

Units

Molecular weight MW (g mol1)

Water Methanol Ethanol Butanol Heptanol

18 32 46 74 116

4.18 2.53 2.44 2.39 2.33

0.998 0.714 0.789 0.809 0.822

1.33 1.33 1.36 1.40 1.42

Sound speed [42] va (km/s)

Extinction coefficient a at k = 1064 nm (cm1)

(K1)

Warming factor bT (cm2 K J1)

1.48 1.12 1.16 1.26 1.31

0.15 [43] 0.13 0.12 [44] 0.05 0.02

0.8  104 4.0  104 3.9  104 3.9  104 3.4  104

3.6  102 7.2  102 6.2  102 2.6  102 1.0  102

dn/dT

change in the index of refraction due to compression of the liquid. The temperature of this region is not changed (the shock wave is not strong). The change of temperature in the central region is calculated from the interferogram using the standard approach [39]. Let us now estimate DT from the interference measurements. The change in the refractive index is approximated using the expression: Dn = Dkk/dc, where Dk = 0.6 is the experimentally measured fringe shift in the warmed region; k = 532 nm is the wavelength of the diagnostic radiation and dc P 2w0 = 70 lm is the diameter of the warmed region. Thus, we obtain Dn 6 4  103. The temperature change can now be evaluated from the relation:

Dn @n Þq ð@T

ð4Þ

@n For water, the constant ð@T Þq = 0.8  104 [40]. Therefore, the corresponding temperature change in water is DT  50 K. This value is in agreement with the result obtained from conservation of energy consideration. The warmed channel in water lasts more than ca. 1 ls and it then deactivates by the process of thermal conductivity. In contrast, a different mechanism is observed in the tested alcohols. The warmed channels in alcohols generate cylindrical shockwaves, expanding in the radial direction. As far as we know, these cylindrical shockwaves have not been reported in the literature. In the following, we study the dynamics of such shockwaves in alcohols:

3.7. Dynamics of cylindrical shock waves in the alcohols Let us analyze the dynamics of the heated region in ethanol during the first hundred nanoseconds. Examples of the interferograms illustrating the warmed region in ethanol and the associated cylindrical shockwave at several delay times are shown in Figure 7. Such data were used for calculating the corresponding changes in the refractive index in the warmed channel and in the associated cylindrical shockwave. The radial distribution of the refraction index change in ethanol is presented in Figure 8. It is seen that the maximum negative change of the refractive index in the warmed channel is on the axis of the heating beam (r = 0). This is where the temperature achieves a maximal value. In general, warming of the liquid is accompanied with increasing the temperature and reducing the index of refraction; compression in the shockwave increases the index of refraction. Thus, the maxima in Figure 8 indicate the locations of the higher compression, namely, the shockwave fronts. Obviously, as time evolves, they are found at larger radii. The results in Figure 8 also indicate that a quantity of the thermal energy absorbed in the focal volume is sufficient for generating the cylindrical shockwave moving in radial direction with the speed of 1.5 km/s (Mach number Ms  1.3). @n Using Eq. (4), and the value of ð@T Þq = 3.9  104 K1 [41], we can estimate the actual temperature change at any time delay and location. For example, the thus calculated temperature change in ethanol, at 22 ns and at r = 0, is DT  10 K. This temperature

Figure 7. Fragments of interferograms measured at different time delays, illustrating the dynamics of a warmed channel in ethanol. The output of the laser pulse was 65 mJ. The radiation goes from right to left. The arrows indicate the planes where the radial distributions of the refraction index were calculated.

64 ns

0.0010

refraction index change /Δn

DT ¼

95 ns

22 ns

0.0005 0.0000 -0.0005 -0.0010 -0.0015 -0.0020 -0.0025 -0.0030 -0.0035 -0.0040 0

50

100

150 radius / mm

200

250

Figure 8. The calculated radial distribution of the refraction index of ethanol in the warmed region at three time delays. The data characterize the cylindrical shockwaves. Solid lines: eye guiding smooth curves.

jump is remarkably lower than the calculations based on conservation of energy: DT  82 K. This discrepancy is mainly attributed to

T. Kovalchuk et al. / Chemical Physics Letters 500 (2010) 242–250

the different time delay: in the first case the temperature change corresponds to a time after the laser pulse ended (pulse duration was of 6 ns). In addition, the central region in ethanol is getting cool due to an effective process of adiabatic expansion. Note that no cylindrical shockwaves are observed in water. The performed estimations have shown that the energy absorbed in water is dissipated by thermal conductivity. Full explanation of this difference between water and the tested alcohols is not yet understood. A possible explanation might be based on the differences in the coefficient of volumetric thermal expansion of these liquids: 207  106 C1 in water (at 20 °C) and 750  106 C1 in ethanol. The above presented results were obtained for ethanol, but similar calculations have been carried out for all tested alcohols. The cylindrical shockwaves were observed in all alcohols. The dynamics are, in principle, very similar. Starting their motion with supersonic speeds the cylindrical shockwaves quickly decelerate and expand asymptotically approaching the speed of sound. Selected interferograms (not shown) were used for calculating the radial distribution of the index of refraction in the warmed channels and the associated cylindrical shockwaves in all alcohols. The results for three compounds are presented in Figure 9, where the index of refraction is presented as a function of radius in a cross-section close the focal plane. The data were collected at comparable short time delays. It is interesting to compare the behavior of ethanol and butanol, which were measured at almost the same time delay. The absorption coefficient of ethanol at k = 1064 nm is three times larger than that of butanol (see Table 1). This explains the higher warming effect, which is evident from the higher negative Dn at zero radius. Also the cylindrical shockwave is more intensive, as can be seen from the larger positive change of the refraction index (at about r = 160 lm). The energy deposition and pressure generation in water and in alcohols are influenced by both the linear absorption coefficient of the respective media (see Table 1) and by the Grüneisen coefficient that governs the translation of heat and thermal expansion into a pressure rise (see Refs. [2,45]. Thermoelastic stress generation might be relevant to the understanding of the cylindrical pressure waves observed in alcohols. For a proper understanding, one will need to know the (temperature dependant) Grüneisen coefficients of water and the alcohols investigated. In this study we provide the

refraction index change / Δn

0.002

ethanol

methanol

τd=11 ns

τd=26 ns

butanol

0.001

τd=10.5 ns

0.000 -0.001 -0.002 -0.003 -0.004 -0.005 0

25 50 75 100 125 150 175 200 225 250 275

radius / μm Figure 9. Radial distributions of the index of refraction in the warmed channels in several alcohols: ethanol (time delay of 11.0 ns), methanol (26 ns) and butanol (10.5 ns). Solid lines: eye guiding smooth curves.

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first experimental results on the differences between breakdown in water and ethanol. Detailed analysis in beyond the scope of this Letter and is now under investigation. 4. Conclusions The time-dependent structure and physical properties of optical breakdown were investigated using interferometric techniques, which allow for both high temporal and spatial resolutions. The results were obtained for tap water and for four alcohols. The laser spark column in the tested liquids just after the heating laser pulse has discrete structure. It consists of numerous micro plasma balls, induced by submicron absorbing inclusion particles. The micro plasma balls evolve with time and they bring about concentric micro-bubbles and spherical shockwaves. These structures and their time-evolution have been measured by interferometric techniques. In addition, the radial distributions of the density between the bubbles and the correspondent spherical shockwave front were estimated for a series of time. At longer delays, warmed channels were observed in the focal volume in all liquids, and their temperature raise and time evolutions were approximated. Several significant differences between breakdown in water and in alcohols were found: (a) the warmed channels in alcohols generate cylindrical shockwaves expanding in radial direction. This effect was not observed in water, where the warmed channels were deactivated by thermal diffusion. No explanation is yet available to this effect; (b) the velocities of the expanding spherical shockwaves and of the micro-bubbles in water are remarkably higher than in alcohols. The main finding in this work is the discrete nature of the plasma column, which lasts up to 100 ns. In all previous reports the plasma was considered as a continuous object. We showed how the plasma transforms from its discrete nature in its very beginning into continuous at later times. This happens when the numerous micro-spherical shockwaves triggered by local inclusion particles expand and combine into a cylindrical shockwave. Acknowledgments This research was supported by the Israel Ministry of Science and Technology (MOST), by the Grand Water Research Institute and by the James Franck Program in Laser Matter Interaction. V.B and G.T. are grateful for financial support by the Ministry of Absorption, provided in the framework of the KAMEA program. References [1] V. Venugopalan, A. Guerra, K. Nahen, A. Vogel, Phys. Rev. Lett. 88 (2002) 078103. [2] A. Vogel, V. Venugopalan, Chem. Rev. 103 (2003) 577. [3] R. Wisbrun, I. Schechter, R. Nießner, H. Schröder, K.L. Kompa, Anal. Chem. 66 (1994) 2964. [4] L. Xu, V. Bulatov, V.V. Gridin, I. Schechter, Anal. Chem. 69 (1997) 2103. [5] V. Bulatov, R. Krasniker, I. Schechter, Anal. Chem. 72 (2000) 2989. [6] B. Dolgin, Y. Chen, V. Bulatov, I. Schechter, Anal. Bioanal. Chem. 386 (2006) 1535. [7] I. Schechter, Rev. Anal. Chem. 16 (1997) 173. [8] A. Miziolek, V. Palleschi, I. Schechter (Eds.), LIBS – Fundamentals and Applications, Cambridge University Press, 2007. [9] V. Bulatov, L. Xu, I. Schechter, Anal. Chem. 68 (1996) 2966. [10] R. Krasniker, V. Bulatov, I. Schechter, Spectrochim. Acta B 56 (2001) 609. [11] V. Bulatov, A. Khalmanov, I. Schechter, Anal. Bioanal. Chem. 375 (2003) 1282. [12] Y. Chen, V. Bulatov, L. Singer, J. Stricker, I. Schechter, Anal. Bioanal. Chem. 383 (7–8) (2005) 1090. [13] G.A. Askar’yan, A.M. Prokhorov, G.F. Chanturiya, G.P. Shipulo, Sov. Phys. JETP 17 (1963) 6. [14] R.G. Brewer, K.E. Riekhoff, Phys. Rev. Lett. 13 (1964) 334. [15] E.F. Carome, C.E. Moeller, N.A. Clark, J. Acoust. Soc. Am. 40 (1966) 1462. [16] C.E. Bell, J.A. Landt, Appl. Phys. Lett. 10 (2) (1967) 46. [17] L.C. Yang, V.J. Menichelli, Appl. Phys. Lett. 19 (11) (1971) 473. [18] V.S. Teslenko, IEEE Trans. Elect. In. 26 (6) (1991) 1195.

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