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Abstract
We proposed a complex method based on a combination of shadow photography and time-resolved Raman spectroscopy to observe the non-stationary laser-induced supercritical state in molecular media. Shadow photography is applied for retrieving pressure values, while Raman spectroscopy with molecular dynamics for temperature estimation. Time resolution of 0.25 ns is achieved by varying the delay between the pump (creating an extreme energy delivery) and the probe laser pulses by the self-made digital delay electronic circuit . The proposed method was employed in liquid carbon dioxide and water. Under nanosecond laser pulse impact, the estimated temperatures and pressures (∼700 K and ∼0.5 GPa) achieved in media are higher than the critical parameters of the samples.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, supercritical technologies are widely used in science and practical applications [1]. Most of their applications are limited to steady-state or quasi-steady-state conditions. Namely, supercritical fluids (SCF) find applications in such diverse areas as the extraction of medicinal products from plant raw materials [2–4], aerogels production [5,6]. Supercritical fluids (SCF) act as a promising chemically active medium for several environmentally friendly technologies. To obtain supercritical fluids, it is necessary to provide a media condition with temperature and pressure exceeding critical values.
Along with this, laser technologies based on pulsed heating of condensed matter or dense gases are actively developing. The laser energy is absorbed and converted into heat and/or a pressure pulse to form SCF in this process. Such pulsed laser technologies include laser ablation, laser generation of nanoparticles in liquids [7–9], laser-induced forward transfer (LIFT) [10–12], laser-induced backside wet etching (LIBWE) [13], and some others. Most SCF technologies use only natural substances, such as carbon dioxide or water [14,15]. Therefore, they are classified as “green” and are of particular additional interest. In mentioned above applications, SCF is utilized in large (usually more than several cm3) volumes. By changing external conditions (pressure and temperature), the macroscopic and microscopic properties can't be modified rapidly; at least the temperature variation is limited by thermodiffusion. In this way, it is possible to create a strongly non-equilibrium state by tightly focusing short and ultrashort laser pulse inside the material [16–18].
Moreover, using commercially available laser systems under tight focusing of short and ultrashort laser pulses, most of substances can be transmitted to the supercritical region on the p-T diagram for a short period [19]. Under intense laser impact in dielectrics, the electron plasma can be generated. The deposited energy density primarily depends on laser-induced plasma because, in dielectrics, laser energy could be transmitted to atoms and molecules through electrons (in non-resonant case) [20]. It is relatively easy to estimate plasma electron density, temperature, and volume or determine the deposited energy density. For example, the all-optical (such as third-harmonic mapping [21], interferometry and shadow photography [22], etc.) or photo-acoustic [23] methods can be implemented for this task. However, the transition from electronic to atomic subsystem is complex, unique for each material. When the laser-induced plasma is located inside media, it becomes a region of the laser energy deposition [24]. Under tight focusing, the laser-plasma is produced, and energy of laser impulse is initially delivered into the volume about 100–1000 µm3. On the sub-ns - ns timescale, due to high (∼103−104 K) local temperatures and pressures (100–1000 MPa) [25,26], the shock waves are generated, and the cavitation bubble is created. Thereby the pressure and temperature in such systems are usually higher than the critical ones [27]. However, the identification of highly non-equilibrium states is a complex task. And if the estimates for shock-induced pressures in the condensed matter were performed even at the picosecond time scale [24], the temperature estimates were obtained experimentally only on a microsecond time scale [28]. It is possible to use Raman spectroscopy to modify matter induced by laser pulses [29]. However, in such an approach, Raman spectroscopy serves as an indicator of structural changes. It is necessary to perform a methodological experiment for quasi-steady conditions or perform numerical simulations.
It is important to note, that the area of the laser impact due to thermodiffusion and shock wave propagation is much (1–2 orders) more than the initial volume of laser-induced plasma. It should also be noted that the numerical calculations performed indicate that almost all materials under short laser exposure formally goes into a supercritical state, i.e. its molecular (or atomic subsystem) has a temperature and pressure above the critical parameters of the medium [25,29]. Nevertheless, under such conditions there is no thermodynamic equilibrium, and the properties of such state are practically unstudied.
In this manuscript, we presented a complex method and experimental setup for time-resolved diagnostics of the laser-induced supercritical state of molecular matter. We used carbon dioxide and water as samples and demonstrated the transition to the supercritical state using shadow-photography and time-resolved Raman scattering to estimate temperature and pressure.
2. Experimental setup
In the experiments pump-probe technique was used, see Fig. 1. The first (pump) pulse is tightly focused into the sample medium, which leads to an extreme (several kJ/cm3) deposited energy densities [23]. The second pulse is used as a probe. We changed electronic delay by generating two trigger pulses for two different laser sources to achieve temporal resolution. We implemented the electronic delay circuit based on FPGA and analog electronics. The main trigger controller is the NI Compact Rio. At the FPGA level, two pulses are generated with up to 1 MHz frequency with a minimum step between pulses of 25 nanoseconds. The compact Rio also runs a real-time system that communicates with a PC via LAN and transfers data to the FPGA. Delays are fine-tuned using a self-made analog circuit that achieves 250 ps steps with a maximum delay of 64 nanoseconds. The jitter of the electronic part of the circuit (measured with a 1 GHz oscilloscope) is less than one ns.
However, the jitter between receiving the trigger and directly generating the laser pulse is in the order of 250 ns. To compensate this jitter, an oscilloscope was installed in the circuit, receiving a signal from two photodetectors or/and for each time delay, several (more than 50 measurements) were carried out and then averaged. In the experiments, we used two lasers with a nanosecond pulse duration (6 ns). Laser radiation at a wavelength of 1053 nm was used (Laser Export Tech 1053) as a pump and at a wavelength of 527 nm (Laser Export Tech 527) as a probe. The energy of the infrared pulse could reach 1.1 mJ, and the energy of the visible pulse could reach 275 µJ. The maximum repetition rate of laser pulses is 4 kHz. An infrared laser pulse was tightly focused by an objective with a numerical aperture NA = 0.45 and a focal length of 2.5 cm into a cell with a supercritical fluid. Laser pulse generates plasma (optical breakdown) inside the medium, with a lifetime of about 100 ps. Laser-induced plasma in a medium is a source of high pressure (up to 1 TPa) and temperature (10000 K). Such high pressures and temperatures lead to the generation of shock waves on time scales of several nanoseconds and the formation of cavitation bubbles (on a sub-µs timescale [24]). The pressure at the front of the shock wave can be estimated from the changes in its speed during propagation in the substance. The experiments with CO2 were carried out in a specially designed high-pressure cell. The cell has 8 quartz windows with a thickness of 1 cm. The pressure can reach 250 bar, which makes it possible to investigate supercritical carbon dioxide. The cell is heated by two band heaters; temperature control is carried out using a thermocouple inserted into the cell. The pressure is controlled with 0.1 bar increment and the temperature with 0.1 Kelvin increments. The experiments with water were also carried out in the cell, however the pressure was atmospheric.
For time-resolved diagnostics, shadow photography and Raman spectroscopy technique were used. Shadow photographs were obtained by a CCD Mind Vision camera (30 fps); uniform illumination in the area was achieved after a probe pulse passed through a diffusion plate. Transferring the image to the matrix was carried out using the same objective to focus the infrared laser pulse; in this case, a spatial resolution is about 1.5 micrometer per pixel. The evolution of shock waves and cavitation bubbles can be observed by varying the time delay between the pump and probe impulses. A dichroic mirror was added to the scheme for Raman spectroscopy, which reflects radiation at 527 nm and transparent to the Raman signal . In this case, a laser pulse at a wavelength of 527 nanometers was transmitted collinearly with an infrared laser pulse. At the same time, a focusing objective was used to collect a signal to the fiber input of the Ocean Insight QE-Pro spectrometer.
In both techniques the probe pulse acts as a strobe. In other words, the effective signal (Raman or the shadow image) is collected only on timescales of the probe pulse (<10 ns). This timescale is much smaller than the minimal exposure time of camera (5 ms) and spectrometer (1 ms). The most part of the acquisition only background is collected. Because the time delay between pump and probe pulse is strictly determined by the hardware (delay generator on Fig. 1), the timing characteristics of spectrometer and camera are unimportant. The jitter and time resolution are fully determined by the delay generator. The background signal (plasma and natural illumination) was obtained without pump pulse and further was subtracted from the data. For shadow photography the frequency of the laser was set to 10 Hz, and the exposure time of the camera equals to 100 ms. In this regime the shock wave or/and cavitation bubble is guaranteed to be present on the shadow photograph (asynchronous synchronization). The analogous approach was applied for spectral measurements. To increase the Raman signal the laser frequency was set to 1kHz and the spectrometer exposure time was 10 seconds. Thereby the signal was averaged over 10,000 laser pulses. The synchronization was achieved by software by instantaneous start of acquisition and the hardware change of time delay. It could lead to the error less than 1% (when the signal is collected for previous time delay). The long-pass (>540 nm) and a bandstop (532 nm) were used to cut the laser radiation. The plasma luminescence was additionally subtracted from the obtained spectra. Time resolution is achieved by varying the delay between the pump and probe laser pulses. The entire system is controlled using specially developed software on LabVIEW. It provides control of the repetition rate of laser pulses, variation of the delay between pump and probe laser pulses with a step of 250 ps, recording an image from a camera, saving data by a spectrometer, and synchronization with the rest of the system. The experiment was fully automated, allowing the complete evolution of the system to be recorded.
To investigate CO2 in the non-equilibrium supercritical state, we used sub-critical liquid CO2 (80 bar, 300 K). The critical point of CO2 is 304.13 K and 72.8 bar. Thereby it is enough to heat liquid CO2 by 4 degrees to reach a supercritical state. We also used distilled water (critical point 217.8 bar, 647.1 K) as a well-characterized sample, which critical point lies far away from the conditions (1 bar 300 K) to investigate post-effects of optical breakdown in the vicinity of the critical point.
3. Pressure and temperature retrieving methodology
3.1 Retrieving of shock wave pressure
For most substances, the pressure is uniquely determined by the shock wave velocity. The shock adiabat relates the speed of particles and the speed of the shock wavefront; for example, for water, it is written as follows [24]:
where, us is the shock wave velocity, u(r,t) is the particle velocity, c0 is sound speed, c1, and c2 are empirical constants c1=5190 m/s и c2 = 25306 m/s. The parameters on the shock wavefront are related by the following equations [24]: where ρ and ρ0 are the density at the shock wave front and unperturbed fluid, respectively, p is the pressure at the shock front, and p∞ is the hydrostatic pressure. Thereby the Eq(1) can be rewritten:For carbon dioxide, a strong dependence of the shock adiabat parameters on pressure and temperature is observed. In this work, to estimate the pressure, we used Eq. (3), and the particle velocity was calculated by the formula [30]:
where α=2.61 km/s*cm3/g, s=1.39, c0=1.33 km/s. (for CO2 up to 500 bar pressures)3.2 Retrieving of temperature
Determining the non-stationary temperature is a much more complex task, and only an estimate is possible. The applied method is based on the fact that a temperature change significantly affects the vibrational-rotational spectrum [31]. Taking into account that some of the vibrations are Raman-active, their spectrum can be recorded experimentally. Unfortunately, there is no simple relationship between the Raman spectrum, temperature, and pressure. One of the possible ways is to measure the Raman spectrum under stationary conditions; the second is to use numerical simulation. The first method is more accurate; however, the second allows one to obtain spectra in a broader range of temperatures and pressures. We used molecular dynamics (MD) to simulate the spectrum of carbon dioxide and water.
For modeling in this work, we used the LAMMPS software package [32]. Modeling was performed for about 100,000 atoms; interatomic interaction was specified by the reax-ff [33] potential for carbon dioxide and TIP4P [34] for water. This number of particles is enough to retrieve the Raman spectra for water and CO2 for 1 bar 300 K with acceptable accuracy, thereby for higher pressures and temperatures. The applied potential are acceptable for pressures up to dozens of GPa and temperatures up to 1000 K for CO2 [35,36] and water [37,38]. It is also important to mention, that the critical point is adequatly retrieved from the simulations [36]. At the first stage, the system was brought into thermodynamic equilibrium (the criterion was the invariability of the internal energy and enthalpy of the system in 100,000 steps). To do this, we consistently simulated a microcanonical ensemble with a Langevin thermostat [39] and a Berendsen barostat [40] (fix nve + fix Langevin + fix pressure / bredson) with a step of 1 fs. To initially achieve termodynamic equilibrium for a given temperature and atmospheric pressure, 100 million steps were taken. After that, the velocity autocorrelation function was calculated. The Fourier transform of the autocorrelation function provides the vibrational-rotational spectrum of the substance.
4. Pressure retrieving procedure
Shadow photographs (Fig. 2) of the laser-induced post-effects in carbon dioxide at minor (less than 10 µs) time delays show a picture typical of optical breakdown in liquid (for example, in water). Namely, the plasma (white area in the center) is surrounded by a dark cavitation bubble and moves away from the plasma formation area by a shock wave. The radius of the shock wave can be easily measured from shadow photographs (resolution about 1.5 µm/pixel). From the shock wave radius dependence on time, it is possible to retrieve the shock wave's velocity (as a derivative) and hence the pressure at the front of the shock wave. The initial pressure can be retrieved by considering the exponential decay of the shock wave velocity over time and using Eq. (4) for water and Eq. (3),(5) for CO2. The entire procedure of pressure retrieving in water was previously described in different publications [12,41,42]. An example of the dependence of the diameter of a shock wave with time and its approximation is shown in Fig. 2. It demonstrates the evolution of the shock wave diameter on time for liquid CO2. We do not show the shadogramms for water because they can be found elsewhere in our previous publications [42,41]. For the laser pulse energy of 800µJ (1053 nm, 6 ns), the initial pressure achieved in the experiments is 500 MPa in water and 78 MPa in liquid CO2 (80 bar, 300 K). Such a significant pressure difference is primarily because water can be considered as an incompressible liquid. Secondary, there is a huge (about 5 times) difference in sound velocity in these fluids (the shock wave pressure depends on the sound speed). The errors of this technique are less than 10% depends from measurements of the shock wave radius.
Fig. 2. (a) - (d) Shadow photographs of laser-induced shock waves in carbon dioxide (297 K, 80 bar). Time delays are shown in the figure. (e) Dependence of the shock wave radius on the delay between the pump and probe pulses.
As it is well known, in water, laser-induced cavitation bubbles, after reaching their maximal radii, start to collapse [24], this process could repeat several times. In contrast to the evolution of cavitation bubbles in water, in CO2, a cavitation bubble, after reaching its maximum size, becomes surrounded by an outer layer. The outer layer has a smaller change in the refractive index compared to the cavitation bubble. In [43], during Ni ablation by ultrashort laser pulses in scCO2, this layer was characterized as a supercritical fluid. In our case, due to the lack of an ablative layer, more complex processes are obtained. At time delays of more than 40 µs, instead of collapse, the cavitation bubble breaks up into many (more than 10) local regions with sizes (10–100 µm). The configuration of these areas differs from an impulse to impulse, and their distribution is stochastic. An example of the distribution of these formations is shown in Fig. 3. Such formations (clusters) could be a result of temeprature heterogeneities. Due to the small difference between critical point and temperature of CO2, the small changes (about 1–30 K) that could be obtained in the matter after laser impact [28] would lead to the appearance of regions with the local supercritical state, which has different density and thereby different refractive index. The characteristic times of a cluster structure formation are about 10–25 µs. The obtained picture is similar to the supercritical opalescence. The light transmission through the region is supressed to the extreme light scaterring on clusters with various size: from 1 µm(or even smalle) to 200 µm. The time duration of the effect is about 200 µs; during this time, the temperature becomes lower than the critical one.
Fig. 3. Shadow photographs of laser-induced cavitation bubbles in carbon dioxide (300 K, 80 bar). Time delays are shown in the figure.
5. Raman spectroscopy
In contrast to pressure, the temperature of the medium is much more difficult to estimate, especially when it is rapidly (on an ns timescale) changes. To estimate temperature under ns laser impact, we used time-resolved Raman spectroscopy. However, it does not solve the inverse problem (temperature recovery from the obtained spectra); it just allows using MD to retrieve Raman for specified parameters (pressure and temperature). However, it is possible to estimate the achieved in the experiments temperatures in the order of magnitude in such an approach. The Raman signal is proportional to the excitation laser power (and thereby to laser intensity). Therefore, the Raman signal was primarily obtained from the focal spot, where laser plasma was generated due to tight focus.
We compared the experimentally obtained spectra calculated from MD for liquid carbon dioxide (300 K, 80 bar) and water (300 K and 1 bar). Figure 4 demonstrates the excellent coincidence between the spectra. At room temperature (298 K) in water (atmospheric pressure) and liquid carbon dioxide (80 bar, 300 K), the Raman spectra contain two peaks (see Fig. 4 and Fig. 5). In water, this is caused by hydrogen bonds and supermolecular structure [44], and Fermi dyad in carbon dioxide. In a transition to the supercritical state, the spectrum of carbon dioxide does not undergo qualitative changes (see Fig. 5). Therefore, it is difficult to estimate the temperature in such a case; however, pressure increases the Raman line growth's width and could be used as an indicator (Fig. 4(c)).
Fig. 4. (a) Experimental and MD-reconstructed Raman spectra of carbon dioxide. (b) Evolution of the CO2 Raman with pressure at a temperature of 320 K. S is the spectral brightness, λ is the Raman shift (c) Evolution of the Raman spectrum width with a change in pressure (MD). δw is the width (FWHM) of the Raman line.
Fig. 5. (a) Experimental and MD-reconstructed Raman spectra of liquid water at atmospheric pressure and room temperature. (b) Modification of the Raman spectra of water with temperature increase. S is the spectral brightness, λ is the Raman shift (с) Evolution of the Raman spectrum width while varying the delay between the probe and power pulses, laser pulse energy 800nJ, w is the width (FWHM) of the Raman line.
In contrast, in water, due to the destruction of hydrogen bonds in the supercritical state, the Raman spectra demonstrate the disappearance of the first peak. The shift position of the maximum in the spectra is significant (more than 10 cm−1) in water, while in carbon dioxide, the maximum position remains practically unchanged (shift less than 1 cm−1). Therefore, it is necessary to monitor the Raman spectra modifications (for example, the Raman line width).
In the stationary case, the transition to the supercritical state is accompanied by a broadening of spectral lines. The maximum broadening in carbon dioxide is achieved at 82 bar, which corresponds to the Widom delta conditions (Fig. 4) [45]. The broadening is caused by the formation of large linear clusters [45], where molecules of CO2 are close-packed. The thermodynamic equilibrium is achieved in each cluster, controversary to the liquid or gaseous CO2, where the all media is in a state of thermodynamic equilibrium. Outside the Widom delta (for 320 K it is achieved for pressures higher than 85 bar) the number of clusters is decreased, and the structure of matter becomes closer to liquids. Such state of matter is called liquid-like supercritical fluid [46]. This leads to the decreasing of the line width. It is worth mentioning that the MD demonstrates the higher broadening of the spectral lines in comparison with the experiment. The difference indicates that in the numerical simulations the distribution of the kinetic energy is broader, i.e. the interaction of molecules is higher than in the experiment.
Performed time-resolved spectroscopy of water (pump pulse energy 800 µJ, duration 6 ns, wavelength 1053 nm; probe pulse energy 200 µJ, duration 6 ns, wavelength 527 nm) shows that a decrease in the Raman line spectral brightness in the region of 3000 cm−1 is observed up to 10 µs, while the spectral line at 3400 cm−1 broadens (broadening corresponds to temperatures of 700–900 K), after which a process of narrowing the width of spectral lines is observed. The maxiamal narrowing is observed for the maximal diameter of the cavitation bubble observed in the experiment. We assume that at this moment the amount of matter in a new phase is maximal, thereby it leads to the maximal change of the Raman signal (it is proportional to the number of particles), see Fig. 5(c). The modification of the water Raman spectrum corresponds to the alteration in the microstructure of water; specifically, the hydrogen network is destroyed in the superctical water [43], leading to the decrease of spectral brightness of the 3100cm−1 line, as it is showed in Fig. 5(c). In a contrast the 3400 cm−1 line broadens in a mirrored way. The effect is identical to CO2. The formation of clusters in the laser-induced supercritical state leads to the broadening of the spectral lines. Nevertheless, the dependence of this spectral component is more promising for monitoring of supercritical water than the 3400 cm−1 line. Thus, because the shadow photograph estimates pressures of the order of 3 GPa for such energies, it can be argued that a local transition to the supercritical state of matter is observed.
6. Conclusion
We proposed a complex all-optical method based on shadow photography and time-resolved Raman spectroscopy and an experimental setup that allows us to diagnose the non-equlibrium extreme supercritical state of matter with a resolution of 0.25 ns. This method is applied to retrieve the evolution of molecular fluids under nanosecond laser impact (t∼6 ns, F∼1000 J/cm2). Moreover, the pressure value is obtained from shadow photography with high (about ten percent) accuracy, and temperature is roughly (with an accuracy of about 100 K for water) estimated by comparing the measured Raman spectra with the numerical simulation result. We showed that temperatures and pressures above critical are reached in the medium within a few microseconds after the optical breakdown. Pressure achieve 500 MPa in water and 78 MPa in liquid CO2; temperatures in water can reach 600–700 K in water. The shadow photographs of carbon dioxide under laser impact demonstrate properties specific to supercritical fluids (high-density fluctuations, the presence of 1–100 µm regions with different properties) caused by a local heat (about 10–50 K). That, in total, makes it possible to assert the laser-controlled transition to the supercritical state.
The proposed approach is convenient to molecular fluids (due to Raman spectroscopy) or fluids whose critical point is close to the room conditions (in terms of retrieving temperature). The laser impact is not limited by nanosecond pulses and can be applied for shorter laser pulses. Moreover, the approach can be used for retrieving pressure and properties during laser ablation in SCF, laser-induced forward transport (LIFT), and laser-induced backside wet etching (LIBWE), which can lead to a better understanding of these physical and chemical processes.
Funding
Russian Foundation for Basic Research (18-29-06035, 18-29-06056, 19-32-60072); Ministry of Science and Higher Education of the Russian Federation (0022-2021-0019).
Disclosures
The authors declare that there are no conflicts of interest related to this article
Data availability
Data underlying the results presented in this paper are not publicly available but may be obtained from the authors upon reasonable request.
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