ACS AuthorChoice. Article Views Altmetric -. Citations 6. Abstract High Resolution Image. The liquid—ice phase transition of water plays a major role in many processes on our globe.
Important examples include glacier melting on earth and heterogeneous ice nucleation on atmospheric aerosols which have been linked to the formation, microphysics, and optical properties of clouds.
Understanding the details of this phase transformation is essential for a manifold of not only atmospheric but also environmental and food science-related disciplines. The transformation of water to ice is generally triggered by nucleation at the surface of particles, and as such, understanding the liquid—solid transformation of water in contact with the surface of relevant materials is of great interest to several disciplines.
Owing to its surface specificity and its sensitivity to the molecular organization of water molecules at buried interfaces, sum-frequency generation SFG spectroscopy has recently been intensely used to study water freezing at solid surfaces.
As this is a second-order nonlinear optical method, the signal is forbidden in centrosymmetric media like bulk water and proton-disordered hexagonal ice, the most common form of ice in the biosphere under standard atmospheric conditions.
However, at the interface, the symmetry is broken, making the interface SFG-active. If, moreover, the IR beam is in resonance with a molecular vibration, the signal is enhanced. In this way, the vibrational spectrum of the interfacial water molecules could be obtained during heterogeneous ice nucleation.
The technique relies on the OH stretch vibration of water changing substantially upon crystallization of water. With this method, Anim-Danso et al. They attributed the transient signal to events taking place near the surface during the ice formation and ice melting. More recently, Lovering et al. The transient signal was attributed to the existence of a transient phase of stacking-disordered ice during the freezing process at water—mineral interfaces.
Both SFG studies showed a transient increase in the signal, albeit with different temporal characteristics several minutes for a neutral water—silica interface 3 and a few tens of seconds for a pH 9. Such a transient signal with a lifetime around 1 min has also been observed in a recent study on immersion freezing next to a mica surface using second harmonic generation spectroscopy.
In agreement with the literature, 1,3,8 we confirm the existence of a transient signal at pH 7 and pH 9 and extend the study to low pH. However, the freezing temperatures we observed in our work are substantially lower compared to those observed by Anim-Danso et al. Here, we ensure that we study specifically heterogeneous freezing at the sapphire—water interface by isolating a water drop using silicon oil. Experimental Section. A detailed description of the experimental setup to perform SFG experiments while freezing a droplet can be found in Abdelmonem et al.
Femtosecond IR and spectrally narrowed VIS pulses are mixed at a sapphire prism—water or prism—ice interface in a copropagating, total internal reflection geometry from the prism side to generate the SFG light. The reflected SFG light is spectrally dispersed by a monochromator and detected by an electron-multiplied charge-coupled device Andor Technologies.
A detailed description and drawing of the assembly of the measuring Teflon cell can be found in ref 8. At each integer of degree, the temperature is held constant for 1. The acquisition time per spectrum is 30 s. The freezing point is defined as the point when a visual inspection using a camera reveals that the droplet is frozen.
The different experiments were repeated 3—5 times. The spectra presented here are corrected for the frequency-dependent IR Fresnel factor, calculated following ref 9. Unfortunately, the complex refractive indices, which are required to evaluate the IR Fresnel coefficients, of ice and liquid water have been reported in the literature only for specific temperatures.
The refractive index of sapphire is calculated from the Sellmeier equation. After Fresnel correction, the spectra are directly proportional to the surface nonlinear susceptibility tensor for SSP polarization. More details about the data analysis and Fresnel factor corrections can be found in the Supporting Information of Abdelmonem et al. Results and Discussion. The non-Fresnel-corrected spectra are plotted in Figure S1. Upon decreasing the temperature from room temperature to the freezing point, the SFG spectra are more or less constant.
The results for the systems mentioned above have been reported in Abdelmonem et al. High Resolution Image. Figure 1 a—d shows spectra at room temperature solid red lines and around the liquid—ice transition dashed red for liquid and blue lines for ice for pH 3, pH 7, pH 9 NaOH , and pH 9 NH 4 OH , respectively.
For all samples, the liquid water signal underwent a gradual change at the surface from room temperature to right above the freezing point and to then change dramatically upon freezing. At low pH, a substantial decrease in the signal upon freezing is followed by a further slower decrease. For pH 7 and 9, the signal around cm —1 increases substantially upon crystallization, especially for pH 9 NH 4 OH.
To illustrate the dynamics of the freezing process, we plot in Figure 2 the SFG intensity at a fixed wavenumber, cm —1 , for the four pH solutions, as a function of time as done by Anim-Danso et al.
The freezing point can be clearly recognized by the sudden change increase or decrease in the SFG intensity around time zero. After freezing, the intensity is also constant upon further cooling down.
For pH 3, the SFG intensity at cm —1 is lower after the freezing event, whereas for the other cases, the signal for the ice state is higher than that for the liquid state.
Moreover, around the phase transition from liquid to solid, the spectral intensity at cm —1 is transiently higher for pH 9 NaOH and pH 7. For pH 9 NH 4 OH , we observe that the spectral intensity at cm —1 is growing in the first minutes after freezing before it reaches a stable value. This means that we observe a transient lower signal than that observed for the ice state.
The results are in qualitative agreement with the results of Lovering et al. The lower intensity can be attributed to a difference in time resolution: our full spectra are acquired in 2 min intervals, whereas Lovering et al. As we observe a transient signal for pH 9 with NaOH and pH 7 in the absence of ions, the presence of ions cannot be the cause of the transient signal, although it may affect the dynamics.
To characterize the temperature-dependent spectra quantitatively, we fit all data using a sum of a nonresonant contribution and three Lorentzian lineshapes—see eq 1.
Following ref 5 , we fit the spectra using three peaks around , , and cm —1 , which have been assigned to, respectively, strongly and weakly hydrogen-bonded interfacial water and surface hydroxyl Al 2 OH groups. For simplicity, the peaks are labeled , , and cm —1. To investigate the temporal changes in the signal, we fit the spectra at all different temperatures. Although describing the spectra by three resonances is clearly an approximation [e.
The center frequencies and linewidths of the resonances were kept constant for each phase liquid and ice in the fit procedure.
Moreover, the nonresonant amplitude and phase are kept at 4 and 5, respectively, for all samples in both the liquid and ice phase. Table 1. Central Frequency in cm —1 of Each Band for all Solutions a. Figure 3 shows the area i.
Figure 3 shows that all band amplitudes are constant for the liquid phase up to the freezing point, at which point a sudden drop or increase is observed and to then stabilize again at a different level for ice.
Comparing the time dependence of the peak amplitudes with the measured SFG intensities at cm —1 Figure 2 , we see notably different transient shapes. The anomalous behavior observed for the SFG intensity shown in Figure 2 , for example, a temporary overshoot of the SFG intensity especially for pH 9 NaOH , is not apparent from the time-dependent amplitudes A q of the modes shown in Figure 3.
Figure 3. Absolute peak amplitude of individual bands for all solutions. It is therefore apparent that the transient signals observed in Figure 2 b,c can be well accounted for by a smooth transition between two states water and ice , without the need for invoking a transient species. The transient intensity signals in Figure 2 can be accounted for by a subtle interference between different peak parameters, changing at slightly different rates, which have a combined effect on the overall intensity see eq 1.
To exclude that the results are depending on the fitting routine, we performed fit procedures with different constraints. The results are plotted in Figure S3. In the first additional fitting routine, the nonresonant amplitude and phase were not globally constraint but still constant within a certain phase liquid—ice like the frequencies and linewidths of the resonances.
The maximum density response where the orbits crowd producing a density enhancement quantifies the orbital support to a given spiral perturbation through periodic orbits. We computed the stellar periodic orbits in order to explore the orbital support to the imposed PERLAS spiral arm potential open squares in the left-hand panels of Fig. This method assumes that stars in circular orbits in an axisymmetric potential, with the same sense of rotation of the spiral arms, are trapped around the corresponding periodic orbit in the presence of the spiral arms.
For this purpose, we calculated a set of central periodic orbits between 50 and 60 and found the density response along them using the conservation of the mass flux between any two successive periodic orbits.
With this information we seek the position of the maximum density response along each periodic orbit filled squares in the left-hand panels of Fig. The method implicitly considers a small dispersion with respect to the central periodic orbit since it studies a region where the flux is conserved.
On the other hand, this dispersion is based on parameters for the galaxies where dynamics is quite ordered, orbits follow their periodic orbit closely, in such a way that we consider this study a good approximation. With this in mind, a model in Fig. Panels on the left-hand column show the stable periodic stellar orbits black solid lines , the response density maxima filled squares , and the imposed spiral arm locus open squares , flanked by two dotted lines that represent the spiral arm width.
Panels on the right-hand column show the gas density distribution after 1. After that, the stellar response forms a slightly smaller pitch angle than the imposed spiral. In the MHD simulation, the gaseous disc responds to the two-arm potential with the now familiar four spiral-armed structure, where the pitch angle of the stronger pair of arms corresponds to that of the imposed pitch angle potential, while the other pair of gaseous arms has a systematically smaller pitch angle, corresponding closely to the regions of periodic orbits crowding.
After that, the stellar response forms a slightly smaller pitch angle than the imposed spiral, while the gas responds with four spiral arms, but the second pair is very weak but with a significantly smaller pitch angle than the imposed spiral arm potential.
The gaseous disc responds with well-defined four spiral arms that extend up to the corotation radius. Note that in this last simulation, there is not much that can be said about the stellar or gaseous orbital support since periodic orbits tend to disappear due to the strong forcing of the imposed spiral arms, meaning that spiral arms would rather be transient by construction in this case and the MHD gaseous disc behaviour is difficult to predict from periodic orbit computations.
However, such as the stellar arms constructed in this case, the gaseous spiral would be transient in likely even shorter time-scales than in the case where periodic orbits exist but settle down systematically in smaller pitch angles than the original imposed spiral arms in the region where periodic orbits do exist.
Note that, in general, the arms that should eventually disappear in this scenario, are the stronger stellar imposed spiral arms see second row of Fig. Therefore, the stellar response density maxima represent the regions of the arms where stars would crowd for long time-scales, this is, where the existence of stable, long-lasting spiral arms would be more likely. On the other hand, if the stellar density response forms a spiral arm with a different pitch than the imposed angle, then the imposed spiral arms triggered on the disc by a bar, an interaction, etc.
These values and the knowledge of the galactic type could provide some information about their nature, i. The formation of four spiral arms in the gas response is, in this scenario, another piece of evidence of a transient nature of the spiral arms in the Milky Way galaxy, as we claim it is the secondary pair of arms in Fig.
In this outline, the gas responds forming a second pair of arms aligned with the locus of the orbital crowding. This lighter structures would likely be preferentially formed by young stars and gas than by evolved stars because of their transient nature, i. Finally, in this framework, the presence of clear and strong branches in spiral galaxies, with smaller pitch angles than the corresponding couple of massive spiral arms on a galaxy, would be a signature of the transient nature of the spiral arms in a given galaxy.
On the other hand, spiral galaxies without evidence of branches could indicate the presence of a longer lasting spiral arm structure. With the use of a detailed three-dimensional, density-distribution based potential for the spiral arms, combined with MHD simulations on a Milky Way-like galactic disc, we have studied the stellar orbital and gaseous response to the galactic potential.
As a first experiment, we constructed a simple cosine potential as the ones commonly employed in literature that reproduced approximately what the density based potential PERLAS exerts on the stellar and gaseous dynamics. The first set of simulations compare the gas response when the disc is perturbed by both spiral arm potential models.
Additionally, we constructed stellar periodic orbits and calculate the stellar response density maxima. With these exercises, we found that only in the case of the PERLAS model the gas and stellar density response based on the existence of periodic orbits is a consistent four-armed spiral structure: a couple of strong gaseous arms located at the position of the imposed stellar arms, and a second pair of weaker gaseous arms located at the position of the stellar orbit crowding.
Since the potential and the stellar density response do not coincide, the spiral arms are prone to destruction. So, the presence of the second gaseous pair is interpreted as a sign of this transiency.
We performed a study of the gas response to two galactic potentials: the density distribution based model PERLAS and the widely employed in the literature cosine potential.
We verified that the gas response a two-armed structure is the same for both models close to the linear regime only, i. In the general case, however i. In the case of the cosine potential, the gas responds invariably forming two spiral arms while, with the PERLAS model, the gas responds with four gaseous spiral arms in the general strong arm case. We increased the strength of the spiral arms represented by the cosine potential up to a point the arms were equivalent and even beyond the mass of a strong bar as an experiment to try to reproduce the gas response provided by the PERLAS model.
However, the answer was always a bisymmetric structure. We conclude that the spiral arm strength is not responsible for the four-arm gas response, but rather it is the product of the forcing generated by the whole density distribution better represented by the PERLAS model that, in turn, forces the periodic orbit response to shift its crowding regions inside the imposed locus of the massive spiral arms.
Using the PERLAS model, we changed the structural parameters of the spiral arms according to the observational and theoretical uncertainties in the determination of the Milky Way's spiral arms in the literature. Applying this scenario to the Milky Way, for the stronger spiral arm values reported in literature i.
Although in this work we applied the models to Milky Way-like galactic discs, it is worth noticing that the results are general. We thank Edmundo Moreno for enlightening discussions that helped to improve this work. Allen C. Amaral L. Lepine J. MNRAS Antoja T. Valenzuela O.
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