Melting Dynamics of Ice in the Mesoscopic Regime

Downloaded by guest on September 25, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1620039114 regime a mesoscopic the Citroni in Margherita ice of dynamics Melting efre ntebl,oecmn h oiac fheteroge- (12). defects of preexisting dominance or surfaces the can by overcoming induced nuclei nucleation, bulk, transition neous the and within, in that from formed wavelength heated be is a sample at (T the light absorb ing” infrared can be of sample can pulse the sample a the by Experimentally, heated tran- surfaces. rapidly and the defects the energy, of and transformation, role nucleus interfacial the during critical solid/melt achieved structures a the local sient form transitions, to the minimum needed the for determine atoms/molecules to of has trying number nucleation in and addressed, revealed (7–11), especially have mechanism been Simulations growth systems. and test nucleation temperature the a been melting have the ice water above heated rapidly (T be submicrometric-sized the can or simu- explain both micrometric- crystals to In experiments, attempt onset. and the transition lations the in a of nanometers, on mechanisms few fundamental changes of structural scale observing length timescale, picosecond the in structure local the of phase. of liquid achievement disruption the the of the and requiring order transitions, crystalline the phase of pressures hindered extreme least to up boundaries (P phase-transition compression, which dynamic struc- exper- by of under art kinetics particularly the intrinsic of transformations, the state tural understand with to made fact, techniques In being imental transition. presently phase is other any effort process for great the as of elucidated, timescales well not characteristic are the and mecha- melting molecular of The nisms encountered. are where boundaries conditions, phase through many temperature going and pressure intersellar, different extrater- and extremely in well planetary as environments, present are restrial Ices drinks. our of preparation the M cell anvil simple scattering from Mie expected than larger magnitude nanoseconds, dynamics. of domains, H-bond of orders liquid hundreds time the takes of a micrometers, growth of for The distances needed reequilibrate. over time to the of scat- sample all Mie the for by resolution, monitored nanosecond is with thereafter tering interfaces evo- The melt/ice melting. which of complete for lution pulse, necessary infrared energy the picosecond of I all a delivers ice by of bulk heated A melting homogeneously regime. the is mesoscopic entire investigating the extremes, in two ice the fill these we time Here, between environment. and gap the surfaces with contact at thermal occurring by limited processes time for macroscopic longer account hand, or millisecond resolution, other with transitions, the to phase On unable of and but observations dynamics. process nanometers following the of of the tens onset unveil the of determine sizes to suitable sample thus with subnanosec- nuclei window sev- a melt covering by time works, addressed for ond experimental been take and have it 2016) theoretical 6, mechanisms does eral December melting long review for The How (received grow? 2017 melt? 2, to crystal May approved a and does DC, Washington, How University, Washington George The Hemley, J. Russell by and Edited Italy; Florence, 50125 Ricerche, delle Nazionale Consiglio Ottica, di Italy; Florence, Sesto, ESErpa aoaoyfrNnLna pcrsoy 01 et,Foec,Italy; Florence, Sesto, 50019 Spectroscopy, Non-Linear for Laboratory LENS–European n eprtrs(T temperatures and ) h yaiso etn aebe tde pt h present the to up studied been have melting of dynamics The m ,it uehae tt hr etn cus easand Metals occurs. melting where state superheated a into ), lnt rmplrie ogair,t h onn rs and frost morning the to our glaciers, on to occurrences ices common polar most from the planet, of one is ice of elting | eprtr jump temperature c siuod hmc e opsiOgn ealc,CniloNzoaedleRcrh,509Sso lrne Italy; Florence, Sesto, 50019 Ricerche, delle Nazionale Consiglio Metallici, Organo Composti dei Chimica di Istituto a,b,1 aul Fanetti Samuele , a eacse 16.Mligi the is Melting (1–6). accessed be can ) up.Wt hs“ietlsrheat- laser “direct this With jump). | superheating a,c | ae heating laser am Falsini Naomi , h rieV sample VI ice or | e a iatmnod hmc,Uiest fPrga -62 eui,Italy Perugia, I-06123 Perugia, of University Chimica, di Dipartimento al Foggi Paolo , ftepoes swl eson the shown, time be will characteristic As the process. melting the accessing of of micrometers, propagation of the the the distances and restore over observe interfaces We completely ice/melt resolution. at to mil- scattering nanosecond needed of with tens time conditions, of the window initial time is a which access We liseconds, (50 sampling: thickness time sample the bulk and the are experiment I this ice of liarities of successive samples the bulk and on melting the refreezing explore to scattering Mie resolved oln 1) rtert n oooyo c n yrt forma- hydrate and 20). ice (19, of compression upon topology dynamic events and under rate tion nucleation premelting the ice or investigate (17), (18), cooling crystals to colloidal per- resolution in the been structures millisecond On have with world. investigations macroscopic formed photographic the side, in experiences macroscopic the to connects consis- delivered. observed, energy still of was amount melting the with incomplete tent an ps 250 At (16). 1073/pnas.1620039114/-/DCSupplemental at online information supporting contains article This Submission. 1 Direct PNAS a is article This paper. interest. the of wrote conflict R.B. no and declare M.C. authors and The data; analyzed N.F. and S.F., M.C., research; formed are crystal realms. bulk the macroscopic connecting the a regime, and mesoscopic in microscopic entire propagation the over melting explored evolu- of thus melting kinetics of The timescale the tion. over quasi-static are experiment (τ pulse the after ps to 150 authors first the the by in attributed occur changes mostly spectral melting the 1.6 Here, ps. of 250 thickness of ultrafast sample an a after with melting 16), com- ice melting Water of picoseconds. signatures T few main sample a a the in with where plete diffraction nm, electron 20 by of (15) thickness alu- gold in and monitored structural been (14) The have minum pulse crystals. heating the molecular following non–H-bonded changes in slower This be modes. takes lattice the process over thermalization relaxation absorbed vibrational the the of via redistribution energy the by increases temperature The uhrcnrbtos ...... n ..dsge eerh .. .. n ..per- N.F. and S.F., M.C., research; designed R.B. and P.F., S.F., M.C., contributions: Author owo orsodnesol eadesd mi:[email protected]fi.it. Email: addressed. be should correspondence whom To fnnscnsadi reso antd lwrta vibra- than slower dynamics. magnitude tional of orders of hundreds is takes and growth micrometers nanoseconds The of of distances temperature. over melting domains heated its liquid homogenously above is within, lattice com- from for the needed therefore, energy the melting; of plete all infra- delivers picosecond pulse a The of pulse. solid/liquid red absorption of the the evolution by generated of the interfaces sizes crystal, archety- the molecular the and H-bonded ice timescales in pal observe the the we for Here, from involved. date heterogeneities to process, structure, known liquid bulk melting not a is of the achievement the to of onset nucleation unfolding complete The Significance ee eueapicosecond a use we Here, barely scale picosecond–nanometer this at knowledge The uphsbe tde ytm-eovdifae pcr (13, spectra infrared time-resolved by studied been has jump b iatmnod hmc g cif nvriyo lrne 50019 Florence, of University Schiff, Ugo Chimica di Dipartimento a,d,e n oet Bini Roberto and , PNAS | ue6 2017 6, June 0p nwtrie(3 n can and (13) ice water in ps ∼20 . a,b T h jm ehiu n time- and technique -jump | n vratm window time a over and µm P, n c I h anpecu- main The VI. ice and o.114 vol. www.pnas.org/lookup/suppl/doi:10. 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CHEMISTRY The experimental insight into the melting dynamics of ices with which we measure the transmission through the sample with has paramount relevance in understanding natural phenomena a fast Si photodiode (Fig. 1C). The focus of the probe (∼150 µm and is a fundamental benchmark for theories at any level of in diameter) lies inside the area irradiated by the pump. When a accuracy. Ices, ubiquitous in terrestrial and extraterrestrial envi- pump pulse is shot, the probe transmission drops to a minimum ronments, are characterized by hydrogen-bond networks that in tens or hundreds of nanoseconds, depending on the amount determine the great complexity of their physical and chemical of deposited energy, and then returns to a static value in a time behavior. The melting line of water borders at least five crys- (micro- to milliseconds) strongly dependent on T0. The trans- talline phases (Ih , III, V, VI, and VII) with different structures mission change is due to scattering at ice/melt interfaces, form- and H-bond arrangements. In this work we investigate the melt- ing with the T jump and evolving in time during melting (due ing dynamics in ice Ih and VI, accessed respectively by the use to superheating) and refreezing (due to the thermal contact with of low temperature and high static pressure, providing an unique the environment that decreases T to the thermal bath tempera- experimental study in the mesoscopic domain and opening the ture T0). When the transmitted beam is blocked (Fig. 1D), a pos- way to investigations in different P and T conditions. itive signal due to off-axis scattered light is consistently observed, with a similar time dependence to that of the transmission change. Results In both configurations the signal amplitude increases as λprobe Temperature Jump and Transient Transmission Loss. Ice Ih and ice decreases, as expected for scattering. As also expected, the trans- VI samples 50 µm thick, at fixed temperature (T0) and pres- mission change is not observed when liquid samples are heated sure (P0), are “instantaneously” heated by a 15-ps pulse of by the T -jump pulse, except at the highest E values (E ≥ 4.5 mJ) light at 1,930 nm (FWHM = 100 nm) (21) with a focus diame- where a strong oscillation of the transmission is observed, likely ter of 400 µm. Ice Ih at ambient pressure is held between flu- due to the formation of vapor bubbles. Otherwise, the trans- orite windows in a cryostat at a static temperature T0 ranging mission of the liquid always remains ∼5–10% higher than the between 254.2 K and 272.6 K. Ice VI is in a sapphire anvil cell, static transmission of ice, and only a weak (compared with that between sapphire anvils, at room temperature and P0 = 1.2 GPa observed in ice) transmission decrease, due to thermal lensing, or 1.4 GPa. The light is absorbed by the ice through excitation is observed (Transmission of the Liquid after the T Jump and Fig. of a vibrational combination band (ν1 + ν2, ν3 + ν2), as shown in S1). The absence of signal from the liquid confirms that the sig- Fig. 1A. The incident energy used (3–9 mJ/pulse) is well below nal observed in ice is not affected by unwanted contributions such the estimated ionization limit (9) and below the threshold of as interferences between pump and probe light on the photodi- absorption saturation. In fact, the measured absorbance of the ode or optical effects on the cell windows. Thermoreflectance (22, sample under irradiation with the pump is ∼0.55 at all energies 23) does not contribute to our signal because of the absence of used. This low absorbance guarantees that the sample is uni- highly reflecting interfaces, and its transient signal would, how- formly irradiated along the beam axis and can thus be uniformly ever, be concluded in ∼1 ns. The transmission loss due to scat- heated across its length. The pump causes an isochoric temper- tering at ice/water interfaces has been used to detect the freezing ature jump (T jump) up to ∼400 K after the pulse, depending of water into ice VII under multiple-shock experiments (6, 24), on the amount of delivered energy (Fig. 1B), and the formation using white light. Here, with monochromatic probes, we can esti- of a superheated crystal at T1 > Tm . This T jump is achieved mate the size and concentration of the scattering domains evolv- through redistribution of the vibrational energy through the lat- ing after the pulse. Several fresh samples were studied, to check tice modes (thermalization), completed in ∼20 ps, during which the reproducibility. Each sample was used for many shots, and melting already starts (13, 16). The estimated pressure change each shot probes a single melting/crystallization event in a crys- (1.3 MPa·K−1) (13) is 50 MPa during the pulse and rapidly tal with slightly different quality. The evolution is monitored for decreases due to melting itself in ice Ih (9). In this experiment, all of the time necessary to recover the initial conditions, and the the energy absorbed in a single pulse exceeds that needed to heat measurements are repeated at time intervals >2 s to allow com- the sample to Tm and to obtain its complete melting (E > 2 mJ plete recrystallization. for ice Ih and E > 3 mJ for ice VI; Physical Values Used in the Complete melting, indicated by an increase in transmission Calculations). to the liquid value, was seldom observed despite delivering an The probe is a monochromatic continuous-wave laser beam excess of energy to achieve the process. Only by using the (we used λprobe = 405 nm, 457.9 nm, 632.8 nm, and 1,064 nm), maximum energy values with 270 K < T0 < 273 K, or piling up

T-jump A liquid C 10 0.4 ice VI Intensity (a.u.) T-jump pulse 8 sample ice Ih 0.2 pinhole 6 Absorbance probe beam 4 pump pulse 0.0 photo- 1800 2000 2200 diode 2 B (nm) D photodiode signal (mV) 650 0

(K) 0 10203040

1 600 time (ms) 550 sample 500 beam 450 stopper 2 400 probe beam 350 0 signal (mV) 300 photo- photodiode 0 10203040 maximum temperature T diode time (ms) 2.02.53.03.54.04.5 absorbed energy E (mJ/pulse)

Fig. 1. Experiment outline. (A) FTIR spectra of liquid water (room conditions), ice Ih (263 K), and ice VI (1.2 GPa) superimposed to the emission spectrum of the pump. (B) Estimate of the initial temperature T1 just after the pulse, for an ice Ih sample at initial temperature T0 = 263 K. The upper and lower limits are ideal cases of no melting and complete melting, respectively, during the 15 ps of the pulse. (C and D) During the experiment the probe beam is collected in two possible configurations to detect the transmission plus the scattering at azimuthal angles 0 < θ < 1.5◦ (C) or the scattering at 2◦ < θ < 7◦ (D). Corresponding time-dependent signals are shown on the left for each configuration (acquired with E = 3.5 mJ, T0 = 269 K, λprobe = 633 nm).

5936 | www.pnas.org/cgi/doi/10.1073/pnas.1620039114 Citroni et al. Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 irn tal. et Citroni 0–2 range the I in ice curves same the of Zoom-in Rate Melting the on Conduction Thermal and of (Effect probed range I 2. Fig. the in ns 500–600 first the in relevant not is conduction mal for thus superheating, the by rate driven a kinetically having be to expect may we (∝ diffusion thermal external the determines on depends timescales two temperature these of magnitude temperature tive quasi-constant initial the at than timescale occurring longer a melting, in value occurs walls initial sample’s the the and reaches it until T environment, external the the pulse with the after that note temperature must sample’s we signal, the the understand To of 2A). evolution (Fig. time crystal the of reference transmission as initial using the absorbance, into Loss. transformed were Transmission curves sion Time-Dependent the of Analysis value. transmission T h ulaindnmc,weepoal h ags difference appear. would largest ices the two probably the between where dynamics, nucleation investigated the range time the In ices. two (t parti- the melt in the similar of very growth are the cles in and differences sug- the structures that measurements however, Our crystal gest, melting. different upon have changes scat- volume ices the different two of The repeatability signal. shot-to-shot tering the represent which bars, of independent of are function a as I performed ice by were constant For ments driven crystal. time growth, the This melt of ns. superheating of 5 the time characteristic to the ns represents constant 15,000 thus from time magnitude monoexponential of the orders 2C, rate. Fig. melting in the τ seen and be superheating can the As reducing latter at phenom- the melting competing tion, two above: the described of times ena characteristic both the on of depends result law curve exponential this the which the reproduces in in well range growth time The monoexponential ns. a 500–1,000 by initial fitted accurately are curves E s 1 srfrne (A, reference. as 0 jm usswt -t -zrt,ddw bev h liquid the observe we did rate, 5-Hz to 1- a with pulses -jump ≥ h ausof values The the of maximum first The > sw ilse h hra odcintruhtesample the through conduction thermal the see, will we As . erae xoetal with exponentially decreases h E i.S2 Fig. . Jteei eodmxmma ogrtms The times. longer at maximum second a is there mJ 3.5 different s sw ics ntenx eto,w aen cesto access no have we section, next the in discuss we as ns) 1 ≥ nlsso h xeietlcre tsotdly.(A, delays. short at curves experimental the of Analysis . Ja hr ekfloe yafs erae For decrease. fast a by followed peak sharp a as mJ 2.5 ). T T T 1 ∝ 0 0 .I particular, In 1B). (Fig. odtosaeicue.Teerrbr ersn h tnaddeviations. standard the represent bars error The included. are conditions e Lower τ n nteaon feeg absorbed energy of amount the on and T 1 ( r h aefrieI ice for same the are t T ) xml fepnnilfi pt h rtmaximum first the to up fit exponential of Example ) − T 0 T T for (t (t ABC m ) . ) E – erae,det h hra contact thermal the to due decreases, A(t T ≥ 0 . J ofimn httether- the that confirming mJ, 2.5 ) n h aeo etn,which melting, of rate the and ) sepce,adsasfive spans and expected, as E, uvs(i.2 (Fig. curves T ∼ .(C µs. T T T h h 1 0 1 hr aymeasure- many where , efidthat find we , n c Iwti error within VI ice and fet ohtert of rate the both affects n hra conduc- thermal and Average ) E and A and h transmis- The T T A 1 0 1 h rela- The . appears B) en the being , Upper and τ E 1 and which , τ 1 h rnmsincrei rnfre noasrac sn h ttctransmission static the using absorbance into transformed is curve transmission The ) aaeesrsligfo h t h ausaeaeae over averaged are values The fit. the from resulting parameters A T 0 1 A 1 usdaoe safnto ftm.Ti imtrmonotonically to diameter of This up estimate time. increases of an function gives a as curves diameter above) two cussed same scattering the the the between of ratio with all the spheres that approximately hypothesis are simplest the domains In time. of tion in signals the estimate of correctly ratio suspension. to perse the with configurations, light, able, two scattered are the we the diameter that scatterer’s of indicates the distribution result of angular estimate the an to yields due is which 1 Fig. of and (D pension to down sizes particle perfect For in theory. Mie-scattering are h the suspensions by expected calibration those with the depend agreement estimate on not to measured does in used values and shown be As particle thus suspension. can single monodisperse and the concentration of the property on scattered a unpolarized the is of or distribution light angular polarized angu- The (for the calculated. be light which can light) scattered from scatter- of particles, the distribution single of lar the elements for matrix cross-section the ing contains output The angles 1 lected. azimuthal (Fig. direction of forward range the the diameter the and medium, wave- particles, surrounding the and particles contains the also of input The (25). length scatterers suspensions spherical monodisperse for of Huffman and Bohren by cross-section reported scattering Mie the and C sample, the as of calculated thickness the was suspension the each of A of (Calibration absorbance) mm as 0.1 (reported or mm 10 Sensitivity quartz Detection path a in optical (C), concentrations with different cuvette and nm 400 and nm, 200 the suspensions with monodisperse SiO 1C, through of transmission Fig. the of measure configuration to the used we Molten ing, the of Size the of Particles. Determination and Setup our of Calibration Domains Molten of Evolution Size 3. m rnmsincre eemaue ntetocon- two the 1 in measured Fig. were of curves figurations transmission nm, 632.8 ( . . m(wc hto u ape)testpi estv to sensitive is setup the samples) our of that (twice mm 0.1 = sca bobnecre banduigdfeetpm nris (B, energies. pump different using obtained curves Absorbance B) o c I ice For = h scmue sn OTA oebsdo h program the on based code FORTRAN a using computed is C 0m)w esrdtesga nbt configurations both in signal the measured we mm) 10 = 2 sca λ aoatce nwtrwt diameters with water in nanoparticles probe C oass u xeietlsniiiyt i scatter- Mie to sensitivity experimental our assess To ∗ and 0 nm, 400 = h C ftepoelgt h ope ercieindexes refractive complex the light, probe the of at ∗ D ∼1.5 h ihtepm f.Tertoo h w signals, two the of ratio The off. pump the with T where , 0 and 6 ,using K, 269 = PNAS n23m n hndcess(i.3). (Fig. decreases then and ms 2.3 in µm C C D 0.01273 = .Teepce rnmsinloss transmission expected The S3). Fig. and 0 mif nm 200 = C | ue6 2017 6, June stepril’ concentration, particle’s the is D C after and µm twihtelgti col- is light the which at D) C T E −3 jm ussa func- a as pulses -jump ≥ . Jand mJ 3.5 = | h absorbance the S3, Fig. with , o.114 vol. 1 µm D D D λ θ ≥ −3 0n,8 nm, 80 nm, 20 = probe 0 m This nm. 409 = ihrsetto respect with o monodis- a for 0ple,adfor and pulses, 10 | o n sus- one For . o 23 no. T 3. nm 632.8 = D upoff, jump λ D D a dis- (as probe Lower fthe of | o a for 5937 h D, = is )

CHEMISTRY 30 as ∼330 K (13, 26), above which the number of melting nuclei AB1.5 Cbecomes independent of T. The model allows us to constrain the scatterers’ concentration 20 C and obtain an estimate for their diameters D, in the approx-

) 1.0 imation of the sample as a monodisperse suspension of water m spheres in ice (Fig. 5A). In fact, the simulation shows that C (

10 D is approximately constant before the catastrophic coalescence,

out/in (%) out/in 0.5 occurring at a time tC where the sharp maximum is observed. During coalescence (t ≥ tC ) C and D can be linked by a packing constraint, such as the simple cubic C = 1/D3. We thus obtain, 0 0.0 05100.0 0.5 1.0 1.5 0246810for the A(t) curves measured with E = 3.5 mJ, D = 430 ± 15 nm −3 time (ms) D ( m) time (ms) and C = 13 µm at tC ∼ 200 ns (Fig. 5B), with very good agree- ment among the λprobe values (Size of the Molten Regions Versus Fig. 3. Determination of the scatterer’s diameter D(t) in our samples by the Time and Fig. S4). Moreover, imposing that the concentration angular distribution of scattering, in the approximation of a monodisperse is constant at C(t) = C(tC ) for 0 < t < tC , we can deduce D(t) suspension of spherical particles. (A) The ratio of the signals measured as a at t < 200 ns (Fig. S4). As shown in Fig. 5B, the melt domains function of time in the two configurations of Fig. 1 C and D (ratio 1C/1D). ∼ ∼ ∼ (B) The calculated ratio of the signals detected with the configurations, as grow slowly in time, from 200 nm to 400 nm in 200 ns. The a function of D. (C) D(t) in our samples obtained by discretely sampling and refreezing starts when the temperature of the sample’s wall, in comparing the curves in A and B. contact with the environment, has reached Tm = 273 K. During freezing, heat is constantly removed by the thermal bath, whereas we can assume that the sample remains at Tm . Thus, the freezing The idealized spherical scatterers in the sample are thus iden- rate should be dependent on the rate of heat diffusion through tifiable as molten domains that grow and evolve until T > Tm the ice/water system to the cell walls, proportional to Tm – T0. To and decrease during refreezing when T = Tm . The estimate of investigate the refreezing rate, we analyzed A(t) curves obtained their dimensions with this method is limited to large delays (t≤ in ice Ih with E = 2.5 mJ and λprobe = 632.8 nm, in a series of 0.3 ms) because the configuration of Fig. 1D is affected by a measurements at different T0 conditions. The decreasing part of strong reflection of the pump beam. Also, it makes use of data the A(t) curves was fitted to an exponential decay. To relate this from two different pulses, meaning two different ice samples, decay to the sample’s state, we estimated here an average diam- and of a weak off-axis scattering signal. Thus, the D(t) values eter D(t) of the molten domains, decreasing with time, assum- obtained with this method are quite approximate but are useful ing C constant in this time range, at a value C2. This value is 3 to get an overall insight into our system. obtained by imposing the packing constraint C2 = 1/D2 , where D2 is the maximum diameter of the drops (1,500 nm) obtained Model of the Melting and Refreezing Sample. The simplest model from the analysis of the angular distribution (Fig. 3). The capable of describing our heated sample and its evolution after resulting V (t) = πD(t)3/6 curves are well fitted to an exponen- excitation takes as the starting point the sample at ∼1 ns after tial decay. As expected, the rate constant 1/τ increases linearly the T jump (the minimum delay experimentally accessed) as with T0 – Tm (Fig. 5C). an already nucleated monodisperse suspension of water spheres randomly positioned in an ice matrix at homogenous tempera- Conclusions ture T1, with initial diameter D1 and initial concentration C1. Time-resolved Mie scattering has been successfully used to mon- T1 is set to 360 K (Fig. 1B); D1 = 25 nm, as estimated in refs. itor the melting and the successive recrystallization of water ices 13 and 16; and C1 is set to a different value for each simula- Ih and VI with a nanosecond time resolution. The melting is tion, ranging between 0.1 µm−3 and 5 µm−3. In the simulation induced by an ultrafast IR pulse resonant with a vibrational (Simulation Details) we impose that the temperature at the sam- combination band and its dynamics are probed from a few ple’s wall T decreases in time to the final value T0 with an expo- nential law. The drops are set to grow, at each time step, all by the same amount, depending on T – Tm , and coalesce when they 350 touch each other. When T < Tm , the drops decrease instead AB -3 of growing. At all time steps, the absorbance is calculated on a 300 C1 =2.5 m

T (K) -3 monodisperse suspension where all of the drops have the aver- C1 =0.9 m 1.0 age diameter. The rate constants for the temperature decrease, -3 C1 =0.1 m drops’ growth, and drops’ decrease are chosen to reproduce the 0.5 0.5

shape of the curve. The simulation does not provide any indica- D ( m) 0.0 tion on the actual timescales of the processes, which are derived 1.0 ) only by the experiment. The simulation is essential to validate -3 0.5 the approximations made. In fact, despite its simplicity and the A(t)

3 C ( m simulation box being quite small (10 × 10 × 10 µm ), it is able 0.0 to reproduce with great detail the experimental curves, as can 0.2 be seen by comparing Figs. 2 and 4. In particular, the effect A(t) 0.0 of increasing C1 reproduces perfectly the effect experimentally 0.0 observed by increasing E (Figs. 2B and 4B). When C1 is suf- time (a. u.) time (a. u.) ficiently large, a critical diameter is reached for which a catas- Fig. 4. Results of the simulation. (A) Time evolution, for an initial con- trophic coalescence occurs, and the resulting A(t) curve has a −3 centration C1 = 0.9 µm , of the temperature T(t), average diameter D(t), sharp maximum (A1). By further increasing C1 a second maxi- and concentration C(t) of the droplets and of the resulting absorbance A(t). mum due to large drops formation appears. This behavior con- The first sharp maximum A1 and the following decrease are due to coales- firms that E, as expected, by determining the initial temperature cence, and the second maximum is due to the formation of larger domains. after the T jump (T1) also determines the initial concentration (B) A(t) curves simulated with different C1 values. Increasing C1, the simula- of melting nuclei. The saturation of A1 with E (Fig. 2C) likely tion reproduces the effect experimentally observed by increasing E (Fig. 2B), indicates a limit superheating temperature, previously estimated suggesting that E determines the initial concentration of melting nuclei.

5938 | www.pnas.org/cgi/doi/10.1073/pnas.1620039114 Citroni et al. Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 irn tal. The et range. Citroni time 1-µs to 1-ns the in dynamics same the with liq- melt equilibrium its at to structure relaxation lattice uid the of indepen- those the are dynamics by demonstrated mil- as to of microseconds dency (micro- initial the rate in slower ior much a for by and has liseconds) growth this the the however, reverses down eventually the process; and slowing with temperature sample’s exchange to the the decreasing heat contributes for The calculations also in (9). environment reproduced window to slows also growth time due as the subnanosecond proceeds, time thus it and in as endothermic, decreases down is interfaces which 16, itself, these melting 13, relax- at However, (9, the interfaces. temperature ice/water implies ps at the melting lattice 250 superheated The the initial domain. of ation the macroscopic con- the of nicely to knowledge that pre- 27) dimensions previous a provide droplets’ the to the nects able of are evolution we (nucleation time homogeneity) cise used tem- size and approximations melting shape strong the law, again the reaches Despite temperature perature. the its spherical when decreases liquid and volume coalescence, of during distribution rearranges monodisperse grows, fea- particles a phenomenological peculiar which simple most in a by model the recrystalliza- reproduced including excellently complete are data, and tures, experimental successive the The to meso- tion. few the up a in regime monitored from are seeds, scopic milliseconds, molecules. melting of these tens absorbing to of around nanoseconds the dynamics at after localized growth picoseconds) entire form of or The (tens latter by energy The created absorbed seeds. hotspots the melt of the relaxation of fast access nucleation therefore the having not to pulse, heating the after nanoseconds 1/∆T on linearly depends (C, decays exponential decays. I exponential ice for as refreezing, reproduced bath during thermal time the of of function temperatures a as domains (C ing hypotheses. packing different with obtained eigdmisfor ( domains coalescence. tering during packing cubic concentration simple of fixed when at for packing, volume evolution in other as system’s decreasing or approximated start cubic domains simple domains, the with Liquid period coalescence model. concentration a constant proposed at the grow spheres, of Cartoon (A) 5. Fig. B A molten -3 D ( m) C ( m ) fraction 0.0 0.5 1.0 1.5 0.0 0.5 10 0 10 -9

vlto fteiewtrsse uigmligadrefreezing. and melting during system ice/water the of Evolution D (nm) 100 200 300 400 500 10 τ 01010200 150 100 50 0 1 -8 on 10 -7 t time (ns) time T C 10 time (s) 0 t T -6 hs nti iecl 1ns–1 (1 timescale this in Thus, . < E 10 > 0 s(E ns 200 E ≥ -5 . Jand mJ 3.5 = T 10 . Jde o fettesml’ behav- sample’s the affect not does mJ 2.5 t m C -4 o u estvt,ieI ice sensitivity, our For . 10 -3 . J.Tesae racnan values contains area shaded The mJ). 3.5 = 10 T 0 -2 banda ecie ntetx and text the in described as obtained , C

T 3 Lower (ms)

0 Volume ( m ) 0.0 0.5 10 20 C 6 ,wt h approximation the with K, 269 = 0 1 10203040500 ni olsec cus After occurs. coalescence until B, (∆T h iecntn fthese of constant time The ) 15-. 050.0 -0.5 -1.0 -1.5 h oueo h scatter- the of volume The ) Inset E = 2.5 mJ E =2.5 Ice I = h T imtro h scat- the of Diameter ) 0 time (ms) 1/ time, decreasing T – T )terelevant the µs) T(K m ). h -1 Absorbance decay h Volume decay Volume n c VI ice and ) tdifferent at C T 2 The (B) . 7 K, 273 = 254.2 K 263.2 K 268.2 K 270.6 K 272.6 K ntesml oafcsdaee of diameter focus focused a is laser to probe sample The verified. the always 126 on was Lightwave power probe laser, the Nd:YAG on mittance an and 405 with nm); CPS nm), (1064 Thorlabs (632.8 suf- diode, 25-LHR-691 is laser tens Griot pulse a some Melles single follows: of Ar a as it an are in heat nm); lasers and (405 ice probe volume the The irradiated by kelvins. the of absorbed melt I energy completely ice the to for ficient Thus, mJ 1.92 (32). 11.5 is VI point is ice melting K the 1 at volume by irradiated volume highest irradiated the 22.6 the at and heat even to reached needed not energy is absorption the of tion of all 0.55 in is constant absorbance the reference The as cell. using empty QE25LP-S-MB), (Gentec-Eo meter energy pyroelectric 0.1 size (pore filters syringe I PVDF ice Durapore MillexVV with tered I Ice Methods and Materials the understanding interior. for Earth’s interest the clathrate great at processes of current mate- formation of bulk concern- and topics in studies hydrates, reactivity heterogeneities dynamic solid-state of of including growth plethora rials, and a formation to the way ing the this paves in used work approach many experimental to The inaccessible timescale methods. a computational in and knowledge domain this mesoscopic of for the advantage benchmark in take a can is that Moreover, simulations and and system phenomena. theory H-bonded phase natural archetypal The the many is unexplored. rule water previously water domain of time of transitions a melting in of dynamics ices, have the We water of here. aspects accessed fundamental not unveiled are thus which kinetics, related nucleation likely the more is to structure crystal the of arrangement specific hra ifso niewtr(hra odciiy k conductivity: k pro- (thermal water, rate-limiting with ice/water consistent for the material, in window’s be diffusion the of could thermal independent are surface results I their The ice cess. through on used diffusion were thermal fluorite) consis- thermal different sample, and with the speckle (sapphire materials by different Window conductivity beam a refreezing. probe and eye the melting by of with see tent scattering can static we the pulse, by pump produced 1D each Fig. After in sample). as the I signal ice Rohde– in scattering a only The on measured RT1024). was recorded (RS and oscilloscope monitored in 2-GHz is collected Schwarz signal to is photodiode placed light The is scattered diameter). (2 stopper the angle beam and a whole beam, removed, the transmitted is directly diaphragm the the the (0 stop to 1D) angle close Fig. small placed of a is at ration beam) light probe collect the to of lens divergence and shape spatial the 1C Fig. of figuration with photodiode APD an frequency cutoff with photodiode 1C irradiated an have the nm to focused pro- is 1,700–2,300 nm can 1,930 it range of at where diameter pulse nm The the mJ/pulse. 1,930 15 at in to efficiency up maximum vide tunable a with pulses nm), 100 15-ps = (FWHM produces Hz). 10 source rate repetition maximum The A; mJ/pulse, PL2143 55 (EKSPLA energy laser maximum Nd:Yag pulses, mode-locked 20-ps a by pumped amplifier and tor spectrum FTIR the (29). measuring HR by IFS120 checked spectrometer is Bruker SAC a the with in VI the ice of then 5 presence chip and The ruby temperature, a room desired of at the rescence GPa to lowered 1.5 is to pressure compressed copper- is a sample and 50 The Easylab) is equipped sample (Almax (SAC) The anvils cell gasket. sapphire beryllium anvil The fluorescence sapphire K. membrane low 250 a z-cut, in to with loaded cooled is water and liquid cryostat desired VI, the Peltier to increased a then is in temperature inserted is which diameter, 50 with spacer (Teflon) polytetrafluoroethylene scletdadfcsdo Vehne Si UV-enhanced a on focused and collected is 1D) (Fig. scattering or ) The h T h h ae slae naro-rsuecl ihCaF with cell room-pressure a in loaded is water the , jm orewsdtrie ymauigtetasiso iha with transmission the measuring by determined was source -jump n c Iaepeae sn ae rmAdih PCgae fil- grade, HPLC Aldrich, from water using prepared are VI ice and T jm ore ecie nrf 1 sa pia aaercgenera- parametric optical an is 21, ref. in described source, -jump o c I(0 1.Teeeg eddt opeeyml the melt completely to needed energy The 31). (30, VI ice for µJ ∼400 ∼ + . WK 2.2 –0m ntesml.Teidpnec ftetrans- the of independence The sample. the on mW ∼5–10 ae,Chrn ar noa9 479n) eN laser, He-Ne a nm); (457.9 90 Innova Sabre Coherent laser, .Teasrac ftesml ne raito with irradiation under sample the of absorbance The µm. < θ < iprg ihaetr – m(eedn on (depending mm 2–8 aperture with diaphragm a ) T −1 jm nryrne sd niaigta satura- that indicating used, ranges energy -jump PNAS h ndaee sue sapesr ag (28). gauge pressure a as used is diameter in µm ·m f 7 c at ◦ −1 H FrtSnos.Frtasiso (con- transmission For Sensors). (First GHz 3 = cetdb h olcigln 2. min mm (25.4 lens collecting the by accepted ) T 0 | 6 and K 269 = o c)bigsoe hntruhthe through than slower being ice) for ue6 2017 6, June ntikesad500 and thickness in µm P ± f 0 c au 12Gao . P) h fluo- The GPa). 1.4 or GPa (1.2 value .0frbt ye fsml n is and sample of types both for 0.30 ∼150 0Mz(aaas I2-2 or SI722-02) (Hamamatsu MHz 60 = < θ < T ,adtetasiso (Fig. transmission the and µm, E 1.5 0 . J(nryasre by absorbed (energy mJ 3.5 = au 242226K.Frice For K). (254.2–272.6 value | hcns n 54mm 25.4 and thickness µm ◦ o.114 vol. .Frsatrn (configu- scattering For ). T h jm nry The energy. -jump ∼ ocekwhether check to h | 2 ndiameter. in µm n .0m for mJ 2.90 and WK 0.6 idw n a and windows o 23 no. o c I ice for µJ ) For µm). −1 | ·m 5939 −1 h

CHEMISTRY −1 −1 −1 −1 windows (k ∼ 9 WK ·m for CaF2, k ∼ 25 WK ·m for sapphire) or at mations, and Movements in Planetary Interiors, from the Alfred P. Sloan the window/sample interfaces (values for interfacial thermal resistance not Foundation); by the Grant Futuro in Ricerca 2010 RBFR109ZHQ funded available). by the Italian Ministero dell’Istruzione, Universita,` Ricerca under the pro- gram Fondo Italiano per la Ricerca di Base (FIRB); and Fondazione Cassa di ACKNOWLEDGMENTS. This work was supported by the Deep Carbon Obser- Risparmio di Firenze under the project “Chimica Ultraveloce ad Altissima vatory initiative (Extreme Physics and Chemistry of Carbon: Forms, Transfor- Pressione.”

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