Raman spectroscopy of optically levitated supercooled water dropletHidenori Suzuki, Yoshiki Matsuzaki, Azusa Muraoka, and Maki Tachikawa Citation: J. Chem. Phys. 136, 234508 (2012); doi: 10.1063/1.4729476 View online: http://dx.doi.org/10.1063/1.4729476 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v136/i23 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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THE JOURNAL OF CHEMICAL PHYSICS 136, 234508 (2012)

Raman spectroscopy of optically levitated supercooled water dropletHidenori Suzuki, Yoshiki Matsuzaki, Azusa Muraoka, and Maki Tachikawaa)

Department of Physics, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan

(Received 5 April 2012; accepted 31 May 2012; published online 21 June 2012)

By use of an optical trap, we can levitate micrometer-sized drops of purified water and cool thembelow the melting point free from contact freezing. Raman spectra of the OH stretching bandwere obtained from those supercooled water droplets at temperatures down to −35 ◦C. Accord-ing to the two-state model, an enthalpy change due to hydrogen-bond breaking is derived fromtemperature dependence of the spectral profile. The isobaric heat capacity calculated from the en-thalpy data shows a sharp increase as the temperature is lowered below −20 ◦C in good agree-ment with conventional thermodynamic measurements. © 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4729476]

I. INTRODUCTION

Although water is one of the most common materials onEarth, it is distinguished from other simple liquids for uniquephysical properties such as a negative thermal expansion be-low 4 ◦C and a thermodynamic singularity around −45 ◦C.1–6

It is generally accepted that strong hydrogen bonding betweenwater molecules is responsible for these characteristics. How-ever, their detailed mechanism and microscopic picture arestill controversial.

There is a hypothesis that predicts the existence of a criti-cal point associated with two phases of liquid water; one witha low density and the other with a high density.7 This ideaof water polyamorphism was inspired by the discovery oflow- and high-density amorphous ice and the first-order phasetransition between the two solid phases.8–10 According to thehypothesis, those solid phases are connected to correspond-ing liquid phases at higher temperatures, and the observedanomalies of liquid water are interpreted as a manifestation ofthe critical phenomenon near the liquid–liquid critical point,so-called the second critical point. Thermodynamic analysisand numerical simulations11–16 predict that the second criti-cal point lies deep in the supercooled region well below thehomogeneous nucleation temperature TH,6, 17 which is about−38 ◦C at 1 bar. Even if the critical point exists, this makes itsdirect observation extremely difficult.

There are other thermodynamic models called thesingularity-free scenario,18, 19 the stability-limit scenario,20

and the critical-point free scenario.21 Each of the three mod-els explains anomalies of liquid water without assuming thesecond critical point. According to Stokely et al.,22 differ-ence of the four scenarios comes from the estimation of thestrength and cooperativity of hydrogen bonds. Careful com-parison with experimental data of supercooled water is im-portant in testing these models.

Since interesting anomalies of liquid water become pro-nounced at temperatures far below the melting point, specialcare should be taken in experiments to avoid freezing of the

a)Author to whom correspondence should be addressed. Electronic mail:tachikaw@isc.meiji.ac.jp.

aqueous sample. Contact freezing on a solid surface is in-evitable for bulk water contained in a vessel, and the liquidwater temperature normally accessible is higher than −25 ◦C.Isolation of water samples in fine glass capillaries23 oremulsion droplets24 effectively reduces the nucleation prob-ability and enabled the measurements of heat capacity,1, 2, 5

isothermal compressibility,3, 5, 6 and the coefficient of thermalexpansion4–6 at temperatures down to −38 ◦C. Those quanti-ties tend to diverge as the temperature approaches −45 ◦C,which is the temperature of the expected Widom line25 at1 bar. They well fit to a scaled parametric equation of statederived on the assumption that the liquid–liquid critical pointdoes exists.26, 27 Water confined in a nanometer-sized pore isfree from freezing even at temperatures below 200 K.28 Thecalorimetric measurements on the nanopore water revealedthat the heat capacity had a maximum around 233 K in fa-vor of the second critical point scenario.29 It should be noted,however, that nanometer-scale confinement generally changesthermodynamic properties of the sample.

As a method of isolating supercooled bulk water fromsolid boundary, particle levitation is a promising option.30

Compared to other levitation techniques such as electrody-namic balance31 and acoustic levitation,32 optical trappingis versatile in manipulation of the position and motion ofthe trapped particles.33, 34 Motivated by atmospheric science,optical levitation has been employed for thermodynamicmeasurements and observation of the freezing processof low-temperature aqueous solutions.35–37 Trapping of amicrometer-sized ice crystal and imaging of crystal growthto a snow flake were also demonstrated.37, 38

Optical trapping enables spectroscopic investigation ofwater medium even in highly supercooled state. Raman spec-troscopy of liquid water provides information on intermolec-ular motions in the hydrogen-bonded network as well as theperturbation to the normal vibrational modes of a single watermolecule.39–56 So far, experiments using the Raman tweezersspectroscopy mostly aimed to probe physical and chemicalprocesses in aqueous aerosol droplets containing salt or acidas a solvent.35, 37, 57–59 On the other hand, Raman spectroscopyhas been applied to detect density fluctuations near the liquid–vapor critical point in several materials.60, 61

0021-9606/2012/136(23)/234508/6/$30.00 © 2012 American Institute of Physics136, 234508-1

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234508-2 Suzuki et al. J. Chem. Phys. 136, 234508 (2012)

In this paper, we analyze Raman spectra from a purifiedwater droplet levitated in air by a dual-beam optical trap.33 Itis our major objective to clarify how thermodynamic anoma-lies appear in spectral profiles of molecular vibrations, andto establish a methodology of spectroscopic investigation ofhighly supercooled bulk water. We focus on the OH stretch-ing band in the frequency range of 2700–3900 cm−1. Ramanspectrum observed between 90 ◦C and −35 ◦C is decomposedinto Gaussian components and their origin and temperaturedependence are discussed. Based on the so-called two-statemodel,62, 63 an enthalpy change due to hydrogen-bond break-ing is obtained from the temperature dependence of the spec-tral profiles. The isobaric heat capacity calculated from theenthalpy data is compared with results of the conventionalmeasurements.2

II. EXPERIMENTAL

A schematic of our experimental setup is shown inFig. 1(a). A detailed description of the trapping optics andthe cooling system is given in Ref. 38. In brief, the opti-cal trap33 uses counter-propagating Gaussian beams from a532 nm Nd:YVO4 laser (Coherent, Verdi-V10). The two

FIG. 1. (a) Schematic of the experimental apparatus. (b) Image of a singlewater droplet in the dual beam optical trap and its Mie scattering fringes.

beams of equal power are focused by a lens pair in such a waythat their beam waists are positioned in front of each other.The trap confines a dielectric particle three-dimensionally inthe center of the two focal points. An axial displacement fromthe equilibrium position causes an imbalance of the radiationpressure forces from the opposing lights, which produces anet restoring force along the optical axis. In radial directions,the optical gradient force works as a restoring force.

The dual-beam trap is installed in an open cold chamberassembled with a copper cylinder and a coolant jacket. Tem-perature distribution inside the chamber is controlled via thecoolant temperature which is adjustable from 25 ◦C to −50 ◦Cwith a refrigerated circulator (Julabo, F83). The ambient tem-perature around the trap region is measured by a thermocou-ple that is positioned 10 mm aside from the trap center not tointercept the laser beams. Temperature difference across theoffset is less than 0.1 K.

Ultrapure water with a resistivity of 18.2 M� · cm isturned into a fine mist and guided to the cold chamber by anultrasonic nebulizer (Omron, NE-U07). Water droplets thathave entered the cold chamber are rapidly thermalized to theambient temperature and become supercooled. The opticaltrap captures a water droplet that has drifted into the laserbeams, as is shown in Fig. 1(b). The size of the droplet canbe accurately determined from the interference fringes dueto Mie scattering of the trapping beams. The diameter of thewater droplets ranges from a few micrometer to several tensmicrometer. The trapped water droplet slightly absorbs the532 nm trapping radiation. The resultant temperature rise es-timated from the absorption coefficient is less than 0.1 K.

Stokes and anti-Stokes photons are scattered from watermolecules excited by the 532 nm radiation. Raman spectra areobserved in the X(Y, X + Y)Z configuration. The pump radi-ation is horizontally polarized, and vertically scattered lightis focused on the input end of an optical fiber feed for theCCD spectrograph (Acton Research, SpectraPro 2300i) afterpassing a depolarizer. The spectral sensitivity of the detectionsystem was calibrated with a NIST-calibrated tungsten halo-gen lamp (Ocean Optics, LS-1). Wavelength calibration of thespectrograph was performed using Ne lines as references.

Figure 2 compares Raman spectrum of the OH stretch-ing band observed at different temperatures from 90.0 ◦C to−34.6 ◦C. For temperatures above −5 ◦C, spectra from an ul-trapure water sample contained in a Pyrex glass cell were

FIG. 2. Raman spectra of the OH stretching band of water at differenttemperatures.

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234508-3 Suzuki et al. J. Chem. Phys. 136, 234508 (2012)

FIG. 3. Decomposition of the Raman spectrum, observed at T = 23.3 ◦Cand −27.7 ◦C, into Gaussian components. Sum of the Gaussian componentsis represented by a red solid line.

recorded. The intensity of the Raman signal depends on thesize of the water droplet being trapped. For the sake of com-parison, a spectral profile was normalized so that its integratedintensity becomes equal. A typical Raman spectrum of thisband has two major peaks. As the temperature is lowered, thelow-frequency peak around 3200 cm−1 becomes more promi-nent than the high-frequency peak around 3400 cm−1, and thewhole spectrum is shifted to lower frequencies. It is also no-ticeable that a shoulder observed around 3600 cm−1 at roomtemperatures disappears at temperatures below −15 ◦C.

Following the conventional analysis of the OH stretch-ing band of H2O,42, 47, 56 the spectrum is decomposed intofive Gaussian components located around 3050, 3200, 3400,3500, and 3650 cm−1, as shown in Fig. 3. The linear com-bination of these components is fitted to the observed spec-tral profiles by adjusting the center frequency, the width, andthe height of the Gauss functions. The ratio of each com-ponent’s integrated intensity to the total intensity is plottedas a function of the temperature in Fig. 4. As the temper-ature rises, relative integrated intensities of the 3200 cm−1

and 3400 cm−1 components (I2 and I3) decrease and that ofthe 3500 cm−1 component (I4) increases. The intensitiesof the 3050 cm−1 and 3650 cm−1 components (I1 and I5)are little dependent on the temperature.

According to the assignment in literature,42, 56 the3200 cm−1 and 3400 cm−1 components are due to thein-phase and out-of-phase stretching modes of a fullyhydrogen-bonded water molecule in tetrahedral groupingof five molecules. Such a molecule forms four hydrogenbonds, two with protons and two with lone electron pairs.The origin of the 3050 cm−1 component is thought to be theFermi resonance between the first overtone of the bendingvibration and the in-phase stretching mode. Breakage ofthe proton-donating bonds yields a water molecule with a

FIG. 4. Temperature dependence of the integrated intensity of eachGaussian component. I1, I2, I3, I4, and I5 represent intensities of the3050 cm−1, 3200 cm−1, 3400 cm−1, 3500 cm−1, and 3650 cm−1 compo-nents, respectively. Solid lines are just a guide to the eye.

freely vibrating OH group. The 3500 cm−1 and 3650 cm−1

components are due, respectively, to vibrations of thehydrogen-bonded OH group and the dangling OH group insuch a molecule. We have confirmed the assignments for thecollective vibrations and the vibration of the dangling bondthorough ab initio MO calculation of vibrational modes fora tetrahedral water pentamer which is a component part ofice Ih structure.56 Geometry optimization and Raman shiftanalysis were made by the Hartree-Fock approach using6-31+G* basis set in GAUSSIAN 09 program package.64

III. ANALYSIS AND DISCUSSION

To describe the structure and thermodynamic proper-ties of liquid water, the so-called two-state model has beenproposed,62, 63 which assumes water is a mixture of twodifferent states of intermolecular bonding. One is an ice-like state where water molecules are coupled by hydrogenbonding to form tetrahedral network. The other is a statewhere water molecules are more densely packed and hy-drogen bonds are disrupted by distortion. The assumptionof two distinct domains in liquid is sometimes criticizedfrom the viewpoint that presumes continuous distribution ofmolecular coordinates.39, 65 Meanwhile, recent data of x-rayspectroscopy66, 67 support the multi-state model, and a newtheoretical approach has been presented based on the two-state model, successfully describing the emergence of the sec-ond critical point.68, 69

Here, we stand on the concept of the two-state modeland divide water molecules into two categories; a moleculewith two OH groups both hydrogen-bonded to the tetrahedralnetwork (hydrogen-bonded molecules), and a molecule withone or two dangling OH groups whose hydrogen bond tonearest neighbors is broken or weakened by severe distortion

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234508-4 Suzuki et al. J. Chem. Phys. 136, 234508 (2012)

of the network (non-hydrogen-bonded molecules). Based onthe assignments, the former contributes to the Raman spectralcomponents I1, I2, and I3, and the latter to the componentsI4 and I5. This is consistent with the observed temperaturedependence of the integrated intensity since thermal motionof molecules disrupts more hydrogen bonds with an increasein temperature.

The ratio I1+I2+I3I4+I5

is proportional to the equilibrium con-stant K,

K = fHB

fNHB

= AI1 + I2 + I3

I4 + I5, (1)

where fHB is the fraction of hydrogen-bonded H2O molecules,fNHB = 1 − fHB the fraction of non-hydrogen-bondedmolecules, and A is a constant independent of the tempera-ture. According to the van’t Hoff equation, ln K is related tothe temperature T as,43, 47, 56

d ln K

d T −1= −�H ◦

R. (2)

Here R is the gas constant, and �H◦ denotes the stan-dard enthalpy change of formation when a hydrogen-bondedmolecule is produced from a non-bonded molecule at 1 bar ofpressure.

In Fig. 5, ln I1+I2+I3I4+I5

is plotted as a function of the in-verse of the temperature. Errors on the vertical scale were es-timated by considering tolerated shifts of the fitted parame-ters. The error bars indicate the range of ln K in which resid-uals between the observed spectral profile and the fitted func-tion always fall within the noise level of the Raman signal.The standard enthalpy change �H◦, obtained from the slopeof the curve, is almost constant over the temperature rangefrom 5 ◦C–90 ◦C, but gradually increases in magnitude as thetemperature is lowered below 0 ◦C. A test function g(x) = ax+ b + cexp (αx) is fitted to the experimental data, and thebest-fitted one is shown by the solid curve in Fig. 5. This func-tion was chosen since it well describes both the linear part be-low x = T−1 = 0.0036 K−1 and the monotonically increasingconvex part above 0.0037 K−1. The value of �H◦ is calculatedto be −2.0 kcal/mol at temperatures between 5 ◦C–90 ◦C, ingood agreement with previous measurements.42, 43, 47, 51

Droplet samples differ in size, and due to evaporation,even a single water drop gradually shrinks during the obser-vation. It should be noted that the pressure inside a water

FIG. 5. van’t Hoff plot derived from the integrated Raman intensities.

droplet is size-dependent and higher than the external pres-sure because of the surface tension. The internal pressure of a5 μm droplet, for example, is about 1.6 bar. However, the en-thalpy of liquid water is little dependent on the pressure. Forthe internal pressure range of the trapped droplets, it is rea-sonably assumed that the enthalpy change derived from thedroplet data is equal to that of bulk water under the standardpressure.5

In the two-state model, the standard heat capacity of liq-uid water is given by,43

Cp = CHBp + (fHB − 1)

∂�H ◦

∂T+ fHB(1 − fHB)

R

[�H ◦

T

]2

,

(3)

where CHBp is the standard heat capacity of hydrogen-bonded

water molecules. The isobaric heat capacity Cp can be derivedas a function of the temperature using experimentally deter-mined fHB and �H◦. Absolute values for fHB can be obtainedfrom g(x) and Eq. (1) if the value of A is known. The enthalpychange �H◦ can be replaced by −R

dg(x)dx

. Two quantities CHBp

and A are treated as adjustable parameters.Figure 6 compares the heat capacity Cp thus derived and

data of the thermodynamic measurements so far reported.2

Data at temperatures below −3 ◦C are those of emulsiondroplets. For the curve in the figure, CHB

p is fixed to 8R, and Ais set to 0.59. The value of A reasonably agrees to the Ramanspectral intensity ratio obtained from our ab initio MO calcu-lation. The empirical curve based on our Raman spectroscopicmeasurements reproduces overall temperature-dependence ofthe heat capacity of liquid water as well as its absolute values.The heat capacity is almost constant above 0 ◦C but exhibitsa sharp increase as the temperature is lowered below −20 ◦C.The curve predicts that the heat capacity of liquid water takesa maximum value around T = 210 K. This unimodal featureis intrinsic to the two-state system, but the curvature of theemulsion data cannot be fitted satisfactorily without introduc-ing the experimentally determined temperature dependenceof �H◦.

According to MD simulations,53, 54 the molecular coor-dinates in liquid water are continuously distributed, and theline shape of the OH stretching band is attributed to inho-mogeneous broadening due to local electric field variations.

FIG. 6. Temperature dependence of the isobaric heat capacity of liquid wa-ter calculated from the experimentally determined parameters according toEq. (3). Data from emulsion measurements2 are shown as crosses.

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234508-5 Suzuki et al. J. Chem. Phys. 136, 234508 (2012)

Raman spectral analysis by Smith et al.51 showed that the riseof temperature gradually distorts intermolecular geometriesand releases more OH oscillators from restriction of hydrogenbonding. Though still inconclusive, the continuum picture issupported by recent numerical analyses and seems more nat-ural as a real water structure. In describing thermodynamicproperties, however, a continuous system may reasonably bemodeled by combination of multiple states with continuouslyvariable fractions. Our approach provides a simple method ofdecomposing the Raman spectrum into two parts with oppo-site temperature dependence to fit into the two-state model.

Raman spectra at much lower temperatures down to−50 ◦C are necessary to test for the existence of the pre-dicted second critical point. The accessible temperature in thepresent spectroscopic measurements was limited by freezingof water droplets, but it could be further lowered by the fol-lowing strategy. Since homogeneous nucleation of ice is astochastic process and the probability of freezing is volume-and surface-dependent,70 the lifetime of supercooled state islargely prolonged for smaller samples. Water of micrometeror submicrometer size is still large enough to have thermo-dynamic properties of a bulk sample. Selective trapping ofa submicrometer droplet can be achieved by first trapping alarger droplet and heating it with an infrared radiation untilthe droplet shrinks to an appropriate size through evaporation.When the heating radiation is turned off, the drop instanta-neously thermalizes to the ambient temperature, and will re-main liquid for a certain amount of time.

IV. CONCLUSION

We have demonstrated that combination of optical trap-ping and Raman spectroscopy is an effective tool to probethermodynamic anomalies of liquid water in highly super-cooled state. Detailed analysis of the OH stretching Ramancomponents, based on the two-state model, yielded temper-ature dependences of the standard enthalpy change and thestandard heat capacity. Anomalous increase of the heat ca-pacity was observed at temperatures below −20 ◦C. Althoughaccessible temperature in the present experiment was limitedto −35 ◦C, rapid cooling and continuous in situ observation ofa submicrometer water drop may push the limit to much lowertemperatures. This versatility of manipulating a single dropletis a major advantage of the optical tweezers spectroscopy,which may be a key to the no-man’s land.14

ACKNOWLEDGMENTS

The authors thank Dr. Tomoko Fukazawa for fruitful dis-cussions on Raman spectroscopy. The computations were per-formed using Research Center for Computational Science,Okazaki, Japan. This work was supported by JSPS Grant-in-Aid for Scientific Research (Grant No. 19340112).

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