Yu-jun JinYun-qin YuYu-xi WngKe LinXio-guo ZhouShi-lin Liu

a.School of Physics and Material Science,Anhui University,Hefei 230039,China

b.Hefei National Laboratory for Physical Sciences at the Microscale,Department of Chemical Physics, University of Science and Technology of China,Hefei 230026,China

Accurate Measurement of Raman Depolarization Ratio in Gaseous CO2

Yu-juan Jina,Yuan-qin Yua?,Yu-xi Wangb,Ke Linb,Xiao-guo Zhoub,Shi-lin Liub

a.School of Physics and Material Science,Anhui University,Hefei 230039,China

b.Hefei National Laboratory for Physical Sciences at the Microscale,Department of Chemical Physics, University of Science and Technology of China,Hefei 230026,China

The Raman depolarization ratios of gaseous CO2in the spectral range of 1240?1430 cm?1are determined with a sensitive photoacoustic Raman spectroscopy,and more accurate data compared to the literature results are presented.The precision of the obtained depolarization ratio is achieved by measuring and ftting the dependence of the PARS signal intensity on the cross angle between the polarizations of two incident laser beams.

Depolarization ratio,Accurate measurement,Photoacoustic Raman spectroscopy,Global ftting

I.INTRODUCTION

Raman spectroscopy is a valuable tool to study the molecular structures and molecular interaction.In Raman measurement,the depolarization ratio is a fundamental physical quantity that indicates the symmetry of a Raman-active vibrational mode of molecules,and defned as the intensity ratio of scattered lightI⊥toI//(ρ=I⊥/I//),whereI⊥andI//are the intensities of scattered photons with polarizations perpendicular and parallel to the polarization plane of the incident beam, respectively[1].Generally,the higher the symmetry of a vibrational mode is,the smaller of its depolarization ratio.Therefore,the accurate determination of the depolarization ratio not only can assign the observed Raman band but also help us to better detect small distortion of molecular structures induced by diferent environments,such as in pure states,in the mixtures or on the interface[2?8].On the other hand,the accurate measurement of the depolarization ratio has also become necessary in the validation of the associated theories on the calculation of molecular polariziabilities and intensities of Raman bands since the accurate prediction of these parameters are still a challenge work in quantum chemistry at present[9].

In the past decades,experimental and theoretical methods have been developed to accurately determine the Raman depolarization ratio based on linear or nonlinear spectral technique[2,4,10?13].Very recently, Jameset al.precisely measured the Raman depolarization ratios for individualQ(J)branch lines of all diatomic hydrogen isotopologues-H2,HD,D2,HT,DT, and T2with an uncertainty of 5%relative to the theoretical values,using a set of complex experimental arrangements and corrected data processing[13].In this work,we measured the depolarization ratio for gaseous carbon dioxide in the spectral range of 1240?1430 cm?1using a sensitive photoacoustic Raman spectroscopy (PARS).

Carbon dioxide is a simple and important molecule since it is signifcantly involved in combustion media (fame,engine)and is major atmospheric component of a number of planets such as Venus and has a dominant contribution to the greenhouse efect in earth’s atmosphere.Also,carbon dioxide can be used as an excellent supercritical solvent,which makes the compound receive a lasting concern from scientists in the feld of weakly bound intermolecular complexes.In order to better understand the role of CO2in the terrestrial atmosphere combustion and supercritical processes,the vibrational spectral properties of CO2have been extensively studied in gaseous and liquid phase as well as solid states[9,14?18].

Recently,the attention has been paid to the intermolecular interaction between CO2and organic liquids(ethanol,acetone and benzene)and complex fuids such as ionic liquids using Raman spectroscopy,motivated not only from the fundamental point of view but also mainly under the impetuous motivation of the interactions of CO2in the feld of environmental studies[23?28].It is known that the Raman depolarization ratios can provide a highly sensitive probe on intermolecular interactions between CO2and complexes in diferent environments.The depolarization ratios of CO2obtained by conventional spontaneous Raman spectroscopy from diferent groups were not consistent [9,14,15,27].Here,we measured the Raman depolarization ratio of CO2by a newly developedI-θcurve (photoacoustic Raman signal intensityvs.the polarization cross-angleθ)method based on a polarized PARS technique,and more accurate data were presented.

The basic theory of PARS has been fully described in Refs.[29?32].Here,only a short review is given. When the frequency diference between two laser beams (called as pump and Stoke beams)is resonant with a Raman-active vibrational transition,the molecules are transferred to the vibrationally excited state by a stimulated Raman scattering process.Then collisions cause the excitation energy to be converted into local heating.This creates a sound wave that is detected by a microphone.The spectral sensitivity of PARS is greatly increased compared to the direct measurement of weak spontaneous Raman scattering photons.The PARS intensity,I,can be expressed as

whereρis Raman depolarization ratio,θis the cross angle between the polarizations of two laser beams.It can be seen that the PARS intensity is periodically dependent on the cross angleθ.By measuring theI-θcurve,the depolarization ratio can be determined by a global ftting with Eq.(1),as shown in Fig.1.

II.EXPERIMENTAL SETUP

The experimental setup has been reported previously in detail[4,30?32].The second-harmonic output of 532.1 nm from a pulsed Nd∶YAG laser(line width 1.0 cm?1,pulse width 10 ns)was split into two beams by a quartz wedge.About 90%of the 532.1 nm laser energy directly entered into the dye laser system(line width 0.05 cm?1)for generating a tunable Stokes beam (570?580 nm),and the remainder was used as a pump beam for PARS.The pump and Stokes beams were focused in the center of the photoacoustic cell with conterpropagating confguration.The generated photoacoustic signal was detected by a sensitive microphone and monitored by an oscilloscope or averaged by a Boxcar integrator.The energies of pump and Stokes beams were typically 7 and 4 mJ/pulse,respectively,and the sample pressure of CO2was kept at 25 Torr.

In order to assure the precision of the measurements of depolarization ratio,the pump and Stokes beams were highly linearly polarized,which were achieved by two Glan-Taylor prisms with an extinction ratio of 10?6.Additionally,the whole passage of the laser beams including the two polarizers and lens as well as quarts window of photoacoustic cell were carefully arranged and adjusted to minimize the polarization distortions from optical components.During the experiment,the polarization of Stokes beam was fxed in the vertical direction while that of pump beam was rotated by aλ/2 wave plate.In this way,the polarization crossangle between the two laser beams was precisely controlled.A typicalI-θcurve is shown in Fig.1 along with a global ftting with Eq.(1).The precision of the obtained depolarization ratio was checked by measuring the depolarization ratio of the totally symmetric stretching mode of CH4at 2917 cm?1and antisymmetric stretching mode at 3020 cm?1,achieving a value of 0.002±0.002 and 0.75±0.005,respectively(the theoretical depolarization ratios of those two modes are 0 and 0.75,respectively).

FIG.1 A typicalI-θcurve of gaseous CO2along with a global ftting with Eq.(1).

III.RESULTS AND DISCUSSION

The polarized and depolarized Raman spectra of gaseous CO2under a low pressure of 25 Torr in the spectral range of 1240?1430 cm?1are presented in Fig.2.It can be seen that there are two intense and sharp peaks at 1387.2 and 1284.3 cm?1with a interval of 102.9 cm?1and an intensity ratio of 1.75,which can be assigned to the Fermi doublet from symmetric stretching fundamentalv1(100)and bending overtone 2v2(0200),respectively,as mentioned above.Although the wavefunctions of the Fermi doublet are severely mixed,we still label them asv1(100)and 2v2(0200),as shown in Fig.2.There are also three weak satellite bands situated at 1408.4,1368.9,and 1264.0 cm?1.According toMontero reports[9],the frst one and the last one can be assigned to another Fermi doublet of CO2from the hot bands corresponding to the transitions(010)→(110) and(010)→(0310),respectively,and the second one corresponds to the symmetric stretching fundamentalv1(100)of isotope C13O2,which has a natural abundance of about 1.1%in pure CO2molecule.It should be mentioned that the hot band at 1264.0 cm?1also contains the weak contribution from the bending overtone 2v2(0200)of C13O2molecule,which is in Fermi resonance with the symmetric stretching fundamental [9].However,the peak intensity of C13O2is so weak that the contribution from overtone 2v2(0200)of C13O2can be neglected.

The Raman depolarization ratios of gaseous CO2measured byI-θcurve method are summarized in Table I along with the available values from Refs.[9,14, 15,27].For a pair of strong Fermi bands at 1284.3 and 1387.2 cm?1,the depolarization ratios determined in the present work are 0.042 and 0.027,respectively. These values are in good agreement with those from other reports except[27],in which the values are 0.07 for both Fermi bands.However,for weak hot bands at 1264.0 and 1408.4 cm?1,the depolarization ratios from diferent literatures are diferent from each other.For the transition(010)→(110)at 1408.4 cm?1,our measured depolarization ratio is 0.054 whereas that from Ref.[14]and Ref.[9]were 0.081 and 0.024,respectively. For the transition(010)→(0310)at 1264.0 cm?1,our result is 0.043 whereas that from Ref.[14]and Ref.[9] were 0.143 and 0.050,respectively.

The depolarization ratios determined in the present work are accurate and reliable.First,in the present work,the depolarization ratio determined from a global ftting of theI-θcurve signifcantly reduces the uncertainty of the ratio between only two intensitiesI⊥andI//in the spontaneous Raman experiment,where the scattered intensityI⊥is too weak to be measured accurately in many cases,especially for the small depolarization ratio of polarized bands.Secondly,the PARS signal originates from a precise matching of the polarizations between two laser beams.This is diferent from the conventional Raman experiment,in which the Raman scattered photos are collected in a fnite solid angle with relatively complex polarizations and the depolarization ratio must be corrected to be accurate.Thirdly, PARS is a very sensitive spectral technique,and especially suitable to detect weak Raman signal.Therefore, for weak hot bands,we can still obtain the accurate depolarization ratio.

In addition to C12O2molecule,we also determined the depolarization ratios for symmetric stretching fundamentalv1(000)of C13O2isotope,which had never been measured previously due to the low natural abundance of C13O2isotope in pure CO2.Although C13O2and C12O2molecules only difer by a neutron,their depolarization ratios are diferent.One is 0.067 and the other is 0.027,as shown in Table I.This indicates that the molecular polarizability of C13O2is diferent from that of C12O2.The diferences brought by neutron in isotopes are refected not only on the depolarization ratio but also on other aspects.For example,many investigations indicate that the formation of hydrogenbonding in liquid D2O are much stronger than that in normal H2O[33].Further theoretical investigations are needed to interpret these subtle diferences.

TABLE I The measured depolarization ratiosρof the gaseous C12O2and C13O2in the spectral range of 1240-1340 cm-1.

FIG.2 The polarized(//)and depolarized(⊥)PARS spectra of gaseous CO2in the spectral range of 1240-1430 cm-1measured under parallel and perpendicular laser polarization confgurations,respectively.The peak labeled with star is from C13O2and the others are from C12O2.

IV.CONCLUSION

We reported the accurate depolarization ratio measurement of gaseous C12O2and C13O2molecules by anewly developedI-θcurve method based on the polarized PARS technique,and the maximum experimental uncertainty is±0.005.As the molecular system of CO2is often used as a model case for comparative studies between theory and experiment and for investigations on the molecular interaction,the accurate depolarization ratio provided here are helpful to quantitatively assess the calculations of the molecular polariziabilities and Raman intensities inab initiomethod in the future and to better understand the role of CO2in diferent environment such as in gaseous,liquid phase,as well as solid state.

V.ACKNOWLEDGMENTS

This work was supported by the National Natural Science Foundation of China(No.20903002,No.21273211, No.91127042,and No.21373194)and the Anhui Provincial Natural Science Foundation(No.1408085MA18), and the National Key Basic Research Special Foundation(No.2013CB834602 and No.2010CB923300).

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10.1063/1674-0068/28/cjcp1409156sional efects in gaseous combustion process,where the CO2molecule is signifcantly involved[20?22].

?Author to whom correspondence should be addressed.E-mail：yyq@ahu.edu.cn,FAX：+86-551-63861257

(Dated:Received on September 17,2014;Accepted on October 23,2014)