Anomalous Behavior of Isotropic Raman Line Shapes near Gas-Liquid Critical Points

1999

Phys. Rev. Lett.

Vibrational phase relaxation near gas-liquid and liquid-solid phase coexistence has been studied by molecular dynamics simulations of N-N stretch in N 2 . Experimentally observed pronounced insensitivity of phase relaxation from the triple point to beyond the boiling point is found to originate from a competition between density relaxation and resonant-energy transfer terms. The sharp rise in relaxation rate near the critical point (CP) can be attributed at least partly to the sharp rise in vibrationrotation coupling contribution. Substantial subquadratic quantum number dependence of overtone dephasing rate is found near the CP and in supercritical fluids. [S0031-9007(99)09318-7] PACS numbers: 61.25.Em, 64.70.Fx Vibrational phase relaxation (VPR) is a powerful tool to probe the interactions of a chemical bond with its surrounding medium [1]. Traditionally, VPR has been studied by the Raman scattering techniques, the most popular being the isotropic Raman line-shape studies [1]. The rate of VPR is proportional to the width of the usually obtained Lorentzian line shape. More recently, nonlinear optical techniques, such as fifth and seventh order responses from the vibrational mode, have been used to study this problem in greater depth [2(a)]. Many interesting new results have been obtained, such as the subquadratic quantum number dependence of overtone dephasing [2].The quantum number dependence of vibrational phase relaxation is usually explained by using the well-known Kubo-Oxtoby theory where the overtone vibrational line shape [I͑v͒ n0 ] for the ͑0, n͒ pair of vibrational levels is related to the normal-coordinate (Q) time correlation function for the nth overtone as [1]The normal-coordinate time correlation for the nth overtone ͓͗Q͑t͒Q͑0͒͘ n0 ] is in turn related to the instantaneous fluctuation in energy between the vibrational quantum levels n and 0, or frequency modulation ͓Dv n0 ͑t͔͒, bywhere v n0 is the vibrational frequency for the 0 to n transition. A cumulant expansion of Eq. (2) [3] leads to the expression of the normal-coordinate time correlation function in terms of the frequency-modulation time correlation function ͗Dv n0 ͑t͒Dv n0 ͑0͒͘ [1(a)]. The fluctuation in frequency gap [Dv n0 ͑t͒] derives contributions from several sources, including the atom-atom (AA) interactions, the resonant energy transfer (RT) between molecules and the vibration-rotation (VR) coupling [1]. While the atomatom interaction terms have been evaluated using analytical methods based on a hydrodynamic description [1(a)] and also at the molecular level using the mode coupling theory [4], the RT and VR contributions are notoriously difficult to evaluate analytically. The simulation work of Oxtoby et al.[5] amply demonstrated the complexity of the correlations and cross correlations of these two terms; even then, that study was restricted to only one thermodynamic state point (near the boiling point) of liquid N 2 . Perhaps as a consequence of the above, many interesting results have remained ill understood and many important que...

Section: Subquadratic Quantum Number Dependence and Other Anomalies Osupporting

confidence: 89%

Subquadratic Quantum Number Dependence and Other Anomalies of Vibrational Dephasing in Liquid Nitrogen: Molecular Dynamics Simulation Study from the Triple Point to the Critical Point and Beyond

Gayathri

1999

Phys. Rev. Lett.

“…On the other hand, resonance-energy transfer (RT) contribution is found to increase with increasing density due to stronger intermolecular interactions among the closely spaced molecules. Similar experimental observations have been reported earlier for the polarized modes of N 2 O in Xe . The RT contribution, often considered small, is found to be close to 50% of the total near the melting point (also the triple point) and gradually decreases as one moves away from the melting point (MP).…”

Section: Resultssupporting

confidence: 88%

Computer Simulation Study of the Density and Temperature Dependence of Fundamental and Overtone Vibrational Dephasing in Nitrogen: Interplay between Different Mechanisms of Dephasing

Gayathri

1999

J. Phys. Chem. A

Vibrational phase relaxation of the fundamental and the overtones of the N−N stretch of nitrogen in pure nitrogen has been studied by extensive molecular dynamics simulations. The thermodynamic state points simulated include states near the melting point, the boiling point, and the critical point, a normal liquid away from the transition, and also supercritical nitrogen. The simulations provide the following results. (1) The well-known result of Clouter and Kiefte (J. Chem. Phys. 1977, 66, 1736) on the pronounced insensitivity of vibrational phase relaxation of the fundamental to the change in thermodynamic conditions from the triple point (TP) to beyond the boiling point (BP) is found to originate from a competition between density relaxation and resonant energy transfer terms. The latter becomes increasingly important as the melting point is approached. (2) It is found that the experimentally observed sharp rise in the relaxation rate near the gas−liquid critical point (CP) can be attributed at least partly to the sharp rise in the contribution of vibration−rotation coupling. (3) The sharp rise in the vibration−rotation coupling in turn leads, in an unusual way, to a substantial subquadratic quantum number dependence of the overtone dephasing rate near the critical point and in supercritical fluids. The quantum number dependence, however, is found to be quadratic in the condensed phase. (4) The quantum number dependence of overtone dephasing is found to be critically dependent on the separation of time scales between the relaxations of the frequency modulation time correlation function and the normal coordinate time correlation function. The two decays must overlap to observe a significant subquadratic quantum number dependence. The latter is found to occur in the supercritical fluid state. (5) In the absence of a clear separation of time scales between the frequency modulation and the normal coordinate time correlation functions and because of the pronounced Gaussian decay of the latter, the Kubo−Oxtoby method of correlating the motionally narrowing limit with a homogeneous line shape becomes ambiguous. (6) An interesting crossover behavior across the liquid−gas phase transition region is observed in the density−temperature dependencies of the overtone dephasing rate. This crossover is most pronounced for higher overtones. (7) Although the simulation results reproduce the experimental data semiquantitatively (within 40% in most cases) and get the trends correct, quantitative agreement has not been achieved. We attribute this to the large number of terms (correlations and cross-correlations) which contribute to dephasing. In addition, the change of pair intermolecular potential with the thermodynamic state may itself play an increasingly important role, particularly in supercritical fluids.

“…This figure is similar to the one observed experimentally (see figure 4 of Ref. [7]). It is interesting to note the sharp rise in the dephasing rate as the CP is approached.…”

supporting

confidence: 91%

“…They measured the Raman spectra along the triple point to the critical point and the behaviour of the lineshape as the critical point is approached from above. Recently Musso et al [7] measured the temperature dependence of the lineshape parameters (i.e shift, width and asymmetry) both along the coexistence and the critical isochore of liquid nitrogen and found that the temperature dependent linewidth (Γ) is λ shaped. The lineshape was found to undergo a change from Lorentzian (away form T c ) to Gaussian (near T c ).…”

mentioning

confidence: 99%

“…Thus, the rise and fall of dephasing rate arises partly from the rise and fall in the density and the vibration-rotation terms. A crossover from Lorentzian-like to Gaussian lineshape can happen when the usually large separation in the time scales of decay of C ω (t) and C Q (t) [7,12] ceases to exist and the two time correlation functions begin to overlap. Indeed, the computed lineshape becomes Gaussian near the from CP.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Vibrational Phase Relaxation along the Critical Isochore of Nitrogen: The Role of Local Density Fluctuations in the Rate Enhancement

Roychowdhury

2003

Phys. Rev. Lett.

Vibrational dephasing of the nitrogen molecule is known to show highly interesting anomalies near its gas-liquid critical point. Here we present theoretical and computational studies of the Raman linewidth of nitrogen along the critical isochore. The linewidth is found to have a lambda-shaped temperature dependence near the critical point. As observed in experimental studies, the calculated line shape becomes Gaussian as the critical temperature (T(c)) is approached. Both the present simulation and a mode coupling theory analysis show that the slow decay of the enhanced density fluctuations near the critical point, probed at the subpicosecond time scales by vibrational frequency modulation, along with an enhanced vibration-rotation coupling, are the main causes of the observed anomalies.