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Q-exponential distribution in time correlation function of water hydrogen bonds Campo, Mario G., Ferri, Gustavo L., Roston, Graciela B. Departamento de

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  • Slide 1
  • q-exponential distribution in time correlation function of water hydrogen bonds Campo, Mario G., Ferri, Gustavo L., Roston, Graciela B. Departamento de Fsica. Facultad de Ciencias Exactas y Naturales de la UNLPam. Uruguay 151. Santa Rosa (L.P.) Argentina. UNIVERSIDAD NACIONAL DE LA PAMPA Facultad de Ciencias Exactas y Naturales V Workshop de Mecnica Estadstica y Teora de la Informacin Mar del Plata Abril 2009
  • Slide 2
  • Water structure: Whats hydrogen bond? HB in water is ~90% electrostatic and ~ 10% covalent. HB restricts the water neighboring. The HB direction is that of the shorter O-H (O donor O aceptor ) A B H Hydrogen bond (HB) In water the HB energy ~23.3 kJ mol-1 compared with 492.2148 kJ mol -1 energy in covalent bond.
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  • Two criteria to define HB: Energetic: O-O distance 3.5 O-O interaction energy > E HB Geometric O-O distance 3.5 O-HO angle > HB
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  • Water structure: HB distribution Water is connected by a random tetrahedral network of HB. HB distribution.
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  • Arrhenius behavior of HB depolarized light scattering experiments Molecular dynamics Whats the importance of the hydrogen bonds? Starr F.W., Nielsen J.K., and Stanley H.E., Phys. Rev. Lett., 82, 2294-2297, (1999). Anomalous properties of water are influenced by the behavior of hydrogen bonding. 10 fs20 fs30 fs40 fs residence time = HB is the mean of the distribution of HB lifetimes time t P(t): History-dependent HB correlation function: probability that an initially bonded pair remains bonded at all times up to time t. energetic geometric P(t) can be obtained from simulations by building a histogram of the HB residence times. Measurements of lifetimes are made depolarized light scattering techniques C.J. Montrose, et al., J. Chem. Phys. 60, 5025 (1974).
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  • Behavior of P(t) do not have neither power-law nor exponential behavior. t/ps Starr F.W., Nielsen J.K., and Stanley H.E., Fast and slow dynamics of hydrogen bonds in liquid water, Phys. Rev. Lett., 82, 2294-2297, (1999). T 350-200 K
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  • GROMACS package. System with 1185 SPC/E water molecules. 12 independent systems at different temperatures(213 to 360 K) and 1 atm. Cut-of radius for the interaction potentials 1.3 nm. Berendsens bath of temperature and pressure. 2.5 ns for equilibration. 5 ns aditional simulation results. t simulation = 2 fs. t data collection = 10 fs. Molecular dynamics simulation 0.4238 e -0.8476 e 0.4238 e
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  • P(t) do not have neither power-law nor exponential behavior. T=273 K Dynamics due libration Geometrical definition of hydrogen bond: minimum O-O separation of 3.5 minimum O H O of 145 > 145 < 3.5
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  • We found that P(t) can be fitting with a q-exponential function ln 1 (x) ln(x)
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  • q(T) behavior ~300K q increase with the decrease of T. q~T -1 (T
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  • ~270 K ~300 K Changes in the hydrogen bond structure with temperature 4 HB above the 3 and 2 HB 4 HB between the 3 and 2 HB 4 HB below of 2 HB and 3 HBs
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  • reciprocal relation between HBs and T (similar to q(T) at T>300 K). ~300 K When T decrease, at ~ 300 K 4 HB percentages exceeds that 2 HB structural transition of [4 HB -tetrahedral structure] to [3 HB -2 HB] structure
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  • ~300 K
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  • below 300 K there are a linear correlation between the tretrahedral structure of water and q.
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  • Cage effect qGaussian distribution of the displacement of particles correlated with anomalous diffusion. [Liu and Goree, Phys. Rev. Lett. 100, 055003 (2008)] mean square displacement (MSD) Subdiffusive behavior cage effect Cage effect occurs in SPC/E model simulations [(Chaterjee et al., J. Chem. Phys. 128, 124511 (2008)]. Cage effect increase with the decrease of T
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  • MSD in our MD simulations Cage effect Slope < 1
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  • The non-Gaussian behavior of the displacement of water molecules was studied calculating the time t*, the time at which the non-Gaussian parameter 2 (t) reaches a maximum. The non-Gaussian parameter is Where r 4 (t) and r 2 (t) are the fourth and second moments of the displacement distribution, respectively. 2 (t) is known to be zero for a Gaussian distribution [M.G. Mazza et al. Phys. Rev. E 76, 031203 (2007)]. 2 ( t ) = 3 h r 4 ( t )i 5 h r 2 ( t )i 1
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  • t* is correlated with f (4) for values corresponding to the systems below 300K. It is observed that f(4) ~ (t*) -1/4. The increase of q is also correlated with the increase of the non-Gaussian behavior of water displacement.
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  • The temporal correlation function of hydrogen bonds P(t), has a q-exponential behavior. q have values above 1, below a characteristic temperature. The increase of q is associated with the increase of the probability of two molecules remain bonded during a longer time t. The temperature (~300 K), at which the transition of q ~ 1 to q > 1 occurs, coincides with that at which the tetrahedral structure of water and the cage effect in the MSD begins to prevail. CONCLUSION
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  • Angell C.A., Water: A Comprehensive Treatise, Plenum Press, New York, (1981). Angell C.A. and Rodgers V., Near infrared spectra y the disrupted network model of normal y supercooled water, J. Chem. Phys., 80, 6245-6252, (1984). Berendsen H.J.C., Grigera J.R., Straatsma T.P., The missing term in effective pair potentials, J. Phys.Chem., 91, 6269-6271, (1987). Berendsen H., Postma J., van Gusteren W., Di Nola A. and Haak J., Molecular dynamics with coupling to an external bath, J. Chem. Phys., 81, 3684-3690, (1984). Berendsen H.J.C., van der Spoel D. and Drunen R.V., GROMACS: a message passing parallel molecular dynamics implementation, Comp. Phys. Comm., 91, 43-56, (1995). Cruzan J.D., Braly L.B., Liu K., Brown M.G., Loeser J.G., and Saykally R.J., Quantifying Hydrogen Bond Cooperativity in Water: VRT Spectroscopy of the Water Tetramer, Science, 271, 59-62, (1996). Debenedetti P.G., Metastable Liquids, Princeton University Press, Princeton, (1996). Eisenberg D. and Kauzmann W., The Structure y Properties of Water, Oxford University Press, New York, (1969). Mallamace F., Broccio M., Corsaro C., Faraone A., Wandrlingh U., Liu L., Mou C., and Chen S.H., The fragile-to-strong dynamics crossover transition in confined water: nuclear magnetic resonance results, J. Chem. Phys., 124, 124-127, (2006). Mishima O. and Stanley H.E., The Relationship between Liquid, Supercooled and Glassy Water, Nature, 396, 329-335, (1998). Montrose C.J., Bcaro J.A., Marshall-Coakley J. and Litovitz T.A., Depolarized Rayleigh scattering y hydrogen bonding in liquid water, J. Chem. Phys., 60, 5025-5029, (1974). Luzar A. and Chandler D., Hydrogen bond kinetics in liquid water, Nature, 379, 55-57, (1996a). Luzar A. and Chandler D., Effect of Environment on Hydrogen Bond Dynamicsin Liquid Water, Phys. Rev. Lett., 76, 928-931, (1996b). Sciortino F. and Fornili S.L., Hydrogen bond cooperativity in simulated water: Time dependence analysis of pair interactions, J. Chem. Phys., 90, 2786-2792, (1989). Stillinger F.H., Theory y molecular models for water, Adv. Chem. Phys., 31, 1-102, (1975). Starr F.W., Nielsen J.K., and Stanley H.E., Fast and slow dynamics of hydrogen bonds in liquid water, Phys. Rev. Lett., 82, 2294-2297, (1999). Starr F.W., Nielsen J.K. and Stanley H.E., Hydrogen-bond dynamics for the extended simple point-charge model of water, Phys. Rev. E., 62, 579-587, (2000). Sutmann G., and Vallauri, R., Dynamics of the hydrogen bond network in liquid water, Journal of Molecular Liquids, 9899, 213224, (2002). Tsallis C., Possible generalization of Boltzmann-Gibbs statistic, Journal of Statistical Physics, 52, 479-487, (1988). Walpole R. and Myers R., Probabilidad y Estadstica, 4 Ed. McGraw Hill, Mxico, (1992). Woutersen S., Emmerichs U. and Bakker H., Femtosecond Mid-Infrared Pump-Probe Spectroscopy of Liquid Water: Evidence for a Two-Component Structure, Science, 278, 658, (1997). References
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  • Thank you ! q-exponential distribution in time correlation function of water hydrogen bonds Campo, Mario G., Ferri, Gustavo L., Roston Graciela B. Departamento de Fsica. Facultad de Ciencias Exactas y Naturales de la UNLPam. Uruguay 151. Santa Rosa (L.P.) Argentina.