Dynamic crossovers in hydration water at 252 and 181 K from experiments, theory and simulations G. Franzese (U. Barcelona) V. Bianco (U. Barcelona) M. G. Mazza (Max-Plank Gottingen) K. Stokely (Columbia U.) F. Bruni (Roma Tre) H. E. Stanley (Boston U.)
Thanks to M. Bernabei (U. Barcelona) S. V. Buldyrev (Yeshiva U.) K. A. Dawson (U.C. Dublin) A. De Simone (Imperial C.) H. Hermann (ETH Zurich) T. Kesselring (ETH Zurich) P. Kumar (Rockfeller U.) F. Leoni (U. Barcelona) E. Lescaris (Boston U.) P. Martin (U. Birmingham) S. Pagnotta (Donostia) I. Santamaría-Holek (UNAM) F. de los Santos (U. Granada) E. G. Strekalova (MIT) E. Valsami-Jones (U. Birmingham) O. Vilanova (U. Barcelona) P. Vilaseca (Trinity C.) L. Xu (Peking U.) ...
Why water has dynamic crossovers? Water hydrating biological Water in surfaces nanoconfinement
Water hydrating lysozyme h=0.3 at low hydration (and low T) forms a water monolayer with no translational diffusion but with rotational diffusion and HB dynamics
An Hamiltonian model for a water monolayer Many-body model for water Franzese, Marqués, Stanley PRE (2003) Kumar, Franzese, Stanley, PRL (2008) Strekalova, Mazza, Stanley, Franzese PRL (2011) Mazza, Stokely, Pagnotta, Bruni, Stanley, Franzese PNAS (2012)
An Hamiltonian model for a water monolayer Many-body model for water Franzese, Marqués, Stanley PRE (2003) We introduce a density field n(x,y) Kumar, Franzese, Stanley, PRL (2008) to identify water-like and gas-like cells Strekalova, Mazza, Stanley, Franzese PRL (2011) Mazza, Stokely, Pagnotta, Bruni, Stanley, Franzese PNAS (2012)
An Hamiltonian model for a water monolayer Many-body model for water vdW E=U(r) E = U(r) interaction
A many-body model for a water monolayer Many-body model for water Directional and covalent component of the hydrogen bond J The state of a water molecule is described introducing 4 bonding variables E=U(r)-JN HB E = U(r) - J N HB cfr. Sastry et al. PRE (1996)
An Hamiltonian model for a water monolayer Many-body model for water 1st shell (five-body) J σ interaction Coopertivity (Quantum effect) E=U(r)-J-J σ E = U(r) - J N HB - J σ N σ V=Nv 0 +N HB v HB V = Nv 0 + N HB v HB
Phase diagram and Anomalies of a hydration monolayer D Supercooled Liquid Water 0.15 iso-D line iso-D line 0.13 0.12 0.1 0.11 0.1 D || (A 2 /ps) D || (A 2 /ps) 0.05 0.09 D-maxima D-maxima 0.08 T 0 T 0 Liquid-Gas Liquid-Gas 0.07 0 0.06 D-minima D-minima 0.05 0.04 TMD TMD 0.03 L-L L-L 0.02 0.35 c P -max c P -max 0.25 75% Density minima Density minima P (GPa) 0.15 hydrated 1400 Amorphous Glassy Water 1000 0.05 600 (Sub-diffusive) surface 200 T (K) F. de los Santos & G. Franzese J. Phys. Chem B 115, 14311 (2011) G. Franzese, et al. JPCM 14, 2201 (2002); PRE 67, 011103 (2003); G. Franzese, et al. JPCM 19, 205126 (2007); JPCM 20, 494210 (2008)
Comparison with experiments for hydrated Myoglobin at low hydration (h=0.35): Subdiffusion at 320K and below Settles & Doster, Faraday Disc (1996), h=0.35 Simulations 0.7 ~ t NS Experiments Result: Subdiffusion is not a consequence of heterogeneity in water-surface interaction, but results from increasing H-bonds correlation F. de los Santos & G. F., J.Phys. Chem B 115, 14311 (2011)
At high T: Diffusion maxima and minima Average N HB /molecule Average (free volume)/molecule are both monotonic!! F. de los Santos & G. F., PRE 85, 010602(R) (2012)
Theoretical explanation Joint probability: to have molecules with at least one free n.n. cell + to break bonds + to have a given enthalpy H Simulations at a given (P , T) Theory Anomalous Diffusion results from competition between H-bonds breaking and free-volume in Cooperative Rearranging Regions of 1nm size Experiments show change in diffusion for confinement below 1nm !! F. de los Santos & G. F., PRE 85, 010602(R) (2012)
Glassy Dynamics at low T (< TminD < TMD) G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) LargeCAVITY >P(C) ≈ T(MD) <T(C) >T(C) # H bonds(T)
Glassy Dynamics at low T (< TminD < TMD) G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) GLASS LargeCAVITY >P(C) ≈ T(MD) <T(C) >T(C) # H bonds(T) GLASS <<P(C) ≈ T(MD) <T(C) >T(C)
Glassy Dynamics at low T (< TminD < TMD) G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) GLASS LargeCAVITY >P(C) DEHYDRATION large τ β =0.7 ≈ T(MD) <T(C) >T(C) Small Cavities <P(C) # H bonds(T) GLASS <<P(C) ≈ T(MD) <T(C) >T(C)
Glassy Dynamics at low T (< TminD < TMD) G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) GLASS LargeCAVITY >P(C) DEHYDRATION large τ β =0.7 Prediction <T(C) LLCP ≈ T(MD) >T(C) β [>T(C)]=0.8, ≈ P(C) β [<T(C)]=0.4 !!! LLCP Max heterogeneity as effect of cooperativity Small Cavities <P(C) # H bonds(T) GLASS <<P(C) ≈ T(MD) <T(C) >T(C)
Comparison with experiments: Myoglobin at low hydration (h=0.35): P<<P(C), T<T(C) P<P(C) β [P(C);<T(C)]=0.4 Doster, BBA (2010), h=0.34 G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) Settles & Doster, Faraday Disc (1996), h=0.35
Comparison with experiments: Myoglobin at low hydration (h=0.35): P<<P(C), T<T(C) GLASS Prediction P<P(C) DEHYDRATION β [>T(C)]=0.8, large τ β [<T(C)]=0.4 !!! β =0.7 Max heterogeneity as effect β [P(C);<T(C)]=0.4 of cooperativity Doster, BBA (2010), h=0.34 LLCP G.Franzese and F. de los Santos J. Phys. Cond Mat. 21, 504107 (2009) Settles & Doster, Faraday Disc (1996), h=0.35
TWO MAXIMA IN RESPONSE FUNCTIONS V. Bianco & G.F. arXiv1212.2847B
Exploring the Phase Diagram Two maxima in response functions Two loci of extrema in the thermal expansivity α P along isotherms and isobars “diverging” maxima STRONGER MINIMUM Valentino Bianco & G.F. arXiv1212.2847B
Exploring the Phase Diagram Two loci of extrema in the thermal expansivity α P along isotherms and isobars LIQUID-LIQUID PHASE TRANSITION LIQUID-LIQUID CRITICAL POINT Valentino Bianco & G.F. arXiv1212.2847B
Order Parameter and Scaling Behavior Gibbs Free Energy Using the mixed-field approach we define the order parameter as m= ρ +sE y t i s n e D Energy In the thermodynamic limit the probability distribution of The order parameter at the critical point approaches the 2D-Ising model critical distribution Valentino Bianco & G.F. arXiv1212.2847B Wilding, Binder Phys A (1996)
Increasing confinement: increasing fluctuations (2D-3D Crossover) Kullback-Leibler deviation Crossover at L/h=50 !! In water stronger confinement could lead to bulk-like behavior for the fluctuations V. Bianco & G.F. arXiv1212.2847B Liu-Panagiotopoulos-Debenedetti deviation
Confining Effect: Critical Crossover Increasing confinement: increasing fluctuations (2D-3D Crossover) For LIQUID-GAS CRITICAL POINT of LJ system the crossover is observed for ( Liu et al 2010) L/h ~ 5 While at the LLCP the crossover occurs at L=25 nm L/h = 50!!! The high cooperative behavior of HB enhances the spreading of critical fluctuations along the network. V. Bianco & G.F. arXiv1212.2847B
Tuning the Cooperativity Strength Singularity-Free Liquid-liquid Crit. Point Crit. Point-Free TMD TMD TMD Stanley & Teixeira1980 Poole et al. 1992 Angell 2008 Sastry et al. 1996 ALL THE SCENARIOS FROM THE SAME MECHANISM
Parameters from Experiments: Liquid-Liquid Critical Point (LLCP) From Experiments: from Ih - liq. => J σ ≈ 1 kJ/mol 4 ε≈ 5.5 kJ/mol (J σ /4 ε≈ 0.2) E HB ( ε , J, J σ ) ≈ 5.8 kJ/mol => J ≈ 6-12 kJ/mol (J/4 ε≈ 1.1-2) * LLCP predicted in a region inaccessible in experiments so far
Widom line? Locus of maxima of correlation length Valentino Bianco & G. Franzese. arXiv1212.2847B Valentino Bianco PhD thesis (2013)
Correlation Length and Widom Line WIDOM LINE: LOCUS OF MAXIMA OF ξ Valentino Bianco & G.F. arXiv1212.2847B Valentino Bianco PhD thesis (2013)
Widom line consistent with fitting from experiments, Weak Cp Max line consistent with “Widom line” from simulations TIP4P/2005 Abascal and Vega JCP (2010) Fuentevilla and Anisimov PRL (2006) Bianco & Franzese arXiv1212.2847B
Holten and Anisimov SciRep (2012) TIP4P/2005 Holten et al. arXiv:1302.5691 (2013) Vega & Abascal JCP (2010) Kumar et al. Bianco & Franzese PNAS (2007) arXiv1212.2847B mW Valentino Bianco PhD thesis (2013)
Connecting dynamics and thermodynamics
Crossing the line of weak Max Cp Kumar, Franzese Franzese and Stanley and Stanley Kumar, Phys. Rev. Lett Lett. 100, . 100, 105701 105701 (2008) Phys. Rev. (2008) w w
Crossing the line of weak Max Cp Kumar, Franzese Franzese and Stanley and Stanley Kumar, Phys. Rev. Lett Lett. 100, . 100, 105701 105701 (2008) Phys. Rev. (2008) w w many HBs few HBs H-Bond Prob.
Crossing the line of weak Max Cp Kumar, Franzese Franzese and Stanley and Stanley Kumar, Phys. Rev. Lett Lett. 100, . 100, 105701 105701 (2008) Phys. Rev. (2008) w w many HBs few HBs H-Bond Prob. Max fluctuation of N HB (single bonds) at C p MAX (weak)
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