Dynamic Crossover Phenomena in Confined Water and Its Relation to the Liquid-Liquid Critical Point: Experiments and MD Simulations Sow-Hsin Chen ([email protected]) Department of Nuclear Science and Engineering, MIT Collaborators: Yang Zhang (MIT), Marco Lagi (MIT), Xiangqiang Chu (MIT) Antonio Faraone (NCNR), Bill Kamitakahara (NCNR), Chung-Yuan Mou (NTU), Kao-Hsiang Liu (NTU), Song-Ho Chong (Institute for Molecular Science, Japan) Francesco Mallamace (Messina), Piero Baglioni (Florence), Emiliano Fratini (Florence) This project is funded by DE-FG02-90ER45429, U.S. DOE. International School of Physics "Enrico Fermi” Summer Course "Complex materials in physics and biology”, 6.29–7.9, 2010 Outline Experimental evidence of the existence of a dynamic crossover and a L-L critical point in supercooled confined water: • Discovery of a density minimum and a peaking in the thermal expansion coefficient. An extensive series of EOS studies of 1-D confined water, leading to a plaucible phase behavior. • Observation of a dynamic crossover in alpha-relaxation times of 1-D, 2-D and 3-D confined water by QENS studies. • Supporting evidence of the dynamic crossover from MD simulations of bulk and confined water and from an extended mode-coupling theory of L-J system. • Evidence of dynamic crossover phenomena in other glass- forming liquids Phase Diagram and Polymorphism of Water and Ice 15 Ice Polymorphs 2 Amorphous Ices LDA & HDA HDA,VHDA Widom Line LDA C2 C1 (HDA)=1.17 g/cm3 (VHDA)=1.25 (LDA)=0.94 t (Ih)=0.92 (Ic)=0.92 (C1)=0.322 P-T Phase Diagram of Superheated Water– Definition of the Widom Line Widom Line M. A. Anisimov, J. V. Sengers, and J. M. H. Levelt Sengers, “Near-critical behavior of aqueous systems,” in Aquesous Systems at Elevated Temperatures and C Pressures: Physical Chemistry in water, Steam and Hydrothermal Solutions, D.A. Palmer, R. Fernandez- Prini and A.H. Harvey (Eds.), 2004 Elsevier Ltd. Peaking of Thermodynamic Response Function when Crossing Widom Line above TC Thermal expansion coefficient vs density Isothermal Compressibility Thermal-expansion Isobaric Specific Coefficient Heat Capacity The reference quantities are taken at pressures of the saturated liquid at 25 ºC. M. A. Anisimov, J. V. Sengers, and J. M. H. Levelt Sengers, “Near-critical behavior of aqueous systems,” in Aquesous Systems at Elevated Temperatures and Pressures: Physical Chemistry in water, Steam and Hydrothermal Solutions, D.A. Palmer, R. Fernandez-Prini and A.H. Harvey (Eds.), 2004 Elsevier Ltd. Anomalous Thermodynamic Properties of Low Temperature Water <(S V)>=VkBT <(S)2>=Nk c 2 B p <(V) >=VkBTT A schematic comparison of the isobaric temperature dependence of the density , thermal expansion coefficient , isothermal compressibility T and isobaric heat capacity cp for water and a simple liquid. [P. G. Debenedetti, J. Phys.: Condens. Matter 15, R1669 (2003)] H. E. STANLEY “Mysteries of Water” Les Houches Lecture, May 1998 Figure 1: Schematic illustration indicating the various Figure 2: Generalization of Fig. 1 to incorporate a second phases of liquid water (color-coded) that are found at control parameter, the pressure. The colors are the same atmospheric pressure. Courtesy of Dr. O. Mishima. as used in Fig. 1. Courtesy of Dr. O. Mishima. Differential scanning calorimetry (DSC) data show no freezing peaks for pore diameters below 19 Å a d 1-D cylindrical tubes arranged in a hexagonal structure. d = sqrt(3)/2*a SEM and microtome TEM micrographs of micron size grains of MCM-41 powder sample. Within each grain it is a perfect 2- d hexagonal lattice without defects. MCM-41 Powder and SANS Intensity Distribution Powder-like MCM- 41 sample Porod’s Law The curve of (d/dT)P vs T for D2O shows a peak at TL= 240 ± 5 K T P 240±5 K P = 1 atm MCM-41S-15 Observation of the density minimum in deeply supercooled confined water D. Liu, Y. Zhang, C.-C. Chen, C.-Y. Mou, P. Poole, and S.-H. Chen, PNAS 104 9570 (2007) Density Extrema in H2O by Optical Method Mallamace, F.; Branca, C.; Broccio, M.; Corsaro, C.; Mou, C.-Y.; Chen, S.-H. PNAS 107 (2007) 18387-18391 MD Simulation of Density vs Temperature along Different Isobars of TIP5P-E Water Phase diagram for stable and supercooled liquid TIP5P-E water. The spacing between different contour colors corresponds to a pressure drop of 25MPa. Selected isobars are indicated. The heavy dashed line denotes the high density/low density liquid (HDL/LDL) coexistence line. The HDL/LDL critical point is located at C* with T*=210 K, P*=310 MPa, and *=1.09 g/cm3. Darker shading indicates the LDL basin. D. Paschek, PRL 94, 217802 (05) Elastic Diffraction Measurements of Supercooled Water Confined in MCM-41-S-15 Y Zhang, A Faraone, W Kamitakahara, K-H Liu, C-Y Mou, J Leao & S-H Chen*, Equation of State of Nanoconfined Water (to be published). Method for Detection of the Liquid-Liquid Phase Transition Y Zhang, SH Chen, et al, to be published. Evidence of the 1st-order Liquid-Liquid Phase Transition Y Zhang, SH Chen, et al, to be published. Density and Expansion Coefficient of Nanoconfined Water under Pressure Y Zhang, A Faraone, WA Kamitakahara, KH Liu, CY Mou, JB Leao, S Chang, SH Chen, to be published. Kink in density profile Discontinuity in Expansion Coefficient Y Zhang, A Faraone, WA Kamitakahara, KH Liu, CY Mou, JB Leao, S Chang, SH Chen, to be published. Determined Phase Diagram from Density Measurements Y Zhang, A Faraone, WA Kamitakahara, KH Liu, CY Mou, JB Leao, S Chang, SH Chen, to be published. 2nd-order and 1st-order phase transition COHEN. QUANTUM STATISTICS AND LIQUID HE-3-HE-4 MIXTURES. Science (1977) vol. 197 (4298) pp. 11-16 Density and Expansion Coefficient of Liquid Helium-4 Definition of a 2nd-order phase transition Density Expansion Coefficent Tl Kink at Tl Niemela and Donnelly. DENSITY AND THERMAL-EXPANSION COEFFICIENT OF LIQUID-HE-4 FROM MEASUREMENTS OF THE DIELECTRIC-CONSTANT. J Low Temp Phys (1995) vol. 98 (1- 2) pp. 1-16 Specific heat capacity of Liquid Helium-4 LIPA et al. HEAT-CAPACITY AND THERMAL RELAXATION OF BULK HELIUM VERY NEAR THE LAMBDA POINT. Physica B (1994) vol. 197 (1-4) pp. 239-248 Phase Diagram of He3- Lambda line normal He3-He4 He4 Mixtures Tricritical Point Superfluid He3-He4 Coexistence region GRAF et al. PHASE SEPARATION AND SUPERFLUID TRANSITION IN LIQUID HE3-HE4 MIXTURES. Phys Rev Lett (1967) vol. 19 (8) pp. 417-& Quasi- and Inelastic Neutron Scattering 2 momentum = hk energy = (hk) /(2m) Ef, kf k=2/l Ei , ki Q = ki - kf Sample h = Ei - Ef 2 d H H k f 1 it 2N Sinc(Q,) R() Sinc (Q,) FS(Q,t)e dt dd 4 ki 2 The dynamic structure factor Sinc(Q,) is proportional to the probability that a neutron is scattered with a momentum transfer Q and an energy transfer to the sample. It is a Fourier transform of the intermediate scattering function FS(Q, t). Spectrometers in NIST Disk Chopper (DCS) and Backscattering (HFBS) spectrometers with resolutions 20 meV and 0.8 meV respectively, have Q ranges: 0.2 Å-1 - 2.0 Å-1, which is broad enough to simultaneously measure both translational and rotational dynamics of the water molecules. I am grateful to NCNR for letting me use up about 30 weeks of beamtime to do these experiments using these two spectrometers over 3 year period. Model for Single-Particle Dynamics in Supercooled Water S. H. Chen, C. Liao, F. Sciortino, P. Gallo, and P. Tartaglia, Phys. Rev. E. 59 6708 (1999) [cited 71] “Formulation and Experimental Verification of the Relaxing Cage Model of Supercooled Water” F (Q,t) Fs (Q,t)exp t/ (Q) T T T T (Q) 0 aQ ; a 0.5Å T 01 Relaxational Dynamics of Supercooled Water in Porous Glass J.-M. Zanotti, M.-C. Bellissent-Funel, and S.-H. Chen, Phys. Rev. E. 59 3084 (1999) [cited 132] Fragile-to-Strong Dynamic Crossover under Pressure Pressure vs. Temperature Phase Diagram of H2O CL-L An extensive quasi-elastic neutron scattering experiment as a function of temperature at high pressures, by Chen’s Group at MIT, identifies the approximate location of the second (liquid-liquid) critical point of water, CL-L, for the first time. L. Liu, S.H. Chen, A. Faraone, C.W. Yan and C.Y. Mou, Phys. Rev. Lett. 95, 117802 (2005) “Relation between the Widom Line and the Strong-Fragile Dynamic Crossover in Systems with a Liquid-liquid Phase Transition”, L. Xu, P. Kumar, S.V. Buldyrev, S.H. Chen, P.H. Poole, F. Sciortino, H.E. Stanley, PNAS 102, 16558 (2005). FSC shown by 1/D of confined water in MCM-41-S-14 and MCM-41-S-18 EA= 4.0 Kcl/Mol measured by NMR F. Mallamace, M. Broccio, C. Corsaro, A. Faraone, U. Wanderlingh, L. Liu, C.-Y. Mou, and S.-H. Chen, “The fragile-to-strong dynamic crossover transition in confined water: NMR results,” J. Chem. Phys. 124, 161102-161105 (2006). FSC shown by <T> of confined water in MCM-41-S-14 and MCM-41-S-18 EA= 5.4 Kcal/Mol measured by QENS A. Faraone, L. Liu, C.-Y. Mou, C.-W. Yen, and S.-H. Chen, “Fragile-to-strong Liquid Transition in Deeply Supercooled Confined Water,” J. Chem. Phys. Rapid Communication 121, 10843-10846 (2004). “New Evidence of the Breakdown of Stokes-Einstein Relation near Fragile-to-Strong Dynamic Crossover in supercooled water” The Violation of Stokes-Einstein Relation in Supercooled water S.-H. Chen, F. Mallamace, C.-Y. Mou, M.