Experiments and MD Simulations

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) >=VkBTT

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

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  it  2N Sinc(Q,)  R() Sinc (Q,)   FS(Q,t)e dt dd 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   01  

 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. Broccio, C. Corsaro, A. Faraone, L. Liu, Proc. Nat. Acad. Sci. USA D T /T const 103, 12974-12978 (2006) [cited 48] Experimental evidence, obtained from NMR and FSC QENS, of a well defined decoupling of transport FSC  properties (the self-diffusion coefficient and the average translational relaxation time), which implies the breakdown of the Stokes-Einstein relation. We further show that such a non- monotonic decoupling reflects the characteristics of the recently observed dynamic crossover, at FSC around 225K (FSC), between the two dynamical behaviors known as fragile and strong, which is a consequence of a change in the hydrogen bond structureJung, Y.-J., ofGarrahan, liquid J.water. P. & Chandler, D. (2004) Phys. Rev. E 69, 061205-1-7. (discusses the fractional SE relation) SER This paper has been awarded the annual Cozzarelli Prize of 2006 by the PNAS editorial board for its outstanding scientific excellence and originality. New Wide Dynamic Range BASIS at SNS

BASIS is a backscattering spectrometer well suited for probing diffusive and relaxational motions of glassy materials, but can also be effectively used for studying some types of collective excitations in condensed matter, such as boson peak. In the quasi-elastic regime of operation, BASIS can be used to probe dynamic processes on the pico- to nano-second time scale. Model Analysis (RCM) of the QENS Spectra Measured by BASIS at SNS

f (Q)(E)   I(Q,E)  N   R(Q,E) (1 f (Q))  FT {FH (Q,t)}

  t  FH (Q,t)  FT (Q,t) F S (Q,t) exp   (Q, T )

The asymmetric resolution function  R(Q,E) was fitted as a sum of 4 gaussians

Dynamic Susceptibility of Supercooled Water and Its Relation to the Dynamic Crossover Phenomenon Y. Zhang, P. Baglioni & S.H. Chen et al., Phys. Rev. E 79, 040201(R) (2009) Three Ways of Estimating the

Crossover Temperature TL Y. Zhang, P. Baglioni & S.H. Chen et al., Phys. Rev. E 79, 040201(R) (2009) Water confined in C-S-H gel of aged Portland cement paste  FS (Q,t)  t   ln (Q,T ) T (Q,t)   FS (Q,t)  T 2 T (Q,T ) (1/T )

 The crossover phenomenon of water confined in aged Portland cement paste. Top) Arrhenius plot of the alpha-relaxation time extracted by QENS data analysis; Middle) The slope of the Arrhenius Plot, showing a peak at the crossover temperature

TL, which is coincident with the heat-flow peak of the DSC cooling scan; Bottom) DSC heat-flow curve of the cooling scan. The substantial heat capacity peak of supercooled water confined within pores of silica gel. The pore size is around 3

nm. Note that the peak position is at TL = 227 K, identical to the one in the DSC cooling scan in the left figure.

Ref: Maruyama S, Wakabayashi K and Oguni M “Thermal Properties of Supercooled Water Confined within Silica Gel Pores” 2004

Slow Dynamics in Complex Systems: 3rd International Symposium, edited by Tokuyama M and Oppenheim I

S H Chen, Y Zhang, M Lagi, S H Chong, P Baglioni and F Mallamace “Evidence of dynamic crossover phenomena in water and other glass-forming liquids: experiments, MD simulations and theory”, J. Phys:condens. Matter 21, 504102 (2009)

The Adam-Gibbs Theory predicts a Dynamic Crossover (change of slope) in the

Arrhenius Plot whenever Cp has a Peak

Adam-Gibbs Theory Configurational Entropy

 A T cp(T ) ln  where Sconf T  T0  dT   T TS T  T T0 T   0 conf  0

Since the Arrhenius Plot of a quantity X is ln(X) vs 1/T, its slope is given by  dln(X)/d(1/T): according to the Adam-Gibbs Theory,

d ln  /  d ln  /  d ln / 0 A  0  0  implies  d 1/ T d 1/ T d1/ T Sconf T  T0     T Tc T Tc

Therefore, assuming that the specific heat

 has a sharp peak at Tc , the slope is larger before Tc and smaller after, as displayed in the picture (in the example, Tc = 240 K).

Inelastic neutron scattering spectra of a 3-D confined water in aged cement paste measured from 300 K down to 180 K in steps of 20 K. A well-defined boson peak at about 5 meV starts building up below the dynamic crossover temperature

TL = 230 ± 10 K (between the cyan and yellow curves). A Bulk Water Model (TIP4P-Ew) MD Gives Similar Results Y. Zhang, P. Baglioni & S.H. Chen et al., Phys. Rev. E 79, 040201(R) (2009) k L. Berthier, G. Biroli, J. P. Bouchaud, L. Cipelletti, D. El Masri, D. B 2 2  4 Q,t T T Q,t L'Hote, F. Ladieu, M. Pierno Science 310, 1797 (2005) cp

 Left: projection in the xy plane of the snapshot of the water configuration inside the silica cavity at T = 220 K. A portion of the silica surface is shown. The larger spheres are silicon atoms, the darker are acidic hydrogens. Right: density profile of oxygen atoms of water along the pore at T = 300 K.

"Dynamic crossover in supercooled confined water: understanding bulk properties through confinement." Gallo, Paola; Rovere, Mauro; Chen, Sow-Hsin, to appear in J. Phys. Chem. Lett. 2010 Self-intermediate scattering functions (SISF) of the oxygen atoms of the free water for Q = 2.25 Å-1 T = 300K (bottom) to T = 190K (top). The dashed lines are the fit to stretched exponential law. Inset: SISF of the oxygen atoms of all the water molecules for Q = 2.25 Å-1 for a selected set of temperatures. "Dynamic crossover in supercooled confined water: understanding bulk properties through confinement." Gallo, Paola; Rovere, Mauro; Chen, Sow-Hsin, J. Phys. Chem. Lett. 2010 1, 729-733. Arrhenius plot of the relaxation time as a function of 1000/T . At high temperature, below 300K, the points are fitted with the FVT formula 2 (bold line). At low temperature the fit is done with the Arrhenius function (long dashed line). Inset: inverse temperature derivative of the logarithm of tau. "Dynamic crossover in supercooled confined water: understanding bulk properties through confinement." Gallo, Paola; Rovere, Mauro; Chen, Sow-Hsin, J. Phys. Chem. Lett. 2010 1, 729-733. Dynamic response functions calculated for all the temperatures investigated. The

temperature of the highest curve corresponds to TL. Inset: specific heat of the system as function of inverse temperature. "Dynamic crossover in supercooled confined water: understanding bulk properties through confinement." Gallo, Paola; Rovere, Mauro; Chen, Sow-Hsin, J. Phys. Chem. Lett. 2010 1, 729-733. Fragile-to-Strong Crossover in -phenyl-o-cresol

LAUGHLIN and UHLMANN, “VISCOUS FLOW IN SIMPLE ORGANIC LIQUIDS”, J. Phys. Chem. (1972) vol. 76, pp. 2317

4 O-terphenyl Dynamic Crossover Phenomenon

(Top) Arrhenius plot of the inverse of the self- diffusion constant; (middle) Arrhenius plot of the viscosity; (bottom) specific heat at constant pressure. The dotted pink lines represent the fit of the self-diffusion and viscosity data with a VFT equation at high temperatures; the green continuous lines are the fit with an Arrhenius law at low temperatures. In each case, Tx is defined by the peak of the specific heat.

Mapes M K, Swalin S F and Ediger M D 2006 J. Phys. Chem. B 110 507 (for self-diffusion coefficient)

Laughlin W T and Uhlmann D R 1972 J. Phys. Chem. 76 2317 (for viscosity and specific heat) The dynamic crossover temperature is perhaps as important as the glass transition temperature: Evidence from liquid transport coefficients (to be published)

Francesco Mallamace, Caterina Branca, Carmelo Corsaro, Nancy Leone, Jeroen Spooren, Sow-Hsin Chen, and H Eugene Stanley

Lower inset: the onset of the breakdown of the SE law for 9 liquids analyzed. Upper inset: the breakdown of the DSE law for 6 liquids. In both cases the breakdowns occur just below the corresponding crossover temperature, identified using the power law approach. The main plot shows a scaled representation of the fractional SE and of the fractional DSE, lower and upper data respectively. In both cases, for all the liquids studied, the scaling exponent takes almost the same value, 0.85±0.02. We note that the onset of the breakdown of the fractional SE and DSE takes place at the same value of viscosity, 1000 Poise. These data demonstrate a remarkable degree of universality in the temperature behavior of the transport properties of supercooled liquids.

Predictions of the e-MCT for a Lennard-Jones system. a), b) and c) Self-intermediate scattering functions at q=1.0, 7.3 and 10.0 (in a reduced unit) respectively, for  = 1-T/TC = -0.10, -0.05, -0.03, -0.01, 0.01, 0.05, and 0.10 from left to right. q = 7.3 corresponds to the first peak in the structure factor, while q = 10.0 is the first minimum. d) Dynamic response function, T(q,t), for q = 7.3. The peak height, T*(Q), increases towards TC and decreases after, as observed in experiments of confined water and MD simulations of bulk water. S H Chen, Y Zhang, M Lagi, S H Chong, P Baglioni and F Mallamace, “Evidence of dynamic crossover phenomena in water and other glass-forming liquids: experiments, MD simulations and theory”, J. Phys:condens. Matter 21, 504102 (2009) Predictions of the e-MCT. The black dots are the incoherent -relaxation

times i(Q,T) calculated from e- MCT for a series of temperatures. The red lines are the best fits to the Q-dependence of the incoherent -relaxation time with the power law expression contained in the Relaxing Cage Model: - i(Q,T) =0(T)(aQ)

S H Chen, Y Zhang, M Lagi, S H Chong, P Baglioni and F Mallamace, “Evidence of dynamic crossover phenomena in water and other glass-forming liquids: experiments, MD simulations and theory”, J. Phys:condens. Matter 21, 504102 (2009)

Predictions of the e-MCT.

The black dots are the coherent -relaxation times

c(Q,T) calculated from e-MCT for a series of temperatures. The red lines are the best fits to the Q- dependence of the coherent -relaxation time with the power law expression : - c(Q,T) = 1(T)(aQ) S(Q).

S H Chen, Y Zhang, M Lagi, S H Chong, P Baglioni and F Mallamace, “Evidence of dynamic crossover phenomena in water and other glass- forming liquids: experiments, MD simulations and theory”, J. Phys:condens. Matter 21, 504102 (2009)

The power law exponents of the coherent and incoherent alpha-relaxation times, as a function of  = 1-T/TC. Asymptotically, the exponents of the power-law Q-dependence of i(Q) and c(Q) become the same i = c = 1.5 at low temperatures, providing an evidence of the strong coupling between self and collective motions below Tc. Evidence of Dynamic Crossover from extended MCT

The α-relaxation time q of the coherent Self-diffusion constant D versus the density correlator at the structure factor inverse temperature Tc/T . The solid peak q = 7.3 versus the inverse curve denotes the result from the temperature Tc/T . The solid curve denotes extended MCT. the result from the extended MCT.

S-H Chong, S-H Chen, F Mallamace, J. Phys.: Condens. Matter 21 (2009) 504101 Top and middle panels: Scaling plot of

Q/Q,Tc and /(Tc) vs. Tc/T of the normalized -relaxation time coh(Q), inc(Q) and viscosity calculated from the eMCT. When their Q-dependence is scaled out in this way, the coherent and incoherent -relaxation times and the viscosity behave essentially the same way, showing a similar crossover phenomenon.

Bottom panel: The slope in the Arrhenius plot of the viscosity shows a

sharp peak at Tc. Therefore it is reasonable to locate the Tc by the peak position of the maximum slope in the Arrhenius plot of the viscosity.

Water Density Distribution in the Pores of MCM-41-S R. Mancinelli et al. J. Phys. Chem. Lett. 2010, 1, 1277–1282

Water density profile in the cylindrical pore Reconstructed P(Q) (1) Our measurement of sample hydrated at the match point (with mole ratio of [D2O]:[H2O]=0.66:0.34) show no evidences of the voids, shown in the above reference.

Measured SANS Intensity Distribution for Water in the Cylindrical Pores of MCM-41-S

(2) Ricci’s model allows water to penetrate 6Å into the silica wall, which cannot be simply explained by the roughness of the wall.

(3) Ricci’s extracted density profiles cannot reproduce the low-Q

scattering intensity distribution. Left: Realistic density distributions in the silica pore. Right: P(Q) of the two density distributions.

Ricci’s simulated Core-Shell distribution SANS Experiment density profile and uniform distribution (shown above)