Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P ≥ 0.16 GPa. The fluctuations of volume apparently diverge at P ≈ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.     

Density and bond-orientational relaxations in supercooled water

ABSTRACT

Recent computational studies have reported evidence of a metastable liquid–liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artefacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artefacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behaviour in the coarse-grained mW model of water. Our findings, therefore, challenge the key physical assumption underlying the competing hypothesis.     

Jamming transition in granular systems

Recent simulations have predicted that near jamming for collections of spherical particles, there will be a discontinuous increase in the mean contact number Z at a critical volume fraction phi(c). Above phi(c), Z and the pressure P are predicted to increase as power laws in phi-phi(c). In experiments using photoelastic disks we corroborate a rapid increase in Z at phi(c) and power-law behavior above phi(c) for Z and P. Specifically we find a power-law increase as a function of phi-phi(c) for Z-Z(c) with an exponent beta around 0.5, and for P with an exponent psi around 1.1. These exponents are in good agreement with simulations. We also find reasonable agreement with a recent mean-field theory for frictionless particles.     

Spatial heterogeneity in liquid–liquid phase transition

Molecular dynamics simulations are performed to investigate the liquid–liquid phase transition(LLPT) and the spatial heterogeneity in Al–Pb monotectic alloys. The results reveal that homogeneous liquid Al–Pb alloy undergoes an LLPT,separating into Al-rich and Pb-rich domains, which is quite different from the isocompositional liquid water with a transition between low-density liquid(LDL) and high-density liquid(HDL). With spatial heterogeneity becoming large, LLPT takes place correspondingly. The relationship between the cooling rate, relaxation temperature and percentage of Al and the spatial heterogeneity is also reported. This study may throw light on the relationship between the structure heterogeneity and LLPT, which provides novel strategies to control the microstructures in the fabrication of the material with high performance.     

Persistence of manifolds in nonequilibrium critical dynamics

We study the persistence probability P(t) that, starting from a random initial condition, the magnetization of a d'-dimensional manifold of a d-dimensional spin system at its critical point does not change sign up to time t. For d'>0 we find three distinct late-time decay forms for P(t): exponential, stretched exponential, and power law, depending on a single parameter zeta=(D-2+eta)/z, where D=d-d' and eta,z are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2 Ising model, P(t) decays as a power law while, for d=3, P(t) decays as a power of t for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.     

Transport properties of supercooled confined water

This article presents an overview of recent experiments performed on transport properties of water in the deeply supercooled region, a temperature region of fundamental importance in the science of water. We report data of nuclear magnetic resonance, quasi-elastic neutron scattering, Fourier-transform infrared spectroscopy, and Raman spectroscopy, studying water confined in nanometer-scale environments. When contained within small pores, water does not crystallise, and can be supercooled well below its homogeneous nucleation temperature T_h. On this basis it is possible to carry out a careful analysis of the well known thermodynamical anomalies of water. Studying the temperature and pressure dependencies of water dynamics, we show that the liquid-liquid phase transition (LLPT) hypothesis represents a reliable model for describing liquid water. In this model, water in the liquid state is a mixture of two different local structures, characterised by different densities, namely the low density liquid (LDL) and the high-density liquid (HDL). The LLPT line should terminate at a special transition point: a low-T liquid-liquid critical point. We discuss the following experimental findings on liquid water: (i) a crossover from non-Arrhenius behaviour at high T to Arrhenius behaviour at low T in transport parameters; (ii) a breakdown of the Stokes-Einstein relation; (iii) the existence of a Widom line, which is the locus of points corresponding to maximum correlation length in the p-T phase diagram and which ends in the liquid-liquid critical point; (iv) the direct observation of the LDL phase; (v) a minimum in the density at approximately 70 K below the temperature of the density maximum. In our opinion these results represent the experimental proofs of the validity of the LLPT hypothesis.     

Spanning Forests and the q-State Potts Model in the Limit q →0

We study the q-state Potts model with nearest-neighbor coupling v=e^βJ−1 in the limit q,v → 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2≤ L ≤ 10, as well as the limiting curves B of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w₀, where w₀ =−1/4 (resp. w₀=−0.1753 ± 0.0002) for the square (resp. triangular) lattice. For w>w₀ we find a non-critical disordered phase that is compatible with the predicted asymptotic freedom as w → +∞. For w0 our results are compatible with a massless Berker–Kadanoff phase with central charge c=−2 and leading thermal scaling dimension x_T,1 = 2 (marginally irrelevant operator). At w=w₀ we find a “first-order critical point”: the first derivative of the free energy is discontinuous at w₀, while the correlation length diverges as w↓ w₀ (and is infinite at w=w₀). The critical ehavior at w=w₀ seems to be the same for both lattices and it differs from that of the Berker–Kadanoff phase: our results suggest that the central charge is c=−1, the leading thermal scaling dimension is x_T,1=0, and the critical exponents are ν=1/d=1/2 and α=1.     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Liquid-liquid phase transition in water

Water shows anomalies different from most of other materials.Different sceniaros have been proposed to explain water anomalies,among which the liquid-liquid phase transition(LLPT)is the most discussed one.It attributes water anomalies to the existence of a hypothesized liquid-liquid critical point(LLCP)buried deep in the supercooled region.We briefly review the recent experimental and theoretical progresses on the study of the LLPT in water.These studies include the discussion on the existence of the first order LLPT in supercooled water and the detection of liquid-liquid critical point.Simulational results of different water models for LLPT and the experimental evidence in confined water are also discussed.     

Liquid-liquid phase transition in elemental carbon: a first-principles investigation

It has been recently suggested that elemental carbon may be a promising candidate to exhibit a liquid-liquid phase transition (LLPT). We report the results of first-principles molecular dynamics simulations showing no evidence of LLPT in carbon, in the same temperature and pressure range where such a transition was found using empirical calculations. Our simulations indicate a continuous evolution from a primarily sp-bonded liquid to an sp(2)-like and an sp(3)-like fluid, as a function of pressure, above the graphite melting line. The discrepancy between quantum and classical simulations is attributed to the inability of empirical potentials to describe complex electronic effects in condensed carbon phases.     

Spatial quantum noise in singly resonant second-harmonic generation

We study the spatial distribution of quantum noise in singly resonant second-harmonic generation. Calculations are performed below threshold for spatial modulational instability. For parameters for which the intracavity fields are modulationally stable the spatial spectrum shows maximum squeezing at k=0, whereas under conditions of modulational instability we find maximum squeezing at finite wave number |k|=k(c), where k(c) corresponds to the classical critical wave number.     

Critical scaling of shear viscosity at the jamming transition

We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity eta is computed as a function of particle volume density rho and applied shear stress sigma, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable sigma/|rho(c)-rho|(Delta), where rho(c) is the critical density at sigma=0 ("point J"), and Delta is the crossover scaling critical exponent. We define a correlation length xi from velocity correlations in the driven steady state and show that it diverges at point J. Our results support the assertion that jamming is a true second-order critical phenomenon.     

Exact solutions for diluted spin glasses and optimization problems

We study the low temperature properties of p-spin glass models with finite connectivity and of some optimization problems. Using a one-step functional replica symmetry breaking ansatz we can solve exactly the saddle-point equations for graphs with uniform connectivity. The resulting ground state energy is in perfect agreement with numerical simulations. For fluctuating connectivity graphs, the same ansatz can be used in a variational way: For p-spin models (known as p-XOR-SAT in computer science) it provides the exact configurational entropy together with the dynamical and static critical connectivities (for p = 3, gamma(d) = 0.818, and gamma(s) = 0.918), whereas for hard optimization problems like 3-SAT or Bicoloring it provides new upper bounds for their critical thresholds ( gamma(var)(c) = 4.396 and gamma(var)(c) = 2.149).     

Surface critical behavior in systems with nonequilibrium phase transitions

We study the surface critical behavior of branching-annihilating random walks with an even number of offspring (BARW) and directed percolation (DP) using a variety of theoretical techniques. Above the upper critical dimensions d(c), with d(c)=4 (DP) and d(c)=2 (BARW), we use mean field-theory to analyze the surface phase diagrams using the standard classification into ordinary, special, surface, and extraordinary transitions. For the case of BARW, at or below the upper critical dimension d相似文献   

Critical phenomena and the quantum critical point of ferromagnetic Zr(1-x)NbxZn2

We present a study of the magnetic properties of Zr(1-x)NbxZn2, using an Arrott plot analysis of the magnetization. The Curie temperature Tc is suppressed to zero temperature for Nb concentration xc = 0.083+/-0.002, while the spontaneous moment vanishes linearly with Tc as predicted by the Stoner theory. The initial susceptibility chi displays critical behavior for x or= xc we find that chi(-1) = chi0(-1) + aT(4/3), where chi0(-1) vanishes as x-->xc. The resulting magnetic phase diagram shows that the quantum critical behavior extends over the widest range of temperatures for x=xc, and demonstrates how a finite transition temperature ferromagnet is transformed into a paramagnet, via a quantum critical point.     

Localization transition of biased random walks on random networks

We study random walks on large random graphs that are biased towards a randomly chosen but fixed target node. We show that a critical bias strength bc exists such that most walks find the target within a finite time when b > bc. For b < bc, a finite fraction of walks drift off to infinity before hitting the target. The phase transition at b=bc is a critical point in the sense that quantities such as the return probability P(t) show power laws, but finite-size behavior is complex and does not obey the usual finite-size scaling ansatz. By extending rigorous results for biased walks on Galton-Watson trees, we give the exact analytical value for bc and verify it by large scale simulations.     

Condensed fraction of an atomic Bose gas induced by critical correlations

We study the condensed fraction of a harmonically trapped atomic Bose gas at the critical point predicted by mean-field theory. The nonzero condensed fraction f(0) is induced by critical correlations which increase the transition temperature T(c) above T(c) (MF). Unlike the T(c) shift in a trapped gas, f(0) is sensitive only to the critical behavior in the quasiuniform part of the cloud near the trap center. To leading order in the interaction parameter a/λ(0), where a is the s-wave scattering length and λ(0) the thermal wavelength, we expect a universal scaling f(0) proportionally (a/λ(0))(4). We experimentally verify this scaling using a Feshbach resonance to tune a/λ(0). Further, using the local density approximation, we compare our measurements with the universal result obtained from Monte Carlo simulations for a uniform system, and find excellent quantitative agreement.     

Ground State and Single Vortex for Bose-Einstein Condensates in Anisotropic Traps

For Bose-Einstein condensation of neutral atoms in anisotropic traps at zero temperature, we present simple analytical methods for computing the properties of ground state and single vortex of Bose-Einstein condensates, and compare those results to extensive numerical simulations. The critical angular velocity for production of vortices is calculated for both positive and negative scattering lengths a, and find an analytical expression for the large-N limit of the vortex critical angular velocity for a 〉0, and the critical number for condensate population approaches the point of collapse for a 〈 0, by using approximate variational method.     

Corrections to finite-size-scaling in two dimensional Potts models

High resolution Monte Carlo simulations are used to examine the finite size behavior of Q-state Potts models in two dimensions. For Q = 3 we find that at the critical point bulk properties are subject to much larger corrections to finite size scaling than were previously realized. For Q = 4 we find that corrections to finite size scaling are subtle and that the multiplicative logarithmic correction is insufficient to correct the dominant terms.