Recent experimental results [1] indicate that phosphorus, a single-component system, can have two liquid phases: a high-density liquid (HDL) and a low-density liquid (LDL) phase. A firstorder transition between two liquids of different densities [2] is consistent with experimental data for a variety of materials [3,4], including singlecomponent systems such as water [5][6][7][8], silica [9] and carbon [10]. Molecular dynamics simulations of very specific models for supercooled water [2,11], liquid carbon [12] and supercooled silica [13], predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular liquid metals [14-21,2]), and such potentials are often used to decribe systems that exhibit a density anomaly [2]. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of the density anomaly.Several explanations have been developed to understand the liquid-liquid phase transition. For example, the two-liquid models [4] assume that liquids at high pressure are a mixture of two liquid phases whose relative concentration depends on external parameters. Other explanations for the liquid-liquid phase transition assume an anisotropic potential [2,[11][12][13]. Here we shall see that liquid-liquid phase transition phenomena can arise solely from an isotropic pair interaction potential with two characteristic lengths.For molecular liquid phosphorus P 4 (as for water), a tetrahedral open structure is preferred at low pressures P and low temperatures T , while a denser structure is favored at high P and high T [1,6,8]. The existence of these two structures with different densities suggests a pair interaction with two characteristic distances. The first distance can be associated with the hard-core exclusion between two particles and the second distance with a weak repulsion (soft-core), which can be overcome at large pressure. Here we will use a generic three dimensional (3D) model composed of particles interacting via an isotropic soft-core pair potential. Such isotropic potentials can be regarded as resulting from an average over the angular part of more realistic potentials, and are often used as a first approximation to understand the qualitative behavior of real systems [14][15][16][17][18][19][20][21][22]2]. For Ce and Cs, Stell and Hemmer proposed a potential with nearest-neighbor repulsion and a weak long-range attraction [15]. By means of an exact analysis in 1D, they found two critical points, with the high-density critical point interpreted as a solid-solid transition. Then analytic calc...

Four scenarios have been proposed for the low-temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism that leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, because there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean-field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model independent. Using estimates from experimental data for H-bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid-liquid critical point at positive pressure.anomalous liquids | liquid-liquid transition | liquid water | mean field | Monte Carlo simulations W ater's phase diagram is rich and complex: more than sixteen crystalline phases (1), and two or more glasses (2-4) have been reported. The liquid state also displays interesting behavior, such as the density maximum for 1 atm at 4°C. The volume fluctuations hðδV Þ 2 i, entropy fluctuations hðδSÞ 2 i, and cross fluctuations between volume and entropy hδV δSi, proportional to the magnitude of isothermal compressibility K T , isobaric specific heat C P , and isobaric thermal expansivity α P , respectively, show anomalous increases in magnitude upon cooling (5). Further, these quantities display an apparent divergence for 1 atm at −45°C (2), hinting at interesting phase behavior in the supercooled region.Microscopically, liquid water's anomalous behavior is understood as resulting from the tendency of neighboring molecules to form hydrogen (H) bonds upon cooling with a decrease of local potential energy, decrease of local entropy, and increase of local volume due to the formation of local open structures of bonded molecules. Different models include these H-bond features, but depending on the assumptions and approximations of each model, different conclusions are obtained for the low-T phase behavior. The relevant region of the bulk-liquid state cannot be probed experimentally, and none of the theories tested because crystallization of bulk water is unavoidable below the homogeneous nucleation temperature T H (−38°C at 1 atm). Four Scenarios for Supercooled WaterDue to the difficulty of obtaining experimental evidence, theoretical and numerical analyses are useful. Four separate scenarios for the pressure-temperature (P-T) phase diagram have been proposed: (I) The stability limit (SL) scenario (6) hypothesizes that the superheated liquid-gas spinodal at negative pressure reenters the positive P region below T H ðPÞ. In this view, the liq...

Water can be supercooled to temperatures as low as −92• C, the experimental crystal homogeneous nucleation temperature T H at 2 kbar. Within the supercooled liquid phase its response functions show an anomalous increase consistent with the presence of a liquid-liquid critical point located in a region inaccessible to experiments on bulk water. Recent experiments on the dynamics of confined water show that a possible way to understand the properties of water is to investigate the supercooled phase diagram in the vicinity of the Widom line (locus of maximum correlation length) that emanates from the hypothesized liquid-liquid critical point. Here we explore the Widom line for a Hamiltonian model of water using an analytic approach, and discuss the plausibility of the hypothesized liquid-liquid critical point, as well as its possible consequences, on the basis of the assumptions of the model. The present analysis allows us (i) to find an analytic expression for the spinodal line of the high-density liquid phase, with respect to the low-density liquid phase, showing that this line becomes flat in the P-T phase diagram in the physical limit of a large number of available orientations for the hydrogen bonds, as recently seen in simulations and experiments (Xu et al 2005 Proc. Natl Acad. Sci. 102 16558); (ii) to find an estimate of the values for the hypothesized liquid-liquid critical point coordinates that compare very well with Monte Carlo results; and (iii) to show how the Widom line can be located by studying the derivative of the probability of forming hydrogen bonds with local tetrahedral orientation which can be calculated analytically within this approach.

When a pristine nanoparticle (NP) encounters a biological fluid, biomolecules spontaneously form adsorption layers around the NP, called “protein corona”. The corona composition depends on the time-dependent environmental conditions and determines the NP’s fate within living organisms. Understanding how the corona evolves is fundamental in nanotoxicology as well as medical applications. However, the process of corona formation is challenging due to the large number of molecules involved and to the large span of relevant time scales ranging from 100 μs, hard to probe in experiments, to hours, out of reach of all-atoms simulations. Here we combine experiments, simulations, and theory to study (i) the corona kinetics (over 10–3–103 s) and (ii) its final composition for silica NPs in a model plasma made of three blood proteins (human serum albumin, transferrin, and fibrinogen). When computer simulations are calibrated by experimental protein–NP binding affinities measured in single-protein solutions, the theoretical model correctly reproduces competitive protein replacement as proven by independent experiments. When we change the order of administration of the three proteins, we observe a memory effect in the final corona composition that we can explain within our model. Our combined experimental and computational approach is a step toward the development of systematic prediction and control of protein–NP corona composition based on a hierarchy of equilibrium protein binding constants.

Using Monte Carlo simulations and mean field calculations for a cell model of water we find a dynamic crossover in the orientational correlation time from non-Arrhenius behavior at high temperatures to Arrhenius behavior at low temperatures. This dynamic crossover is independent of whether water at very low temperature is characterized by a ''liquid-liquid critical point'' or by the ''singularity-free'' scenario. We relate to fluctuations of hydrogen bond network and show that the crossover found for for both scenarios is a consequence of the sharp change in the average number of hydrogen bonds at the temperature of the specific heat maximum. We find that the effect of pressure on the dynamics is strikingly different in the two scenarios, offering means to distinguish between them. DOI: 10.1103/PhysRevLett.100.105701 PACS numbers: 64.70.Ja, 05.40.ÿa, 64.70.qj Two different scenarios are commonly used to interpret the anomalies of water [1,2]: (i) The liquid-liquid critical point (LLCP) scenario hypothesizes that supercooled water has a liquid-liquid phase transition line that separates a low-density liquid (LDL) at low temperature T and low pressure P and a high-density liquid (HDL) at high T and P and terminates at a critical point C 0 [3]. From C 0 emanates the Widom line T W P, the line of maximum correlation length in the (T, P) plane. Response functions, such as the isobaric heat capacity C P , the coefficient of thermal expansion P , and the isothermal compressibility K T , have maxima along lines that converge toward T W P upon approaching C 0 [Figs. 1 and 2(a)]. (ii) The singularityfree (SF) scenario hypothesizes the presence of a line of temperatures of maximum density T MD P with negative slope in the (T, P) plane. As a consequence, K T and j P j have maxima that increase upon increasing P, as shown using a cell model of water. The maxima in C P do not increase with P, suggesting that there is no singularity [4] [ Fig. 2(b)].Above the homogeneous nucleation line T H P where data are available, the two scenarios predict roughly the same equilibrium phase diagram. Here we show that dynamic measurements should reveal a striking difference between the two scenarios. Specifically, the low-T dynamics depends on local structural changes, quantified by the variation in the number of hydrogen bonds, that are affected by pressure differently for each scenario. We find this result by studying-using Monte Carlo (MC) simulations and mean field calculations -a cell model which has the property that by tuning a parameter its predictions conform to those of either the LLCP or the SF scenario [5]. This cell model is based on the experimental observations that on decreasing P at constant T, or on decreasing T at constant P, (i) water displays an increasing local tetrahedrality where the sum is over NN cells, 0 < J < is the bond energy, a;b 1 if a b and a;b 0 otherwise, andwhere P k;' i denotes the sum over the IM bond indices (k, l) of the molecule i and J > 0 is the IM interaction energy with J < J, which models th...

We study a model for water with a tunable intramolecular interaction J , using mean-field theory and off-lattice Monte Carlo simulations. For all J у0, the model displays a temperature of maximum density. For a finite intramolecular interaction J Ͼ0, our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely preempted by inevitable freezing. For J ϭ0, the liquid-liquid critical point disappears at Tϭ0.

We investigate by molecular dynamics simulations a continuous isotropic core-softened potential with attractive well in three dimensions, introduced by Franzese [J. Mol. Liq. 136, 267 (2007)], that displays liquid-liquid coexistence with a critical point and waterlike density anomaly. Besides the thermodynamic anomalies, here we find diffusion and structural anomalies. The anomalies, not observed in the discrete version of this model, occur with the same hierarchy that characterizes water. We discuss the differences in the anomalous behavior of the continuous and the discrete model in the framework of the excess entropy, calculated within the pair correlation approximation.

Using event-driven molecular dynamics simulations, we study a three-dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point C 1 and a liquid-liquid critical point C 2 . For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and gives us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft-core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.