Liquid Polymorphism and Density Anomaly in a Lattice Gas Model

We present a simple model for an associating liquid in which polymorphism and density anomaly are connected. Our model combines a two dimensional lattice gas with particles interacting through a soft core potential and orientational degrees of freedom represented through thermal \char`\"{}ice variables\char`\"{} . The competition between the directional attractive forces and the soft core potential leads to a phase diagram in which two liquid phases and a density anomaly are present. The coexistence line between the low density liquid and the high density liquid has a positive slope contradicting the surmise that the presence of a density anomaly implies that the high density liquid is more entropic than the low density liquid

Liquid Polymorphism and Double Criticality in a Lattice Gas Model

We analyze the possible phase diagrams of a simple model for an associating liquid proposed previously. Our two-dimensional lattice model combines oreintati onal ice-like interactions and \"{}Van der Waals\"{} interactions which may be repulsive, and in this case represent a penalty for distortion of hydrogen bonds in the presence of extra molecules. These interactions can be interpreted in terms of two competing distances, but not necessarily soft-core. We present mean -field calculations and an exhaustive simulation study for different parameters which represent relative strength of the bonding interaction to the energy penalty for its distortion. As this ratio decreases, a smooth disappearance of the doubl e criticality occurs. Possible connections to liquid-liquid transitions of molecul ar liquids are suggested

Intra-molecular coupling as a mechanism for a liquid-liquid phase transition

We study a model for water with a tunable intra-molecular interaction $J_\sigma$, using mean field theory and off-lattice Monte Carlo simulations. For all $J_\sigma\geq 0$, the model displays a temperature of maximum density.For a finite intra-molecular interaction $J_\sigma > 0$,our calculations support the presence of a liquid-liquid phase transition with a possible liquid-liquid critical point for water, likely pre-empted by inevitable freezing. For J=0 the liquid-liquid critical point disappears at T=0.Comment: 8 pages, 4 figure

Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly

We investigate the phase behavior of a single-component system in 3 dimensions with spherically-symmetric, pairwise-additive, soft-core interactions with an attractive well at a long distance, a repulsive soft-core shoulder at an intermediate distance, and a hard-core repulsion at a short distance, similar to potentials used to describe liquid systems such as colloids, protein solutions, or liquid metals. We showed [Nature {\bf 409}, 692 (2001)] that, even with no evidences of the density anomaly, the phase diagram has two first-order fluid-fluid phase transitions, one ending in a gas--low-density liquid (LDL) critical point, and the other in a gas--high-density liquid (HDL) critical point, with a LDL-HDL phase transition at low temperatures. Here we use integral equation calculations to explore the 3-parameter space of the soft-core potential and we perform molecular dynamics simulations in the interesting region of parameters. For the equilibrium phase diagram we analyze the structure of the crystal phase and find that, within the considered range of densities, the structure is independent of the density. Then, we analyze in detail the fluid metastable phases and, by explicit thermodynamic calculation in the supercooled phase, we show the absence of the density anomaly. We suggest that this absence is related to the presence of only one stable crystal structure.Comment: 15 pages, 21 figure

Study of random sequential adsorption by meansof the gradient method

By using the gradient method (GM) we study random sequential adsorption (RSA) processes in two dimensions under a gradient constraint that is imposed on the adsorption probability along one axis of the sample. The GM has previously been applied successfully to absorbing phase transitions (both first and second order), and also to the percolation transition. Now, we show that by using the GM the two transitions involved in RSA processes, namely percolation and jamming, can be studied simultaneously by means of the same set of simulations and by using the same theoretical background. For this purpose we theoretically derive the relevant scaling relationships for the RSA of monomers and we tested our analytical results by means of numerical simulations performed upon RSA of both monomers and dimers. We also show that two differently defined interfaces, which run in the direction perpendicular to the axis where the adsorption probability gradient is applied and separate the high-density (large-adsorption probability) and the low-density (low-adsorption probability) regimes, capture the main features of the jamming and percolation transitions, respectively. According to the GM, the scaling behaviour of those interfaces is governed by the roughness exponent α = 1/(1 + ν), where ν is the suitable correlation length exponent. Besides, we present and discuss in a brief overview some achievements of the GM as applied to different physical situations, including a comparison of the critical exponents determined in the present paper with those already published in the literature

Improving oscillations by increasing the occupancy of all binding sites.

<p>Peak frequency (panel A) and the quality factor <i>Q</i>_90% (panel B) as a function of <i>ϵ</i> and <i>λ</i>, for oscillations in the number fluctuations of repressor for the same parameter as <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151086#pone.0151086.g005" target="_blank">Fig 5</a>, but with <i>a</i>₀ = 0.15 <i>μ</i>M min⁻¹ and <i>g</i>₀ = 0.15 min⁻¹.</p

The number of binding sites enhances oscillatory behavior.

<p>Peak frequency (panel A) and the quality factor <i>Q</i>_90% (panel B) as a function of <i>ϵ</i> and <i>λ</i>, for oscillations in the number fluctuations of repressor for the same parameter than <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151086#pone.0151086.g004" target="_blank">Fig 4</a>, but with <i>N</i> = 5 instead of <i>N</i> = 3.</p

Power spectral densities.

<p>Normalized power spectral density of the fluctuations of repressor obtained by averaging 8000 periodograms from stochastic simulations of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151086#pone.0151086.g002" target="_blank">Fig 2</a> (black dots), and the approximate normalized power spectral density computed by using <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0151086#pone.0151086.e020" target="_blank">Eq (4)</a> (red curve). indicates the peak frequency, and Δ<i>ω</i> is the difference of the two frequencies at which the power takes the 90% of the peak value. The frequency <i>ω</i> is given in radians per minute (rad min⁻¹).</p

Sketch of the autorepressive single-gene loop with three binding sites.

<p>The repressor molecules <i>R</i> (red) can bind to regulatory sites (green) on the DNA inhibiting its own synthesis. Inset: Cascade of reactions where <i>X</i>_<i>i</i> represents the promoter with <i>i</i> bound repressors, and <i>k</i>_{<i>i</i>,<i>j</i>} the transition rates.</p