This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the state diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and coworkers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, as well as explains isochronal superposition for strongly correlating viscous liquids.
如果液体在NVT系综中的维里和势能热平衡波动超过90%相关，则该液体被称为强相关[Phys. Rev. Lett. 100，015701（2008）]。强关联液体的波动很好地近似的逆幂律分子间势。基于这一事实，我们在这里定义“同构线”的状态图中的强关联液体。它是从计算机模拟的Kob-Andersen二进制Lennard-Jones液体，没有老化与两个同构点之间的跳跃。同构状态点具有相同的过剩熵、相同的约化平均弛豫时间、相同的（约化）动力学和相同的标度径向分布函数。最后，我们计算了伦纳德-琼斯型液体的维里/势能图中的同构方程，并表明所有此类12-6液体都具有相同的同构;这些可以缩放为主同构。
Isomorphs, hidden scale invariance, and quasiuniversality
本文首先建立了具有良好同构的经典液体（Roskilde简单液体）势能函数的近似标度性质。这种“伪齐次”性质明确表明--以及在何种意义上--这样的系统具有隐藏的标度不变性。第二部分给出了单原子Roskilde简单液体的准普适性的势能公式，最近根据约化坐标常势能超曲面的准普适性单参数族的存在性将其合理化[J. C. Dyre，Phys.Rev.E87，022106（2013）]。新的配方涉及一个准通用的简化坐标势能函数。一些后果，这是讨论。
An alternative approach to the phonon theory of liquids: An analytical study of Frenkel frequency and heat capacity as a function of pressure and temperature
Density scaling of the diffusivity in viscous liquids: Identification of the scaling exponent with the pressure derivative of the isothermal bulk modulus
基于改进的状态方程，假设等温体积模量随压力线性增加，重新审视了早期导出的粘性液体的密度缩放扩散率函数[Phys. Rev. E 79，032501（2009）]。在不对标度指数和Gruneisen参数之间的相互关系作任何假设的情况下，证明了标度指数与等温体积模量的压力导数是一致的.我们进一步讨论可能的标度指数和Gruneisen参数之间的互连。
In recent years lines along which structure and dynamics are invariant to a good approximation, so-called isomorphs, have been identified in the thermodynamic phase diagrams of several model liquids and solids. This paper reports computer simulations of the transverse and longitudinal collective dynamics at different length scales along an isomorph of the Lennard-Jones system. Our findings are compared to corresponding results along an isotherm and an isochore. Confirming the theoretical prediction, the reduced-unit dynamics of the transverse momentum density is invariant to a good approximati…
Many-body interactions can play a relevant role in water properties. Here we study by Monte Carlo simulations a coarse-grained model for bulk water that includes many-body interactions associated to water cooperativity. The model is efficient and allows us to equilibrate water at extreme low temperatures in a wide range of pressures. We find the line of temperatures of maximum density at constant pressure and, at low temperature and high pressure, a phase transition between high-density liquid and low-density liquid phases. The liquid-liquid phase transition ends in a critical point. In the su…
The local pressure tensor is non-unique, a fact which has generated confusion and debate in the seventy years since the seminal work by Irving Kirkwood. This non-uniqueness is normally attributed to the interaction path between molecules, especially in the interfacial-science community. In this work we reframe this discussion of non-uniqueness in terms of the location, or reference frame, used to measure the pressure. By using a general mathematical description of the liquid-vapour interface, we obtain a reference frame that moves with the interface through time, providing a new insight into t…
In the companion paper [T. S. Ingebrigtsen and H. Tanaka, J. Phys. Chem. B 119, 11052 (2015)] the effect of size polydispersity on the nature of Lennard-Jones (LJ) liquids, which represent most molecular liquids without hydrogen bonds, was studied. More specifically, it was shown that even highly size polydisperse LJ liquids are Roskilde-simple (RS) liquids. RS liquids are liquids with strong correlation between constant volume equilibrium fluctuations of virial and potential energy and are simpler than other types of liquids. Moreover, it was shown that size polydisperse LJ liquids have isomo…
We report a molecular dynamics study of liquid cesium at ambient pressure intended to check the possibility of liquid-liquid phase transformation at $T=590$ K. We find the presence of small kinks on thermodynamic characteristics of the system, but no phase transition.
The magnitude of the high frequency, static dielectric permittivity is used to determine the density of tetramethyl tetraphenyl trisiloxane, a non-associated glass-forming liquid, as a function of temperature and pressure. We demonstrate that the properties in the glassy state are affected by the pressure applied to the liquid during vitrification. This behavior is normal for hydrogen-bonded liquids and polymers, but unanticipated by models of simple liquids.
Pressure-energy correlations and thermodynamic scaling in viscous Lennard-Jones liquids
我们使用分子动力学模拟结果的粘性二元Lennard-Jones混合物检查势能和维里之间的相关性。根据最近的一项提议[U。R.佩德森等等，Phys. Rev. Lett. 100，015701（2008）]，发现两个量的波动是强相关的，表现出比例常数γ，在数值上等于分子间势函数的逆幂律近似的斜率的三分之一。相关性在更高的密度下更强，其中原子间的分离在逆幂律近似更准确的范围内。这些相同的液体符合其动力学的热力学标度，标度指数等于Gamma。因此，能量和压力之间的强相关性和热力学标度的属性都反映了一个潜在的逆幂律表示捕捉有趣的功能，致密，高粘度液体的动力学的能力。
Since a rigorous microscopic treatment of a nematic fluid system based on a pairwise interaction potential is immensely complex we had introduced a simple mean field potential which was a modification of the Maier-Saupe potential in a previous paper. Building up on that here we have modified that potential to take into account the various aspects of a smectic A-nematic phase transition. In particular we have studied the dependence of the phase transition on the coupling coefficient between the nematic and smectic order parameters which in turn depends on the length of alkyl chain, existence of…
We describe a method to determine whether a material has isomorphs in its thermodynamic phase diagram. Isomorphs are state points for which various properties are invariant in reduced units. Such materials are commonly identified from strong correlation between thermal fluctuations of the potential energy, U, and the virial W, but this identification is not generally applicable to real materials. We show from molecular dynamic simulations of atomic, molecular, and polymeric materials that systems with strong U-W correlation cannot be pressure densified; that is, the density obtained on cooling…
The frequency dependent specific heat has been measured under pressure for the molecular glass forming liquid 5-polyphenyl-4-ether in the viscous regime close to the glass transition. The temperature and pressure dependence of the characteristic timescale associated with the specific heat is compared to the equivalent timescale from dielectric spectroscopy performed under identical conditions. It is shown that the ratio between the two timescales is independent of both temperature and pressure. This observation is non-trivial and demonstrates the existence of specially simple molecular liquids…
In this work, molecular dynamics simulations are performed to estimate the equilibrium pressure of liquid confined in nanopores. The simulations show that the pressure is highly sensitive to the pore size and can significantly change from absolute positive to negative values for a very small (0.1 nm) change in pore size. The contribution from the solid-liquid interaction always dominates the pressure in the first liquid layer adjacent to the surface and the sensitiveness of pressure on the pore size is due to the atom distribution in the liquid layers. A surface influence number S is introduce…
Employing X-ray photon correlation spectroscopy we measure the kinetics and dynamics of a pressure-induced liquid-liquid phase separation (LLPS) in a water-lysozyme solution. Scattering invariants and kinetic information provide evidence that the system reaches the phase boundary upon pressure-induced LLPS with no sign of arrest. The coarsening slows down with increasing quench depths. The $g_2$-functions display a two-step decay with a gradually increasing non-ergodicity parameter typical for gelation. We observe fast superdiffusive ($γ\geq 3/2$) and slow subdiffusive ($γ< 0.6$) motion associ…
We consider the surface pressure of a colloid-laden liquid interface. As micron-sized particles of suitable wettability can be irreversibly bound to the liquid interface on experimental timescales, we use the canonical ensemble to derive an expression for the surface pressure of a colloid-laden interface. We use this expression to show that adsorption of particles with only hard-core interactions has a negligible effect on surface pressures from typical Langmuir-trough measurements. Moreover, we show that Langmuir-trough measurements cannot be used to extract typical interparticle potentials. …
We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulation. An external pressure restricts local motions of a single molecule within its cage and triggers the slowing down of cooperative mobility. While the ECNLE theory and simulation generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulation indicates a decrease of fragility as pressure above 10…
A swollen phase observed between the liquid-crystalline phase and the interdigitated phase induced by pressure and/or adding ethanol in DPPC aqueous solution
First-principles molecular dynamics (FPMD) simulations are performed on 6 and 12% Na in dense liquid N. A detailed description of structural and electronic properties leading to an understanding of the effect of Na-doping on the polymerization phase transition of N is presented. Compression of the mixtures from 5 to 90 GPa shows three distinct regions of characteristic local order separated by pressures near 30 and 65 GPa. Computation of Gibbs free energies of mixing shows that these mixtures are thermodynamically stable beyond 20 and 15 GPa for 6 and 12 % Na respectively.
Liquids in oil-bearing porous media assume complex shapes that depend on the reservoir characteristics and the wetting properties of the liquid. The wide variation in the geometry of rock formations makes it difficult to accurately predict the capillary pressure of small volumes of liquid and hence the likelihood of being able to move it. Here we consider the situation in which a small volume of liquid surrounds an upright cylinder on a flat substrate and predict the shape that the liquid takes and its capillary pressure. We validate our predictions by comparing with Surface Evolver simulation…
Superhydrophobicity is connected to the presence of gas pockets within surface asperities. Upon increasing the pressure this "suspended" state may collapse, causing the complete wetting of the rough surface. In order to quantitatively characterize this process on nanostructured surfaces, we perform rare-event atomistic simulations at different pressures and for several texture geometries. Such approach allows us to identify for each pressure the stable and metastable states and the free energy barriers separating them. Results show that, by starting from the superhydrophobic state and increasi…
Broadband dielectric spectroscopy (BDS) of pure 5OCB and nanocolloids consisting of 5OCB and paraelectric or ferroelectric BaTiO${_3}$ nanoparticles (NPs) was performed on varying pressure or temperature. We found strong impact of NPs on static and dynamic phase behavior. In particular, strongest effects on pretransitional behavior were observed for a relatively low concentration of NPs which we attribute to the NPs-induced disorder. Paramagnetic or ferromagnetic character of NPs did not significantly influence measurements. However, several features measured using temperature or pressure path…
We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows-down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and non-polymeric supramolecules are carried out at ambient and elevated pressures. The numerica…
We predict the volume of liquid recovered from different-shaped prismatic channels following gas displacement. This recovery factor depends strongly on the contact angle at which the gas-liquid interfaces meet the walls of the channel. We show that scaling the contact angle by a critical value, dependent on the channel shape, leads to a master curve for the recovery factor.} Our numerical simulations with the Surface Evolver are supported by theoretical calculations for the capillary entry pressure in a channel with a triangular or rectangular cross-section and for the interface shape in a "sc…
Joint physically and chemically pattered surfaces can provide efficient and passive manipulation of fluid flow. The ability of many of these surfaces to allow only unidirectional flow mean they are often referred to as fluid diodes. Synthetic analogues of these are enabling technologies from sustainable water collection via fog harvesting, to improved wound dressings. One key fluid diode geometry features a pore sandwiched between two absorbent substrates, an important design for applications which require liquid capture while preventing back-flow. However, the enclosed pore is particularly ch…
Glass-to-glass and liquid-to-liquid phase transitions were observed many years ago in bulk and confined water with or without applied pressure. It is shown that they result from the competition of two-liquid phases separated by an enthalpy difference depending on temperature. The model is based on the classical nucleation equation of these phases completed by this enthalpy saving existing at all temperatures and a pressure contribution. The thermodynamic parameters of amorphous water, the multiple glass transition temperatures, the enthalpy changes, and the temperature of maximum density under…
Since its initial discovery more than fifteen years ago, the thermodynamical scaling of the dynamics of supercooled liquids has been used to provide many new important insights in the physics of liquids, particularly on the link between dynamics and intermolecular potential. A question that has long been discussed is whether the scaling exponent gamma is a constant or it depends on pressure. Here we offer a simple method to determine the pressure dependence of gamma using only the pressure dependence of the glass transition and the equation of state. Using this new method we find that for the …
A characteristic property of many soft matter systems is an ultrasoft effective interaction between their structural units. This softness often leads to complex behavior. In particular, ultrasoft systems under pressure demonstrate polymorphism of complex crystal and quasicrystal structures. Therefore, it is of interest to investigate how different can be the structure of the fluid state in such systems at different pressures. Here we address this issue for the model liquid composed of particles interacting through the harmonic-repulsive pair potential. This system can form different crystal st…
A liquid drop impacting a smooth solid substrate splashes by emitting a thin liquid sheet from near the contact line of the spreading liquid. This sheet is lifted from the substrate and ultimately breaks apart. Surprisingly, the splash is caused by the ambient gas, whose properties dictate when and if the sheet is created. Here I focus on two aspects of this process. Using high-speed imaging I find that the time of thin-sheet creation displays a different quantitative dependence on air pressure if the sheet is created during the early stages of spreading, rather than when the liquid has alread…
