arXiv subjects

Thomas B. Schrøder

Publications and source records attributed to Thomas B. Schrøder.

At least 37 records · Page 2Linked to original sources

arXiv2015

Scaling of the dynamics of flexible Lennard-Jones chains. II. Effects of harmonic bonds

The previous paper [Veldhorst et al., J. Chem. Phys. 141, 054904 (2014)] demonstrated that the isomorph theory explains the scaling properties of a liquid of flexible chains consisting of ten Lennard-Jones particles connected by rigid bonds. We here investigate the same model with harmonic bonds. The introduction of harmonic bonds almost completely destroys the correlations in the equilibrium fluctuations of the potential energy and the virial. According to the isomorph theory, if these correlations are strong a system has isomorphs, curves in the phase diagram along which structure, dynamics and the excess entropy are invariant. The Lennard-Jones chain liquid with harmonic bonds does have curves in the phase diagram along which the structure and dynamics are invariant. The excess entropy is not invariant on these curves, which we refer to as "pseudoisomorphs". In particular this means that Rosenfeld's excess-entropy scaling (the dynamics being a function of excess entropy only) does not apply for the Lennard-Jones chain with harmonic bonds.

cond-mat.soft↗

arXiv2015

Invariants in the Yukawa system's thermodynamic phase diagram

This paper shows that several known properties of the Yukawa system can be derived from the isomorph theory, which applies to any system that has strong correlations between its virial and potential-energy equilibrium fluctuations. Such "Roskilde-simple" systems have a simplified thermodynamic phase diagram deriving from the fact that they have curves (isomorphs) along which structure and dynamics in reduced units are invariant to a good approximation. We show that the Yukawa system has strong virial potential-energy correlations and identify its isomorphs by two different methods. One method, the so-called direct isomorph check, identifies isomorphs numerically from jumps of relatively small density changes (here 10%). The second method identifies isomorphs analytically from the pair potential. The curves obtained by the two methods are close to each other; these curves are confirmed to be isomorphs by demonstrating the invariance of the radial distribution function, the static structure factor, the mean-square displacement as a function of time, and the incoherent intermediate scattering function. Since the melting line is predicted to be an isomorph, the theory provides a derivation of a known approximate analytical expression for this line in the temperature-density phase diagram. The paper's results give the first demonstration that the isomorph theory can be applied to systems like dense colloidal suspensions and strongly coupled dusty plasmas.

cond-mat.soft↗

arXiv2015

Explaining why simple liquids are quasi-universal

It has been known for a long time that many simple liquids have surprisingly similar structure as quantified, e.g., by the radial distribution function. A much more recent realization is that the dynamics are also very similar for a number of systems with quite different pair potentials. Systems with such non-trivial similarities are generally referred to as "quasi-universal". From the fact that the exponentially repulsive pair potential has strong virial potential-energy correlations in the low-temperature part of its thermodynamic phase diagram, we here show that a liquid is quasi-universal if its pair potential can be written approximately as a sum of exponential terms with numerically large prefactors. Based on evidence from the literature we moreover conjecture the converse, i.e., that quasi-universality only applies for systems with this property.

cond-mat.stat-mech↗

arXiv2014

The variation of the dynamic susceptibility along an isochrone

Koperwas {\it et al.} showed in a recent paper, Phys. Rev. Lett. {\bf 111}, 125701 (2013), that the dynamic susceptibility $χ_4$ as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known non-invariance of the isothermal bulk modulus. Considering the version of $χ_4$ defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

cond-mat.stat-mech↗

arXiv2014

Simplicity of condensed matter at its core: Generic definition of a Roskilde-simple system

The theory of isomorphs is reformulated by defining Roskilde-simple systems (those with isomorphs) by the property that the order of the potential energies of configurations at one density is maintained when these are scaled uniformly to a different density. Isomorphs remain curves in the thermodynamic phase diagram along which structure, dynamics, and excess entropy are invariant, implying that the phase diagram is effectively one-dimensional with respect to many reduced-unit properties. In contrast to the original formulation of the isomorph theory, however, the density-scaling exponent is not exclusively a function of density and the isochoric heat capacity is not an exact isomorph invariant. A prediction is given for the latter quantity's variation along the isomorphs. Molecular dynamics simulations of the Lennard-Jones and Lennard-Jones Gaussian systems validate the new approach.

cond-mat.soft↗

arXiv2014

Cooee bitumen II: Stability of linear asphaltene nanoaggregates

Asphaltene and smaller aromatic molecules tend to form linear nanoaggregates in bitumen.Over the years bitumen undergoes chemical aging and during this process, the size of the nanoaggregate increases. This increase is associated with an increase in viscosity and brittleness of the bitumen, eventually leading to road deterioration. This paper focuses on understanding the mechanisms behind nanoaggregate size and stability. We used molecular dynamics simulations to quantify the probability of having a nanoaggregate of a given size in the stationary regime. To model this complicated behavior, we chose first to consider the simple case where only asphaltene molecules are counted in a nanoaggregate. We used a master equation approach and a related statistical mechanics model. The linear asphaltene nanoaggregates behave as a rigid linear chain. The most complicated case where all aromatic molecules are counted in a nanoaggregate is then discussed. The linear aggregates where all aromatic molecules are counted seem to behave as a flexible linear chain.

physics.chem-ph↗

arXiv2014

Scaling of the dynamics of flexible Lennard-Jones chains

The isomorph theory provides an explanation for the so-called power law density scaling which has been observed in many molecular and polymeric glass formers, both experimentally and in simulations. Power law density scaling (relaxation times and transport coefficients being functions of $ρ^{γ_S}/T$, where $ρ$ is density, $T$ is temperature, and $γ_S$ is a material specific scaling exponent) is an approximation to a more general scaling predicted by the isomorph theory. Furthermore, the isomorph theory provides an explanation for Rosenfeld scaling (relaxation times and transport coefficients being functions of excess entropy) which has been observed in simulations of both molecular and polymeric systems. Doing molecular dynamics simulations of flexible Lennard-Jones chains (LJC) with rigid bonds, we here provide the first detailed test of the isomorph theory applied to flexible chain molecules. We confirm the existence of isomorphs, which are curves in the phase diagram along which the dynamics is invariant in the appropriate reduced units. This holds not only for the relaxation times but also for the full time dependence of the dynamics, including chain specific dynamics such as the end-to-end vector autocorrelation function and the relaxation of the Rouse modes. As predicted by the isomorph theory, jumps between different state points on the same isomorph happen instantaneously without any slow relaxation. Since the LJC is a simple coarse-grained model for alkanes and polymers, our results provide a possible explanation for why power-law density scaling is observed experimentally in alkanes and many polymeric systems. The theory provides an independent method of determining the scaling exponent, which is usually treated as a empirical scaling parameter.

cond-mat.soft↗

arXiv2014

Isomorph invariance of classical crystals' structure and dynamics

This paper shows by computer simulations that some crystalline systems have curves in their thermodynamic phase diagrams, so-called isomorphs, along which structure and dynamics in reduced units are invariant to a good approximation. The crystals are studied in a classical-mechanical framework, which is generally a good description except significantly below melting. The existence of isomorphs for crystals is validated by simulations of particles interacting via the Lennard-Jones pair potential arranged into a face-centered cubic (FCC) crystalline structure; the slow vacancy-jump dynamics of a defective FCC crystal is also shown to be isomorph invariant. In contrast, a NaCl crystal model does not exhibit isomorph invariances. Other systems simulated, though in less detail, are the Wahnstrom binary Lennard-Jones crystal with the ${\rm MgZn_2}$ Laves crystal structure, monatomic FCC crystals of particles interacting via the Buckingham pair potential and via a novel purely repulsive pair potential diverging at a finite separation, an ortho-terphenyl molecular model, and SPC/E hexagonal ice. Except for NaCl and ice, the crystals simulated all have isomorphs. Based on these findings and previous simulations of liquid models, we conjecture that crystalline solids with isomorphs include most or all formed by atoms or molecules interacting via metallic or van der Waals forces, whereas covalently- or hydrogen-bonded crystals are not expected to have isomorphs. Crystals of ions or dipolar molecules constitute a limiting case for which isomorphs are only expected when the Coulomb interactions are relatively weak. We briefly discuss the consequences of the findings for theories of melting and crystallization.

cond-mat.stat-mech↗

arXiv2014

Estimating the density-scaling exponent of a monatomic liquid from its pair potential

This paper investigates two conjectures for calculating the density dependence of the density-scaling exponent of a single-component, pair-potential liquid with strong virial potential-energy correlations. The first conjecture gives an analytical expression for the density-scaling exponent directly in terms of the pair potential. The second conjecture is a refined version of this, which involves the most likely nearest-neighbor distance determined from the pair-correlation function. The two conjectures for the density-scaling exponent are tested by simulations of three systems, one of which is the standard Lennard-Jones liquid. While both expressions give qualitatively correct results, the second expression is more accurate.

cond-mat.soft↗

arXiv2013

COOEE bitumen. Chemical aging

We study chemical aging in "COOEE bitumen" using molecular dynamic simulations. This model bitumen is composed of four realistic molecule types: saturated hydrocarbon, resinous oil, resin, and asphaltene. The aging reaction is modelled by the chemical reaction: "2 resins $\rightarrow$ 1 asphaltene". Molecular dynamic simulations of four bitumen compositions, obtained by a repeated application of the aging reaction, are performed. The stress autocorrelation function, the fluid structure, the rotational dynamics of the plane aromatic molecules, and the diffusivity of each molecule, are determined for the four different compositions. The aging reaction causes a significant dynamics slowdown, which is correlated to the aggregation of asphaltene molecules in larger and dynamically slower nanoaggregates. Finally, a detailed description of the role of each molecule types in the aggregation and aging processes is given.

physics.chem-ph↗

arXiv2013

Statistical mechanics of Roskilde liquids: Configurational adiabats, specific heat contours and density dependence of the scaling exponent

We derive exact results for the rate of change of thermodynamic quantities, in particular the configurational specific heat at constant volume, $C_V$, along configurational adiabats (curves of constant excess entropy $S_{\textrm{ex}}$). Such curves are designated isomorphs for so-called Roskilde liquids, in view of the invariance of various structural and dynamical quantities along them. Their slope in a double logarithmic representation of the density-temperature phase diagram, $γ$ can be interpreted as one third of an effective inverse power-law potential exponent. We show that in liquids where $γ$ increases (decreases) with density, the contours of $C_V$ have smaller (larger) slope than configurational adiabats. We clarify also the connection between $γ$ and the pair potential. A fluctuation formula for the slope of the $C_V$-contours is derived. The theoretical results are supported with data from computer simulations of two systems, the Lennard-Jones fluid and the Girifalco fluid. The sign of $dγ/dρ$ is thus a third key parameter in characterizing Roskilde liquids, after $γ$ and the virial-potential energy correlation coefficient $R$. To go beyond isomorph theory we compare invariance of a dynamical quantity, the self-diffusion coefficient along adiabats and $C_V$-contours, finding it more invariant along adiabats.

cond-mat.stat-mech↗

arXiv2013

Four-component united-atom model of bitumen

We propose a four-component molecular model of bitumen. The model includes realistic chemical constituents and introduces a coarse-graining level that suppresses the highest frequency modes. Molecular dynamics simulations of the model are being carried out using Graphic-Processor-Units based software in time spans in order of microseconds, and this enables the study of slow relaxation processes characterizing bitumen. This paper focuses on the high-temperature dynamics as expressed through the mean-square displacement, the stress autocorrelation function, and rotational relaxation. The diffusivity of the individual molecules changes little as a function of temperature and reveals distinct dynamical time scales as a result of the different constituents in the system. Different time scales are also observed for the rotational relaxation. The stress autocorrelation function features a slow non-exponential decay for all temperatures studied. From the stress autocorrelation function, the shear viscosity and shear modulus are evaluated at the highest temperature, showing a viscous response at frequencies below 100 MHz. The model predictions of viscosity and diffusivities are compared to experimental data, giving reasonable agreement. The model shows that the asphaltene, resin and resinous oil tend to form nano-aggregates. The characteristic dynamical relaxation time of these aggregates is different from the homogeneously distributed parts of the system, leading to strong dynamical heterogeneity.

physics.chem-ph↗

arXiv2013

The Rosenfeld-Tarazona expression for liquids' specific heat: A numerical investigation of eighteen systems

We investigate the accuracy of the expression of Rosenfeld and Tarazona (RT) for the excess isochoric heat capacity, C_V^{ex} \propto T^{-2/5}, for eighteen model liquids. Previous investigations have reported no unifying features of breakdown for the RT expression. Here liquids with different stoichiometric composition, molecular topology, chemical interactions, degree of undercooling, and environment are investigated. We find that the RT expression is a better approximation for liquids with strong correlations between equilibrium fluctuations of virial and potential energy, i.e., Roskilde simple liquids [Ingebrigtsen et al., Phys. Rev. X 2, 011011 (2012)]. This observation holds even for molecular liquids under severe nanoscale confinement, the physics of which is completely different from the original RT bulk hard-sphere fluid arguments. The density dependence of the specific heat is predicted from the isomorph theory for Roskilde simple liquids, which in combination with the RT expression provides a complete description of the specific heat's density and temperature dependence.

cond-mat.soft↗

arXiv2013

Isomorph invariance of Couette shear flows simulated by the SLLOD equations of motion

Non-equilibrium molecular dynamics simulations were performed to study the thermodynamic, structural, and dynamical properties of the single-component Lennard-Jones and the Kob-Andersen binary Lennard-Jones liquids. Both systems are known to be strongly correlating, i.e., have strong correlations between equilibrium thermal fluctuations of virial and potential energy. Such systems have good isomorphs, i.e., curves in the thermodynamic phase diagram along which structural, dynamical, and some thermodynamic quantities are invariant when expressed in reduced units. The SLLOD equations of motion were used to simulate Couette shear flows of the two systems. We show analytically that these equations are isomorph invariant provided the reduced strain rate is fixed along the isomorph. Since isomorph invariance is generally only approximate, a range of shear rates were simulated to test for the predicted invariance, covering both the linear and non-linear regimes. For both systems, when represented in reduced units the radial distribution function and the intermediate scattering function collapse for state points that are isomorphic. The strain-rate dependence of the viscosity, which exhibits shear thinning, is also invariant along an isomorph. Our results extend the isomorph concept to the state-state non-equilibrium situation of a shear flow, in which the phase diagram is three dimensional because the shear rate defines the third dimension.

cond-mat.soft↗

arXiv2012

Do the repulsive and attractive pair forces play separate roles for the physics of liquids?

According to standard liquid-state theory repulsive and attractive pair forces play distinct roles for the physics of liquids. This paradigm is put into perspective here by demonstrating a continuous series of pair potentials that have virtually the same structure and dynamics, although only some of them have attractive forces of significance. Our findings reflect the fact that the motion of a given particle is determined by the total force on it, whereas the quantity usually discussed in liquid-state theory is the individual pair force.

cond-mat.soft↗

arXiv2012

Thermodynamics of condensed matter with strong pressure-energy correlations

We show that for any liquid or solid with strong correlation between its $NVT$ virial and potential-energy equilibrium fluctuations, the temperature is a product of a function of excess entropy per particle and a function of density, $T=f(s)h(ρ)$. This implies that 1) the system's isomorphs (curves in the phase diagram of invariant structure and dynamics) are described by $h(ρ)/T={\rm Const.}$, 2) the density-scaling exponent is a function of density only, 3) a Gr{ü}neisen-type equation of state applies for the configurational degrees of freedom. For strongly correlating atomic systems one has $h(ρ)=\sum_nC_nρ^{n/3}$ in which the only non-zero terms are those appearing in the pair potential expanded as $v(r)=\sum_n v_n r^{-n}$. Molecular dynamics simulations of Lennard-Jones type systems confirm the theory.

cond-mat.soft↗

arXiv2012

What constitutes a simple liquid?

Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair potentials. We suggest that a simple liquid should be defined instead by the property of having strong correlation between virial and potential energy equilibrium fluctuations in the NVT ensemble. There is considerable overlap between the two definitions, but also some notable differences. For instance, in the new definition simplicity is not a property of the intermolecular potential only because a liquid is usually only strongly correlating in part of its phase diagram. Moreover, according to the new definition not all simple liquids are atomic (i.e., with radially symmetric pair potentials) and not all atomic liquids are simple. The main part of the paper motivates the new definition of liquid simplicity by presenting evidence that a liquid is strongly correlating if and only if its intermolecular interactions may be ignored beyond the first coordination shell (FCS). This is demonstrated by NVT simulations of structure and dynamics of 15 atomic and molecular model liquids with a shifted-forces cutoff placed at the first minimum of the radial distribution function. No proof is given that the chemical characterization follows from the strong correlation property, but it is shown to be consistent with the existence of isomorphs in strongly correlating liquids' phase diagram. Finally, we note that the FCS characterization of simple liquids calls into question the basis for standard perturbation theory, according to which the repulsive and attractive forces play fundamentally different roles for the physics of liquids.

cond-mat.soft↗

arXiv2011

Beyond power-law density scaling: Theory, Simulation, and Experiment

Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. Many liquids have been shown to obey power-law density scaling, according to which the relaxation time is a function of density to some power over temperature. We show that power-law density scaling breaks down for larger density variations than usually studied. This is demonstrated by simulations of the Kob-Andersen binary Lennard-Jones mixture and two molecular models, as well as by experimental results for two van der Waals liquids. A more general form of density scaling is derived, which is consistent with results for all the systems studied. An analytical expression for the scaling function for liquids of particles interacting via generalized Lennard-Jones potentials is derived and shown to agree very well with simulations. This effectively reduces the problem of understanding the viscous slowing down from being a quest for a function of two variables to a search for a single-variable function.

cond-mat.soft↗