Athermal Systems Research Articles

Analysis and applications of a group contribution sPC-SAFT equation of state

A group contribution (GC) method for estimating pure compound parameters for the molecular-based perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EoS) is proposed in a previous work [A. Tihic, G.M. Kontogeorgis, N. von Solms, M.L. Michelsen, L. Constantinou, Ind. Eng. Chem. Res. 47 (2008) 5092–5101]. In this paper, an investigation of the predictive capability of the GC sPC-SAFT EoS through comparison of the method’s predictions for compounds with high molecular weights and several selected binary mixtures of industrial significance with experimental data such as thiols, sulphides and polynuclear aromatics is presented. Additionally, predictions of activity coefficient at infinite dilution for athermal systems are compared with the results using existing activity coefficient models. The results show that calculated pure compound parameters using the proposed GC method allow satisfactory representation of experimental data of investigated systems with the sPC-SAFT EoS. Moreover, the variety of functional groups in the available GC scheme ensures broad applications of the GC sPC-SAFT EoS.

Asymmetric Exclusion Processes with Constrained Dynamics

Asymmetric exclusion processes with locally reversible kinetic constraints are introduced to investigate the effect of nonconservative driving forces in athermal systems. At high density they generally exhibit rheological-like behavior, negative differential resistance, two-step structural relaxation, dynamical heterogeneity and, possibly, a jamming transition driven by the external field.

Structural transitions in granular packs: statistical mechanics and statistical geometry investigations

We investigate equal spheres packings generated from several experiments and from a large number of different numerical simulations. The structural organization of these disordered packings is studied in terms of the network of common neighbours. This geometrical analysis reveals sharp changes in the network's clustering occurring at the packing fractions (fraction of volume occupied by the spheres respect to the total volume, $\rho$) corresponding to the so called Random Loose Packing limit (RLP, $\rho \sim 0.555$) and Random Close Packing limit (RCP, $\rho \sim 0.645$). At these packing fractions we also observe abrupt changes in the fluctuations of the portion of free volume around each sphere. We analyze such fluctuations by means of a statistical mechanics approach and we show that these anomalies are associated to sharp variations in a generalized thermodynamical variable which is the analogous for these a-thermal systems to the specific heat in thermal systems.

Direct Observation of Medium-Range Crystalline Order in Granular Liquids Near the Glass Transition

Collective behavior of driven granular matter is often strikingly analogous to that of thermal systems. Here we use a vibrated quasi-two-dimensional granular matter as a model system and investigate the mechanism of the liquid-glass transition. We demonstrate by direct observation the existence of long-lived medium-range crystalline order, which is found to be closely related to both dynamic heterogeneity and slow dynamics. Our findings are remarkably similar to recent numerical results on model thermal liquids and thus open an intriguing possibility of understanding the dynamic arrest in both thermal and athermal systems in a unified manner.

Smectic ordering in athermal systems of rodlike triblock copolymers

The phase behavior of the system of parallel rigid triblock copolymers is examined using the second virial density functional theory. The triblock particle consists of two identical infinitely thin hard rods of finite lengths on the opposite ends of one central hard cylinder with nonzero length and diameter. Stability analyses and free energy calculations show that the system of parallel particles can form not only uniform nematic and smectic A phases but also a smectic C phase. The stability and structure of the tilted structure are controlled by only the diameter and the length of the central cylinder segment. Interestingly, the diameter affects only the layer tilting and the periodicity, but not the packing fraction of the nematic to smectic-C transition. For all values of cylinder length the usual smectic A and smectic C transitions compete with each other and no nematic-columnar transition is observed. At low and high cylinder lengths the smectic A phase is stabilized first, while the smectic C is the most stable for intermediate length values.

Classical and recent free-volume models for polymer solutions: A comparative evaluation

In this work, two “classical” (UNIFAC-FV, Entropic-FV) and two “recent” free-volume (FV) models (Kannan-FV, Freed-FV) are comparatively evaluated for polymer–solvent vapor–liquid equilibria including both aqueous and non-aqueous solutions. Moreover, some further developments are presented here to improve the performance of a recent model, the so-called Freed-FV. First, we propose a modification of the Freed-FV model accounting for the anomalous free-volume behavior of aqueous systems (unlike the other solvents, water has a lower free-volume percentage than polymers). The results predicted by the modified Freed-FV model for athermal and non-athermal polymer systems are compared to other “recent” and “classical” FV models, indicating an improvement for the modified Freed-FV model for aqueous polymer solutions. Second, for the original Freed-FV model, new UNIFAC group energy parameters are regressed for aqueous and alcohol solutions, based on the physical values of the van der Waals volume and surface areas for both FV-combinatorial and residual contributions. The prediction results of both “recent” and “classical” FV models using the new regressed energy parameters are significantly better, compared to using the classical UNIFAC parameters, for VLE of aqueous and alcohol polymer systems.

Microstructure and Self-Assembly of Inhomogeneous Rigid Rodlike Chains between Two Neutral Surfaces: A Hybrid Density Functional Approach

We use a hybrid density functional approach to investigate the microstructure and self-assembly of inhomogeneous rigid rodlike chains between two neutral surfaces, i.e., two hard walls. In the calculation, the rodlike molecule is modeled as a rigid rod linearly connected by the tangent sphere beads. The hybrid method combines a single-chain Monte Carlo (MC) simulation for the ideal-gas part of Helmholtz energy and a DFT approach for the excess Helmholtz energy. The DFT approach includes a modified fundamental measure theory for the excluded-volume effect, the first order thermodynamics perturbation theory for chain connectivity, and the mean field approximation for the van der Waals attraction. We investigate the effect of the chain length (i.e., aspect ratio) of the rodlike molecule and the separation between two surfaces on the microstructure and self-assembly of inhomogeneous rigid rodlike chains. For the athermal systems, the rodlike chain fluids present a smaller partitioning coefficient compared to the flexible chain fluids. For the thermal systems, lamellar thin films formed by the rigid rodlike molecules perpendicular to the neutral surface are observed. The effects of the head-head interaction and the separation on the self-assembly of the rodlike chain fluids in the slit are investigated.

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

We perform molecular dynamics simulations of model frictionless granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time t(l) required for the velocity profiles to become linear and find that t(l) increases as a power law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.

An improved prediction result of entropic‐FV model for vapor–liquid equilibria of solvent–polymer systems

AbstractIn this work, entropic expressions of UNIFAC‐FV and Entropic‐FV models were evaluated by using an extensive database of infinite dilution vapor–liquid equilibrium (VLE) data of athermal systems containing polypropylene, polyethylene, and polyisobutylene. For the infinite dilution athermal systems, performance of the Entropic‐FV model was better than that of the UNIFAC‐FV model. Then, finite concentration VLE data of non‐athermal systems that consisted of 16 polymers and 36 solvents containing a large variety of solvent–polymer systems ranging from nonpolar to polar substances were considered to optimized 46 pairs of group interaction parameters of the Entropic‐FV model. For systems containing polar solvents of three types of solvents studied, revised group interaction parameters gave significant improvements from 17.9 to 13.0% average absolute deviation (AAD) of solvent activities. For overall results, improvements were achieved from 15.1 to 12.4% AAD. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1145–1153, 2005

Effective Temperature in Athermal Systems Sheared at Fixed Normal Load

We perform molecular dynamics simulations of repulsive athermal systems sheared at fixed normal load to study the effective temperature TL defined from time-dependent fluctuation-dissipation relations for density. We show that these systems possess two distinct regimes as a function of the ratio TS/V of the granular temperature to the potential energy per particle. At small TS/V, these systems are pressure controlled and TL is set by the normal load. In contrast, they behave as quasiequilibrium systems with TL approximately TS that increases with the shear rate at large TS/V. These results point out several problems with using TL in thermodynamic descriptions of slowly sheared athermal systems.

Velocity Profiles in Repulsive Athermal Systems under Shear

We conduct molecular dynamics simulations of athermal systems undergoing boundary-driven planar shear flow in two and three spatial dimensions. We find that these systems possess nonlinear mean velocity profiles when the velocity u of the shearing wall exceeds a critical value u(c). Above u(c), we also show that the packing fraction and mean-square velocity profiles become spatially dependent with dilation and enhanced velocity fluctuations near the moving boundary. In systems with overdamped dynamics, u(c) is only weakly dependent on packing fraction phi. However, in systems with underdamped dynamics, u(c) is set by the speed of shear waves in the material and tends to zero as phi approaches phi(c), which is near random close packing at small damping. For underdamped systems with phi<phi(c), u(c) is zero; thus they possess nonlinear velocity profiles at any nonzero u.

Dynamics of Driven Systems from Newtonian to Athermal Limits

The dynamics and properties of driven flowing systems are examined using non-equilibrium molecular dynamics (NEMD) simulations in conjunction with an energy landscape analysis. The systems are analyzed as a function of temperature and driving rate, and span the range from high temperature/low driving rate to low temperature/high driving rate. In the high temperature/low driving rate limit the dynamics are due to thermally activated transitions, while in the low temperature/high driving rate limit the dynamics are due to the external driving force. The purpose of this investigation is to link the properties of flowing thermal system (e.g. liquids and colloids) to flowing athermal systems (e.g. foams and granular materials).

Local stress relaxation and shear banding in a dry foam under shear.

We have developed a realistic simulation of 2D dry foams under quasistatic shear. After a short transient, a shear-banding instability is observed. These results are compared with measurements obtained on real 2D (confined) foams. The numerical model allows us to exhibit the mechanical response of the material to a single plastication event. From the analysis of this elastic propagator, we propose a scenario for the onset and stability of the flow localization process in foams, which should remain valid for most athermal amorphous systems under creep flow.

A simulation study of lyotropic isotropic–nematic phase transitions in polydisperse chain systems

The isotropic–nematic (I–N) phase behavior of athermal chain-length polydisperse systems was investigated by molecular simulation. The approach adopted involved the formulation of a novel semigrand Gibbs-type of ensemble for polydisperse chain systems, the use of extrapolation methods (like histogram reweighting) to target polydispersities of interest, and the implementation of both intermutation moves among species and expanded-ensemble moves (for the transfer of the shortest chains) to attain chemical potential equilibration. This approach was first used to illustrate how the results of a system with bimodal polydispersity distribution can be used to get coexistence data for a bidisperse system of short and long chains, thereby circumventing the need to insert/delete the longest molecules. Simulations were then used to examine the effect of osmotic pressure (concentration) and the shape of the chain-length polydispersity function on the I–N phase transitions. In agreement with the predictions of Flory theory, the phase behavior of a unimodal (Poisson) parent distribution showed significant partitioning of the components between the coexisting phases, wherein longer chains concentrate in the nematic phase. Within the biphasic region, the order parameter in the nematic phase increased with pressure despite the growing proportion of shorter chains. Very short chains, like dimers and trimers, were found to be disordered in the nematic phase. Partitioning effects are more pronounced when the parent system had a flatter or a bimodal chain-length distribution. Flory theory gives a good description of the partition effects, but significantly overestimates the coexisting concentrations and the nematic ordering.

The nature of the colloidal 'glass' transition.

The dynamically arrested state of matter is discussed in the context of athermal systems, such as the hard sphere colloidal arrest. We believe that the singular dynamical behaviour near arrest expressed, for example, in how the diffusion constant vanishes may be 'universal', in a sense to be discussed in the paper. Based on this we argue the merits of studying the problem with simple lattice models. This, by analogy with the the critical point of the Ising model, should lead us to clarify the questions, and begin the program of establishing the degree of universality to be expected. We deal only with 'ideal' athermal dynamical arrest transitions, such as those found for hard sphere systems. However, it is argued that dynamically available volume (DAV) is the relevant order parameter of the transition, and that universal mechanisms may be well expressed in terms of DAV. For simple lattice models we give examples of simple laws that emerge near the dynamical arrest, emphasising the idea of a near-ideal gas of 'holes', interacting to give the power law diffusion constant scaling near the arrest. We also seek to open the discussion of the possibility of an underlying weak coupling theory of the dynamical arrest transition, based on DAV.

Stokes-Einstein-like relation for athermal systems and glasses under shear.

Finite temperature and athermal simulations are used to determine the viscosity mu and diffusivity D for systems undergoing shear flow at shear rate gamma and temperature T. Athermal simulations show that mu approximately gamma(-1) and D approximately gamma due to strain-activated relaxations, leading to an athermal Stokes-Einstein-like relation muD=C(ASE). Finite temperature simulations show that at high T the Stokes-Einstein relation muD=C(SE)T is followed, and as T decreases muD diverges in the Newtonian limit, but muD reaches the constant value C(ASE) for finite gamma. These different behaviors of muD suggest that particle dynamics are fundamentally different as jamming is approached by reducing a driving force as opposed to cooling, and that dynamic heterogeneities play a different role in shear-induced dynamics.

Studies of polymer conformation and dynamics in two dimensions using simulations based on the Dynamic Lattice Liquid (DLL) model

The Dynamic Lattice Liquid (DLL) model has been implemented as a simulation algorithm for two-dimensional (2-D) polymeric systems. The model can work with density factor ρ=1 and became a basis for a parallel algorithm, which takes into account coincidences of elementary molecular motion attempts resulting in local cooperative structural transformations. Systematic studies of athermal polymer systems on the two-dimensional triangular lattice are presented for various concentrations of linear polymers with respect to an explicitly considered solvent. Both static and dynamic properties are characterized. The simulation results reflect molecular packing and other properties of monomolecular polymer layers, which can be relevant to these obtained in some thin film formation techniques.

Application of density functional theory to tethered polymer chains: Athermal systems

Athermal, tethered chains are modeled with density functional (DFT) theory for both the explicit solvent and continuum solvent cases. The structure of DFT is shown to reduce to self-consistent-field theory in the incompressible limit where there is symmetry between solvent and monomer, and to single-chain-mean-field (SCMF) theory in the continuum solvent limit. We show that by careful selection of the reference and ideal systems in DFT theory, self-consistent numerical solutions can be obtained, thereby avoiding the single chain Monte Carlo simulation in SCMF theory. On long length scales, excellent agreement is seen between the simplified DFT theory and molecular dynamics simulations of both continuum solvents and explicit-molecule solvents. In order to describe the structure of the polymer and solvent near the surface it is necessary to include compressibility effects and the nonlocality of the field.

Revision of UNIFAC group interaction parameters of group contribution models to improve prediction results of vapor–liquid equilibria for solvent–polymer systems

The objective of this work was to improve the accuracy of group contribution models for prediction of solvent activities in polymer solutions by revising UNIFAC group interaction parameters using a wide range of vapor–liquid equilibrium (VLE) data of solvent–polymer systems. The group contribution models considered in this work were UNIFAC-FV, Entropic-FV, GK-FV and UNIFAC-ZM models. A total of 142 systems that consisted of 16 polymers and 36 solvents containing a large variety of solvent–polymer systems ranging from non-polar to polar substances were considered to optimize 46 pairs of group interaction parameters. Data considered were split up into systems containing alkane and cycloalkane, aromatic, and polar solvents. For athermal systems, the UNIFAC-FV model gave the best results. Therefore, the model was used in optimizing the group parameters. Revised group interaction parameters were found to improve the reliability of VLE predictions in solvent–polymer systems. A significant improvement of prediction results was achieved by UNIFAC-FV model from 20.0 to 10.8% absolute average deviation (AAD) in solvent activities for systems containing polar solvents and from 16.7 to 10.9% AAD for all systems. The prediction results of GK-FV and UNIFAC-ZM models were also improved.

Shape distribution and correlation between size and shape of star-branched tetrahedral lattice chains in athermal and theta systems

By means of Monte Carlo simulation, linear (F=2) and star-branched tetrahedral lattice chains with F=3–12 arms of length n=480 connected to a hard core consisting of MIN(5,F+1) segments (the total number of segments thus ranging from 963 to 5765) were produced for athermal and theta conditions. Nonreversal random walks (random walks without backfolding bonds) were generated as a reference. Several quantities (asphericity factor δ*, prolateness factor S*, and shape factors sfi*) characteristic of the instantaneous shape of molecules—being based on the orthogonal components of the squared radius of gyration taken along the principal axes of inertia—were computed. The probability distributions of these quantities were calculated and their interdependence as well as their correlation with quantities characteristic of the size of configurations was analyzed. Shape and size of star-branched chains for athermal as well as for theta conditions are highly correlated as earlier found for linear chains and random walk stars. The broadness of distribution functions decreases with increasing number of arms, but remains appreciably for F=12, the system with the largest functionality evaluated.