Ideal contribution to the macroscopic quasiequilibrium entropy of anisotropic fluids

Ilg, Patrick; Hütter, Markus; Kröger, Martin

doi:10.1103/physreve.83.061713

Cited by 8 publications

(22 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Ilg et al [90,236,[299][300][301] developed a molecularly-derived constitutive equation for low-molecular-weight FENE polymer melts from thermodynamically guided simulations and, also, applied similar concepts to sheared demixing systems [302], liquid crystals [303][304][305][306] and ferrofluids [307,308].…”

Section: Molecularly-derived Constitutive Equationmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

Self Cite

View full text Add to dashboard Cite

The mechanical and physical properties of polymeric materials originate from the interplay of phenomena at different spatial and temporal scales. As such, it is necessary to adopt multiscale techniques when modeling polymeric materials in order to account for all important mechanisms. Over the past two decades, a number of different multiscale computational techniques have been developed that can be divided into three categories: (i) coarse-graining methods for generic polymers; (ii) systematic coarse-graining methods and (iii) multiple-scale-bridging methods. In this work, we discuss and compare eleven different multiscale computational techniques falling under these categories and assess them critically according to their ability to provide a rigorous link between polymer chemistry and rheological material properties. For each technique, the fundamental ideas and equations are introduced, and the most important results or predictions are shown and discussed. On the one hand, this review provides a comprehensive tutorial on multiscale computational techniques, which will be of interest to readers newly entering this field; on the other, it presents a critical discussion of the future opportunities and key challenges in the multiscale geometric mapping matrix between all-atomistic and coarse-grained models N number of monomers per chain N e entanglement length, which is the number of monomers between two entanglements n v number of polymer chains per unit volume n ij (n 0 (r ij )) entanglement number (at equilibrium) between particle pairs i and j p r , P R configurational probability distributions in all-atomistic and coarse-grained models, respectively R ee end-to-end distance of polymer chain R G radius of gyration of polymer chain s segment index/contour length variable along primitive chain S(q) single chain coherent dynamic scattering function Z number of entanglements per chain, defined as Z = N/N e α exponent in standard Mittag-Leffler function σ

show abstract

Section: Molecularly-derived Constitutive Equationmentioning

confidence: 99%

Challenges in Multiscale Modeling of Polymer Dynamics

et al. 2013

Self Cite

View full text Add to dashboard Cite

show abstract

“…18,19 One of the main aspects of this study is the obtention of free energies able to describe the transition from orientational disordered to ordered states in relation to density or temperature conditions. 1,2 The evaluation of this free energy is a difficult task 7 in which meanfield theories of anisotropic molecules in suspensions or pure systems have proven to be very powerful.…”

Section: Introductionmentioning

confidence: 99%

“…The two general approaches to the determination of the free-energy function can be categorized as equilibrium and dynamic ones, and lead to different non-trivial structural and dynamic properties of nematic liquid crystals. 1,2,4,7,18,19 Equilibrium approaches are focused on the direct calculation of the canonical distribution function, the partition function, and the free energy by taking into account the general symmetry properties of the system. 11,14,19,20 For uniaxial systems, this implies that the fourth order scalar orientational parameter can be expressed in terms of the second order scalar orientational parameter.…”

Section: Introductionmentioning

confidence: 99%

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Híjar

Hoyos

Santamaría‐Holek

2012

The Journal of Chemical Physics

View full text Add to dashboard Cite

Pattern formation in uniaxial polymeric liquid crystals is studied for different dynamic closure approximations. Using the principles of mesoscopic non-equilibrium thermodynamics in a mean-field approach, we derive a Fokker-Planck equation for the single-particle non-homogeneous distribution function of particle orientations and the evolution equations for the second and fourth order orientational tensor parameters. Afterwards, two dynamic closure approximations are discussed, one of them considering the relaxation of the fourth order orientational parameter and leading to a novel expression for the free-energy like function in terms of the scalar order parameter. Considering the evolution equation of the density of the system and values of the interaction parameter for which isotropic and nematic phases coexist, our analysis predicts that patterns and traveling waves can be produced in lyotropic uniaxial nematics even in the absence of external driving.

show abstract

“…In addition, the Lagrange multiplier obeys a similar relation as the dual variable to the orientational order parameter, Λ = −∂(βF)/∂Q, see Equation (21). The generalized free energy can always be split as F = F id + F int , where the contribution of the ideal orientational entropy F id = −T S id in the absence of inter-particle interactions (H = 0) has been worked out recently [29]. There, a rather accurate interpolation formula was found,…”

Section: From Micro To Macromentioning

confidence: 99%

“…Taking advantage of the known form of the ideal orienational free energy for non-interacting particles F id from [29], we subtract this term from ∆F and are left with the interaction contribution…”

Section: ∆F / Nktmentioning

confidence: 99%

Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals

Gupta

Ilg

2013

Polymers

Self Cite

View full text Add to dashboard Cite

The Landau-de Gennes theory provides a successful macroscopic description of nematics. Cornerstone of this theory is a phenomenological expression for the effective free energy as a function of the orientational order parameter. Here, we show how such a macroscopic Landau-de Gennes free energy can systematically be constructed for a microscopic model of liquid crystals formed by interacting mesogens. For the specific example of the Gay-Berne model, we obtain an enhanced free energy that reduces to the familiar Landau-de Gennes expression in the limit of weak ordering. By carefully separating energetic and entropic contributions to the free energy, our approach reconciles the two traditional views on the isotropic-nematic transition of Maier-Saupe and Onsager, attributing the driving mechanism to attractive interactions and entropic effects, respectively.

show abstract

Ideal contribution to the macroscopic quasiequilibrium entropy of anisotropic fluids

Cited by 8 publications

References 32 publications

Challenges in Multiscale Modeling of Polymer Dynamics

Challenges in Multiscale Modeling of Polymer Dynamics

Pattern formation from consistent dynamical closures of uniaxial nematic liquid crystals

Energetic and Entropic Contributions to the Landau–de Gennes Potential for Gay–Berne Models of Liquid Crystals

Contact Info

Product

Resources

About