Computational Approaches for Structure Formation in Multicomponent Polymer Melts

Müller, Marcus

doi:10.1002/9783527630257.ch5

Cited by 3 publications

(5 citation statements)

References 151 publications

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“…The calculation of the bonded energy is straightforward since explicit coordinates are available. However, to calculate the collective variables ρ(r) and Q(r) from the particle coordinates in the simulations the δ-function in equations ( 4) has to be replaced with a smoothed function, as has been discussed in detail in [58]. Various approaches have been proposed defining the weighting function either in continuum space [25][26][27] or via a grid [18,59,19,23].…”

Section: The Simulation Approachmentioning

confidence: 99%

“…Thus the calculation of the non-bonded energy of a given configuration becomes straightforward and MC sampling can be used. It is instructive [19,58] to substitute the collective variables, as defined in equations (12), into the discretized effective Hamiltonian. After some algebra (for more details see the appendix) the final result reads…”

Section: The Simulation Approachmentioning

confidence: 99%

“…Two magnified snapshots of the same melt obtained for the isotropic (υ = 2.12) and the nematic phase (υ = 4.54) are shown on the right. All P3HT chains are identical; however a two-colour scheme is used to facilitate visualization of the assigning function is a model parameter which controls the average range of the non-bonded interactions [19,58]. In our case this range is important for controlling the thermodynamic behaviour of the system, namely the isotropic-nematic transition.…”

Section: The Simulation Approachmentioning

confidence: 99%

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Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

Daoulas

Rühle

Kremer

2012

J. Phys.: Condens. Matter

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We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.

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Section: The Simulation Approachmentioning

confidence: 99%

Section: The Simulation Approachmentioning

confidence: 99%

Section: The Simulation Approachmentioning

confidence: 99%

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Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

Daoulas

Rühle

Kremer

2012

J. Phys.: Condens. Matter

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“…2 N can be studied by molecular simulation. In section 3.3 we will study molecules with N = 16 384, which is not feasible with a Lennard-Jones bead-spring model [46].…”

Section: Dynamic Single-chain-in-mean-field Simulations Of a Soft Coa...mentioning

confidence: 99%

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

Léonforte¹,

Servantie²,

Pastorino³

et al. 2011

J. Phys.: Condens. Matter

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Abstract. The properties of polymer liquids on hard and soft substrates are investigated by molecular dynamics simulation of a coarse-grained bead-spring model and dynamic single-chain-in-mean-field (SCMF) simulations of a soft, coarse-grained polymer model. Hard, corrugated substrates are modelled by an FCC LennardJones solid while polymer brushes are investigated as a prototypical example of a soft, deformable surface. From the molecular simulation we extract the coarse-grained parameters that characterise the equilibrium and flow properties of the liquid in contact with the substrate: the surface and interface tensions, and the parameters of the hydrodynamic boundary condition. The so-determined parameters enter a continuum description like the Stokes equation or the lubrication approximation.At high temperatures the Navier slip condition provides an appropriate description of the flow past hard, corrugated surfaces. The position, x b , where the hydrodynamic boundary condition is to be enforced, agrees with the location of the liquid-solid interface and the slip length can be consistently identified by comparing planar shear flow and parabolic, pressure-driven flow. If the surface become strongly attractive or the surface is coated with a brush, the Navier slip condition will fail to consistently describe the flow at the boundary. This failure can be traced back to a boundary layer with an effective, higher viscosity.The solvent flow past a polymer brush induces a cyclic, tumbling motion of the tethered chain molecules. The collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations in the flow. Both, molecular dynamics as well as dynamic SCMF simulations, provide evidence that the flow past a polymer brush cannot be described by Brinkmann's equation.The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. The steady state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface.On a soft, deformable substrate like a polymer brush, we observe a lifting up ofFlow past hard and soft surfaces 2 the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters to maximise the deformation at the three-phase contact.

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“…Copolymers have gained increasing attention in the last decades—from the technological as well as from the theoretical point of view1–20—as they offer numerous possibilities of adjusting molecular properties, eventually leading to complex materials featuring new and promising characteristics. In case of block copolymers, e.g., phase separation21, 22 occurs if a repulsive interaction between segments of different sub‐chains (blocks) is operative.…”

Section: Introductionmentioning

confidence: 99%

Concentration Dependence of Size, Shape, and Orientation of Copolymers, 1 – Linear Diblock and 4‐arm Hetero Star Polymers

Nardai

Zifferer

2011

Macro Theory & Simulations

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By use of dissipative particle dynamics (DPD) symmetric mictoarm star polymers with four arms and the degenerated case of a linear diblock copolymer (consisting of moderately hostile monomers) are simulated in a selective solvent for concentrations reaching from high dilution to the solvent free bulk. They are analyzed with respect to size, shape, morphology and mobility and compared to their constituent homopolymers. For larger concentrations the shape of pair distribution functions as well as representative snapshots show the development of lamellae, accompanied by characteristic changes of chain/star properties. In addition the influence of the size of the simulation box on the thickness d and orientation of lamellae in bulk is utilized to study the correlation between chain/star properties and d in detail.magnified image

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Computational Approaches for Structure Formation in Multicomponent Polymer Melts

Cited by 3 publications

References 151 publications

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

Concentration Dependence of Size, Shape, and Orientation of Copolymers, 1 – Linear Diblock and 4‐arm Hetero Star Polymers

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