Microphase separation in topologically constrained ring copolymers

Weyersberg, A.; Vilgis, Thomas A.

doi:10.1103/physreve.49.3097

Cited by 19 publications

(28 citation statements)

References 21 publications

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“…The random phase approximation, with assumed Gaussian statistics, shows 48,49) that the transition to the ordered lamellar phase occurs at the temperature T ring = 1.78T linear (for symmetric rings), where T linear is the temperature for the transition to the lamellar phase in the linear diblock copolymer system. This result compares very well with simulations 47) , despite the fact that the ring statistics is certainly not Gaussian. When we decrease the temperature the rings strongly stretch along the axis connecting the centers of mass of two blocks.…”

Section: Introductionsupporting

confidence: 79%

“…The result for the microphase separation obtained in the random phase approximation has been confirmed in the computer simulations 47) . This result is in fact surprising, since in the random phase approximation it is assumed that chains adopt the Gaussian configurations, whereas in the ring system the constraints are such that the statistics is not Gaussian even in the limit of N → ∞.…”

Section: A Ring Copolymerssupporting

confidence: 63%

“…This result is in fact surprising, since in the random phase approximation it is assumed that chains adopt the Gaussian configurations, whereas in the ring system the constraints are such that the statistics is not Gaussian even in the limit of N → ∞. The scaling exponent for the radius of gyration is ν = 0.45 (R g ∼ N ν ) as has been found in computer simulations 47,81,82 and theory 46b) . The comparison of the radius of gyration for the linear diblock chain and ring diblock chain is shown in Fig.19.…”

Section: A Ring Copolymersmentioning

confidence: 67%

“…The same applies to ring diblock copolymers 47) . As the temperature is lowered the strong increase (20-25%) in the distance between the center of masses of two blocks is observed (Fig.20).…”

Section: A Ring Copolymersmentioning

confidence: 98%

“…The topological constraint introduced by this chain architecture, prevents the different chains from entangledment or self-knotting ( gives the more accurate value 46b) of ν = 0.445. For the ring diblock copolymer the computer simulations 47) give ν = 0.45. Please note that at high temperature the scaling in the melt of ring polymers should be the same as in the ring diblock copolymer system.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Hołyst

Vilgis

1996

Macro Theory & Simulations

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The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers.The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chain close to critical points, fluctuations induced shift of phase boundaries. In particular

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Section: Introductionsupporting

confidence: 79%

Section: A Ring Copolymerssupporting

confidence: 63%

Section: A Ring Copolymersmentioning

confidence: 67%

Section: A Ring Copolymersmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Hołyst

Vilgis

1996

Macro Theory & Simulations

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Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Müller¹

1999

Macromol. Theory Simul.

106

113

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SUMMARY: Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory-Huggins theory becomes quantitatively correct in the long chain length limit, when the v parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the v parameter from small-angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like v p aqb 3 for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self-consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1a N p . Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non-additive monomer shapes, one has a large positive chain-length-independent entropic contribution to the v parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the v parameter of the order 10 -3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non-entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End-functionalized homopolymers of different...

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Monte Carlo studies of static properties of interacting lattice polymers with the cooperative‐motion algorithm

Gauger

Weyersberg

Pakuła

1993

Macro Theory & Simulations

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SUMMARYIn this paper we review some applications of the cooperative-motion simulation algorithm to dense polymer melts. The basic idea behind the algorithm and its implementation on a computer are discussed. Furthermore we show how to include intra-and intermolecular interactions in the simulation. Exemplary results are presented concerning on one hand the static properties of athermal and semiflexible lattice polymers and on the other hand the phase behaviour of polymer mixtures and diblock copolymers.

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Microphase separation in topologically constrained ring copolymers

Cited by 19 publications

References 21 publications

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

The structure and phase transitions in polymer blends, diblock copolymers and liquid crystalline polymers: The Landau‐Ginzburg approach

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Monte Carlo studies of static properties of interacting lattice polymers with the cooperative‐motion algorithm

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