Onset of Chain Entanglements in Block Copolymer Lamellae

Pan, Xiaohong; Shaffer, James P.

doi:10.1021/ma951907y

Cited by 10 publications

(22 citation statements)

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“…There have been some simulation studies of chain motion in the lamellar phase of diblock copolymers. Pan and Shaffer carried out a lattice Monte Carlo simulation of diffusion in a strongly segregated symmetric (χ N = 45) diblock system. The stated purpose of this work was to check whether the entanglement length N e , as determined from the variation of the diffusion constant with the chain length, is different from N e in a homopolymer melt.…”

Section: Introductionmentioning

confidence: 99%

Statics and Dynamics of Symmetric Diblock Copolymers: A Molecular Dynamics Study

1999

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Extensive molecular dynamics simulations are carried out to study static and dynamic properties of symmetric diblock copolymer melts, both in the disordered and in the lamellar phases. The lamellar phase is constructed using the natural lamellar spacing, determined from constant pressure simulations. The non-Gaussian character of the chains in the disordered phase is demonstrated and quantified. In the lamellar phase, the density profile of the separate blocks, as well as the interface thickness are determined as a function of chain length N and AB interaction parameter ε, and compared with experiments and other theoretical results. Single chain and single block form factors indicate that the chains in the lamellar phase are distorted into stick-like objects. Our results in the disordered phase show a stronger dependence of the diffusion constant on the chain length than observed in previous simulations. Diffusion within the lamellar plane for systems with chains of length N ≤ 100 monomers is found to be almost independent of ε, in agreement with the predictions by Barrat and Fredrickson for Rouse chains. Diffusion perpendicular to the lamellae is exponentially suppressed with increasing ε. Simulations with even longer chains (up to N = 400 monomers) indicate that, in the strong segregation regime, chain stretching lowers the entanglement density and shifts the tube motion characteristic of the chain dynamics in homogeneous melts of long chains toward much longer chains.

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Section: Introductionmentioning

confidence: 99%

Statics and Dynamics of Symmetric Diblock Copolymers: A Molecular Dynamics Study

1999

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“…In this work, we have presented Monte Carlo simulation results for polymer melts and blends with a range of densities, compositions and chain lengths. In order to represent the two components of a binary blend, we have generalized Shaffer's bond fluctuation model for athermal melts 51,52,53 by introducing attractive interactions between occupied non-bonded nearest neighbor sites on the lattice. The interactions parameters employed in this work are ǫ AA = −1ǫ and ǫ BB = −2ǫ for like interactions between monomers of type A and B, respectively, and ǫ AB = −2ǫ for interactions between unlike monomers.…”

Section: Discussionmentioning

confidence: 99%

“…Shaffer's bond fluctuation model 51,52,53 is a lattice model for polymer chains, where the monomers occupy sites of a simple cubic lattice. In the following, we will take the size of the unit cell, i.e.…”

Section: Blend Model For Monte Carlo Simulationmentioning

confidence: 99%

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Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Luettmer-Strathmann

Mantina

2006

The Journal of Chemical Physics

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Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.

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“…Later, intense work has been devoted to studying ordered lamellar structures below the ODT in melts of symmetrical diblock copolymers, and analyzing them with respect to their structure, their dynamics, and their fluctuations [320][321][322][323][324][325][326][327][328][329][330][331]. Simulation studies of asymmetric diblock copolymer melts have also reproduced most of the other mesophases -the cylindrical phase, the bcc sphere phase, and even the gyroid phase [204,211,235,[332][333][334][335].…”

Section: Copolymer Systemsmentioning

confidence: 99%

Theory and Simulation of Multiphase Polymer Systems

Schmid

2011

Handbook of Multiphase Polymer Systems

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The theory of multiphase polymer systems has a venerable tradition. The 'classical' theory of polymer demixing, the Flory-Huggins theory, was developed in the 1940s [1,2]. It is still the starting point for most current approaches -be they improved theories for polymer (im)miscibility that take into account the microscopic structure of blends more accurately, or sophisticated field theories that allow to study inhomogeneous multicomponent systems of polymers with arbitrary architectures in arbitrary geometries. In contrast, simulations of multiphase polymer systems are quite young. They are still limited by the fact that one must simulate a large number of large molecules in order to obtain meaningful results. Both powerful computers and smart modeling and simulation approaches are necessary to overcome this problem.In the limited space of this chapter, we can only give a taste of the state-of-the-art in both areas, theory and simulation. Since the theory has reached a fairly mature stage by now, many aspects of it are covered in textbooks on polymer physics [3][4][5][6][7][8][9]. The information on the state-of-the art of simulations is much more scattered. This is why we have put some effort into putting together a representative list of references in this area -which is of course still far from complete.The chapter is organized as follows. In Section II, we briefly introduce some basic concepts of polymer theory. The purpose of this part is to make the chapter accessible to readers who are not very familiar with polymer physics; it can safely be skipped by the others. Section III is devoted to the theory of multiphase polymer systems. We recapitulate the Flory-Huggins theory and introduce in particular the concept of the Flory interaction parameter (the χ parameter), which is a central ingredient in most theoretical descriptions of multicomponent polymer systems. Then we focus on one of the most successful mean-field theories for inhomogeneous (co)polymer blends, the self-consistent field theory. We sketch the main idea, discuss various Handbook of Multiphase Polymer Systems, First Edition. Edited by Abderrahim Boudenne, Laurent Ibos, Yves Candau, and Sabu Thomas.

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Onset of Chain Entanglements in Block Copolymer Lamellae

Cited by 10 publications

References 31 publications

Statics and Dynamics of Symmetric Diblock Copolymers: A Molecular Dynamics Study

Statics and Dynamics of Symmetric Diblock Copolymers: A Molecular Dynamics Study

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Theory and Simulation of Multiphase Polymer Systems

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