Monte Carlo phase diagram for diblock copolymer melts

Matsen, Mark W.; Griffiths, Geoffrey; Wickham, Robert A.; Vassiliev, Oleg N

doi:10.1063/1.2140286

Cited by 57 publications

(46 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…This results in complex finite size artefacts. Nevertheless, phase diagrams have been obtained in recent years [337][338][339]. Particle-based and field-based simulations have provided evidence that for symmetrical diblock copolymers ( f = 1/2), the transition to the lamellar phase is shifted [224,340], compared to the mean-field phase diagram, and becomes first order [340][341][342], in agreement with the theoretical expectation [116] (see Section 3.…”

Section: Copolymer Systemssupporting

confidence: 74%

“…Two examples of phase diagrams obtained with different simulation methods are shown in Figure 3.8: One was calculated by Matsen et al [338] using Monte Carlo simulations of copolymers with length N = 30 in a simple lattice model (left), and one by Lennon et al [342] using field-theoretical calculations (right) at Ginzburg parameter C = 50. Both phase diagrams significantly improve on the SCF phase diagram of Figure 3.5 (right) in the weak segregation regime, and reproduce the main qualitative features of the experimental phase diagram (Figure 3.5, left): The transitions are first order everywhere.…”

Section: 25)mentioning

confidence: 99%

“…In recent years, researchers have also begun to simulate melts of more complex copolymers, e.g., starblock copolymers [343][344][345][346][347], rod-coil copolymers [348,349], diblock copolymers with one crystallizing component [338] and from field-theoretical Complex-Langevin simulations (Ginzburg parameter C = 50) by Lennon et al (right). [342] Symbols L,C,G correspond to diblock phases of Courtesy of reference [342].…”

Section: 25)mentioning

confidence: 99%

See 2 more Smart Citations

Theory and Simulation of Multiphase Polymer Systems

Schmid

2011

Handbook of Multiphase Polymer Systems

View full text Add to dashboard Cite

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.

show abstract

Section: Copolymer Systemssupporting

confidence: 74%

Section: 25)mentioning

confidence: 99%

Section: 25)mentioning

confidence: 99%

See 1 more Smart Citation

Theory and Simulation of Multiphase Polymer Systems

Schmid

2011

Handbook of Multiphase Polymer Systems

View full text Add to dashboard Cite

show abstract

“…In particular, those simulations [12] show a direct transition from disordered phase to C and G nanophases like in experiment [19] and particle Monte Carlo simulation [28,29], but unlike the SCFT phase diagram [9].…”

Section: A-b-b Melts Can Self-assemble Inmentioning

confidence: 74%

Diblock Copolymer Melt in Spherical Unit Cells of Higher Dimensionalities

et al. 2012

View full text Add to dashboard Cite

Using self-consistent eld theory in spherical unit cells of various dimensionality, D = 1, 2, 3, and 4, we calculate phase diagram of a diblock, A-b-B, copolymer melt in 4-dimensional space, d = 4. The phase diagram is parameterized by the chain composition, f , and incompatibility between A and B, quantied by the product χN . We predict 4 stable nanophases: layers, cylinders, 3D spherical cells, and 4D spherical cells. We also calculate orderdisorder and orderorder transition lines. In the strong segregation limit, that is for large χN , the orderorder transition compositions are determined by the strong segregation theory in its simplest form, for D = 1, 2, 3, and 4.

show abstract

“…In the study of diblock copolymer melts, Matsen et al also observed a hysteresis loop between the cooling and heating energy curves. [50,51] Figure 16 shows the typical temperature dependence of the heat capacity C v for the confined systems, as well as for the bulk one. We can clearly see that there are two peaks in each C v curve.…”

Section: The Variation Of Morphologies and Chainmentioning

confidence: 99%

Simulated Annealing Study of Self‐Assembly of Symmetric ABA Triblock Copolymers Confined in Cylindrical Nanopores

Wang

Jin

et al. 2008

Macro Theory & Simulations

View full text Add to dashboard Cite

We report a simulated annealing study of the self‐assembly of symmetric lamella‐forming ABA triblock copolymers confined in cylindrical nanopores. We systematically examine the dependence of the self‐assembled morphologies and structural parameters on the degree of confinement and the strength of the surface preference. We find that the confined morphologies for the symmetric ABA triblocks with fA = 1/2 are similar to those for the symmetric or nearly symmetric AB diblock copolymers under the same confinement. We also find that different structural parameters can reflect different information. The predicted bridging fraction value for the bulk phase is in good agreement with previously established values, whereas the predicted values for the confined morphologies change with both the degree of confinement and the strength of the surface preference. We further explore the self‐assembling process by examining the morphology and various ensemble‐averaged thermodynamic quantities and structure parameters as a function of the reduced temperature.

show abstract

Monte Carlo phase diagram for diblock copolymer melts

Cited by 57 publications

References 54 publications

Theory and Simulation of Multiphase Polymer Systems

Theory and Simulation of Multiphase Polymer Systems

Diblock Copolymer Melt in Spherical Unit Cells of Higher Dimensionalities

Simulated Annealing Study of Self‐Assembly of Symmetric ABA Triblock Copolymers Confined in Cylindrical Nanopores

Contact Info

Product

Resources

About