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Monte Carlo phase diagram for diblock copolymer melts
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Image of FIG. 1.
FIG. 1.

(a) Experimental (Ref. 2) and (b) theoretical (Ref. 3) phase diagrams measured using polystyrene-polyisoprene diblock copolymers and calculated using SCFT. In (a), the solid dots denote the experimental data points, while the curves serve only as a guide to the eye. In (b), the solid dot marks the mean-field critical point where the L, C, and S regions all merge.

Image of FIG. 2.
FIG. 2.

Configurations taken at , 36, 60 (disordered), and 61 (cylindrical) from a Monte Carlo heating run involving diblocks of monomers and composition of on a lattice of size . The and monomers are denoted by dark and light spheres, respectively, while the vacancies have been omitted.

Image of FIG. 3.
FIG. 3.

The and 61 configurations from Fig. 2 shown with all the segments and the interfacial segments stripped away. The ordered phase at is cylindrical (C) as demonstrated by the two side views.

Image of FIG. 4.
FIG. 4.

Order parameter from Monte Carlo runs where the system is cooled from into the ordered cylindrical phase and then heated back into the disordered state. Results are presented for three degrees of polymerization: (a) , (b) , and (c) .

Image of FIG. 5.
FIG. 5.

(a) Average number of monomer contacts vs segregation obtained from Monte Carlo cooling runs for three different molecular weights. (b) Hysteresis loop produced by cooling (◯) and subsequent heating (◇) runs.

Image of FIG. 6.
FIG. 6.

Radii of gyration evaluated for (a) an entire molecule , (b) an block , and (c) a block . (d) Separation between the and block centers of mass . Each quantity is plotted relative to its mean-field value corresponding to random-walk statistics (Ref. 19).

Image of FIG. 7.
FIG. 7.

(a) Structure function plotted against wave number at a series of segregations from disordered melts containing diblocks of and . (b) Peak position and (c) height plotted as a function of segregation for three different molecular weights, , 30, and 40.

Image of FIG. 8.
FIG. 8.

Order parameter for cooling (◯) and heating (◇) runs for a series of compositions, , obtained from diblock copolymer of size in a simulation box of size .

Image of FIG. 9.
FIG. 9.

Order parameter for cooling (◯) and heating (◇) runs for diblocks of and contained in a simulation box of size . The inset shows the order parameter of four additional cooling runs all starting from the same initial configuration at , but with different random seeds.

Image of FIG. 10.
FIG. 10.

Configurations from the heating run in Fig. 9 showing the minority-component segments (for added clarity, the interfacial segments have again been removed). The lamellar structure at exhibits a grain boundary that anneals out by .

Image of FIG. 11.
FIG. 11.

Configuration of a perforated-lamellar (PL) phase obtained from a diblock copolymer melt with a composition of and and a segregation of in a simulation box of size . The configuration is repeated to the right, but with the front segments removed to reveal perforations through minority-component lamellae.

Image of FIG. 12.
FIG. 12.

Monte Carlo phase diagram showing the location of the ODT and identifying the ordered phases: lamellar (L), perforated-lamellar (PL), and cylindrical (C). The error bars at each composition represent the width of the hysteresis loop; the solid curves simply serve as convenient guides to the eye. An effective interaction parameter is used to account for the presence of vacancies in the simulations, but no attempt is made to account for the slight difference between the lattice and continuum definitions of necessary for a quantitative comparison with Fig. 1.


Generic image for table
Table I.

Monte Carlo ODT’s for a diblock composition of , and three different degrees of polymerization, , 30, and 40. Each molecular weight is examined with four different system sizes . Round brackets denote that the system did not fully order until the heating cycle.

Generic image for table
Table II.

Monte Carlo ODT’s for diblock copolymer molecules of at various compositions, to 15, each examined with two different system sizes, and 60. Asterisks indicate transitions that were accompanied by a pronounced spike in the heat capacity, and round brackets denote those simulations where the system did not fully order until the heating cycle.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Monte Carlo phase diagram for diblock copolymer melts