Monte Carlo simulation diblock copolymer

Figure 22 Typical conformations of a diblock AB copolymer taken from Monte Carlo simulations. The copolymers are...

Monte Carlo simulation for diblock copolymers confined in curved surfaces... 

Fig. 48a. Normalized inverse scattering intensity NS l(q, e) observed in the Monte Carlo simulation of a block copolymer model on the simple cubic lattice (see Fig. 44) plotted vs the normalized inverse temperature eN. b Reciprocal structure factor S (q ) -l(cxrcfes, left scale) and q ( squares, right scale) plotted vs temperature for a nearly symmetric diblock copolymer of polystyrene/poly (cis— 1,4) isoprene (Mw = 15 700). Filled symbols refer to cooling, open symbols to heating runs. The straight tine indicates the extrapolation to a spinodal temperature (T,) that occurs above the actual transition temperature (Tmst). where the data show a jump. From Stuhn et al. [323],...

Finally, Mattice and coworkers have used lattice Monte Carlo simulations for various studies of micellization of block copolymers in a solvent, including micellization of triblock copolymers [43], steric stabilization of polymer colloids by diblock copolymers [44], and the dynamics of chain interchange between micelles [45]. Their studies of the self-assembly of diblock copolymers [46-48] are roughly equivalent to those of surfactant micellization, as a surfactant can in essence be considered a short-chain diblock copolymer and vice versa. In fact, Wijmans and Linse [49,50] have also studied nonionic surfactant micelles using the same model that Mattice and coworkers used for a diblock copolymer. Thus, it is interesting to compare whether the micellization properties and theories of long-chain diblock copolymers also hold true for surfactants. 

Weyersberg A, Vilgis TA (1993) Phase transitions in diblock copolymers Theory and Monte Carlo simulations. Phys Rev E 48(l) 377-390... 

Capillary waves do not only broaden the width of the interface but they can also destroy the orientational order in highly swollen lamellar phases (see Fig. 1 for a phase diagram extracted from Monte Carlo Simulations). Those phases occur in mixtures of diblock-copolymers and homopolymers. The addition of homopolymers swells the distance between the lamellae, and the self-consistent field theory predicts that this distance diverges at Lifshitz points. However, general considerations show that mean-field approximations are bound to break down in the vicinity of lifshitz points [61]. (The upper critical dimension is du = 8). This can be quantified by a Ginzburg criterion. Fluctuations are important if... 

Figure 15.8 The lamellae structures formed by diblock copolymers in constrained spaces predicted by Monte Carlo simulation [48], (a) Barrel, (b) spherical (cut view). He et al. [48]. Reproduced with permission of Elsevier. (See color plate section for the color representation of this figure.)...

Besold G, Hassager O, Mouritsen OG. Monte Carlo simulation of diblock copolymer microphases by means of a fast off-lattice model. Comput Phys Commun 1999 121 542. 

Wang Q, Nealey PE, de Pablo JJ. Monte Carlo simulations of asymmetric diblock copolymer thin films confined between two homogeneous surfaces. Macromolecules 2001 34 3458. 

He XH, Song M, Liang HJ, Pan CY. Self-assembly of the symmetric diblock copolymer in a confined state Monte Carlo simulation. J Chem Phys 2001 114 10510. 

Figure 5.11 Order-disorder transition (ODT) of a symmetric diblock copolymer studied by a soft, coarse-grained, off-lattice model. Monte Carlo simulations are performed in the npT ensemble and the pressure is kept constant at pb /kgT = 18 (with b = Reo/VW-l)-Xo = 1.5625. The invariant degree of polymerization, and the chain discretization are indicated in the key. The figure presents the excess thermodynamic potential, per...

Werner A, Schmid F, Binder K, Muller M (1996) Diblock copolymers at a homopoly mer homopolymer interface a Monte Carlo simulation. Macromolecules 29 8241 8248... 

The present chapter has centered on experimental efforts performed to study confined polymer crystallization. However, molecular dynamics simulations and dynamic Monte Carlo simulations have also been recently employed to study confined nucleation and crystallization of polymeric systems [99, 147]. These methods and their application to polymer crystallization are discussed in detail in Chapter 6. A recent reference by Hu et al. reviews the efforts performed by these researchers in trying to understand the effects of nanoconfinement on polymer crystallization mainly through dynamic Monte Carlo simulations of lattice polymers [147, 311]. The authors have performed such types of simulations in order to study homopolymers confined in ultrathin films [282], nanorods [312] and nanodroplets [147], and crystallizable block components within diblock copolymers confined in lamellar [313, 314], cylindrical [70,315], and spherical [148] MDs. 

Figure 3 Morphologies of bulk cylinder-forming diblock copolymers confined in cylindrical pores from Monte Carlo simulations. The model diblock copolymer is at the strong segregation region and so the cylinders are robust. The morphologies can be viewed as different arrangements of the basic cylindrical structure. Reproduced from Yu, B. Jin, Q. Ding, D. et a . Macromolecules 2008, 41,4042, with permission. Copyright 2008, American Chemical Society.

The same group also investigated the case of ring diblock copolymers in a common 0 solvent, a good solvent, and in selective solvents, using theoretical (renormalization group theory) and numerical simulation (Monte Carlo) methods [288]. In this way the average dimensions of each block and of the whole molecule were obtained and compared with results on linear diblock copolymers. 

Nonetheless, Monte Carlo results suggest that in order for a copolymer to be an effective compatibilizer in polymer blends, the copolymer must be blocky in nature. This interpretation of the simulation results are in agreement with the experimental results which show that the random copolymers that are better than the diblock copolymer at compatibilizing a blend are those that are blockier than a statistical random copolymer. The copolymers that do not behave as effectively as a compatibilizer are more alternating than a statistically random copolymer. 

Theoretical approximations and morphology predictions were recently carried out for miktoarm star terpolymers of the ABC type. The literature concerning theoretical predictions for this complex architeaure is rather limited, as the synthesis of such materials leading to morphologically three-phase stmaures has been developed rather recently. The behavior of miktoarm star terpolymers was simulated using the Monte Carlo calculation method. This approach was already used for the microdomain structural behavior of diblock copolymers of the AB type, and the consideration that needed to be taken into account for the calculations was the addition of the C chain at the common junction point of the A... 

Figure 17 Illustration of DSA simulations of chemical epitaxy (left two columns) or graphoepitaxy (right columns). The top row shows straight or wavy chemical patterns ortopographical walls on a simulated substrate. Green regions are selective for the A block (red) and yellow regions selective forthe B block (blue) of a model block copolymer, while gray surfaces are neutral. DSA of a disordered thin film of symmetric AB diblock copolymer was simulated in the presence of each substrate pattern using single chain in mean-field Monte Carlo to produce the self-assembled structures in the bottom row.

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