Copolymer systems, simulated

W. Gozdz, R. Holyst. From the plateau problem to minimal surfaces in lipids, surfactants and diblock copolymer systems. Macromol Theory Simul 5 321-332, 1996. 

We will then examine other flexible polymer crystallization instances which may be interpreted, at least qualitatively, in terms of the bundle model. We will concentrate on crystallization occurring through metastable mesophases which develop by quenching polymers like isotactic polypropylene, syndiotactic polypropylene etc. In principle also hexagonal crystallization of highly defective polymers, and order developing in some microphase-separated copolymer systems could be discussed in a similar perspective but these two areas will be treated in future work. A comparison between the bundle approach and pertinent results of selected molecular simulation approaches follows. 

When the confined surfaces suffer from a weak interaction with block copolymer, either parallel or vertical lamellar structures for AB diblock copolymer systems under flat and curved confinements could exhibit, as shown in Figure 27. From theoretical predictions (Turner, 1992 Walton et al., 1994) and simulations (Wang et al., 2000 Yin et al., 2004), the frustration between d and L0 could result in the alternative appearance of parallel lamellar and vertical lamellar structures under flat confinements. A question is naturally arisen can both concentric cylinder barrel and sector column structures appear under the curved confinement ... 

Here, we describe and compare the results of simulations for two multichain systems corresponding to alternating and protein-like HA copolymers [212], The multichain systems consisting of 127-unit copolymers were simulated for the range of the effective interaction parameter / (which is similar to the Flory-Huggins parameter) under solvent conditions when single chains can form strongly collapsed conformations. 

The simulation techniques presented above can be applied to all first order phase transitions provided that an appropriate order parameter is identified. For vapor-liquid equilibria, where the two coexisting phases of the fluid have the a similar structure, the density (a thermodynamic property) was an appropriate order parameter. More generally, the order parameter must clearly distinguish any coexisting phases from each other. Examples of suitable order parameters include the scalar order parameter for study of nematic-isotropic transitions in liquid crystals [87], a density-based order parameter for block copolymer systems [88], or a bond order parameter for study of crystallization [89]. Having specified a suitable order parameter, we now show how the EXEDOS technique introduced earlier can be used to obtain in a particularly effective manner for simulations of crystallization [33]. The Landau free energy of the system A( ) can then be related to P,g p( ((/"))... 

The dependences of on t indicate that quasi-regular copolymers are synthesized in the CDSD regime when the adsorption interaction is sufficiendy strong. Indeed, we see that these copolymers are characterized by a periodic variation of the composition along the chain. For the system simulated, the period of this variation is about 20 segments. Therefore, the formation of copolymers with blodcy primary stmctures can be observed. 

Note, however, two recent review papers, one on off-lattice MC methods for coarse-grained models of polymeric materials [71] and one on MC applied to block copolymer systems [61], in which off-lattice simulations pertaining to self-assembly are discussed. 

The structure of the simulated block copolymer systems has been characterized in detail [38-40]. Temperature dependencies of various structural parameters have shown that all of them change in a characteristic way in correspondence to Tqdt- The microphase separation in the diblock copolymer system is accompanied by chain extension. The chains of the diblock copolymer start to extend at a temperature well above that of the transition to the strongly segregated regime. This extension of chains is related also to an increase of local orientation correlations, which appear well above the transition temperature. On the other hand, the global orientation correlation factor remains zero at temperature above the microphase separation transition and jumps to a finite value at the transition. 

Besides the above presented example, the CMA has been applied for simulation of various other copolymer systems with more complex topology [42] of macromolecules and other distributions of comonomers along chains [43,44]. In all cases, the high computational efficiency of the method has enabled detailed information about the structure and dynamics to be obtained, including also the microphase separated states, in which the dynamics becomes considerably slower. 

In Section II we look more closely at the computational aspects of DPD, before focusing attention on the specific application to polymer systems. Section III describes the matching of simulation parameters to the properties of real polymer systems, with an emphasis on the relation between the conservative force field and the common Flory-Huggins / parameter for mixtures. The dynamics of individual polymer chains in a solvent and in a melt are discussed in Section IV, and the ordering dynamics of quenched block copolymer systems is described in Section V. A summary and conclusions are given in Section VI. 

DPD simulations of the PVBPA-PEEK-PVBPA block copolymer system were performed to investigate its phase morphology. This way DPD simulation in multiscale was used in predicting phase morphologies for different block sizes, topologies and connectivities and to ultimately suggesting candidate copolymers for synthesis. DPD simulation of such a complex polymer necessarily involves parameterization of the cross-interaction parameters. This was done with the help of MD simulations. 

In conclusion, we have demonstrated that linear A-B-C block copolymers can form the double-diamond morphology, but not gyroid. It is evident that the simulation method is useful for investigating morphologies of block copolymer systems. Future studies should include the phase diagram of two-component block copolymers. 

Zhang LS, Sevink A, Schmid F. Hybrid lattice Boltz-mann/dynamic self-consistent field simulations of microphase separation and vesicle formation in block copolymer systems. Macromolecules 2011 44 9434. 

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