Study of Segregation in Non-Dilute Solutions of Linear Diblock Copolymers and Symmetric Miktoarm (or Janus Star) Polymers Using Monte Carlo Simulations with the Bond Fluctuation Model

Abstract

The bond fluctuation model was employed to characterize the approach to the mesophase separation transition of pure linear AB copolymers and symmetric miktoarms, also called Janus, star polymers, Af/2Bf/2 , where f = 6 or 12 is the total number of arms, in a common good solvent. We consider a concentration sufficiently high to mimic the melting behavior and also a lower concentration. The segregation between A and B units is represented by a repulsive interaction parameter, . Different total numbers of units are also considered. Results for different properties, such as the molecular size, the asphericity and orientational correlation of blocks, or arms, of different compositions are obtained as a function of the segregation parameter. We also calculate scattering structure factors. The initial effect of segregation on the scattering with opposite contrast factors between the A and B blocks can be explained with a common description based on the random phase approximation for both the linear copolymers and the f = 6 miktoarms, once the numerical form factors of the different molecules in their particular systems are considered. However, the results for f = 12 clearly deviate from this description probably due to some degree of ordering in the position of highly armed molecules.

Enhancing Polymer Blend Compatibility with Linear and Complex Star Copolymer Architectures: A Monte Carlo Simulation Study with the Bond Fluctuation Model

“…In Table 1 , we show the results for the size and asphericity of individual molecules, β = 0. As expected, the ratios between the star and linear radius of gyration, as well as the asphericities in the melt state, are consistent with previous data [ 28 , 36 ] for single unperturbed molecules, and they do not show remarkable mixture effects.…”

“…Moreover, according to this conclusion, is bracketed between the values Φ melt ≅ 0.31 and Φ melt = 0.62. This range includes the value Φ melt = 0.5 previously proposed for the BFM model [ 35 ] and the smaller value Φ melt = 0.36 resulting from the analysis of our previous BFM results for symmetric miktoarm polymers [ 28 ].…”

“…β is proportional to the bare Flory–Huggins parameter. According to the determination of the theta state in single-chain calculations with the BFM, χ ≅ 5 β [ 28 ]. We take this relationship as a reference, though it is not totally clear that it can be applied to describe the behavior of other systems.…”

“…We also calculate the total scattering intensity, obtained by the general expression where we can assign different values for the site contrast factors f i . With the choice of scattering factors 1, −1, and 0 for the sites occupied by the A and B units and the central and unoccupied sites, respectively [ 28 ], and taking into account that each unit in a site actually blocks eight sites in the lattice, we obtain the scattering function whose values can be compared with the results of the prediction of the random phase approximation [ 31 , 32 ] (RPA) for nearly homogeneous systems or for a symmetric blend of homopolymers composed of A or B units of similar volumes. P ( q ) is the form factor, or individual contribution to the scattering, of molecules in the absence of intermolecular interferences, P ( q ) = 1 for q = 0.…”

“…This comparison allows us to explore how close the systems are to homogeneity at different distance ranges. Similarly, setting the scattering factors as 1 − Φ /8 for the sites occupied by A or B units and − Φ /8 for the rest of sites, we can detect any possible segregation, or inhomogeneity, in the global distribution of units with respect to the voids in the system, representing the solvent [ 28 ]. In systems where star polymers act as compatibilizers, setting factors as Φ linear and − Φ star for the sites occupied by linear molecules and stars, respectively, allows us to study the possible segregation between polymers of different morphologies.…”