Alternating multiblock copolymers exhibiting protein-like transitions in selective solvents: A Monte Carlo study S. Wołoszczuk a , M. Banaszak a, * , P. Knychała a , K. Lewandowski a , M. Radosz b a Faculty of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznan, Poland b Soft Materials Laboratory, Department of Chemical and Petroleum Engineering, University of Wyoming Laramie, WY 82071-3295, USA article info Keyword: Modeling and simulation abstract We present a lattice Monte Carlo study of a series of block copolymer chains in selective solvents of varying quality, first using a diblock chain of the length of N ¼ 32 with a 16–16 microarchitecture, and then – two multiblock chains of N ¼ 64 and N ¼ 128, with ð8—8Þ 4 and ð16—16Þ 4 microarchitectures, respectively. We report a variety of thermodynamic and structural properties, such as energy, specific heat, end-to-end distance and radius of gyration both for the whole chain and for individual blocks. The simulations have demonstrated that a multiblock copolymer in a selective solvent exhibits pro- tein-like behavior undergoing a two-step transition, first from a swollen state to a secondary ‘pearl-neck- lace’ state and then to a tertiary super-globular state as the solvent quality decreases, i.e. upon cooling. We have found that mean-squared end-to-end distances of multiblock chains decrease as the tempera- ture is reduced, as expected. Ó 2008 Elsevier B.V. All rights reserved. 1. Introduction Block copolymers are very interesting due to applications of their rich structural and phase behavior [1]. Remarkable progress has been made in this regard in areas including but not limited to designing materials of desired mechanical properties, self- assembling systems [2], molecular electronics [3] and the pharma- ceutical industry (e.g. biodegradable polymers for drug carriers and controlled release systems [4]). With respect to chain microarchi- tecture, we can differentiate diblock, triblock and multiblock copolymers, even very complicated systems such as star-block copolymers [5] or P-shaped copolymers [6]. Wei et al. [7] conjec- tured that alternating multiblock copolymers made of double-ar- row-like ‘hard’ segments and spring-like ‘soft’ blocks can form auxetic materials. Multiblock copolymers are also used as model proteins in biotechnology [8,9]. For example, Lee et al. [10] have demonstrated, starting with the Edwards Hamiltonian, that a mul- tiblock copolymer chain can form a secondary ‘pearl-necklace’ con- formation and a tertiary ‘super-globule’ conformation of behavior reminiscent of that of proteins. In this work, we aim at a Monte Carlo (MC) simulation of a single alternating multiblock copolymer chain in a selective solvent. The solvent’s selectivity implies that the energy of interaction between the solvent and a type of chain segments is different from that between the solvent and another type of chain segments. Deteriorating the solvent’s quality causes a collapse of a homopolymer chain from a swollen state to a com- pact globular state [11–17]. In a good solvent, a homopolymer chain remains in a swollen state and its mean-squared end-to- end distance is < R 2 > N 2m , where m ¼ 0:588. In a poor solvent, the chain becomes a compact globule with m ¼ 1 3 . The swollen and globular states are separated by a H (theta) state, where the effective attractive and repulsive interactions cancel each other [18,19]. At the theta point, the polymer chain behaves like an ideal Gaussian chain with m ¼ 1=2, so that < R 2 > N. It is also known that the Flory v interaction parameter is 1 2 in the H state. Since the solvent quality cannot be controlled with temperature, the chain can be said to be in the H state at the H temperature, T H . At higher temperatures, the v parameter is smaller and the solvent is good, whereas at lower temperatures the v parameter may be greater than 1 2 resulting in a poor solvent. In the case of a copolymer, the situation is more complicated [13,20–23]. The copolymer chain can be placed in either a selective or a nonselective solvent. The solvent’s selectivity implies that its interaction with the chain a depends on the type of block consid- ered. In the case of a nonselective solvent, the copolymer chain be- haves in many ways like a homopolymer chain, as the strength of interaction between the solvent and an individual block is inde- pendent of the latter. At the same time, selective solvents favor one of the copolymer blocks. The goal of this MC multiblock chain study is to demonstrate that the transitions from a swollen conformation to the second-or- der ‘pearl-necklace’ conformation and from the ‘pearl-necklace’ structure to the third-order super-globular conformation can be 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.06.022 * Corresponding author. E-mail address: mbanasz@amu.edu.pl (M. Banaszak). Journal of Non-Crystalline Solids 354 (2008) 4138–4142 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol