Microphase separation in bottlebrush polymers under poor-solvent conditions

Molecular-dynamics simulations are used to study the structure of bottlebrush polymers with rigid backbones, for various grafting densities, side chain lengths, and varying solvent quality. While we confirm different states of the bottlebrush proposed by Sheiko et al. (Eur. Phys. J. E, 13 (2004) 125) we find that the transition between stretched and collapsed brushes occurs in a rather gradual manner. The pearl-necklace structure occurring at intermediate grafting densities and rather low temperatures has a pronounced medium-range order along the backbone. Copyright c © EPLA, 2009 Molecular bottlebrushes consist of a long macromolecule serving as a “backbone” on which many flexible side chains are densely grafted [1–11]. There is a lot of recent interest in both the chemical synthesis [1,2,9,10] and characterization of physical properties by various experimental techniques (light and neutron scattering, atomic force microscopy, electron microscopy, etc.) [3–11]; some of this work is motivated by the use of these cylindrical brushes as building blocks in functional supramolecular structures. Also, applications for actuators and sensors are discussed [12,13], since the structure of these stimuliresponsive polymers can change quickly when external parameters such as pH of the solution, temperature etc. are varied. However, due to the interplay of the local conformation of a side chain and the global configuration of the backbone the interpretation of experimental data on bottlebrushes is controversial [3,4,6]. Even in the goodsolvent regime, although many theoretical analyses have been presented [14–28], the application of scaling concepts is problematic [27,28]. The most interesting phenomena (which also are potentially useful for applications [12,13]) occur when the solvent quality changes. While it is well known that single flexible chains collapse into dense globules [29] (or, alternatively, crystallize [30,31]) when the solvent quality becomes poor, much more complex structures (e.g. toroids, disk-like globules, etc. [30,32]) form from semiflexible chains in poor solvents. An interesting competition between the behavior of the flexible side chains and the (typically) much stiffer backbone under poor-solvent conditions must be expected. In addition, just as for polymer brushes on flat substrates the interplay between grafting density σ and side chain length N causes lateral segregation between dense “clusters” rather than uniform collapse in some intermediate regime under poor-solvent conditions [33–35], similar lateral microphase separation along the backbone of a bottlebrush can be expected [36,37]. Apart from qualitative scaling predictions for the phase diagram that one should expect for the bottlebrush [36] and qualitative observations for a lattice model with very short side chains (up to N = 12 only [37]), this type of lateral microphase separation in bottlebrushes has not yet been characterized. In the following, we fill this gap and describe large-scale molecular-dynamics simulations of an off-lattice model of a bottlebrush under variable solvent conditions to provide a first test of the proposed phase diagram [36]. Our evidence shows that all the states proposed by Sheiko et al. [36] indeed occur, but one should not mistake the lines separating these states (fig. 1) as sharp phase transitions but rather interpret them as smooth crossovers. In order to motivate fig. 1, we recall that above the θ-point chains are swollen R∝N0.59, while at the θ-point chain radii in dilute solution scale as R∝√N with chain length N . This linear dimension of “mushrooms” grafted onto a line has to be compared with the distance σ−1 between grafting points. Thus, for T near θ the cross-sectional radius Rcs of a cylindrical bottlebrush scales as Rcs = √ Nfbb(N σ); (1)