Statistical Mechanics of Aggregation and Crystallization for Semiflexible Polymers

By means of multicanonical computer simulations, we investigate thermodynamic properties of the aggregation of interacting semiflexible polymers. We analyze a mesoscopic beadstick model, where nonbonded monomers interact via Lennard-Jones forces. Aggregation turns out to be a process, in which the constituents experience strong structural fluctuations, similar to peptides in coupled folding-binding cluster formation processes. In contrast to a recently studied related proteinlike hydrophobic-polar heteropolymer model, aggregation and crystallization are separate processes for a homopolymer with the same small bending rigidity. Rather stiff semiflexible polymers form a liquid-crystal-like phase, as expected. In analogy to the heteropolymer study, we find that the first-order-like aggregation transition of the complexes is accompanied by strong system-size dependent hierarchical surface effects. In consequence, the polymer aggregation is a phase-separation process with entropy reduction. Cluster formation and crystallization of polymers are processes which are interesting for technological applications, e.g., for the design of new materials with certain mechanical properties or nanoelectronic organic devices and polymeric solar cells. From a biophysical point of view, the understanding of peptide oligomerization, but also the (de)fragmentation in semiflexible biopolymer systems like actin networks is of substantial relevance. This requires a systematic analysis of the basic properties of the polymeric cluster formation processes, in particular, for small polymer complexes on the nanoscale, where surface effects are competing noticeably with structure-formation processes in the interior of the aggregate. A further motivation for investigating the aggregation transition of semiflexible homopolymer chains derives from the intriguing results of our recent study of a similar aggregation process for peptides [1, 2], which were modeled as heteropolymers with a sequence of two types of monomers, hydrophobic (A) and hydrophilic ones (B). By (a)E-mail: [email protected] (b) E-mail: [email protected] (c)E-mail: [email protected] specializing the previously employed heteropolymer model to the apparently simpler homopolymer case, we aim by comparison at isolating those properties which are mainly driven by the sequence properties of heteropolymers. In fact, while in both cases the aggregation transition is a phase-separation process, we will show below that for homopolymers the aggregation and crystallization (if any) are separate conformational transitions – unlike our study of heteropolymer aggregates where they were found to coincide [1, 2]. The physical origin causing these differences will be explained within the microcanonical formalism [3,4], which proves [1,2] to be particularly suitable for this type of problem. We thus consider the same model as in [1, 2], but here we assume that all monomers iμ = 1, . . . , N (μ) of the μth chain (μ = 1, . . . ,M) at positions iμ are hydrophobic (A). The bonds between adjacent monomers are taken to be rigid (bead-stick model) and pairwise interactions among nonbonded monomers are modeled by a LennardJones potential VLJ(riμjν ) = 4[r −12 iμjν − r iμjν ] , (1)