Monte Carlo


The precise control of the folded structure of synthetic polymers is commonly sought after in the development of nanomaterials for diverse applications. We use Wang-Landau Monte Carlo simulations of coarse-grained copolymers to explore the design parameters of these systems on their pathway to collapse, as well as a lattice based Monte Carlo technique to study the self-assembly of such collapsed single-chain, polymeric nanoparticles upon evaporation.


The combination of supramolecular chemistry and the continuous advancement in precision polymer synthesis has paved the way to the engineering of nanoscopically ordered materials that can respond to various types of stimuli. Applications of such ordered self-assembled materials include nanodevices for personalized medicine, catalysis in water, semiconductor integrated circuit design and subnanometer porous films for separation processes. The range of diverse applications of these materials demand a precise knowledge of the interplay between the various non-covalent interactions and the resulting nanoscale architecture. Generic coarse-grained models play an important conceptual role in this respect as they can yield detailed structural information by systematically exploring the design space of supramolecular ordered materials.

Polymer folding

Precise control over folded conformations of synthetic polymers is highly desirable in the development of functional nanomaterials for diverse applications. Introducing monomers capable of strong intramolecular hydrogen bonding is a promising route to achieve this control. We have used Wang-Landau Monte Carlo simulations of coarse-grained copolymers to explore the design parameters of these systems on their pathway to collapse. The highly directional nature of hydrogen-bonded supramolecular interactions is modelled by a directional non-bonded potential while a harmonic bending potential is used to take into account the flexibility of the polymer chain, thus making it possible to look at the interplay of both factors. The figure schematically shows the coarse-grained co-polymer sequence studied, with backbone monomers (red, type A) containing one sticky bit (blue, type B) on every fifth bead. Between two blue stick bits a strong directional interaction potential is used, while all other interactions are weaker standard isotropic Lennard Jones interactions.

The introduction of directional interactions in the copolymer chain leads to a sharper coil-globule collapse when compared to homopolymers composed of isotropic interacting beads only. Simultaneously, some of the stiffness-dependent structural properties become exacerbated when directional beads are present. Analysis of the simulations showed that for highly flexible chains there is the prevalence of a collapse of the backbone, while as chain stiffness increases folding of the co-polymer due to the directional interactions becomes the dominant feature [Soft Matter 8, 7610-7616 (2012)].


Evaporative self-assembly of dilute solutions containing single-chain polymeric nanoparticles results in characteristic morphologies imaged using atomic force microscopy. Understanding the evaporative self-assembly process is a critical step in ultimately engineering the spatial organization of SCPNs on surfaces, which can for example lead to diverse hierarchically constructed, catalytically active materials. Quantitative mapping of experimental AFM images with coarse-grained self-assembly models gives access to microscopic interaction parameters that describe nanoparticle-nanoparticle and nanoparticle-solvent interactions. We have used 2D lattice-gas simulations as illustrated in the figure for a small example lattice of 11x11 cells, containing either solvent, gas or a nanoparticle, where a nanoparticle always occupies 3x3 neighboring cells. In this particular configuration, the nanoparticle is unable to move to the left, as one of the neighbouring cells is in a gaseous state. Quantitative comparison of experimental data to morphologies obtained by the simulations shows that the nonequilibrium patterns emerge from a complex interplay between dewetting, solvent evaporation and nanoparticle diffusion [Chem. Commun. 49, 3122-3124 (2013)].


If you have any questions on this research subject, please contact Bart Markvoort, Peter Hilbers or Tom de Greef.