Folding of electrostatically charged beads-on-a-string as an experimental realization of a theoretical model in polymer science

The "beads-on-a-string" model for folding of polymers is a cornerstone of theoretical polymer science. This communication describes a physical model of beads-on-a-string, based on the folding of flexible strings of electrostatically charged beads in two dimensions. The system comprises millimeter-scale Teflon and Nylon-6,6 (spherical or cylindrical) beads (approximately 6 mm in diameter) separated by smaller (approximately 3 mm) poly(methyl methacrylate) (PMMA) spherical beads, threaded on a flexible string. The smaller, uncharged beads define the distances between the larger beads, and control the flexibility of the string. During agitation of the sequence of beads on a planar, horizontal paper surface, tribocharging generates opposite electrostatic charges on the larger Nylon and Teflon beads, but leaves the smaller PMMA beads essentially uncharged; the resulting electrostatic interactions cause the string to fold. Examination and comparison of two models--one physical and one theoretical--may offer a new approach to understanding folding, collapse, and molecular recognition at an abstract level, with particular opportunity to explore the influence of the flexibility of the string and the shape of the beads on the pattern and rate of folding. The physical system is, thus, an analog computer, simulating the theoretical beads-on-a-string model in two dimensions; this system makes it possible to test hypotheses connecting "sequence" to "folding", rapidly and conveniently, while exploring nonlinearities and other complexities omitted from the theoretical model.