  Carbon nanoscroll is a unique topologically open configuration of graphene
nanoribbon possessing outstanding properties and application perspectives due
to its morphology. However molecular dynamics study of nanoscrolls with more
than a few coils is limited by computational power. Here, we propose a simple
model of the molecular chain moving in the plane, allowing to describe the
folded and rolled packaging of long graphene nanoribbons. The model is used to
describe a set of possible stationary states and the low-frequency oscillation
modes of isolated single-layer nanoribbon scrolls as the function of the
nanoribbon length. Possible conformational changes of scrolls due to thermal
fluctuations are analyzed and their thermal stability is examined. Using the
full-atomic model, frequency spectrum of thermal vibrations is calculated for
the scroll and compared to that of the flat nanoribbon. It is shown that the
density of phonon states of the scroll differs from the one of the flat
nanoribbon only in the low (omega<100 cm-1) and high (omega>1450 cm-1)
frequency ranges. Finally, the linear thermal expansion coefficient for the
scroll outer radius is calculated from the long-term dynamics with the help of
the developed planar chain model. The scrolls demonstrate anomalously high
coefficient of thermal expansion and this property can find new applications.
