One of the most celebrated achievements
in polymer physics is the
finding of simple scaling laws that correlate molecular behaviors
with molecular size. Scaling relations of 2D macromolecules between
the conformation and size have been extensively investigated in theory.
However, in contrast to their 1D counterparts, the fundamental correlation
of conformation with the size, bending rigidity, and surface interaction
still remains unsolved in both experiments and theory. Here we report
the scaling relations of 2D macromolecules by using single-layer graphene
oxide as the model, underpinning a general framework to understand
and measure their thermodynamic and rheological behaviors. Using Ubbelohde
capillary rheology, we experimentally determined the Flory-type and
Mark–Houwink–Sakurada scaling rules in the self-avoiding,
good-solvent regime through the critical overlapping concentration
(C
* ∼ L
–0.87, L is the lateral size) and intrinsic viscosity
([η] ∼ M
α, α
= 0.33, M is the molecular weight). The measured
exponent γ = 0.87 is well located between self-avoiding (4/5)
and rigid (1) limit, indicating a nearly flat conformation and semiflexible
nature, and α = 0.33 differs from the value of polymers (0.5–0.8),
signaling the dimensional constraint. The discussion of conformational
size-scaling relations is complemented by dissipative particle dynamics
simulations, which clarify the effects of size and bending resistance
of 2D macromolecules as well as the solvent that tunes their surface
interaction, resulting in conformation transitions among nearly flat,
folded, and crumpled phases.