**Conformational Scaling Relations of Two-Dimensional Macromolecular
Graphene Oxide in Solution**

P Li and SJ Wang and FX Meng and Y Wang and F Guo and S Rajendran and C Gao and ZP Xu and Z Xu, MACROMOLECULES, 53, 10421-10430 (2020).

DOI: 10.1021/acs.macromol.0c01425

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-*
similar to L-0.87, L is the lateral size) and intrinsic viscosity (**eta**
similar to M-alpha, alpha = 0.33, M is the molecular weight). The
measured exponent gamma = 0.87 is well located between self-avoiding
(4/5) and rigid (1) limit, indicating a nearly flat conformation and
semiflexible nature, and alpha = 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.

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