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

Abstract

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.

One-pot route to convert technical lignin into versatile lignin esters for tailored bioplastics and sustainable materials

“…82 For graphene oxide MHS  parameter of 0.33 was reported related to a self-avoiding sheet with a moderate bending rigidity. 86 In the current study, F3, F4, and F5 (lower MW fractions) had an α value approaching 0 and are essentially dense non-draining "particles" in solution without excluded volume. (Figure 6a) These significant differences in their conformation further highlight the importance of fractionation as the lignin derivatives would behave very differently in material applications.…”

Thermally fluctuating, semiflexible sheets in simple shear flow

“…For large k B T/k, the zero-shear viscosity would be related to equilibrium sheet conformations, which may be dependent on the chemistry of particular experimental systems of interest. 43 In addition to viscosity, first normal stress differences can be calculated using the stresslet data from the minimumvolume bounding ellipsoids. Fig.…”

“…Since the 1980s, the equilibrium and statistical mechanical properties of sheets (or ''tethered membranes'' as they are often called to distinguish them from fluid membranes that lack fixed connectivity) has been widely studied from theoretical, [24][25][26][27][28][29][30][31] computational, [32][33][34][35][36][37][38][39][40] and experimental [41][42][43] viewpoints. Much of this work has focused on a phase transition from a flat state to a crumpled state as k B T/k is increased, a transition that does not exist for polymers, the 1D analogue of tethered membranes.…”

Multi-Scale Structure–Mechanical Property Relations of Graphene-Based Layer Materials

“…Folded conformation can be obtained by introducing ions (i.e., Ca 2+ ) as short-range interaction in GO sheets with slight out-of-plane corrugation [ 126 ]. More recently, Li et al [ 127 ] constructed a general description of thermodynamic and rheological behaviors of 2D macromolecules dispersed in solutions based on experimental and dissipative particle dynamics simulations, which provides a fundamental framework that can be used in the understanding and control of their assembly and processing in solution toward applications.…”