Determination of the lateral dimension of graphene oxide nanosheets using analytical ultracentrifugation

In this paper, a method to determine the lateral dimensions of 2D nanosheets directly in suspension by analytical ultracentrifugation (AUC) is shown. The basis for this study is a well-characterized and stable dispersion of graphene oxide (GO) monolayers in water. A methodology is developed to correlate the sedimentation coefficient distribution measured by AUC with the lateral size distribution of the 2D GO nanosheets obtained from atomic force microscopy (AFM). A very high accuracy can be obtained by virtue of counting several thousand sheets, thereby minimizing any coating effects or statistical uncertainties. The AFM statistics are further used to fit the lateral size distribution obtained from the AUC to determine the unknown hydrodynamic sheet thickness or density. It is found that AUC can derive nanosheet diameter distributions with a relative error of the mean sheet diameter of just 0.25% as compared to the AFM analysis for 90 mass% of the particles in the distribution. The standard deviation of the size-dependent error for the total distribution is found to be 3.25%. Based on these considerations, an expression is given to calculate the cut size of 2D nanosheets in preparative centrifugation experiments.