A Statistical Approach to Raman Analysis of Graphene-Related Materials: Implications for Quality Control

Abstract

A statistical method to determine the number of measurements required from nanomaterials to ensure reliable and robust analysis is described. Commercial products utilizing graphene are in their infancy and recent investigations of commercial graphene manufacture have attributed this to the lack of robust metrology and standards by which graphene and related carbon materials can be measured and compared. Raman spectroscopy is known to be a useful tool in carbon nanomaterial characterization, but to provide meaningful information, in particular for quality control or management, multiple spectra are needed. Herein we present a statistical method to quantify the number of different spectra or other microscale measurements that should be taken to reliably characterize a graphene material. We have recorded a large number of Raman measurements and studied the statistical convergence of these data sets. We use a graphical approach to monitor the change in summary statistics and a Monte Carlo based bootstrapping method of data analysis to computationally resample the data demonstrating the effects of underanalyzing a material; for example, graphene nanoplatelets may require over 500 spectra before information about the exfoliation efficiency, particle size, layer number, and chemical functionalization is accurately obtained.