A Meta-Analysis to Revisit the Property-Aggregation Relationships of Carbon Nanomaterials: Experimental Observations versus Predictions of the DLVO Theory

Contradicting relationships between physicochemical properties of nanomaterials (e.g., size and ζ-potential) and their aggregation behavior have been constantly reported in previous literature, and such contradictions deviate from the predictions of the classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. To resolve such controversies, in this work, we employed a meta-analytic approach to synthesize the data from 46 individual studies reporting the critical coagulation concentration (CCC) of two carbon nanomaterials, namely, graphene oxide (GO) and carbon nanotube (CNT). The correlations between CCC and material physicochemical properties (i.e., size, ζ-potential, and surface functionalities) were examined and compared to the theoretical predictions. Results showed that the CCC of electrostatically stabilized carbon nanomaterials increased with decreasing nanomaterial size when their hydrodynamic sizes were smaller than ca. 200 nm. This is qualitatively consistent with the prediction of the DLVO theory but with a smaller threshold size than the predicted 2 μm. Above the threshold size, the material ζ-potential can be correlated to CCC for nanomaterials with moderate/low surface charge, in agreement with the DLVO theory. The correlation was not observed for highly charged nanomaterials because of their underestimated surface potential by the ζ-potential. Furthermore, a correlation between the C/O ratio and CCC was observed, where a lower C/O ratio resulted in a higher CCC. Overall, our findings rationalized the inconsistency between experimental observation and theoretical prediction and provided essential insights into the aggregation behavior of nanomaterials in water, which could facilitate their rational design.