Simplified tube form factor for analysis of small-angle scattering data from carbon nanotube filled systems

Abstract

This work presents an analysis method for small‐angle scattering data utilizing a simplified tube (hollow cylinder) form factor. The simplified form factor captures the rod‐like character of a tube at long length scales (one‐dimensional), the sheet‐like character of the tube wall at intermediate length scales (two‐dimensional), and the surface characteristics of a tube at small length scales while suppressing the deep minima seen in the exact form factor. Ultra‐small‐angle X‐ray scattering data from composites made with multi‐walled carbon nanotubes and a bismaleimide resin are analyzed using the simplified form factor and compared with scanning electron micrographs. Although a hollow core is not evident via microscopy, a solid rod form factor does not fit the data. However, a tube form factor does fit the data and generates reasonable geometric parameters. At higher concentrations, evidence for aggregation is seen in the data. Aggregation is accommodated by including a fractal structure factor within the simplified approach, allowing facile analysis of data from aggregated (poorly dispersed) fillers.

Illumination of Conjugated Polymer in Solution Alters Its Conformation and Thermodynamics

“…Thus, this data is fit to the fractal flexible cylinder model, a model that accounts for a sample that is composed of flexible cylinders that aggregate into fractal entities. 29 This experiment was completed for a series of concentration and solvents, and that data is currently being analyzed. Interestingly, MEH-PPV that is dissolved in deuterated THF shows significantly greater difference in the "light" and "dark" samples than similar samples dissolved in deuterated styrene, a substantially better MEH-PPV solvent.…”

“…Moreover, the larger scattering intensity signifies that the polymer chains are not individually dispersed but are likely aggregated. Thus, this data is fit to the fractal flexible cylinder model, a model that accounts for a sample that is composed of flexible cylinders that aggregate into fractal entities . This experiment was completed for a series of concentration and solvents, and that data is currently being analyzed.…”

Comparison of quasistatic to impact mechanical properties of multiwall carbon nanotube/polycarbonate composites

“…To account for flexibility and disorder in the MWNTs, we fit to fractal rod and fractal tube models. 38,39 These models assume rodlike behavior for distances less than a persistence length and random fractal character for length scales larger than the persistence length. In both cases, however, the best fit is achieved with the persistence length comparable to the diameter of the rods in the model, which, within our assumptions, implies there is no rodlike character at all.…”

Morphology and Dispersion of Pristine and Modified Carbon Nanofibers in Water

“…The simplified tube form factor approximates an exact tube model but suppress the oscillations that are found for exact models. (Justice, Wang et al 2007) The simplified tube model fits the data reasonably well except at intermediate q, where it seems to underestimate the size of the relevant size scale (tube outer radius). Based on the fit to the simplified tube form factor, one might naively conclude that dispersion is down to the level of individual tubes.…”