Dispersions of Polymer-Modified Carbon Nanotubes: A Small-Angle Scattering Investigation

Abstract

Carbon nanotubes (CNTs) were modified with polystyrene (PS) using self-initiated photografting photopolymerization. In order to optimize their utilization in CNT/polymer nanocomposites, a thorough characterization of their dispersions in solvents is of key importance. Using small-angle scattering, we have studied the effect of the modification on the agglomeration behavior in dilute toluene dispersions. Whereas small-angle X-ray scattering gives overall information, small-angle neutron scattering together with the use of deuterated solvents highlights the polymer shells or the CNTs. The structure of the CNTs and their agglomerates were modeled as fractal aggregates of homogeneous or core–shell cylinders for single- and multiwalled CNTs, respectively. In this way, we have characterized the dispersibility of the CNTs as well as the thickness of the shell formed by the grafted polymers in dependence on the time of polymerization.

Small-angle scattering from multiphase fractals

“…Once experimental intensity curves for a number of values of ρ 0 is available, one can fit the data with Eq. (17) and obtain the exponents τ 1 and τ 2 and the coefficients a 1 and a 2 as a function of the surrounding density ρ 0 . Then plotting √ a 1 versus ρ 0 yields the scattering density ρ 1 of the first fractal as the contrast match point, and the quantity n 1 V 2 1 /L τ1 1 .…”

“…One can prepare a number of samples, which differ only in the density ρ 0 of solvent or solid matrix, and measure their SAS intensities; this is the method of contrast variation, initially suggested by Stuhrmann [21]. Fitting formula (17) in conjunction with equations (18) and (19) suggests the extension of this method when it is applied not for the scattering intensity itself but for the coefficients a 1 and a 2 . Indeed, fitting each intensity curve with Eq.…”

“…The most common case is a curve showing only the transition between two power-law regimes, while the Guinier region and the Porod region at high q are usually missing. Nevertheless, one can exploit the interpolation formula (17) even in this case. Fig.…”

“…6b and 6c, respectively, one can clearly see plateaus corresponding to the coefficients a 1 and a 2 in Eq. (17), to which the Stuhrmann method of contrast variation can be applied. The further we are, in the plateau region, from the crossover point, the better the approximation (see the previous section).…”

“…SAS data (X-ray or neutron) often show a succession of power-law regimes whose scattering exponents are taking arbitrarily values from −4 to −1 [11][12][13][14][15][16][17]. On a double logarithmic scale, the scattering intensity looks like connected straight-line segments.…”