Comment on “Correlation between Porosity and Electrical-Mechanical Properties of Carbon Nanotube Buckypaper with Various Porosities”

الملخص EN

With great interest we read a recently published article entitled “Correlation between Porosity and Electrical-Mechanical Properties of Carbon Nanotube Buckypaper with Various Porosities” authored by Ling Liu and colleagues in Journal of Nanomaterials [1].

There are certain concerns and issues that question the methodology, reliability of results, and related analysis.

One of the key concerns is that the authors have prepared three sets of samples of randomly aligned multiwalled carbon nanotubes (MWCNTs) in the form of buckypapers (BPs) with IDs 1# BPs, 2# BPs and 3# BPs, having exceptionally low levels of porosity, that is, 11.3%, 21.1%, and 39.3%, respectively.

The porosity (ξ) and fibre volume fraction (Vf) of any porous material are related to each other, as shown in the following equation [2]:(1)ξ=1-Vf.Based upon the above equation, Vf of sample IDs 1# BPs, 2# BPs and 3# BPs are 88.7%, 78.9%, and 60.7%, respectively.

Such values of Vf can be obtained neither through any experimental route for fabricating randomly aligned carbon nanotubes (CNTs) nor from theoretical perspective.

To prove this point, we hypothetically analysed the maximum fibre volume fraction (Vfm) of BPs through the work of Pan et al.

[3] dealing with the fibrous network that also includes the case of randomly oriented fibres.

Considering each CNT as a fibre in the network [4, 5], the fibrous network consists of three basic segments, namely, the mean length (separation distance) between the centres of two adjacent fibres (b-), the mean length of contacts (b-b), and the mean free fibre length (b-f) (see [3] for details).

Hence, the proportions of free length of fibre (m) and that of contact length (n) are given below:(2)m=b-fb-,n=b-bb-, m+n=1.Theoretically, m≥0; in case this inequality is violated; the free fibre length between the contacts will not exist, which eventually leads to Vfm.

Based upon these considerations, Pan et al.

[3] have formulated the general relationship between Vfm and the orientation distribution of fibres, as shown below:(3)Vfm<π8RI,I=∫0πdθ∫0πJθ,φsinθΩθ,φdφ,Jθ,φ=∫0πdφ′∫0πsinχΩθ′,φ′sinθ′dθ′,sinχ=1-cosθcosθ′+sinθsinθ′cosφ-φ′21/2,R=∫0πdθ∫0πdφΩθ,φJ′θ,φsinθ,J′θ,φ=∫θ1′θ2′dθ′∫φ1′φ2′dφ′Ωθ′,φ′1sinχsinθ′,π-sin-11s>χ>sin-11s,where I is an orientation parameter defining the orientation characteristics of fibres in the assembly, χ is the angle between the two axes of fibres having defined types of orientation distributions Ωθ,φ and Ω(θ′,φ′), and s is the aspect ratio.