Energetics of Hybrid Structures between Cycloparaphenylene and Carbon Nanotubes: A Dispersion-Corrected Density Functional Theory Study

Abstract

Dispersion-corrected density functional theory (DFT) calculations examined energetically preferable hybrid structures between [13]­cycloparaphenylene ([13]­CPP) and an armchair (m,m) tube (5 ≤ m ≤ 9). Tube-in-ring and ring-on-tube structures, denoted by (m,m)@[13]­CPP and [13]­CPP–(m,m), respectively, were considered. DFT-based energy-decomposition analyses revealed that the key factors determining the stability of the hybrid structures are attractive long-range interactions between [13]­CPP and the (m,m) tube and the energy penalty required for the deformation of [13]­CPP. The long-range interactions in (m,m)@[13]­CPP become more significant with an increase in the tube diameter. The [13]­CPP deformation in (m,m)@[13]­CPP varies with the degree of deviation between the radius difference between [13]­CPP and a tube (Δr) and the van der Waal contact distance between two carbon atoms (3.35 Å). Accordingly, the stability of (m,m)@[13]­CPP depends on the tube diameter. Particularly, (8,8)@[13]­CPP, whose Δr is close to 3.35 Å, is highly stabilized among (m,m)@[13]­CPP because of a negligible energy penalty for the [13]­CPP deformation. In contrast, the stability of [13]­CPP–(m,m) is less sensitive to the tube-diameter, and their attractive long-range interactions are weaker than those in (m,m)@[13]­CPP. Consequently, a tube-in-ring structure whose radius difference is close to 3.35 Å is the most preferable among hybrid structures between [13]­CPP and an (m,m) tube.

Competition between Hydrogen Bonding and Dispersion Force in Water Adsorption and Epoxy Adhesion to Boron Nitride: From the Flat to the Curved

“…We are interested in the relation between the curvature of BNNT and its affinity for epoxy resin, which seems to have remained to be clarified. Note that theoretical studies on the effect of the curvature of the tube surface on the interaction with molecules have been done extensively for CNTs. , …”

“…Note that theoretical studies on the effect of the curvature of the tube surface on the interaction with molecules have been done extensively for CNTs. 96,97 In general, with respect to the adhesion of polymers to BNNTs, the smaller the curvature of the nanotube, the larger the surface contact area between the nanotube and the polymer, and the more attractive the interaction in between. 25,98 However, as we have learned from our calculations of water adsorption on BNNTs, increasing the curvature of the tube improves the hydrogen-bond-accepting capacity of the N atom of BNNTs.…”

Roles of Carbon Nanotube Confinement in Enhancing Second-Order Nonlinear Optical Properties of Triiodobenzene Aggregates

“…In other words, B97D calculations can evaluate dispersion interactions with the same level of accurate CCSD­(T) calculations; at the same time, their computational cost is much lower than that of CCSDT. Since B97D calculations are cost-effective, they are applicable for describing long-range interactions in nanocarbon hybrid structures. − In fact, our previous studies employed B97D calculations to successfully reveal key interactions determining hybrid structures consisting of π-conjugated molecules and tubes. − ,, …”

“…33−36 In fact, our previous studies employed B97D calculations to successfully reveal key interactions determining hybrid structures consisting of π-conjugated molecules and tubes. [18][19][20][21][22]37,38 The current study will focus on the structures of nanotubes containing the BzI 3 multimer denoted by n × BzI 3 , where n is the number of BzI 3 molecules (1 ≤ n ≤ 4). For this purpose, we considered armchair (7,7), (8,8), and (9,9) tubes, whose optimized diameters are 9.3, 10.6, and 12.3 Å, respectively.…”

Theoretical understanding of stability of mechanically interlocked carbon nanotubes and their precursors

“…These indicate that cost-effective B97D calculations are feasible to well estimate the long-range interactions in nanomaterials containing a hundred atoms. [43][44][45][46] In fact, we successfully determined hybrid structures consisting of p-conjugated molecules and tubes [47][48][49][50][51][52][53][54] by using B97D calculations. For example, we investigated the energetics of armchair nanotubes inside a cycloparaphenylene (CPP) structure ((a,a)@CPP).…”