Mini Review Volume 4 Issue 5

^{1}National State University, Kharkov Polytechnic Institute, Ukraine^{2}B.I. Verkin Institute for Low Temperature Physics and Engineering, Ukraine

**Correspondence:** Lykah VA, Institute of Physics and Engineering, National State University “Kharkov Polytechnic Institute”, 2 Kirpichov str., Kharkov, 61002, Ukraine

Received: February 16, 2018 | Published: September 24, 2018

**Citation: **Lykah VA, Syrkin ES. Adsorption, functionalization and electrostatic multipolar interactions at CNT and graphene surfaces. *Int J Biosen Bioelectron*. 2018;4(5):22110.15406/ijbsbe.2018.04.00130

The functionalizing molecules (atoms) at a surface are considered for charge transfer between a molecule and substrate (CNT or graphenes). It is shown that at initial and intermediate stage of functionalization the intermolecular interaction can be described as electrostatic dipoles and quadrupoles ones. This model explains a homogeneous (sometimes periodic) distribution of adsorbed particles found in the experiments.

**Keywords:** adsorption, charge transfer, multi pole electrostatic interaction, graphenes, CNT Pacs 79.60.Dp

Carbon nanotubes (CNTs) are 1D nano materials, quantization along axis exists; CNT is considered as quantum wire or quantum dot.^{1} Functionalization is powerful method for tuning CNTs quantum energy levels and physical properties. Functionalization of 2D graphene and bigraphene layers is also applied widely. The theory was developed^{2} for energy spectra tuning in the semiconducting nanowires and polarons formation as the result of functionalization by molecular layers with (i) radial degree of freedom, (ii) conformational transition in the molecules and (iii) incommensurate structures. Periodic distribution of metals, metal organic^{3} and conducting polymers at CNT surface was found by TEM.^{4 }The charge transfer^{3} leads to electron and hole (pair), spatially separated in neighboring substrate (CNT) and a molecule or atom. The aim of this work is theoretical consideration of initial stages of functionalization with the charge transfer. It is shown that the electron-hole pairs can be presented as the dipole and quadrupole moments with long range interaction. We consider situation of enough small molecules with relatively large distance between ones. At short range distances, compared with the molecules size, the proposed method would be applied with higher error. The charge transfer is example of a general contact interaction of molecules with different electro negativity. Thus, in comparison with CNT and graphene we have electronegative molecules with F, Cl, O, N. P, S atoms and electropositive metals or metal-organic complexes. In further consideration we suppose the molecules (atoms) to be electropositive and the electronic clouds of the transferred charge to be negative, they are shown in Figure 1. A dipole vector^{5} *d = qr* is shown as arrow between centers of negative and positive charges in Figure 1. Following to^{5,6 }we write dipole-dipole interaction as:

${U}_{dd}=\frac{{d}^{2}}{{R}^{3}}[({\omega}_{1}{\omega}_{2})-3({\omega}_{{}_{1}}n)({\omega}_{2}n)]$ ………(1)

where R is the radius-vector between centers of the dipoles 1 and 2,$R=\left|R\right|$ the unit vectors ${\omega}_{1}$ ,${\omega}_{2}$ and $n$ are directed along ${d}_{1}$ ${d}_{2}$ and $R$ Force between two particles for (1) is

${F}_{ij}=-\frac{d{U}_{ij}(R)}{dR}=-\frac{1}{dR}[\frac{A}{{R}^{K}}]=\frac{K}{R}{U}_{ij}(R)$ …..(2)

where factor *A* is function of all parameters except distance *R*. In (1) power *k* = 3 and U_{ij} = U_{dd}. In next formulae k = 4; 5 and U_{ij }= U_{Qd};U_{QQ}. Positive F means repulsion. The dipoles configuration in Figure 1 gives according (1, 2) F_{12} > 0 and F_{13} < 0 because of $({\omega}_{1}n)$
=0 and $({\omega}_{1}{\omega}_{2})$
> 0
but $({\omega}_{1}{\omega}_{3})$
< 0Increasing of the functionalizing molecules concentration leads to formation of different clusters^{3,4 }which can't be described in the present model. Only the small clusters with the multiple numbers N of the molecules can be described by (1) applying *d _{N} = Nd_{1}*. A renormalization of the charge transfer can arise depending on the cluster size (multiple numbers

${U}_{Qd}=-\frac{3Qd}{2{R}^{4}}[({\omega}_{1}n)+2({\omega}_{1}{\omega}_{2})({\omega}_{2}n)-5({\omega}_{1}n){({\omega}_{2}n)}^{2}]$ …….(3)

${U}_{QQ}=-\frac{3{Q}^{2}}{4{R}_{0}{}^{5}}[1-5{({\omega}_{1}n)}^{2}-5{({\omega}_{2}n)}^{2}+2{({\omega}_{1}{\omega}_{2})}^{2}+35{({\omega}_{1}n)}^{2}{({\omega}_{2}n)}^{2}-20({\omega}_{1}n)({\omega}_{2}n)({\omega}_{1}{\omega}_{2})]$ …..(4)

Here *Q* is the nanobelts quadrupolar moment, *R* is the distance between centers of a quadrupole and a dipole or between two quadrupoles, *n*,${\omega}_{1}$
, ${\omega}_{2}$
are unit vectors. *nǁ R.* In (3) ${\omega}_{1}$

and A_{QQ} =(3=4)*Q*^{2} in (4,2) means repulsing.

**Figure 1** The adsorbed molecules or atoms (yellow spheres) at substrate (CNT, graphene) with transferred electrons (blue ellipses) gives repulsion of dipoles d1ǁǁd2. Opposite dipoles d1; d3 are attracted at semiconducting CNT or bi graphene.

None.

The authors have no conflicts of interests in this work.

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