Dispersion Model

The ionic liquid (IL) dispersant is used to disperse MWCNTs. The cation- π interaction and the hydrophobic force of the alkyl groups in the IL-MWCNT hybrid solution interaction are the dominant forces. The IL is a kind of electrolyte composed of two ions, the cation and anion. An IL of 1-hexadecyl-3-methylimidazolium chloride (HDMIC)in useis chemically expressed in Figure 5.1. Usually, the cation part of IL is a kind of imidazolium, which attached with a long alkyl group.

Figure 5.1 The chemical expression of HDMIC ionic liquid dispersant.

The force between the cations and π electrons of MWCNTs is named as cation-π interaction force [12]. It is a kind of electro-static force or ionic charge force. By cation-π interaction, the cations are attached on the surface of MWCNTs. Figure 5.2 shows the aggregated MWCNTs are mixed with IL then dissolved into the N-methylpyrrolidone (NMP) solvent.

Figure 5.2 (a) Schematic diagram of aggregated MWCNTs, (b) ionic liquid (IL), and (c) aggregated MWCNTs with IL in NMP solvent.

MWCNT

MWCNT:

MWCNT

MWCNT:

IL

+

Cation ion of IL:

Alkyl group of IL:

IL

+

Cation ion of IL:

Alkyl group of IL:

IL

++

Cation ion of IL:

Alkyl group of IL:

(a) (b)

NMP (c)

The dispersion phenomenon after well mixing IL by stirring the hybrid solution. The cation ions of IL are uniformly attached on the MWCNTs, and the hydrophobic forces between the alkyl groups of IL make the dispersion via the steric isolation effect, as shown in Figure 5.3 (a). The dispersion effect increases as the IL ratio increases, as shown in Figure 5.3 (b).

The alkyl group is a long-chain hydrocarbon attached on the imidazolium cation.

There are forces between an alkyl group and other alkyl groups due to their hydrophobic attraction property. These hydrophobic forces contribute to the dispersion of MWCNTs since their steric isolation effect. The alkyl groups of IL will also interact with the non-polar polyimide molecules, while a matrix material mixed together, such as the polyimide matrix.

The cation-π interaction force is a kind of ionic charge force. It can be expressed in the Coulomb electrostatic force [20], formula as

( )

Figure 5.3 (a) Schematic diagram of MWCNTs dispersed by IL, (b) well-dispersion MWCNTs by IL.

₂ charges with coulomb unit, the ε is the dielectric constant in vacuum, R is the distance ⁰ between cation and π electron. The total interaction force between cations and π electrons can be expressed as

The interaction force between two alkyl groups is the gradient of potential energy, and is named as hydrophobic force (Fh). There are similar studies for the hydrophobic force. For example, Christenson and Claesson [21] observed from their experiments that the hydrophobic forces measured between Langmuir-Blodgett (L-B) deposited monolayers of long-chain hydrocarbon and fluorocarbon surfactants on mica clearly followed a double-exponential force law [21]

Fh/R = C1exp(-H/D1) + C2exp(-H/D2) (5-7)

where the R is the mean radius of curvature of the interacting bodies, and the H is the closest separation between the two curved surfaces. The C₁ and D₁ represent the short-range part of the interaction and the C2 and D2 the long-range part. The C1 and C2 are pre-exponential factors. The D1 and D2 are known as the decay length.

Another example, surface-tension model can be used to calculate the hydrophobic force between two hydrocarbon molecules such as force between two methane molecules in water [22].

where G∆ is the corresponding free energy change, σ is surface-tension parameter, R is the separate distance between two methane molecules, ∆ is the change in the solvent-A accessible area. f is the hydrophobic force.

Before adding IL dispersant, the binding energy of van der Waals force between a hexagonal ring on a MWCNT and another hexagonal ring on neighboring MWCNT is the order of 1 kcal/mol [16]. After adding IL dispersant, they have three major interaction forces involved. The predominant is the cation-π interaction which has the binding energy of the order 9.4 kcal/mol [20], the minor binding energy is contributed from the hydrophobic interaction including the binding energy between alkyl groups and the binding energy between alkyl groups and matrix molecules.

Cation-π interaction belongs to ionic charge force with a binding energy greater than that of weak van der Waals force. Besides, according to equation (5-1), the van der Waals potential energy is approximately proportional to 1₆

R for the attraction. And the van der Waals force is in a relative small scale in comparison to the other forces, such as cation-π and hydrophobic forces. For example, the cation-π binding energy between the organic ion of NMe4+

and benzene in equation (5-4) is around 9.4 kcal/mol [20] and the binding energy of hydrophobic interaction between two methanes is around 2.7 kcal/mol [21].

However, the binding energy of the weak van der Waals force in equations (5-1) is usually less than 1 kcal/mol [16]. Table 5.1 lists the binding energies of the van der Waals interaction,the ionic charge interaction, the alkyl group interaction, and the alkyl and matrix interaction. Overall, the predominant binding energy of cation-π interaction is greater than the binding energy of aggregated MWCNTs. Ultimately, a fine dispersion of MWCNTs in the matrix in the presence of IL occurs.

Table 5.1 Binding energies of van der Waals force, cation- π interaction, alkyl-alkyl interaction, and alkyl-polyimide interaction.

Type

Energy Without IL

Binding energy van der Waals cation-π alkyl-alkyl alkyl-PI Binding energy (kcal/mol) 1 9.4 2.7 2.7

Reference [16] [20] [22] [22]

Dispersion with IL