How long is a piece of string?  You can't have 'the zeta potential of an amine functionalized multiwall carbon nanotube'. Zeta potential is a holistic property of the system - the CNT and the liquid (aqueous) environment that surrounds it.  ZP is affected by the chemistry of the surface (obviously), the pH of the surrounding dispersant, and the presence of polyvalent ions and their concentration among other things.  Why is ZP important in your system?

thanks for your answer 

whereas we want to disperse amine functionalized into water, and then injection CO2 in this solution,we want to understand ZP in the pH range 6-9.

Under these conditions we'd expect to see the zeta potential as being negative with the amine group present.  However, the chemistry is key and injection of the CO2 will tend to produce a slightly acid environment.  It's easy to actually measure the ZP under a range of conditions (e.g. varying carbonate - a model system - concentration as CO2 would form bubble - and these bubbles could carry a charge too). Indeed perhaps the density difference with bubbles adhering to the CNT's would overcome any ZP forces (attractive or repulsive).

thanks for your answer and guidance.