I think you can easily measure the mass of carnon nanotubes per square millemeter, and measure the averaged diameter and wall thickness. then to determoine average (!) length is quite easy. Good luck.

C.D. Scott, S. Arepalli, P. Nikolaev, R.E. Smalley: Appl. Phys. A 72, 573 (2001)

This paper describes an eligant means of measurment of growth rate. Also there is an errata to this paper.Appl. Phys. A 74, 11 (2002) / Digital Object Identifier (DOI) 10.1007/s003390101005

you can do this by using the SEM to measure the length of the CNTs and then divided this by the growth time it simply give you the growth rate GOOD LUCK

Try different successive deposition time ex. 5, 10 , 15 min , then find the SEM images of each sample measuring the length. & with simple calculation of dividing the lengths by growth time, you have the growth rate.

Unfortunately the growth rates of a carbon nanotube typically vary with time due to: (1) Contamination of the catalyst surface, (2) Catalyst growth (Ostwald Ripening.) (3) Catalyst interaction with the substrate if you are doing forest growth, (4) Catalyst becoming surrounding by graphene thereby blocking the reaction, (5) depletion of the active fuel due to transport problems in your process or hindrance by the surrounding forest, and (6) poisoning of the catalysts by various substances. Therefore the growth rate is usually non-linear and the result depends on when in the process you measure it. The papers I cited above, measure growth rate a very short times and the results are consistent with carbon diffusion rate in iron. These CNT growth rates are 10s of microns per second (this was a high temperature process) and obviously slow down due to one or more of the above reasons.

My ideas, however I never did this before. Make TEM images, do dropcasting to TEM grid from diluted suspension to be able to separate individual nanotubes. Use ImageJ program, which can be helpful for measuring length. Try to run couple of CVD synthesis with shorter synthesis times to make smaller tubes, which will be easier to handle and use those data to determine the rate.

Given the entangled and twisting nature of your CNTs, this is not easy to do. However, S Fisenko's answer is on the right track. If you can somehow measure the total mass of the CNTs, in principle you can determine their lengths. However, there are two difficulties associated with this. (1) I'm not sure you have enough carbon mass to actually be able to weigh the CNTs, even using a microbalance. (2) Even if you could weigh the carbon mass due to deposition (by comparing the total substrate weight before and after CNT growth), from your image, it is still very difficult to determine how many CNTs you have per unit area.

So, how do you accomplish these two measurements. For the total carbon mass, you can perform RBS (if you have access). I've actually published an example of using this method for far less mass of CNTs than you have. [Siegal et al, APL, 80, 2171 (2002).] This will provide you with a determination of total carbon atoms/unit area. Of course, it measures all carbon, even carbonaceous material that may be depositing as a film on your substrate underneath your mass of CNTs.

For the average length, this will be more difficult due to the twisting nature of your CNTs. Your best bet is do take a cross-sectional image of your CNTs. The resolution will suffer, however, you should be able to get a better idea of the average lengths.

Good luck.

Not easy to determine the growth rate when according to what is shown on the SEM image not necessarily only MWCNT are here produced;

Growth rates of nanotubes and nanofibers, depend on growth mechanisms which affect not only the length, but also the wall thickness and the wall structure and the material deposited between the nanotubes..

All these depend first of distance between growing tubes and on density of catalytic active centers on the substrates where the tubes are nucleating, and on several other effects which can alter this distance with time; Then is to be considered

-Pollution condensing on CNT walls affecting also the surface diffusion of adsorbed carbon atoms on the CNT wall and therefore affecting the CNT growth rate.

- Formation of other types of graphenic particles and DLC between the tubes

- CNT wall thickness or formation of nanofibers (corresponding to "filled" nanotubes and where sp3 atomic rearrangement can exist which are induced by activation effects produced by condensing and recombining CHx radicals in a Plasma enhanced CVD process.

Therefore, I would first recommend to look at which sort of carbon structure exist within a nanotube and all around them with micro-Raman, ( to check existence of breathing modes, shape and width of the so called D peak, shape of so-called 2D peak, G side peaks etc.) and to check the filling of the tube. and try to get some estimation about which part of condensing material is in form of a tube or of a fiber or in form of graphitic (or DLC) material between the tubes, before measuring the weight of condensed carbon material and the diameter and wall thickness.

I do not known which parameter of the PECVD process you can change temperature, dissociation ionization, pressure, PECVD device design, power and chamber geometry, bias, plasma potential, precursor gases design etc. However , if possible I would recommend to change these parameter in order to produce clearer structure in the deposited material.

Thank you all for your contributions. All are valuable to me.

@Stephane, I have done Raman analysis and there are D, G, 2D, G', all peaks are present. My tubes are mutiwalled. So, no RBM is seen. My deposition temperature is around 800 C and I use microwave plasma for my deposition. The substrate is not biased and substrate id Inconel 600. At this temperature I think DLC should not be formed. As for other types of graphenic particles my higher resolution SEM images did not show anything mostly but yes there may be some as you said (I obviously didi not scan my whole 1/2 inch dia substrate). As for clearer structure, I am working on my experimental parameters especially by changing the gas ratio and tinkering with few other parameters.

if it is possible for you to prepare some SEM Micrograph during several steps of growth, Image Analyzing techniques (specially with MATLAB) could be a suitable way to quantify the results.

If you use the decomposition of methane, for example, you can use the chromatographic analysis of the exhausted gases (hydrogen). Using the calculation of the reagents amount you can calculate the rate of the carbon phase deposition, in a suggestion that the main reaction is the decomposition of hydrocarbon to carbon and hydrogen directly. Also, you can find a kinetic mechanism of your process and then calculate the rate of the carbon phase deposition!

So I have no experience with CNTs, but it seems like due to the random nature of the growth process you need something that measures the quantity of CNT material, then assume a mean diameter and wall thickness to get total length of CNTs produced per unit time.

Someone already suggested weighing, where of course there is low signal. What about dispersing all the CNTs in a solvent and measuring optical transmission? You could do the same with a known quantity of CNTs to determine how much you produced.

David Rushmore indicates why this is not an easy task very eloquently. Furthermore, there is clearly many stages in the growth phase that need to be taken into account. Most recently we have found that there appears to be an incubation period for the source hydrocarbon within the catalyst before a linear growth phase takes place. This is illustrated in the following paper.

https://www.researchgate.net/publication/236183277_Efficient_coupling_of_optical_energy_for_rapid_catalyzed_nanomaterial_growth_High_quality_carbon_nanotube_synthesis_at_low_substrate_temperatures

Please note this is a new growth technique called the Photo-Thermal CVD of CNT, which appears to give very high quality CNT growth at high growth rates and lower substrate temperatures ... even suitable and compatible with CMOS/MEMS processes. A practical example where we had to use SEM to measure growth rates .... that appears to give reasonable results.

Enjoy reading the paper ...

Article Efficient Coupling of Optical Energy for Rapid Catalyzed Nan...