Here is an answer to your first question (attached).

http://www.bimat.org/assets/pdf/nu_05_43zussman.pdf

Here is something to your second question.

http://cdn.intechopen.com/pdfs/6810/InTech-Carbon_fiber_based_microelectrodes_and_microbiosensors.pdf

Your last question is a tough one. As I understand, individual carbon fiber is indeed very sensitive to UV light. To make it UV resistant, you have to use it with some proper resins. At the same time, speaking about possible uses of carbon fiber, it is transparent to radiation (radiolucent) and totally invisible in x-rays, which makes it a valuable material for medical purposes.

http://www.protechcomposites.com/pages/About-Carbon-Fiber.html

Thank you for your answer. I am reviewing the papers.

Northolt, M. G., and J. J. M. Baltussen. "The tensile and compressive deformation of polymer and carbon fibers." Journal of applied polymer science 83, no. 3 (2002): 508-538.

Maurtis Northolt does a wonderful job of explaining fiber mechanics in this paper. Northolt does not cite Steven R Allen, who is an important voice in the world of high performance fibers; you'll ned to do a scholar search on him author:(Allen SR). You can get the very important Allen/Farris/Thomas Air Force reports at dtic.mil

To the question about the use of carbon fibers without a resin, you need to understand about the relatively low compressive strain to failure of the fiber.

The elastic loop test measures the onset of compressive failure in a fiber as a loop in the fiber is tightened; so does SR Allen's tensile recoil test. Search ("elastic loop test" carbon) several open papers are worth looking at. The teach about buckling of the microstructure.

In transverse compression, carbon fibers are much more likely to crush than organic fibers like PPTA. The transverse properties of carbon fibers will limit application to items where those forces can be minimized. You should read

Singletary, J., H. Davis, M. K. Ramasubramanian, W. Knoff, and M. Toney. "The transverse compression of PPTA fibers Part I Single fiber transverse compression testing." Journal of materials science 35, no. 3 (2000): 573-581.

Singletary, J., H. Davis, Y. Song, M. K. Ramasubramanian, and W. Knoff. "The transverse compression of PPTA fibers Part II Fiber transverse structure." Journal of materials science 35, no. 3 (2000): 583-592.

González, Carlos, and Javier LLorca. "Mechanical behavior of unidirectional fiber-reinforced polymers under transverse compression: microscopic mechanisms and modeling." Composites Science and Technology 67, no. 13 (2007): 2795-2806.

In my work, (ballistic impact), we know that although the mechanical properties of carbon fibers suggest that they will performa quite well as armor materials, they don't. see

https://www.researchgate.net/publication/256816090_Dimensionless_parameters_for_optimization_of_textile-based_body_armor_systems?ev=prf_pub and

https://www.researchgate.net/publication/256816199_Decoupled_response_of_textile_body_armor?ev=prf_pub

That has everything to do with transverse properties. Carbon fibers crush under a transverse load, Kevlar PBO, UHMWPE and nylon fibers deform plastically.

Conference Paper Dimensionless Parameters for Optimization of Textile Based B...

Conference Paper Decoupled response of textile body armor.

I'd be areful thinking about carbon fiber as "totally invisible in x-rays"

These guys may have a comment about that. Chu, Benjamin, and Benjamin S. Hsiao. "Small-angle X-ray scattering of polymers." Chemical Reviews 101, no. 6 (2001): 1727-1762. http://www-ssrl.slac.stanford.edu/materialscatter/pubs/chem_rev_101_1727.pdf

You just need to do a scholar search, but you may need to go to the library the get articles. There is this

http://stuff.mit.edu/afs/athena.mit.edu/course/3/3.91/OldFiles/www/slides/J_Composite_Materials2002v36p2713.pdf

thank you for your answer.

I would like to contact with a research group that produces individual carbon fibers with different response and conditions.

Again, you should ask the Oracle (google) first, but Satish Kumar at Georgia Tech https://www.researchgate.net/profile/Satish_Kumar103/ does that work from a theoretical perspective.

I don't know why you ask, but I suspect you already know that what's important to a manufacturing guy may be not so interesting to a research guy.

Toray, Mitsubishi, Toho, Nippon Graphite, and Hexcel do everything but most businesses are reluctant to openly discuss technology behind their core business.

In the past 7 years I did some research on the use of single carbon fibres. They can be used as electrode tools for electrochemical machining or as strain sensors. Some people work on building PV cells or other energy harvesting devices on single fibres. I also tried some ways to separate single fibres from bundles.

Here are some paper hints for you:

Mäder, Thomas; Nestler, Daisy; Wielage, Bernhard (2011): Strain Sensing using Single Carbon Fibres. In: Wo Il Lee (Hg.): 18th International Conference on Composite Materials. Jeju, 21.08.2011 - 26.08.2011. The British Composites Society.

Wielage, Bernhard; Gatzen, Hans-Heinrich; Mäder, Thomas; Nestler, Daisy; Belski, Alexander (2010): Analyses of Sensor Films on a Carbon Fibre. In: Journal of Materials Science and Engineering 4 (9), S. 20–27.

Wielage, Bernhard; Mäder, Thomas; Nestler, Daisy (2010): Optimisation and Characterisation of Magnetoelastic Microsensors. In: Madjid Fathi, Alexander Holland, Fazel Ansari und Christian Weber (Hg.): Integrated Systems, Design and Technology 2010, S. 155–167.

Mäder, Thomas; Nestler, Daisy; Scheffler, Susann; Wielage, Bernhard (2012): Verfahren zur Vereinzelung von Kohlenstofffasern aus Rovings. In: Bernhard Wielage (Hg.): Tagungsband zum 15. Werkstofftechnischen Kolloquium. Chemnitz (Werkstoffe und werkstofftechnische Anwendungen, 47).

Reinecke, H.; Wielage, B.; Förster, R.; Mucha, H.; Mäder, Thomas (2006): Electrochemical µ-wire cutting. In: Third International Symposium on ElectroChemical Machining Technology. Fraunhofer IKTS Dresden.

Shtein, Max; O’Connor, B.; Yadav, A.; Pipe, K.; Morris, S.E; Bayram, Y. et al. (2011): Novel device architectures for enabling energy harvesting, lighting, and communicationsfunctionalities in composites. In: Wo Il Lee (Hg.): 18th International Conference on Composite Materials. Jeju, 21.08.2011 - 26.08.2011. The British Composites Society.

some more papers.

mechanical characterization:

Gołębiewska, B.; Więcek, T.; Wasilewski, A. (2010): Measurement of the Poisson's ratio for the fibers using diffraction method, S. 77450O. DOI: 10.1117/12.871997.

Krucinska, I.; Stypka, T. (1991): Direct measurement of the axial poisson's ratio of single carbon fibres. In: Compos. Sci. Technol. 41 (1), S. 1–12.

Krucinska, I.; Stypka, T. (1991): Direct measurement of the axial poisson's ratio of single carbon fibres. In: Compos. Sci. Technol. 41 (1), S. 1–12.

properties vs. structure:

Bennett, S. C.; Johnson, D. J.; Johnson, W. (1983): Strength-structure relationships in PAN-based carbon fibres. In: Journal of Materials Science 18 (11), S. 3337–3347. DOI: 10.1007/BF00544159.

electrical properties:

Conor, P. C.; Owston, C. N. (1969): Electrical Resistance of Single Carbon Fibres. In: Nature 223 (5211), S. 1146–1147. DOI: 10.1038/2231146b0

sensor applications:

Park, C. S.; Kang, B. S.; Lee, D. W.; Choi, Y. S. (2006): Single carbon fiber as a sensing element in pressure sensors. In: Applied Physics Letters 89 (22).