In the present paper, we ascertain two novel findings on chiral-index-selective binding/separating of single-walled carbon nanotubes (SWNTs) with a nonaromatic polymer, poly(dialkylsilane) (PSi). PSi is a typical sigma-conjugated polymer, composed of alkyl side chains attached to the silicon (Si)-catenated main chain. First, PSi's with linear alkyl side chains showed significant diameter-selective wrapping for SWNTs with ca. 0.9 nm in diameter, resulting in the selective separation of (7,6) and (9,4) SWNTs. Its driving force was demonstrated to be cooperative CH-pi interactions among the alkyl side chains of PSi's and the curved graphene of SWNTs. Second, the dynamic wrapping behavior of PSi's onto SWNTs was elucidated with time-resolved UV spectroscopy. Highly anisotropic UV absorption of PSi along the Si main chain was utilized as a "chromophoric indicator" to monitor the global/local conformations, which enabled us to track kinetic structural changes of PSi's on SWNTs. Consequently, we concluded that upon wrapping, flexible/helical PSi with an average dihedral angle (phi) of 145 degrees and Kuhn's segment length (lambda(-1)) of 2.6 nm interconverted to the more stiffer/planar conformation with 170 degrees and lambda(-1) of 7.4 nm. Furthermore, through kinetic analyses of the time-course UV spectra, we discovered the fact that PSi's involve three distinct structural changes during wrapping. That is, (i) the very fast adsorption of several segments within dead time of mixing (<30 ms), following (ii) the gradual adsorption of loosely wrapped segments with the half-maximum values (tau(1)) of 31.4 ms, and (iii) the slow rearrangement of the entire chains with tau(2) of 123.1 ms, coupling with elongation of the segment lengths. The present results may be useful for rational design of polymers toward chiral-index-selective binding/separating of desired (n,m) SWNTs.