Theory of tagged polymer method in small-angle X-ray scattering

Summary It was shown that the conformation of a single polymer chain in concentrated solutions and in undiluted state can be estimated from the small-angle X-ray scattering of randomly tagged polymer mixed in the systems. The randomly tagged polymer means the polymer containing heavy atoms at randomly selected positions along the molecule. The excess scattering of the tagged polymer is obtained by subtracting the scattering of the untagged polymer solution (or bulk) from that of the mixture solution (or bulk) containing the tagged and untagged polymers. The excess scattering obtained in this way contains the contributions of some undesirable cross terms of the scattering amplitude. The method for the experimental evaluation of these terms and the conditions under which these terms are negligible are discussed. It was found that the cross terms can be neglected when the contrast in scattering power between the tagged and untagged scattering units is sufficiently large, and the number of the tags per tagged molecule is not so small.The distribution of the tags in the tagged molecules was also taken into consideration. By averaging the theoretical scattered intensity over all possible positions of the tags, it was found that the excess scattering is practically proportional to the scattering function of the untagged polymer when the number of the tags per tagged molecule is not so small. Experimental verification of this theory was shown.It was also shown experimentally that the conformational change, which may be caused by the effect of the tags, can be eliminated by the extrapolation of the results obtained for a series of tagged polymers with various tag contents to zero tag content.With 2 figures