2020/12/27 by Kazumi Suematsu, Suematsu, Kazumi, Haruo Ogura +5
Chemical Engineering · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #Rheology and Fluid Dynamics Studies #Scientific Research and Discoveries #Soft Condensed Matter (cond-mat.soft)
paper · pdf · doi:10.48550/arxiv.2012.13893
openalex publication_date 2020/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The segment distribution around the center of gravity is investigated for a special comb polymer (triangular polymer) having the side chains of the same generation number, g, as the main backbone. Common to all the other polymers, the radial mass distribution is expressed as the sum of the distribution functions for the end-to-end vectors, \rGh\, from the center of gravity to the monomers on the hth generation; the result being, for a large g, φtriang(s)=(1)/(N)\∑h=1g(\fracd2π⟨ rGh2⟩)(d)/(2)Exp(-\fracd2⟨ rGh2⟩s2)+∑h=2g∑j=1g-h(\fracd2π⟨ r_Ghj2⟩)(d)/(2)Exp(-\fracd2⟨ r_Ghj2⟩s2)\It is found that the mean square of the radius of gyration varies as ⟨ sN2⟩0\doteq(7)/(15) g l2, as g→∞. Since g∝ √(N) for the triangular polymer, this leads to ⟨ sN2⟩01/2∝ N1/4, giving the same exponent as observed for the randomly branched polymer. On the basis of the present result, we put forth that all the known polymers obey the equality: ⟨ sN2⟩0=A g l2, where A is a polymer-species-dependent coefficient and also depends on the choice of the root monomer. We discuss the extension of this empirical equation.