We evaluate the correlation function and gyration radius of a theta-shaped polymer and those of a ring polymer via the Monte-Carlo simulation with/without excluded volume and the Gaussian model. We generate random equilateral chains whose structure is given by either a theta-3 graph or a loop. In the Gaussian model, the mean-square (MS) gyration radius of theta-shaped chains is given by 2/3 times gyration radius of ring-shaped chains of the same number of segments. Similarly, the ring polymer has half MS gyration radius compared with the linear polymer having the same number of segments. Therefore, the MS gyration radius of a linear chain with n segments, a ring chain with 2n segments and a theta-3 chain with 3n segments are equal to each other. It is also the case for the Monte-Carlo simulation without excluded volume. In the Monte-Carlo simulation with excluded volume, the MS gyration radius of a theta-3 graph polymer with 3n segments is larger than that of a ring polymer with 2n segments. The MS gyration radius of a ring polymer with 2n segments is larger than that of a linear polymer with n segments. Here we recall that they are equal in the case of ideal chains.

Statistical mechanics of theta-shaped and ring-shaped polymer chains

255th National Meeting (2018)

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