Conformational properties of strictly two-dimensional equilibrium polymers
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| Format: | Preprint |
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2025
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| _version_ | 1866915421924360192 |
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| author | Wittmer, J. P. Cavallo, A. Johner, A. |
| author_facet | Wittmer, J. P. Cavallo, A. Johner, A. |
| contents | Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths $N$ and surface fractions $ϕ$ compact configurations with fractal perimeters. We show here by means of Monte Carlo simulations of reversibly connected hard disks (without branching, ring formation and chain intersection) that polydisperse self-assembled equilibrium polymers with a finite scission energy $E$ are characterized by the same universal exponents as their monodisperse peers. Consistently with a Flory-Huggins mean-field approximation, the polydispersity is characterized by a Schulz-Zimm distribution with a susceptibility exponent $γ=19/16$ for all not dilute systems and the average chain length $<N> \propto \exp(δE) ϕ^α$ thus increases with an exponent $δ= 16/35$. Moreover, it is shown that $α=3/5$ for semidilute solutions and $α\approx 1$ for larger densities. The intermolecular form factor $F(q)$ reveals for sufficiently large $<N>$ a generalized Porod scattering with $F(q) \propto 1/q^{11/4}$ for intermediate wavenumbers $q$ consistently with a fractal perimeter dimension $d_s=5/4$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_00649 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformational properties of strictly two-dimensional equilibrium polymers Wittmer, J. P. Cavallo, A. Johner, A. Soft Condensed Matter Statistical Mechanics Two-dimensional monodisperse linear polymer chains are known to adopt for sufficiently large chain lengths $N$ and surface fractions $ϕ$ compact configurations with fractal perimeters. We show here by means of Monte Carlo simulations of reversibly connected hard disks (without branching, ring formation and chain intersection) that polydisperse self-assembled equilibrium polymers with a finite scission energy $E$ are characterized by the same universal exponents as their monodisperse peers. Consistently with a Flory-Huggins mean-field approximation, the polydispersity is characterized by a Schulz-Zimm distribution with a susceptibility exponent $γ=19/16$ for all not dilute systems and the average chain length $<N> \propto \exp(δE) ϕ^α$ thus increases with an exponent $δ= 16/35$. Moreover, it is shown that $α=3/5$ for semidilute solutions and $α\approx 1$ for larger densities. The intermolecular form factor $F(q)$ reveals for sufficiently large $<N>$ a generalized Porod scattering with $F(q) \propto 1/q^{11/4}$ for intermediate wavenumbers $q$ consistently with a fractal perimeter dimension $d_s=5/4$. |
| title | Conformational properties of strictly two-dimensional equilibrium polymers |
| topic | Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2507.00649 |