Defining Ideal Phantom Polymer Networks
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910255487647744 |
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| author | Nanavati, Hemant Das, Sushanta |
| author_facet | Nanavati, Hemant Das, Sushanta |
| contents | Elastomers are modeled as networks with $ϕ$-functional junctions containing $N$ ideal, $n$-segment, freely jointed chains (FJCs) per unit volume (p.u.v.). Our compact model of the exact FJC length probability density (Treloar, 1975), accurately yields their exact distribution moments (Flory, 1969). The governing geometry of fluctuations of $N_X = 2N/ϕ$ junctions p.u.v., parametrically maps their $λ$(elongation ratio)-dependent distribution to an equivalent FJC consisting of $n_{fϕ} = (n/ϕ)(1-Λ)$ segments, where $Λ= (1/3n)(λ^2 + 2/λ))$. The resulting elastic pre-factor, $N_{\text{eff}}kT = (N - ηN_X)kT$, with junction effectiveness $η= ϕ(1-Λ)/(ϕ-Λ)$, defines ideal phantom networks |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16188 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Defining Ideal Phantom Polymer Networks Nanavati, Hemant Das, Sushanta Soft Condensed Matter Elastomers are modeled as networks with $ϕ$-functional junctions containing $N$ ideal, $n$-segment, freely jointed chains (FJCs) per unit volume (p.u.v.). Our compact model of the exact FJC length probability density (Treloar, 1975), accurately yields their exact distribution moments (Flory, 1969). The governing geometry of fluctuations of $N_X = 2N/ϕ$ junctions p.u.v., parametrically maps their $λ$(elongation ratio)-dependent distribution to an equivalent FJC consisting of $n_{fϕ} = (n/ϕ)(1-Λ)$ segments, where $Λ= (1/3n)(λ^2 + 2/λ))$. The resulting elastic pre-factor, $N_{\text{eff}}kT = (N - ηN_X)kT$, with junction effectiveness $η= ϕ(1-Λ)/(ϕ-Λ)$, defines ideal phantom networks |
| title | Defining Ideal Phantom Polymer Networks |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2405.16188 |