\begin{algorithmic}[1]
\State possible pair list $\gets$ conventional neighbour list
\State new pair list $\gets \varnothing$
\ForAll{stickers $i$}
    \State $N_{bonds}[i]\gets0$
\EndFor
\State shuffle possible pair list
\ForAll{pairs $(i,j) \in$ possible pair list}
    \State $\Delta E_{ij} \gets U_{bound}(r_{ij})-U_{unbound}(r_{ij})$
    \If {$(i,j) \in$ previous pair list}
        \If {$X\sim U(0,1)>\exp(-\Delta E_{ij})$}
            \State append $(i,j)$ to new pair list
            \State $N_{bonds}[i]\gets N_{bonds}[i]+1$
            \State $N_{bonds}[j]\gets N_{bonds}[j]+1$
        \EndIf
    \ElsIf{$N_{bonds}[i]<functionality$ \textbf{ and } $N_{bonds}[j]<functionality$}
        \If {$X\sim U(0,1)<\exp(-\Delta E_{ij})$}
            \State append $(i,j)$ to new pair list
            \State $N_{bonds}[i]\gets N_{bonds}[i]+1$
            \State $N_{bonds}[j]\gets N_{bonds}[j]+1$
        \EndIf
    \EndIf
\EndFor
\State previous pair list $\gets$ new pair list
\end{algorithmic}

\begin{algorithmic}
[1]
\State possible pair list $\gets$ conventional neighbour list
\State new pair list $\gets \varnothing$
\ForAll{stickers $i$}
\State $N_{bonds}[i]\gets0$
\EndFor
\State shuffle possible pair list
\ForAll{pairs $(i,j) \in$ possible pair list}
\State $\Delta E_{ij} \gets U_{bound}(r_{ij})-U_{unbound}(r_{ij})$
\If {$(i,j) \in$ previous pair list}
\If {$X\sim U(0,1)>\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\ElsIf{$N_{bonds}[i]<functionality$ \textbf{ and } $N_{bonds}[j]<functionality$}
\If {$X\sim U(0,1)<\exp(-\Delta E_{ij})$}
\State append $(i,j)$ to new pair list
\State $N_{bonds}[i]\gets N_{bonds}[i]+1$
\State $N_{bonds}[j]\gets N_{bonds}[j]+1$
\EndIf
\EndIf
\EndFor
\State previous pair list $\gets$ new pair list
\end{algorithmic}
{
    "title": "evanescent gels: competition between sticker dynamics and single chain   relaxation",
    "id": "2302.13623",
    "abstract": "solutions of polymer chains are modelled using non-equilibrium brownian dynamics simulations, with physically associative beads which form reversible crosslinks to establish a system-spanning physical gel network. rheological properties such as the zero-shear-rate viscosity and relaxation modulus are investigated systematically as functions of polymer concentration and the binding energy between associative sites. it is shown that a system-spanning network can form regardless of binding energy at sufficiently high concentration. however, the contribution to the stress sustained by this physical network can decay faster than other relaxation processes, even single chain relaxations. if the polymer relaxation time scales overlap with short-lived associations, the mechanical response of a gel becomes ``evanescent'', decaying before it can be rheologically observed, even though the network is instantaneously mechanically rigid. in our simulations, the concentration of elastically active chains and the dynamic modulii are computed independently. this makes it possible to combine structural and rheological information to identify the concentration at which the sol-gel transition occurs as a function of binding energy. further, it is shown that the competition of scales between the sticker dissociation time and the single-polymer relaxation time determines if the gel is in the evanescent regime.",
    "categories": "cond-mat.soft",
    "doi": "",
    "created": "2023-02-27",
    "updated": "2024-02-10",
    "authors": [
        "dominic robe",
        "aritra santra",
        "gareth h. mckinley",
        "j. ravi prakash"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2302.13623"
}
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