## 2 Materials and Methods  
### Dissipative Particle Dynamics Approach  
We first briefly introduce the DPD approach we use to model the phase separation and crosslinking reaction; more details of the DPD methodology can be found in the original publications [25; 26; 27]. The beads in DPD represent groups of atoms; the motion of these beads is governed by [PERSON]'s equations of motion [27]: \(d\mathbf{r}_{i}/dt=\mathbf{v}_{i}\), \(d\mathbf{p}_{i}/dt=\sum\limits_{j\
eq i}\mathbf{F}_{ij}\), where \(\mathbf{r}_{i}\), \(\mathbf{v}_{i}\), and \(\mathbf{p}_{i}=m\mathbf{v}_{i}\) are the position, velocity, and momentum of a particle \(i\) of mass \(m\), respectively, and \(\mathbf{F}_{ij}\) is the pairwise additive force exerted on the particle \(i\) by the particle \(j\). The summation is taken over all the particles within the chosen cut-off distance \(r_{c}\), which effectively introduces a characteristic length scale of the model. The total force acting between the non-bonded beads consists of three contributions [27]: \(\mathbf{F}_{ij}=\mathbf{F}_{ij}^{C}+\mathbf{F}_{ij}^{D}+\mathbf{F}_{ij}^{R}\), where \(\mathbf{F}_{ij}^{C}\) is a purely repulsive conservative force, \(\mathbf{F}_{ij}^{D}\) is dissipative, and \(\mathbf{F}_{ij}^{R}\) is a random force. We chose the conservative force based on the soft repulsion potential [27]:  
\[\mathbf{F}_{ij}^{C}= \begin{cases}a_{ij}\Big{(}1-\frac{r_{ij}}{r_{c}}\Big{)}\mathbf{e}_ {ij}&\big{(}r_{ij}<r_{c}\big{)}\\ 0&\big{(}r_{ij}\geq r_{c}\big{)}\end{cases}  \tag{1}\]  
where \(a_{ij}\) is the maximum repulsion between the beads \(i\) and \(j\), \(r_{ij}=|\mathbf{r}_{ij}|\) is the distance between the centers of these beads, \(\mathbf{r}_{ij}=\mathbf{r}_{i}-\mathbf{r}_{j}\), and \(\mathbf{e}_{ij}=\mathbf{r}_{ij}/r_{ij}\). The repulsion parameter between the beads of the same type, \(a_{ii}\), is typically calculated based on the degree of coarse-graining [27; 45]. Herein, we chose \(a_{ii}=78\,k_{B}T/r_{c}\); this parametrization is derived based on the compressibility of water and corresponds to coarse-graining of three water molecules into a single bead [45], so that the volume of a single bead is approximately 90 A\({}^{3}\). The repulsion parameter for the dissimilar beads, \(a_{ij}\), is chosen based on the affinity between the moieties these beads represent as detailed below. Remaining contributions to the total force read [27]\(\mathbf{F}_{ij}^{D}=-\gamma\omega^{D}\left(r_{ij}\right)\left(e_{ij}\mathbf{v}_{ij} \right)e_{ij}\) and \(\mathbf{F}_{ij}^{R}=\sigma\omega^{R}\left(r_{ij}\right)\zeta_{ij}\Delta t^{-1/2} \mathbf{e}_{ij}\), respectively, where \(\gamma\) and \(\sigma\) are the strengths of the dissipative and random forces, \(\mathbf{v}_{ij}=\mathbf{v}_{i}-\mathbf{v}_{j}\) is the relative bead velocity, and \(\Delta t\) is the simulation time step. The \(\zeta_{ij}\) is a symmetric Gaussian distributed random variable with zero mean and unit variance, \(<\zeta_{ij}(t)>=0\), \(\left\langle\zeta_{ij}(t)\zeta_{ij}(t^{\prime})\right\rangle=\left(\delta_{ik} \delta_{jl}+\delta_{il}\delta_{jk}\right)\delta(t-t^{\prime})\). The \(\mathbf{F}_{ij}^{D}\) and \(\mathbf{F}_{ij}^{R}\) are coupled through the fluctuation-dissipation theorem [26] for which the following two conditions are imposed [27]: \(\omega^{D}\left(r_{ij}\right)=\left(\omega^{R}\left(r_{ij}\right)\right)^{2}\), and \(\sigma^{2}=2\gamma k_{B}T/m\), where \(k_{B}\) is the Boltzmann constant and \(T\) is temperature. We chose the weight function [27]\(\omega^{R}\left(r_{ij}\right)=\left(1-r_{ij}/r_{c}\right)\) for \(r_{ij}\leq r_{c}\). Within the polymer strands, the beads are connected by harmonic bonds with the interaction potential \(U_{bond}=K_{bond}\big{(}r_{ij}-r_{b}\big{)}^{2}/2\), where \(K_{bond}=10^{3}\,k_{B}T/r_{c}^{2}\) and \(r_{b}=0.7\,r_{c}\) are chosen [46] as the spring constant and the equilibrium bond length, respectively.