Tanmay Biswas, Gerhard Kahl, and Gaurav P. ShrivastavInstitut f¨ur Theoretische Physik, TU Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria(Dated: March 26, 2024)Phase separation plays an role in determining the self-assembly of biological and soft-matter systems. In biological systems, liquid-liquid phase separation inside a cell leads to the formation of various macromolecular aggregates. The interaction among these aggregates is soft, i.e., these can significantly overlap at a small energy cost. From the computer simulation point of view, these complex macromolecular aggregates are generally modeled by the so-called soft particles. The effective interaction between two particles is defined via the generalized exponential potential (GEM-n) with n = 4. Here, using molecular dynamics simulations, we study the phase separation dynamics of a size-symmetric binary mixture of ultrasoft particles. We find that when the mixture is quenched to a lower temperature below the critical temperature, the two components spontaneously start to separate. Domains of the two components form, and the equal-time order parameter reveals that the domains grow in a power-law manner with exponent 1/3, which is consistent with the Lifshitz-Slyozov law for conserved systems. Further, the static structure factor shows a power-law decay with exponent 4 consistent with the Porod law.
If we then plot the xA-values of the peaks in P (xA) for the dierent temperatures we obtain the phase diagram, shown in the bottom panel of Fig. 4. Below the critical temperature, Tc, we see the characteristic coexistence line, separating the two above mentioned phases. (a) T = 1.8 (b) T = 1.4 (c) T = 1.0 y
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3. Color-coded representation of i (as dened in the text) for selected snapshots. Upper panels: perspective views of snapshots of the system at (a) T = 1.8, (b) T = 1.4, and (c) T = 1.0. Lower panels: cross sections of the respective upper panels, taken at z = L/2. The actual value of i [0, 1] of a cell with index i can be extracted from the respective colorcodes, depicted on the right hand side of the snapshots. The critical temperature Tc can be extracted from these data by tting the dierence in the concentrations of the two coexisting phases (indices (1) for the B-rich and (2) for the A-rich phase, respectively), i.e., (x(2) A ) (as obtained from the positions of the maxima of the distribution function P (xA) with the usual functional form : A x(1) A x(1) x(2) A = B(1 T /Tc); here, B and Tc are tting parameters, anticipating that the phase separation scenario at hand pertains to the 3DIsing universality class, i.e., 0.325. The inset of the 4
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4 provides evidence that (x(2) A can indeed be nicely tted via Eq. (10); the tted values are: B = 3.52 0.05 and Tc = 1.351 0.001. 8 (a) T=1.8 T=1.4 T=1.3 T=1.0 6 ) A x ( P 4 2 0 0 0.2 0.4 0.6 0.8 xA 1.35 (b) 1.3 1.25 T 1.2 1.15 1.1 1.05 0.2 0.15 0.1 0.05 0 1.28 / 1 A x 1.3 1.32 1.34 T 1 0 0.2 0.4 0.6 0.8 xA FIG. 4. Top panel (a): probability distribution, P (xA) (as dened in the text) as a function of xA for selected, dierent temperatures (as labeled). Bottom panel (b): symbols values of the coexistence densities x(1) A (as identied as maxima of P (xA)) for the dierent (sub-critical) temperatures investigated in this study. The red line displays the function specied in Eq. (10), using the tting parameters given in the text. The inset shows hx(2) as a function of A temperature T ; the dotted line displays again the function specied in Eq. (10). A and x(2) (1/) x(1) A i
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C. Phase separation dynamics We proceed by exploring the non-equilibrium dynamics of the mixture when quenched from a high temperature to a low, subcritical temperature. We start o from the equilibrated mixture at T = 3.0 which is in a homogeneous phase. We instantaneously quench the system down to T = 0.68 ( 0.5Tc), i.e., to a state located inside the coexistence region of the phase diagram. The two components of the system demix, forming A-rich and 1 1
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