Reptational dynamics in dissipative particle dynamics simulations of polymer melts

Understanding the fundamental properties of polymeric liquids remains a challenge in materials science and soft matter physics. Here, we present a simple and computationally efficient criterion for topological constraints, i.e., uncrossability of chains, in polymeric liquids using the dissipative particle dynamics (DPD) method. No new length scales or forces are added. To demonstrate that this approach really prevents chain crossings, we study a melt of linear homopolymers. We show that for short chains the model correctly reproduces Rouse-like dynamics whereas for longer chains the dynamics becomes reptational as the chain length is increased—something that is not attainable using standard DPD or other coarse-grained soft potential methods.

Figure 1

Two bonds crossing each other. If Eq. (5) is satisfied, crossings cannot occur.

Figure 2

The snapshots present ten superpositions of configurations for a chain of length $N=256$ taken at times 100 apart. Gray: times up to 500 (in DPD time units); black: times from 500 to 1000. (a) Rouse dynamics ($a=25$, $k=50$) and (b) reptation ($a=100$, $k=200$).

Figure 3

(a) Radial distribution function in the case of $N=256$. The arrow shows the distance $r_{\min }$, and the inset shows the region at lengths shorter than $r_{\min }$. As seen in the figure, the condition is well fulfilled for the largest $a$. As the parameter $a$ becomes smaller, the deviations grow. (b) Bond-length distribution $(N=256)$. The inset shows the region at values larger than ${\ell }_{\max }$. The arrows show a set of $r_{\min }$ and ${\ell }_{\max }$ values that satisfy Eq. (5) in the case $a=200$.

Figure 4

(a) The radius of gyration as a function of chain length for different parameters. (b) The end-to-end vector autocorrelation ($a=100$, $k=200$) for chains of different length.

Figure 5

(a) Scaling of the longest relaxation time $\tau$. There is a crossover from Rouse scaling $(\tau \propto N^2)$ to reptation $(\tau \propto N^3)$. (b) Similarly, the proper scaling limits are reached for the diffusion coefficient $D$.