Influence of molecular-weight polydispersity on the glass transition of polymers

It is well known that the polymer glass transition temperature $T_g$ is dependent on molecular weight, but the role of molecular-weight polydispersity on $T_g$ is unclear. Using molecular-dynamics simulations, we clarify that for polymers with the same number-average molecular weight, the molecular-weight distribution profile (either in Schulz-Zimm form or in bimodal form) has very little influence on the glass transition temperature $T_g$, the average segment dynamics (monomer motion, bond orientation relaxation, and torsion transition), and the relaxation-time spectrum, which are related to the local nature of the glass transition. By analyzing monomer motions in different chains, we find that the motion distribution of monomers is altered by molecular-weight polydispersity. Molecular-weight polydispersity dramatically enhances the dynamic heterogeneity of monomer diffusive motions after breaking out of the “cage,” but it has a weak influence on the dynamic heterogeneity of the short time scales and the transient spatial correlation between temporarily localized monomers. The stringlike cooperative motion is also not influenced by molecular-weight polydispersity, supporting the idea that stringlike collective motion is not strongly correlated with chain connectivity.

Figure 1

(a) The chain length dependence of $T_g$ for monodisperse polymers with different persistence lengths. (b) The fitting of $T_g\sim 1/N$ to the Fox-Flory equation. For $l_p=1.69$, 1.78, and 1.94, the corresponding $T_{g\infty }$ are 0.45, 0.63, and 0.79, respectively. It is clear that the mass dependence of our bead spring chain model conforms to the Fox-Flory equation, which is in accordance with previous reports [14, 15].

Figure 2

The variation of Schulz-Zimm distribution for systems with $〈N〉=12$. It shows that with increasing PDI, both the number of short chains and the length of the longest chain increase. The total number of polymer chains is 1500.

Figure 3

(a) The bond orientational autocorrelation function, $P_2\left(t\right)$. (b) The probability that a dihedral has not visited all three states $gauch{e}^{+}$, $trans$, and $gauch{e}^{-}$ after a given time $t$, $P_{3\text{state}}\left(t\right)$. The PDI values for SZ distribution are 1.1, 1.3, and 1.9. The PDI values for bimodal distribution are 1.444 and 5.0.

Figure 4

The MSD over all monomers $g_0\left(t\right)$ and the MSD of the mass center of chains $g_3\left(t\right)$ for systems with various PDIs at $T=0.74$. The PDI values for SZ distribution are 1.3 and 1.9. The PDI values for bimodal distribution are 1.444 and 5.0. We have also determined the number-average end-end mean-square distance $R_{\text{ee}}^2$ for systems with various PDIs, and we find that the value, which is about $27{\sigma }^2$, is weakly influenced by polydispersity and temperature. Here, we use a dashed line to label the time when $g_0\left(t\right)$ is comparable to $R_{\text{ee}}^2$, which is about $2.2\times {10}^4{(m{\sigma }^2/\epsilon )}^{0.5}$.

Figure 5

The polydispersity (a) and temperature dependence (b) of the normalized distribution function of the relaxation times $F\left[ln\left(\tau \right)\right]$ for $P_2\left(t\right)$.

Figure 6

(a) A comparison between including and not including $s=1$ in the definition of the average string size and the corresponding polydispersity index of the string size ${\mathrm{PDI}}_S$. (b) The influence of chain length polydispersity on the string size $\langle S_{w2}\rangle$ and ${\mathrm{PDI}}_S$. The PDI values for SZ distribution are 1.3 and 1.9.

Figure 7

The temperature dependence of the string size $\langle S_{w2}\rangle$ and the distribution ${\mathrm{PDI}}_S$ for monodisperse (a) and polydisperse (b) systems.

Figure 8

MSD of different groups in monodisperse (a) and polydisperse (b) systems. The larger number means that the monomers belong to longer chains for polydisperse systems. For clarity, we leave out the data of G2 and G4.

Figure 9

Non-Gaussian parameters for systems with various polydispersity at the same temperature (a) and at different temperatures (b). The PDI values for SZ distribution are 1.1, 1.3, and 1.9. The PDI values for bimodal distribution are 1.444 and 5.0.

Figure 10

The variation of four-point susceptibilities with temperature and PDI. The PDI values for SZ distribution are 1.1, 1.3, and 1.9. The PDI values for bimodal distribution are 1.444 and 5.0.