Do Deviations from Reptation Scaling of Entangled Polymer Melts Result from Single- or Many-Chain Effects?

By studying the relaxation of small amounts of short entangled “probe” chains in a high molecular weight matrix, we show that the deviations from reptation scaling of the longest relaxation time are not as much dominated by single-chain effects (usually referred to as contour length fluctuations or CLF) as assumed by current mesoscopic models but also originate to a very significant extent from mutual chain relaxation effects. This result is in fact consistent with literature data on tracer and self-diffusion. Moreover, tube theories also overpredict the influence of CLF on the plateau modulus. Improved theories, simulations, and careful experiments are urgently needed to resolve this important question.

Figure 1

Experimental (points) and predicted (thin lines) [10] retardation factors for the longest relaxation time as a function of the entanglement number $Z$. Experimental data should mainly be compared with $R_{\mathrm{peak}}$. Refer to 10 for the definitions of $R_{\mathrm{cross}}$ and $R_{\mathrm{term}}$. Horizontal dashed line: constant retardation factor of about 2.5 predicted by the dynamic tube dilution model [16] for the well-entangled case. Thick solid line: $-0.3$ slope.

Figure 2

Longest relaxation time ${\tau }_d$ for the probe chains in two entangled environments, plotted as ${\tau }_d/Z^3$ vs $Z$ to highlight deviations from the reptation scaling. The PI (circles) and PS (triangles) data were superimposed on the PBD (squares) data by a vertical shift. The thin line represents the prediction by the Likhtman-McLeish (LM) theory [10] in the absence of CR.

Figure 3

Self-chain and tracer diffusion coefficients $D_s$ and $D_{tr}$ [26, 27, 28, 29, 30, 32] plotted as ($D_s$ or $D_{tr}$) $M^{2.0}$ vs $Z$ to highlight deviations from the reptation scaling. The dashed line is the $-0.35$ slope considered by Lodge [6].

Figure 4

$G_{\mathrm{app}}^0$ vs $Z$ or $M$: $G_{\mathrm{app}}^0$ normalized by $G_N^0=1.15\mathrm{MPa}$. Data obtained from 20 and references in 12. Solid and dashed lines represent the normalized predicted $G_{\min }^{\prime }$ by the Likhtman-McLeish model [10] with and without CR.