Correction Cite This: ACS Macro Lett. 2018, 7, 1039−1039
pubs.acs.org/macroletters
Correction to “Consequences of Grafting Density on Linear Viscoelastic Behavior of Graft Polymers” Ingrid N. Haugan, Michael J. Maher, Alice B. Chang, Tzu-Pin Lin, Robert H. Grubbs, Marc A. Hillmyer, and Frank S. Bates* ACS Macro Lett. 2018, 7 (5), 525−530. DOI: 10.1021/acsmacrolett.8b00116 normalized units). Assuming a density of 1.25 g/cm3 and M = 3244 g/mol for the PLA side chains yields nsc = 37 (note that the number of chemical repeat units is 45 and the molar mass of the ω-norbornenyl group has been subtracted from the macromonomer molar mass). In the process of plotting the predicted values of G e /G e,lin according to eq 2, we inadvertently used an erroneous multiplicative factor in computing ng. Thus, the plotted values of Ge/Ge,lin were larger than those actually predicted by eq 2 and the prediction by Daniel et al. was erroneously shifted upward and to the left. A corrected version (with a more commonly accepted number of minor tick marks) of Figure 4 is shown. Our original analysis concluded that the data at high ng were consistent with eq 2, and the highest ng polymers were thus labeled as loose combs (LC). With the correct calculation, the theory actually predicts values of Ge/Ge,lin that are 2−4× lower than what is experimentally observed. Nevertheless, the curvature in Ge/Ge,lin with ng is qualitatively similar to what is predicted by eq 2 for ng > 10, suggesting that the results for z ≤ 0.25 can be characterized as falling within the LC/DC regime. A direct transition from the comb to the dense brush (DB) limit occurs with further reduction at ng < 10 without any evidence of the loose brush (LB) regime, as originally concluded. We reiterate that the relatively low degrees of polymerization (ng, nsc) for the experimental system are likely to compromise quantitative comparison with the mean-field theory (n → ∞).
T ACS Macro Lett. Downloaded from pubs.acs.org by 185.251.70.27 on 08/12/18. For personal use only.
his Addition and Correction corrects an error in Figure 4. This correction does not impact the data analysis or general conclusions associated with this publication.
Figure 4. Normalized plateau modulus Ge/Ge,lin plotted vs inverse grafting density ng. The inset shows the scaling predicted by Daniel et al. for four regimes: dense brush (DB), loose brush (LB), dense comb (DC), and loose comb (LC), where the numbers identify the scaling exponents. This inset emphasizes the scaling of Ge/Ge,lin, and does not predict the range of the regimes. The blue curve shows the predictions of eq 2, which applies to the LC and DC regimes. These results indicate that the graft polymers transition abruptly from the comb to DB regime without evidence of the LB regime.
Figure 4 in the manuscript presents the prediction by Daniel et al. as eq 2,
ji n zy Ge = Ge,linjjjj1 + sc zzzz j ng z (2) k { plotted along with our experimental data. The degrees of polymerization nsc and ng, which are proportional to the side chain (sc) length and spacing between graft (g) chains along the backbone, respectively, were calculated based on a constant reference volume of 118 Å3. Given this, the definition of ng is −3
ng =
2.68 z
(E1)
where 0 ≤ z ≤ 1 is the grafting density (e.g., the spacing between grafts for 100% grafts or z = 1 is 2.68 volume © XXXX American Chemical Society
Received: August 7, 2018 1039
DOI: 10.1021/acsmacrolett.8b00592 ACS Macro Lett. 2018, 7, 1039−1039
