Comment pubs.acs.org/Macromolecules
Reply to “Comment on ‘Determination of Nucleus Density in Semicrystalline Polymers from Nonisothermal Crystallization Curves’” Alfréd Menyhárd,*,†,‡ Márton Bredács,‡ Gergely Simon,‡ and Zsuzsanna Horváth†,‡ †
Laboratory of Plastics and Rubber Technology, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, Mű egyetem rakpart 3. H/1, H-1111 Budapest, Hungary ‡ Institute of Materials Science and Environmental Chemistry, Research Center for Natural Sciences, Hungarian Academy of Sciences, Magyar tudósok körútja 2, H-1117 Budapest, Hungary
Macromolecules 2015, 48, 2561−2569. DOI: 10.1021/acs.macromol.5b00275
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he authors of the article1 appreciate the valuable comments on their work, which indicates that the estimation of nucleus density is an important issue and should be investigated in spite of the fact that the kinetics of crystallization has been studied for a long time and numerous models exist in this field. The author of the Comment2 pointed out that N is incorrectly defined as the “number of nuclei” because it “is in fact a number density of nuclei”, a term that has been used in several publications already. However, in our article this quantity is correctly defined as the number of nuclei indeed. On the basis of the basic equations of crystallization, we described in our original article the evolution of crystalline volume in the following form (eq 13 in the original article): 4 ΔVcr = N π (GT ti)3 3
basic kinetic equations of crystallization. However, in our approach, the nature of nucleation is not necessary to be proven before the prediction of the number of nuclei. Prof. Martins also claimed that the way we handled the impingements during crystallization is questionable, and we agree with this statement. However, we purposely pointed out that the solution used in our paper is one possible correction function, but the correction of impingements can be handled in other ways as well. Our approach can be modified and improved in this point indeed. In conclusion, our goal was to develop an approach for the calculation of nucleus density, which is simple and easy to use, and offer a viable solution for researchers in this area even if it contains some simplifications and can be improved further in the future.
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(1)
*E-mail
[email protected] (A.M.).
According to eq 1, if N nuclei are growing with the growth rate of GT for the time increment ti, ΔVcr corresponds to the crystalline volume formed within ti. Prof. Martins pointed out that that our equation provides a number instead of a density, and he is right. We have to note here, however, that in eq 21 the meaning of N is the overall number of nuclei formed in one cubic meter during crystallization (since all the calculations were related to one cubic meter); thus, for simplicity’s sake we called the resulting quantity as “nucleus density” in the end. Moreover, we clearly distinguished N and Nt, the overall number of nuclei and number of nuclei formed within a short time increment (or temperature increment at constant cooling rate), respectively. Our original idea was to relate eq 1 directly to the crystallization trace recorded experimentally in a DSC measurement under dynamic conditions. The presented equation relates the crystalline volume developed within a short incremental time to the predicted amount of crystalline volume grown on existing nuclei. In reality, the formation of crystalline volume recorded experimentally can exceed the one calculated from the growth of existing nuclei, and in this case the approach predicts the formation of new nuclei. If the evolution of the crystalline phase matches the growth of existing nuclei, according to our approach new nuclei do not form, which corresponds to the simple case of instantaneous nucleation. In existing models, the case of instantaneous nucleation must or at least supposed or to be proven in order to be able to use the © XXXX American Chemical Society
AUTHOR INFORMATION
Corresponding Author Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Menyhárd, A.; Bredács, M.; Simon, G.; Horváth, Z. Macromolecules 2015, 48, 2561−2569. (2) Martins, J. A. Macromolecules 2015, DOI: 10.1021/acs.macromol.5b01618.
Received: September 22, 2015 Accepted: September 29, 2015
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DOI: 10.1021/acs.macromol.5b02051 Macromolecules XXXX, XXX, XXX−XXX
