Reply to the Letter to the Editor
1
Reply: Professor Han has three criticisms of our article: our viscosity equation has no rheo- logical significance, our assumption of w =0 is unjustified, and we failed to reference his 1991 article. We agree that our viscosity equation is em- pirical. Viscosity does not enter into the model except as a measure of mixing of the two diffusing polymers. As stated on page 982 of our article we actually ‘‘used the ex- perimental data as a master curve, and a third-order spline interpolation method to find the viscosity of the blends at any concen- tration.’’ We disagree that w , 0 is required for mis- cibility of two polymers. From Flory–Hug- gins theory with chains of equal length N, the criterion for miscibility is wN = 2. However, even if w for HDPE/LLDPE blends were slightly negative this would not change the conclusion of our article, namely that a sin- gle, concentration dependent-diffusion coeffi- cient can model their mutual diffusion. On the last point we did review the Kim and Han 1991 article in an early stage of this study. We could have included it for completeness on the subject of mutual dif- fusion in polymers. However, we do not find that the subject of this article is directly related to our study, and nor would its results alter the discussion or conclu- sions of our article. In Kim and Han, the effect of processing conditions on the inter- facial layer thickness between two miscible polymer layers is considered. They solve unsteady state mutual diffusion into a semi-infinite space. In our article, we solve quasi-static, mutual diffusion between two miscible polymers using 32 coextruded layers. Our diffusion problem is an unsteady-state finite boundary problem, i.e. mutual diffusion in the 32 layers bounded by two solid walls. Therefore, we do not think our article simply ‘‘reinvents the wheel’’. With increasing number of research groups using multilayer structures to study mutual diffusion, we believe (along with the reviewers of the AIChE Journal) that our methodology is a valua- ble contribution. Rui Zhao ExxonMobil Chemical Company, BTEC-West, Specialty Elastomers Technology Baytown, TX 77520 E-mail: [email protected] Chris Macosko Professor of Chemical Engineering and Materials Science and Director of I PRIME, The Industrial Partnership for Research in Interfacial and Materials Engineering, University of Minnesota, 421 Washington Av. Minneapolis MN 55455 E-mail: [email protected] AIChE Journal, Vol. 53, 3019 (2007) Ó 2007 American Institute of Chemical Engineers DOI 10.1002/aic.11284 Published online September 17, 2007 in Wiley InterScience (www.interscience.wiley.com). AIChE Journal November 2007 Vol. 53, No. 11 Published on behalf of the AIChE DOI 10.1002/aic 3019
Transcript of Reply to the Letter to the Editor
Reply:
Professor Han has three criticisms of ourarticle: our viscosity equation has no rheo-logical significance, our assumption of w = 0is unjustified, and we failed to reference his1991 article.
We agree that our viscosity equation is em-pirical. Viscosity does not enter into themodel except as a measure of mixing of thetwo diffusing polymers. As stated on page982 of our article we actually ‘‘used the ex-perimental data as a master curve, and athird-order spline interpolation method tofind the viscosity of the blends at any concen-tration.’’
We disagree that w, 0 is required for mis-cibility of two polymers. From Flory–Hug-gins theory with chains of equal length N, thecriterion for miscibility is wN = 2. However,
even if w for HDPE/LLDPE blends wereslightly negative this would not change theconclusion of our article, namely that a sin-gle, concentration dependent-diffusion coeffi-cient can model their mutual diffusion.On the last point we did review the Kim
and Han 1991 article in an early stage ofthis study. We could have included it forcompleteness on the subject of mutual dif-fusion in polymers. However, we do notfind that the subject of this article isdirectly related to our study, and nor wouldits results alter the discussion or conclu-sions of our article. In Kim and Han, theeffect of processing conditions on the inter-facial layer thickness between two misciblepolymer layers is considered. They solveunsteady state mutual diffusion into asemi-infinite space. In our article, we solvequasi-static, mutual diffusion between twomiscible polymers using 32 coextrudedlayers. Our diffusion problem is anunsteady-state finite boundary problem, i.e.mutual diffusion in the 32 layers boundedby two solid walls. Therefore, we do not
think our article simply ‘‘reinvents thewheel’’. With increasing number ofresearch groups using multilayer structuresto study mutual diffusion, we believe(along with the reviewers of the AIChEJournal) that our methodology is a valua-ble contribution.
Rui Zhao
ExxonMobil Chemical Company,
BTEC-West,
Specialty Elastomers Technology
Baytown, TX 77520
E-mail: [email protected]
Chris Macosko
Professor of Chemical Engineering
and Materials Science and Director
of I PRIME, The Industrial Partnership for
Research in Interfacial and Materials
Engineering, University of Minnesota,
421 Washington Av.
Minneapolis MN 55455
E-mail: [email protected]
AIChE Journal, Vol. 53, 3019 (2007)� 2007 American Institute of Chemical EngineersDOI 10.1002/aic.11284Published online September 17, 2007 in WileyInterScience (www.interscience.wiley.com).
AIChE Journal November 2007 Vol. 53, No. 11 Published on behalf of the AIChE DOI 10.1002/aic 3019
