Abstract.
The thermal behavior of semirigid semicrystalline polymers differs significantly from that of flexible-chain polymers. The origin of the differences is believed to lie in the higher energy expenditure associated with the formation of adjacent re-entry folds at the crystalline surface in the case of semirigid chains. The effect of constraints imposed by the interlamellar amorphous regions on the neighboring crystals was studied with temperature-resolved synchrotron radiation small-angle X-ray scattering (SAXS). The analysis of SAXS patterns with a generalized paracrystalline lamellar stack model indicates that melting of a semirigid-chain polymer is not a random process but that the crystals grown in the smallest amorphous gaps melt first. This suggests that the hitherto largely neglected geometrical confinement effects may play an important role in determining the thermodynamic stability of semirigid-chain polymer crystals.
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References
D.A. Ivanov, A.M. Jonas, Macromolecules 31, 4546 (1998).
D.A. Ivanov, A.M. Jonas, R. Legras, Polymer 41, 3719 (2000).
C. Basire, D.A. Ivanov, Phys. Rev. Lett. 85, 5587 (2000).
D.A. Ivanov, Z. Amalou, S.N. Magonov, Macromolecules 34, 8944 (2001).
M. Pyda, A. Boller, J. Grebowicz, H. Chuah, B.V. Lebedev, B.J. Wunderlich, J. Polym. Sci. Part B 36, 2499 (1998).
J. Yang, G. Sidoti, J. Liu, P.H. Geil, C.Y. Li, S.Z.D. Cheng, Polymer 42, 7181 (2001).
W.T. Chung, W.J. Yeh, P.D. Hong, J. Appl. Polym. Sci. 83, 2426 (2002).
B.J. Wang, C.Y. Li, J. Hanzlicek, S.Z.D. Cheng, P.H. Geil, J. Grebowicz, Polymer 42, 7171 (2001).
J. Wu, J.M. Schultz, J.M. Samon, A.B. Pangelinan, H.H. Chuah, Polymer 42, 7141 (2001).
J.M. Samon, A.B. Pangelinan, H.H. Chuah, Polymer 42, 7161 (2001).
S.Z.D. Cheng, M.Y. Cao, B. Wunderlich, Macromolecules 19, 1868 (1986).
D.A. Ivanov, R. Legras, A.M. Jonas, Macromolecules 32, 1582 (1999).
G. Vigier, J. Tatibouet, A. Benatmane, R. Vassoille, Colloid Polym. Sci. 270, 1182 (1992).
W. Ruland, Colloid Polym. Sci. 255, 417 (1977).
M. Strobl, G.R. Schneider, J. Polym. Sci. 18, 1343(1980).
S.B.R. Hosemann, Direct Analysis of Diffraction by Matter, North-Holland, (1962).
D.A. Ivanov et al. , unpublished.
M.H.J. Koch, J.Bordas, Nucl. Instrum. Methods 208, 435 (1983).
C.J. Boulin, R. Kempf, A. Gabriel, M.H.J. Koch, Nucl. Instrum. Methods A 269, 312 (1988).
G. Rapp, A. Gabriel, M. Dosiére, M.H.J. Koch, Nucl. Instrum. Methods A 357, 178 (1983).
D. Svergun, M.H.J. Koch, unpublished.
A.J.C. Wilson, E. Prince, International Tables for Crystallography, C, Kluwer Academic Publishers, Dordrecht (1999).
J.T. Koberstein, B. Morra, R.S. Stein, J. Appl. Cryst. 13, 34 (1980).
Some technical problems related to implementation of the correlation function analysis are critically reviewed in B. Goderis, H. Reynaers, M.H.J. Koch, V.B.F. Mathot, J. Polym. Sci. Part B 37, 1715 (1999).
F.J. Balta-Calleja, C.G. Vonk, X-ray Scattering of Synthetic Polymers, Elsevier, Amsterdam, (1989).
The existence of such amorphous regions perturbed by the nearby crystalline surfaces was recently demonstrated for a binary blend of similar semirigid-chain aromatic polyester with TEM using selective staining: D.A. Ivanov, T. Pop, D. Yoon, A. Jonas, Macromolecules 35, 9813 (2002).
W.H. Press et al. , Numerical Recipes in C, The Art of Scientific Computing, Plenum Press, New York (1988).
The code used for fitting SAXS curves with the generalized Hosemann model is available from D.A.I. on request.
M. Al-Hussein, G. Strobl, Eur. Phys. J. 6, 305 (2001).
G.R. Strobl, M.J. Schneider, I.G. Voigt-Martin, J. Polym. Sci. Polym. Phys. Ed. 18, 1361 (1980).
The presence of negative parts of the interface distribution function near the origin testifies that the curves were probably undercorrected for the density transition layers.
The second maximum in the interface distribution function corresponding to frame 274 is a barely visible shoulder.
B.J. Crist, J. Polym. Sci. Polym. Phys. Ed. 39, 2454 (2001).
It is important to note that the degree of transformation by number, t, can behave differently from the linear crystallinity, \(\varphi_{c, \rm lin}\equiv\frac{L_c}{L_B}\), or bulk crystallinity by volume if crystal reorganization occurs on heating, i.e. if L c varies with temperature. In terms of the classical approach, the parameter t is equivalent to the surface-to-volume ratio, which could be obtained from Porod’s fits.
For large N used in the computations, the following inequality holds: \(I_{B} \gg I_{c}\), i.e. the total intensity is approximately proportional to the product AN (cf. Eqs. ([5], [A.8])). The decrease of A on heating does not signify that there is melting of entire stacks each containing N crystals. Rather, it means that the stack boundaries in this case are not invariant with temperature. Thus, in this model the fact that the stack height increases due to the evolution of h a (l) implies that grouping of crystals in stacks of N can be considered as purerly formal. As one of the reviewers noted, such image of the melting proccess is not conceptually trivial. In fact, the same result will be obtained if one would fix the stack height and vary N accordingly. The latter approach is, however, more difficult to realize practically.
Since for an infinite stack model the number of lamellae equals that of interlamellar amorphous layers, i.e. (1−t), one can quantify the evolution of amorphous regions by analyzing the functions \(\Delta h_{a,T}\). In this case, the integral \(\int\limits_{l_1 \;}^{ \l_2 \;}\Delta h_{a,T}(l) \mathrm{d}l \equiv \int\limits_{l_1 \;}^{ \l_2 \;}\left ((1-t) h_{a,T}(l)-h_{a,T_{\rm c}}(l) \right ) \mathrm{d} l\) gives the number fraction of amorphous regions ranging from l 1 to l 2 which disappears (if negative) or appears (if positive) by transformation t(T), where t(T) is defined with respect to the initial state, i.e. \(t(T_{\rm c}) = 0\).
Each isolated melting crystal evidently eliminates two adjacent amorphous regions.
R.K. Verma, B.S. Hsiao, Trends Polym. Sci. 4, 312 (1996).
ATHAS Databank available online: http://web.utk.edu/ athas/databank/phenylen/ptt/ptt.html.
J.-M. Huang, F.C. Chang, J. Polym. Sci. Part B 38, 934 (2000).
I.M. Ward, Mechanical Properties of Solid Polymers, Wiley Interscience, London(1971).
J. Brandrup, E.H. Immergut, Polymer Handbook, John Wiley & Sons, New York, (1989), third edition.
It should be noted that the compressibility does not appear to be a very material-sensitive parameter and reveals only a small variation when switching from rubbery to glassy polymers.
In this derivation the electron density of the stack surroundings, \(\rho_{\rm surroundings}\), was put to zero. Generally, a constant infinite background can always be safely subtracted from the model, since it generates the delta-function located at the origin, which cannot be detected experimentally. This substraction, obviously, does not affect the intra-stack electron density contrast.
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Received: 5 March 2004, Published online: 4 May 2004
PACS:
61.41. + e Polymers, elastomers, and plastics - 64.70.Dv Solid-liquid transitions - 81.10.Aj Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation
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Ivanov, D.A., Hocquet, S., Dosiére, M. et al. Exploring the melting of a semirigid-chain polymer with temperature-resolved small-angle X-ray scattering. Eur. Phys. J. E 13, 363–378 (2004). https://doi.org/10.1140/epje/i2003-10082-x
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DOI: https://doi.org/10.1140/epje/i2003-10082-x