conference papers
Gibbs–Thomson analysis of crystalline poly(9,9-di-n-octyl-2,7-fluorene)
aDepartment of Materials Science and Engineering, National Dong Hwa University, Hualien 974, Taiwan, bInstitute of Materials Science and Engineering, National Sun Yat-sen University, Kaohsiung 804, Taiwan, cNational Synchrotron Radiation Research Center, Hsinchu 300, Taiwan, and dDepartment of Chemical Engineering, National Tsing Hua University, Hsinchu 300, Taiwan
*Correspondence e-mail: acsu@mx.nthu.edu.tw
Based on results of small-angle X-ray scattering and differential scanning calorimetric measurements, the equilibrium melting temperature and basal surface energy (σe) of crystalline poly(9,9-di-n-octyl-2,7-fluorene) (PFO) were preliminarily estimated as ca 451.6 K and 0.084 J m−2, respectively, via Gibbs–Thomson analysis. This σe value leads to a value of 76 kJ mol−1 for the work of fold that greatly exceeds the values for typical polymers, reflecting the semi-rigid nature of the PFO backbone and consistent with the large-loop folds proposed earlier for this particular conjugated-backbone polymer. This is in strong contrast to the commonly held belief that conjugated polymers are generally too rigid to form folded-chain lamellar crystals.
Keywords: equilibrium melting temperature; basal plane surface energy; Gibbs–Thomson analysis; poly(9,9-di-n-octyl-2,7-fluorene).
1. Introduction
Using poly(9,9-di-n-octyl-2,7-fluorene) [PFO, one of the most studied `fruit flies' of semiconducting polymers (Kraft et al., 1998; Friend et al., 1999)] as an example, we showed conclusively in a previous electron microscopy study that, in contrast to common belief, a conjugated polymer may indeed form single crystals of folded-chain lamellae (Chen et al., 2004). We have further argued that, in view of the semi-rigid nature of the PFO backbone, the formation of single crystals is unlikely to follow the adjacent re-entry mode of regime I crystallization in the Hoffman–Lauritzen picture (Hoffman et al., 1976); instead, crystallization of PFO appears to proceed through attachment and coalescence of nanograins (ca 10 to 20 nm in size, much smaller than the contour length of the PFO chains) of collapsed chains to the crystal-growth front. We have therefore conjectured that the folds must be inherently loose and loop-like to avoid excessive penalties from unfavorable conformations in tight folds (Chen et al., 2004). It is therefore of interest to have an estimate of the basal plane surface energy (σe) involved in such a loose-loop case.
By means of differential scanning calorimetric (DSC) and small-angle X-ray scattering (SAXS) measurements, here we show that the melting behavior of PFO is reminiscent of typical semicrystalline polymers. In addition, results of a straightforward Gibbs–Thomson analysis indicate that the equilibrium melting temperature Tmo = 451.6 K and σe = 0.084 J m−2. The latter is only moderately higher than typical values for semicrystalline polymers, which reflects the semi-rigid nature of the PFO backbone on the one hand and, on the other hand, is consistent with the loose-loop (and nonadjacent re-entry) folds proposed earlier for this particular conjugated-backbone polymer.
2. Experimental
The characteristics of the PFO sample have been described previously (Chen et al., 2004). Differential scanning calorimetric (DSC) measurements were made using a TA Q100 instrument routinely calibrated using indium and lead standards at a heating rate of 20 K min−1 and operated under a stream of nitrogen gas. The typical DSC sample size is ca 3 mg.
Small-angle X-ray scattering (SAXS) was used to characterize the crystalline lamellar morphology of PFO. Prior to SAXS characterization, all the samples (discs ca 6 mm in diameter and ca 0.4 mm in thickness) were crystallized at selected temperatures (Tc) in a high-temperature stage (Linkam THMS-600 connected to a TMS-91 temperature controller) under a protective nitrogen atmosphere for different periods of time (tc = 1 to 12 h, after which the crystallization process had practically ended) at temperatures ranging from Tc = 397 to 417 K. Samples were always heated to Tmax = 523 K for 1 min to erase previous thermal histories, followed by jumping to Tc for isothermal crystallization and subsequent quenching into ice water.
SAXS measurements were performed at the BL01B beamline of the National Synchrotron Radiation Research Center (NSRRC). The wavelength of the incident X-ray beam was λ = 0.1181 nm (10.5 keV). With a sample-to-detector distance of 1571.4 mm and a beamstop of 4 mm diameter, we collected SAXS data using a one-dimensional position-sensitive detector (PSD). All the SAXS data were corrected for sample transmission, background, and the detector sensitivity. The modulus of the scattering vector q [= 4πsin(θ/2)/λ], defined by the scattering angle θ and the wavelength λ of the X-rays, was calibrated using silver behenate. More details of the SAXS setup and the instrument calibration may be found in an earlier report (Lai et al., 2005).
To enhance the scattering intensity, a stack of four PFO discs with the same thermal history was used in the SAXS measurement. Further corrections for removing irrelevant scattering characteristics at the low-q and high-q extremes were subsequently made using the Porod law (Roe, 2000; Higgins & Benoit, 1994) and the Debye–Bueche equation (Higgins & Benoit, 1994), as described in detail elsewhere (Liao et al., 2002) , before final presentation as Lorentz-corrected profiles (Higgins & Benoit, 1994; Liao et al., 2002).
3. Results
Given in Fig. 1(a) are representative SAXS profiles of isothermally crystallized PFO specimens after Lorentz correction. Measured scattering intensities are generally weak, as the electron density contrast is only modest. This is reflected in the noise level in Fig. 1(a). As shown in Fig. 1(b), noise was nevertheless smoothed out during construction of the normalized one-dimensional (1D) correlation function (Higgins & Benoit, 1994; Strobl, 1996)
which represents a statistically averaged low-resolution view of the two-phase lamellar structure. Table 1 summarizes the processing conditions and morphological characteristics determined graphically (Strobl, 1996) from γ1(z), including the long period (L), the crystalline lamellar thickness (lc), the amorphous layer thickness (la) and the fractional crystallinity Xc = lc/L.
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Corresponding DSC traces of these PFO specimens are shown in Fig. 2(a). The glass transition is easily identifiable at Tg ≃ 333 K. In the high-temperature range, there exist generally two endotherms: the one marked as TL (which is ca 7 to 14 K above Tc) is attributed to initial melting of crystallites formed at Tc, whereas the high-temperature endotherm at TH near 433 K is attributed to final melting of reorganized crystallites, as it is independent of Tc and is always located at the same position (Chen et al., 2005) in spite of differences in crystallization conditions. To minimize errors arising from the effects of specimen superheating and melting-reorganization of crystallites during the DSC scan, we have operationally identified the melting temperature (Tm) with the onset (Tonset) of the low-temperature endotherm TL. On the basis of the combined area (ΔH) under the endotherms and Xc determined from SAXS profiles, the heat of fusion ΔHf for perfectly crystalline PFO is estimated as 73 (12) J g−1. Values of these relevant parameters are also summarized in Table 1.
In terms of the Gibbs–Thomson model (Wunderlich, 1980), Tm of lamellar crystals depends on the crystalline lamellar thickness and the basal plane surface energy σe according to
where ρ is the crystal density. A linear relationship is therefore expected when plotting Tm against lc-1, such as that given in Fig. 2(b) in the present case of PFO. From the values of the intercept and the slope, we find that Tmo = 451.6 K and σe = 0.084 J m−2 with ΔHf ≃ 73 J g−1 (Table 1) and theoretical density (Chen et al., 2004) of 1.041 g ml−1. In addition, from ΔHf ≃ 73 J g−1 = 29 kJ mol−1 and Tmo = 452 K, one deduces that the entropy of fusion ΔSf = ΔHf/Tmo ≃ 64 J mol−1 K−1.
4. Discussion
4.1. Comparison with σe of other polymers
Reported σe values for a given polymer are often notoriously scattered. Taking polyethylene (PE) as a representative example, σe values ranging from 0.04 to 0.10 J m−2 (i.e., a span of ±40% on the basis of the mean value of 0.07 J m−2) have been reported in the last four decades (Hocquet et al., 2003). Many of the reported σe values were based on Lauritzen–Hoffman analysis of spherulitic growth rates (Hoffman et al., 1976). In view of the large number of fitting parameters required in such an analysis, it is not really surprising that strong discrepancies exist in the σe values obtained for a given polymer by different groups of researchers. In our opinion, reliable values are those determined from the more rigorous Gibbs–Thomson approach. Limiting to the latter case would also facilitate more consistent comparison with present results of Gibbs–Thomson analysis on PFO. On the basis of such a criterion of data selection, one finds that σe = ca 0.06 J m−2 for PE (Hocquet et al., 2003), syndiotactic polypropylene (Supaphol et al., 2000), and poly(L-lactide) (Baratian et al., 2001), ca 0.05 J m−2 for isotactic polypropylene (Yamada et al., 2003), ca 0.03 J m−2 for poly(oxyethylene) (Schoenherr & Frank, 2003), and ca 0.02 J m−2 for the β phase of syndiotactic polystyrene (Wang et al., 2002). It is clear that no consistent trend may be identified with chain rigidity. The present value of σe = 0.084 J m−2 for PFO indeed lies at the high end, but is only slightly higher than that of PE. As the fringed micelle model dictates strongly increased steric repulsion (Sperling, 2001) with lateral crystal size, this only moderately high value of σe implies that the fringed micelle model in its strict sense is unlikely to be applicable to PFO.
4.2. Comparison based on work of fold
For comparison with flexible polymers within the framework of tight folding in the adjacent re-entry model, a more meaningful parameter for comparison purposes would be the work of fold g instead of σe. Values of g typically lie within in the range 10 to 40 kJ mol−1, increasing qualitatively with backbone rigidity from flexible polymers such as PE and polyethers to more rigid chains such as isotactic polystyrene and poly(p-phenylene sulfide) (Hoffman et al., 1976). For the present case of PFO, we have g = 76 kJ mol−1 as calculated from the unit-cell dimensions a = 25.6 and b = 23.4 Å (Chen et al., 2004). This value is way beyond the usual range of g values and certainly reflects the rigidity of PFO backbone. The issue, then, is whether this corresponds to large loops of folds as we proposed.
4.3. Folding of PFO chains
The polyfluorene backbone is not collinear, forming an angle of 160° between successive monomer units (Grell et al., 1999). The shortest possible fold would then correspond to nine monomers (each 0.83 nm in length), spanning 5 nm across the basal plane. This corresponds to an average of 8.4 kJ mol−1 for a monomer in the loop for torsional displacements from the equilibrium chain conformation, which is a mild increase in energy and entirely possible to achieve as indicated by preliminary results of our molecular mechanics calculations.
To achieve efficient packing at the fold surface, however, these large loops must orient themselves in a particular direction to avoid steric conflicts. It is then gratifying to note that our morphological observations (Chen et al., 2007) indeed show long {100} and short {110} facets (i.e., sword-like) in micrometre-sized single crystals of PFO, reminiscent of growth habits of orthorhombic PE. Drawing an analogy to the case of PE, where chains are known to fold along the {110} plane, one is tempted to speculate that the fold plane in the case of PFO might also be {110}. In addition, these folds must have a pair of chains folding together to avoid steric conflicts for the eight-chain unit-cell structure (Chen et al., 2004). The pairing (or embracing) action has been noted previously (Chen et al., 2004). This type of paired folding would require a span of ca 1.74 nm to match the unit-cell dimensions, which is much shorter than that of the tight nine-monomer fold discussed above. It follows that more monomers are required to constitute such fold structure. Assuming a loop shape like the silhouette of an old-fashioned electric light bulb, we estimated that 21 monomers are needed. This brings the increase in torsional energy per monomer down further to ca 3.6 kJ mol−1. As neighboring pairs along the {110} plane fold in opposite basal planes, the large bulb head, ca 5 nm in diameter, does not seem serious: allowing a slight distribution of loop heights would easily alleviate steric repulsion. Such a fold structure would corresponds to an amorphous region ca 7 nm in thickness and hence predicts a minimum value of la as ca 14 nm, consistent with our SAXS results in Table 1. The model is certainly only speculative at the present stage and awaits further confirmations.
The discussion above corresponds to the ideal limit of perfect folding. As in many polymer crystals grown from melt under large supercoolings, the random-switchboard model is likely to serve as a more realistic representation (Sperling, 2001). This means a thick amorphous layer on top of the fold plane, in agreement with the range of 15 to 22 nm observed here. Like general cases described by the random-switchboard model, one would also expect a high density of defects (Sperling, 2001) in PFO crystals; this is particularly likely in view of stronger steric complications resulting from the unusually large loop size of PFO folds. The short lifetime (several seconds, an order of magnitude lower than typical melt-grown polymer crystals) of diffraction patterns for polyfluorene crystals under an electron beam (Chen et al., 2005, 2006) is therefore a natural consequence.
Acknowledgements
We gratefully acknowledge financial support from the Ministry of Education (Program for Promoting Academic Excellence of Universities, grant No. 91E-FA04-2-4A) and the National Science Council (grant No. NSC92-2216-E-110-009).
References
Baratian, S., Hall, E. S., Lin, J. S., Xu, R. & Runt, J. (2001). Macromolecules, 34, 4857–4864. CrossRef CAS
Chen, S. H., Chou, H. L., Su, A. C. & Chen, S. A. (2004). Macromolecules, 37, 6833–6838. Web of Science CrossRef CAS
Chen, S. H., Su, A. C. & Chen, S. A. (2005). J. Phys. Chem. B, 109, 10067–10072. Web of Science CrossRef PubMed CAS
Chen, S. H., Su, A. C. & Chen, S. A. (2007). Macromolecules. In the press.
Chen, S. H., Su, A. C., Su, C. H. & Chen, S. A. (2006). J. Phys. Chem. B, 110, 4007–4013. Web of Science CrossRef PubMed CAS
Friend, R. H., Gymer, R. W., Holmes, A. B., Burroughes, J. H., Marks, R. N., Taliani, C., Bradley, D. D. C., dos Santos, D. A., Gredas, J. L., Loglund, M. & Salaneck, W. R. (1999). Nature (London), 397, 121–128. CrossRef CAS
Grell, M., Bradley, D. D. C., Ungar, G., Hill, J. & Whitehead, K. S. (1999). Macromolecules, 32, 5810–5817. Web of Science CrossRef CAS
Higgins, J. S. & Benoit, H.C. (1994). Polymers and Neutron Scattering. New York: Oxford University Press.
Hocquet, S., Dosiere, M., Thierry, A., Lotz, B., Koch, M. H. J., Dubreuil, N. & Ivanov, D. A. (2003). Macromolecules, 36, 8376–8384. CrossRef CAS
Hoffman, J. D., Davis, G. T. & Lauritzen, J. I. (1976). Treatise in Solid State Chemistry, edited by N. B. Hannay. New York: Plenum.
Kraft, A., Grimsdale, A. C. & Holmes, A. B. (1998). Angew. Chem. Int. Ed. Engl. 37, 402–428. CrossRef
Lai, Y. H., Sun, Y. S., Jeng, U., Song, Y. F., Tsang, K. L. & Liang, K. S. (2005). Nucl. Instrum. Methods Phys. Res. B, 238, 205–213. Web of Science CrossRef CAS
Liao, W. P., Lin, T. L., Woo, E. M. & Wang, C. (2002). J. Polym. Res. 9, 91–96. Web of Science CrossRef CAS
Roe, R. J. (2000). Methods of X-ray and Neutron Scattering in Polymer Science. Oxford University Press.
Schoenherr, H. & Frank, C. W. (2003). Macromolecules, 36, 1199–1208. Web of Science CrossRef CAS
Sperling, L. H. (2001). Introduction to Physical Polymer Science, 3rd ed., ch. 6. New York: Wiley.
Strobl, G. (1996). The Physics of Polymers. Berlin: Springer.
Supaphol, P., Spruiell, J. E. & Lin, J. S. (2000). Polym. Int. 49, 1473–1482. Web of Science CrossRef CAS
Wang, C., Cheng, Y. W., Hsu, Y. C. & Lin, T. L. (2002). J. Polym. Sci. Polym. Phys. 40, 1626–1636. Web of Science CrossRef CAS
Wunderlich, B. (1980). Macromolecular Physics, Vol. 3, ch. 8. New York: Academic Press.
Yamada, K., Hikosaka, M., Toda, A., Yamazaki, S. & Tagashira, K. (2003). J. Macromol. Sci. B42, 733–752. CrossRef CAS
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