J. Phys. Chem. B 2008, 112, 1065-1070
1065
ARTICLES Influence of a Crown Ether Comonomer on the Temperature-Induced Phase Transition of Poly(N-isopropylacrylamide) Hydrogels Katalin Kosik,† Erzse´ bet Wilk,† Erik Geissler,‡ and Krisztina La´ szlo´ *,† Department of Physical Chemistry and Materials Science, Budapest UniVersity of Technology and Economics, Budapest 1521, Hungary, and Laboratoire de Spectrome´ trie Physique CNRS UMR5588, UniVersite´ J. Fourier de Grenoble, B.P. 87, 38402 St Martin d’He` res cedex, France ReceiVed: July 5, 2007; In Final Form: October 25, 2007
Copolymerization of thermosensitive hydrogels based on poly(N-isopropylacrylamide) (PNIPA) is a possible route to enhanced storage capacity of guest molecules. This article describes the synthesis of the amphiphilic crown ether N9-propenoyl-3,6,12,15-tetraoxa-9,21-diazabicyclo[15.3.1]heneicosa-1(21),17,19-triene (CE) and its incorporation into a PNIPA hydrogel (PNIPA/CE). Mechanical measurements on the gel show that the CE units contribute to the elasticity of the network, but the swelling ratio in water is reduced compared to the unmodified system. The comonomer reduces the temperature of the volume phase transition (VPT), TVPT, and broadens the transition. Both the enthalpy and the entropy associated with the VPT decrease. Scattering measurements indicate that the local structural features on the scale of 10 Å are unchanged, but the CE units form large clusters, the size of which increases with rising temperature. In the phase-separated state above TVPT these clusters are distributed on the polymer-water interface.
Introduction Responsive soft materials have become the focus of intense research activity as their potential in biomedical and environmental applications is increasingly appreciated. Their operating principle relies on materials whose volume changes abruptly, i.e., that display a volume phase transition (VPT), under an appropriate stimulus. Hydrogels based on N-isopropylacrylamide (NIPA) are widely used for this purpose. The VPT of polyNIPA (PNIPA) in pure water occurs at a temperature TVPT (≈34 °C) that is convenient for many applications. Despite the abundant literature on PNIPA, however, the mechanism of the transition at a local scale and the thermodynamic parameters governing the phenomenon remain incompletely understood. Knowledge of the material properties in the vicinity of the VPT is essential for any application working in this temperature range. Numerous studies conducted over the past 15 years on temperature-sensitive PNIPA copolymer hydrogels have confirmedthatthethermosensitivitycanbemodifiedbycomonomers.1-8 Inclusion of comonomers modifies the delicate hydrophilichydrophobic balance of the network chains. A rough measure of this effect can be found in the polar surface area (PSA) of the monomers, a procedure that estimates the hydrophilic character of a given molecule by summing the (tabulated) effective surface area of each polar fragment belonging to it.9 By comparing the molar value of the PSA of the comonomer with that of NIPA the influence of the comonomer on the properties of the gel can be estimated. In the scheme of Ertl et * Corresponding author: e-mail
[email protected], tel +36-1-4631893, fax +36-1-463-3767. † Budapest University of Technology and Economics. ‡ Universite ´ J. Fourier de Grenoble.
al.,9 the value of the PSA of the NIPA monomer is found to be 29 Å2, which, with a molar mass M ) 113, corresponds to 1545 m2 mol-1. Specifically chosen comonomers can also serve to enhance the response of the gel toward foreign molecules present in the solvent. Potential applications for such systems range from drug delivery vectors to sensors or actuators responding to pollutants in waste or drinking water. Even with hydrophobic comonomers, however, TVPT does not descend below 30 °C.5 Recently, it was reported that poly(ethylene oxide) (PEO)-PNIPA copolymer hydrogels exhibit a first-order phase transition in the temperature range 35-40 °C; i.e., PEO slightly increases the hydrophilic behavior of PNIPA.6 An even more marked increase in TVPT was found with the weakly charged electrolyte comonomer, acrylic acid.7 These examples suggest that the hydrophilichydrophobic balance of PNIPA can be preserved by a suitable choice of amphiphilic comonomer. Crown ethers (CE) decorated with aromatic groups are good candidates since they contain several ethoxy units, the polar nature of which compensates for the hydrophobicity of the aromatic groups. Benzo-CE copolymerized with NIPA has been shown to display a TVPT that increases when specific ions are present in the diluent; i.e., the CE exhibits ion selectivity.10,11 In addition to their response to small ions, the aromatic component of CEs enhances affinity for aromatic molecules. Macroscopic hydrogels composed of poly(NIPA-co-40-allyldibenzo-18-crown-6) have recently been prepared, albeit in a mixed solvent (H2O/THF). Owing to the steric hindrance of the large ring structure (M ) 400), however, the molar ratio of crown ether to NIPA in this system did not exceed 2.5%.8 It is
10.1021/jp075227w CCC: $40.75 © 2008 American Chemical Society Published on Web 01/09/2008
1066 J. Phys. Chem. B, Vol. 112, No. 4, 2008 SCHEME 1: Formula of N9-Propenoil-3,6,12,15-tetraoxa-9,21-diazabicyclo[15.3.1]heneicosa-1(21),17,19-triene (CE)
notable that the polar surface area of this crown ether, 55 Å2, i.e., 828 m2 mol-1, is appreciably smaller than that of NIPA. The present paper reports the synthesis of a new crown ether, N9-propenoyl-3,6,12,15-tetraoxa-9,21-diazabicyclo[15.3.1]heneicosa-1(21),17,19-triene (C18O5N2H26) (CE, see Scheme 1). This molecule, of molar mass 350, was used to prepare a random copolymer with NIPA, together with N,N′-methylenebis(acrylamide) (BA) as a cross-linker. Owing to its single aromatic ring and increased number of heteroatoms (two nitrogens and one oxygen atom), the hydrophilic character of the CE comonomer is enhanced. Its polar surface area, 70 Å2 (1200 m2 mol-1), is thus significantly closer to NIPA than the comonomer in ref 8. The present paper investigates the macroscopic and microscopic properties of the resulting copolymer hydrogel by means of swelling measurements in water, differential scanning calorimetry (DSC), and small-angle neutron and X-ray scattering (SANS and SAXS). The aim of this article is to describe the underlying structure of the CE-PNIPA copolymer hydrogel. Modifications to the structure in response to its interaction with aromatic molecules are the subject of ongoing research. Experimental Section Synthesis. N9-Propenoyl-3,6,12,15-tetraoxa-9,21-diazabicyclo[15.3.1]heneicosa-1(21),17,19-triene (CE) was prepared as follows. To a solution of 3,6,12,15-tetraoxa-9,21-diazabicyclo[15.3.1]heneicosa-1(21),17,19-triene12 (4.1 g, containing 0.5 g of mineral oil, i.e., 12.1 mmol) in dry tetrahydrofuran (THF) (36 mL) was added triethylamine (1.8 mL, i.e., 13 mmol), and then, with ice cooling, freshly distilled acryloyl chloride (1.2 mL, i.e., 14 mmol) was added and the mixture stirred for 24 h. Triethylamine hydrochloride was filtered off and washed with a small amount of THF. After neutralizing the excess acid chloride with methanol, the solution was evaporated, and the residue was chromatographed on silica gel (150 g) with toluene-ethanol 9:2 as eluent. Yield: 3.1 g (73%) of a viscous oil that crystallized on standing; mp 70 °C. Its density at 25 °C was measured by pycnometry to be 1.24 g cm-3. 1H NMR (CDCl ): δ ) 3.31 (m, 2 H), and 3.45 (m, 2 H), 3 (8,10-CH2), 3.58 (m, 4 H,), and 3.51 (m, 4 H) (4,5,7,11,13,14CH2),. 3.72 (m, 4 H), 4.63 (s, 4 H. 2,16-CH2), 5.66 (dd, J ) 10.5 and 1.8 Hz, 1 H, 3′-Htrans), 6.18 (dd, J ) 16.5, 1.8 Hz, 1
Kosik et al. H, 2′-H), 6.66 (dd, J ) 16.5, 10.5 Hz, 1 H, H-3′cis), 7.38 (dd, J ) 7.8 and 3.5 Hz, 2 H, 18,20-H), 7.81 (t, J ) 7.8 Hz, 1 H, 19-H). 13C NMR (CDCl ): δ ) 70.26, 71.03, 71.35, 71.53, 72.15, 3 72.19, 75.03, 75.10, 123.23, 129.4, 159.29, 159.42, 130.08, 138.94. PNIPA/CE random copolymer gels were synthesized by dissolving CE and BA in a 0.74 M NIPA solution. After bubbling with nitrogen, N,N,N′,N′-tetramethylethylenediamine (TEMED) and ammonium persulfate (APS) were added to the mixture. Polymerization at 20 °C yielded gels with molar ratio ([NIPA] + [CE])/[BA] ) 158. Gel films of thickness 2 mm were prepared and then dialyzed in water to remove unreacted chemicals. The films were cut into disks of diameter 7 mm, dried, and stored above concentrated sulfuric acid. For the SANS measurements, gel disks of diameter 16 mm and thickness 1 mm were prepared. Measurement of the UV transmission in the vicinity of the CE absorption peak at 261 nm indicated that the final molar ratio of [CE]/[NIPA] in the network is 1/60. Swelling Measurements. Swelling measurements followed the procedure described in ref 13. The dry gel disks were placed in contact with water and equilibrated at 20.0 ( 0.2 °C for 48 h. Swelling was determined gravimetrically, assuming volume additivity and taking for the density of the dry polymer F ) 1.115 g cm-3.14 Stress-strain measurements were made as described in ref 15. DSC. Differential scanning microcalorimetric measurements were made on powdered samples in a MicroDSCIII apparatus (SETARAM, France), as described elsewhere.14 The DSC scanning rate was 0.02 °C/min. SAXS. Small-angle X-ray scattering measurements were carried out at the BM2 beamline of the European Synchrotron Radiation Facility (Grenoble, France), using an incident wavelength of λ ) 0.77 Å (16 keV). The wavelength spread of the beam from the Si 111 monochromator was ∆λ/λ ≈ 1.4 × 10-4. The range of wave vectors explored was 0.01 Å-1 < q < 1 Å-1, where
q)
4π sin(θ/2) λ
(1)
and θ is the scattering angle. Standard corrections were applied for dark current and the background signal of pure water.14 Measurements were made at 24 and 40 °C. SANS. Small-angle neutron scattering measurements were made on the D11 instrument at the Institut Laue Langevin, Grenoble, France, as well as at the KWS 1 instrument at the I.F.F. Forschungszentrum Ju¨lich, Germany. The wave vector range was 2 × 10-3 < q < 0.25 Å-1. The incident neutron wavelength λ was 8 Å with a wavelength spread ∆λ/λ ) 0.1. The sample temperature was maintained at 20 °C. Corrections for detector response, scattering from the quartz windows and incoherent background were applied. Results and Discussion Uniaxial compression measurements of the elastic modulus G of the unmodified and modified gels with similar monomer/ cross-linker ratio (150) were made at swelling equilibrium. The values found were almost identical, namely G ) 1.9 kPa and G ) 2.1 kPa, respectively. These results are comparable to measurements obtained for polyacrylamide/water gels synthesized under similar conditions of concentration and crosslinking.16 The similarity between the moduli of the modified and unmodified PNIPA gels implies that during copolymeri-
Poly(N-isopropylacrylamide) Hydrogels
J. Phys. Chem. B, Vol. 112, No. 4, 2008 1067
Figure 2. DSC response of the PNIPA and PNIPA/CE gel. dT/dt ) 0.02 °C/min. Note different heat flow scales for the two systems (leftand right-hand ordinate axes, respectively).
Figure 1. Equilibrium swelling of PNIPA/CE (b) and PNIPA (O) hydrogels.
zation the CE molecules are incorporated into the NIPA chains and play an elastically active role in the polymer network. The macroscopic swelling degree of the polymer gels is defined by 1/φ, where φ is the polymer volume fraction at swelling equilibrium. Figure 1 shows the variation with temperature T of 1/φ for the PNIPA/CE gel, compared to that of PNIPA with monomer/cross-linker ratio ) 150. The accuracy of these measurements is about 5%. The PNIPA/CE gel swells less than PNIPA, and its VPT occurs at a lower temperature. Since the values of the elastic modulus G of the two systems are almost identical, it can be concluded that the copolymer is less hydrophilic than the unmodified gel. This result is consistent with the lower specific polar surface area of CE than NIPA (1200 and 1545 m2 mol-1, respectively). Although the shapes of the two swelling curves 1/φ(T) are similar, the variation at the VPT is more gradual for the copolymer gel. At TVPT the copolymer gel becomes white and the volume decreases to a value that remains constant with further increase in temperature. In the high-temperature state, the copolymer gel contains about 50% v/v water compared with about 80% in the case of pure PNIPA. To determine the temperature of the phase transition, however, a more precise estimate can be gained by DSC measurements. The DSC measurements, shown in Figure 2, indicate that the sharp endothermic peak observed in PNIPA becomes broad and flat in the copolymer gel. The broadening is reflected in the extended temperature range between the onset temperature and the peak position in the PNIPA/CE gel. The onset temperature coincides with the transition temperatures seen in Figure 1. Within experimental error, no shift in the baseline is observed at the transition. It follows that the specific heat is continuous through the transition, and it is sufficient for the present purposes to derive the associated enthalpy without resorting to the integral form of the Gibbs-Helmholtz equation.17 The enthalpy of deswelling (Table 1) is appreciably smaller in the modified gel. The slow scanning rate allows the entropy change during the deswelling process to be estimated. In both systems the entropy is positive, as befits the endothermic nature of the transition, but as could be expected, its value is perceptibly smaller for the more complex copolymer gel. This reduction in enthalpy
Figure 3. SAXS response of PNIPA gels at T ) 24 and 40 °C.
TABLE 1: Characteristic Data from Low Scanning Rate DSC Response onset temp (°C) peak temp (°C) enthalpy (J/g dry gel) entropy (J/K g dry gel)
PNIPA/CE
PNIPA
25.9 30.2 37 0.124
33.9 34.1 57 0.186
and entropy may be related to changes in the accessible surface area of the polymer, a notion discussed by Grinberg et al.18 It is not idle to point out that the sign of the entropy change is opposite to that expected in the Flory-Rehner theory of network swelling and deswelling.19 In the latter theory, the entropy is assumed to consist of only two components: that due to mixing between polymer and solvent and that due to stretching of the network chains. The experimentally observed sign of the heat transfer in the present case is direct evidence that this system is dominated by a third effect, namely the loss of order among the water molecules surrounding the polymer chains.20-22 This extra entropic contribution, due to orientation and density disorder among the solvent molecules, is overlooked in lattice models of solutions, for which only positional entropy is considered. SAXS and SANS measurements probe the nanoscale structure of the gels. While SANS yields information in the lower range
1068 J. Phys. Chem. B, Vol. 112, No. 4, 2008
Kosik et al.
∆I(q) ∝ (1 + q2RG2/6)-2
Figure 4. SAXS response of PNIPA/CE gels at T ) 24 and 40 °C. Inset: difference spectrum ∆I(q) ) INIPA/CE(q) - INIPA(q) at 24 °C, together with the corresponding fit to eq 3.
of scattering vectors, the absence of incoherent scattering in SAXS observations allows measurements to be extended into a higher q region. Below q ) 0.1 Å-1, the SAXS spectrum of the unmodified PNIPA gel at 24 °C, shown in Figure 3, exhibits solution-like behavior characteristic of osmotic concentration fluctuations.23 These are generally described by an OrnsteinZernike relation of the form24
I(q) ∝ (1 + q2ξ2)-1
(2)
in which ξ is the correlation length of the polymer in solution. Fitting eq 3 to the low-q region of the spectrum in Figure 3 yields ξ ≈ 38 Å. This behavior is consistent with SANS measurements by other workers.25 In the higher q range of Figure 3, a distinct shoulder is visible in the SAXS curves at q ≈ 0.5 Å-1, implying a characteristic spacing between subunits d ) 2π/q ≈ 12 Å. When the temperature is raised to 40 °C, the shoulder develops into a clearly resolved peak at q ≈ 0.56 Å-1 (d ) 11 Å), visible both in Figure 3 for PNIPA and in Figure 4 for the copolymer gel. Inspection of Figures 3 and 4 shows that the position of the peak is independent of the presence of the CE. This feature, which lies outside the q range normally explored in small-angle scattering from polymers, should not be confused with a peak of appearance similar to, but of different physical origin from, that found in polyelectrolyte solutions26,27 and gels.7 In the system studied here, which possesses no polyelectrolyte character, the peak is located at a much higher value of q than in polyelectrolyte systems and is simply due to the side groups of the polymer chain, the positions of which are correlated along the backbone. At high temperature these tend to form clusters in the polymer-rich phase. The influence of the CE comonomer on the swollen structure of the PNIPA/ CE gel appears at larger length scales, i.e., at smaller values of q. At 24 °C the effect of the CE becomes significant at q < 0.03 Å (Figure 4), corresponding to distances 2π/q in excess of 100 Å. On subtracting the signal of the PNIPA sample from that of the copolymer gel, the difference signal ∆I(q) ) INIPA/CE(q) - INIPA(q) can be expressed in terms of a DebyeBueche expression of the form
(3)
where RG is the radius of gyration of the clusters. The factor 1/6 in eq 3 comes from the definition of the radius of gyration. The value of RG found from the fit of eq 3 to the difference signal, displayed in the inset of Figure 4, is 180 Å. At 40 °C, i.e., above TVPT, the SAXS spectra in Figures 3 and 4 display an extended region of power law behavior at low q. In the unmodified PNIPA the exponent of the power law is m ) -4. The scattering is therefore dominated by smooth surfaces.28 In the PNIPA/CE gels, on the other hand, the slope in this region is smaller, m ≈ -3.65, characteristic of rough surfaces having a surface dimensionality Ds ) 6 + m ) 2.35.29 The change in scattering behavior is thus a consequence of the CE clusters in the polymer-rich phase. At 40 °C, where the PNIPA segments are hydrophobic, the CE molecules with their hydrophilic ring can reduce the free energy by populating the polymer-water interface. A distribution of this type would contribute to the interface roughness. SANS furnishes information of a similar nature to SAXS. The intensity, however, is no longer determined by the difference in electron density between the polymer and solvent, but rather by the difference in neutron scattering length density. This means in particular that, by appropriately adjusting the ratio of H2O to D2O in the solvent, the signal from a selected component of the matrix can be made to vanish. The general features of the spectra from the SAXS and SANS observations are similar to each other, but owing to the difference in experimental conditions, notably the temperature, and to the strong temperature sensitivity of the samples, the results are not identical. In Figure 5 the SANS response of the PNIPA/CE gel at 20 °C in pure D2O is compared with that of the unmodified PNIPA gel. In both systems the intensity at the lowest observed values of q displays an apparent power law behavior I(q) ∝ q-m, where m ≈ 2.9, resulting from large-scale structural inhomogeneities. The absence of curvature at low q (≈0.002 Å-1) implies that their size is greater than 2π/0.002 ≈ 3000 Å. Such scattering features are common in gels and result from random crosslinking.30 In the q range 0.003 Å-1 < q < 0.1 Å-1 the PNIPA/ CE gel exhibits significantly stronger scattering than that of the unmodified gel, which indicates the presence of a different class of clusters that are smaller in size. Proceeding as for the SAXS measurements, the difference ∆I(q) between the two intensities, with and without CE, in the central region of this q range (Figure 5, inset) also follows a Debye-Bueche relationship, for which the radius of gyration is RG ) 84 Å (continuous line). The forms of eqs 2 and 3 correspond to different types of structure: the asymptotic q-4 behavior for the former implies sharp interfaces and a denser structure than the loose polymer distribution underlying the Ornstein-Zernicke expression (eq 2). The large difference in the value of RG found by SANS at 20 °C (84 Å) and that by SAXS at 24 °C (180 Å) illustrates the increase in size of the structural inhomogeneities as the onset temperature of the transition in this gel (25.9 °C) is approached (Table 1). To determine the relative contribution of the chemical species in these clusters, the gel was swollen in a mixture of 18% D2O and 82% H2O (v/v). With this solvent composition the scattering length density coincides with that of PNIPA, and the corresponding coherent SANS signal vanishes. Any detectable response can then be attributed to CE molecules. Figure 6 shows SANS spectra of the two gels swollen in this isotopic solvent mixture. Within experimental error the signal from the PNIPA gel is, as expected, zero. The response of the PNIPA/CE gel,
Poly(N-isopropylacrylamide) Hydrogels
J. Phys. Chem. B, Vol. 112, No. 4, 2008 1069 In spite of the approximations involved, the most serious of which is the assumption of additivity of the contribution from the clusters in Figure 5, these results lend strong support to the conclusion that the cluster composition is rich in CE. Furthermore, the observation that the clusters increase in size as the temperature is raised from 20 to 24 °C is a sign of their associative nature. As such associations can create entanglements over large distance scales, this feature illustrates one of the possible steric hindrance mechanisms that could account for the observed broadening of the transition temperature in the PNIPA/ CE gels. Conclusions
Figure 5. SANS response of PNIPA (lower data set) and PNIPA/CE (upper data set) gels at T ) 20 °C in pure D2O. Inset: difference spectrum in the central region with fit to data.
Figure 6. SANS response of PNIPA (O) and PNIPA/CE (×) gels at T ) 20 °C at the contrast matched condition for PNIPA with 82% H2O/18% D2O. Continuous line is fit to eq 3 with RG ) 84 Å.
however, does not vanish, indicating that the chemically distinct species CE forms clusters. The CE content of the clusters can be ascertained in the following way. From the knowledge of the density of the CE monomers (d ) 1.24 g cm-3) and their chemical composition, the value of the neutron scattering length density of CE is found to be FCE ) 1.50 × 1010 cm-2. It follows that the ratio of the contrast factors of CE in water with 100% D2O and with 18% D2O is (FD2O - FCE)2/(FD2O18% - FCE)2 ) 37. This ratio, calculated for pure CE, can be compared with the equivalent ratio of intensities from the experimental observations in the inset of Figure 5 and in Figure 6. On setting RG ) 84 Å and fitting the data of Figure 6 to eq 3 (continuous line), the ratio of the two experimentally measured intensities extrapolated to q ) 0 is found to be 4.0/0.185 ) 21. It follows that the CE content of the clusters is approximately 21/37, i.e., somewhat more than 50%. It should be added that the data lying above the fitted curve at low q in Figure 6 are a sign that larger clusters are also present. A reasoning similar to that given above indicates that these have a lower concentration of CE. It is also pertinent to mention that such clusters can act as a reinforcing filler and thus contribute to the elastic modulus of the network.31
When NIPA is copolymerized with CE into a hydrogel, the swelling ratio in water decreases with respect to the unmodified gel. The invariance of the elastic modulus implies that the CE is incorporated into the network chains of the gel. The temperature of the VPT is lowered and the transition broadened by the CE, while DSC measurements show that both the enthalpy and the entropy associated with the VPT are diminished. Scattering observations show that on a local scale (≈10 Å) the structure of the gels is not measurably changed. In the swollen state far from VPT, however, CE tends to generate clusters with a radius of the order of 100 Å. As the transition temperature is approached, the clusters tend to aggregate, thus increasing their size up to several hundred angstroms. In the nonequilibrium high-temperature phase that develops during deswelling, these clusters populate the polymer-water interface. Acknowledgment. K.K. acknowledges a French government scholarship as well as Socrates/Erasmus and Rhoˆne-Alpes (MIRA) mobility fellowships. We thank Miha´ly No´gra´di for the synthesis of the crown ether, Isabelle Grillo and Cyrille Rochas for their invaluable help with the scattering experiments, and the Institut Laue Langevin for access to the D11 smallangle scattering instrument. Thanks are also due to the European Synchrotron Radiation Facility for access to the French CRG beamline BM2 and to the I.F.F. Forschungszentrum Ju¨lich, Germany, for access to the KWS 1 instrument. The technical support of Gyo¨rgy Bosznai is deeply appreciated. This research was supported by the Hungarian grant NKFP Nο. 3A/081/2004 and by the joint EU-Hungarian Government grant GVOP-3.2.22004-07-0006/3.0. References and Notes (1) Feil, H.; Bae, Y. H.; Feijen, J.; Kim, S. W. Macromolecules 1993, 26, 2496. (2) Qiu, Y.; Park, K. AdV. Drug DeliVery ReV. 2001, 53, 321. (3) Xiao, X. C.; Chu, L. Y.; Chen, W. M.; Wang, S.; Xie, R. Langmuir 2004, 20, 5247. (4) Szila´gyi, A.; Zrı´nyi, M. Polymer 2005, 46, 10011. (5) Xue, W.; Hamley, I. W. Polymer 2002, 43, 3069. (6) Bhalerao, V. S.; Varghese, S.; Lele, A. K.; Badiger, M. V. Polymer 1998, 39, 2255. (7) Shibayama, M.; Tanaka, T.; Han, C. C. J. Chem. Phys. 1992, 97, 6842. (8) Zhang, X. Z.; Zhang, J. T.; Zhuo, R. X.; Chu, C. C. Polymer 2002, 43, 4823. (9) Ertl, P.; Rohde, B.; Selzer, P. J. Med. Chem. 2000, 43, 3714. (10) Irie, M.; Misumi, Y.; Tanaka, T. Polymer 1993, 34, 4531. (11) Ito, T.; Hioki, T.; Yamaguchi, T.; Shinbo, T.; Nakao, S.; Kimura, S. J. Am. Chem. Soc. 2002, 124, 7840. (12) Krespan, C. G. J. Org. Chem. 1975, 40, 1205. (13) La´szlo´, K.; Kosik, K.; Rochas, C.; Geissler, E. Macromolecules 2003, 36, 7771. (14) La´szlo´, K.; Kosik, K.; Geissler, E. Macromolecules 2004, 37, 10067. (15) Horkay, F.; Zrı´nyi, M. Macromolecules 1982, 15, 1306. (16) Hecht, A. M.; Geissler, E. J. Phys. (Paris) 1978, 39, 631. (17) Privalov, P. L. AdV. Protein Chem. 1979, 33, 167.
1070 J. Phys. Chem. B, Vol. 112, No. 4, 2008 (18) Grinberg, V. Y.; Dubovik, A. S.; Kuznetsov, D. V.; Grinberg, N. V.; Grosberg, A. Y.; Tanaka, T. Macromolecules 2000, 33, 8685. (19) Flory, P. J.; Rehner, J., Jr. J. Chem. Phys. 1943, 11, 521. (20) Molyneux, P.; Frank, H. P. J. Am. Chem. Soc. 1961, 83, 3169. (21) Shibayama, M.; Mizutani, S.; Nomura, S. Macromolecules 1996, 29, 2019. (22) Cho, E. C.; Lee, J.; Cho, K. Macromolecules 2003, 36, 9929. (23) Mallam, S.; Horkay, F.; Hecht, A. M.; Rennie, A. R.; Geissler, E. Macromolecules 1991, 24, 543. (24) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell: Ithaca, NY, 1979. (25) Shibayama, M.; Tanaka, T.; Han, C. C. J. Chem. Phys. 1992, 97, 6829.
Kosik et al. (26) Moan, M. J. Appl. Crystallogr. 1978, 11, 519. (27) Nierlich, M.; Williams, C. E.; Boue´, F.; Cotton, J. P.; Daoud, M.; Farnoux, B.; Jannink, G.; Picot, C.; Moan, M.; Wolff, C.; Rinaudo, M.; de Gennes, P. G. J. Phys. (Paris) 1979, 40, 701. (28) Porod, G. In Glatter, O., Kratky, O., Eds.; Small Angle X-ray Scattering; Academic: London, 1982. (29) Hasmy, A.; Anglaret, E.; Foret, M.; Pelous, J.; Jullien, R. Phys. ReV. B 1994, 50, 6006. (30) Bastide, J.; Leibler, L.; Prost, J. Macromolecules 1990, 23, 1821. (31) Llorente, M. A.; Andrady, A. L.; Mark, J. E. J. Polym. Sci., Polym. Phys. Ed. 1981, 19, 621.
