Macromolecules 1995,28, 5535-5546
8636
Structure and Thermal Properties of New Comblike Polyamides: Helical Poly(P-L-aspartate)sContaining Linear Alkyl Side Chains F. L6pe~-Carrasquero,+** S. Montserrat,' A. Martinez de Ilarduya,+and S. Muiioz-Guerra*J Departamento de Ingenierta Quimica, ETSIIB, Universidad Politdcnica de Cataluiia, Diagonal 647, E-08028 Barcelona, Spain, and Departamento de Mciquinas y Motores Thmicos, ETSIIT, Universidad Politkcnica de Cataluiia, Coldn 11, E-08222 Terrassa, Spain Received January 27, 1995; Revised Manuscript Received May 6, 1995@
ABSTRACT: The structure and thermal properties of a series of novel comblike polyamides derived from nylon 3, poly(a-n-alkyl B-L-aspartate)s ( n being the number of carbons in the linear alkyl side group) with n = 6, 8 , 12, 18, and 22, were investigated. Polarizing infrared and solid-state 13C CP-MAS NMR measurements revealed that these polyamides adopt a-helix-like conformations and that these structures are retained at high temperatures. Two first-order transitions at temperatures T1 and Tz separating three structurally distinct phases, namely, A, B, and C, were characterized for polymers with n 2 12 by DSC and X-ray and electron diffraction methods. 21' and TZranged from -15 to +75 "C and from 50 to 129 "C, respectively, for n increasing from 12 to 22. Phase A (T 2'1) consisted of a layered structure of main chain helices with side chains crystallized in a separated hexagonal lattice. Phase B (TI < T < Tz) was found to be substantially like phase A but with side chains in the molten state. Phase C ( T > T z ) was interpreted as a uniaxial arrangement of independent helices embedded in the amorphous side chain matrix. Microscope optical observations suggested that a cholesteric-nematic rearrangement is probably implied in the B-C transition. Members with n = 6 and 8 displayed a peculiar behavior. The octyl derivative crystallized by annealing in a three-dimensional structure composed of 13/4 helices of the type reported for poly(B-L-aspartate)s bearing short side chains while the uncrystallized polymer was arranged as in phase B. On the contrary, the hexyl derivative could neither crystallize nor organize in a layered structure. It was concluded from this study that the title compounds follow closely the general pattern of behavior described for poly( y-n-alkyl a-L-glutamateh, a family of thermotropic polypeptides that has received great attention in recent years.
Introduction Poly(a-alkyl P-L-aspartate)s are nylon 3 derivatives with an alkoxycarbonylgroup stereoregularly attached to every third backbone carbon atom of the repeating unit. These polymers are closely related to poly(y-alkyl a-L-glutamate)s,a well-known class of synthetic polypeptides which, by analogy, can be regarded as deriving from nylon 2. In this nomenclature, a, P, and y refer to the carbonyl position relative to the amino group in the corresponding parent amino acid. A schematic representation of the chemical formulas for the constitutional repeating units of these two families of polymers is given in Figure 1. Studies carried out by our group a few years ago showed that poly(a-isobutyl P-L-aspartate) is able to crystallize in helical structures with features similar to the familiar a-helix of polypeptides and that the helical conformation is retained even in s ~ l u t i o n . l - Certain ~ properties related to the stiff helical nature of the macromolecule, such as formation of cholesteric liquid phases4 and pie~oelectricity,~ were subsequently observed for this polyamide. Very recent studies made on other poly(a-alkyl P-L-aspartate)s including a variety of side chain compositions have shown that formation of helical structures seems to be a property common to the whole family of these compounds.6-8 Among the different helical arrangements observed so far, the helix
* To whom all correspondence should be addressed.
t Departamento de Ingenieria Quimica, ETSIIB.
*
Permanent address: Departamento de Quimica, Facultad de Ciencias, Universidad de Los Andes, MBrida 5101A,Venezuela. 8 Departamento de Maquinas y Motores TBrmicos, ETSIIT. Abstract published in Advance ACS Abstracts, July 1, 1995. @
A
(1)
0
(11)
Figure 1. Chemical formulas for the structural units of the poly(a-alkyl /3-L-aspartate)s(I)and poly(y-alkyl a-L-g1utamate)s (11).
containing 13 residues in 4 turns appears to be the conformationmost frequently adopted. This consists of a right-handed helix with an axial repeat of -2 nm and hydrogen bonds set between the amino group of the i residue and the carbonyl group of the i 3 r e ~ i d u e . ~ Although there is a close resemblancebetween this helix and the a-helix, the precise geometry of the molecule turns out to be noticeably different due to the opposite orientation assumed by the amido group with respect to the polarity of the main chain.1° a-Helical polypeptides bearing long paraffinic branches are remarkable because the rodlike character of the main chain is coupled with a flexible hydrophobic phase with which it is usually incompatible. There is a side chain critical length above which the supramolecular organization changes dramatically, giving rise to a series of unusual properties distinctive of the so-called comblike polymers.ll These polymers attract great attention not only in their own in the study of supramolecular assemblies but also because they are promising materials for novel practical applications. Comblike poly(a-L-g1utamate)sand poly(a-L-aspartatels have been extensively investigated by several Japanese g r o ~ p s l ~ - ~ ~ during the past decade, and they continue to be an
0024-9297/95/2228-5535$09.00/0 0 1995 American Chemical Society
+
5536 Lopez-Carrasquero e t al. object of research nowadays.15J6 In particular, Wat a n a b e et a1.12carried o u t a systematic examination of the s t r u c t u r e a n d thermal properties of poly(a-Lglutamatels with long linear alkyl side chains. These a u t h o r s found that w h e r e a s the lower members of the family crystallize following the principle of optimum packing, higher homologs with alkyl groups containing t e n o r more carbons t e n d to adopt a biphasic layered structure a n d m a y generate thermotropic liquid crystals in a cholesteric or nematic arrangement. S u c h systems structurally resemble lyotropic mesophases with the flexible lateral c h a i n s in the molten state playing the role of the solvent. A critical review of these novel liquid crystalline polypeptides including their synthesis, characterization, a n d properties has been recently reported by Daly et a1.l' In this work we are interested in poly(a-n-alkyl p-Laspartatels, i.e., poly(P-L-aspartate)s bearing linear alkyl side chains, abbreviated PAALA-n, where n represents the n u m b e r of carbon a t o m s contained in the alkyl group. A general method of synthesis has been recently developed b y us, which allows one to obtain t h e s e compounds for a wide range of n with a high degree of stereoregularity and large molecular weights.lsJg While the structure of lower members of the series ( n 5 4)has been investigated in great detail as to conclude that t h e y behave like poly(a-isobutyl p-La ~ p a r t a t e )no , ~ similar studies concerning members with side chains of m e d i u m o r large size h a v e been m a d e to date. In t h e present study, a number of PAALA-n w i t h n ranging from 6 to 22 h a v e been examined by using a combination of techniques which include X-ray a n d electron diffraction, CP-MAS NMR, polarized infrared, a n d calorimetry measurements. The object is to evaluate t h e influence of the side chain length on the structure a n d thermal properties of these polymers a n d to know how t h e y compare to poly(y-n-alkyl a+ g l u t a m a t e l s with branches of similar sizes. Although an analogous p a t t e r n of behavior m a y b e reasonably anticipated, certain differences between the two families will b e expected from their dissimilarities in chemical structure. The additional methylene present in the main chain of poly(P-L-aspartate)s involves a less dense distribution of side chains in the space a n d will increase the flexibility of the main chain. Moreover, the mobility of t h e side chain will b e more hindered than in poly(ag l u t a m a t e l s since t h e alkoxycarbonyl group is directly anchored to the polymer backbone.
Experimental Section Materials. The five poly(a-n-alkyl B-L-aspartate)s used in this work were prepared by nonassisted anionic ring-opening polymerization of the corresponding optically pure 69-4(alkoxycarbonyl)-2-azetidinones.A detailed account of the synthesis of these polymers and their corresponding monomers has been published elsewhere.8120 The docosyl derivative (n = 22) was synthesized specifically for this work by applying the same method. Some data of these polymers relevant to this study are given in Table 1. Their molecular weights are in the range 200 000-450 000, they are soluble in chloroform, and they stand up well to temperatures above 200 "C. Poly(y-n-octadecyl a-L-glutamate) was used in this work for comparative purposes and was prepared by Prof. K. Yoshioka (University of Tokyo) by transesterification of poly(y-methyl a-L-glutamate) (M,= 500 000) with stearyl alcohol. The content of this polymer in residual methyl ester groups is reported to be less than 5%.22 Measurements. Densities were measured by the flotation method in aqueous KBr solutions or methanol-water mixtures. For polarized infrared dichroism, films prepared by
Macromolecules, Vol. 28, No. 16, 1995 Table 1. Data of Poly(a-n-alkyl@-aspartate)s Studied in This Work 2.1 1.07 307 n-CsHn 199.28 4.4 1.06d 341 n-CsH17 227.31 4.2 0.99 348 n-ClzH25 283.41 2.0 1.03 330 n-CleH3.i 367.57 1.01 323 423.39 -2 n-C22H45" a Obtained by anionic polymerization of (S)-4-(docosoxycarbonyl)-a-azetidinonein dichloromethanewith sodium pyrrolidone as initiator. Estimated by viscosimetry by using the Mark-Houwink equation reported for poly(y-benzyl a-L-glutamate).21 Peak maxima observed in the high-temperature region of DSC curves. The same density is obtained whether the polymer is crystallized or not. casting from chloroform were cut into strips and stretched under heating up to about 10 times their original length. Alternatively, orientation was accomplished with the polymer incorporated in a film of poly(ethy1ene oxide) (PEO) according to the method described by Ingwall et ~ 1 A . chloroform ~ ~ solution containing 2.5% (w/v) of PEO and 0.1% (w/v) of the polymer under investigation was evaporated to dryness and the resulting composite film stretched at room temperature. Infrared spectra were registered on a Perkin-Elmer 2000 FTIR instrument equipped with a gold wire polarizer. To minimize errors due to the polarization monochromators, the orientation axis of the sample was placed at f 4 5 " with respect to the direction of the entrance slit. Dichroic ratios (IV-L) of characteristic peaks were calculated from the absorbances measured for the parallel and perpendicular orientations of the sample to the infrared polarization vector. Calorimetric measurements were performed with a Mettler TA-400 thennoanalyzer equipped with a low temperature range DSC-30 differential scanning calorimetric module at a heating rate of 10 "C/min under a nitrogen atmosphere and calibrated with indium standard. Samples weights of about 6 mg were used. Optical microscopy observations were made under a Nikon polarizing microscope provided with a Mettler FP-80 heating stage. X-ray diffraction diagrams were obtained on flat films in a Statton-type camera using nickel-filtered copper radiation of wavelength 0.1542 nm and calibrated with molybdenum sulfide (do02 = 0.6147 nm). Polymer films prepared by casting from chloroform were placed with their surface either parallel or normal to the X-ray beam direction. Thermodiffractograms were recorded from unoriented films in a Siemens D-500 diffractometer with Cu Ka radiation provided with a TPK-A Park heating stage and a scintillation counter. For electron diffraction, films less than 50 nm thick were prepared by spreading a 1%chloroform solution onto a water surface. A Philips EM-301 instrument operating in the selected-area mode at 100 kV was used for this work. Solid-state 13CCP-MAS NMR spectra were recorded at 75.5 MHz in the temperature range -40 to f 8 0 "C. A Bruker AMX-300 NMR instrument equipped with a CP-MAS accessory and a variable-temperature unit was used. Samples of 50-200 mg weight were spun at 3.9-4.2 kHz in a cylindrical ceramic rotor. All the spectra were acquired with contact and repetition times of 2 ms and 10 s, respectively, and 256 and 1024 transients were accumulated. The spectral width was 31.2 kHz, and the number of data points was 4K. Chemical shifts were externally calibrated against the higher field peak of adamantane appearing at 29.5 ppm relative t o TMS.
Results and Discussion Transition Temperatures of PAALA-n. The DSC t h e r m o g r a m s of PAALA-6 to PAALA-22 registered at heating are shown in Figure 2. To avoid traces overlapping, only the region between -50 and +200 "C has been represented except for PAALA-22, whose whole t h e r m o g r a m has been reproduced for illustration. As s e e n for PAALA-22, all traces exhibit a prominent peak above 300 "C corresponding to the melting-decomposi-
New Comblike Polyamides 5537
Macromolecules, Vol. 28, No. 16, 1995 I
160,
-
I
,
12
n
I
I
16
14
n
18
22
20
QUI
V
PAALAl
l
.
,
.
-100
,
,
.
.
'
,
,
,
100
0
,
, 200
'C
300
Figure 2. DSC thermograms of PAALA-n with T2 peaks made apparent in enhanced traces. Inset: Temperature domains of phases A, B, and C in PAALA-12, -18, and -22 defined by their corresponding 21' ( 0 )and T2 (0)temperatures. Table 2. Calorimetric Data of Transitions in Poly(a-n-alkyl/?-L-aspartate)swith n z 12 transition A B transition B
-
Tia
A"f
UP
PAALA-12 -15 PAALA-18 54-64 PAALA-22 60-75
1172 4850 7290
4.5 14.4 20.9
polymer
("C) (cal/mol)(caY(mo1K))
ncc
7'2
("C)
1.9/2.8 50 7.9B.8 117 11.9h2.8 129
-C
.W (caVmo1) 130 100 110
4Two and three maxima are observed for PAALA-18 and PAALA-22, respectively. Entropy changes approximately estimated by taking 21' as the temperature of the highest peak.
Number of Crystallized methylenes calculated by using enthalpic and entropic values of 650 caVmol and 1.64 caV(mo1 K), respectively.
tion of the polymer. This process is known to be common to the whole family of poly@-L-aspartatels and to take place along two successive steps involving intramolecular imidation and scission of the main chain, respectively.* At temperatures below 200 "C, the thermal behavior of PAALA-n was found t o be strongly dependent on the size of the side chain. Whereas no appreciable heat exchange was detected for PAALA-6 and -8, two endotherms at temperatures 2'1 and TZ(TI< 2'2)) the former much more intense than the latter, were observed in the traces of PAALA-n with n I 12. Both peaks tend to move toward higher temperatures as the length of the side chain increases. T1 ranges from -15 "C for PAALA-12 to about 75 "C for PAALA-22, while the corresponding Tz vanes from 50 t o 129 "C. The enthalpy associated with the endotherm at T1 was found to increase with the side chain length and it ranges from 1.2 to 7.3 kcaymol. In contrast, the amount of heat flux observed at Tz is about 0.10-0.15 kcaVmol and its variation with composition is practically negligible. The calorimetric data obtained from PAALA-n with n L 12 (Table 2) are highly comparable, in both temperatures and enthalpies, with those reported for poly(y-n-alkyl a-L-glutamatelswith side chains of simi-
lar lengths.12*22By analogy with them, the thermal transition taking place at TImay be attributed to the fusion of the alkyl side chains leading to a partially disordered structure while the weak endotherm observed at TZcould be related to a rearrangement of the structure generated a t Ti. Accordingly, three phases, A, B, and C, with existence domains limited by the corresponding temperatures 1'2 and TZwill be distinguished in PAALA-n with n L 12, as diagrammatically represented in the inset of Figure 2. The fact that no paraffinic melting transitions are found for PAALA-8 and PAALA-6 is simply due to the insufficient length that the alkyl side chain has in these cases to crystallize by itself; this is in complete agreement with the thermal behavior reported for poly(a-L-glutamate)s12where a length of ten carbons is the minimum required to generate stable side chain crystals. Structure of PAALA-n at Room Temperature. 1. X-ray Diffraction. Cast films of PAALA-n placed normal to the incident beam produced Debye-Scherrer patterns with similar features. They all consist of a more or less diffuse ring of spacing about 0.40-0.45 nm as well as an intense sharp ring of spacing ranging from 1.7 t o 3.6 nm for n increasing from 6 to 22. When these films were diffracted in the edge-on position, oriented patterns consistent with a uniplanar orientation of the polymer were obtained for all cases except for PAALA6. After stretching, all PAALA-n without exception produced fiber diffraction patterns revealing further differences among the polymers. Diagrams from stretched PAALA-18 and -22 display an equatorial row of reflections corresponding to successive orders of a basic spacing of 3.1 and 3.6 nm, respectively. In addition, an approximate hexagonal array of six intense spots with a spacing -0.42 nm appears in the wide-angle region. Conversely, diagrams from stretched PAALAS to PAALA-12 merely consist of two intense arced-shaped reflections centered on the equator and near the meridian, respectively, which correspond to the two rings appearing in powder diagrams. Illustrative examples of each type of diagram are shown in Figure 3 for PAALA-18 and -12, and all the X-ray spacings observed at room temperature for every PAALA-n investigated in this work are compared in Table 3. According to the model described for a variety of comblike polymers containing polymethylene side groups,11J2~24 the X-ray scattering features displayed by PAALA-n with n I12 can be interpreted in terms of a biphasic structure with main chains arranged side-byside in layers and side chains segregated in a paraffinic phase filling the interlayer space. The reflections contained in the small-angle region of scattering are related to the spatial repeats associated with the layered structure. On the other hand, any orderly arrangement adopted by the paraffinic phase will become reflected in the pattern appearing in the wide-angle region. The discrete pattern of reflections displayed in the wideangle region of diagrams of PAALA-18 and -22 demonstrates that side chains are crystallized in these two polymers whereas the diffuse scattering appearing instead in diagrams of PAALA-12 reveals that the paraffinic phase must be in a disordered state in this case. Provided that X-ray diagrams were registered at room temperature, these two versions of the biphasic model, i.e., with the paraffinic microphase crystallized or not, should correspond respectively to phases A and B defined above on the basis of calorimetric measurements.
Macromolecules, Vol. 28, No.16, 1995
5538 Mpez-Carrasquero et al.
b
-0.45m
C
-0.45lWtl
1
2.4nm
2Anm
2.4m
d d
f
e
Figure 3. X-ray diffraction diagrams of films of PAALA-18(a-c) and PAALA-12 (d-fl taken at room temperature. The polymer film was in a vertical plane. (a and d) Cast film viewed with the beam incident normal to the surface (transversal view). (b and e) Cast film viewed with the beam incident parallel to the surface (edge view). (c and D Stretched film; the direction of stretching was vertical and the beam was normal to the surface. Sets of diagrams similar to a-c and d-f were recorded from PAALA-22 and PAALA-8, respectively. Only the most characteristicreflections are indicated on the pictures; a complete list of all the spacings recorded for the five PAALA-n is given in Table 3.
Table 3. Observed X-ray Spacings (nm)oP Poly(a-n-alky1&baspartate)s at Room TemperatureD PAALA-6 PAALA-8 PAALA-12 PAALA-18 PAALA-22 low-angleregion 1.7 (vs) 1.8 (vs) 2.4 (vs) 3.10 (v8) 3.60 (vs) 1.50 (m) 1.04 (w) 0.75 (vw)
wide-angle regionb
0.45 (m, d)
0.45 (m, d)
0.45 (m, d)
0.46 (m, d) 0.42-0.41 (vs),(100) 0.24 (vw), (110)
1.80 (6) 1.19 (m) 0.86 (w) 0.72 (vw) 0.45 (m, d)
0.42-0.41 (vs). (100) 0.25 (vw). (110)
Visual estimates ofintensities denoted as v8 (very strong),s (strong),m (medium),w (weak),vw (very weak), and d (diffuse). Indexing given for the paraffinic hexagonal lattice of a0 = 0.49 nm.
With respect to the scattering observed in the smallangel region, it is noteworthy that only one Bragg spacing, which corresponds to the interlayer distance Lo, becomes defined on the equator of the diagram and no off-meridional reflections are seen in such a region. This means that the positional long-range ordering of the structure must be restricted along that direction normal to the layer plane; i.e., successive layers are irregularly sheared. Furthermore, the fact that higher orders of the LObasic spacing are brought out only when the polymer is in phase A (compare diagrams b and e in Figure 3) indicates that the regular stacking of the strata in such a phase is partially lost after the melting of the side chains. The X-ray diffraction features displayed by PAALA-8 are quite similar to those displayed by PAALA-12 for both unoriented and oriented films. Therefore, the same type of structure may be reasonably assumed for both polymers at room temperature; i.e., the structure of
PAALA-8 must be close to that of PAALA-12 in phase B. On the other hand, the X-ray results obtained from PAALAB evidence clearly that side chains are not ordered in this polymer, and in this respect it behaves similarly to PAAJA-8 and -12. However, this PAALA differs from all others in that no uniplanar orientation is adopted by the polymer in cast films. Such a difference together with certain density considerations, which will be discussed in the appropriate section, suggest that PAALA-6 helices should not be arranged in layers but merely packed in a uniaxial structure with an average intermolecular distance LOof 1.7 nm. 2. Main Chain Conformation. X-ray diffraction data of PAALA-n with n 2 6 are insufficient to ascertain the conformation assumed by the main chain in these polymers. Although the -0.45 nm arced-shaped reflection appearing on the meridian of oriented diagrams might be attributed to the fourth layer line of a 1314 helix of the type commonly found in poly(fl+aspartate)s
New Comblike Polyamides 5539
Macromolecules, Vol. 28, No. 16, 1995
o.o+
3soo
I , )
3100
le00
,
, 1600
;
, 1400
crn -1 cm-I Figure 4. Infrared spectra of PAALA-n recorded with the polarization vector parallel (solid line) and perpendicular (broken line) t o the orientationaxis: (a)pure films; (b) polymer-PEO films. The spectra of poly(y-n-octadecyla-L-glutamate)(PALG-18) and PAALA-4 are included for comparison. Inset: Polarized spectra of oriented polyethylene in the 1600-600 cm-l region. Table 4. Polarized Infrared Spectral Data of Poly(a-n-alkylB-L-aspartate)s band position (crn-') in parallellperpendicular polarized spectra and their corresponding dichroic ratios, R (I V I ) polymer
amide A
amide I
PAALA-4d
328713288 1.93 328513286 2.76 328513283 2.45 328213286 2.47 328713287 1.87 328413285 2.08 328713288 2.03
1656/1656 1.99 1654/1655 2.42 165511656 1.94 1655/1656 2.00 1654/1657 1.17 165411656 1.14 1654/1656 1.68
PAALA-6 PAALA-8 PAALA-12 PAALA-18 PAALA-22
PUG-18'
amide I1 1543/1558 1.59 1542/1558 1.80 154311544 1.77 1541/1544 2.36 1541/1557 1.15 1541/1557 1.31 155011550 0.49
C=O ester 1748/1749 0.69 174111749
(CHz),
fmn?
Sb yo
(OF
0.25 0.37
0.80
174311745 0.81 174011738 0.94 174111742 0.94 1741/1742 0.93 1738/1738 1.05
0.31 0.33 7211720 1.27 7211721 1.32 721/721 1.45
0.22 0.21
62
0.26 0.24
63
0.41 0.31
66
Minimum orientation factor calculated on the basis of the dichroic ratio of the amide A band in PAALA-n and the amide I1 band in PALG-18. Orientation parameter for the alkyl side chain. Averaged angle of the side chain axis to the stretching axis. Data taken [I
from ref 10. e Poly( y-n-octadecyl a-L-glutamate).
containing short side chains, lower order layer lines needed to characterize this conformation are here missing due to the lack of azimuthal order in the structure. Polarized infrared spectroscopy has furnished strong evidence to infer that these polymers are arranged in a a-helix-like conformation close to that adopted by the lower members of the series. The infrared spectra of stretched films of PAALA-n recorded with the polarization vector parallel and perpendicular to the direction of stretching are shown in Figure 4. The spectra obtained under similar conditions from poly(a-n-butyl P-L-aspartate), which is known to be in the 13/4 helical conformation, and from the a-helical poly(y-n-octadecyl a-L-glutamate) are included for comparison. Estimates of dichroic ratios for the characteristic absorption bands associated with the stretching modes of amide A (-3280 cm-l, OCNH), amide 1(-1650 cm-l, OCNH), amide I1 (-1540 cm-', OCNH), and ester side group (-1740 cm-l, COO) of the five PAALA-n under study and the
reference compounds are listed in Table 4. A parallel dichroism demonstrative of an a-helix-like conformation is exhibited by both the amide A and amide I bands of all the polymers examined. The parallel dichroism exhibited by the amide I1 band of PAALA-n is known to be a feature characteristic of the 1314 helix, which contrasts with the perpendicular dichroism that this band displays in a-helical polypeptides. A recent study combining infrared dichroism with modeling analysis has proved that such a discrepancy arises from the different inclination assumed by the amido group with respect to the chain axis in these two helices.1° 3. Crystallized Side Chains. X-ray and DSC measurements have shown that the side chains of PAALA-18 and -22 in phase A are crystallized in an independent paraffinic microphase and that a similar structure is likely assumed by PAALA-12 a t temperatures below -15 "C. The mode of packing adopted by the side chains within the crystallites, their orientation
5540 Mpez-Carrasquero et al
Macromolecules, Vol. 28, No. 16, 1995
S=
Figure 5. I
