Macromolecules 1986, 19, 2497-2501 (13) Hull, W. E. Two Dimensional NMR; Bruker Analytische Messtechnik Karlsruhe, 1982. (14) Marshall, J. L. Carbon-Carbon and Carbon-Proton NMR Couplings; Verlag Chemie: Deerfield Beach, FL, 1983. (15) Note that while the appearance of the chlorobenzene-d, spectra at 108 OC is quite different from that observed in either the toluene-d8 or CDCl:, spectra at 40 OC,' the resolved pentads appear in the same chemical shift order. A similar 2D NMR experiment with CDC1, at 40 OC as solvent has been carried out to check the validity of using the assignments given in ref
2497
8. In the CDC1, spectrum the mmrm and rmrm and the mmrr and rmrr pentads do not show the same degree of resolution. (16) There is, unfortunately, insufficient resolution of heptads or hexads in the 'H NMR spectrum to allow us to prove ',C=O heptad assignments. (17) The relative intensity of these peaks will be a function of the values chosen for the delays T~ and T* (see above). Couplings of ca. 2 and 7-9 Hz are expected for torsion angles of 60° (erythro H) and 180' (threo H), respectively (see ref 14, pp 22-26, assuming conformation as indicated in ref 1).
Crystalline Poly(3-ethyl-3-methyloxetane) Antonio Bello,* Ernest0 Perez, and Jose M. Gdmez Fatou SecciBn de Fisica y Fisicoquimica de Polimeros, Znstituto de Pldsticos y Caucho, C.S.Z.C., Madrid-6, Spain. Received March 25, 1986 ABSTRACT The monomer 3-ethyl-3-methyloxetane was polymerized in methylene chloride with triethyloxonium hexafluoroantimonate as initiator in the range 273-203 K. In all cases a semicrystalline polymer was obtained that showed only a single melting peak. Half-crystallization times, enthalpies of fusion, and melting temperatures were obtained as a function of crystallization conditions. The equilibrium melting temperature and the enthalpy of fusion were found to be 333 K and 1.5 kcaljmol, respectively. From the X-ray diffraction pattern of a uniaxially stretched sample, a fiber period of 6.5 8,was obtained. These results are analyzed in terms of the microstructure of the polymer.
Introduction Polymers derived from oxacyclobutane and its 3,3-dialkyl derivatives can be obtained by ring-opening polymerization:' r
1
We have previously reported some features related to the termination reaction of the cationic polymerization of oxacyclobutane and 3,3-dimethyloxetane. In these systems, besides normal propagation, inter- and intramolecular reactions of the growing species take place, producing less reactive ions. The relative amounts of each species are dependent on the substituents bearing the cyclic oxide and on the experimental conditions of polymerization. Substituents considerably modify the physical properties of polyoxetanes. Thus, in previous work2we have reported changes in the main thermal transitions and in the solubility in a series of symmetrical derivatives of oxetane, 3,3-dimethyloxetaneand 3,3-diethyloxetane. Due to their structural regularity, these polymers are easily crystallizable from the melt state, and, depending on the temperature of crystallization, several polymorphs can be obtained.2i3 However, properties of unsymmetrical derivatives have been less studied, although a change in properties related to the crystallinity would be expected, enhancing others related to the amorphous content such as solubility. In order to explore the influence of unsymmetrical pendent groups on the properties of polyoxetanes, we describe in this paper some features of the synthesis and thermal properties of poly(3-ethyl-3-methyloxetane)(PEMO). From the point of view of its structure, this polymer is placed between poly(3,3-dimethyloxetane) (PDMO) and poly(3,3-diethyloxetane)(PDEO). For this reason, the present paper also compares the thermal behavior of PEMO, PDMO, and PDEO. 0024-9297/86/2219-2497$01.50/0
Experimental Section Materials. The monomer, 3-ethyl-3-methyloxetane (EMO), was synthesized from the corresponding 1,3-diol as described by Schmoyer and Case.4 The monomer, after being dried over calcium hydride, was distilled several times in a vacuum line over Na mirrors and stored in tubes equipped with Teflon stopcocks. Ita purity was better than 99.9% as determined by gas chromatography. The 90-MHz 'H NMR spectrum of E M 0 shows a triplet a t 0.87 ppm, a singlet at 1.25 ppm (two CH3 groups), a quartet a t 1.65 ppm (CH, side chain), and a quartet at 4.35 ppm (OCHP geminal coupling). Triethyloxonium hexatluoroantimonate was used as the initiator of the polymerization and was prepared from benzoyl fluoride, antimony pentafluoride, and diethyl ether. Procedures. The polymerization of E M 0 was carried out in methylene chloride, and the resulting polymer was isolated by precipitation into methanol. The samples were filtered and dried under vacuum. The sample chosen for this work had an intrinsic viscosity of 3.0 dL/g as measured in cyclohexane at 298 K. The 360-MHz 'H NMR spectrum of the polymer synthesized a t 203 K as described above in deuterated chloroform as solvent at 40 "C shows a quartet a t 1.32 ppm (CH, side chain) and an AB system centered at 3.12 ppm (OCH,) (JAB= 8.8 Hz) (Figure 1). The resonances of these three groups do not offer any information about the stereoregularity of this polymer. Therefore, a 13C NMR spectrum was obtained at 90.55 MHz. The general experimental conditions were as follows: proton decoupling, pulse width 25 ps, relaxation delay 2.5 s, and 32K data points with 0.462 Hz per point, with the resolution slightly enhanced by means of a Lorentz-Gauss multiplication of the FID. Spectra were taken for samples in deuteriobenzene and deuteriochloroform, and, in all the cases, only five signals were present, each one due to the five different carbons of the structural unit. There is no sign of splitting of the peaks due to differences in tacticity (Figure 2). A Mettler TA 3000 DSC-30 calorimeter was used for the calorimetric measurements. The curves were obtained at a heating rate of 10 K/min after predetermined crystallization conditions or thermal treatments.
Results and Discussion Polymerization. Several cationic polymerizations of 3-ethyl-3-methyloxetane (EMO) were carried out in the range 273-203 K. In a typical experiment, the polymerization was performed with methylene chloride as diluent 0 1986 American Chemical Society
2498 Bello et al.
Macromolecules, Vol. 19, No. 10, 1986
b
0
223 2
3
1
wm.
273
0
Figure 1. 'H NMR spectra of PEMO at 360 MHz in deuteriochloroform.
T
323
(OK)
Figure 3. DSC of PEMO (scan rate 10 K/min): (a) sample crystallized at 273 K; (b) sample quenched in liquid N2 1404
76.30
I
I
39,Sl
120
-
100
-
80
1 A
Figure 2. 90.5-MHz 13C NMR spectrum of poly(3-ethyl-3-
methyloxetane).
at 273 K, with a 0.62 M solution of monomer and 1.3 X M triethyloxonium hexafluoroantimonate as initiator. The polymerization was over shortly after mixing of the solutions, such that the heat suddenly evolved raised the temperature considerably. The speed of this polymerization is in strong contrast with the slowness of the polymerization of the unsubstituted oxetane under similar experimental conditions. This is not due to reactivity differences of these monomers but, probably, to the diminution of the concentration of the propagating species in the unsubstituted oxetane as the polymerization progresses. This diminution is due to an extensive inter- and intramolecular chain transfer to the polymer, giving unstrained oxonium ions of low reactivity. The existence of this reaction in the polymerization of oxetane has been shown from kinetic and viscosimetric e~periments.~ In the case of the 3-ethyl-3-methyloxetane the presence of two pendent substituents must decrease the chance of this transfer reaction because these two pendent groups shield the oxygens, reducing the polarity and the donor-acceptor capability of the ether group of the polymer as compared with the unsubstituted polyoxetane. For these reasons, a high concentration of living species must be maintained during the polymerization. This fact has been demonstrated by measuring on a vacuum viscometer the time of flux of a living solution before and after its deactivation with triethylamine. These measurements showed differences of less than 1%, which correspond to a low degree of association of the propagating species. Solubility. The solubility depends on the structure of the polymer. PEMO has low solubility in polar solvents such as methylene chloride or acetone and is very compatible with nonpolar solvents such as cyclohexane. Thus, it is very similar to PDMO and PDEO but quite different from polyoxetane (POX), for which the reverse situation
0
' 230
I
0 240
250
270
260
Tc
280
290
300
(OK)
Figure 4. Half-crystallization time against temperature of
crystallization.
was found (high solubility in methylene chloride while cyclohexane is a 0 solvent). At least two reasons can be given for this behavior. One is that dialkyl substitution in the 3-position shields the oxygen of the polymer backbone, reducing the donor-acceptor capability of the polymer as compared with the unsubstituted polyoxetane. The other is that substitution in this position decreases the polar character of the main chain and favors conformations that place pairs of bond dipoles in antiparallel positions. Probably, both-steric effects and the polar character of the chain-influence the solubility.6 Thermal Properties. Calorimetry was used to determine the glass transition temperature ( T J ,the melting temperature (Tm), and the enthalpy of fusion (AH,). A sample of PEMO after crystallization from the melt at 273 K over 24 h was analyzed in the calorimeter starting from 173 K. The calorimetric curve obtained for PEMO is shown in Figure 3. The temperature was raised at a heating rate of 10 K min-' and two thermal transitions were observed. One was located around 227 K, corresponding to the glass transition, and the other was seen at 303 K, corresponding to an endothermic peak at the melting temperature. When the sample was quenched from the melt into liquid nitrogen, the DSC curve obtained under the above conditions displayed only the glass transition without exhibiting cold crystallization or melting peaks. This indicates that the PEMO has a considerable crystallization induction time. The same behavior has been reported for PDM0.2 Several isothermal crystallizations were carried out in the range 289-245 K, the overall crystallization being
Macromolecules, Vol. 19, No. 10, 1986
Crystalline Poly(3-ethyl-3-methyloxetane)2499
as
1.0
(qp4.103
’.’
2.0
Figure 6. Melting point depression of PEMO in methylcyclo-
hexane.
2;3
298 Tc(OK)
323
Figure 5. Melting temperature against crystallization temper-
ature.
~~
Table I Glass Transitions, Melting Temperatures, and Heats and EntroDies of Fusion of Polyoxetanes To,K Tmo,K A?I, cal/g AS, cal/g polymer
poly(3,3-dimethyloxetane) 223 poly( 3-ethyl-3-methyl227 oxetane) poly(3,3-diethyloxetane) 243
348 333
25.6 15.0
0.074
363
21.9
0.060
0.045
followed by dilatometry. In Figure 4, 70.5,the time required to obtain 50% transformation, is plotted vs. T,, the temperature of crystallization. The overall Crystallization rate shows a maximum at T, = 263 K, being diffusion and nucleation controlled below and above this temperature, respectively. Relatively large times of induction were observed for the crystallization of PEMO; thus, for the maximum rate, induction times of -20 min were found, and undercoolings aroung 50-60 K must be used in order to obtain experimentally convenient rates. The equilibrium melting temperature, Tm0,is an important parameter that not only reflects the molecular and conformational characteristics of a chain but, when used in analyzing crystallization kinetics, also yields important parameters related to the mechanism of crystallization. It is well-known from crystallization theory that crystals of finite size, when heated sufficiently rapidly so that their thickness remains unaltered, melt at T , < Tmoaccording to the relationship Tm0- T , = (l/Z)(a/n)(Tmo- T,) (1) where a = uKf ,u is the ratio of the interfacial free energy per repeating unit emerging from the basal plane of a mature crystallite to that of a critical nucleus, n = [/tn, where 5 and 5, are the sizes of the mature crystallite and of the critical nucleus, respectively, and Z is 1 or 2 according to the nucleation mode. Analysis of the melting temperature after isothermal crystallization was carried out by calorimetry. The results are plotted in Figure 5. The usual extrapolation to the point where T , = T, gives an equilibrium melting temperature of 333 K and the slope of the linear extrapolation equals 0.5. This is lower than the values reported for PDMO and PDEO (Table I). The equilibrium heat of fusion of PEMO was measured by the diluent method, using methylcyclohexane as a diluent. According to Flory’s relationship, the depression of the melting temperature is given by
Tm0and T, are the melting temperatures of pure polymer and the polymer-diluent mixture, respectively, AHuis the heat of fusion per polymer repeat unit, R is the gas constant, Vu/V1is the ratio of the molar volumes of the repeating units and the diluent, & is the volume fraction of the diluent, and B is the interaction parameter for the polymer-solvent pair. The density of the amorphous polymer was obtained from dilatometric measurements well above the melting temperature, giving a value p = 0.927 g/cm3 at 298 K. With this value of p together with 0.768 g/cm3 for the diluent, we obtained AHu = 1.5 kcalfmol (Figure 6). This result leads to an entropy of fusion A S = AHU/Tmo = 4.5 cal mol-’ K-l. The thermal transitions and thermodynamic parameters of fusion for PEMO deduced from equilibrium quantities are given in Table I. For comparison, the values of the two parent polymers PDMO and PDEO are included. The glass transition temperature follows the order PDMO < PEMO < PDEO and is less affected by the substitution of one methyl by one ethyl group than when both substituents are altered. As the number of carbon atoms of the pendent groups increases, Tgfor the polymers also increases. It is normally observed that when the chain length of the pendent group increases, Tg decreases, the magnitude of this effect being largely dependent on the nature of the side group with respect to the main chain. Thus, in poly(viny1n-alkyl ethers), Tgdecreases around 308 K as the alkyl side lengthens from methyl to n-butyl.’ This “internal plasticization” effect, brought about because the substituents increase the available volume for the main chain, is opposed in these polyoxetanes by the restrictions to internal rotation of the main chain introduced by the change of the substituents. Consequently, the intramolecular factors predominate over the intermolecular ones. It is useful to compare the melting behavior of PEMO with those of the two symmetrical parent polymers, PDMO and PDEO. Both show, depending on the crystallization temperature, one or two melting endotherms. Each is associated with a crystalline form. Thus, when a PDMO sample is isothermally crystallized below 273 K, the DSC curve shows only one peak at 305 K, but when the isothermal crystallization temperatures are in the range 273-289 K, two melting peaks are clearly discerned in the DSC curves, one in the region of 305 K and another about 321 K. The last one increases with T,while the peak at 305 K completely disappears at temperatures higher than 289 K.* After isothermal crystallization of PDEO below 293 K, the DSC curve shows only one melting peak at 330 K. When T, is raised to 298-313 K, two melting peaks are observed, one at 330 K and the other at 346 K; this last melting peak is observed only when T,is increased to 318 K. Thus, differences between the unsymmetrical and
2500 Bello et al.
Figure 7.
FiIir~p S , 1 t < r n 01 ~ < > Ii\ cI t h \ I I methyloxetane) l(l(i(i'h'11 rwrm tcmpwatiire
stretched about
symmetrical polymers are exhibited in that over a wide range of crystallization conditions one finds one melting peak for PEMO and two for PDMO and PDEO. For these two polymers it was established by X-ray analysis that differences in the melting peaks correspond to different X-ray structures? Three crystal structures of PDMO have been described by Tadokoro et a1.,3 and each structure is associated with a different molecular conformation. The three modifications have in common that in the four-bond repeat unit ( O W - C ) the two carbon-oxygen bonds are in the trans conformation, the differences being in the conformation of the other two C-C bonds. Thus, in PDMO, form I, the molecular conformation is all trans, T,; in form I1 (monoclinic), T3GT3G:and in form 111 (orthorhombic), (T,G.J? Fiber periods of 4.84.8.35. and 6.5 A,respectively are observed. Only two crystal structures have been found for PDEO, the one with a high melting temperature having a planar zigzag conformation and the modification that melts at low temperature having a (T,G,), conformation.' With regard to PEMO, the presence of a melting peak indicates that, despite unsymmetrical substitution, the chains of this polymer are regularly arranged in the crystalline unit cell. X-ray diffraction patterns were obtained on molded films with a Philips X-ray diffradometer using nickel-filtered Cu Ka radiation. On an undeformed sample, the peaks were found at 28 Bragg angles of 9.4O (m), 16.6" (s), and 24.9' (w) (s, m, and w stand for strong, medium, and weak intensities). In order to get some additional structural information, we recorded fiber diffractograms. The sample was uniaxially stretched about 1000% from the amorphous state at room temperature. Upon deformation the sample necks and shows a marked degree of preferred orientation, and this remains even when the stress is relaxed if the sample is given time to crystallize. Flat-plate X-ray diffraction patterns, with normal and tilted films, allowed measurement of the fiber period. This was determined from the equatorial second-layer distance on a tilting fiber diagram, obtaining a value of 6.5 A. For standard values for bond lengths and angles, the calculated repeat distance for two monomer units with a T,GZ conformation is 6.86 ,&. The two observed equatorial reflections, correlated with the interfiber packing, correspond to spacings of 5.3 and 9.4 A (Figure 7). The presence of crystallinity in a polymer with unsymmetrical substituents can be attributed to several causes. One of them is the stereoregularity. X-ray techniques were extensively applied in early work on polymer tacticity, and deductions about stereoregularity were sometimes made on the basis of ease of crystallization. Actually, there are examples in polymers with unsymmetrical substituents in
Macromolecules, Vol. 19, No. 10, 1986
which the presence of diffraction peaks is not directly related to tacticity.p'O As stated in the Experimental Section, the 'H NMR spectrum of PEMO at 360 MHz fails to show any sign of stereoirregularity. To check this point further we used 13CNMR spectroscopy, which has proven to be a powerful tool for detecting structural features in polymers. As pointed out by Ivin, triad configurational sensitivity can be expected for structural units with four atoms in the main chain." Although in other polyoxetanes such as poly(2methyloxetane) (PMO) -(OCH(CH,)CH,CH,)-, is+, syndio-, and heterotactic triads have been reported by NMR analysis at 67.89 MHz, from the splitting of the methine I3C signals,"apparently the similarity of methyl and ethyl substituents in PEMO compared with the proton and methyl group in PMO precludes a t 90.55 MHz the observation of any signals due to stereochemical configuration. However, for PEMO, the presence of only one signal for each carbon could also be attributed to the fact that the polymer has only one stereochemical form, isotactic or syndiotactic. From the point of view of the chemistry of the cationic polymerization of oxetanes initiated by triethyloxonium hexafluoroantimonate, such an explanation seems unreasonable since it requires great steric control by the growing oxonium ion over the cyclic monomer. The propagation step in the polymerization is an SN2reaction in which the oxygen center of the cyclic ether acts as a nucleophile, attacking the a-CH, group of the oxonium ion. The carbons bearing the substituents in the incoming ether and in the cyclic oxonium ion are far enough apart, separated by four bonds, so that there is no steric hindrance between them. Both sides of the cyclic ion are equally accessible for the nucleophilic monomer, and, in this way, a product with random configuration should be predominantly formed. Some support for the formation of a random polymer is the fact that the modification of the temperature of polymerization usually produces changes in tacticity because an increase of temperature corresponds to a more random propagation. All the polymers we have synthesized show the same NMR spectrum. Moreover, changes of stereoregularity should affect properties such as melting point and rate of crystallization. However, in samples of PEMO prepared with triethyloxonium hexafluoroantimonate in a wide interval of temperatures, from 273 to 203 K,this influence has not been observed. Thus, from considerations of the polymerization mechanism PEMO should have a predominantly random configuration. However, we failed to find experimental proof of this fact and, consequently, the problem of the stereoregularity in this polymer is an open question. Certainly, the most straightforward way of explaining the observed crystallinity in this polymer is t o suppose that it is more or less stereoregular. Nevertheless it can be also be argued that a low level of regularity is not a hindrance to crystallinity. As is well-known, the presence of crystallinity does not mean that the polymer crystal lattices are absolutely regular and repetitive. In proteins, for example, there is a varied sequence of chemical side groups along the chains, which can nevertheless pack in a basically regular fashion. Some insight into the perfection of crystalline structure can be obtained by comparing the thermodynamic parameters of the melting of PEMO with the other two symmetrical polyoxetanes PDMO and PDEO (Table I). The equilibrium melting temperature is in the order PDEO > PDMO > PEMO, with the higher value for the more heavily substituted symmetrical derivative. The minimum
Macromolecules 1986,19, 2501-2508
value for PEMO corresponds with the lowest enthalpy and entropy of melting. This last quantity is usually of paramount importance in determining the melting temperature, and a low value is often interpreted as due to restricted flexibility of the macromolecule in the molten state.13 This is not the case in those polyoxetanes that are characterized by a high degree of flexibility. The most flexible of these polyoxides, in the equilibrium sense of having the smallest characteristic ratio, is poly(trimethylene oxide) -(O(CH2)&.14 Its low melting temperature has been associated with a high degree of conformational disorder in the molten state corresponding a large value of Sm.15The conformationalrandomness is only slightly diminished by the restrictions that the dialkyl substitution at the 3-position adds to the rotations of the 0-C bonds. The steric encumbrance is scarcely modified on passing from PDMO to PEMO and PDEO and consequently the lower entropy of fusion of PEMO in comparison with the other two polymers c a n be related to a disordered structure in the crystalline state. The departure from the regularity will alter the entropy of this state, leading to a decreased entropy of fusion. In conclusion, the synthesis of PEMO, carried out under experimental conditions where a random placement of the substituents along the chain is expected, gives a polymer that is crystallizable from the melt state. Its thermal properties are well described by a two-phase model, amorphous and crystalline.
2501
Acknowledgment. Financial support from the Comisidn Asesora de Investigacidn Cientifica y TBcnica is gratefully acknowledged. Registry No. PEMO (SRU), 103349-60-6; PEMO (homopolymer), 103349-59-3; triethyloxonium hexafluoroantimonate, 19554-80-4.
References and Notes (1) Penczek, S.; Kubisa, P.; Matyjaszewski, K. Adu. Polym. Sci. 1980, 37.
(2) PBrez, E.; Gbmez, M. A.; Bello, A,; Fatou, J. G. Colloid Polym. Sci. 1983, 261, 571. (3) Takahashi, Y.; Osaki, Y.; Tadokoro, H. J. Polym. Sci., Polym. Phys. Ed. 1980,18, 1863. (4) Schmoyer, L. F.; Case, L. C. Nature (London) 1960,187,592. (5) Bello, A,; PBrez, E.; Fatou, J. G. Makromol. Chem. 1984, 185, 249. (6) PBrez, E.; Gbmez, M. A.; Bello, A.; Fatou, J. G. J. Appl. Polym. Sci. 1982, 27, 3721. (7) Haldon, R. A,; Schell, W. J.; Simha, R. J. Macromol. Sci. ( B ) 1967, I, 759. (8) Wunderlich, W. Macromol. Phys. 1973, 1. (9) Lupinacci, D.; Winter, W. T. J.Polym. Sci., Polym. Phys. Ed. 1982, 20, 1013. (10) Lovinger, A. J.; Cais, R. E. Macromolecules 1984, 17, 1939. (11) Ivin, K. J. J. Polym. Sci., Polym. Symp. 1978, No. 62, 89. (12) Kops, J.; Hvilsted, S.; Spanggaard, H. Macromolecules 1980, 13, 1058. (13) Mandelkern, L. Crystallization of Polymers; McGraw-Hill: New York, 1964. (14) Takahashi, Y.; Mark, J. E. J.Am. Chem. SOC.1963,98,3756. (15) PBrez, E.; Fatou, J. G.; Bello, A. Eur. Polym. J.,in press.
Theory of Microphase Separation in Graft and Star Copolymers Monica Olvera de la Cruz*t and Isaac C. Sanchez* Institute for Materials Science and Engineering, National Bureau of Standards, Gaithersburg, Maryland 20899. Received March 13, 1986
ABSTRACT: Phase stability criteria and static structure factors have been calculated for simple AB graft copolymers, for star copolymers with equal numbers of A and B arms, and for n-arm star diblock copolymers. The A-B interactions are characterized by the usual x parameter. The fraction of A monomer in the graft copolymer is denoted as f and the fractional position along the A chain backbone a t which the B graft is chemically linked is denoted as T. When T = 0 or 1the graft copolymer degenerates to a simple diblock copolymer. Leibler previously calculated that the critical value, (xN),, a t which an AB diblock copolymer containing N monomer units undergoes microphase separation is 10.5. This critical value occurs at f = 0.5 and is the only composition for which the transition is second order. According to the present theory, a graft copolymer (0 < T < 1) does not have a critical point for any f; i.e., all transitions are first order. For a given T , the spinodal = 13.5. However, star copolymers values, (xN),,always reach a minimum value at f = 0.5; for T = f = 0.5, (xN), with equal numbers ( n )of A and B arms each containing N / 2 monomers (f = 0.5) have a critical point at (xN), = 10.5 for all values of n. Like the graft copolymers, the n-arm star diblock copolymers (each arm is a diblock copolymer of composition f containing N monomer units) do not have a critical point. At f = 0.5, ( x N ) , equals 8.86, 7.07, 5.32, and 4.33 for n = 2, 4, 10, and 30, respectively. At a spinodal point the static structure factor S(q) diverges at a finite wave vector q*. Near a critical point q * / 2 ~determines the periodicity of the lowest symmetry-ordered structure (mesophase) and is expressed in units of the copolymer's radius of gyration R.
Introduction It is well-known from Flory-Huggins theory that a binary mixture of A and B homopolymers phase separates at a critical value of the interaction parameter x given by (XN), = 4
(1)
when each of the homopolymers has N/2 monomer units. Leibler' was the first to point out that a simple 5050 NBS Guest Scientist from the University of Massachusetts.
* Current address: Alcoa Laboratories, Alcoa Center, P A
15069.
0024-9297/86/2219-2501$01.50/0
diblock AB copolymer containing N monomer units has a larger critical x value:
-
(xru), = 10.5
(2)
Since classically x 1/T (T is temperature), this implies that phase separation is more difficult (requires a lower temperature) in diblock copolymers than in analogous homopolymer systems. Chemically joining two homopolymers of the same size to form a diblock copolymer reduces the critical temperature for phase separation by a factor of 2.6. In this paper the effects of other molecular architectures on the phase separation and critical behavior 0 1986 American Chemical Society
