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(29) de Gennes, P.-G. C. R. Seances Acad. Sci., Ser. B 1980,B291, 219. (30) Prager, S.;Tirrell, M. J. Chem. Phys. 1981,75, 194. (31) Jud, K.; Kausch, H. H.; Williams, J. G. J. Mater. Sci. 1981,16, 204. (32) Wool, R. P.; OConnor, K. M. J. Polym. Sci., Polym. Lett. Ed. 1982.20,7. (33) Kim, Y. H.; Wool, R. P. Macromolecules 1983,16,1115. (34) Adolf, D. B.; Tirrell, M.; Prager, S. J. Polym. Sci., Polym. Phye. Ed. 1985,23,413.
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(35) Kausch, H. H. Polymer Fracture, 2nd ed.; Springer-Verlag: New York, 1985. (36) Hull, D.; Hoare, L. Plast. Rubber: Mater. Appl. 1976,1,65. (37) Dettenmaier, M. Adv. Polym. Sci. 1983,52,57. (38) Kramer. E. J. Adv. Polvm. Sci. 1983,52. 1. (39) Evans, K. E. J. Po1ym.-Sci.,Polym. Phys. Ed. 1987,25,353. (40) Wei, K. H.; Malone, M. F.; Winter, H. H. Polym. Eng. Sci. 1986,26,1012. (41) Lumpkin, 0. J.; Zimm, B. H. Biopolymers 1982,21, 2315. (42) Slater, G. W.; Noolandi, J. Macromolecules 1986, 19, 2356.
Temperature Dependence of Tracer Diffusion of Homopolymers into Nonequilibrium Diblock Copolymer Structures Peter F. Green* Sandia National Laboratories, Albuquerque, New Mexico 87185-5800
Thomas P . Russell IBM Research Division, Almaden Research Center, San Jose, California 95120-6099
Robert J6rbme and Maryse Granville Laboratory of Molecular Chemistry and Organic Catalysis, University of Liege, Liege, Belgium. Received April 2, 1988; Revised Manuscript Received June 27, 1988
ABSTRACT The morphology of polystyrene/poly(methyl methacrylate) (PSIPMMA) diblock copolymers was investigated as a function of temperature by using small-angle X-ray scattering. It was found that the microphase separation was enhanced up to temperatures in excess of 200 "C. At 175 O C the copolymers remained microphase separated when mixed with PS or PMMA homopolymer at homopolymer concentrations less than 50%, provided the molecular weight of the homopolymer was less than or equal to the total molecular weight of the copolymer. The temperature dependence of the tracer coefficients, D*Hc, of deuteriated polystyrene (d-PS) chains diffusing into two symmetric PS/PMMA diblock copolymers was studied by using forward recoil spectrometry (FRES). D*Hc/T was found to have the same temperature dependence as D*m/T, where D*HH is the tracer diffusion coefficient of d-PS chains diffusing into PS. A comparison of the temperature dependence of the zero-shear rate viscosity, qo, of PS indicates that D*Hc/T and v0-l have essentially the same temperature dependence. Experiments on the diffusion of deuteriated poly(methy1methacrylate) (d-PMMA) also indicated that D*Hc/T and v0-' have the same temperature dependence.
Introduction In a previous paper we reported the results of the molecular weight dependence of the tracer diffusion of deuteriated polystyrene (d-PSI and deuteriated poly(methy1 methacrylate) (d-PMMA) chains into three symmetric diblock copolymers of polystyrene (PS)/polylmethyl methacrylate) (PMMA).' The copolymer samples were prepared by solution casting using toluene, which is a nonselective solvent for either component. The morphologies of films prepared in this manner were characterized by using small-angle X-ray scattering (SAXS).ll2 The SAXS measurements indicated that the copolymers were microphase separated and the long period characterizing the combined thicknesses of the PS and PMMA rich domains was found to increase with the square root of the number of monomer segments which comprise the copolymer chain. In addition, the interface separating the two domains was large, on the order of 50 A. It was also found that the domains are not highly oriented with respect to the film surface. An important consideration in studying the diffusion of a thin layer of a homopolymer initially on the surface of the copolymer is how much of the copolymer surface is accessible to the homopolymer. This, of course, is controlled by the relative surface coverage of each component on the copolymer surface. The coverage is influenced by, among other factors, the relative surface energy of each of the homopolymers which comprise the copolymer, the solvent used, and the rate at which it is extracted from the 0024-9297/89/2222-0908$01.50/0
~opolymer.~ An X-ray photoelectron spectroscopy analysis of the surface of these films indicates that there are appreciable amounts of both components on the surface.ll3 This is reasonable since in the present case a nonselective solvent was used and the surface energies of the homopolymer components differ by a fraction of a dyne per en ti meter.^ The tracer diffusion Coefficient,' D*HC, of d-PS and d-PMMA chains of degree of polymerization NH which diffused into the copolymer hosts scaled as Nn2 provided that NH was less than -Nc, where N c is the degree of polymerization of the copolymer chain. The diffusion coefficient of the homopolymer chains that diffused into the copolymer hosts was found to be an order of magnitude lower than that of the chains that diffuse into the corresponding homopolymer hosts. This large reduction was attributed to three factors: a purely partitioning effect since only half of the volume is available to the diffusing chain, the tortuosity of the domains, and the domain orientation. The sample processing conditions were shown to have a pronounced influence on D*Hc. For example, when methylene chloride was used as a solvent for casting the copolymer films the diffusion coefficient was reduced by a factor of 2, evidently because the microphase separation of the copolymer was not as well developed as in the toluene case. In addition, the effect of annealing the ascast copolymer films for times on the order of 3 h or exposing them to toluene vapor for similar time periods before the diffusion process was to increase D*HCby ap0 1989 American Chemical Society
Tracer Diffusion of Homopolymers 909
Macromolecules, Vol. 22, No. 2, 1989 proximately a factor of 2. Upon annealing the copolymer
films or exposing them to toluene vapors for approximately 1 day prior to the diffusion experiments, D * Hwas ~ found to decrease by a factor of 3 below the value obtained by diffusing into the as-cast films. These results suggest that the nonequilibrium morphologies formed during the initial solvent casting approach thermodynamic equilibrium first by an increase in the long-range order followed by a reorientation of the microdomains parallel to the copolymer/air interface. This is consistent with recent transmission electron microscopy (TEM)5studies which indicate that at thermodynamic equilibrium the lamellar domains of symmetric diblock copolymers orient parallel to the free surface such that the lower surface energy component is on the surface. This paper describes a forward recoil spectrometry study of the temperature dependence of the diffusion of d-PS and d-PMMA chains into the symmetric diblock PS/PMMA copolymers. The morphological changes which occur on mixing the copolymers with the corresponding homopolymer were investigated by using small-angle X-ray scattering.
Experimental Section Two symmetric diblock PS/PMMA copolymers were used in this study, one copolymer comprised of a PS block of molecular and the weight 42OOO and the PMMA block of 42OOO (42K/42K) other with a PS component of molecular weight 157000 and a PMMA block of 162000 (157K/162K).The synthesis and characterization of the copolymers have been discussed in a separate paper.s The number of monomer segments, N H ,that comprise the diffusing homopolymer chains were such that N H < Nc/2. NC is the total number of monomer segments that comprise the PS/PMMA block copolymer chain. For the diffusion studies a thin film of the isotopically labeled (deuteriated) homopolymer (- 15 nm) was allowed to diffuse from the surface of the copolymer film to depths on the order of 800 nm. Forward recoil spectrometry, which has been discussed in detail elsewhere,' was used to determine the volume fraction versus depth profile of the deuteriated homopolymer in the copolymer host. In this experiment a monoenergetic beam of helium ions of energy 3.0 MeV impinges on a target at an angle a with respect to the target normal. The projectiles undergo a number of kinematic collisions with the target nuclei. As a result of these collisions some of these nuclei recoil from different depths in the sample. The energy with which a particle gets detected, Ed, is characteristic of the depth from which it recoiled and its mass. One obtains from this experiment a spectrum of the particle yield (number of recoils that get detected with energy between EdAE/2 and Ed + AE/2, where A E / 2 is the energy width of a channel in the multichannel analyzer) versus Ed. The experiment can, therefore, differentiate between protons and deuterons in the sample and the depth from which they recoiled. The number of particles that recoil from a given depth within the sample is characteristicof the concentration of particles at that depth. This spectrum is then converted to one of volume fraction of deuteriated polymer versus depth. The diffusion coefficient was then extracted from this profile by using the solution to the diffusion equation, assuming that D is independent of concentration.'*' Care was taken to ensure that the diffusion coefficients extracted from the profiles of volume fraction of labeled polymer versus depth were independent of composition at the concentrations used in this study which were on the order of 1-5%. This was done by diluting the layer containing the labeled polymer with a much higher molecular weight unlabeled polymer, of identical chemical structure, which would diffuse a few orders of magnitude more slowly than the labeled polymer, Hence the high molecular weight component would remain relatively immobile while the deuteriated homopolymer diffused. Within experimental error the diffusion coefficients measured with and without dilution of the isotopically labeled component were identical. An additional experiment was done to investigate the effects of concentration on diffusion. Mixtures of a block copolymer of degree of polymerization Nc with varying compositions of a homopolymer with degree of polymerization NH= 0.5Nc were
i
- 5
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T
Q
d
P P
-E
1
I
I
I
50 0
100 0 T
150 0
- 3
T 200 0
("C)
Figure 1. Bragg long period, L,spacing (0) and the thickness of the transition zone, E (a),for the PS/PMMA (42K/42K)
copolymer as a function of temperature. prepared. The volume fraction of the homopolymer in the blend was as high as 20%. Homopolymer chains with NH = 0.5Nc were diffused into the blend. The diffusion coefficient of the homopolymer into the blend as a function of the homopolymer concentration in the mixture exhibited a shallow minimum in the blend whose composition initially contained 10% of the homopolymer content. This minimum was a factor of 2 lower than the case where initially there is no homopolymer present in the copolymer. These experiments demonstrate that the diffusion rate is insensitive to compositions of homopolymer in the composition range over which our experiment was conducted (i.e., 1-5% for NH
Nc/%
Small-angle X-ray scattering measurements were performed on beamline I-IV at the Stanford Synchrotron Radiation Laboratory. Details of the facility can be found Briefly, the white radiation from a bending magnet was focused vertically with a Wcm, Pt-coated float glass mirror and horizontally by an asymmetrically cut &(Ill) crystal to a point ca. 0.5 mm X 300 pm on the detector plane. Slits before the sample reduced parasitic scattering. Detectors before and after the specimen monitored the incident beam flux and the attenuation factor of the specimen. Temperature control of the specimen mounted in a cell with Kapton windows was achieved with a Mettler FP85 hot stage with a control of better than 0.1 "C. The entire small-angle X-ray (SAXS)profile was recorded with a photodiode array detector. Camac electronicswere used to scan the detector and store the data on a hard disk for later use.
Results and Discussion Copolymer Morphology. SAXS measurements on copolymer films cast from toluene solutions clearly exhibited scattering profiles characteristic of a microphaseseparated morphology. As shown previously,' both firstand third-order reflections were evident in the profiles. The long period, L, characteristic of the periodicity in the morphology, is given in Figure 1along with the width of the transition zone, E , between the PS and PMMA microdomains as a function of temperature for the 42K/42K copolymer. Below the glass transition temperature both L and E remain constant. At temperatures in excess of this, L was found to increase by an amount that was slightly in excess of the thermal expansion coefficients of the PS and PMMA microdomains and E was found to decrease. Over the temperature range of the diffusion studies, the microphase-separated morphology was maintained. In fact, from these data there does not appear to be any tendency for the copolymer to undergo a disordering. This is further supported by the temperature dependence of the total integrated scattering or invariant, Q. Shown in Figure 2 is the invariant for the 42K/42K copolymer as a function of temperature. The experimental uncertainty in Q is approximately *lo%. Q is found t o
Macromolecules, Vol. 22, No. 2, 1989
910 Green et al.
t
'O
60 -
-02
E(A1 50 40 -
> t 20
40
60
80
100
120
140
160
EIL
i
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Tl"C)
Figure 2. Total integrated scattering Q for the 42K/42K PSI PMMA diblock copolymer as a function of temperature. The solid line is the calculated invariant assuming complete microphase separation, taking into account the thermal expansion coefficient of the PS and PMMA domains.
increase up to ca. 125 "C whereupon it remains constant or, at best, slightly decreases. The solid line in this figure is the calculated value of Q, assuming complete phase separation of the microdomain morphology into pure PS and PMMA domains. The discrepancy between the calculated and experimental values of Q at T 125 "C indicates that an equilibrium phase purity had not been achieved. For T > 125 "C, the calculated and experimental values agree quite well, providing strong evidence that the morphology is comprised of pure PS and PMMA microdomains. Even at temperatures in excess of 200 "C, microphase separation and the phase purity are retained with no indications of phase mixing. According to the theory of Leibler'O for symmetric diblock copolymers in the weak segregation limit, microphase separation into a lamellar morphology is expected when xA$vc > 10.5 where xm is the Flory-Huggins interaction parameter between the PS and PMMA segments. The results in Figures 1 and 2 for the 42K/42K copolymer suggest, therefore, that xm > 0.013. This value of xm is greater than that determined for PS and PMMA homopolymers by other meth0ds.l' This may indicate that xm for the block copolymer differs from xAB for these homopolymers due to the coupling of the dissimilar blocks. In this study several different PS/PMMA copolymers were investigated. It is important, therefore, to ensure that the characteristics of the microphase-separated morphology remain constant. As stated previously, the size 3f the domains increases with the square root of the number of monomers in the copolymer. In Figure 3, the width of the interface between the PS and PMMA domains, E , and the ratio of E to the long period, L (effectively twice the thickness of either the PS or PMMA domains), is shown as a function of the total number of monomer units in the copolymer, Nc. The width of the interface was determined assuming a sigmoidal gradient in the concentration between the phases where the Gaussian smoothing function has a full width a t halfmaximum of a. E is then given by (12a)'I2. The magnitude of E was found to increase slightly with the molecular weight of the copolymer. However, given the precision to which E can be determined, i.e., to within f15% or, for the copolymers studied here, to within f8 A, this increase can only be considered marginal a t best. However, the ratio of E / L decreases. This is not surprising since it suggests that the extent of microphase separation is enhanced with increasing molecular weight. Increasing the molecular weight increases xNc and, consequently, the extent of phase separation will be enhanced. Morphology of Block Copolymer/Homopolymer Mixtures. The variation of the morphology a t the homopolymer/block copolymer interface as a function of the
1
30
1 OL
103 NC
Figure 3. Width of the diffuse phase boundary, E , determined from the analysis of the high scattering vector portion of the SAXS profiles and the ratio of E to the long period, L , as a function of the number of monomer segments on the copolymer.
composition of the homopolymers and the molecular weight of the homopolymer relative to that of the copolymer is important for the interdiffusion studies. At this interface the concentration of the homopolymers varies from 1 in the pure homopolymer to 0 in the copolymer phase. Ideally it would be desirable to characterize the dependence of the morphology on the position in the interface. Electron microscopy would be best suited for this purpose, however, two factors hamper such studies. First, PMMA is severely decomposed in the electron beam. Preliminary studies at room temperature resulted in a distortion of the morphology. Second, quenching the homopolymer/copolymer bilayer to room temperature could induce artifacts on the size scale of interest. As an alternative to this SAXS studies were performed on a series of homopolymer/copolymer mixtures where the weight fraction of the homopolymer was varied from 0 to 0.75. The experiments concentrated on mixtures of the 42K/42K copolymer with narrow molecular weight distribution PS and PMMA, where the molecular weight of the homopolymer was varied from 28 000 to 400 000. All measurements were performed a t 175 "C which is well above the glass transition temperatures of each block. In Figure 4 the variation in the long period is shown as a function of the weight fraction of the homopolymer. Provided the molecular weight of the homopolymer was less than the total molecular weight of the copolymer, the long period was found to increase. In the case of mixtures with PS, the long period was found to increase in direct proportion to the weight fraction of the homopolymer. The solid line in Figure 4a was calculated assuming this proportionality describes the experimental values of L. This result is somewhat surprising since it would indicate that the lamellar morphology is retained at a weight fraction of polystyrene homopolymer of 0.2, which corresponds to a total PS concentration of 0.6, where a lamellar-to-cylindrical morphology transformation would have been expected, Measurements at higher PS concentrations were not possible, since the scattering maximum fell outside of the instrumental resolution. For mixtures of PS where the molecular weight of the homopolymer was 390000,the long period was found to be invariant, indicating that the homopolymer was excluded from the copolymer morphology. This is not surprising since the solubility of the homopolymer in the copolymer decreases rapidly with increasing homopolymer molecular weight.12 More complex behavior was found for mixtures of PMMA with the 42K/42K copolymer. For molecular weights of PMMA less than 100000 the long period was found to increase with increasing concentration of the
Tracer Diffusion of Homopolymers 911
Macromolecules, Vol. 22, No. 2, 1989
XH
Figure 5. Diffuse phase boundary E as a function of the weight fraction of added homopolymer XH.The filled points represent mixtures of the 42K/42K copolymer with PS where the molecular weight of the homopolymer is 27000 (a),45000 (A),and 115000 (A). The open points represent mixtures of the copolymer with and 107000 ('7). PMMA of molecular weights 44000 (0)
XPS
t
1
h 0.3
05
01
XPMMA
Figure 4. (a, Top) Long period L characteristic of the average center-to-center distance between like domains as a function of the weight fraction of PS homopolymer Xpg. The data shown are for different molecular weights of the added homopolymer with the 42K/42K copolymer. In particular, the data shown are for P s molecular weights of 27000 ( O ) , 45000 (A),115000 (A), and 390000 (m). The solid line was drawn assuming that the long period increased in direct proportion to the added PS homopolymer. (b, Bottom) Long period as a function of the weight fraction of added PMMA homopolymer XpMm,where the molecular weight of the homopolymer is 44 OOO (O), 107000 (A),and 400000 @). The dashed line was drawn assuming that the long period increased in direct proportion to the weight fraction of added PMMA homopolymer.
homopolymer but the increase was less pronounced than that seen for the mixtures with PS. The dashed line in Figure 4b is the proportional increase in L with weight fraction of the homopolymer as was drawn in Figure 4a. It is seen that even for mixtures of the 42K/42K copolymer with a PMMA homopolymer of molecular weight 45 000, the increase in L is less than that seen for the PS mixtures. The origins of these differences is not known precisely and any arguments given at this time would only be speculative. However, it is clear that the homopolymer is incorporated within the microphase-separated morphology of the copolymer. In contrast to this behavior, mixtures of PMMA (400000) with the 42K/42K copolymer do not alter the position of the long period, clearly showing the immiscibility of the homopolymer with the copolymer. An interesting and important observation was made concerning the width of the boundary between the PS and PMMA microdomains as a function of the added homopolymer. Shown in Figure 5 is a composite plot of E as a function of the weight function of added homopolymer. Regardless of the molecular weight or concentration of the
homopolymer, E was found to remain constant at 50 f 5 A. Since L continuously increases with an increase in the homopolymer concentration, on a relative scale, the extent of phase separation, based upon the diminution of the ratio of EIL, is enhanced with the addition of the homopolymer. Therefore, at equilibrium, while the addition of the homopolymer may induce transformations in the morphology, the microphase-separated morphology remains well defined. At the homopolymer/copolymer interface during the interdiffusion process a precise description of the morphology will depend upon the rate of change in the concentration gradient a t the interface in relation to the rate at which morphological transformations can occur. However, it is evident from these studies that a phaseseparated morphology will be retained and the added homopolymer, which for our purposes is the PS or PMMA diffusing into the copolymer, will remain within the PS or PMMA domain of the copolymer, respectively. Temperature Dependence of Diffusion. In view of these results it is reasonable to compare the temperature dependence of the diffusion of the homopolymer chains into the copolymer host with that of the diffusion of homopolymers into homopolymers of the same chemical structure. The temperature dependence of diffusion in homopolymer-homopolymer systems is well understood. Theory predicts that the ratio of the tracer diffusion coefficient, D*, of a homopolymer into a homopolymer of the same structure to the temperature, D*/ T , and the inverse of the zero shear viscosity, q-l, in the same system should have nearly the same temperature dependence.13-14 This follows from the argument that the temperature dependence of D*/T and 17 is dominated by the monomeric friction coefficient, lo: T/D* lo (1)
-
and 17
- lo
The temperature dependence of the zero-shear rate viscosity is well described by the Vogel-Fulcher e q ~ a t i o n ' ~ , ' ~ log 9 = A + B / ( T - To) (3) where To and B are Voegel parameters. It follows that log D*/T = A ' - B / ( T - To) (4) This temperature dependence is consistent with data obtained in a number of polymeric systems.17-19 In these equations A and A' are constants obtained from experi-
Macromolecules, Vol. 22, No. 2, 1989
912 Green et al.
10-12
c
10-11
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10-12
10.~7
0
Figure 8. Plot of log D*HcTmf/T versus T - T for the diffusion of d-PS (M= 27 000) into PS/PMMA (42K/12K) (B) and PS/ PMMA (157K/162K) (A). The line was computed by using eq 4 with B = 710 and To = 49 "C. Each set of data has been normalized to the same curve. I
0
20
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40
60
100
T-Tg
Figure 6. Dependence of log D*H~T,f/Tversus T - T for the diffusion of d-PMMA into PS/PMMA (42K/42K) [A) and PS/PMMA (157K/162K) (A). Each set of data has been normalized to the same curve.
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10-16 140
Figure 7. Temperature dependence of the tracer diffusion and of the shift coefficient of d-PMMA diffusing into PMMA (0) factor obtained from the shear compliance data of PMMA ( 0 ) (data was taken from Table I of ref 16 and the constants B = 1118 and To = 35 "C obtained from ref 12). Each set of data has been normalized to the same curve. mentally measured values of 7 or D*/T. Shown in Figure 6 is a plot of log D*Hc/Tfor the diffusion of d-PMMA ( M = 21 000) into the copolymer hosts 42K/42K and 157K/162K as a function of T - T gwhere Tg= 115 "C is taken to be the glass transition temperature of PMMA. Both sets of data were superposed on the same curve by multiplying the data representing diffusion into the 42K/42K copolymer by 2.2. This factor has its origin in previous measurements1 where is was shown that the homopolymer chains diffused by a factor of 2.2 more rapidly into the 42K/42K copolymer than into the 157K/160K copolymer, due primarily to differences in morphology. The curve drawn through the data was computed by using eq 4. The constants B = 1118 and To = 35 "C are the Vogel parameters of PMMA which were obtained from its zero-shear rate viscosity q0.l6 We may compare this with the temperature dependence of the diffusion of d-PMMA into PMMA shown in Figure 7, which is represented by the open circles. The shaded circles represent the temperature dependence of the inverse of the shift factor of PMMA which was obtained from the shear compliance data of Plazek et aL20 Equation 4, using the same values of B nd Toas above, was used to compute the curve drawn through the data. Similar comparisons may be made between the temperature dependence of the diffusion of d-PS into the P S and into the copolymer hosts with that of the v0-l of PS. The dependence of log D*Hc/Ton T - Tgfor the diffusion of d-PS into the copolymers 42K/42K and 175K/162K is shown in Figure 8, where T = 100 "C is the glass transition temperature of PS. The data representing diffusion into
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Figure 9. Temperature dependence of the diffusion of d-PS of M = 110000 (0) and 430000 ( 0 )into PS. The line drawn through the data was computed with eq 4 by using B = 710 and To = 419 "C. This data was taken from ref 13. Each set of data has been normalized to the same curve. I
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10-12
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Figure 10. Temperature dependence of d-PS of M = 110000 (0) and 87000 (A) diffusing into PS/PMMA (157K/162K). Each set of data has been normalized to the same curve. the 157K/162K host were multiplied by a factor of 1.6, for reasons discussed previously,l in order to superimpose both sets of data. The constants B = 710 and To= 49 "C were used in eq 4 in order to compute the solid line drawn through the data. These constants are the same ones used to fit the todata of PS.21 Using the same equation, together with the same constants, the solid line in Figure 9 was computed. The data in this figure represent the diffusion of d-PS of molecular weight M = 430000 and 110 000 into high molecular weight PS. Both sets of data were normalized to the same curve by multiplying the diffusion coefficients of the M = 110000 chains by (110/430).2 Figure 10 shows a plot of the diffusion of d-PS
Tracer Diffusion of Homopolymers 913
Macromolecules, Vol. 22, No. 2, 1989 chains of molecular weights M = 87 000 and 110000 into the copolymer 157K/162K. At temperatures in excess of T - Tg = 100 "C, the temperature dependence of the diffusion process becomes somewhat weaker than the diffusion of d-PS into PS. In comparing the temperature dependence of the diffusion of d-PS and d-PMMA, one finds that PMMA has a stronger dependence than PS. The d-PMMA chains diffuse into PMMA approximately 1 order of magnitude more slowly than d-PS into PS. These differences are, of course, related to differences in the friction coefficients of both homopolymers. The fact that the same temperature lependences are observed for D*HH/T and D*HC/T for Ah homopolymers is strong evidence that not only are the systems microphase separated at elevated temperatures but the homopolymers diffuse within the domains whose structures are identical with their own. These findings are consistent with the SAXS measurements on the copolymers and copolymer/ homopolymer mixtures discussed previously. These results have very important implications. Despite the fact that these microphase-separated domains are small, they exhibit many of the properties inherent in the bulk, since apart from the differences between the magnitudes of D*HC and D*HH, both diffusion coefficients appear to be controlled by the same parameters.
Conclusion The annealing of a block copolymer with a highly nonequilibrium morphology necessarily implies that the system will tend toward an equilibrium morphology where the microphase separated morphology is characterized by long-rrfnge order. Provided there is a difference between the surface tensions of the two components, the domain structure will orient parallel to the air/copolymer interface.3 These structural transformations could significantly affect the interdiffusion process as shown earlier.' However, on the basis of the observations in this study that D*Hc/T and D*HHIT exhibit the same temperature dependence and, as shown previously,' D*Hc varies as NH-2 if NH < Nc, these structural transformations must be slow in comparison to the diffusion time scales. This suggests that annealing times in excess of the diffusion time scales would be necessary to allow the copolymers to approach an equilibrium morphology. The results of this study clearly show that the microphase-separated morphology in PS/PMMA copolymers is retained a t elevated temperatures in excess of 200 "C. Both sets of measurements show that the microdomain morphology is also retained with the addition of a homopolymer. The homopolymer is found to be incorporated within the microdomain of the copolymer that is of identical structure with its own provided NH 5 NO It appears, as discussed earlier,' that the diffusion of PS or PMMA
homopolymers into the diblock PS/PMMA copolymers differs from that into homopolymers primarily because of the tortuosity of the microphase-separated domains and the domain orientation which characterize the copolymer structure. Though the annealing of the copolymer/homopolymer bilayer films for diffusion should effect the morphology, any reorganization process in the homopolymer/copolymer systems must be slow in comparison to the diffusion time scales. In copolymer systems where such structural changes are comparable to the diffusion time scales, the temperature dependence or molecular weight dependences seen in this system should not be observed.
Acknowledgment. Part of this work was performed a t Sandia National Laboratories under Contract DEAC04-76DP00789 supported by the United States Department of Energy and also a t the Stanford Synchrotron Radiation Laboratory, which is supported by the Department of Energy, Division of Basic Energy Sciences, and the National Institute of Health, Biotechnology Resource Program, Division of Research Resources. Registry No. PS, 9003-53-6; PMMA, 9011-14-7; (S)(MMA) (block copolymer), 106911-77-7. References and Notes Green, P. F.; Russell, T. P.; JBrBme, R.; Granville, M. Macromolecules, in press. Russell, T. P.; JgrBme, R., manuscript in preparation. Green, P. F.; Christensen, T.; Russell, T. P.; JBrBme, R., ac cepted for publication in Macromolecules. Wu, S. Polymer Interfaces and Adhesion; Marcel Dekker: New York, 1982. Henkee, C. S.;Thomas, N.; Fetters, L. J. J. Mater. Sci. 1988, 23, 1685.
Ouhadi, T.; Fayt, R.; JBrtime, R.; Teyssie, P. Polym. Commun. 1986,27,212;U.S. Patent 4461 847,1984. Mills, P. J.; Green, P. F.; Palmstrom, C. J.; Mayer, J. W.; Kramer, E. J. Appl. Phys. Lett. 1984,45,958. Stephenson, G. B. Ph.D. Thesis, Stanford University, 1982. Russell, T. P.; Koberstein, J. T. J. Polym. Sci., Phys. Ed. 1986, 23, 1109.
Leibler, L.Macromolecules 1980,13,1602. Wu, S. In Polymer Blends; Paul, D. R., Newman, S., Eds.; Academic: New York, 1978;Vol. 1. Whitmore, M. D.; Noolandi, J. Macromolecules 1985,18,2486. Doi, M.; Edwards, S. F. J. Chem. SOC.,Faraday Trans. 2 1978, 1809,1818.
Graessley, W. W. J.Polym. Sci., Polym. Phys. Ed. 1980,18,27. Ferry, J. D. Viscoelastic Properties of Polymers; 3rd ed.; Wiley: New York, 1980. Berry, G. C.; Fox, T. G. Adv. Polym. Sci. 1968,5,261. Green, P. F.; Kramer, E. J. J. Mater. Res. 1986,1, 202. Nemoto, N.; Landry, M. R.; Noh, I.; Yu, H. Polym. Commun. 1984,25,141.
Antonietti, M.; Coutandin, J.; Sillescu, H. Macromol. Chem.,
Rapid Commun. 1984,5,525.
Plazek, D. J.; Tan, V.; ORourke, V. M. Rheol. Acta 1974,13, 367.
Graessley, W. W.; Roovers, J. Macromolecules 1979,12,959.
