Defect-Mediated Block Copolymers

Defect-Mediated Rheology of Block Copolymers Steven D. Hudson, Karl R. Amundson,

Hong G. Jeon, and Steven D. Smith

discussion will focus on a recent studv 4 of the response of lamellar block copoly mers to compression and dilation of their lamellae.

Experimental Procedure In a stud\' of the response of a block copolv mer to layer compression and dilation, the materials used were polYstyrene/polY(methy 1 methacrylate) (PS/PMMA) svmmetric diblock copoly mers. The\' were svnthesized anionically under nit;ogen atmosphere, as described in a related article.' For copolymers hav ing a total molecular weight of 3] and 4] kg/mol, a lamellar microstructure was confirmed bv TEM. and the cor responding orde;- disorder-tra n si tion (ODT) temperatures, ]S2 and 296 C, re spectively, were measured by rheological methods. Vacuum compression molded disks (S-mm diameter, 1 mm thick) were analvzed using a Rheometries RMS sao torsion a 1 rheometer with parallel -plate geometf\', as described elsewhere.' Ultrathin sections (~70 nm) of various orientations were taken from different locations within the specimen, mounted on copper grids, stained with Ru04 va por, and examined bv TEM at 100 k\,4 Studies of the response to layer com pression and dilation were performed b\' applving normal strains to block copol\; mers with a well-aligned lamellar micro structure in the direction of the lamellar normal n. These experiments required a well-aligned microstructure. Alignment was achieved by large-amplitude shear from an initially unaligned state. The morphology of this initial state depends on sample historv. A rather coarse grained 'unoriented state was achieved by applying a dilational stress of more than 10% to a previously aligned mate rial. This process is described in more detail near the end of this article. A much more fine-grained texture can be produced b:' heating above the disorder ing temperature and then by cooling. To disorder the lower molecular-weight ma terial, the specimen was heated to 210 D C before cooling to the experimental tem perature of 173°C. For a specimen that has been held at ]73°C for 30 min the average grain size is approximately 200 nm, or approximatelY eight layer spacings. The density of defects found in the fine-grained sta rting state is ex tremely high, and their classification is difficult. For the higher molecular weight polymer, because of concern over degradation near the disordering tem perature, only the coarse-grained start ing state was used. D

Introduction Block copolymer melts with a near symmetric composition can microphase separate to form a lamellar morpholog\' where unfavorable monomeric inter actions are reduced .by an antiparallel layering of the polymer chains (see Fig ure 2, discussed later). The svmmetrv of such a block copolymer is th~ same a~ for small-molecule, smectic-A liquid crvs tals, which also exhibit (parallel or anti parallel) layering.! Because of their shared svmmetry, their quasistatic me chanical properties are of the same form. To lowest order, the energy of distortion of the lamellar pattern can be expressed as a sum of a compressional/dilational and a bend energy (see, for example, Reference 2): F = 1/2 B £' + 1/2 K (\' . n)2

director has been observed. c -!! In this report, we discuss defect structure and how the much more nscous nature of these polymeric layered materials in fluences the dIstribution and relative population of each defect tvpe. We also discuss how these defects can control material stress-relaxation behavior. The

(1)

where n is a unit vector normal to the layers, and £ and \' . n are the layer dila tional and bending strain, respectively. B and K are the corresponding moduli. These have been measured only recently for block copolymers. 34 The ratio of thes~ moduli yields a characteristic micro scopic le~gth: (2)

which is calculated to be a fraction of the layer spacing d 0'° Similarities are also found in the dv namic properties of polymeric and small molecule smectics. 6 These similarities are found at low strain rate and ampli tude where the rheological response is controlled by their similar layered struc tures and associated defects: During ei ther steady or dynamic shear, certain defect and domain motions are induced such that a steady-state alignment of the

Figure 1. TEM micrograph showing an isolated defect m a well-aligned specimen of polystyrene/poly(methyl methacrylate) (PS/PMMA). The shear direction is horizontal and the velocity-gradient direction is vertical. An elementary edge dislocation is evident in this field of view. While the PMMA microdomain is discontinuous for thiS defect. for other dislocations the PS microdomam is discontinuous. Copolymer asymmetry IS one factor that can bias the dislocation core structure. The defect density. estimated from a sampling of TEM Images. IS approximately 106 cmlcm 3 No pairing or clustering of dislocations was found.

v-/ 42

10

MRS BULLETIN/SEPTEMBER 1995

F

Defect-Mediated Rheology of Block Copolymers

Results and Discussion

k j

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y j

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3.

t

5

As the specimen was sheared, the tex ture aligned, and the number of defects was reduced. A very high degree of alignment was achieved after starting in the coarse-grained state and performing several thousand cycles of shearing. Shown in Figure 1 is a section from a higher molecular-weight copolymer that was sheared from the coarse-grained state. The specimen was subjected to sev eral thousand cycles of large-amplitude shearing at 200°C at a frequency of 5 rad/s and an amplitude of 125%. Fi nally, the specimen was held at tempera ture for 1 h before cooling slowly to room temperature, maintaining zero force on the specimen. Elementary edge disloca tions (Figure 1), in which a single lamella is discontinuous, are the most common remaining defects. The presence of these defects is not inconsistent with good alignment because the defects invoke only weak distortions in far field. These defects playa major role in the relaxation behavior of the well-aligned state 4 When a compressive strain is ap plied nom al to the layers, a large stress is observea initially. Although a homo polymer yields a similar molecular short time response, some of this response may also be associated with relaxation of composition fluctuations. After this mo lecular relaxation, a finite stress associ ated with layer compression remains. This residual-stress component can only be relieved by motion of the microstruc ture. The applied stress provides a free energy bias for molecular rearrangement near each edge dislocation, causing the defect to climb (translate in the layer plane) and the junction-point density at the lamellar interface to equilibrate. At low stress levels, the velocitv of the de fect is linear with stress, v = p. (7", and the mobility is proportional to the diffusion coefficient l2 0 perpendicular to the layers:

bD

fJ..=-

nkT

(3)

where n is the number of molecules in a volume b J , and b is the magnitude of the Burgers vector. The mobility therefore has the appropriate scaling with defect size, that is, -lib'. Using this model, the stress-relaxation rate is also proportional to the stress so that the stress is predicted to decay exponentially, as observed ex perimentally4 The experimental time constant is on the order of 100 s, being several orders of magnitude longer than molecular time scales. Taking into


Figure 2. Schematic representation of the effect of applied shear on a screw dislocation in a diblock copolymer. The random-coil molecules are represented by straight lines; gray and black ends represent, respectively, the PMMA and PS segments. (a) A section of the core of a screw dislocation at rest, around which the microdomain interface adopts, for example, a right-handed helical configuration. (b) As the specimen is sheared, the layers slide past one another. Since the molecules are not completely relaxed, the defect itself is also sheared. Compression and extension of chains in the core is evident. Given the right-handed sense of this defect, shearing will cause the defect line to rotate so that the upper portion of the defect rotates toward the reader.

account the measurement of the diffu sion coefficient lJ and the defect density, the stress relaxation is consistent with a mechanism of dislocation climb: An interesting question is whether de fects could be created by the applied stress. Our small-strain experiments suggest that they are not created in sig nificant number. If defects were to be created under stress, more defects would be present under high levels of stress, and the relaxation would be nonexpo nential. However, for applied strains ranging from 0.5 to 4.2% at 220°C, the re laxation remained exponential and the characteristic time remained the same, at 120 s.

To evaluate the strain at which defect generation is possible, let us consider the energy required for creating a defect when a well-aligned microstructure is compressed along its director. Excluding heterogeneous nucleation, the lowest

energy defects are the ones of smallest extent, that is, the ones forming loops. The energy of a dislocation loop is 14 Floop

b i+r-KIn r [ -I b I ] + Fe ) K I2rra ( A 2 2d o . Klbl = 2rra-(4) =

A

where a is the radius, b is the Burgers vector of the dislocation loop whose magnitude may be some integer multiple of do-the undistorted layer spacing, and Fe is the core energy of the disloca tion. When the loop is created in an en vironment where the lamellae are com pressed or dilated, the strain energy is changed. For example, if the defect in serts extra layers into the specimen, the compressive strain energy above and be low the loop is increased. On the other hand, if the Burgers vector is negative,

43


that is, if it forms an effective pore in the lamellae, compressive strain energy will be lowered. Consider a tube defined by translation of the defect loop along the director. The reduction in stress can be estimated by the approximation that the stress is reduced within the tube by an amount as if bid 0 lavers are removed from the sample, and 'that the stress out side the region is unchanged. The change in stress density within the tube is

(5) where e is the applied compressive strain before the presence of the defect. Note that the change in strain energy is nega tive when a dislocation adds lavers (b > 0) under tension (e > 0) or whe'n it causes perforations under compression. The sum of these two energies gives the total energy of creation of a dislocation loop in a strain field: Ftotal

=

27TKlbla/A -7TeBba 2

(6)

The form of this equation is of a nucle ation process in two dimensions where the strain energy provides the energy analogous to bulk energy. There is a critical radius a* beyond which the loop will grow and below which the loop will shrink: a* = Allel

(7)

Figure 3. TEM micrograph of a specimen of the lower molecular-weight material after partial alignment. The applied shearing is in the same direction as in Figures 1 and 2. Seen in the center of this image is a grain in which the lamellae are vertical. A narrow wall separates this grain from the material outside where the lamellae are generally horizontal. Grains of intermediate orientation are not frequently observed.

whenever the product "be" is positive. The activation energy for nucleation is Ftot.l(a')

=

7TKb/ e.

(8)

Since the product Kb f?r elementary edge dislocations (_lO- 'j erg) is approxi mately equal to kT, the nucleation of de fects is negligible until the strain reaches the order of unity. A few percent strain, therefore, is insufficient to create stable defects that can contribute to long-time stress relaxation. However, even a low level of strain energy can modify the energy and therefore the population of subcritical island/pore concentration fluctuations. How this shift in popula tion can modify the apparent layer mod ulus is a question to be addressed in the future. Finally, during the large-strain alignment process, dislocation nucleation may be important because misaligned regions may experience sufficiently large compressive strains. Edge dislocations are only one of the several types of defects present in smec tic systems to yet these are by far the most common in our well-aligned specimens.

44

This is surprising since elementary edge dislocations are rare in typical smectic fluids. The defect most common in well aligned smectics is the screw disloca tion. 16 A screw dislocation can be likened to a spiral staircase where the lamellae are arranged like floors of a building. Since the screw dislocation has no long range distortion, the defect would only be observed if it were contained within the section film thickness. The screw dislocation would appear as several stag gered lamellae joined by a less intense zigzag pattern.l~ These have not been ob served in our well-aligned specimens; the discontinuous lamella can be identi fied and the continuitv of all other lamellae is clear (Figure i). It should be noted that, if the section plane is inclined with respect to the defect line, the image of a screw dislocation will appear edge like. However, unless the defect has sub stantial edge character, the zigzag will extend over at least a few lamellae. In spite of differences in observability, it is significant that, after examining several

sections, hundreds of edge defects and no screw defects have been observed. We therefore conclude that edge defects are more prevalent than screw defects in our well-aligned specimens and that the shearing process must limit screw and favor edge dislocations. At first review, it seems unlikelv that shearing limits screw and favors' edge dislocations because the shear stress is perpendicular to the Burgers vector, and no force on either defect is expected. Ix However, the viscoelastic nature of these copolymer chains is important. When shearing at rates that are fast compared to the molecular relaxation time, the deformation becomes non-affine, as in dicated by the motion of the screw dislo cation relative to the background flow. At finite rates, some tilting and stretching of the defect remains (Figure 2), producing some layer compression and extension in the defect core. Given the helical nature of the dislocation, compression and ten sion will be present on opposite sides of the core, and the dislocation will rotate



out of plane in a preferred direction, thus converting it to edge character. A recent report discusses conversion of a screw dislocation to edge character through the application of compressive stress normal to the lavers.]' Ha\'i~g explained the existence of edge dislocations, we now explain why elementan' dislocations of the same sign do not aggregate to form a compound dislocation, comprising disclinations. Clustering is the normal case for smec tics because the overall enerav is reb, duced, owing to the logarithmic term in Equation 4. These disclinations are nor mally found in special focal conic shapes. However, it has been pointed out that, in the presence of an external field, defects can onlv cluster within distances smaller than a characteristic length ~ imposed by the applied field21121 It turns out that this characteristic length during shear is eas ily made to be equal to or Jess than a single lamellar thickness d". At the center of compound dislocations, lamellae are oriented perpendicular to the direction favored by the applied field. These lamel lae will experience compression during shear. The characteristic length imposed by the shear field is

Figure 4. TEM micrograph of a specimen that was slowiy extended while bemg cooled. The total tensile strain was approximately 15%. As the lamellar micro structure buckled. tilt walls formed parallel to the tensile direction (vertical). The horizontal directIOn is the neutral direction of the previous shear ailgnment process.

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46

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