Chemical composition effects on the fracture of polystyrene-block-poly(methyl methacrylate)block copolymers

Materials

PS-b-PMMA was synthesized by anionic polymerization. Styrene and methyl methacrylate were added sequentially after the initiation of the polymer with sec-butyl lithium in tetrahydrofuran (THF) at −78 °C. To reduce the reactivity of the polystyryl anion in THF, diphenyl ethylene was added before the addition of methyl methacrylate. Degassed 1-butanol was used to terminate the reaction.21 Two PS-b-PMMAs were synthesized and fractionated by liquid chromatography, and their average molecular weights and chemical compositions are summarized in Table 1.

Fractionation of PS-b-PMMA by the Chemical Composition Difference

PS-b-PMMA solution samples were prepared in a solvent mixture of THF and iso-octane (IO) with 55 vol % THF at a concentration of 3% (w/v). The solution was added to a bare silica gel column (60-Å pore size; Aldrich) to selectively adsorb PS-b-PMMA over PS homopolymer precursors. The adsorbed PS-b-PMMA on the silica surface was separated into three fractions (F1, F2, and F3 in Table 1) by the following procedure. First, fraction F1 was obtained by the rinsing of the PS-b-PMMA-adsorbed silica column with a mixed THF/IO solvent with 58 vol % THF. Then, F2 and F3 were subsequently fractionated via rinsing with 61 and 64 vol % THF, respectively. The molecular weight distributions of the fractionated PS-b-PMMAs were characterized by size exclusion chromatography (SEC) with a LabAlliance model 500 ultraviolet–visible detector. ¹H NMR (Varian 500 Unity) was used to characterize the average chemical composition of PMMA in the mother and fractionated PS-b-PMMA samples.

Craze Characterization and Sample Preparation

To quantify the crazing process for polymer thin films, the copper-grid technique22 was employed. Thin films of PS-b-PMMA (∼0.5 μm thick) were spin-cast onto a glass substrate at 1000 rpm from 5.0 wt % toluene and floated on a water surface. Then, the polymer film was picked up by a copper grid, which was previously coated with the same PS-b-PMMA BCP. Finally, the sample polymer film and copper grid were bonded by a short exposure (several seconds) to the solvent toluene and dried at room temperature for 20 h. Figure 4 (shown later) presents a schematic diagram representing uniaxial tensile deformation. By taking advantage of the plastic deformation of the copper grid (annealed at 600 °C for 10 min in vacuo), this technique allowed us to examine many samples in each grid for the statistical analysis of the fracture behavior under uniaxial strains. At strain regular intervals, the strained films on the copper grid were examined with reflective optical microscopy (OM) and atomic force microscopy (AFM). For AFM, a Digital Instrument Multimode atomic force microscope was used in the tapping mode. Transmission electron microscopy (TEM) was also performed to characterize the craze formation and fibril breakdown with a JEOL CM-12 operating at an accelerating voltage of 120 kV.

Chemical Composition Distribution in the BCPs

Because of the polydispersity of each block, as-synthesized AB diblock copolymers should exist as mixtures of polymer chains with different chemical compositions. Experimentally, Tanaka et al.23 showed an approximately 30 mol % compositional distribution of PS-b-PMMA BCP with preparative-scale thin-layer chromatography. Podesva et al.24 also showed divergence in the distribution of chemical heterogeneity in PS-b-PI BCPs synthesized by a modified anionic polymerization procedure. For an AB diblock copolymer, when B is the compositionally minor block, the maximum and minimum chemical compositions in the as-synthesized AB diblock copolymers due to the polydispersity of the molecular weights can be estimated by the calculation of the compositions of a chain with the shortest A blocks and longest B blocks and then a chain with the longest A blocks and shortest B blocks for a given polydispersity index (PDI) of A and B. Figure 2 shows the calculated maximum and minimum chemical compositions (molar fractions) of the B block in AB diblock copolymers containing 700 A units and 300 B units on average (A₇₀₀–B₃₀₀) at different PDIs of A and B. For example, when the PDI of A₇₀₀ and B₃₀₀ is 1.05, the actual number of repeating units in A and B is 700 ± 50 and 300 ± 35, respectively. Therefore, the maximum and minimum molar fractions of B have been calculated to be 335/(335 + 650) = 0.26 and 265/(265 + 750) = 0.34, respectively. This suggests that the polydispersity of each block will significantly contribute to the broadness of the chemical composition distribution in the as-synthesized BCPs. The polydispersity of each block alone at PDI = 1.1, for example, will produce about a 10 mol % compositional difference in A₇₀₀–B₃₀₀ diblock copolymers.

Table 1 summarizes the average chemical compositions of three PS-b-PMMA BCPs fractionated from as-synthesized mother PS-b-PMMAs with liquid chromatography. PS-b-PMMA BCP1 [weight-average molecular weight (M_w) = 94,000 g/mol, weight-average molecular weight/number-average molecular weight (M_w/M_n) = 1.09, and molar fraction of PMMA (x_PMMA) = 0.35] was separated into three fractions: x_PMMA = 0.24, x_PMMA = 0.31, and x_PMMA = 0.46. Sample BCP2 (M_w = 65,000 g/mol, M_w/M_n = 1.06, and x_PMMA = 0.28) was fractionated into three samples: x_PMMA = 0.16, x_PMMA = 0.30, and x_PMMA = 0.35. Therefore, we were able to experimentally fractionate PS-b-PMMA BCP samples, with the PMMA composition differing by about 20 mol %. In addition, the chemical compositional distribution in each fraction must be narrower than that in the mother BCP samples because the liquid chromatography separation was achieved in terms of the chemical composition difference. Although the chemical compositions of the fractionated BCPs are significantly different, SEC profiles (Fig. 3) suggest that the molecular weight distribution of each fraction remains relatively unchanged from that of the mother BCP samples. Therefore, by employing a sample set of a BCP mother, F1, F2, and F3, we can study the effects of the chemical composition difference and broadness on the fracture behavior of PS-b-PMMA while maintaining a similar average molecular weight for each BCP sample.

Fracture Studies of the PS-b-PMMA BCPs

The fracture behavior of BCPs is generally affected not only by molecular factors, such as the homopolymer molecular weight,25 copolymer composition,26 and chain architecture,12, 27 but also by processing parameters, such as the shear alignment13 and thermal aging.14 In particular, the mechanical behavior of BCPs with anisotropic ordered structures is further complicated13, 28 because it depends on the extent of long-range ordering and the direction of macroscopic deformation. Because of such morphological complexity, it is difficult to understand the fracture properties of BCPs in terms of their molecular factors. To avoid such morphological complications originating from processing conditions, we have deliberately limited the ordering of BCPs to a short range by spin-coating BCP films without further thermal annealing.

The copper-grid technique, developed by Lauterwasser and Kramer,22 has been employed to determine the strains for developing crazes or catastrophic failure. Figure 4(b) shows reflective OM images of 0.5-μm-thick PS-b-PMMA BCP films bonded onto copper grids as a function of the applied tensile strain. As shown in Figure 4(c), the development of crazes is identified as dark lines perpendicular to the extension direction with reflective OM. When the sample films are stretched further after the development of crazes, a shadow in the reflective OM images starts to appear, and this is attributed to the catastrophic failures of the film [Fig. 4(d)].22

As shown in Figure 5, both AFM and TEM support the formation of fibril-like structures in the craze region. However, the typical width of the crazed region in BCP1 films does not exceed 0.5 μm, indicating that the films are quite brittle even at M_w = 94,000 g/mol. When BCP2 films (M_w = 65,000 g/mol) were examined, the samples were so brittle that fibril breakdown occurred immediately after the formation of crazes. Therefore, craze-depth characterization of BCP2 films could not be performed by AFM. Because each copper grid contained many polymer films bonded to the copper-grid frame, many sample films were examined at once for the statistical analysis of craze development or fibril breakdown at various strains from a single copper-grid extension experiment. Specifically, the fractions of crazed or failed films were statistically analyzed and plotted as a function of the applied strains (Fig. 6).

Chemical Composition Effects on Crazeand Fibril Breakdown

The median strains for crazing and fibril breakdown were determined when the fraction of square films exhibiting crazing or fibril breakdown reached 0.5. Figure 7(a,b) shows the median strains of crazing and fibril breakdown from several copper-grid experiments for a set of mother and fractionated samples of BCP1 and BCP2, respectively. These sample sets are ideal for us to understand the effects of the average chemical composition difference on the fracture behaviors while keeping the same average molecular weight within each set. As the chemical composition (x_PMMA) increases from 0.24 to 0.46 in a series of BCP1 fractionated samples (M_w = 94,000 g/mol), the average median strain for crazing increases from 1 to 2.6%. Such chemical composition dependence can be similarly observed for the fibril breakdown, which increases from 1.1 to 3.3% in the BCP1 fractionated samples. The BCP1 mother sample (x_PMMA = 0.35) exhibits median strains for crazing and fibril breakdown at 2.0 and 3.0%, respectively. This suggests that the average chemical composition plays a major role in determining the median strains for crazing and fibril breakdown, regardless of whether the mother or fractionated BCP1 samples (i.e., whether compositionally broader mother or narrower fractionated samples) are used.

The chemical composition broadness, however, seems to affect the reproducibility of the fraction–strain curves from the repeated copper-grid experiments. We took advantage of the statistical analysis nature of the copper-grid experiment to characterize the fracture behavior, and the fractional curves in Figure 6 show the statistical development of crazes as a function of the applied strain for the BCP1 mother and BCP1 F2 fraction. From 14 copper-grid experiments of the BCP1 mother sample [x_PMMA = 0.35; Fig. 6(a)], the standard deviations of the median strains for crazing and fibril breakdown are 1 and 1.5%, respectively. On the contrary, the fractionated F2 sample (x_PMMA = 0.31), which has a chemical composition and molecular weight similar to those of the mother sample, exhibits very reproducible median strain values for crazing and fibril-breakdown behavior [Fig. 6(b)]. The standard deviations of the median strains for crazing and fibril breakdown for F2 from several copper-grid experiments are 0.01 and 0.17%, respectively.

Figure 7(b) shows the median strains for crazing and fibril breakdown in a series of BCP2 mother and fractionated samples (M_w = 65,000 g/mol) that have a lower molecular weight than the BCP1 samples (M_w = 94,000 g/mol). Unlike the BCP1 samples, these BCP2 samples have shown little chemical composition dependence on their fracture behaviors. Because the molecular weight of BCP2 is very low, all the samples are already quite brittle, exhibiting fibril breakdown as soon as the craze occurs at a strain of about 1%. It is important to understand why the BCP1 samples show a composition-dependent fracture behavior, whereas the fracture behaviors of the BCP2 samples display little dependence on the chemical composition. Such a contrasting difference in the fracture behaviors of the BCP1 and BCP2 samples should be attributed to the molecular weight differences, which eventually affect chain entanglements in BCPs. Specifically, we have found that the molecular weights of less entangled PMMA domains in the PS-b-PMMA samples play a crucial role in determining the fracture behavior of the BCPs.

As the minor PMMA molecular weight increases for a given molecular weight of a BCP, not only is there an increase in the chemical composition (x_PMMA), but there is also an enhancement of the entanglement density within the PMMA domains. Because the molecular weight between entanglements (M_e)29, 30 is 17,000 for PS and 13,000 g/mol for PMMA, M_n/M_e is lower for the PMMA block, except for BCP1 F3, in our study (see Table 1). From the molecular weight dependence on the fracture behaviors of monodisperse PS, Yang et al.31, 32 have shown that there exists a molecular weight window of M_n/M_e (2 ≤ M_n/M_e ≤12) in which the fracture properties strongly depend on the molecular weight. In the case of higher molecular weight BCP1 samples, M_n/M_e of the PMMA block changes from 1.7 to 3.3 [inset of Fig. 7(a)] when x_PMMA increases from 0.24 to 0.46. Therefore, the observed chemical composition dependence on the fracture properties in the BCP1 samples is attributed to the enhancement of M_n/M_e in the minor PMMA domains, which are located within the window of 2 ≤ M_n/M_e ≤12. On the contrary, M_n/M_e of the PMMA block for lower molecular weight BCP2 samples varies from 0.8 to 1.7 [inset of Fig. 7(b)]. Because these ratios are located outside the window, the fracture properties of the PMMA domains in BCP2 do not depend on the molecular weight change of the PMMA blocks.