Fluorescence labeling enables component- and location-specific measurements of the glass transition temperature (Tg) in complex polymer systems. Here we characterize the Tg of fluorescently labeled poly(methyl methacrylate) homopolymers (PMMA-py) blended at low concentrations into an unlabeled lamellar poly(n-butyl methacrylate-b-methyl methacrylate) diblock copolymer (PBMA-PMMA). In this system, the PMMA-py homopolymer is sequestered within the PMMA domains of the diblock copolymer and subject to soft confinement by the domains of the lower-Tg PBMA block, which lowers the homopolymer Tg by ∼5 K beyond the contribution of segmental mixing. In contrast to the PMMA block in the diblock copolymer, the PMMA-py homopolymer is not covalently bound to the interdomain interface. A comparison of Tg for the homopolymers in the blends to Tg for diblock copolymers with equivalent labeled segment density profiles reveals that the homopolymer's Tg is consistently ∼10 K higher than for diblock segments at the same location within the domain structure, highlighting the dominant contribution of a covalent bond across the interface to the perturbation of the chain dynamics in the block copolymer.
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TY - JOUR
T1 - Role of Chain Connectivity across an Interface on the Dynamics of a Nanostructured Block Copolymer
AU - Christie, Dane
AU - Register, Richard A.
AU - Priestley, Rodney D.
N1 - Funding Information: Christie Dane Register Richard A. * Priestley Rodney D. † Department of Chemical and Biological Engineering, Princeton Institute for the Science and Technology of Materials, Princeton University , Princeton, New Jersey 08544, USA * Corresponding author. firstname.lastname@example.org † Corresponding author. email@example.com 12 December 2018 14 December 2018 121 24 247801 20 September 2018 © 2018 American Physical Society 2018 American Physical Society Fluorescence labeling enables component- and location-specific measurements of the glass transition temperature ( T g ) in complex polymer systems. Here we characterize the T g of fluorescently labeled poly(methyl methacrylate) homopolymers (PMMA-py) blended at low concentrations into an unlabeled lamellar poly( n -butyl methacrylate- b -methyl methacrylate) diblock copolymer (PBMA-PMMA). In this system, the PMMA-py homopolymer is sequestered within the PMMA domains of the diblock copolymer and subject to soft confinement by the domains of the lower- T g PBMA block, which lowers the homopolymer T g by ∼ 5 K beyond the contribution of segmental mixing. In contrast to the PMMA block in the diblock copolymer, the PMMA-py homopolymer is not covalently bound to the interdomain interface. A comparison of T g for the homopolymers in the blends to T g for diblock copolymers with equivalent labeled segment density profiles reveals that the homopolymer’s T g is consistently ∼ 10 K higher than for diblock segments at the same location within the domain structure, highlighting the dominant contribution of a covalent bond across the interface to the perturbation of the chain dynamics in the block copolymer. National Science Foundation 10.13039/100000001 DMR-1420541 Air Force Office of Scientific Research 10.13039/100000181 FA9550-12-1-0223 The presence of chemical heterogeneity in a single polymer chain underpins the scientific and technological relevance of diblock copolymers. In sufficiently long diblock copolymer chains, wherein the interactions between dissimilar ( A and B ) segments are repulsive, the dissimilar blocks separate from each other over the length scale of the polymer chain [1,2] , yielding periodic domains of order 10–100 nm enriched in one segment type, divided by internal interfaces. Local mixing between the two blocks still occurs, such that each segment type has a concentration profile that varies continuously across the domain period, from being rich in A to rich in B . Nanostructured diblock copolymers present excellent systems to investigate the relationships between nanoscale confinement, segmental mixing, the confining interfaces, and the glass transition temperature ( T g ). The parameters governing the domain T g —namely, the bulk T g of the A and B homopolymers, the confinement length scale, the degree of segmental mixing, and the interfacial thickness—can be systematically varied by choosing the block chemistries and total chain length. Blends of block copolymers and their constituent homopolymers offer an experimental system wherein polymer chains exist under similar confinement conditions as the neat diblock copolymer, with the difference being the lack of attachment of the homopolymer to the interface [3–6] . Provided that a characterization tool which enables component-specific measurements of T g is utilized, the effect of chain connectivity across the domain interface can be unambiguously quantified. Even in miscible polymer blends, the dynamics of a component cannot be described by the blend-averaged value if the components are weakly interacting and have a large dynamic contrast, i.e., a large difference in bulk T g [7–11] . The dynamics of a component in the blend can be understood through the phenomenon of self-concentration described by Lodge and McLeish  : In the neighborhood of an A segment, within a volume defined approximately by the cube of a Kuhn length, the segmental concentration of A is elevated relative to its average value in the blend due to chain connectivity, biasing the individual component dynamics towards those of the pure component [13,14] . In nanostructured diblock copolymers with a large T g contrast, there are, thus, contributions to dynamic heterogeneity which are operative over different length scales [15,16] . At the length scale of a Kuhn segment, local mixing between the blocks acts to perturb a component’s T g in a similar manner to miscible polymer blends. At the length scale of the domain period ( d ), the high- and low- T g blocks exist under soft and hard confinement conditions, respectively. Under soft confinement, a polymer’s T g can be depressed relative to bulk [17,18] . Previously  , we characterized the component dynamics of a nanostructured block copolymer with a large T g contrast via the incorporation of a fluorescent monomer at selected positions along the chain interrogated via temperature-dependent fluorescence spectroscopy. In this Letter, we advance the understanding of soft confinement on T g by quantifying the depression attributable to the connectivity of the block across the domain interface. The experimental system consists of blends of a lamellar poly( n -butyl methacrylate- b -methyl methacrylate) diblock copolymer (PBMA-PMMA) with 2 vol % of a pyrene-labeled poly(methyl methacrylate) homopolymer (PMMA-py). The homopolymers span a molecular weight ( M ) range of 8.4 – 69 kg / mol , each with a labeling level of < 0.5 mol % . The T g contrast in this system is 96 K; PMMA is the high- T g component. Comparing the cases where the fluorescent label resides on the PMMA homopolymer vs on the PMMA block of the diblock copolymer reveals that attachment of the PMMA block to the PBMA block (and thereby to the domain interface) produces the principal reduction in T g —larger than that resulting from segmental mixing or from confining the homopolymer within the block copolymer domain structure. The structure of the blend of a dilute PMMA-py homopolymer with a symmetric (volume fraction ϕ PMMA = ϕ PBMA = 0.5 ) lamellar PBMA-PMMA diblock copolymer is schematically shown in the inset of Fig. 1(a) . The blend is defined in terms of the segregation strength of the diblock copolymer ( χ N , where χ represents the Flory interaction parameter and N the degree of polymerization of the diblock), the volume fraction of a component in the diblock ( ϕ PMMA , BCP ), the volume fraction of the homopolymer in the blend ( ϕ h ), and the molecular weight of the homopolymer relative to that of the diblock copolymer ( α = M h / M BCP )  . For the diblock employed here, M BCP = 47 kg / mol , the domain period d = 27 nm , and χ N / ( χ N ) ODT ≈ 2.4  , where ( χ N ) ODT is the segregation strength at the order-disorder transition. The component distributions are quantitatively calculated here via self-consistent field theory (SCFT)  using open-source software developed by Arora et al.  . The green curve in Fig. 1(a) shows the composition profile of PMMA segments in the neat diblock over one domain period starting in the center of the PBMA-rich domain ( x / d = 0 or 1). For blends at ϕ h = 0.02 , the value of d is predicted by SCFT to increase by a maximum of 1.5% at α = 1.48 , relative to the neat diblock, a negligible increase in agreement with experiments [22,23] . The interfacial thickness represented by vertical dashed lines in Fig. 1 was previously determined using small angle x-ray scattering  on the neat diblock copolymer and is predicted by SCFT to be essentially unaffected by blending with 2 vol % homopolymer. At the α values employed in this work, the PMMA homopolymer strongly partitions into the PMMA-rich domains of the diblock; with increasing α , the homopolymer is more strongly localized in the center of the PMMA domain. These features are quantitatively captured in the SCFT results shown in Fig. 1(b) . 1 10.1103/PhysRevLett.121.247801.f1 FIG. 1. (a) Local volume fraction (segment density) profiles of PMMA segments belonging to the diblock copolymer ( ϕ PMMA , BCP ) for three different cases, all with the diblock χ N / ( χ N ) ODT = 2.4 : neat diblock (green), and ϕ h = 0.02 blends with α = 0.18 (black) and α = 1.48 (red). Dashed vertical lines demarcate the width of the interface. Inset: Schematic of a self-assembled lamellar blend of a PBMA-PMMA diblock copolymer and a dilute PMMA-py homopolymer, where the label (yellow) is randomly located along the homopolymer chain. (b) Corresponding segment density profiles for PMMA segments belonging to the PMMA-py homopolymer ( ϕ PMMA , h ) for the same two blends as in (a). The T g of the PMMA-py homopolymers of varying M was characterized using temperature-dependent fluorescence spectroscopy according to procedures described previously [19,24] ; details are provided in the Supplemental Material  . In brief, the total fluorescence emission intensity from the pyrene labels was measured upon cooling from the melt; a decrease in the slope of the intensity vs temperature upon transitioning from the melt to the glass signifies T g . Figure 2 shows the determination of T g for the PMMA-py homopolymer with M h = 8.4 kg / mol ( α = 0.18 ), both neat (filled symbols) and blended into the diblock at ϕ h = 0.02 (open symbols); the homopolymer T g in the blend is depressed by 12 K relative to its bulk value. A similar trend is observed at all values of α as shown in the inset of Fig. 2 ; the four homopolymers in bulk show an average T g = 385 K , weakly increasing with M h  , while the same homopolymers show an average T g = 373 K in the dilute blends. However, T g for the PMMA blocks in the neat diblock is lower still: For a PBMA-PMMA diblock selectively labeled at the PMMA chain end, which shows a labeled segment density profile comparable to the homopolymer profiles in Fig. 1(b) , T g = 364 K  . Thus, Fig. 2 conveys the surprising result that the PMMA homopolymer dynamics in the blend appear to be slower ( T g ≈ 373 K ) than those of neighboring PMMA segments from the diblock chains ( T g ≈ 364 K ), which are attached to the PBMA-PMMA domain interface. 2 10.1103/PhysRevLett.121.247801.f2 FIG. 2. Temperature dependence of the integrated fluorescence emission intensity and the corresponding linear fits in the glassy and rubbery regions of a PMMA-py homopolymer ( M h = 8.4 kg / mol ) either in bulk (solid symbols) or blended at a 2% volume fraction into the unlabeled PBMA-PMMA diblock copolymer. Integrated intensities are normalized to unity at the highest temperature and shifted vertically in the figure for clarity. Inset: Local T g vs α for PMMA-py homopolymers in the bulk (open circles, data from Ref.  ) or blended into an unlabeled diblock copolymer (blue squares); error bars indicate ± 1 standard deviation. The dashed black horizontal line is the bulk T g (385 K) of the PMMA homopolymer at M h ≅ 20 kg / mol . The dashed red horizontal line is the T g (364 K) of a neat PBMA-PMMA diblock copolymer labeled at the chain end  . To properly gauge the impact of block connectivity across the domain interface, three factors which can influence T g need to be considered: (1) segmental mixing (i.e., plasticization of PMMA segments by PBMA segments, when ϕ PMMA < 1 locally), (2) depression of the PMMA T g through soft confinement  by the PBMA domains analogous to T g depression by a free surface [17,30] , and (3) the influence of block connectivity, i.e., whether the PMMA segments being probed are covalently bound to a PBMA block (and, therefore, to the domain interface) or not. In the neat diblock case examined previously  , factors 2 and 3 are inextricably combined, since all PMMA blocks are connected to PBMA blocks. However, in the present work, comparison of the neat diblock and dilute homopolymer blend cases allows these effects to be separated. The first of these three factors, segmental mixing, can be captured through the well-known Fox equation  , Eq. (1) , while also accounting for the local self-concentration  of PMMA segments due to chain connectivity through Eq. (2) : 1 T g ( ϕ eff , PMMA ) = ϕ eff , PMMA T g , PMMA + 1 − ϕ eff , PMMA T g , PBMA , (1) ϕ eff , PMMA = ϕ s + ( 1 − ϕ s ) ϕ PMMA . (2) In Eq. (2) , ϕ PMMA is the local volume fraction of PMMA segments at any point within the domain structure, while ϕ s is the self-concentration of PMMA segments. Previous measurements  have shown that Eqs. (1) and (2) satisfactorily describe the T g in disordered PBMA-PMMA diblocks, wherein the two blocks are intimately mixed, with ϕ s = 0.38 . The expected T g , if segmental mixing were the only effect operative, is then calculated by linearly weighting the local T g calculated from Eqs. (1) and (2) by the labeled segment distribution obtained from SCFT (see Supplemental Material  Fig. S4 and Ref.  ). The T g so calculated for the diblock labeled at the PMMA end is 378 K  , only ∼ 7 K below the T g of bulk PMMA and much higher than the observed T g = 364 K . Thus, as previously noted  , segmental mixing makes only a modest contribution to the PMMA T g depression observed in the neat diblock; the dominant factors are soft confinement and/or block connectivity, but these two cannot be separated in the neat diblock. To isolate the effect of block connectivity, the T g values measured on the dilute blends in Fig. 2 should be compared with the T g measured on a selectively labeled neat diblock having exactly the same labeled segment density distribution; in this way, both segmental mixing and the effect of soft confinement are exactly matched between the two cases, since the labeled segments are in precisely the same distribution of environments and at the same distribution of distances from the PBMA-PMMA domain interface. Figure 3(a) shows the SCFT-calculated labeled segment density distributions for two different label positions in the neat diblock: 20% and 72% of the distance along the PMMA block ( J + 20 and J + 72 ) from the block junction ( J ). For comparison, the labeled segment density distributions for the α = 0.29 and α = 0.73 blends are shown as dashed curves. Amongst all possible label positions in the diblock, J + 72 corresponds to the narrowest calculated segment density distribution (most strongly localized in the PMMA domain center); for label positions beyond 72% of the PMMA block length, the additional conformational freedom associated with the chain end actually broadens the distribution  . Experimentally, a PBMA-PMMA diblock [ ( χ N ) / ( χ N ) ODT ≈ 2.4 ] labeled at J + 72 shows T g = 364 ± 3 K (1 standard deviation) by fluorimetry [see Supplemental Material  Fig. S2(a)]. The α = 0.29 blend has a similar labeled segment density distribution to J + 72 but an experimental T g = 372 ± 4 K . This difference reflects the effect of block connectivity: an 8 K ( ± 5 K ) depression of the PMMA T g by tethering it to a PBMA block (in the diblock) vs having it “float free” within the PMMA domain (in the blend). 3 10.1103/PhysRevLett.121.247801.f3 FIG. 3. (a) Segment density profiles across one domain period for two label positions in the diblock copolymer (solid lines) or labeled homopolymer segments in the ϕ h = 0.02 blend at two values of α (dashed lines) across one domain period. All profiles are normalized to equal area. (b) Normalized segment density profiles for the four labeled homopolymers (varying α ), all in blends at ϕ h = 0.02 (solid curves). The dashed curve superimposed on each solid curve represents the best-fit weighted sum of the labeled segment density profiles in the neat diblock [ χ N / ( χ N ) ODT = 2.4 ] corresponding to six discrete label positions along the PMMA block. To make a similar comparison for the other values of α , the labeled segment density distributions for six different label positions in the neat diblock [ J + 20 and J + 72 shown in Fig. 3(a) plus J , J + 5 , J + 50 , and J + 100 (end labeled) from Ref.  ] were summed, with weights adjusted to match the sum to the homopolymer’s segment density distribution in the blend. Applying these same weights to the measured values of T g for each selectively labeled diblock was previously demonstrated to satisfactorily reproduce the T g for PBMA-PMMA diblocks where the label was uniformly distributed along the PMMA block  . For the α = 0.73 and α = 1.48 cases, since the homopolymer segment density distribution is narrower than the narrowest block copolymer distribution ( J + 72 ), the J + 20 profile—which has most of its segments just beyond the interface [see Fig. 3(a) ]—needed to be accorded a negative weight (see Supplemental Material  for details). Figure 3(b) compares the homopolymer segment densities with the best-fit weighted sums of the labeled diblock segment densities; an excellent match is achieved in all cases. Figure 4 captures and separates the three aforementioned effects quantitatively. Each blend is characterized on the abscissa by the average distance ( z ) of the labeled segments from the nearest interface [at x / d = 0.25 or 0.75 in Fig. 3(b) ]. As α increases, the homopolymer segments become progressively more localized in the domain center, so z increases monotonically with α . The experimental T g values for the labeled homopolymers in the blends are shown as the blue squares. The black (filled) circles represent the T g values expected simply from segmental mixing [effect 1 calculated locally according to Eqs. (1) and (2) and averaged across the homopolymer’s segment density profile]. Segmental mixing produces a modest 4–9 K depression in T g relative to the value for bulk PMMA (385 K), with the magnitude of the depression decreasing with increasing z (increasing localization of the homopolymer in the PMMA-rich domain center). The white (open) triangles represent the T g values calculated by applying the weights obtained from the summation in Fig. 3(b) to the experimentally measured T g values  for the selectively labeled diblocks; these calculated values should incorporate the contributions from all three effects. Recall that the J + 72 labeled diblock showed T g = 364 K ; the open symbols in Fig. 4 naturally bracket this value. At low α , where the homopolymer segment density distribution is broader than J + 72 [Fig. 3(a) ], T g < 364 K for the sum of the block copolymer segment density distributions because of both enhanced segmental mixing (more labeled PMMA segments in interfacial region) and stronger soft confinement (smaller z , labeled PMMA segments closer on average to PBMA domain); conversely, at high α , both segmental mixing and the proximity to the interface are reduced and T g > 364 K . But these effects are modest; the average T g represented by the four open triangles in Fig. 4 is 363 K, far below the average experimental value (blue points) of T g = 373 K for labeled homopolymers in diblock matrices. 4 10.1103/PhysRevLett.121.247801.f4 FIG. 4. Local T g for the four PMMA-py homopolymers in ϕ h = 0.02 blends with the diblock (blue squares; dashed blue curve is guide to the eye) plotted against the average distance ( z ) of the homopolymer segments from the nearest PBMA-PMMA domain interface. For comparison, the T g values calculated simply from segmental mixing [via Eqs. (1) and (2) ] are shown as the filled circles, while the T g values calculated for a selectively labeled diblock having the same labeled segment density distribution as the homopolymer are shown as the open triangles; the uncertainties in T g are propagated from the uncertainties in the T g values uses as inputs to the calculations. Comparison of the three curves reveals the magnitude of each of the three effects contributing to T g depression in nanostructured block copolymers: (1) segmental mixing, (2) soft confinement, and (3) block connectivity across the domain interface. From top to bottom, the three sets of points in Fig. 4 progressively incorporate the three effects alluded to above. The black symbols consider only segmental mixing (effect 1), which produces a 4–9 K depression relative to the bulk PMMA T g = 385 K . The experimental (blue) points contain contributions from both segmental mixing and confinement (effects 1 and 2); confinement, therefore, produces an additional reduction in T g of approximately 5 K (the black and blue curves are parallel to within the experimental uncertainty, indicating that the principal effect of varying α is to change the extent of segmental mixing). Finally, the open symbols incorporate all three effects (segmental mixing, confinement, and block connectivity) because they are calculated for a selectively labeled diblock (in which all three effects are present) having the same labeled segment density distribution as the homopolymer in the blend. Block connectivity (effect 3) is thus seen to produce an additional T g depression of ∼ 10 K . In other words—and quite unexpectedly—attachment of the PMMA block to the PBMA block, and thereby to the domain interface, produces a larger T g depression than either confinement by the domain structure or segmental mixing. The results obtained here complement previous studies of homopolymers in hard confinement, where a substantial increase in the local T g was observed by covalently bonding (grafting) polymer chains to a solid substrate vs simply coating the polymer onto the same weakly interacting substrate [32–34] or when the polymer layer being probed rests atop a grafted brush layer attached to a hard substrate [35–37] . The present study highlights the utility of fluorescence labeling and temperature-dependent spectroscopy, which provide component-specific measurements of T g to probe features of the glass transition in complex polymer systems. In the present case, this approach reveals that even in intimate blends, neighboring—and chemically identical—segments (PMMA here) can exhibit different local dynamics when attached to a chemically distinct—and distant—block (PBMA here). This work was supported by the National Science Foundation (NSF) Materials Research Science and Engineering Center Program through the Princeton Center for Complex Materials (Grant No. DMR-1420541). D. C. acknowledges the support of a NSF graduate research fellowship. R. D. P. acknowledges the AFOSR through PECASE Grant No. FA9550-12-1-0223.  1 L. Leibler , Macromolecules 13 , 1602 ( 1980 ). MAMOBX 0024-9297 10.1021/ma60078a047  2 M. W. Matsen and F. S. Bates , Macromolecules 29 , 1091 ( 1996 ). MAMOBX 0024-9297 10.1021/ma951138i  3 A. M. Mayes , T. P. Russell , S. K. Satija , and C. F. Majkrzak , Macromolecules 25 , 6523 ( 1992 ). MAMOBX 0024-9297 10.1021/ma00050a022  4 M. W. Matsen , Phys. Rev. Lett. 74 , 4225 ( 1995 ). PRLTAO 0031-9007 10.1103/PhysRevLett.74.4225  5 Y. Miwa , K. Yamamoto , T. Tanabe , S. Okamoto , M. Sakaguchi , M. Sakai , and S. Shimada , J. Phys. Chem. B 110 , 4073 ( 2006 ). JPCBFK 1520-6106 10.1021/jp056502m  6 K. R. Shull , A. M. Mayes , and T. P. 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PY - 2018/12/12
Y1 - 2018/12/12
N2 - Fluorescence labeling enables component- and location-specific measurements of the glass transition temperature (Tg) in complex polymer systems. Here we characterize the Tg of fluorescently labeled poly(methyl methacrylate) homopolymers (PMMA-py) blended at low concentrations into an unlabeled lamellar poly(n-butyl methacrylate-b-methyl methacrylate) diblock copolymer (PBMA-PMMA). In this system, the PMMA-py homopolymer is sequestered within the PMMA domains of the diblock copolymer and subject to soft confinement by the domains of the lower-Tg PBMA block, which lowers the homopolymer Tg by ∼5 K beyond the contribution of segmental mixing. In contrast to the PMMA block in the diblock copolymer, the PMMA-py homopolymer is not covalently bound to the interdomain interface. A comparison of Tg for the homopolymers in the blends to Tg for diblock copolymers with equivalent labeled segment density profiles reveals that the homopolymer's Tg is consistently ∼10 K higher than for diblock segments at the same location within the domain structure, highlighting the dominant contribution of a covalent bond across the interface to the perturbation of the chain dynamics in the block copolymer.
AB - Fluorescence labeling enables component- and location-specific measurements of the glass transition temperature (Tg) in complex polymer systems. Here we characterize the Tg of fluorescently labeled poly(methyl methacrylate) homopolymers (PMMA-py) blended at low concentrations into an unlabeled lamellar poly(n-butyl methacrylate-b-methyl methacrylate) diblock copolymer (PBMA-PMMA). In this system, the PMMA-py homopolymer is sequestered within the PMMA domains of the diblock copolymer and subject to soft confinement by the domains of the lower-Tg PBMA block, which lowers the homopolymer Tg by ∼5 K beyond the contribution of segmental mixing. In contrast to the PMMA block in the diblock copolymer, the PMMA-py homopolymer is not covalently bound to the interdomain interface. A comparison of Tg for the homopolymers in the blends to Tg for diblock copolymers with equivalent labeled segment density profiles reveals that the homopolymer's Tg is consistently ∼10 K higher than for diblock segments at the same location within the domain structure, highlighting the dominant contribution of a covalent bond across the interface to the perturbation of the chain dynamics in the block copolymer.
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U2 - 10.1103/PhysRevLett.121.247801
DO - 10.1103/PhysRevLett.121.247801
M3 - Article
C2 - 30608727
AN - SCOPUS:85059138915
VL - 121
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 24
M1 - 247801