understanding the decreased segmental dynamics of supported

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Applied Pysics

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strongly through the ? lm; neutron re ? ectivity of selectivelydeuterated PS multilayer ? lms has revealed signi ? cant di ? er-ences in thermal expansion for bulk, near-surface, and near-substrate regions.32,33These measurements have shownenhanced thermal expansion near the free surface with anassociated decrease in T g , while the layer near the substrateappears to have a near zero coe ? cient of thermal expansion(CTE).32,33The question of whether the transitions betweenthese regions are gradual18,21,34 ? 36or abrupt remainsunsettled,7but these interfacial gradients can be quite longrange; for example, the gradient in T g extends up to tens ofnanometers into the ? lm.18,32These competing e ? ects between the substrate and the freesurface play an important role in determining whether T g willincrease or decrease for a given polymer ? substrate system.37Furthermore, they suggest that apparent qualitative discrep-ancies in nanocon ? nement e ? ects observed through di ? erentmeasurement techniques may be a result, at least in part, oftheir relative sensitivities to di ? erent domains within the ? lm.However, most thin ? lm measurements provide only an averageof the T g (or dynamics), with the time and/or length scalesensitivies intrinsic to these measurements determining howthis average is obtained. Thus, the sensitivity to these di ? erentapparent layers in the ? lm may be strongly dependent on themeasurement technique selected. For example, the temper-ature-dependent thickness variations quanti ? ed with ellipsom-etry38or re ? ectivity39will likely be most sensitive to the morethermally expansive layers (e.g., surface and bulk), and thesemeasurements tend to ? nd that T g decreases with decreasing? lm thickness as the fraction of surface layer increases.To better understand how nanocon ? nement impacts glassformation in polymer thin ? lms, several groups have begun tosystematically investigate the impact of bulk polymer propertiessuch as tacticity in poly(methyl methacrylate),40the pendantgroups on PS,41or the length of alkyl side chains inmethacrylates42on nanocon ? nement e ? ects. No simplerelationship of T g alteration to bulk glass formation behavior,such as the size of the cooperatively rearranging regions (CRR)as determined from the Donth method43in the Adam ? Gibbs44context, was found in these cases, but simulation work hassuggested that the range of interfacial alterations in dynamics isrelated to the size scale of CRRs.34,45,46Additionally, recentwork from Torkelson and co-workers has suggested thatfragility,47a measure of the abruptness in temperature glassformation process, is well correlated with the magnitude of T galterations.48Since the Adam ? Gibbs theory of glass formationsuggests that more fragile glass-formers exhibit larger scaleCRRs,44these two observations are qualitatively consistent.Recently, it has become clear that these thin ? lm nano-con ? nement e ? ects are sensitive to subtle di ? erences ininterfacial interactions40associated with changes in polymerarchitecture, since adsorption interactions49,50and interfacialtension51,52are modi ? ed by chain branching and tacticity. Forexample, Glynos et al.53illustrated that the thickness depend-ence of T g with star PS architectures is dependent on thenumber of branched chains, f, and the molecular mass, M n , ofthe arm. For small f and large M n s on the arms in thin star PS? lms, the T g depression is consistent with linear PS, but as fincreases and/or M n decreases, an inversion occurs with T gincreasing as the ? lm thickness decreases.53This increase in T ghas been attributed to stronger adsorption of the PS at thesubstrate with increasing number of arms on the star.53In asimilar vein, Nealey and co-workers suggested that the T g ofsupported polymer thin ? lms increases linearly with thestrength of polymer ? substrate adhesion.12The aging rate forstar PS is also dependent on f and M n of the arms.54,55Theseresults suggest that chain architecture e ? ects might also displaydi ? erent sensitivities to thin ? lm nanocon ? nement whenprobed with the di ? erent measurement techniques and therebyprovide further insight into the roles of the di ? erent interfacesand help to rationalize the apparent discrepancies in theliterature.As T g measurements are generally interpreted in terms ofdynamics,56direct measures of dynamics in the thin polymer? lms can prove quite useful. Unlike dielectric spectroscopy, nomodi ? cations to the substrate for electrical connections arerequired with inelastic neutron scattering (INS), so theseneutron techniques should provide ideal measurementtechniques for direct comparison between standard measure-ments, such as ellipsometry or ? uorescence intensity, and directdynamic measurements. However, prior INS measurements ofPS ? lms supported on silicon substrates indicate a decrease inhigh frequency mobility and suggest a corresponding enhance-ment in apparent T g for thin PS ? lms,57which is counter tomost ellipsometry16,38,58,59and ? uorescence intensity14,38measurements. In the past, seemingly contradictory trends inapparent T g have been rationalized in terms of the di ? eringsensitivity of a ? xed-time-window experiment to di ? erentrelaxation processes.57A prior comparison of ? uorescenceintensity and ellipsometry measurements illustrated the greatersensitivity of ? uorescence to the free surface, leading to agreater reduction in T g reported by ? uorescence intensitymeasurements.38This implies that INS may be more sensitiveto the slow dynamics associated with the substrate interfacethan ellipsometry or ? uorescence.In order to gain further insight into the dependence of themeasurement technique on the reported nanocon ? nemente ? ect, here we employ INS to study dynamics of a silicon-supported comb PS that has a thickness-invariant ellipsometricT g down to approximately 10 nm (see Figure S3B inSupporting Information).60Since INS measurements areprimarily sensitive to hydrogen atom density,60,61this approachenables comparison with prior results for di ? erent architectures(linear, star,54,55hyperbranched,61comb, and centipede60) ofPS by retaining a similar polymer chemistry. Unlike ellisometricresults, INS measurements used here suggest an enhancementof T g and concurrent suppression in nanosecond-time scaledynamics, at all temperatures, as thickness is reduced. Thisdi ? erence between INS and ellipsometry measurements isconsistent with prior reports for linear PS.57Implicit in theimpression of a contradiction between these measurements arethe assumptions that T g can be inferred from nanosecond timescale measurements of the Debye ? Waller factor ? u2 ? and that? u2 ? should track in some universal way with the structuralrelaxation time of the polymer. Here we argue that neither ofthese assumptions is valid and that these two measurementsmay therefore be entirely consistent. This outcome is consistentwith a growing body of evidence that suggests commonly heldrelationships between T g and other physical properties, such asmechanical response62 ? 64that are valid for bulk polymers mayfail in nanocon ?