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We have shown how simple changes in the backbone rigidity in a series of model glass-forming polymers leads to differences in the confinement effects as probed by different material properties. The glass transition temperature as measured from the temperature dependence of the density shows that the difference inTg between

the bulk and free-standing thin films becomes smaller as the rigidity is increased.

This measure of Tg as comparable to the common ellipsometry experiments that

are used to extract Tg for thin films; however, if we directly measure the structural

relaxation time of our films using the intermediate scattering function, Fs(q, t),

we obtain a different picture. From the data in Table 1, we see that the change in Text

g upon confinement is approximately the same for all systems, although we

emphasize that this requires a large extrapolation in the relaxation times. Nev- ertheless, it is clear that by comparing the effects of confinement on τα and τbond

for each of the three polymer systems, the magnitude of the confinement effect can vary strongly depending on the property measured. We attribute these differences

0 0.2 0.4 0.6 0.8 1 T / T_g,bulk 100 101 102 E Y,bulk a 0 0.2 0.4 0.6 0.8 1 T / T_g,bulk 10-2 10-1 100 101 102 E Y x10-1 x10-2 b

Figure 2.6: Young’s moduli as a function of temperature for kθ = 0 (black circles),

kθ = 1.5 (red squares), and kθ = 3.0 (blue diamonds). (a) Young’s moduli for bulk

polymers; the dashed line for kθ = 1.5 represents Young’s moduli as obtained from

uniaxial deformation, while the points were calculated using the stress fluctuation formulae. (b) Young’s moduli for films (filled symbols) and bulk polymers (open symbols); the red data were multiplied by 10−1_{, while the blue data were multiplied}

by 10−2_{. The dashed line through the red data represents Young’s moduli for the}

0 0.2 0.4 0.6 0.8 1 T / T_g,bulk 0 0.1 0.2 0.3 0.4 0.5 vxy

Figure 2.7: Poisson’s ratio as a function of temperature for kθ = 0 (black circles),

kθ = 1.5 (red squares), andkθ = 3.0 (blue diamonds). The films are represented by

the hollow symbols, while the bulk polymers are represented by the filled symbols. our model glass-forming polymers. It remains unknown the extent to which this type of ordering could occur in experimental systems, and the comparison is further complicated by the lack of side-groups in our model polymers.

Several experiments have investigated confinement effects on polymers with varying chemistries [58, 248, 247, 172]. However, many of the previous studies have focused on changes in the polymer side group, which could potentially induce different effects than those induced by changing the polymer backbone chemistry. Torres et al. [248] have systematically modified the backbone stiffness and inves-

tigated the confinement effects on both Tg and the Young’s modulus, Ey. Our

results presented here where we observe a decrease in the effects of confinement

on Tg as measured from the temperature dependence of the density for more rigid

confinement, while each of our model polymer systems each become slightly softer when confined to thin films. One important difference between our work and that of Ref. [248] is that the experimental films were supported on a PDMS substrate, while our films are free standing, which may account for some of the differences.

Recently, Paeng and co-workers have examined the effect of polymer chemistry on the segmental dynamics using fluorescence recovery techniques [172]. They inter- pret their results in terms of a mobile surface layer that coexists with bulk polymer

dynamics, and the size of the mobile layer grows as Tg is approached from be-

low. Isothermal measurements just below the bulk Tg for poly(styrene) produced a

two-step response function that contained a mobile surface layer as well as a bulk process, which was present in PS thin films as thin as 17 nm [174]. Interestingly, the temperature dependence of this surface process is very similar to that of the nanoparticle embedding experiments of Fakhraai and Forrest [64]. In the model polymers examined here, we do not observe a bulk relaxation rate at any location in our films, and the transition from the mobile surface to the slower dynamics in the center of the film is gradual over the thickness of the film (see Fig. 2.4). The lack of a bulk process in the center of our film may be a result of our films being only

11σ thick, which would correspond to approximately 10 nm in laboratory units.

Our simulations are the first calculations of the Poisson’s ratio, ν, in thin films

of which we are aware. We observe an appreciable decrease in ν for all of our

from buckling experiments that are commonly employed to extract the mechanical properties of thin polymer films [247, 248, 233]. The buckling experiments measure

a plane strain modulus, ¯E, which is related to the more common Young’s modulus

EY through Poisson’s ratio as ¯E = Ey/(1−ν2). This implies that in materials

where ¯E does not change upon confinement, the Young’s modulus may in fact be

different from the bulk if it is compensated by a change in ν.

One goal of our work was to explore whether any bulk properties of glass for- mation could be indicative of the nanoscale confinement effects. The accepted def- inition of the fragility of a polymer glass is the activation energy given by the tem-

perature dependence of τα at the experimental glass transition temperature where

τα ≈ 100 s. Since these long time scales are not accessible to MD simulations, we

must resort to other correlations to characterize the fragility of a glass-forming liq- uid [193, 191, 237, 168, 231]. One simple measure of the fragility is the value of the

D parameter from the fits of the VFT equation to our structural relaxation time,

τα, where D is typically in the range of 1 (fragile glasses) to 100 (strong glasses).

As shown in Table 2.1, all three polymers have relatively small D values, implying that all of our polymeric systems are fragile polymers. We do, however, see signifi-

cant changes in D with polymer rigidity, where our rigid polymers are nearly half

of our fully flexible ones. The lack of a distinct connection between fragility and the magnitude of the confinement effects is also commonly observed experimentally [30, 172, 58].

As discussed above, ideas related to the so-called cooperative rearrangements that have their origins in the Adam-Gibbs theory of glass formation [1] are fre- quently invoked to explain confinement effects [172, 193, 190]. The physical picture is that in materials with large degrees of cooperative motion, the surfaces will affect the dynamics of the glass on length scales comparable to the cooperative rearrange- ments. There are both experimental [172, 59] and computational [193] examples where the magnitude of the confinement effect and the size of the cooperative re- arrangements appear to correlate strongly with each other. However, the effect is not universal [30]; In Fig. 2.3, we identify the size of the string-like rearrangements as the cooperative domains and find that each of the three systems exhibit approx-

imately the same size of cooperative rearrangements at a common T /Tg. However,

the confinement effects measured by the change inTgdeduced from the temperature

dependence of the density varies strongly between the three systems, and thus the cooperative dynamics are not a universal indicator of the confinement effects.