Session P50: Focus Session: Dynamics of Polymers: Phenomena due to Confinement; Glass Transition

Theoretical prospects for understanding the glass transition in polymer thin films

Observations of confinement effects on the glass transition in thin polymer films remain vexing to theorists. Many experiments at sufficiently low frequencies consistently find that the free surfaces of many polymer films, whether freely suspended or supported, have anomalously low glass transition temperatures. This surface effect appears to be independent of molecular weight, and persists 10-20nm into the film. In contrast, freely suspended films have been observed by ellipsometry and other bulk-sensitive techniques to have anomalously low film-averaged $T_g$ values, depending strongly on both film thickness and molecular weight for Mw above about $4 \times 10^5$g/mol. The dependence on Mw persists to astonishingly large values ( $\sim 10^7$g/mol). Recent work of Pye and Roth strongly suggests the presence of two distinct mechanisms in these films, one operative at the free surface and Mw-independent, one depending on Mw and giving a weak second glass transition at considerably lower temperatures. In this talk, I will review the status of various theoretical proposals we have explored for explaining some of these disparate phenomena, including the effects of interrupted percolation at the free surface and the ``sliding mechanism'' originally suggested by de Gennes for Mw-dependent lowering of $T_g$. I will describe the present prospects for a successful theory, as well as suggest some potentially helpful experiments and analysis.   

Cooperative Length Scale and Fragility of Polystyrene under Confinement

While thin films are an attractive model system to investigate the impact of confinement on glassy behavior, extending studies beyond thin films to geometries of higher dimensionalities is vital from both scientific and technological viewpoints. In this talk, we present the impact of confinement on the characteristic length at the glass transition as well as the fragility for confined polystyrene (PS) nanoparticles under isochoric conditions. We measure the glass transition temperature ($T_{g})$, fictive temperature ($T_{f})$ and isochoric heat capacity of silica-capped PS nanoparticles as a function of diameter via differential scanning calorimetry. From the measurement of $T_{f}$, we obtain the isochoric fragility, and via the fluctuation formula, the characteristic length at the glass transition. We illustrate that confinement under isochoric conditions for PS nanoparticles leads to a significant increase in the isochoric fragility while the characteristic length is reduced with size. At the minimum the results demonstrate a relationship between fragility and the characteristics length of isochorically-confined polymer that is not intuitive from the Adam-Gibbs theory.   

Impact of systematic chain architecture changes on the glass transition and modulus of thin polymer films

We will discuss two systems that significantly impact the thin film behavior with minor changes in chemistry and chain architecture. First, two polymers based on 5-(2-phenylethylnorbornene) are examined. Depending on the polymerization route chosen, the resulting polymer backbone is comprised of either bicyclic (norbornyl) units, which leads to a relatively rigid polymer with a high bulk T$_{g}$, or monocyclic (cyclopentyl) units, which leads to a more flexible structure with a lower bulk T$_{g}$. The modulus and T$_{g}$ of the rigid bicyclic polymer is thickness independent down to $<$10 nm, whereas the modulus of the more flexible monocyclic polymer decreases with decreasing thickness. By hydrogenation of the pendant phenyl ring to the cyclohexyl counterpart, we illustrate that minor changes in the relative flexibility of the side chain do not impact the observed thin film behavior. Second, a series of polystyrene with controlled branching including linear, comb, 6-arm star and centipede. Based upon the molecular mass of the arms, the comb polymer has a significantly larger persistence length and interestingly exhibits only a modest decrease in T$_{g}$ (9 K) at 5 nm, while the moduli is thickness independent.   

A Direct Relationship between Enhanced Surface Mobility and Tg Reduction in Thin Polymer Films

Cooling rate dependent Tg measurements of thin polymer films show a strong correlation between the cooling rate and the confinement effects. It is observed that the Tg is more strongly dependent on the cooling rate as the film thickness is decreased. The confinement effects also become weaker at higher cooling rates and it appears that both for thick films and high cooling rates the confinement effect vanishes. The results can be plotted on an Arrhenius plot by assuming that the cooling rate is inversely related to the relaxation time as the temperature that the system falls out of equilibrium (Tg). The surface relaxation times can be independently measured using nano-hole relaxation and nanoparticle embedding techniques and the results can be plotted on the same Arrhenius plot. It is observed that the surface relaxation has much weaker temperature dependence, with an activation energy that matches the limit of zero film thickness for the rate-dependent Tg measurements. The strong correlation between surface properties obtained by direct mechanical measurements with the Tg measurements obtained by ellipsometry suggest that these two phenomena are from the same origin and one cannot be explained without the other.   

Reduced Glass Transition Temperatures of Thin Polymer Films - Confinement Effect or Artifact?

For two decades there have been reports of measurements of reduced glass transition temperatures ($T_{\mathrm{g}}$) in polymer, and in particular poly-styrene, films. These results have motivated theoretical models and a variety of sophisticated experiments probing interfacial polymer properties. While the much larger reductions in $T_{\mathrm{g}}$ for free standing films have suggested the importance of the free surface, a significant concern has been raised about a possible correlation between anomalous dynamics and incomplete equilibration of the sample. Here, we present new ellipsometry measurements which unambiguously address this concern. The glass transition in free standing and supported films can be changed by many 10's of degrees by manipulating the interfacial properties. Taken together with previous work the results clearly reveal the importance of free interfaces as we transition from two, to one, to zero free interfaces.   

Confinement in thin polymer films near Tg leads to factors of 10 to 1000 reductions in dye translational diffusion

A breakthrough time/fluorescence resonance energy transfer method is used to measure out-of-plane translational diffusion coefficients of small-molecule dyes in thin polymer films near the glass transition temperature, Tg. The bulk translational diffusion coefficient is a strong function of dye size, increasing by a factor of 100 in polystyrene when dye molecular volume decreases by 25{\%}. Reduction in PS film thickness below 500 nm leads to a factor of 1000 decrease in Disperse Red 1 diffusion coefficient while reduction below 140 nm leads to slightly more than a factor of 10 decrease in decacyclene diffusion coefficient. At a thickness less than 100 nm, the diffusions coefficients for the two dyes are identical with error. Similar effects have been observed in poly(methyl methacrylate) and polysulfone films at Tg + 3 K. These effects are not directly correlated with the Tg-confinement effect in these polymers as the length scales for confinement effects are much smaller in the case of Tg and in some of the polymers both diffusivity and Tg decrease with confinement.   

Measuring the glass transition of polymer nanodroplets

Despite almost 2 decades of measuring the glass transition temperature (T$_{g})$ in thin polymer films, there is no consensus on the magnitude (or even the existence) of observed T$_{g}$ reductions. Recent suggestions that reduced T$_{g}$~values in thin polystyrene films may be nothing more than a complicated artifact of sample preparation must be taken very seriously. Reduced T$_{g}$~values are reported only for polymer films prepared on a non-wetting substrate where the film is unstable with respect to dewetting. In all cases only kinetic metastability allows one to measure a T$_{g}$ value The fundamental problem is that an unambiguous measure of T$_{g~}$can only be obtained as the sample is cooled from the equilibrium liquid. No experiments involving thin polymer films have yet satisfied this condition. Our approach is to use samples prepared in the equilibrium state atop a non-wetting substrate (a collection of spherical caps). Since the droplets are already in the equilibrium state, they can be annealed for arbitrarily large times without evolution of the structure. We describe dilatometric measurements of~T$_{g}$ for nanometer sized spherical caps of polystyrene~This technique can be used to investigate the effect of annealing history and to extend the studies of T$_{g}$ in high surface area to volume systems beyond polymers and into other molecular glass forming materials   

Molecular motion in polymer thin films exhibits fast and slow subpopulations.

The reorientation of dilute fluorescent probes in thin polymer films was studied using a photobleaching technique. The existence of two subsets of probe molecules with different dynamics was revealed by temperature-ramping and isothermal anisotropy measurements. For freestanding polystyrene films, the slow subset shows bulk-like dynamics while the more mobile subset reorients 4 orders of magnitude faster at Tg - 5 K. The difference in dynamics becomes larger as temperature decreases and disappears as temperature approaches Tg. We interpret the fraction of the sample with fast dynamics as a high mobility layer at the film surfaces. The thickness of this mobile surface layer increases with temperature and does not depend on the molecular weight of the polymer and total film thickness. The mobile surface layer exists in various freestanding polymer thin films including polystyrene and poly(methyl methacrylate) and is also present in supported films of these polymers.   

Confinement Effects of Neighboring Polymer Domains on the Tgs of Infinitely Dilute Blend Components and Ultrathin Film Layers

Using fluorescence, we study the glass transition temperature (Tg) of a polymer species near the limit of infinite dilution. In blends with very dilute polystyrene (PS), intrinsic (unlabeled) and extrinsic dye-labeled fluorescence exhibit quantitative agreement for PS component Tgs. Dilute (0.1 wt{\%}) PS Tg is strongly perturbed towards the matrix Tg; e.g., 38 C in PnBMA and 119 C in PMMA. These dilute component Tgs yield a range of self-concentrations (0.18-0.47) in the framework of the Lodge-McLeish model. We also study multilayer, nanoconfined films with neighboring polymer domains by fluorescence. For PS supported on a bulk underlayer, the Tg of sub-100 nm PS is perturbed towards the underlayer Tg. For example, the 45 C Tg of a 14-nm PS layer on bulk PnBMA approaches the Tg for 0.1 wt{\%} PS in PnBMA. These results underscore the role of neighboring polymer domains on the dynamics of an infinitely dilute species or an ultrathin polymer film layer and indicate that Tg-confinement effects in blends and thin films can be viewed as variations of the same physical phenomenon.   

Molecular Weight Dependent and Independent Glass Transition Temperature Reductions Coexisting in High MW Free-Standing Polystyrene Films

Using transmission ellipsometry, we have measured the thermal expansion of ultrathin, high molecular weight (MW), free-standing polystyrene films over an extended temperature range. For two different MWs, we observed two distinct reduced glass transition temperatures (Tgs), separated by up to 60 K, within single films with thicknesses h less than 70 nm. The lower transition follows the previously seen MW dependent, linear Tg(h) behavior, while we also observe the presence of a much stronger upper transition that is MW independent and exhibits the same Tg(h) dependence as supported and low MW free-standing films. This represents the first experimental evidence indicating that two separate mechanisms can act simultaneously on thin free-standing polymer films to propagate enhanced mobility from the free surface into the material. The change in thermal expansion through the transitions indicate that $\sim $90{\%} of the film (matrix) solidifies at the upper transition with only $\sim $10{\%} of the material remaining mobile, freezing in at the lower transition. Surprisingly, when we compare our results to the existing literature, and especially the low MW free-standing film data, we conclude that the upper transition encompasses the free surface region and associated gradient in dynamics. This leaves open the question about where the small ($\sim $10{\%}) fraction of material that has ultrafast, MW dependent dynamics resides within the film.   

Glass Transition and Physical Aging in Thin Polymer Films: A Unified Picture of Confinement

The effect of confinement on the glass transition, structural relaxation, and other material properties has garnered a great deal of attention during the past two decades. Despite the common misperception, there is considerably more agreement than disagreement (or ``controversy'') of the phenomena in the existing literature. This talk will summarize current experimental findings in the field, focusing on the author's recent work that links physical aging in thin polymer films to Tg changes near a free surface. We also demonstrate that the intricate molecular weight dependence of the film thickness dependent Tg reductions in free-standing films result from two separate mechanisms acting simultaneously on the films. From these results a universal picture is starting to emerge with some effects common to colloidal and small molecule glasses as well.