Session Y42: Focus Session: Dynamics of Polymers--Phenomena due to Confinement--Theory, Wrinkling, and Glass Transitions

Twinkling Fractal Analysis of Confinement Effects on the Glass Transition of Thin Films

The Twinkling Fractal Theory (TFT) of the Glass Transition has recently been verified experimentally [J.F. Stanzione, et al., ``Observing the twinkling fractal nature of the glass transition'', J. Non-Cryst. Solids (2010), doi:10.1016/j.jnoncrysol.2010.06.041] Here we apply the TFT to understand nanoconfinement effects on T$_{g}$ for amorphous thin films of thickness h with free and adhered surfaces. The TFT states that T$_{g}$ occurs when the dynamic clusters percolate rigidity at the rate of testing $\gamma $. The lifetime $\tau $ of these fractal clusters of size R behaves as $\tau \sim $R$^{\delta }$ exp $\Delta $E/kT, where $\delta $=D$_{f}$/d$_{f}$ in which D$_{f}$ is the fractal dimension and d$_{f}$=4/3 is the fracton dimension for the vibrational density of states g($\omega )\sim \omega ^{df}$. The activation energy $\Delta $E = $\beta $[T$^{\ast 2}$-T$_{g}^{2}$] in which $\beta \quad \approx $ 0.3 cal/mol $^{o}$K$^{2}$ and T*$\approx $1.2T$_{g}$. In confined spaces, only clusters of size R$<$h can exist and these have a very fast relaxation time compared to the bulk. Thus, for free surfaces, T$_{g}$ must be dropped at that test rate to percolate rigidity and we obtain the familiar expression T$_{g}$(h)/T$_{g\infty } \quad \approx $ [1-(B/h)$^{\delta }$] where $\delta \approx $1.8 when D$_{f} \quad \approx $2.5 and B is a known constant. For thin films adhered to solid substrates, T$_{g}$ increases in accord with the adhesion energy$\Delta $A as $\Delta $E$\to \Delta $E+$\Delta $A and the adhered cluster lifetime increases. As the rate of testing $\gamma $ increases, the confinement effects diminish as T$_{g}$ increases in accord with T$_{g}(\gamma )$ = T$_{go}$ + (k/2$\beta )$ ln $\gamma $/$\gamma _{o}$.   

Mechanical properties of thin polymer films close to the glass transition: a mesoscale model

Polymer dynamics slows down in the vicinity of a solid substrate (when interactions are sufficiently strong), as can be evidenced experimentally by measuring the glass transition temperature Tg in thin films. We extend here the Long and Lequeux model which quantitatively accounts for this effect. We describe the mechanical properties of the polymers on the scale of dynamical heterogeneities (of a few nanometers). We propose a constitutive relation regarding the local relaxation time, the local stress, and the deformation history. The mechanical equations coupled to these constitutive relations are solved, allowing to reach a scale of a few tens of nanometers and macroscopic time scales. In particular, we measure the elastic modulus G' as a function of temperature, for various films thicknesses. This measurement allows for measuring the glass transition temperature of the film as a function of thickness. The results show that the glass transition temperature is shifted as compared to the bulk (corresponding to large film thickness), depending on the strength of the polymer/substrates interaction, with values which are consistent with experimental results.   

A Simple Approach to Free Volume Transport in Molten/Glassy Material

A key component of microscopic models for the glass transition, in polymer thin films and more generally, is the local dynamics of free volume, which governs what portions of a near-glassy liquid are mobile at a given instant in time. For example, our recent Delayed Glassification (DG) model implements a proposal of de Gennes that segment-sized kinks of free volume may travel from a free surface into a film along polymeric loops or bridges, helping to plasticize material within some accessible distance from the surface. Recently, we have constructed a simple model for `the mobility of mobility', i.e., how local mobility is itself transported through a dense liquid slightly above Tg. Our simple model results in growing cooperativity lengths and intermittency timescales as Tg is approached from above. If time permits, we shall also describe how the model may be adapted to describe the approach to glassy behavior in supported and freestanding films.   

Deviations in mechanical properties of ultrathin polymer films via surface wrinkling

In ultrathin polymer films (h $<$ 100 nm), the measurement of stress relaxation and Young's modulus is a difficult problem due to the delicate nature of such thin films and the lack of appropriate measurement tools for this length scale. Recent work has shown that the Young's modulus of ultrathin glassy polymer films can be measured by a wrinkling-based metrology. Interestingly, the modulus of such thin films was observed to deviate considerably from their bulk counterparts. Building off these observations, we have shown that the rate of structural relaxation and the temperature dependence of the film modulus can also be obtained by following the `relaxation' of strain-induced wrinkling patterns back to their flat equilibrium state. By measuring the decay or relaxation of surface undulations in compressed thin films, we demonstrate that the structural relaxation of the polymer film is highly thickness-dependent and obeys Arrhenius temperature dependence with an activation energy that decreases progressively with decreasing film thickness. This gives rise to an overall broadening of glass transition and to a relatively weak temperature dependence of structural relaxation.   

Calorimetry of Thin Films -- From Single Layer Glass Transitions to Inter-layer Diffusion in Double Layers

Nanocalorimetry allows studying the glass transition in nanometer thin films. One of the striking results of fast scanning (FSC) as well as alternating current (AC) calorimetry is the commonly observed constant Tg in thin films down to a few nm. Blends of polystyrene and poly(phenylene oxide) (PS/PPO) confined in thin films (down to 6 nm) were investigated by AC nanocalorimetry. For this blend, we see even for the thinnest films (6 nm, corresponding to about half of PPO's radius of gyration Rg) only one unchanged glass transition. The good miscibility between PS and PPO remains even in ultrathin films. Finally, we show that our chip calorimeter is sensitive enough to study the inter-layer diffusion in ultrathin films. The PS chains in a 150 nm PS/PPO double layer that is prepared by spin coating PPO and PS thin films in tandem gradually diffuse into the PPO layer when heated above the Tg of PS, forming a PSxPPO100-x blend. However, on top of the PSxPPO100-x blend, there exists a stable pure PS like layer (ca. 30nm in our case) that does not diffuse into the blend beneath even staying at its liquid state over 10 hours.   

$T_{g}$ depression and segmental dynamics of polystyrene thin films

The glass transition temperature ($T_{g})$ of polymer thin films has been a subject of intense debate in the last two decades. (Pseudo)thermodynamic determinations, such as calorimetry and ellipsometry, generally suggest a significant depression of $T_{g}$, whereas the dynamic $T_{g}$, measured by techniques such broadband dielectric spectroscopy and AC-calorimetry directly probing the molecular mobility, is found to be unchanged. The present study provides a resolution to this controversy on polystyrene by showing that the experimental relaxation time obtained from (pseudo)thermodynamic techniques, and the intrinsic molecular relaxation time can be rescaled on a master curve, only accounting for the thickness of the film. Furthermore the thickness and cooling rate dependence of the (pseudo)thermodynamic $T_{g}$ is quantitatively captured by the free volume holes diffusion model. In this framework, the $T_{g}$ depression emerges from the ability of thinner films to maintain equilibrium, due to the shortest distance free volume holes have to diffuse to the polymer interface.   

Evidence for Two Simultaneous Mechanisms Causing Tg Reductions in High Molecular-Weight Free-Standing Films Observed as Dual Glass Transitions More Than 30 K Apart in a Single Film

Glass transition temperature (Tg) changes seen in nanoconfined polymer films have been well documented over the past 15+ years. Supported films exhibit a molecular-weight (MW) independent Tg reduction that manifests itself as a gradient in dynamics emanating from the free surface. Low MW free-standing films show qualitatively the same Tg reduction as supported films, but with the presence of two free surfaces resulting in a Tg reduction that is twice as large for a given film thickness. In contrast, high MW free-standing films exhibit a qualitatively different behavior with a linear reduction in Tg that is MW dependent, potentially described by de Gennes' sliding mode theory. These observations suggest that there may exist two separate mechanisms which can propagate enhanced mobility from the free surface into the film. With ellipsometry measurements over an extended temperature range, we have observed two reduced Tgs more than 30 K apart in individual high MW free-standing polystyrene films suggesting that both mechanisms act simultaneously within a film. These results may explain recent studies on high MW free-standing films using different experimental techniques that contradict the original literature.   

Demonstration of Glass Transition Temperature Depression in Thin Supported Polystyrene Films Using Internal Standard

Clear evidence for glass transition temperature (Tg) depression in $\sim$ 5 nm thick atactic polystyrene (Mw = 212 kg/mol) films supported on silicon substrates is demonstrated by ellipsometry in vacuum [1]. Transition in polystyrene droplets formed by dewetting is used as an internal reference. Both temperature-modulated [2] and linear temperature scanning techniques are utilized; measurements are performed at $10^{-6} - 10^{-8}$ torr residual gas pressure. The method is sensitive enough to observe glass transition in 1 $-$ 2 nm thick supported polystyrene films. Our recent study shows appreciable reduction of Tg in less than 10 $-$ 20 nm thick samples; Tg versus thickness function is found to follow a step-like curve originally reported by [3]. The curve is characterized by moderate (about 17 K) constant Tg depression for thickness less than 7 $-$ 8 nm. References: [1]. M. Y. Efremov, S. S. Soofi, A. V. Kiyanova, C. J. Munoz, P. Burgardt, F. Cerrina, and P. F. Nealey, Rev. Sci. Instrum., 79, 043903 (2008). [2]. M. Y. Efremov, A. V. Kiyanova, and P. F. Nealey, Macromolecules, 41, 5978 (2008). [3] T. Miyazaki, K. Nishida, and T. Kanaya, Phys. Rev. E, 69, 061803 (2004).   

Effect of Packing Density on the Measurement of Glass Transition Temperatures in Thin Film

In the measurement of \textit{Tg} of polymers, a break or jump in some properties is seen at the transition temperature. For bulk polymer, the measurement of \textit{Tg} by different methods has similar result. However, the results reported for thin films have shown quite disagreement among different experimental methods. We used NMR and fluorescence spectroscopy to detect interchain distance and found that the thin film and the freeze-dried polymers show reduced packing densities. And we also found no thickness dependence of \textit{Tg} in thin film and no changes of \textit{Tg} in the freeze-dried polymer measured by calorimetric method or by dynamic mechanical thermal analysis. However the \textit{Tg} in the same samples measured by thermo-mechanical analysis or by positron annihilation lifetime spectroscopy is significantly lower than that in bulk polymers. We argue that the reduction in packing density is a major factor which causes the disagreement among \textit{Tg} measured by different methods for thin films. During the processes of some measurements, an unjamming transition is proposed to take place, which reduces \textit{Tg}.   

The Effect of Molecular Weight on the Glass Transition Temperature of Polymer Thin Films

The thickness dependence of glass transition temperature (Tg) of polymer thin films has attracted considerable attention in both technological and scientific fields. With decreasing polymer film thickness d, the Tg(d) can decrease, increase or remain constant lying on the details of measurement techniques and sample preparation, etc. Using the recently developed differential alternating current chip calorimeter, we directly measured the calorimetric Tg of polystyrene thin films with various molecular weights. We found that when the molecular weight of polystyrene is below the critical chain entanglement, its Tg in a thin film with a thickness of 15 nm can reduce by 20 degrees (compared to bulk sample). However, the Tg of polystyrene film above the entanglement molecular weight remains constant as the film thickness changes. We argue that the molecular weight plays an important role in the thickness dependence of glass transition temperature of polymer thin films.   

Glassy dynamics within surface-bound molecular monolayers

Dynamics within a monolayer collection of surface-bound substituted-alkyl chains are studied with narrow-band dielectric spectroscopy. A transition from independent (intra-molecular) motion in low density systems to complex, glassy (inter-molecular) motion as the density is increased is observed. At high density, both the glassy mode [1,2] and the sub-Tg relaxation [3] have direct analogy to equivalent relaxations in polyethylene. Thus this experimental approach enables observation of the formation of a fragile glass as an explicit function of density; in addition by altering the molecular characteristics and surface arrangement, resultant changes in the nature of the glass transition (its glass transition temperature Tg and fragility m) can be determined. The effects of packing efficiency, chain length, and molecule-molecule interactions, as tuned by altering dipoles within the chain, will be discussed.\\[4pt] [1] M. C. Scott\textit{ etal.}, \textit{ACS Nano} \textbf{2}, 2392 (2008);\\[0pt] [2] M. Beiner, and H. Huth, \textit{Nature Materials} \textbf{2}, 595 (2003);\\[0pt] [3] Q. Zhang\textit{ et al.}, \textit{J. Phys. Chem. B} \textbf{110}, 4924 (2006).   

Interchain Coupling in Thin Polymer Film Studied by Fluorescence Nonradiative Energy Transfer

According to many views, the glass transition temperature (Tg) changes with decreasing polymer film thickness. There is an ongoing debate on the origin of the changes. As an important parameter, however, the interchain distance of thin film was still a challenge. We used Non-radiative energy transfer (NET) method to characterize polymer interchain proximity and association in polymer thin film, by attaching carbazolyl probe (donor) or anthryl probe (accepter) to the side groups of polymethyl methacrylate (PMMA) chain, respectively. We measured the NET results of PMMA films on silicon and found that the NET results decreased with decreasing film thickness. The NET results represented the interchain distance or density. With decreasing film thickness h, the density of the films decreased, which caused an increment of the polymer chain mobility. That might help us to understand the physical nature Tg changes.   

Impact of annealing and adsorption on the distribution of segmental mobility and tracer diffusivity of ultrathin films of polystyrene

We show experimental evidence that the changes ultrathin films undergo during annealing are strongly correlated to the amount of chains irreversibly adsorbed at the interface. A careful analysis of the time evolution of the dielectric function during annealing steps above Tg revealed three different regimes: at times much shorter than the adsorption time, the thickness of the adsorbed layer is constant and the interface mimics the effect of a free surface (packing frustration); upon increase of surface coverage, the films undergo a series of metastable states characterized by the largest changes in the deviations from bulk behavior; finally, when the thicknesses of the irreversibly adsorbed layer doubles its starting value, the system approach a new equilibrium whose properties are fixed by the new interfacial configurations. Our picture is further confirmed by the effect of annealing on the distribution of glass transition temperatures [1], dielectric relaxation strength and tracer diffusivity at different distances from the adsorbing interface. \\[4pt] [1] Rotella, Napolitano et al. Macromolecules, 2010, 43, 8686-8691