Glass transition dynamics of stacked thin polymer films

Thickness Dependence of Segmental Dynamics in Free-Standing Thin Films Predicted by a Dynamically Correlated Network Model

The anomalous dynamics and glass transition behaviors of supercooled liquids under nanoconfinement, such as ultrathin polymer films, have attracted much attention in recent decades. However, a complete elucidation of this mechanism has not yet been achieved. For the dynamics of bulk materials without confinement, we previously proposed a dynamically correlated network (DCN) model, which was found to agree well with the experimental data. The model assumes that segments with thermal fluctuations are dynamically correlated to their neighbors to form string-like clusters, which eventually grow into networks as temperature decreases. In this study, we applied the DCN model to nanoconfined free-standing films by using a simple cubic lattice sandwiched between two free surface layers consisting of virtual "uncorrelated" segments. The average size of DCNs at lower temperatures decreased with decreasing thickness because of confinement. This trend was associated with a decrease in the percolation temperature at which the size of DCN diverges. It was also revealed that the fractal dimension of the generated DCNs exhibits a peak with respect to temperature. The segmental relaxation time for free-standing polystyrene films was evaluated, and the predicted thickness dependence of the glass transition temperature qualitatively agreed with the experimental data. The results suggest that the concept of DCN is compatible with the dynamics of free-standing thin films.

Experimental and Modeling Comparison of the Dynamics of Capped and Freestanding Poly(2-chlorostyrene) Films

Proximity to a nonrepulsive wall is commonly considered to cause slower dynamics, which should lead to greater relaxation times for capped thin polymer films than for bulk melts. To the contrary, here we demonstrate that Al-capped films of poly(2-chlorostyrene) exhibit enhanced dynamics with respect to the bulk, similar to analogous freestanding films. To quantitatively resolve the impact of interfaces on whole film dynamics, we analyzed the experimental data via the Cooperative Free Volume rate model. We found that the interfacial region adjacent to a cap contains an excess of free volume (relative to the bulk) about half of that proximate to a free surface. Employing a useful analogy between confinement and pressure effects, we estimated that the effect of capping an 18 nm freestanding film would be equivalent to applying a pressure increase of 19 MPa.

The dynamics of freestanding films: predictions for poly(2-chlorostyrene) based on bulk pressure dependence and thoughtful sample averaging

In this paper we model the segmental relaxation in poly(2-chlorostyrene) 18 nm freestanding films, using only data on bulk samples to characterize the system, and predict film relaxation times (τ) as a function of temperature that are in semi-quantitative agreement with film data. The ability to translate bulk characterization into film predictions is a direct result of our previous work connecting the effects of free surfaces in films with those of changing pressure in the bulk. Our approach combines the Locally Correlated Lattice (LCL) equation of state for prediction of free volume values (V_free) at any given density (ρ), which are then used in the Cooperative Free Volume (CFV) rate model to predict τ(T, V_free). A key feature of this work is that we calculate the locally averaged density profile as a function of distance from the surface, ρ_av(z), using the CFV-predicted lengthscale, L_coop(z), over which rearranging molecular segments cooperate. As we have shown in the past, ρ_av(z) is significantly broader than the localized profile, ρ(z), which translates into a relaxation profile, τ(z), exhibiting a breadth that mirrors experimental and simulated results. In addition, we discuss the importance of averaging the log of position dependent relaxation times across a film sample (〈log τ(z)〉), as opposed to averaging the relaxation times, themselves, in order to best approximate a whole sample-averaged value that can be directly compared to experiment.

Nature of dynamic gradients, glass formation, and collective effects in ultrathin freestanding films

Molecular, polymeric, colloidal, and other classes of liquids can exhibit very large, spatially heterogeneous alterations of their dynamics and glass transition temperature when confined to nanoscale domains. Considerable progress has been made in understanding the related problem of near-interface relaxation and diffusion in thick films. However, the origin of "nanoconfinement effects" on the glassy dynamics of thin films, where gradients from different interfaces interact and genuine collective finite size effects may emerge, remains a longstanding open question. Here, we combine molecular dynamics simulations, probing 5 decades of relaxation, and the Elastically Cooperative Nonlinear Langevin Equation (ECNLE) theory, addressing 14 decades in timescale, to establish a microscopic and mechanistic understanding of the key features of altered dynamics in freestanding films spanning the full range from ultrathin to thick films. Simulations and theory are in qualitative and near-quantitative agreement without use of any adjustable parameters. For films of intermediate thickness, the dynamical behavior is well predicted to leading order using a simple linear superposition of thick-film exponential barrier gradients, including a remarkable suppression and flattening of various dynamical gradients in thin films. However, in sufficiently thin films the superposition approximation breaks down due to the emergence of genuine finite size confinement effects. ECNLE theory extended to treat thin films captures the phenomenology found in simulation, without invocation of any critical-like phenomena, on the basis of interface-nucleated gradients of local caging constraints, combined with interfacial and finite size-induced alterations of the collective elastic component of the structural relaxation process.

To Understand Film Dynamics Look to the Bulk

We show that shifts in dynamics of confined systems relative to that of the bulk material originate in the properties of bulk alone, and exhibit the same form of behavior as when different bulk isobars are compared. For bulk material, pressure-dependent structural relaxation times follow τ(T,V)∝exp[f(T)×g(V)]. When two states (isobars) of the material, "1" and "2", are compared at the same temperature this leads to a form τ_{2}∝τ_{1}^{c}, where c=g[V_{2}(T)]/g[V_{1}(T)]. Using equation of state analysis and two models for P-dependent dynamics, we show that c is approximately T independent, and that it can be very simply expressed in terms of either the (free) volume above the close packed state (V_{free}) or the activation energy for cooperative motion. The effect of changing state through a shift in pressure (P_{1} to P_{2}) is thus mechanistically traceable to cooperativity changing with density, through V_{free}. The connection with confined dynamics follows when 1 and 2 are taken as bulk and film at ambient P, differing in density only due to the film surface. The general form for τ(T,V) also illuminates why samples in different states (film vs bulk, high P vs low) trend toward the same relaxation behavior at high T.

Substrate Roughness Speeds Up Segmental Dynamics of Thin Polymer Films

We show that the segmental mobility of thin films of poly(4-chlorostyrene) prepared under nonequilibrium conditions gets enhanced in the proximity of rough substrates. This trend is in contrast to existing treatments of roughness which conclude it is a source of slower dynamics, and to measurements of thin films of poly(2-vinylpiridine), whose dynamics is roughness invariant. Our experimental evidence indicates the faster interfacial dynamics originate from a reduction in interfacial density, due to the noncomplete filling of substrate asperities. Importantly, our results agree with the same scaling that describes the density dependence of bulk materials, correlating segmental mobility to a term exponential in the specific volume, and with empirical relations linking an increase in glass transition temperature to larger interfacial energy.

Direct observation of mobility of thin polymer layers via asymmetric interdiffusion using neutron reflectivity measurements

In this study, we investigated the diffusion dynamics at the interface between deuterated poly(methyl methacrylate) (d-PMMA) and protonated poly(methyl methacrylate) (h-PMMA) in two-layered thin films of d- and h-PMMA layers via neutron reflectivity (NR) measurements during isothermal annealing above the glass transition temperature T_g. When T_g of d-PMMA was higher than that of h-PMMA, the d-PMMA layer thickness increased with increasing annealing time t_a and, simultaneously, the h-PMMA layer thickness decreased. However, the opposite t_a dependence of the layer thicknesses was observed, if the T_g of d-PMMA was decreased by the increase in the fraction of the low-molecular weight d-PMMA: With increasing t_a, the d-PMMA layer thickness decreased and the h-PMMA layer thickness increased when T_g of d-PMMA was lower than that of h-PMMA. This change in the t_a dependence of the layer thickness was related to the change in the mobility of the d-PMMA layer accompanied by the change in the T_g value of d-PMMA. With the decrease in the d-PMMA layer thickness from 49 nm to 13 nm, when the h-PMMA layer thickness was maintained, the t_a dependence of the layer thickness changed and the mobility of the d-PMMA layer dramatically increased. These results suggest that the mobility of thin polymer films can be determined by the observation of interfacial dynamics via NR measurements.

Solution filtering affects the glassy dynamics of spincoated thin films of poly(4-chlorostyrene)

We investigated the impact of sample preparation on the glassy dynamics of thin films of poly(4-chlorostyrene), a polymer whose molecular mobility is particularly sensitive to changes in the specific volume. Samples were obtained by spincoating, the technique most commonly used to prepare thin organic layers, which consists of pouring dilute polymer solutions onto a plate rotating at a high rate. Our experimental results demonstrate that filtering the solutions before spincoating affects the value of the segmental relaxation time of the as-prepared films. Thin polymer layers obtained via filtered solutions show accelerated segmental dynamics upon confinement at the nanoscale level, once below 100nm, while the samples obtained via unfiltered solutions exhibit bulk-like dynamics down to 15-20nm. We analyzed these results by means of the cooperative free volume rate model, considering a larger free volume content in thin films obtained via filtered solutions. The validity of the model predictions was finally verified by measurements of irreversible adsorption, confirming a larger adsorbed amount, corresponding to a higher specific volume, in the case of samples obtained via unfiltered solutions. Our results prove that filtering is a crucial step in the preparation of thin films, and it could be used to switch on and off nanoconfinement effects.

Irreversible Adsorption Governs the Equilibration of Thin Polymer Films

We demonstrate that the enhanced segmental motion commonly observed in spin cast thin polymer films is a nonequilibrium phenomenon. In the presence of nonrepulsive interfaces, prolonged annealing in the liquid state allows, in fact, recovering bulk segmental mobility. Our measurements prove that, while the fraction of unrelaxed chains increases upon nanoconfinement, the dynamics of equilibration is almost unaffected by the film thickness. We show that the rate of equilibration of nanoconfined chains does not depend on the structural relaxation process but on the feasibility to form an adsorbed layer. We propose that the equilibration of the thin polymer melts is driven by the slow relaxation of interfacial chains upon irreversible adsorption on the confining walls.

Interfacial interaction and glassy dynamics in stacked thin films of poly(methyl methacrylate)

Neutron reflectivity and dielectric permittivity of alternately stacked thin films of protonated and deuterated poly(methyl methacrylate) were measured to elucidate a correlation between the time evolution of the interfacial structure and the segmental dynamics in the stacked thin polymer films during isothermal annealing above the glass transition temperature. The roughness at the interface between two thin layers increases with the annealing time, whereas the relaxation rate and strength of the α-process decrease with an increase in the annealing time. A strong correlation between the time evolution of the interfacial structure and the dynamics of the α-process during annealing could be observed using neutron reflectivity and dielectric relaxation measurements.

Glass transition of polymers in bulk, confined geometries, and near interfaces

When cooled or pressurized, polymer melts exhibit a tremendous reduction in molecular mobility. If the process is performed at a constant rate, the structural relaxation time of the liquid eventually exceeds the time allowed for equilibration. This brings the system out of equilibrium, and the liquid is operationally defined as a glass-a solid lacking long-range order. Despite almost 100 years of research on the (liquid/)glass transition, it is not yet clear which molecular mechanisms are responsible for the unique slow-down in molecular dynamics. In this review, we first introduce the reader to experimental methodologies, theories, and simulations of glassy polymer dynamics and vitrification. We then analyse the impact of connectivity, structure, and chain environment on molecular motion at the length scale of a few monomers, as well as how macromolecular architecture affects the glass transition of non-linear polymers. We then discuss a revised picture of nanoconfinement, going beyond a simple picture based on interfacial interactions and surface/volume ratio. Analysis of a large body of experimental evidence, results from molecular simulations, and predictions from theory supports, instead, a more complex framework where other parameters are relevant. We focus discussion specifically on local order, free volume, irreversible chain adsorption, the Debye-Waller factor of confined and confining media, chain rigidity, and the absolute value of the vitrification temperature. We end by highlighting the molecular origin of distributions in relaxation times and glass transition temperatures which exceed, by far, the size of a chain. Fast relaxation modes, almost universally present at the free surface between polymer and air, are also remarked upon. These modes relax at rates far larger than those characteristic of glassy dynamics in bulk. We speculate on how these may be a signature of unique relaxation processes occurring in confined or heterogeneous polymeric systems.

The architecture of the adsorbed layer at the substrate interface determines the glass transition of supported ultrathin polystyrene films

To elucidate the mechanism underlying the effect of polymer/solid interfacial interactions on the dynamics of thin polymer films, the glass transition of thin end-functionalized polystyrene films supported on SiO₂-Si, such as proton-terminated PS (PS-H), α,ω-dicarboxy-terminated PS (PS-COOH), and α,ω-dihydroxyl-terminated PS (PS-OH), was investigated. All the PS films exhibited a substantial depression in T_g with decreasing film thickness, while the extent of such depression was strongly dependent on the chemical structure of the end groups and molecular weights. It was found that T - T of the various PS films increased linearly with increasing h_ads/R_g, in which h_ads is the thickness of the interfacial adsorbed layer and R_g is the radius of gyration of PS. The h_ads/R_g is a direct reflection of the macromolecular chain conformation within the adsorbed layer which was affected by its end groups and molecular weights. These findings are in line with the work of Napolitano, and present direct experimental evidence.

Segmental and local dynamics of stacked thin films of poly(methyl methacrylate)

The glass transition temperature and the dynamics of the α and β processes have been investigated using differential scanning calorimetry and dielectric relaxation spectroscopy during successive annealing processes above the glass transition temperature for stacked thin films of poly(methyl methacrylate) (PMMA) of various thicknesses. The glass transition temperature and the dynamics of the α process (segmental motion) of as-stacked PMMA thin films exhibit thin-film-like behavior, insofar as the glass transition temperature is depressed and the dynamics of the α process are faster than those of the bulk system. Annealing at high temperature causes the glass transition temperature to increase from the reduced value and causes the dynamics of the α process to become slower approaching those of the bulk. Contrary to the segmental motion, the relaxation time of the β process (local motion) of the stacked PMMA thin films is almost equal to that of the bulk PMMA and is unaffected by the annealing process. However, the relaxation strengths of both the α process and β process show a strong correlation between each other. The sum of the relaxation strengths remains almost unchanged, while the individual relaxation strengths change during the annealing process. The fragility index of the stacked PMMA thin films increases with annealing, which suggests that the glassy state of the stacked thin films changes from strong to fragile.

Glassy dynamics of soft matter under 1D confinement: how irreversible adsorption affects molecular packing, mobility gradients and orientational polarization in thin films

The structural dynamics of polymers and simple liquids confined at the nanometer scale has been intensively investigated in the last two decades in order to test the validity of theories on the glass transition predicting a characteristic length scale of a few nanometers. Although this goal has not yet been reached, the anomalous behavior displayed by some systems--e.g. thin films of polystyrene exhibit reductions of Tg exceeding 70 K and a tremendous increase in the elastic modulus--has attracted a broad community of researchers, and provided astonishing advancement of both theoretical and experimental soft matter physics. 1D confinement is achieved in thin films, which are commonly treated as systems at thermodynamic equilibrium where free surfaces and solid interfaces introduce monotonous mobility gradients, extending for several molecular sizes. Limiting the discussion to finite-size and interfacial effects implies that film thickness and surface interactions should be sufficient to univocally determine the deviation from bulk behavior. On the contrary, such an oversimplified picture, although intuitive, cannot explain phenomena like the enhancement of segmental mobility in proximity of an adsorbing interface, or the presence of long-lasting metastable states in the liquid state. Based on our recent work, we propose a new picture on the dynamics of soft matter confined in ultrathin films, focusing on non-equilibrium and on the impact of irreversibly chain adsorption on the structural relaxation. We describe the enhancement of dynamics in terms of the excess in interfacial free volume, originating from packing frustration in the adsorbed layer (Guiselin brush) at t(*) ≪ 1, where t(*) is the ratio between the annealing time and the time scale of adsorption. Prolonged annealing at times exceeding the reptation time (usually t(*) ≫ 1 induces densification, and thus reduces the deviation from bulk behavior. In this Colloquium, after reviewing the experimental approaches permitting to investigate the structural relaxation of films with one, two or no free surfaces by means of dielectric spectroscopy, we propose several methods to determine gradients of mobility in thin films, and then discuss on the unexploited potential of analyses based on the time, temperature and thickness dependence of the orientational polarization via the dielectric strength.