Comparing refractive index and density changes with decreasing film thickness in thin supported films across different polymers

Anomalously High Dielectric Strength and Capacitive Energy Density of Thin Entangled Glassy Polymer Films

The influence of high-intensity electric fields on the stability of polymeric materials is a problem of interest in the design of next-generation energy storage and electronic devices, and for understanding the limits of stability of polymer films exposed to large electric fields generally. Here, we show that the dielectric strength of entangled glassy polymer films increases as an inverse power-law of the film thickness h for "ultrathin" films below a micron in thickness. The dielectric strength enhancement in these polymer films becomes as large as ≈2 GV/m in films thinner than 100 nm, but in this thickness regime, the increase of the dielectric strength depends strongly on the polymer mass, sample aging time, and the method of film preparation. The enhancement of the dielectric breakdown strength is attributed to the mechanical instability of the elastic film subjected to sufficiently large electric fields and a large, but not generally well-understood, enhancement of effective stiffness of entangled glassy polymer films subject to large deformations, an effect that has previously been observed to become greatly enhanced when such films are made thinner. As a proof of principle regarding applications, we utilize ultrathin glassy polymer films of the type studied in our paper to fabricate polymeric nanocapacitors having ultrahigh discharge energy densities (U d max) as large as 27 J/cm3 and having efficiencies greater than 80%. These efficiency values at comparable charge densities are significantly higher than those of competing ferroelectric polymer materials, and we anticipate that our observations will inspire the creation of practical high-energy density nanocapacitor devices for advanced energy storage applications.

A Bayesian Inference Approach to Accurately Fitting the Glass Transition Temperature in Thin Polymer Films

We present a Bayesian inference-based nonlinear least-squares fitting approach developed to reliably fit challenging, noisy data in an automated and robust manner. The advantages of using Bayesian inference for nonlinear fitting are demonstrated by applying this approach to a set of temperature-dependent film thickness h(T) data collected by ellipsometry for thin films of polystyrene (PS) and poly(2-vinylpyridine) (P2VP). The glass transition experimentally presents as a continuous transition in thickness characterized by a change in slope that in thin films with broadened transitions can become particularly subtle and challenging to fit. This Bayesian fitting approach is implemented using existing open-source Python libraries that make these powerful methods accessible with desktop computers. We show how this Bayesian approach is more versatile and robust than existing methods by comparing it to common fitting methods currently used in the polymer science literature for identifying T g. As Bayesian inference allows for fitting to more complex models than existing methods in the literature do, our discussion includes an in-depth evaluation of the best functional form for capturing the behavior of h(T) data with temperature-dependent changes in thermal expansivity. This Bayesian fitting approach is easily automated, capable of reliably fitting noisy and challenging data in an unsupervised manner, and ideal for machine learning approaches to materials development.

High-density stable glasses formed on soft substrates

Enabled by surface-mediated equilibration, physical vapour deposition can create high-density stable glasses comparable with liquid-quenched glasses aged for millions of years. Deposition is often performed at various rates and temperatures on rigid substrates to control the glass properties. Here we demonstrate that on soft, rubbery substrates, surface-mediated equilibration is enhanced up to 170 nm away from the interface, forming stable glasses with densities up to 2.5% higher than liquid-quenched glasses within 2.5 h of deposition. Gaining similar properties on rigid substrates would require 10 million times slower deposition, taking ~3,000 years. Controlling the modulus of the rubbery substrate provides control over the glass structure and density at constant deposition conditions. These results underscore the significance of substrate elasticity in manipulating the properties of the mobile surface layer and thus the glass structure and properties, allowing access to deeper states of the energy landscape without prohibitively slow deposition rates.

Eliminating the Tg-confinement and fragility-confinement effects in poly(4-methylstyrene) films by incorporation of 3 mol % 2-ethylheyxl acrylate comonomer

Nanoconfined poly(4-methylstyrene) [P(4-MS)] films exhibit reductions in glass transition temperature (Tg) relative to bulk Tg (Tg,bulk). Ellipsometry reveals that 15-nm-thick P(4-MS) films supported on silicon exhibit Tg - Tg,bulk = - 15 °C. P(4-MS) films also exhibit fragility-confinement effects; fragility decreases ∼60% in going from bulk to a 20-nm-thick film. Previous research found that incorporating 2-6 mol  % 2-ethylhexyl acrylate (EHA) comonomer in styrene-based random copolymers eliminates Tg- and fragility-confinement effects in polystyrene. Here, we demonstrate that incorporating 3 mol  % EHA in a 4-MS-based random copolymer, 97/3 P(4-MS/EHA), eliminates the Tg- and fragility-confinement effects. The invariance of fragility with nanoconfinement of 97/3 P(4-MS/EHA) films, hypothesized to originate from the interdigitation of ethylhexyl groups, indicates that the presence of EHA prevents the free surface from perturbing chain packing and the cooperative mobility associated with Tg. This method of eliminating confinement effects is advantageous as it relies on the simplest of polymerization methods and neat copolymer only slightly altered in composition from homopolymer. We also investigated whether we could eliminate the Tg-confinement effect with low levels of 2-ethylhexyl methacrylate (EHMA) in 4-MS-based or styrene-based copolymers. Although EHMA is structurally nearly identical to EHA, 4-MS-based and styrene-based copolymers incorporating 4 mol  % EHMA exhibit Tg-confinement effects similar to P(4-MS) and polystyrene. These results support the special character of EHA in eliminating confinement effects originating at free surfaces.

Isotropic and Anisotropic Complex Refractive Index of PEDOT:PSS

In this work, the complex refractive indexes of seven PEDOT:PSS samples, three with isotropic behavior and four with optical anisotropy, were determined. For the anisotropic samples, the ordinary and extraordinary components of the refractive index were described. The effect of the film thickness, measurement technique and preparation method on the extinction coefficient (k) and refractive index (n) of each sample was also discussed. Important differences (up to 20% in the average n) were found among the samples investigated. In most anisotropic films, the mean value of the extraordinary component was between 7 and 10% higher than that of the ordinary. In the three isotropic films, the average k rose when the film thickness increased. Moreover, the different sets of refractive index data were fitted to three different models: the original Forouhi-Bloomer model, the Liu (2007) model and the revised version of the Forouhi-Bloomer model (2019). In general, Liu's model gave better results, with small errors in n and k (<7.81 and 4.68%, respectively, in all the cases). However, this model had seven fitting parameters, which led to significantly longer computation time than the other two models. The influence of the differences in the measurement of the complex refractive index on the simulation of the optical properties of PEDOT:PSS multilayers was discussed. The results showed that n must be known precisely to accurately calculate the light absorption in a multilayer, without ignoring the isotropic or anisotropic behavior of the material or the influence of the layer thickness on its optical properties. This study aids in the development of simulation and optimization tools that allow understanding the optical properties of PEDOT:PSS films for their potential applications in organic optoelectronic devices, such as organic solar cells.

Growth kinetics of the adsorbed layer of poly(bisphenol A carbonate) and its effect on the glass transition behavior in thin films

The glass transition behavior of thin films of poly(bisphenol A carbonate) (PBAC) was studied employing ellipsometry. The glass transition temperature increases with the reduction of the film thickness. This result is attributed to the formation of an adsorbed layer with a reduced mobility compared to bulk PBAC. Therefore, for the first time, the growth kinetics of the adsorbed layer of PBAC was investigated, prepared by leaching samples from a 200 nm thin film which were annealed for several times at three different temperatures. The thickness of each prepared adsorbed layer was measured by multiple scans using atomic force microscopy (AFM). Additionally, an unannealed sample was measured. Comparison of the measurements of the unannealed and the annealed samples provides proof of a pre-growth regime for all annealing temperatures which was not observed for other polymers. For the lowest annealing temperature after the pre-growth stage only a growth regime with a linear time dependence is observed. For higher annealing temperatures the growth kinetics changes from a linear to a logarithmic growth regime at a critical time. At the longest annealing times the films showed signs of dewetting where segments of the adsorbed film were removed from the substrate (dewetting by desorption). The dependence of the surface roughness of the PBAC surface on annealing time also confirmed that the films annealed at highest temperatures for the longest times desorbed from the substrate.

End-Tethered Chains Increase the Local Glass Transition Temperature of Matrix Chains by 45 K Next to Solid Substrates Independent of Chain Length

The local glass transition temperature T_g of pyrene-labeled polystyrene (PS) chains intermixed with end-tethered PS chains grafted to a neutral silica substrate was measured by fluorescence spectroscopy. To isolate the impact of the grafted chains, the films were capped with bulk neat PS layers eliminating competing effects of the free surface. Results demonstrate that end-grafted chains strongly increase the local T_g of matrix chains by ≈45 K relative to bulk T_g, independent of grafted chain molecular weight from M_n = 8.6 to 212 kg/mol and chemical end-group, over a wide range of grafting densities σ = 0.003 to 0.33 chains/nm² spanning the mushroom-to-brush transition regime. The tens-of-degree increase in local T_g resulting from immobilization of the chain ends by covalent bonding in this athermal system suggests a mechanism that substantially increases the local activation energy required for cooperative rearrangements.

Enhanced Dielectric Strength and Capacitive Energy Density of Cyclic Polystyrene Films

The maximum capacitive energy stored in polymeric dielectric capacitors, which are ubiquitous in high-power-density devices, is dictated by the dielectric breakdown strength of the dielectric polymer. The fundamental mechanisms of the dielectric breakdown, however, remain unclear. Based on a simple free-volume model of the polymer fluid state, we hypothesized that the free ends of linear polymer chains might act as “defect” sites, at which the dielectric breakdown can initiate. Thus, the dielectric breakdown strength of cyclic polymers should exhibit enhanced stability in comparison to that of their linear counterparts having the same composition and similar molar mass. This hypothesis is supported by the ∼50% enhancement in the dielectric breakdown strength and ∼80% enhancement in capacitive energy density of cyclic polystyrene melt films in comparison to corresponding linear polystyrene control films. Furthermore, we observed that cyclic polymers exhibit a denser packing density than the linear chain melts, an effect that is consistent with and could account for the observed property changes. Our work demonstrates that polymer topology can significantly influence the capacitive properties of polymer films, and correspondingly, we can expect polymer topology to influence the gas permeability, shear modulus, and other properties of thin films dependent on film density.

Complexities in Modeling Organic Aerosol Light Absorption

Aerosol particles dynamically evolve in the atmosphere by physicochemical interactions with sunlight, trace chemical species, and water. Current modeling approaches fix properties such as aerosol refractive index, introducing spatial and temporal errors in the radiative impacts. Further progress requires a process-level description of the refractive indices as the particles age and experience physicochemical transformations. We present two multivariate modeling approaches of light absorption by brown carbon (BrC). The initial approach was to extend the modeling framework of the refractive index at 589 nm (nD), but that result was insufficient. We developed a second multivariate model using aromatic rings and functional groups to predict the imaginary part of the complex refractive index. This second model agreed better with measured spectral absorption peaks, showing promise for a simplified treatment of BrC optics. In addition to absorption, organic functionalities also alter the water affinity of the molecules, leading to a hygroscopic uptake and increased light absorption, which we show through measurements and modeling.

Gradient in refractive index reveals denser near free surface region in thin polymer films

A gradient in refractive index that is linear in magnitude with depth into the film is used to fit ellipsometric data for thin polymer films of poly(methyl methacrylate) (PMMA), polystyrene (PS), and poly(2-vinyl pyridine) (P2VP). We find that the linear gradient model fits provide more physically realistic refractive index values for thin films compared with the commonly used homogeneous Cauchy layer model, addressing recent reports of physically unrealistic density increases. Counter to common expectations of a simple free volume correlation between density and dynamics, we find that the direction of refractive index (density) gradient indicates a higher density near the free surface, which we rationalize based on the observed faster free surface dynamics needed to create vapor deposited stable glasses with optimized denser molecular packings. The magnitude of refractive index gradient is observed to be three times larger for PMMA than for PS films, while P2VP films exhibit a more muted response possibly reflective of a decoupling in free surface and substrate dynamics in systems with strong interfacial interactions.

Simultaneous Determination of Refractive Index and Thickness of Submicron Optical Polymer Films from Transmission Spectra

High-transparency polymers, called optical polymers (OPs), are used in many thin-film devices, for which the knowledge of film thickness (h) and refractive index (n) is generally required. Spectrophotometry is a cost-effective, simple and fast non-destructive method often used to determine these parameters simultaneously, but its application is limited to films where h > 500 nm. Here, a simple spectrophotometric method is reported to obtain simultaneously the n and h of a sub-micron OP film (down to values of a few tenths of a nm) from its transmission spectrum. The method is valid for any OP where the n dispersion curve follows a two-coefficient Cauchy function and complies with a certain equation involving n at two different wavelengths. Remarkably, such an equation is determined through the analysis of n data for a wide set of commercial OPs, and its general validity is demonstrated. Films of various OPs (pristine or doped with fluorescent compounds), typically used in applications such as thin-film organic lasers, are prepared, and n and h are simultaneously determined with the proposed procedure. The success of the method is confirmed with variable-angle spectroscopic ellipsometry.

Glasses denser than the supercooled liquid

When aged below the glass transition temperature, [Formula: see text], the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid-liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N'-bis(3-methylphenyl)-N,N'-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid-liquid phase transition temperature ([Formula: see text]) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Polymers under nanoconfinement: where are we now in understanding local property changes?

Polymers are increasingly being used in applications with nanostructured morphologies where almost all polymer molecules are within a few tens to hundreds of nanometers from some interface. From nearly three decades of study on polymers in simplified nanoconfined systems such as thin films, we have come to understand property changes in these systems as arising from interfacial effects where local dynamical perturbations are propagated deeper into the material. This review provides a summary of local glass transition temperature T_g changes near interfaces, comparing across different types of interfaces: free surface, substrate, liquid, and polymer-polymer. Local versus film-average properties in thin films are discussed, making connections to other related property changes, while highlighting several historically important studies. By experimental necessity, most studies are on high enough molecule weight chains to be well entangled, although aspects that connect to lower molecule weight materials are described. Emphasis is made to identify observations and open questions that have yet to be fully understood such as the evidence of long-ranged interfacial effects, finite domain size, interfacial breadth, and chain connectivity.