Molecular Aspect Ratio Research Articles

Giant Molecular Shape Amphiphiles Based on Polystyrene–Hydrophilic [60]Fullerene Conjugates: Click Synthesis, Solution Self-Assembly, and Phase Behavior

This paper reports a comprehensive study on the synthesis and self-assembly of two model series of molecular shape amphiphiles, namely, hydrophilic [60]fullerene (AC(60)) tethered with one or two polystyrene (PS) chain(s) at one junction point (PS(n)-AC(60) and 2PS(n)-AC(60)). The synthesis highlighted the regiospecific multiaddition reaction for C(60) surface functionalization and the Huisgen 1,3-dipolar cycloaddition between alkyne functionalized C(60) and azide functionalized polymer to give rise to shape amphiphiles with precisely defined surface chemistry and molecular topology. When 1,4-dioxane/DMF mixture was used as the common solvent and water as the selective solvent, these shape amphiphiles exhibited versatile self-assembled micellar morphologies which can be tuned by changing various parameters, such as molecular topology, polymer tail length, and initial molecular concentration, as revealed by transmission electron microscopy and light scattering experiments. In the low molecular concentration range of equal or less than 0.25 (wt) %, micellar morphology of the series of PS(n)-AC(60) studied was always spheres, while the series of 2PS(n)-AC(60) formed vesicles. Particularly, PS(44)-AC(60) and 2PS(23)-AC(60) are synthesized as a topological isomer pair of these shape amphiphiles. PS(44)-AC(60) formed spherical micelles while 2PS(23)-AC(60) generated bilayer vesicles under identical conditions. The difference in the self-assembly of PS(n)-AC(60) and 2PS(n)-AC(60) was understood by the molecular shape aspect ratio. The stretching ratio of PS tails decreased with increasing PS tail length in the spherical micelles of PS(n)-AC(60), indicating a micellar behavior that changes from small molecular surfactant-like to amphiphilic block copolymer-like. For the series of PS(n)-AC(60) in the high molecular concentration range [>0.25 (wt) %], their micellar morphological formation of spheres, cylinders, and vesicles was critically dependent upon both the initial molecular concentration and the PS tail length. On the other hand, the series of 2PS(n)-AC(60) remained in the state of bilayer vesicles in the same concentration range. Combining both of the experimental results obtained in the low and high molecular concentrations, a systematic morphological phase diagram was constructed for the series of PS(n)-AC(60) with different PS tail lengths. The versatile and concentration-sensitive phase behaviors of these molecular shape amphiphiles are unique and have not been systematically explored in the traditional surfactants and block copolymers systems.

Synthesis and optical behaviour of hydrogen-bonded liquid crystals based on a chiral pyridine derivative

Three series of cholesteryl-containing supramolecular hydrogen-bonded (H-bonded) liquid crystal (LC) complexes with different number of fluoro-substituent were synthesised and characterised. Cholesteryl isonicotinate as proton acceptor and 4-n-alkoxybenzoic acids with or without fluoro-substituent as proton donor had been mixed in tetrahydrofuran to obtain H-bonded LC complexes. The effect of lateral substitution and the length of terminal chain in the H-bonded precursors on the formation of the supramolecular complexes had been examined. It was found that the introduction of fluoro substituent on the induced mesogens could widen the molecular width and thus reduce the molecular aspect ratio of the complexes, therefore it could lead to compress the formation of the LCs. However, the fluoro substituent played a positive role in enhancing the intermolecular interactions and stabilising the H-bond structure of the complexes. The influence of terminal length on the mesogenic behaviours is also discussed. On increasing the spacer length, the clear point and the thermal range of induced mesophase-like cholesteric phase decreased, and an induced chiral smectic phase began to appear in some complexes with long terminal tails.

Three-dimensional molecular dynamics simulations of reorientation process and backflow generation in nematic liquid crystals under application of electric fields

The dynamic responses of nematic liquid crystals in a parallel-plate cell under the application of electric fields were investigated using three-dimensional molecular dynamics simulations, which should provide more precise dynamics as compared to those in two-dimensional molecular dynamics simulations as in our previous work [Sunarso et al., Appl. Phys. Lett. 93, 244106 (2008)]. The study is focused on the reorientation process and the generation of backflow, which should be important in the development of liquid crystalline actuators. It is shown that bulk reorientation is coupled with the generation of backflow owing to the conversion of electric-field-induced molecular rotation into bulk translational motion. The increase in electric torque due to the increase in electric field strength results in a faster change in the bulk orientation, thus accelerating the development of the flow field and increasing the magnitude of the generated velocity field. Different initial orientation angles result in similar dynamics, although the magnitude of the generated velocity decreases with increasing initial orientation angle. The development of velocity profiles confirms the results of the experiment and the simulation using a macroscopic continuum approach. Simulations under various molecular aspect ratios show that with an increase in the aspect ratio, the reorientation process becomes slower due to the increase in moment of inertia and elastic torque, whereas the magnitudes of the velocity show the trade-off between the speed of the orientation change and the effectiveness of the molecular motion conversion. Furthermore, the simulation results show the spatial variation in the reorientation process as the result of interplay between electric torque, elastic torque, and backflow.

Calorimetric and thermodynamic study of glass-forming monohydroxy alcohols

In this work, we review and concurrently discuss earlier and recent experiments performed on simple aliphatic glass-forming monoalcohols at low temperatures. By doing this, we find an interesting model system to explore different relevant issues concerning molecular glass-forming liquids and even the glass transition phenomenon itself. They include the role played by the molecular aspect ratio in vitrification/crystallisation kinetics, the reported appearance of particular cases of polymorphism and polyamorphism, and the influence of chemical isomerism and the location of the hydrogen bond on lattice dynamics and, hence, on low-temperature properties of glasses.

A numerical study based on a weakly compressible formulation for thermosolutal convection in vertical cavities

Laminar thermosolutal convection in cavities with uniform, constant temperature and mass fraction profiles at the vertical side is studied numerically. The study is conducted in the case where an inert carrier gas (species “1”) present in the cavity is not soluble in species “2”, and do not diffuse into the walls. A mass flux of species “2” into the cavity occurs at the hot vertical wall and a mass flux out of the cavity occurs at the opposite cold wall. The weakly compressible model proposed in this work was used to investigate the flow fields, and heat and mass transfer in cavities filled with binary mixtures of ideal gases. The dimensionless form of the seven governing equations for constant thermophysical properties, except density, show that the problem formulation involves ten dimensionless parameters. The results were validated against numerical results published in the literature for purely thermal convection, and thermodynamic predictions for transient thermosolutal flows. A parametric study has been performed to investigate the effects of the initial conditions, molecular weight ratio, Lewis number, and aspect ratio of the cavity for aiding or opposing buoyancy forces. For the range of parameters considered, the results show that variations in the density field have larger effects on mass transfer than on heat transfer. For opposing buoyancy forces, the numerical simulations predict complex flow structures and possible chaotic behavior for rectangular vertical cavities according to the value of the molecular weight ratio.

Advances in generalised van der Waals approaches for the isotropic–nematic fluid phase equilibria of thermotropic liquid crystals–an algebraic equation of state for attractive anisotropic particles with the Onsager trial function

In this contribution we provide a review and reformulation of perturbation theories (generalised van der Waals approaches) for the description of the fluid phase behaviour and orientational ordering transitions of thermotropic nematic liquid crystals. Free-energy functionals of the basic Onsager form are used as the platform for the development of a general formulation that reduces to the specific forms of the various theories that have found common use. A novel closed analytical description of the thermodynamic properties and degree of nematic order is then obtained by employing the Onsager trial function to represent the orientational distribution function in terms of a single parameter. The latter essentially constitutes an algebraic equation of state for the nematic phase appropriate for use in engineering applications. The description of ordering transitions with scaled-Onsager theories and suitable trial functions has already been illustrated by its application to systems of hard spherocylinders (HSCs), indicating that the approach provides an excellent representation of the orientational order of the hard-core (athermal) system [Mol. Phys. 106, 649 (2008)]. Here, the hard-body model is extended to account for attractive interactions (treated at the van der Waals level) of a general isotropic/anisotropic form (e.g., Lennard-Jonesium (LJ), square-well (SW), Maier–Saupe (MS), etc.). The adequacy of our generalised van der Waals–Onsager theory is exemplified by an analysis of the vapour–liquid, liquid–nematic, and vapour–nematic phase equilibria for hard spherocylinders with attractive square-well interactions (HSC-SW). The effect of the potential range and molecular aspect ratio on the vapour–liquid–nematic equilibria and orientational ordering transitions is examined to investigate the van der Waals limit (corresponding states) of the ordering phase behaviour. In the case of systems with an aspect ratio of ∼5 the corresponding-states limit is reached when the range is about 16 times the molecular diameter. For progressively longer molecules with an attractive range that follows their long dimension, the fluid–nematic equilibrium is enhanced to the point that the vapour–liquid boundary becomes metastable relative to fluid–nematic equilibria. In the case of molecules of very large aspect ratio (∼50), an additional region of nematic–nematic coexistence is exhibited by the system.

A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

The molecular theory of Onsager [L. Onsager, Ann. N.Y. Acad. Sci. 51, 627 (1949)] for liquid crystals is developed and extended to describe ordering transitions in systems of generic cylindrically symmetrical molecules. A number of new analytical results are discussed for particles characterised by a general form of the excluded-volume interaction. Our description makes use of the Onsager trial function (OTF) to represent the orientational distribution and degree of anisotropy. Algebraic expressions for the thermodynamic properties, which provide a particularly tractable description of the isotropic–nematic equilibria, are also presented. The degree of orientational order can be represented by a simple cubic equation in the molecular parameters (molecular diameter and aspect ratio) and thermodynamic variables (temperature and number density). Onsager's theory was originally developed at the level of the second virial coefficient; here the Parsons–Lee decoupling approximation is used to describe the higher-body contributions in a straightforward manner. The adequacy of treating the scaled Onsager (Parsons–Lee) free-energy functional within the OTF formalism to describe anisotropic states is illustrated by examining systems of hard spherocylinders. An excellent representation of the equation of state of the isotropic and nematic phases and the ordering transition is demonstrated for molecules of moderate aspect ratio (L/D = 5). Algebraic equations of state of the type developed here are suitable for practical engineering applications involving anisotropic fluids particularly in the case of multicomponent systems; our general analytical results for the averages of orientational functions will turn out to be useful in the development of a description of molecules with more realistic attractive and Maier–Saupe interactions.

Surface adsorption of comb polymers by Monte Carlo simulations

This paper reports off-lattice Monte Carlo simulations of highly-branched comb homopolymers weakly adsorbed on a flat, featureless surface showing only covolume and dispersion interactions with the adsorbate. A minimal coarse-grained model, described by hard spheres connected by harmonic springs, was employed. The interaction energy of the adsorbed combs and linear chains is first discussed as a function of the molecular mass and of the number of beads in contact with the surface. The molecular size is then investigated as a function of backbone length and branching density at a fixed arm size. The apparent swelling exponents of the adsorbed combs are larger than those of the corresponding linear chains, and much larger than that of the free molecules. This result indicates a surface-induced stiffening of the comb backbone, further studied through the persistence length lpers. It is found that lpers increases upon adsorption over the free-molecule value, more so the larger is the branching density. Finally, the thickness of the adsorbed layer, the surface-induced molecular anisotropy and the molecular aspect ratio are investigated as a function of branching density and molecular mass.

The influence of molecular structure on helical twisting power of chiral azobenzene compounds

Photochromic chiral azobenzene compounds with different molecular structures were synthesized, and a cholesteric phase was induced by mixing each chiral azobenzene compound with a non‐photochromic chiral compound in a host nematic liquid crystal, E44. Helical pitch and, thus, helical twisting powers (HTP) of the chiral azobenzene compounds and the non‐photochromic chiral compound were determined by Cano's wedge method. Molecular structures of the chiral azobenzene compounds were predicted by means of determining their molecular aspect ratio (L/D) with semiempirical molecular calculations (MOPAC at PM3 level). The effects of molecular structure on HTP of the chiral azobenzene compounds are studied in detail. Molecular structures of chiral azobenzene compounds significantly influence their HTPs.

Stability of Nematic and Smectic Phases in Rod-Like Mesogens with Orientation−Dependent Attractive Interactions

The stability of isotropic (I), nematic (N), smectic A (Sm A), and hexatic (Hex) liquid crystalline phases is studied for a fluid of molecules with a rod-like shape and dispersive interactions dependent on orientation. The fluid is modeled with the spherocylindrical Gay-Berne-Kihara interaction potential proposed in a recent work, with parameters favoring parallel pair orientations. The liquid crystal phase diagram is characterized for different molecular aspect ratios by means of Monte Carlo simulations in the isobaric-isothermal ensemble. Three types of triple points are observed, namely, I-Sm A-Hex, I-N-Sm A, and N-Sm A-Hex, leading to island-shape domains for the smectic A phase. The resulting phase diagrams are compared with those derived previously for prolate fluids of ellipsoidal and spherocylindrical symmetry. It is concluded that the stability of the layered phases with respect to the nematic phase is enhanced in the spherocylindrical fluids due to geometrical constraints. Furthermore, the anisotropy of the dispersive interactions induces a stronger dependence of the overall phase diagram on temperature and aids in the energetic stabilization of the hexatic crystalline phase with respect to the fluid smectic A phase.

Comprehensive Interpretation of Gel Electrophoresis Data

From temperature analysis of polyacrylamide gel electrophoresis data for rigid-rod DNA analytes, it is proposed that an entropic force term is responsible for the discrepancy between Ogston-Morris-Rodbard-Chrambach model predictions and experimental results. This entropic force originates from reduction of the orientational freedom of anisotropic analytes in small pores of polyacrylamide gels. Time-dependent fluorescence anisotropy decay measurements confirm that, even in the absence of an external field, orientation of anisotropic analytes is restricted in polyacrylamide gels. A new comprehensive model is proposed that takes this effect into consideration. Predictions based on this model are found to compare favorably with experimental data for linear and three-arm asymmetrically branched rigid-rod DNA analytes covering a broad range of molecular aspect ratios and sizes. A new length scale is also proposed for describing the effect of analyte topology on electrophoretic mobility. This length scale reduces to the analyte radius of gyration in the limiting cases of spherically symmetric and linear rigid-rod species. Based on these results, a general approach is proposed for interpreting gel electrophoresis data of charged analytes possessing simple and complex topologies.

Exact Scaling Laws for Electrical Conductivity Properties of Nematic Polymer Nanocomposite Monodomains

The purpose of this paper is to connect two critical aspects of nanocomposite materials engineering: the knowledge of the orientational distribution of quiescent or flowing anisotropic macromolecules, and homogenization theory of composites with spheroidal inclusions at low volume fractions. The nano-elements considered herein are derived from the class of high-aspect-ratio nematic polymers, either rod-like or platelet spheroids. By combining the two features, we derive the effective electrical conductivity tensor in closed form. Scaling properties of enhanced conductivity versus volume fraction and weak shear rate become explicit. The most dramatic effect is that the effective conductivity tensor inherits hysteresis, bi-stability, and discontinuous jumps from the isotropic–nematic first-order phase transition. These formulas reveal finer estimates that depend on a competition between two inherently extreme parameters in nematic polymer nanocomposites: the molecular aspect ratio and the conductivity ratio of the inclusions and matrix. Herein, we confine our attention to steady monodomain orientational distributions at rest and in weak shear flows, which serve as benchmarks and guides for future extensions and numerical approaches.

Numerical Analysis of the Rheology of Polymeric Liquid Crystals (3rd Report, Evaluation of a Second Order Tensor Type Constitutive Equation)

We have evaluated numerically a second order tensor type constitutive equation which includes both a molecular shape factor and a quadratic closure approximation, by means of comparing the results with the solutions obtained from the original Doi equation without closure approximations. The second order tensor type constitutive equation can simulate three types of director behaviors such as tumbling, wagging and aligning, by setting the molecular shape factor to be smaller than its inherent value based on the molecular aspect ratio. The shear stress and the first normal stress difference determined from the tensor type constitutive equation qualitatively agree with stresses obtained from the Doi equation, for low shear rate. When shear rate is high, however, even qualitative agreement is not obtained. Therefore, the constitutive equation is applicable to slow flows or situations where a velocity field is so simple that only an orientation field is a consideration.

A novel orientation-dependent potential model for prolate mesogens

An intermolecular potential is introduced for the study of molecular mesogenic fluids. The model combines distinct features of the well-known Gay-Berne and Kihara potentials by incorporating dispersive interactions dependent on the relative pair orientation to a spherocylinder molecular core. Results of a Monte Carlo simulation study focused on the liquid crystal phases exhibited by the model fluid are presented. For the chosen potential parameters, molecular aspect ratio L*=5 and temperatures T*=2, 3, and 5, isotropic, nematic, smectic-A, and hexatic phases are found. The location of the phase boundaries as well as the equation of state of the fluid and further thermodynamical and structural parameters are discussed and contrasted to the Kihara fluid. In comparison to this latter fluid, the model induces the formation of ordered liquid crystalline phases at lower packing fractions and it favors, in particular, the appearance of layered hexatic ordering as a consequence of the greater attractive interaction assigned to the parallel side-to-side molecular pair configurations. The results contribute to the evaluation of the role of specific interaction energies in the mesogenic behavior of prolate molecular liquids in dense environments.

Monodomain response of arbitrary aspect ratio nematic polymers in general linear planar flows

Various rheological devices (plane Couette cell, four-roll mill, film tenter) impose approximately linear, planar flow, from which nematic polymers have been characterized across ranges of flow type and strength. Theoretical predictions of monodomain responses of nematic liquids are predominantly for simple shear flows, studied from disparate scale models: continuum theory of Leslie–Ericksen, mesoscopic theory of Landau, deGennes and many others, and kinetic theory of Hess, Doi and Edwards. Our goal here is to illustrate consequences of a monodomain correspondence principle of kinetic and mesoscopic theory for nematic polymers consisting of arbitrary aspect ratio spheroids. The principle states that the bulk rheology of monodisperse nematic polymers for all linear flows in the plane of shear and any concentration can be deduced directly from a model system consisting of pure shear flow and a renormalized molecular aspect ratio parameter. The observation that there is a “trade-off” between molecule shape and flow is not new (cf. [Proc. R. Soc. London, Ser. A 102 (1922) 161; Proc. R. Soc. London, Ser. A. 146 (1934) 501; Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, 1974; J. Rheol. 42 (5) (1998) 1095]). Our contribution is to precisely formulate the principle in terms of the solution space of kinetic or mesoscopic models coupled with the relationship between stresses: a two-parameter model generates solutions for an entire four-parameter family of experiments. The wealth of predictions, and available numerical codes, for nematic polymer response in simple shear can be brought to bear on different flow types. We then illustrate a variety of concrete applications. As a primary example, we deduce the monodomain attractors and phase transitions versus flow-type for four-roll mill flow settings of a nematic polymer. We further provide continuous families of planar flow types of different aspect ratio liquids that have identical monodomain dynamics. Finally, we analyze pure planar extension and straining flows as a limit of the correspondence principle.

A Kinetic Theory for Solutions of Nonhomogeneous Nematic Liquid Crystalline Polymers With Density Variations

The kinetic theory developed in [1] for solutions of nonhomogeneous nematic liquid crystalline polymers (LCPs) of spheroidal molecular configurations is extended to account for the translational diffusion and the related spatial density variation. The new theory augments the effect of the density variation to the intermolecular potential, Smoluchowski equation and the elastic stress. It accounts for the molecular aspect ratio as well as the finite range molecular interaction so that it is applicable to liquid crystals ranging from rodlike liquid crystals at large aspect ratios to discotic ones at small aspect ratios. It also exhibits enhanced shape effects in the viscous stress and warrants a positive entropy production, thereby, the second law of thermodynamics. Moment averaged, approximate, mesoscopic theories for complex flow simulations are obtained via closure approximations. In the limit of weak distortional elasticity, weak translational diffusion, and weak flows, the theory yields the torque balance equation of the well-known Ericksen-Leslie theory.

Classical Molecular Dynamics Simulation of Kappa Squared Factor in Resonance Energy Transfer for Linear Dipole Models

Molecular dynamics simulations of linear models interacting through a dipolar Kihara intermolecular potential are presented. Molecular orientation correlations are used to calculate the orientational factor kappa squared in the resonance energy transfer (RET) as a function of the intermolecular separation. The distance, R 0 (2/3), at which the simulated systems show an isotropic behavior is calculated and an analysis of the dependence of R 0 (2/3) on microscopic properties (molecular aspect ratio and dipole moment) as well on thermodynamics (temperature and density) is presented. An explanation of the use of metallic cations as probes in RET is given and some relations of our models with biological molecules are pointed out.

Full-tensor alignment criteria for sheared nematic polymers

The shear problem for nematic polymers consists in characterizing all stable stationary orientational distributions, steady and unsteady, versus shear rate and material parameters. Continuum theory [cf. Leslie (1968), Ericksen (1960)] provides formulas for the shear response of liquid crystals in terms of a single viscosity ratio, the Leslie tumbling parameter λL. Kuzuu and Doi (1983, 1984) developed a weak-flow asymptotic analysis of kinetic theory, which gives a molecular basis for all continuum theory parameters. In this paper, we develop a mesoscopic extension of the Kuzuu–Doi method, applicable to any tensor model. Our method yields orientational and rheological features of nematic polymers in weak shear with explicit formulas, parametrized by the parameters of the second-moment tensor model. This provides an explicit mesoscopic theory solution to the problem posed by Marrucci and Greco (1993) of how orientational degeneracy of quiescent nematic equilibria breaks in weak shear, leaving a finite set of steady stationary states, whose number, type (in-plane, out-of-plane), stability, phase transitions, and rheological properties scale with parameters of the model. An intriguing feature to resolve is the multiple transitions associated with distinct steady distributions (logrolling, in-plane flow alignment, out-of-plane alignment), each with its analog of the Leslie criterion |λL|=1. We illustrate our method and its physical predictions by solving the weak shear problem for the Doi quadratic closure model, whose material parameters are nematic concentration and molecular aspect ratio. The predictions are confirmed with numerical simulations of the model, and compared with experimental data in weak shear from the review article of Burghardt (1998). We further predict scaling properties due to changes in concentration and aspect ratio that are less readily available from experiments.The shear problem for nematic polymers consists in characterizing all stable stationary orientational distributions, steady and unsteady, versus shear rate and material parameters. Continuum theory [cf. Leslie (1968), Ericksen (1960)] provides formulas for the shear response of liquid crystals in terms of a single viscosity ratio, the Leslie tumbling parameter λL. Kuzuu and Doi (1983, 1984) developed a weak-flow asymptotic analysis of kinetic theory, which gives a molecular basis for all continuum theory parameters. In this paper, we develop a mesoscopic extension of the Kuzuu–Doi method, applicable to any tensor model. Our method yields orientational and rheological features of nematic polymers in weak shear with explicit formulas, parametrized by the parameters of the second-moment tensor model. This provides an explicit mesoscopic theory solution to the problem posed by Marrucci and Greco (1993) of how orientational degeneracy of quiescent nematic equilibria breaks in weak shear, leaving a finite set o...

A comparison of mesogenic properties for one- and two-ring dipentyl derivatives of p-carboranes, bicyclo[2.2.2]octane, and benzene

A series of nonpolar single- and two-ring dipentyl derivatives of p-carboranes, bicyclo[2.2.2]-octane and benzene was investigated in the pure state and in binary mixtures with a nematic host. The resulting virtual nematic-isotropic transition temperatures [T NI] for single ring compounds were compared with those for two ring compounds. All [T NI] were compared with the molecular aspect ratios X and filling fractions F obtained from MNDO calculations. The highest effectiveness in promotion of the nematic phase was found for bicyclo[2.2.2]octane and 12-vertex p-carborane and ascribed to exceptional molecular rigidity and electronic properties, respectively. Results show that a high filling fraction F and molecular stiffness are the necessary factors for a highly stable nematic phase.

Monodisperse Oligofluorenes Forming Glassy-Nematic Films for Polarized Blue Emission

The first series of monodisperse glass-forming, nematic oligofluorenes was synthesized following a divergent−convergent approach. Both chain length and pendant structure were found to affect solid morphology and phase transition temperatures. With optimized structural parameters, a Tg close to 150 °C and a Tc beyond 375 °C were achieved. This material class is characterized by its ability to form monodomain glassy nematic films via spin-coating, thermal annealing at 10 to 20 °C above Tg for 15−30 min, and cooling to room temperature without encountering crystallization. The absorption and emission dichroic ratios of 80−90-nm-thick films increase from 7 to 17 with an increasing molecular aspect ratio, while the photoluminescence quantum yield varies erratically from 43 to 60%. Superior stability of emissive color and of emission dichroic ratio and that against thermally activated crystallization were also demonstrated through prolonged heating of a film at 10 °C above Tg under argon.