Glass-Transition Cooperativity Onset in a Series of Random Copolymers Poly(n-butyl methacrylate-stat-styrene)

Cooperative strings and glassy dynamics in various confined geometries

Previously, we developed a minimal model based on random cooperative strings for the relaxation of supercooled liquids in the bulk and near free interfaces, and we recovered some key experimental observations. In this article, after recalling the main ingredients of the cooperative string model, we study the effective glass transition and surface mobility of various experimentally relevant confined geometries: freestanding films, supported films, spherical particles, and cylindrical particles, with free interfaces and/or passive substrates. Finally, by canceling and restarting any cooperative-chain realization reaching the boundary with a smaller number of steps than the bulk cooperativity, we account for a purely attractive substrate, and explore the impact of the latter in the previous geometries.

Cooperative strings in glassy nanoparticles

Motivated by recent experimental results on glassy polymer nanoparticles, we develop a minimal theoretical framework for the glass transition in spherical confinement. This is accomplished using our cooperative-string model for supercooled dynamics, that was successful at recovering the bulk phenomenology and describing the thin-film anomalies. In particular, we obtain predictions for the mobile-layer thickness as a function of temperature, and for the effective glass-transition temperature as a function of the radius of the spherical nanoparticle - including the existence of a critical particle radius below which vitrification never occurs. Finally, we compare the theoretical results to experimental data on polystyrene from the recent literature, and we discuss the latter.

Revisiting the glass transition and dynamics of supercooled benzene by calorimetric studies

The glass transition and dynamics of benzene are studied in binary mixtures of benzene with five glass forming liquids, which can be divided into three groups: (a) o-terphenyl and m-xylene, (b) N-butyl methacrylate, and (c) N,N-dimethylpropionamide and N,N-diethylformamide to represent the weak, moderate, and strong interactions with benzene. The enthalpies of mixing, ΔH(mix), for the benzene mixtures are measured to show positive or negative signs, with which the validity of the extrapolations of the glass transition temperature T(g) to the benzene-rich regions is examined. The extrapolations for the T(g) data in the mixtures are found to converge around the point of 142 K, producing T(g) of pure benzene. The fragility m of benzene is also evaluated by extrapolating the results of the mixtures, and a fragility m ∼ 80 is yielded. The obtained T(g) and m values for benzene allow for the construction of the activation plot in the deeply supercooled region. The poor glass formability of benzene is found to result from the high melting point, which in turn leads to low viscosity in the supercooled liquid.

Cooperative strings and glassy interfaces

We introduce a minimal theory of glass formation based on the ideas of molecular crowding and resultant string-like cooperative rearrangement, and address the effects of free interfaces. In the bulk case, we obtain a scaling expression for the number of particles taking part in cooperative strings, and we recover the Adam-Gibbs description of glassy dynamics. Then, by including thermal dilatation, the Vogel-Fulcher-Tammann relation is derived. Moreover, the random and string-like characters of the cooperative rearrangement allow us to predict a temperature-dependent expression for the cooperative length ξ of bulk relaxation. Finally, we explore the influence of sample boundaries when the system size becomes comparable to ξ. The theory is in agreement with measurements of the glass-transition temperature of thin polymer films, and allows quantification of the temperature-dependent thickness hm of the interfacial mobile layer.

Method for estimating the cooperativity length in polymers

The problem of estimating the size of the cooperatively rearranging regions (CRRs) in supercooled polymeric melts from an analysis of the α-process in ordinary relaxation experiments is addressed. The mechanism whereby a CRR changes its configuration is viewed as consisting of two distinct steps: a reduced number of monomers reaches initially an activated state, allowing for some local rearrangement; then, the subsequent regression of the energy fluctuation may take place through the configurational degrees of freedom, thus allowing for further rearrangements on larger length scales. The latter are indeed those to which the well-known Donth's scheme refers. Local readjustments are described in the framework of a canonical formalism on a stationary ensemble of small-scale regions, distributed over all possible energy thresholds for rearrangement. Large-scale configurational changes, instead, are described as spontaneous processes. Two main regimes are envisaged, depending on whether the role played by the configurational degrees of freedom in the regression of the energy fluctuation is significant or not. It is argued that the latter case is related to the occurrence of an Arrhenian dependence of the central relaxation rate. Consistency with Donth's scheme is demonstrated, and data from the literature confirm the agreement of the two methods of analysis when configurational degrees of freedom are relevant for the fluctuation regression. Poly(n-butyl methacrylate) is chosen in order to show how CRR size and temperature fluctuations at rearrangement can be estimated from stress relaxation experiments carried out by means of an atomic force microscopy setup. Cases in which the configurational pathway for regression is significantly hindered are considered. Relaxation in poly(dimethyl siloxane) confined in nanopores is taken as an example to suggest how a more complete view of the effects of configurational constraints would be possible if direct measurements of temperature fluctuations were combined with the proposed analysis.

Ellipsometry measurements of glass transition breadth in bulk films of random, block, and gradient copolymers

Bulk films of random, block and gradient copolymer systems were studied using ellipsometry to demonstrate the applicability of the numerical differentiation technique pioneered by Kawana and Jones for studying the glass transition temperature (T (g)) behavior and thermal expansivities of copolymers possessing different architectures and different levels of nanoheterogeneity. In a series of styrene/n -butyl methacrylate (S/nBMA) random copolymers, T (g) breadths were observed to increase from approximately 17( degrees ) C in styrene-rich cases to almost 30( degrees ) C in nBMA-rich cases, reflecting previous observations of significant nanoheterogeneity in PnBMA homopolymers. The derivative technique also revealed for the first time a substantial increase in glassy-state expansivity with increasing nBMA content in S/nBMA random copolymers, from 1.4x10(-4) K-1 in PS to 3.5x10(-4) K-1 in PnBMA. The first characterization of block copolymer T (g) 's and T (g) breadths by ellipsometry is given, examining the impact of nanophase-segregated copolymer structure on ellipsometric measurements of glass transition. The results show that, while the technique is effective in detecting the two T (g) 's expected in certain block copolymer systems, the details of the glass transition can become suppressed in ellipsometry measurements of a rubbery minor phase under conditions where the matrix is glassy; meanwhile, both transitions are easily discernible by differential scanning calorimetry. Finally, broad glass transition regions were measured in gradient copolymers, yielding in some cases extraordinary T (g) breadths of 69- 71( degrees ) C , factors of 4-5 larger than the T (g) breadths of related homopolymers and random copolymers. Surprisingly, one gradient copolymer demonstrated a slightly narrower T (g) breadth than the S/nBMA random copolymers with the highest nBMA content. This highlights the fact that nanoheterogeneity relevant to the glass transition response in selected statistical copolymers can be comparable to or exceed that observed in moderately phase-segregated gradient copolymers.

Retardation time spectra computed from complex compliance functions

This work describes the calculation of retardation time spectra by minimization of the square of the differences between experimental compliance results and those recalculated from the spectra. Spectra were computed taking analytical complex dielectric results as the basis of the minimization process. Comparison of the spectra computed from both the complex dielectric permittivity and the dielectric loss with those calculated analytically shows that minimization methods based on complex dielectric permittivity data are more accurate than those based only on loss dielectric results.

Broadband dielectric study of the glass transition in poly(ethyleneglycol)-water mixture

We performed broadband dielectric measurements of a polyethyleneglycol-water mixture in the frequency range between 10 GHz and 1 microHz and the temperature range between 300 and 133 K. One relaxation process is observed throughout the whole temperature range. The temperature dependence of the relaxation time clearly obeys the Vogel-Fulcher law above 183 K, and the Arrhenius law below 183 K. This observed relaxation process is the secondary process, and the primary process related to the glass transition is masked by the low-frequency ionic contribution below 183 K. The glass transition concerned with the masked primary process leads to the Vogel-Fulcher to Arrhenius transition of the secondary process.

Relation between the α-Relaxation and Johari−Goldstein β-Relaxation of a Component in Binary Miscible Mixtures of Glass-Formers

The coupling model was applied to describe the alpha-relaxation dynamics of each component in perfectly miscible mixtures A(1-x)B(x) of two different glass-formers A and B. An important element of the model is the change of the coupling parameter of each component with the composition, x, of the mixture. However, this change cannot be determined directly from the frequency dispersion of the alpha-relaxation of each component because of the broadening caused by concentration fluctuations in the mixture, except in the limits of low concentrations of either component, x --> 0 and x --> 1. Fortunately, the coupling model has another prediction. The coupling parameter of a component, say A, in the mixture determines tau(alpha)/tau(JG), the ratio of the alpha-relaxation time, tau(alpha), to the Johari-Goldstein (JG) secondary relaxation time, tau(JG), of the same component A. This prediction enables us to obtain the coupling parameter, n(A), of component A from the isothermal frequency spectrum of the mixture that shows both the alpha-relaxation and the JG beta-relaxation of component A. We put this extra prediction into practice by calculating n(A) of 2-picoline in binary mixtures with either tri-styrene or o-terphenyl from recently published broadband dielectric relaxation data of the alpha-relaxation and the JG beta-relaxation of 2-picoline. The results of n(A) obtained from the experimental data show its change with composition, x, follows the same pattern as assumed in previous works that address only the alpha-relaxation dynamics of a component in binary mixtures based on the coupling model. There is an alternative view of the thrust of the present work. If the change of n(A) with composition, x, in considering the alpha-relaxation of component A is justified by other means, the theoretical part of the present work gives a prediction of how the ratio tau(alpha)/tau(JG) of component A changes with composition, x. The data of tau(alpha) and tau(JG) of 2-picoline mixed with tri-styrene or o-terphenyl provide experimental support for the prediction.

Dielectric study of the α and β processes in supercooled ethylene glycol oligomer–water mixtures

Broadband dielectric measurements for 65 wt % ethylene glycol oligomer (EGO)-water mixtures with one to six repeat units of EGO molecules were performed in the frequency range of 10 microHz-10 GHz and the temperature range of 128-298 K. In the case of the water-EGO mixtures with one and two repeat units of the EGO molecule (small EGO), the shape of the dielectric loss peak of the primary process is asymmetrical about the logarithm of the frequency of maximum loss above the crossover temperature, T(C). The asymmetric process continues to the alpha process at a low frequency, and an additional beta process appears in the frequency range higher than that of the alpha process below T(C). In contrast, the water-EGO mixtures with three or more repeat units of the EGO molecule (large EGO) show a broad and symmetrical loss peak of the primary process above T(C). The symmetric process continues to the beta process, and an additional alpha process appears in the frequency range lower than that of the beta process below T(C). These different scenarios of the alpha-beta separation related to the shape of the loss peak above T(C) are a result of the difference in the cooperative motion of water and solute molecules. The solute and water molecules move cooperatively in the small EGO-water mixtures above T(C), and this cooperative motion leads to the asymmetric loss peak above T(C) and the alpha process below T(C). For the large EGO-water mixtures, the spatially restricted motion of water confined by solute molecules leads to the symmetric loss peak above T(C) and the beta process below T(C).

Cooperativity of the beta-relaxations in aromatic polymers

The dielectric loss spectra of a series of copolyesters of poly(ethylene terephthalate) and poly(ethylene isophthalate) have been measured as a function of temperature in a broad frequency range (10(-1)-10(9) Hz). By these measurements, the merging of the two relevant relaxations alpha and beta has been studied. The beta processes exhibit a complex temperature dependence, showing a clear Arrhenius dependence at temperatures well below the glass transition temperature, a transition zone where the characteristic relaxation time of this process nearly does not change with temperature, and an Arrhenius behavior with a higher activation energy for temperatures above the glass transition. The analysis of these results indicates that the beta relaxation in these systems presents typical characteristics of a genuine Johari-Goldstein process. This finding has been interpreted as due to the full monomer extension of the molecular motions involved in the beta relaxation in agreement with recent proposals.

Classification of secondary relaxation in glass-formers based on dynamic properties

Dynamic properties, derived from dielectric relaxation spectra of glass-formers at variable temperature and pressure, are used to characterize and classify any resolved or unresolved secondary relaxation based on their different behaviors. The dynamic properties of the secondary relaxation used include: (1) the pressure and temperature dependences; (2) the separation between its relaxation time taubeta and the primary relaxation time taualpha at any chosen taualpha; (3) whether taubeta is approximately equal to the independent (primitive) relaxation time tau0 of the coupling model; (4) whether both taubeta and tau0 have the same pressure and temperature dependences; (5) whether it is responsible for the "excess wing" of the primary relaxation observed in some glass-formers; (6) how the excess wing changes on aging, blending with another miscible glass-former, or increasing the molecular weight of the glass-former; (7) the change of temperature dependence of its dielectric strength Deltaepsilonbeta and taubeta across the glass transition temperature Tg; (8) the changes of Deltaepsilonbeta and taubeta with aging below Tg; (9) whether it arises in a glass-former composed of totally rigid molecules without any internal degree of freedom; (10) whether only a part of the molecule is involved; and (11) whether it tends to merge with the alpha-relaxation at temperatures above Tg. After the secondary relaxations in many glass-formers have been characterized and classified, we identify the class of secondary relaxations that bears a strong connection or correlation to the primary relaxation in all the dynamic properties. Secondary relaxations found in rigid molecular glass-formers belong to this class. The secondary relaxations in this class play the important role as a precursor or local step of the primary relaxation, and we propose that only they should be called the Johari-Goldstein beta-relaxation.

Minimal model for Beta relaxation in viscous liquids

Contrasts between beta relaxation in equilibrium viscous liquids and glasses are rationalized in terms of a double-well potential model with structure-dependent asymmetry, assuming structure is described by a single order parameter. The model is tested for tripropylene glycol where it accounts for the hysteresis of the dielectric beta loss peak frequency and magnitude during cooling and reheating through the glass transition.

New approach to characterise physicochemical properties of solid substrates by inverse gas chromatography at infinite dilution. II. Study of the transition temperatures of poly(methyl methacrylate) at various tacticities and of poly(methyl methacrylate) adsorbed on alumina and silica

The determination of the temperature transitions in polymers and more particularly when polymers are adsorbed on oxides is very important in many industrial processes. In this second part, we used inverse gas chromatography (IGC) at infinite dilution to determine the second order transition temperatures of poly(methyl methacrylate) (PMMA) adsorbed (or not) on alumina or on silica. Three types of PMMA were used: atactic (a), syndiotactic (syndio) and isotactic (iso). The IGC technique allowed to obtain the net retention volume Vn and the dispersive component of the surface energy gamma(s)d for various theoretical models of molecules, using the results of Part I. By plotting RT ln Vn as a function of (1/T) or gamma(s)d as a function of the temperature T, we proved the presence of three particular temperatures that correspond respectively to the transition temperature relative to beta-relaxation (Tbeta), the glass transition temperature (Tg), and the liquid-liquid transition temperature or order-disorder transition (T1.1). Results obtained in this part allowed us to show the effect of the tacticity of PMMA and the recovery fraction of polymer adsorbed on alumina or silica on the transition temperatures.