Dielectric investigation of the temperature dependence of the nonexponentiality of the dynamics of polymer melts

On the Mutual Relationships between Molecular Probe Mobility and Free Volume and Polymer Dynamics in Organic Glass Formers: cis-1,4-poly(isoprene)

We report on the reorientation dynamics of small spin probe 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) in cis-1,4-poly(isoprene) (cis-1,4-PIP10k) from electron spin resonance (ESR) and the free volume of cis-1,4-PIP10k from positron annihilation lifetime spectroscopy (PALS) in relation to the high-frequency relaxations of cis-1,4-PIP10k using light scattering (LS) as well as to the slow and fast processes from broadband dielectric spectroscopy (BDS) and neutron scattering (NS). The hyperfine coupling constant, 2A_zz '(T), and the correlation times, τ _c(T), of cis-1,4-PIP10k/TEMPO system as a function of temperature exhibit several regions of the distinct spin probe TEMPO dynamics over a wide temperature range from 100 K up to 350 K. The characteristic ESR temperatures of changes in the spin probe dynamics in cis-1,4-PIP10k/TEMPO system are closely related to the characteristic PALS ones reflecting changes in the free volume expansion from PALS measurement. Finally, the time scales of the slow and fast dynamics of TEMPO in cis-1,4-PIP10k are compared with all of the six known slow and fast relaxation modes from BDS, LS and NS techniques with the aim to discuss the controlling factors of the spin probe reorientation mobility in polymer, oligomer and small molecular organic glass-formers.

Single molecule studies reveal temperature independence of lifetime of dynamic heterogeneity in polystyrene

Polymeric systems close to their glass transition temperature are known to exhibit heterogeneous dynamics that evolve both over time and space, comparable to the dynamics of small molecule glass formers. It remains unclear how temperature influences the degree of heterogeneous dynamics in such systems. In the following report, a fluorescent perylene dicarboximide probe molecule that reflects the full breadth of heterogeneity of the host was used to examine the temperature dependence of the dynamic heterogeneity lifetime in polystyrene at several temperatures ranging from the glass transition to 10 K above this temperature via single molecule microscopy. Contrary to prior reports, no apparent temperature dependence of time scales associated with dynamic heterogeneity was detected; indeed, the probe molecules report characteristic dynamic heterogeneity lifetimes 100-300 times the average alpha-relaxation time (τ_α) of the polystyrene host at all temperatures studied.

Molecular dynamic heterogeneity in relation to free volume and relaxation dynamics in organic glass-formers: oligomeric cis-1,4-poly(isoprene)

Herein, a combined study of the molecular rotation dynamics and free volume in cis-1,4-poly(isoprene) using two external probing techniques via ESR and PALS together with relaxation dynamics of the host medium via BDS is presented. The spectral evolution of the spin probe TEMPO from simulations over a wide range from 100 K up to 300 K exhibits three different regions of its correlation time consisting of a slow regime at low temperatures followed by the molecular dynamic heterogeneity zone from T = T = 155 K = 0.82 × T up to T_c ≅ 236 K = 1.26 × T and ending with a fast regime at high temperatures with the further characteristic ESR temperatures, T = 186 K ≅ T and T = 260 K. These are in close coincidence with four characteristic PALS temperatures: T = 160 K, T = 190 K, T = 227 K, and T = 263 K. Finally, using BDS, we revealed that the high-frequency features of the structural relaxation of 1,4-PIP 0.8k were related to the observed effects in the ESR and PALS response of the liquid state.

Primary α and secondary β relaxation dynamics of meta-toluidine in the liquid state investigated by broadband dielectric spectroscopy

We report a broadband dielectric spectroscopic (BDS) study on the clustering fragile glass-former meta-toluidine (m-TOL) from 187 K up to 289 K over a wide frequency range of 10^-3-10⁹ Hz with focus on the primary α relaxation and the secondary β relaxation above the glass temperature T_g. The broadband dielectric spectra were fitted by using the Havriliak-Negami (HN) and Cole-Cole (CC) models. The β process disappearing at T_β,disap = 1.12T_g exhibits non-Arrhenius dependence fitted by the Vogel-Fulcher-Tamman-Hesse equation with T_0β^VFTH in accord with the characteristic differential scanning calorimetry (DSC) limiting temperature of the glassy state. The essential feature of the α process consists in the distinct changes of its spectral shape parameter β_HN marked by the characteristic BDS temperatures T_B1^βHN and T_B2^βHN. The primary α relaxation times were fitted over the entire temperature and frequency range by several current three-parameter up to six-parameter dynamic models. This analysis reveals that the crossover temperatures of the idealized mode coupling theory model (T_c^MCT), the extended free volume model (T₀^EFV), and the two-order parameter (TOP) model (T_m^c) are close to T_B1^βHN, which provides a consistent physical rationalization for the first change of the shape parameter. In addition, the other two characteristic TOP temperatures T₀^TOP and T_A are coinciding with the thermodynamic Kauzmann temperature T_K and the second change of the shape parameter at around T_B2^βHN, respectively. These can be related to the onset of the liquid-like domains in the glassy state or the disappearance of the solid-like domains in the normal liquid state.

Dielectric relaxation of polymers: segmental dynamics under structural constraints

In this article we review the recent polymer literature where dielectric spectroscopy has been used to investigate the segmental dynamics of polymers under the constraints produced by self-structuring. Specifically, we consider three cases: (i) semicrystalline polymers, (ii) segregated block-copolymers, and (iii) asymmetric miscible polymer blends. In these three situations the characteristics of the dielectric relaxation associated with the polymer segmental dynamics are markedly affected by the constraints imposed by the corresponding structural features. After reviewing in detail each of the polymer systems, the most common aspects are discussed in the context of the use of dielectric relaxation as a sensitive tool for analyzing structural features in nanostructured polymer systems.

The Modified VFT law of glass former materials under pressure: Part II: Relation with the equation of state

The dynamical properties of glass formers (GFs) as a function of P, V, and T are reanalyzed in relation with the equations of state (EOS) proposed recently (Eur. Phys. J. E 37, 113 (2014)). The relaxation times τ of the cooperative non-Arrhenius α process and the individual Arrhenius β process are coupled via the Kohlrausch exponent n S(T, P). In the model n S is the sigmoidal logistic function depending on T (and P, and the α relaxation time τ α of GFs above T g verifies the pressure-modified VFT law: log τ α ∼ E β /nsRT, which can be put into a form with separated variables: log τ α ∼ f(T)g(P). From the variation of n S and τ α with T and P the Vogel temperature T 0 (τ α → ∝, n S = 0) and the crossover temperature (also called the merging or splitting temperature) T B (τ α ∼ τ β, n S ∼ 1) are determined. The proposed sm-VFT equation fits with excellent accuracy the experimental data of fragile and strong GFs under pressure. The properties generally observed in organic mineral and metallic GFs are explained: a) The Vogel temperature is independent of P (as suggested by the EOS properties), the crossover is pressure-dependent. b) In crystallizable GFs the T B (P) and Clapeyron curves T m(P) coincide. c) The α and β processes have the same ratio of the activation energies and volume, E*/V* (T- and P-independent), the compensation law is observed, this ratio depends on the anharmonicity Slater-Grüneisen parameter and on the critical pressure P* deduced from the EOS. d) The properties of the Fan Structure of the Tangents (FST) to the isotherms and isobars curves log τ versus P and T and to the isochrones curves P(T). e) The scaling law log τ = f(V (Λ) ) and the relation between Γ and γ. We conclude that these properties should be studied in detail in GFs submitted to negative pressures.

Glassy Interfacial Dynamics of Ni Nanoparticles: Part I Colored Noise, Dynamic Heterogeneity and Collective Atomic Motion

Most condensed materials exhibit a significant fraction of atoms, molecules or particles that are strongly interacting with each other, while being configured geometrically at any instant of time in an 'amorphous' state having a relatively uniform density. Recently, both simulations and experiments have revealed that the dynamics of diverse condensed amorphous materials is generally characterized by significant heterogeneity in the local mobility and by progressively increasing collective motion upon cooling that takes the form of string-like collective particle rearrangements. The direct experimental observation of this type of collective motion, which has been directly linked to the growing relaxation times of glass-forming materials, and its quantification under different thermodynamic conditions, has so far been restricted to colloidal and driven granular fluids. The present work addresses the fundamental problem of how to determine the scale of this type of collective motion in materials composed of molecules or atoms. The basic premise of our work is that large scale dynamic particle clustering in amorphous materials must give rise to large fluctuations in particle mobility so that transport properties, especially those related to particle mobility, should naturally exhibit noise related to the cooperative motion scale. In our initial exploratory study seeking a relationship of this kind, we find 1/fα or 'colored noise', in both potential energy and particle displacements fluctuations of the atoms within the glassy interfacial layer of Ni nanoparticles (NPs). A direct relation between the particle displacement (mobility) noise exponent α and the average polymerization index of the string-like collective motion L is observed for a range of NP sizes, temperatures and for surface doping of the NPs with other metal atoms (Ag, Au, Pt) to change of fragility of the glassy interfacial layer at the surface of the Ni NPs. We also introduce a successful analytic model to understand this relationship between α and L.

Relationships between Positron Lifetime and Dynamics of Polymers

In this work positron annihilation lifetime spectroscopy (PALS) is employed to study the ortho-Positronium lifetime parameters τ3>, σ3 and I3 in two structurally simple amorphous polymers 1,2-poly(butadiene) and cis-1,4-poly(isoprene). The ortho-Positronium mean lifetime parameter τ3> is compared with dynamics data from broadband dielectric spectroscopy (BDS) and electron spin resonance (ESR) experiments. Coincidences of characteristic temperatures from PALS with BDS and ESR experiments show close relationships between positron lifetime and dynamics of polymers.

Positron annihilation and relaxation dynamics from dielectric spectroscopy: poly(vinylmethylether)

We report on the temperature dependence of the lifetime of the ortho-positronium (o-Ps), τ(3), annihilation in amorphous polymer poly(vinylmethylether) (PVME) from positron annihilation lifetime spectroscopy (PALS). We show that the behavior of τ(3)(T) can be divided into five regions, each of them having a linear temperature dependence, and that the crossover PALS temperatures situated at T(b1)(G), 0.76T(g)(PALS), T(b1)(L) = 1.14T(g)(PALS) and T(b2)(L) = 1.37T(G)(PALS), and marking the discontinuity in the free volume microstructure are related to various dynamic features from neutron scattering (NS) and broadband dielectric spectroscopy (BDS). First, a slight change in the PALS response in the glassy PVME at T(b1)(G) is related to the onset of the excess wing in an apparent correspondence with the fast secondary β motion from NS. A further slight bend in the liquid state at T(b1)(L) is related to a high-frequency tail of the primary α process as well as to the slow secondary β relaxation from BDS. In addition, it lies also in the vicinity of the crossover temperature, T(B)(βKWW), in the spectral dispersion of the primary α process, indicating a connection of the change in the o-Ps lifetime with the variation in the width of the primary α relaxation times distribution. Finally, the τ(3) value at T(b2)(L) is close to the mean relaxation time of the primary α process, τ(α), in coincidence with the crossover in the secondary effective β process between two regimes in the liquid PVME. All these relationships point to very close connections between the PALS response and the dynamic behavior of PVME, which can be explained in terms of the temperature dependence of the probability function of the liquid-like and the solid-like domains, as obtained from the two-order parameter (TOP) model description of the liquid to glass transition in glass-formers.

Extracting energy and structure properties of glass-forming liquids from structural relaxation time

A comprehensive examination of the kinetic liquid model (Wang et al 2010 J. Phys.: Condens. Matter 22 455104) is carried out by fitting the structural relaxation time of 26 different glass-forming liquids in a wide temperature range, including most of the well-studied materials. Careful analysis of the compiled reported data reveals that experimental inaccuracies should not be overlooked in any 'benchmark test' of relating theories or models (e.g. in Lunkenheimer et al 2010 Phys. Rev. E 81 051504). The procedure, accuracy, ability, and efficiency of the kinetic liquid model are discussed in detail and in comparison with other available fitting methods. In general, the kinetic liquid model could be verified by 17 of the 26 compiled data sets and can serve as a meaningful approximative method for analyzing these liquids. Nonetheless, further experimental examinations in a wide temperature range are needed and are called for. Through fitting, the microscopic details of these liquids are extracted, namely, the enthalpy, entropy, and cooperativity in structural relaxation, which may facilitate further quantitative analysis to both the liquidus and glassy states of these materials.

Stretched Exponential Stress Relaxation in a Thermally Reversible, Physically Associating Block Copolymer Solution

The shear stress relaxation of a thermally reversible, physically associating solution formed from a triblock copolymer in solvent selective for the mid-block was found to be well described over a broad temperature range by a stretched exponential function with a temperature independent ‘stretching exponent’, β ≈ 1/3. This same exponent value has been suggested to have particular significance in describing structural relaxation in a wide range of disordered viscoelastic materials ranging from associating polymer materials (‘gels’) to glass-forming liquids. We quantify the temperature dependence of the high frequency, or short time, shear modulus as function of temperature and find that this property also follows a variation often observed in gels and glass-forming materials.

Positron annihilation response and broadband dielectric spectroscopy: salol

A phenomenological analysis of the ortho-positronium (o-Ps) annihilation from positron annihilation lifetime spectroscopy (PALS) and the dynamics from broadband dielectric spectroscopy (BDS) are reported on a small molecular glass former of intermediate H-bonding and fragility: salol. The dielectric spectra extend over a very broad frequency range of about 2 × 10(-2)-3.5 × 10(11) Hz, providing information on the α-relaxation, the secondary relaxation giving rise to the excess wing, and the shallow high-frequency minimum in the micro- to milli-meter wave range. A number of empirical correlations between the o-Ps lifetime, τ(3)(T), and the various spectral and relaxation features have been observed. Thus, the phenomenological evaluation of the τ(3)(T) dependence of the PALS response of the amorphous sample reveals three characteristic PALS temperatures: T(g)(PALS), T(b1)(L) = 1.15T(g)(PALS) and T(b2)(L) = 1.25T(g)(PALS), which are discussed in relation to similar findings for some typical small molecular vdW- and H-bonded glass formers. A slighter change of the slope at T(b1)(L) appears to be related to the transition from excess wing to the primary α-process-dominated behavior, with the secondary process dominating in the deeply supercooled liquid state below T(b1)(L). The high-temperature plateau effect in the τ (3)(T) plot occurs at T(b2)(L) and agrees with the characteristic Stickel temperature, T(B)(ST), marking a qualitative change of the primary α process, but it does not follow the relation T(b2)(L) < T(α) [τ(3)(T(b2)) < τ(α)]. Both effects at T(b1)(L) and T(b2)(L) correlate with two crossovers in the spectral shape and related non-exponentiality parameter of the structural relaxation, β (KWW). Finally, the application of the two-order parameter (TOP) model to the structural relaxation as represented by the primary α relaxation times from BDS leads to the characteristic TOP temperature, T(m)(c), close to T(b1) from PALS. Within this model the phenomenological interpretation is offered based on changes in the probability of occurrence of solid-like and liquid-like domains to explain the dynamic as well as PALS responses. In summary, all the empirical correlations support further very close connections between the PALS response and the dielectric relaxation behavior in small molecule glass formers.

Temperature behavior of the Kohlrausch exponent for a series of vinylic polymers modelled by an all-atomistic approach

The Kohlrausch-Williams-Watt (KWW) function, or stretched exponential function, is usually employed to reveal the time dependence of the polymer backbone relaxation process, the so-called α relaxation, at different temperatures. In order to gain insight into polymer dynamics at temperatures higher than the glass transition temperature T(g), the behavior of the Kohlrausch exponent, which is a component of the KWW function, is studied for a series of vinylic polymers, using an all-atomistic simulation approach. Our data show very good agreement with published experimental results and can be described by existing phenomenological models. The Kohlrausch exponent exhibits a linear dependence with temperature until it reaches a constant value of 0.44, at 1.26T(g), revealing the existence of two regimes. These results suggest that, as the temperature increases, the dynamics progressively change until it reaches a plateau. The non-exponential character then describes subdiffusive motion characteristic of polymer melts.

Phenomenological theory of structural relaxation based on a thermorheologically complex relaxation time distribution

The aim of this work is to explore the consequences on the kinetics of structural relaxation of considering a glass-forming system to consist of a series of small but macroscopic relaxing regions that evolve independently from each other towards equilibrium in the glassy state. The result of this assumption is a thermorheologically complex model. In this approach each relaxing zone has been assumed to follow the Scherer-Hodge model for structural relaxation (with the small modification of taking a linear dependence of configurational heat capacity with temperature). The model thus developed contains four fitting parameters. A least-squares search routine has been used to find the set of model parameters that fit simultaneously four DSC thermograms in PVAc after different thermal histories. The computer-simulated curves are compared with those obtained with Scherer-Hodge model and the model proposed by Gómez and Monleón. The evolution of the relaxation times during cooling or heating scans and also during isothermal annealing below the glass transition has been analysed. It has been shown that the relaxation times distribution narrows in the glassy state with respect to equilibrium. Isothermal annealing causes this distribution to broaden during the process to finally attain in equilibrium the shape defined at temperatures above Tg.

Proton momentum distribution in a protein hydration shell

The momentum distribution of protons in the hydration shell of a globular protein has been measured through deep inelastic neutron scattering at 180 and 290 K, below and above the crossover temperature Tc=1.23Tg, where Tg=219 K is the glass transition temperature. It is found that the mean kinetic energy of the water hydrogens shows no temperature dependence, but the measurements are accurate enough to indicate a sensible change of momentum distribution and effective potential felt by protons, compatible with the transition from a single to a double potential well. This could support the presence of tunneling effects even at room temperature, playing an important role in biological function.

A comparative molecular simulation study of the glass former ortho-terphenyl in bulk and freestanding films

We performed molecular dynamics simulations of the low-molecular weight organic glass former ortho-terphenyl in bulk and freestanding films. The main motivation is to provide molecular insight into the confinement effect without explicit interfaces. Based on earlier models of ortho-terphenyl we developed an atomistic model for bulk simulations. The model reproduces literature data both from simulations and experiments starting from specific volume and diffusivity to mean square displacement and radial distribution functions. After characterizing the bulk model we form freestanding films by the elongation and expansion method. These films give us the opportunity to study the dynamical heterogeneity near the glass transition through in-plane mobility and reorientation dynamics. We finally compare the model in bulk and under confinement. We found qualitatively a lower glass transition temperature for the freestanding film compared to the bulk.

Moderately and strongly supercooled liquids: A temperature-derivative study of the primary relaxation time scale

The primary relaxation time scale tau(T) derived from the glass forming supercooled liquids (SCLs) is discussed within ergodic-cluster Gaussian statistics, theoretically justified near and above the glass-transformation temperature T(g). An analysis is given for the temperature-derivative data by Stickel et al. on the steepness and the curvature of tau(T). Near the mode-coupling-theory (MCT) crossover T(c), these derivatives separate by a kink and a jump, respectively, the moderately and strongly SCL states. After accounting for the kink and the jump, the steepness remains a piecewise conitnuous function, a material-independent equation for the three fundamental characteristic temperatures, T(g), T(c), and the Vogel-Fulcher-Tamman (VFT) T(0), is found. Both states are described within the heterostructured model of solidlike clusters parametrized in a self-consistent manner by a minimum set of observable parameters: the fragility index, the MCT slowing-down exponent, and the chemical excess potential of Adam and Gibbs model (AGM). Below the Arrhenius temperature, the dynamically and thermodynamically stabilized clusters emerge with a size of around of seven to nine and two to three molecules above and close to T(g) and T(c), respectively. On cooling, the main transformation of the moderately into the strongly supercooled state is due to rebuilding of the cluster structure, and is attributed to its rigidity, introduced through the cluster compressibility. It is shown that the validity of the dynamic AGM (dynamically equivalent to the standard VFT form) is limited by the strongly supercooled state (T(g) < T < T(c)) where the superrigid cooperative rearranging regions are shown to be well-chosen parametrized solidlike clusters. Extension of the basic parameter set by the observable kinetic and diffusive exponents results in prediction of a subdiffusion relaxation regime in SCLs that is distinct from that established for amorphous polymers.

Glassy behavior of a percolative water-protein system

We show that is possible to look at the glass transition as a percolation transition in phase space. This study has been carried out on a hydrated globular enzyme for which the thermodynamic transition and the percolative transition could have a functional significance. The approach adopted is based on the identity of roles played respectively by the glass transition temperature T(o) and the critical hydration threshold h(c) for the percolation of protons on the surface and through the protein, given that dynamical arrest is observed at temperatures and hydration below T(o) and h(c). Theoretical predictions for temperature dependence of the nonexponentiality parameter, beta(KWW) , appearing in the KWW relaxation function, indicate that at high temperatures, beta(KWW) remains insensitive to temperature changes, whereas in the vicinity of the glass transition, beta(KWW) is linearly increasing with temperature. The low temperature limit of beta(KWW) is about 1/3 and its temperature-independent behavior starts at 1.23 T(g): both predictions have been verified in the present study.

The Adam–Gibbs equation and the out-of-equilibrium α relaxation of glass forming systems

The temperature dependence of the alpha-relaxation time out of equilibrium has been investigated by means of dielectric relaxation in a series of fragile glass formers including several polymers. The influence of physical aging on this behavior has also been studied. The experimental results have been quantitatively compared with the predictions of the Adam-Gibbs equation. It has been found that, whereas for small molecule glass formers the experimental values of the apparent activation energy agree quite well with the prediction of the Adam-Gibbs equation, for polymers the experimental activation energy values are systematically higher. Moreover, whereas for small molecule glass formers the experimental values of the apparent activation energy remains essentially unaffected by physical aging, for polymers a pronounced reduction of the experimental apparent activation energy is observed. These results are found to be consistent with the Adam-Gibbs equation if a significant temperature variation of the configurational entropy in the investigated temperature range would occur for nonannealed polymers, being the possible variation hardly noticeable for the small molecules. With this assumption, all the obtained results would support the validity of the Adam-Gibbs equation for describing the temperature dependence of the time scale of the alpha-relaxation also out of equilibrium, at least for fragile glass formers.