Intermittent-contact local dielectric spectroscopy of nanostructured interfaces.

Local dielectric spectroscopy (LDS) is a scanning probe method, based on dynamic-mode atomic force microscopy (AFM), to discriminate dielectric properties at surfaces with nanometer-scale lateral resolution. Until now a sub-10 nm resolution for LDS has not been documented, that would give access to the length scale of fundamental physical phenomena such as the cooperativity length related to structural arrest in glass formers (2-3 nm). In this work, LDS performed by a peculiar variant of intermittent-contact mode of AFM, named constant-excitation frequency modulation, was introduced and extensively explored in order to assess its best resolution capability. Dependence of resolution and contrast of dielectric imaging and spectroscopy on operation parameters like probe oscillation amplitude and free amplitude, the resulting frequency shift, and probe/surface distance-regulation feedback gain, were explored. By using thin films of a diblock copolymer of polystyrene (PS) and polymethylmethacrylate (PMMA), exhibiting phase separation on the nanometer scale, lateral resolution of at least 3 nm was demonstrated in both dielectric imaging and localized spectroscopy, by operating with optimized parameters. The interface within lamellar PS/PMMA was mapped, with a best width in the range between 1 and 3 nm. Changes of characteristic time of the secondary (ß) relaxation process of PMMA could be tracked across the interface with PS.

Lateral resolution of electrostatic force microscopy for mapping of dielectric interfaces in ambient conditions.

The attainable lateral resolution of electrostatic force microscopy (EFM) in an ambient air environment on dielectric materials was characterized on a reference sample comprised of two distinct, immiscible glassy polymers cut in a cross-section by ultramicrotomy. Such a sample can be modeled as two semi-infinite dielectrics with a sharp interface, presenting a quasi-ideal, sharp dielectric contrast. Electric polarizability line profiles across the interface were obtained, in both lift-mode and feedback-regulated dynamic mode EFM, as a function of probe/surface separation, for different cases of oscillation amplitudes. We find that the results do not match predictions for dielectric samples, but comply well or are even better than predicted for conductive interfaces. A resolution down to 3 nm can be obtained by operating in feedback-regulated EFM realized by adopting constant-excitation frequency-modulation mode. This suggests resolution is ruled by the closest approach distance rather than by average separation, even with probe oscillation amplitudes as high as 10 nm. For better comparison with theoretical predictions, effective probe radii and cone aperture angles were derived from approach curves, by also taking into account the finite oscillation amplitude of the probe, by exploiting a data reduction procedure previously devised for the derivation of interatomic potentials.

On the pressure dependence of the thermodynamical scaling exponent γ.

Since its initial discovery more than fifteen years ago, the thermodynamical scaling of the dynamics of supercooled liquids has been used to provide many new important insights in the physics of liquids, particularly on the link between dynamics and intermolecular potential. A question that has long been discussed is whether the scaling exponent γS is a constant or does it depends on pressure. An alternative definition of the scaling parameter, γI = ∂ ln T/∂ ln ρ|X has been presented in the literature, and has been erroneously considered equivalent to γS. Here we offer a simple method to determine the pressure dependence of γI using only the pressure dependence of the glass transition and the equation of state. Using this new method we find that for the six nonassociated liquids investigated, γI always decreases with increasing pressure. Importantly in all cases the value of γI remains always larger than 4. Liquids having γI closer to 4 at low pressure show a smaller change in γI with pressure. We argue that this result has very important consequences for the experimental determination of the functional form of the repulsive part of the potential in liquids. Comparing the pressure and temperature dependence of γS and γI we find, contrary to what has been assumed in the literature to date, that these two parameters are not equivalent and have very different pressure and temperature dependences.

On the experimental determination of the repulsive component of the potential from high pressure measurements: What is special about twelve?

In this paper, we present an overview of results in the literature regarding the thermodynamical scaling of the dynamics of liquids and polymers as measured from high-pressure measurements. Specifically, we look at the scaling exponent γ and argue that it exhibits the limiting behavior γ → 4 in regimes for which molecular interactions are dominated by the repulsive part of the intermolecular potential. For repulsive potentials of the form U(r) ∝ r-n, γ has been found to be related to the exponent n via the relation γ = n/3. Therefore, this limiting behavior for γ would suggest that a large number of molecular systems may be described by a common repulsive potential U(r) ∝ r-n with n ≈ 12.

The complex behavior of the "simplest" liquid: Breakdown of density scaling in tetramethyl tetraphenyl trisiloxane.

Dielectric relaxation measurements, in combination with density determinations, on tetramethyl tetraphenyl trisiloxane (DC704) over an unusually broad range of temperatures and pressures revealed a state-point dependency in its density scaling exponent. This is the first unambiguous experimental demonstration of a breakdown of density scaling in a nonassociated glass-forming material, and unanticipated for DC704, among the "simplest" of liquids, having a constant breadth of the relaxation dispersion and a Prigogine-Defay ratio near unity characteristic of approximate single-parameter systems. We speculate that the anomalous behavior has origins in the large value of its scaling exponent and relative flexibility of the chemical structure.

Nonlinear dielectric spectroscopy of propylene carbonate derivatives.

Nonlinear dielectric measurements were carried out on two strongly polar liquids, 4-vinyl-1,3-dioxolan-2-one (VPC) and 4-ethyl-1,3-dioxolan-2-one (EPC), having chemical structures differing from propylene carbonate (PC) only by the presence of a pendant group. Despite their polarity, the compounds are all non-associated, "simple" liquids. From the linear component of the dielectric response, the α relaxation peak breadth was found to be invariant at a fixed value of the relaxation time, τα. From spectra from the nonlinear component, the number of dynamically correlated molecules was determined; it was also constant at fixed τα. Thus, two manifestations of dynamic heterogeneity depend only on the time constant for structural reorientation. More broadly, the cooperativity of molecular motions for non-associated glass-forming materials is connected to (i.e., reciprocally governs) the time scale. The equation of state for the two liquids was also obtained from density measurements made over a broad range of pressures and temperatures. Using these data, it was determined that the relaxation times of both liquids conform to density scaling. The effect of density, relative to thermal effects, on the α relaxation increases going from PC < VPC < EPC.

Communication: Effect of density on the physical aging of pressure-densified polymethylmethacrylate.

The rate of physical aging of glassy polymethylmethacrylate (PMMA), followed from the change in the secondary relaxation with aging, is found to be independent of the density, the latter controlled by the pressure during glass formation. Thus, the aging behavior of the secondary relaxation is the same whether the glass is more compacted or less dense than the corresponding equilibrium liquid. This equivalence in aging of glasses formed under different pressures indicates that local packing is the dominant variable governing the glassy dynamics. The fact that pressure densification yields different glass structures is at odds with a model for non-associated materials having dynamic properties exhibited by PMMA, such as density scaling of the relaxation time and isochronal superposition of the relaxation dispersion.

Dynamics of poly(vinyl methyl ketone) thin films studied by local dielectric spectroscopy.

Local dielectric spectroscopy, which entails measuring the change in resonance frequency of the conducting tip of an atomic force microscope to determine the complex permittivity of a sample with high spatial (lateral) resolution, was employed to characterize the dynamics of thin films of poly(vinyl methyl ketone) (PVMK) having different substrate and top surface layers. A free surface yields the usual speeding up of the segmental dynamics, corresponding to a glass transition suppression of 6.5° for 18 nm film thickness. This result is unaffected by the presence of a glassy, compatible polymer, poly-4-vinyl phenol (PVPh), between the metal substrate and the PVMK. However, covering the top surface with a thin layer of the PVPh suppresses the dynamics. The speeding up of PVMK segmental motions observed for a free surface is absent due to interfacial interactions of the PVMK with the glass layer, an effect not seen when the top layer is an incompatible polymer.

The "anomalous" dynamics of decahyroisoquinoline revisited.

Decahydroisoquinoline (DHIQ) appears to be a unique material-the only non-associated, simple liquid with dynamics deviating from density scaling. To examine whether this anomaly is real, the density, ρ, of DHIQ was measured at temperatures, T, as low as 214 K and pressures up to ∼1.2 GPa. This enabled the equation of state (EoS) to be determined, without extrapolation, over the range of thermodynamic conditions for which the relaxation times had been reported. Using this less ambiguous EoS, we find that within the precision of the available relaxation times, the latter are a function of T/ρ(3.9), contrary to previous reports. Thus, the behavior of DHIQ is unexceptional; similar to every non-associated liquid tested to date, its dynamics comply with density scaling.

The effect of nanoclay on the rheology and dynamics of polychlorinated biphenyl.

The thermal, rheological, and mechanical and dielectric relaxation properties of exfoliated dispersions of montmorillonite clay in a molecular liquid, polychlorobiphenyl (PCB), were studied. The viscosity enhancement at low concentrations of clay (≤5%) exceeded by a factor of 50 the increase obtainable with conventional fillers. However, the effect of the nanoclay on the local dynamics, including the glass transition temperature, was quite small. All materials herein conformed to density-scaling of the reorientation relaxation time of the PCB for a common value of the scaling exponent. A new relaxation process was observed in the mixtures, associated with PCB molecules in proximity to the clay surface. This process has an anomalously high dielectric strength, suggesting a means to exploit nanoparticles to achieve large electrical energy absorption. This lower frequency dispersion has a weaker dependence on pressure and density, consistent with dynamics constrained by interactions with the particle surface.

Dynamic correlation length scales under isochronal conditions.

The origin of the dramatic changes in the behavior of liquids as they approach their vitreous state-increases of many orders of magnitude in dynamic time scales and transport properties-is a major unsolved problem in condensed matter. These changes are accompanied by greater dynamic heterogeneity, which refers to both spatial variation and spatial correlation of molecular mobilities. The question is whether the changing dynamics are coupled to this heterogeneity; that is, does the latter cause the former? To address this, we carried out the first nonlinear dielectric experiments at elevated hydrostatic pressures on two liquids, to measure the third-order harmonic component of their susceptibilities. We extract from this the number of dynamically correlated molecules for various state points and find that the dynamic correlation volume for non-associated liquids depends primarily on the relaxation time, sensibly independent of temperature and pressure. We support this result by molecular dynamic simulations showing that the maximum in the four-point dynamic susceptibility of density fluctuations is essentially invariant along isochrones for molecules that do not form hydrogen bonds. Our findings are consistent with dynamic cooperativity serving as the principal control parameter for the slowing down of molecular motions in supercooled materials.

Effect of Interface Interaction on the Segmental Dynamics of Poly(vinyl acetate) Investigated by Local Dielectric Spectroscopy.

The segmental dynamics of poly(vinyl acetate) (PVAc) thin films were measured in the presence of an aluminum interface and in contact with an incompatible polymer, poly(4-vinylpyridine). The local dielectric relaxation was found to be faster in thin films than in the bulk; however, no differences were observed for the various interfaces, including a PVAc/air interface. These results show that capping of thin films, even with a rigid material, does not necessarily affect the dynamics, the speeding up herein for capped PVAc was equivalent to that for the air interface. The insensitivity of the dynamics to the nature of the interface affords a means to engineer thin films while maintaining desired mechanical properties. Our findings for PVAc also may explain the discordant results that have been reported in general for the effect of air versus rigid interfaces on the local segmental relaxation of thin films.

Determination of the thermodynamic scaling exponent for relaxation in liquids from static ambient-pressure quantities.

An equation is derived that expresses the thermodynamic scaling exponent, γ, which superposes relaxation times τ and other measures of molecular mobility determined over a range of temperatures and densities, in terms of static physical quantities. The latter are available in the literature or can be measured at ambient pressure. We show for 13 materials, both molecular liquids and polymers, that the calculated γ are equivalent to the scaling exponents obtained directly by superpositioning. The assumptions of the analysis are that the glass transition T(g) is isochronal (i.e., τ(α) is constant at T(g), which is true by definition) and that the pressure derivative of the glass temperature is given by the first Ehrenfest relation. The latter, derived assuming continuity of the entropy at the glass transition, has been corroborated for many glass-forming materials at ambient pressure. However, we find that the Ehrenfest relation breaks down at elevated pressure; this limitation is of no consequence herein, since the appeal of the new equation is its applicability to ambient-pressure data. The ability to determine, from ambient-pressure measurements, the scaling exponent describing the high-pressure dynamics extends the applicability of this approach to a broader range of materials. Since γ is linked to the intermolecular potential, the new equation thus provides ready access to information about the forces between molecules.

The fragility of liquids and colloids and its relation to the softness of the potential.

A parameter that is often used to characterize the dynamics of supercooled liquids is the dynamic fragility, however it is still debated how the fragility is related to other physical properties. Recent experimental data on colloidal systems have found that fragility decreases with increasing softness of the intermolecular potential. This result is in apparent disagreement with recent molecular dynamics simulations reporting the opposite behavior. Herein, using the thermodynamical scaling exponent γ as a measure of the steepness of the potential we show how these different results can be reconciled and also agree with previous results obtained for the dynamics of supercooled liquids at high pressures.

Comparing dynamic correlation lengths from an approximation to the four-point dynamic susceptibility and from the picosecond vibrational dynamics.

Recently an alternative approach to the determination of dynamic correlation lengths ξ for supercooled liquids, based on the properties of the slow (picosecond) vibrational dynamics, was carried out [Hong, Novikov, and Sokolov, Phys. Rev. E 83, 061508 (2011)]. Although these vibrational measurements are typically conducted well below the glass transition temperature, the liquid is frozen at T(g), whereby structural correlations, density variations, etc., manifested at low temperatures as spatial fluctuations of local elastic constants, can be related to a dynamic heterogeneity length scale for the liquid state. We compare ξ from this method to values calculated using an approximation to the four-point dynamic susceptibility. For 26 different materials we find good correlation between the two measures; moreover, the pressure dependences are consistent within the large experimental error. However, ξ from Boson peak measurements above T(g) have a different, and unrealistic, temperature dependence.

Density-scaling and the Prigogine-Defay ratio in liquids.

The term "strongly correlating liquids" refers to materials exhibiting near proportionality of fluctuations in the potential energy and the virial pressure, as seen in molecular dynamics simulations of liquids whose interactions are comprised primarily of van der Waals forces. Recently it was proposed that the Prigogine-Defay ratio, Π, of strongly correlating liquids should fall close to unity. We verify this prediction herein by showing that the degree to which relaxation times are a function T/ρ(γ), the ratio of temperature to density with the latter raised to a material constant (a property inherent to strongly correlating liquids) is reflected in values of Π closer to unity. We also show that the dynamics of strongly correlating liquids are governed more by density than by temperature. Thus, while Π may never strictly equal 1 for the glass transition, it is approximately unity for many materials, and thus can serve as a predictor of other dynamic behavior. For example, Π â‰« 1 is indicative of additional control parameters besides T/ρ(γ).

On the low frequency loss peak in the dielectric spectrum of glycerol.

We measured dielectric spectra of glycerol at pressures exceeding 1 GPa in order to examine the slow Debye-like peak. This peak is not a relaxation process, but its frequency is consistent with an origin in dielectric discontinuities due to impurities. These heterogeneities have a non-negligible bulk modulus and are identified as volatile, relatively non-polar liquid contaminants. Although this slow peak is often found in the dielectric spectra of polyalcohols, it is not an intrinsic feature thereof, unlike the ostensibly similar relaxation peak in monoalcohols.

Insights on the origin of the Debye process in monoalcohols from dielectric spectroscopy under extreme pressure conditions.

The dielectric spectra of most simple liquids are characterized by two relaxation processes: (i) the alpha-process, an intense, broad non-Debye relaxation with a non-Arrhenius temperature dependence and (ii) a beta process, evident mainly below the glass transition and having nearly Arrhenius temperature behavior. However, the dielectric spectra of monoalcohols show three processes: two that resemble those of normal liquids and a third very intense Debye peak at lower frequencies, which is non-Arrhenius. Interestingly, this third process is not observed with other techniques such as light scattering and mechanical spectroscopy. There is a disagreement in the literature concerning the nature of this third relaxation. We investigated 2-ethyl-1-hexanol under high pressures (up to approximately 1.4 GPa) over a broad range of temperatures. The Debye process, which is the slowest, is strongly affected by pressure. At higher pressures the relaxation times and intensities of the two non-Arrhenius relaxations become more nearly equal. In light of these results, we propose a modified interpretation of the relaxation processes and their underlying structures in monoalcohols.

Molecular dynamics study of thermodynamic scaling of the glass-transition dynamics in ionic liquids over wide temperature and pressure ranges.

Experimentally, superpositioning of dynamic properties such as viscosity, relaxation times, or diffusion coefficients under different conditions of temperature T, pressure P, and volume V by the scaling variable TV(gamma) (where gamma is a material constant) has been reported as a general feature of many kinds of glass-forming materials. In the present work, molecular dynamics (MD) simulations have been performed to study the scaling of dynamics near the glass-transition regime of ionic liquids. Scaling in the simulated 1-ethyl-3-methylimidazolium nitrate (EMIM-NO(3)) system has been tested over wide ranges of temperatures and pressures. TV(gamma) scaling of the dynamics is well described by master curves with gamma = 4.0 +/- 0.2 and 3.8 +/- 0.2 for cation and anion, respectively. Structures and Coulombic terms of the corresponding states are found to be quite similar. The temperature and pressure dependence of the pair correlation function show similar trends and therefore can be superpositioned onto the master curve. Although the behaviors with gamma = 4 might be expected from the relation, gamma = n/3, for the dynamics with the soft-core-type potential U = epsilon(sigma/r)(n), with n = 12, pair potentials used in the MD simulation have a more complex form, and not all the repulsive terms can play their roles in the heterogeneous structures determined by ion-ion interactions. Scaling is related to the common part of effective potentials related to the pair correlation functions, including the many-body effect in real space.