Intermolecular distance and density scaling of dynamics in molecular liquids.

A broad variety of liquids conform to density scaling: relaxation times can be expressed as a function of the ratio of temperature to density, the latter raised to a material constant γ. For atomic liquids interacting only through simple pair potentials, the exponent γ is very nearly equal to n/3, where n is the steepness of the intermolecular potential, while for molecular liquids having rigid bonds and built using the same interatomic potential, γ > n/3. We find that for this class of molecular liquids, γ = n/δ, where the parameter δ relates the intermolecular distance to the density along an isomorph (the line of approximately constant dynamics and structure). δ depends only on the molecular structure and not the interatomic potential.

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.

Pressure densified 1,3,5-tri(1-naphthyl)benzene glass. I. Volume recovery and physical aging.

The effects of pressure densification on 1,3,5-tri(1-naphthyl)benzene (TNB) are assessed from volumetric and calorimetric measurements. The pressure densified glass (PDG) has higher density than conventional glass (CG), but unlike ultrastable TNB glass prepared using vapor deposition which also has elevated density, TNB PDG exhibits higher enthalpy and lower thermal stability than when formed at ambient pressure. PDG also exhibits anomalous physical aging. Rather than evolving monotonically toward the equilibrium density, there is an overshoot to a lower density state. Only when the density of the PDG becomes equivalent to the corresponding CG does the density begin a slow approach toward equilibrium.

Segmental and secondary dynamics of nanoparticle-grafted oligomers.

The local segmental and secondary dynamics of tetramethylene oxide oligomer grafted to silica nanoparticles (NPs) were investigated as a function of grafting density and molecular weight. Grafting slows the segmental (α) dynamics, but gives rise to faster secondary (ß) motions. Interestingly, the magnitude of these effects decreases with the extent of grafting (i.e., surface coverage), as well as with oligomer molecular weight. The disparity in dynamical effects reflects the decoupling of the segmental and more local ß dynamics, the former is associated with stronger dynamic correlations that extend over a greater spatial range. This results in greater sensitivity to interactions, including tethering of the chains to the NP surface.

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.

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.

A test for the existence of isomorphs in glass-forming materials.

We describe a method to determine whether a material has isomorphs in its thermodynamic phase diagram. Isomorphs are state points for which various properties are invariant in reduced units. Such materials are commonly identified from strong correlation between thermal fluctuations of the potential energy, U, and the virial W, but this identification is not generally applicable to real materials. We show from molecular dynamic simulations of atomic, molecular, and polymeric materials that systems with strong U-W correlation cannot be pressure densified, that is, the density obtained on cooling to the glassy state and releasing the pressure is independent of the pressure applied during cooling.

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.

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.

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.

Phase behavior and dynamics of a cholesteric liquid crystal.

The synthesis, equation of state, phase diagram, and dielectric relaxation properties are reported for a new liquid crystal, 4(')-butyl-4-(2-methylbutoxy)azoxybenzene (4ABO5*), which exhibits a cholesteric phase at ambient temperature. The steepness of the intermolecular potential was characterized from the thermodynamic potential parameter, Γ = 4.3 ± 0.1 and the dynamic scaling exponent, γ = 3.5 ± 0.2. The difference between them is similar to that seen previously for nematic and smectic liquid crystals, with the near equivalence of Γ and γ consistent with the near constancy of the relaxation time of 4ABO5* at the cholesteric to isotropic phase transition (i.e., the clearing line). Thus, chirality does not cause deviations from the general relationship between thermodynamics and dynamics in the ordered phase of liquid crystals. The ionic conductivity of 4ABO5* shows strong coupling to the reorientational dynamics.

Are polar liquids less simple?

Strong correlation between equilibrium fluctuations under isochoric conditions of the potential energy, U, and the virial, W, is a characteristic of liquids that implies the presence of certain dynamic properties, such as density scaling of the relaxation times and isochronal superpositioning of the relaxation function. In this work we employ molecular dynamics simulations on methanol and two variations, lacking hydrogen bonds and a dipole moment, to assess the connection between the correlation of U and W and these dynamic properties. We show, in accord with prior results of others [T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X 2, 011011 (2012)], that simple van der Waals liquids exhibit both strong correlations and the expected dynamic behavior. However, for polar liquids this correspondence breaks down--weaker correlation between U and W is not associated with worse conformance to density scaling or isochronal superpositioning. The reason for this is that strong correlation between U and W only requires their proportionality, whereas the expected dynamic behavior depends primarily on constancy of the proportionality constant for all state points. For hydrogen-bonded liquids, neither strong correlation nor adherence to the dynamic properties is observed; however, this nonconformance is not directly related to the concentration of hydrogen bonds, but rather to the greater deviation of the intermolecular potential from an inverse power law (IPL). Only (hypothetical) liquids having interactions governed strictly by an IPL are perfectly correlating and exhibit the consequent dynamic properties over all thermodynamic conditions.

Effect of binding to carbon black on the dynamics of 1,4-polybutadiene.

The nature of the interactions of polymers at the surface of nanoparticles is crucial to understanding the dynamics and their relation to mechanical properties. The effect of binding (both chemical attachment and physical adsorption) on the local and global dynamics of chain molecules remains a controversial subject. Using neutron scattering and dynamic mechanical spectroscopies, we measured the slow conformational and terminal relaxations, as well as the fast local dynamics, of 1,4-polybutadiene (PBD) containing carbon black (CB) particles. We observed a substantial decrease in the flexibility of bound segments at temperatures through the glass transition temperature, T(g). The longer range motions of the PBD become more suppressed and cooperative as temperature decreases, while the relaxation time of the fast local dynamics is little affected by the CB particles. The mobile fraction of PBD is less sensitive to temperature when bound. Mechanical spectroscopy indicates that both the local segmental dynamics and the global chain modes are slowed by the filler. These results are consistent with transient structural arrest of the slow dynamics of atoms adjacent to the particles.

Anomalous electrical conductivity behavior at elevated pressure in the protic ionic liquid procainamide hydrochloride.

Using broadband dielectric spectroscopy, we investigated the effect of hydrostatic pressure on the conductivity relaxation time τ{σ} of the supercooled protic ionic liquid, procainamide hydrochloride, a common pharmaceutical. The pressure dependence of τ{σ} exhibited anomalous behavior in the vicinity of the glass transition T{g}, manifested by abrupt changes in activation volume. This peculiar behavior, paralleling the change in temperature dependence of τ{σ} near T{g}, is a manifestation of the decoupling between electrical conductivity and structural relaxation. Although the latter effectively ceases in the glassy state, free ions retain their mobility but with a reduced sensitivity to thermodynamic changes. This is the first observation of decoupling of ion migration from structural relaxation in a glassy conductor by isothermal densification.

Synthesis of phosphine and antibody-azide probes for in vivo Staudinger ligation in a pretargeted imaging and therapy approach.

The application of intact monoclonal antibodies (mAbs) as targeting agents in nuclear imaging and radioimmunotherapy is hampered by the slow pharmacokinetics of these molecules. Pretargeting with mAbs could be beneficial to reduce the radiation burden to the patient, while using the excellent targeting capacity of the mAbs. In this study, we evaluated the applicability of the Staudinger ligation as pretargeting strategy using an antibody-azide conjugate as tumor-targeting molecule in combination with a small phosphine-containing imaging/therapeutic probe. Up to 8 triazide molecules were attached to the antibody without seriously affecting its immunoreactivity, pharmacokinetics, and tumor uptake in tumor bearing nude mice. In addition, two (89)Zr- and (67/68)Ga-labeled desferrioxamine (DFO)-phosphines, a (177)Lu-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA)-phosphine and a (123)I-cubyl phosphine probe were synthesized and characterized for their pharmacokinetic behavior in nude mice. With respect to the phosphine probes, blood levels at 30 min after injection were <5% injected dose per gram tissue, indicating rapid blood clearance. In vitro Staudinger ligation of 3.33 µM antibody-azide conjugate with 1 equiv of radiolabeled phosphine, relative to the azide, in aqueous solution resulted in 20-25% efficiency after 2 h. The presence of 37% human serum resulted in a reduced ligation efficiency (reduction max. 30% at 2 h), while the phosphines were still >80% intact. No in vivo Staudinger ligation was observed in a mouse model after injection of 500 µg antibody-azide, followed by 68 µg DFO-phosphine at t = 2 h, and evaluation in blood at t = 7 h. To explain negative results in mice, Staudinger ligation was performed in vitro in mouse serum. Under these conditions, a side product with the phosphine was formed and ligation efficiency was severely reduced. It is concluded that in vivo application of the Staudinger ligation in a pretargeting approach in mice is not feasible, since this ligation reaction is not bioorthogonal and efficient enough. Slow reaction kinetics will also severely restrict the applicability of Staudinger ligation in humans.

On the density scaling of liquid dynamics.

Superpositioning of relaxation data as a function of the product variable TV(γ), where T is temperature, V the specific volume, and γ a material constant, is an experimental fact demonstrated for approximately 100 liquids and polymers. Such scaling behavior would result from the intermolecular potential having the form of an inverse power law (IPL), suggesting that an IPL is a good approximation for certain relaxation properties over the relevant range of intermolecular distances. However, the derivation of the scaling property of an IPL liquid is based on reduced quantities, for example, the reduced relaxation time equal to T(1∕2V - 1∕3) times the actual relaxation time. The difference between scaling using reduced rather than unreduced units is negligible in the supercooled regime; however, at higher temperature the difference can be substantial, accounting for the purported breakdown of the scaling and giving rise to different values of the scaling exponent. Only the γ obtained using reduced quantities can be sensibly related to the intermolecular potential.

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.