Density Scaling of the Structural and Johari–Goldstein Secondary Relaxations in Poly(methyl methacrylate)

How does pressure affect the molecular dynamics, intramolecular interactions, and the relationship between structural (α) and secondary (JG-β) relaxation above and below the glass transition temperature in binary mixtures of H-bonded API - probucol and acetylated saccharides?

In this paper, the molecular dynamics as well as inter- and intramolecular interactions in the homogenous solid dispersions (SDs) of active pharmaceutical ingredient - probucol (PRO) with acetylated glucose (acGLU), acetylated sucrose (acSUC), and sucrose acetoisobutyrate (aibSUC), prepared in 5:1 molar ratio, have been investigated using broadband dielectric (BD) and Fourier transform infrared (FTIR) spectroscopy. Importantly, high pressure dielectric measurements revealed that as for neat PRO, a breakdown of the isochronal structural (α) and JG-β exact superpositioning, due to increasing separation between both processes under compression, can also be detected in its mixtures with acetylated saccharides (acSACCHs). Furthermore, the analysis of temperature dependences of JG-β-relaxation times for PRO and PRO-acSACCH SDs at selected isobaric conditions indicated the increase in the cooperativity of the secondary process (reflected in the value of the activation entropy, ΔS_β) at elevated pressure in all systems. The mere addition of the small amount of excipient to neat PRO (p = 0.1 MPa) resulted in a greater value of ΔS_β (it was the most noticeable in the case of aibSUC). Further FTIR studies carried out on the pressure densified glasses of PRO, and binary mixtures suggested that the observed changes in the cooperativity of the JG-β-process, as well as the failure of the exact isochronal superpositioning of α- and JG-β relaxation times, are due to varying H-bond pattern in the examined single- and two-component systems at high compression/in the presence of saccharide.

Chain Flexibility and the Segmental Dynamics of Polymers

Using molecular dynamics simulations, we examine the dynamics of a family of model polymers with varying chain length and torsional potential barriers. We focus on features of the dynamics of polymers that are seen experimentally but absent in simulations of freely rotating and freely jointed chains. The reduced effect of volume on the segmental dynamics with increasing chain length, a capacity for pressure densification, and the deviation from constant Johari-Goldstein relaxation time at a constant segmental relaxation time all have a common origin, torsional rigidity, and these effects become increasingly apparent for more rigid chains.

Molecular dynamics and the translational-rotational coupling of an ionically conducting glass-former: amlodipine besylate

We studied the conductivity relaxation originating from a glass-former composed of cations and anions, and the relation to the structural α-relaxation at temperatures above and below the glass transition temperature. The material chosen was amorphous amlodipine besylate (AMB), which is also a pharmaceutical with a complex chemical structure. Measurements were made using differential scanning calorimetry (DSC), broadband dielectric spectroscopy (BDS) and X-ray diffraction, and the characterization was assisted using density functional theory (DFT). The X-ray diffraction pattern confirms the amorphous nature of vitrified AMB. Both the ionic and dipolar aspects of the dynamics of AMB were examined using these measurements and were used to probe the nature of the secondary conductivity and dipolar relaxations and their relation to the conductivity α-relaxation and the structural α-relaxation. The coupling model predictions and quantum mechanical simulations were used side by side to reveal the properties and nature of the secondary conductivity relaxation and the secondary dipolar relaxation. Remarkably, the two secondary relaxations have the same relaxation times, and are one and the same process performing dual roles in conductivity and dipolar relaxations. This is caused by the translation-rotation coupling of the AMB molecule. Thus, AMB has both conductivity α- and β-relaxations, and application of the coupling model shows that these two relaxations are related in the same way as the structural α-relaxation and the Johari-Goldstein β-relaxation are. This important result has an impact on the fundamental understanding of the dynamics of ionic conductivity.

Why is the change of the Johari–Goldstein β-relaxation time by densification in ultrastable glass minor?

Coupling-Model-based theoretical explanation of the minor change of JG β-relaxation achieved by ultrastability in contrast to the dramatic change in α-relaxation.

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.

Thermodynamic scaling of relaxation: insights from anharmonic elasticity

Using molecular dynamics simulations of a molecular liquid, we investigate the thermodynamic scaling (TS) of the structural relaxation time [Formula: see text] in terms of the quantity [Formula: see text], where T and ρ are the temperature and density, respectively. The liquid does not exhibit strong virial-energy correlations. We propose a method for evaluating both the characteristic exponent [Formula: see text] and the TS master curve that uses experimentally accessible quantities that characterise the anharmonic elasticity and does not use details about the microscopic interactions. In particular, we express the TS characteristic exponent [Formula: see text] in terms of the lattice Grüneisen parameter [Formula: see text] and the isochoric anharmonicity [Formula: see text]. An analytic expression of the TS master curve of [Formula: see text] with [Formula: see text] as the key adjustable parameter is found. The comparison with the experimental TS master curves and the isochoric fragilities of 34 glassformers is satisfying. In a few cases, where thermodynamic data are available, we test (i) the predicted characteristic exponent [Formula: see text] and (ii) the isochoric anharmonicity [Formula: see text], as drawn by the best fit of the TS of the structural relaxation, against the available thermodynamic data. A linear relation between the isochoric fragility and the isochoric anharmonicity [Formula: see text] is found and compared favourably with the results of experiments with no adjustable parameters. A relation between the increase of the isochoric vibrational heat capacity due to anharmonicity and the isochoric fragility is derived.

Variation of the dynamic susceptibility along an isochrone

Koperwas et al. showed in a recent paper [Phys. Rev. Lett. 111, 125701 (2013)] that the dynamic susceptibility χ4 as estimated by dielectric measurements for certain glass-forming liquids decreases substantially with increasing pressure along a curve of constant relaxation time. This observation is at odds with other measures of dynamics being invariant and seems to pose a problem for theories of glass formation. We show that this variation is in fact consistent with predictions for liquids with hidden scale invariance: Measures of dynamics at constant volume are invariant along isochrones, called isomorphs in such liquids, but contributions to fluctuations from long-wavelength fluctuations can vary. This is related to the known noninvariance of the isothermal bulk modulus. Considering the version of χ4 defined for the NVT ensemble, data from simulations of a binary Lennard-Jones liquid show in fact a slight increase with increasing density. This is a true departure from the formal invariance expected for this quantity.

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.

Hidden scale invariance in condensed matter

Recent developments show that many liquids and solids have an approximate "hidden" scale invariance that implies the existence of lines in the thermodynamic phase diagram, so-called isomorphs, along which structure and dynamics in properly reduced units are invariant to a good approximation. This means that the phase diagram becomes effectively one-dimensional with regard to several physical properties. Liquids and solids with isomorphs include most or all van der Waals bonded systems and metals, as well as weakly ionic or dipolar systems. On the other hand, systems with directional bonding (hydrogen bonds or covalent bonds) or strong Coulomb forces generally do not exhibit hidden scale invariance. The article reviews the theory behind this picture of condensed matter and the evidence for it coming from computer simulations and experiments.

Characteristics of the structural and Johari-Goldstein relaxations in Pd-based metallic glass-forming liquids

The dynamics of Pd-based metallic glass-forming liquids (Pd(40)Ni(10)Cu(30)P(20), Pd(42.5)Ni(7.5)Cu(30)P(20), Pd(40)Ni(40)P(20), and Pd(30)Ni(50)P(20)) was studied by mechanical spectroscopy and modulated differential scanning calorimetry (MDSC). We found that the change in composition has a significant effect on the α relaxation dynamics; the largest difference corresponds to an increase of the glass transition temperature Tg of ∼ 15 K, for materials in which 30% Ni was substituted by 30% Cu (i.e., from Pd(40)Ni(40)P(20) to Pd(40)Ni(10)Cu(30)P(20)). We also found that all Pd-based metallic glasses have very similar fragilities, 59 < m < 67, and Kohlrausch stretched exponents, 0.59 < βKWW < 0.60. It is interesting that the values of m and βKWW correlate well with the general relation proposed by Böhmer et al. for nonmetallic glass formers (Böhmer, R.; et al. J. Chem. Phys. 1993, 99, 4201-4209), which for the observed βKWW values predicts 58 < m < 61. From a linear deconvolution of the α and β relaxations, we find that the substitution of the Ni with Cu induced a large change in the time constant of the Johari-Goldstein relaxation, τβ. The activation energy, Uβ, of the β relaxation was largely independent of chemical composition. In all cases, 25 < Uβ/RT < 28, a range in agreement with results for other glass formers (Kudlik, A.; et al. Europhys. Lett. 1997, 40, 649-654 and Ngai, K. L.; et al. Phys. Rev. E 2004, 69, 031501). From the heat capacity and mechanical loss, estimates were obtained for the number of dynamically correlated units, Nc; we find significantly larger values for these metallic glass-forming liquids than Nc for other glass-forming materials.

Revisiting the influence of chain length on the α- and β-relaxations in oligomeric glass formers

Dielectric relaxation measurements of a series of oligo(propylene glycol) dimethyl ethers, CH3-O-[CH2-CH(CH3)-O]N-CH3, including samples with the number of PG units N = 1, 2, 3, 7, 17, 34, and 69, were made by Mattsson et al. [Phys. Rev. Lett. 94, 165701 (2005)] at ambient pressure. The objective of the study was to relate the change of properties of the glass transition dynamics to the number of monomer units N in the chain. Not examined in the previous publication is how the change of the width of the frequency dispersion of the α-relaxation with N is related to the observed change in the α-β bifurcation characterized by the ratio, τ(α)(T(g))/τ(β)(T(g)). In this paper, the frequency dispersion of the dimer, trimer, and heptamer are fitted by the Fourier transform of the Kohlrausch stretched exponential function, φ(t) = exp[-(t/τ(α))(1-n)]. Determined from experimental data, both τ(α)(T(g))/τ(β)(T(g)) and n increase with N. More interestingly, we find τ(α)(T(g))/τ(β)(T(g)) has approximately the same value as [τ(α)(T(g))/t(c)](n) with t(c) = 2 ps, in accordance with the prediction of the Coupling Model of approximate relation between τ(α) and τ(β) given by τ(β) ≈ (t(c))(n)(τ(α))(1-n). Considered also are previously unpublished dielectric loss spectra of the heptamer taken at different combinations of T and P with τ(α)(T,P) fixed by Roland et al. [Phys. Rev. B 77, 012201 (2008)]. The dielectric loss data show not only the α-loss peaks superpose but also the high frequency flank including the barely resolved JG β-relaxation superposes approximately. This is again consistent with the approximate relation between τ(α) and τ(β) from the Coupling Model because n is unchanged on varying P and T with τ(α)(T,P) kept constant, and t(c) is a constant. The additional advance made herein has the benefit of enhancing the impact of the earlier experimental studies of the oligo(propylene glycol) dimethyl ethers on current understanding of the dynamics of glass transition.