Short‐range order in glycerol. A molecular dynamics study

Probing Molecular Packing of Amorphous Pharmaceutical Solids Using X-ray Atomic Pair Distribution Function and Solid-State NMR

The structural investigation of amorphous pharmaceuticals is of paramount importance in comprehending their physicochemical stability. However, it has remained a relatively underexplored realm primarily due to the limited availability of high-resolution analytical tools. In this study, we utilized the combined power of X-ray pair distribution functions (PDFs) and solid-state nuclear magnetic resonance (ssNMR) techniques to probe the molecular packing of amorphous posaconazole and its amorphous solid dispersion at the molecular level. Leveraging synchrotron X-ray PDF data and employing the empirical potential structure refinement (EPSR) methodology, we unraveled the existence of a rigid conformation and discerned short-range intermolecular C-F contacts within amorphous posaconazole. Encouragingly, our ssNMR 19F-13C distance measurements offered corroborative evidence supporting these findings. Furthermore, employing principal component analysis on the X-ray PDF and ssNMR data sets enabled us to gain invaluable insights into the chemical nature of the intermolecular interactions governing the drug-polymer interplay. These outcomes not only furnish crucial structural insights facilitating the comprehension of the underlying mechanisms governing the physicochemical stability but also underscore the efficacy of synergistically harnessing X-ray PDF and ssNMR techniques, complemented by robust modeling strategies, to achieve a high-resolution exploration of amorphous structures.

Structures of glass-forming liquids by x-ray scattering: Glycerol, xylitol, and D-sorbitol

Synchrotron x-ray scattering has been used to investigate three liquid polyalcohols of different sizes (glycerol, xylitol, and D-sorbitol) from above the glass transition temperatures T_g to below. We focus on two structural orders: the association of the polar OH groups by hydrogen bonds (HBs) and the packing of the non-polar hydrocarbon groups. We find that the two structural orders evolve very differently, reflecting the different natures of bonding. Upon cooling from 400 K, the O⋯O correlation at 2.8 Å increases significantly in all three systems, indicating more HBs, until kinetic arrests at T_g; the increase is well described by an equilibrium between bonded and non-bonded OH with ΔH = 9.1 kJ/mol and ΔS = 13.4 J/mol/K. When heated above T_g, glycerol loses the fewest HBs per OH for a given temperature rise scaled by T_g, followed by xylitol and by D-sorbitol, in the same order the number of OH groups per molecule increases (3, 5, and 6). The pair correlation functions of all three liquids show exponentially damped density modulations of wavelength 4.5 Å, which are associated with the main scattering peak and with the intermolecular C⋯C correlation. In this respect, glycerol is the most ordered with the most persistent density ripples, followed by D-sorbitol and by xylitol. Heating above T_g causes faster damping of the density ripples with the rate of change being the slowest in xylitol, followed by glycerol and by D-sorbitol. Given the different dynamic fragility of the three liquids (glycerol being the strongest and D-sorbitol being the most fragile), we relate our results to the current theories of the structural origin for the difference. We find that the fragility difference is better understood on the basis of the thermal stability of HB clusters than that of the structure associated with the main scattering peak.

The structural α-relaxation times of prilocaine confined in 1 nm pores of molecular sieves: quantitative explanation by the coupling model

The molecular glass-former and pharmaceutical, prilocaine, distinguishes itself by exhibiting seven general and fundamental dynamic and thermodynamic properties [Z. Wojnarowska, et al., J. Phys. Chem. B, 2015, 39, 12699.], all of which have been explained using the coupling model. What has not been studied before are the changes in properties of the structural α-relaxation of prilocaine when subjected to extreme nano-confinement in spaces with a size of about 1 nm. Recently, Ruis et al. [G. N. Ruiz, et al., Phys. Chem. Chem. Phys., 2019, 21, 15576.] measured the α-relaxation times, τ_α,conf(T), of prilocaine confined in 1 nm pores of molecular sieves. They found that τ_α,conf(T) are significantly reduced from those of bulk prilocaine, τ_α,bulk(T), and assume a weaker temperature dependence. The data in toto pose a challenge for any theory of glass transition to explain quantitatively. The coupling model (CM) was applied to this problem to predict the α-relaxation times of prilocaine when cooperativity is removed, which is expected because only a few prilocaine molecules can fit into the 1 nm pores. The results from the CM are in quantitative agreement with the experimental values of τ_α,conf(T) and the temperature dependence. The success is nontrivial because no other extant theory can do the same to the best of our knowledge.

Predicting the α-relaxation time of glycerol confined in 1.16 nm pores of zeolitic imidazolate frameworks

Uhl et al. [J. Chem. Phys., 2019, 150, 024504] studied the molecular dynamics of glycerol confined in a microporous zeolitic imidazolate framework (ZIF-8) with well-defined pore diameters of 1.16 nm by broadband dielectric spectroscopy. Of interest is a fast process in the central part of the pores identified as the α-relaxation of the confined supercooled glycerol with relaxation times τα,conf(T) reduced from τα,bulk(T) of bulk glycerol and having a temperature dependence different from the super-Arrhenius temperature of the latter. The focus of Uhl et al. was relating the confined molecular dynamics to the cooperativity length scales Lcorr(T) of molecular motion above the glass transition, and deducing the limiting high-temperature value of the correlation length of about 1.22 nm. Not yet considered by anyone are the observed values of τα,conf(T) and temperature dependence. Since the cooperativity length scales Lcorr(T) were found to be larger than the pore size of ZIF-8 over the temperature range studied and the density of the glycerol in the pore is possibly lower than the bulk, the cooperativity of the α-relaxation of glycerol confined in ZIF-8 is drastically reduced. Thus, within the framework of the Coupling Model (CM), τα,conf(T) should be nearly the same as the primitive relaxation time τ0(T) for glycerol when devoid of intermolecular coupling and cooperativity. Consistent with the absence of cooperativity of the glycerol confined in ZIF-8, we find the calculated τα,conf(T) are either the same or slightly longer than the calculated values of τ0(T). The quantitative prediction of the CM is verified. At this time we know of no other theory that can make such a quantitative prediction.

On the interpretation of shear viscosity ultrasonic measurements

This article discusses the possibility of using the measurements of ultrasonic wave parameters to estimate numerical values of shear and bulk viscosities on-line. It is noted that to increase the reliability of such estimates, it is necessary to introduce classification criteria for liquids. The on-line classification of liquids can be carried out through the measurement and comparison of the real and imaginary parts of liquid acoustic shear impedances. When the measured real and imaginary parts of the impedance are equal, the calculated ultrasonic viscosity values do not differ from the shear viscosity measured by a capillary viscometer. This occurs in liquids with a shear viscosities of less than 0.015 … 0.02 Pa ∗ s (i.e., low-viscous liquids). If the real and imaginary components of the liquid shear impedance are not equal, however, the proportionality coefficient between the viscous tensor and the shear strain rate becomes a complex number, and the calculated shear viscosity values are significantly different from values obtained by the capillary viscometer. This holds true in viscous liquids. The interpretation of the results in viscous non-polymeric liquids is considered in detail within the framework of the Maxwell model, and also within the framework of a proposed shear viscosity relaxation model. The influence of the relaxation process on the measured values of ultrasonic shear viscosity is considered. As an example, the model takes into account the presence of small molecular clusters in viscous liquids. The propagating viscous wave breaks the equilibrium distribution of the clusters, which in turn causes the relaxation process. It is shown that the shear viscosity of such liquids calculated from the ultrasonic data becomes a complex quantity depending on the frequency. A scheme for bulk viscosity measurements in the on-line mode is proposed. To find numerical values of the bulk viscosity, it is necessary to measure the real and imaginary components of the liquid shear impedance and the absorption coefficient of the longitudinal waves (if the thermal conductivity contribution can otherwise be neglected). Then the Stokes sound absorption coefficient and, accordingly, the numerical value of the bulk viscosity coefficient can be calculated.

Elastic properties of liquid and glassy propane-based alcohols under high pressure: the increasing role of hydrogen bonds in a homologous family

We have measured the elastic moduli of liquid and glassy n-propanol and propylene glycol (PG) under pressure by ultrasonic techniques and have recalculated similar characteristics for glycerol from the previous experiment. All three substances form a ternary homologous family with the common formula C3H8-n(OH)n (n = 1, 2, 3), where the number of hydrogen bonds per molecule increases with the number of oxygen atoms approximately as ≈2n. In turn, the enhancement of hydrogen bonding results in an increase in elastic moduli (bulk modulus for liquids or bulk and shear moduli for glasses) from n-propanol to glycerol at all pressures, while the volume per molecule Vm shows the opposite trend at atmospheric pressure in spite of an increase in the molecular size. Nevertheless, the ratios between the Vm values at pressure P > 0.05 GPa are inverted in liquids and tend to the ratios of molecule volumes which indicates a decrease of the relative contribution of hydrogen bonds to the repulsive intermolecular forces with increasing pressure regardless of increase or decrease in the number of hydrogen bonds and their strength. A similar volume behavior is observed for glasses at T = 77 K. We have also established that the relative difference between corresponding moduli of liquid or glassy n-propanol and PG is remarkably less than that between corresponding values for PG and glycerol. We explain this property by the formation of a three-dimensional network of hydrogen bonds in glycerol, where the number of hydrogen bonds per molecule is close to six.

Thermal conductivity of Glycerol's liquid, glass, and crystal states, glass-liquid-glass transition, and crystallization at high pressures

To investigate the effects of local density fluctuations on phonon propagation in a hydrogen bonded structure, we studied the thermal conductivity κ of the crystal, liquid, and glassy states of pure glycerol as a function of the temperature, T, and the pressure, p. We find that the following: (i) κcrystal is 3.6-times the κliquid value at 140 K at 0.1 MPa and 2.2-times at 290 K, and it varies with T according to 138 × T(-0.95); (ii) the ratio κliquid (p)/κliquid (0.1 MPa) is 1.45 GPa(-1) at 280 K, which, unexpectedly, is about the same as κcrystal (p)/κcrystal (0.1 MPa) of 1.42 GPa(-1) at 298 K; (iii) κglass is relatively insensitive to T but sensitive to the applied p (1.38 GPa(-1) at 150 K); (iv) κglass-T plots show an enhanced, pressure-dependent peak-like feature, which is due to the glass to liquid transition on heating; (v) continuous heating cold-crystallizes ultraviscous glycerol under pressure, at a higher T when p is high; and (vi) glycerol formed by cooling at a high p and then measured at a low p has a significantly higher κ than the glass formed by cooling at a low p. On heating at a fixed low p, its κ decreases before its glass-liquid transition range at that p is reached. We attribute this effect to thermally assisted loss of the configurational and vibrational instabilities of a glass formed at high p and recovered at low p, which is different from the usual glass-aging effect. While the heat capacity, entropy, and volume of glycerol crystal are less than those for its glass and liquid, κcrystal of glycerol, like its elastic modulus and refractive index, is higher. We discuss these findings in terms of the role of fluctuations in local density and structure, and the relations between κ and the thermodynamic quantities.

Polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator

A polarizable empirical force field for acyclic polyalcohols based on the classical Drude oscillator is presented. The model is optimized with an emphasis on the transferability of the developed parameters among molecules of different sizes in this series and on the condensed-phase properties validated against experimental data. The importance of the explicit treatment of electronic polarizability in empirical force fields is demonstrated in the cases of this series of molecules with vicinal hydroxyl groups that can form cooperative intra- and intermolecular hydrogen bonds. Compared to the CHARMM additive force field, improved treatment of the electrostatic interactions avoids overestimation of the gas-phase dipole moments resulting in significant improvement in the treatment of the conformational energies and leads to the correct balance of intra- and intermolecular hydrogen bonding of glycerol as evidenced by calculated heat of vaporization being in excellent agreement with experiment. Computed condensed phase data, including crystal lattice parameters and volumes and densities of aqueous solutions are in better agreement with experimental data as compared to the corresponding additive model. Such improvements are anticipated to significantly improve the treatment of polymers in general, including biological macromolecules.

Salty glycerol versus salty water surface organization: bromide and iodide surface propensities

Salty NaBr and NaI glycerol solution interfaces are examined in the OH stretching region using broadband vibrational sum frequency generation (VSFG) spectroscopy. Raman and infrared (IR) spectroscopy are used to further understand the VSFG spectroscopic signature. The VSFG spectra of salty glycerol solutions reveal that bromide and iodide anions perturb the interfacial glycerol organization in a manner similar as that found in aqueous halide salt solutions, thus confirming the presence of bromide and iodide anions at the glycerol surface. Surface tension measurements are consistent with the surface propensity suggested by the VSFG data and also show that the surface excess increases with increasing salt concentration, similar to that of water. In addition, iodide is shown to have more surface prevalence than bromide, as has also been determined from aqueous solutions. These results suggest that glycerol behaves similarly to water with respect to surface activity and solvation of halide anions at its air/liquid interface.

Molecular dynamics simulation study of glycerol-water liquid mixtures

To study the effects of water on conformational dynamics of polyalcohols, Molecular Dynamics simulations of glycerol-water liquid mixtures have been carried out at different concentrations: 42.9 and 60.0 wt % of glycerol, respectively. On the basis of the analysis of backbone conformer distributions, it is found that the surrounding water molecules have a large impact on the populations of the glycerol conformers. While the local structure of water in the liquid mixture is surprisingly close to that in pure liquid water, the behavior of glycerols can be divided into three different categories where roughly 25% of them occur in a structure similar to that in pure liquid of glycerol, ca. 25% of them exist as monomers, solvated by water, and the remaining 50% of glycerols in the mixture form H-bonded strings as remains of the glycerol H-bond network. The typical glycerol H-bond network still exists even at the lower concentration of 40 wt % of glycerol. The microheterogeneity of water-glycerol mixtures is analyzed using time-averaged distributions of the sizes of the water aggregates. At 40 wt % of glycerol, the cluster sizes from 3 to 10 water molecules are observed. The increase of glycerol content causes a depletion of clusters leading to smaller 3-5 molecule clusters domination. Translational diffusion coefficients have been calculated to study the dynamical behavior of both glycerol and water molecules. Rotational-reorientational motion is studied both in overall and in selected substructures on the basis of time correlation functions. Characteristic time scales for different motional modes are deduced on the basis of the calculated correlation times. The general conclusion is that the presence of water increases the overall mobility of glycerol, while glycerol slows the mobility of water.

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

Theory of relaxation dynamics in glass-forming hydrogen-bonded liquids

We address the relaxation dynamics in hydrogen-bonded supercooled liquids near (but above) the glass transition, measured via broadband dielectric spectroscopy (BDS). We propose a theory based on decomposing the relaxation of the macroscopic dipole moment into contributions from hydrogen-bonded clusters of s molecules, with s(min) < or = s < or = s(max) . The existence of s(max) is translated into a sum rule on the concentrations of clusters of size s . We construct the statistical mechanics of the supercooled liquid subject to this sum rule as a constraint, to estimate the temperature-dependent density of clusters of size s . With a theoretical estimate of the relaxation time of each cluster, we provide predictions for the real and imaginary parts of the frequency-dependent dielectric response. The predicted spectra and their temperature dependence are in accord with measurements, explaining a host of phenomenological fits like the Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as a particular example, we demonstrate quantitative correspondence between theory and experiments. The theory also demonstrates that the alpha peak and the "excess wing" stem from the same physics in this material. The theory also shows that in other hydrogen-bonded glass formers the excess wing can develop into a beta peak, depending on the molecular material parameters (predominantly the surface energy of the clusters). We thus argue that alpha and beta peaks can stem from the same physics. We address the BDS in constrained geometries (pores) and explain why recent experiments on glycerol did not show a deviation from bulk spectra. Finally, we discuss the dc part of the BDS spectrum and argue why it scales with the frequency of the alpha peak, providing an explanation for the remarkable data collapse observed in experiments.