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Register a new userEffects of Cooling Rate on Structural Relaxation in Amorphous Drugs: Elastically Collective Nonlinear Langevin Equation Theory and Machine Learning Study
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Theoretical approaches are formulated to investigate the molecular mobility under various cooling rates of amorphous drugs. We describe the structural relaxation of a tagged molecule as a coupled process of cage-scale dynamics and collective molecular rearrangement beyond the first coordination shell. The coupling between local and non-local dynamics behaves distinctly in different substances. Theoretical calculations for the structural relaxation time, glass transition temperature, and dynamic fragility are carried out over twenty-two amorphous drugs and polymers. Numerical results have a quantitatively good accordance with experimental data and the extracted physical quantities using the Vogel-Fulcher-Tammann fit function and machine learning. The machine learning method reveals the linear relation between the glass transition temperature and the melting point, which is a key factor for pharmaceutical solubility. Our predictive approaches are reliable tools for developing drug formulation.
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We analyze multiple new issues concerning activated relaxation in glassy hard sphere fluids and molecular and polymer liquids based on the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory. By invoking a high temperature reference state, a near universality of the apparent dynamic localization length scale is predicted for liquids of widely varying fragility, a result that is relevant to recent simulation studies and quasi-elastic neutron scattering measurements. In contrast, in the same format strongly non-universal behavior is found for the activation barrier that controls long time relaxation. Two measures of cooperativity in ECNLE theory are analyzed. A particle-level total displacement associated with the alpha relaxation event is found to be only of order 1-2 particle diameters and weakly increases with cooling. In contrast, an alternative cooperativity length is defined as the spatial scale required to recover the full barrier and bulk alpha time. This length scale grows strongly with cooling due to the emergence in the deeply supercooled regime of collective long range elastic fluctuations required to allow local hopping. It becomes very large as the laboratory Tg is approached, though is relatively modest at degrees of supercooling accessible with molecular dynamics simulation. The alpha time is found to be exponentially related to this cooperativity length over an enormous number of decades of relaxation time that span the lightly to deeply supercooled regimes. Moreover, the effective barrier height increases almost linearly with the growing cooperativity length scale. An alternative calculation of the collective elastic barrier based on a literal continuum mechanics approach is shown to result in very little change of the theoretical results for bulk properties, but leads to a much smaller and less temperature-sensitive cooperativity length scale.
We develop the elastically collective nonlinear Langevin equation theory of bulk relaxation of glass-forming liquids to investigate molecular mobility under compression conditions. The applied pressure restricts more molecular motion and therefore significantly slows-down the molecular dynamics when increasing the pressure. We quantitatively determine the temperature and pressure dependence of the structural relaxation time. To validate our model, dielectric spectroscopy experiments for three rigid and non-polymeric supramolecules are carried out at ambient and elevated pressures. The numerical results quantitatively agree with experimental data.
We theoretically investigate structural relaxation and activated diffusion of glass-forming liquids at different pressures using both the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory and molecular dynamics (MD) simulation. An external pressure restricts local motions of a single molecule within its cage and triggers the slowing down of cooperative mobility. While the ECNLE theory and simulation generally predict a monotonic increase of the glass transition temperature and dynamic fragility with pressure, the simulation indicates a decrease of fragility as pressure above 1000 bar. The structural relaxation time is found to be linearly coupled with the inverse diffusion constant. Remarkably, this coupling is independent of compression. Theoretical calculations agree quantitatively well with simulations and are also consistent with prior works.
Magneto-rheological elastomers (MREs) are functional materials that can be actuated by applying an external magnetic field. MREs comprise a composite of hard magnetic particles dispersed into a nonmagnetic elastomeric matrix. By applying a strong magnetic field, one can magnetize the structure to program its deformation under the subsequent application of an external field. Hard MREs, whose coercivities are large, have been receiving particular attention because the programmed magnetization remains unchanged upon actuation. Hence, once a structure made of a hard MRE is magnetized, it can be regarded as magnetized permanently. Motivated by a new realm of applications, there have been significant theoretical developments in the continuum description of hard MREs. By reducing the 3D description into 1D or 2D via dimensional reduction, several theories of hard magnetic slender structures such as linear beams, elastica, and shells have been recently proposed. In this paper, we derive an effective theory for MRE rods under geometrically nonlinear 3D deformation. Our theory is based on reducing the 3D magneto-elastic energy functional for the hard MREs into a 1D Kirchhoff-like description. Restricting the theory to 2D, we reproduce previous works on planar deformations. For further validation in the general case of 3D deformation, we perform precision experiments with both naturally straight and curved rods under either constant or constant-gradient magnetic fields. Our theoretical predictions are in excellent agreement with both discrete simulations and precision-model experiments. Finally, we discuss some limitations of our framework, as highlighted by the experiments, where long-range dipole interactions, which are neglected in the theory, can play a role.
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes n terms of the ratio $B/A$, where $A$ is volume coefficient and $B$ is surface-area coefficient associated with the local number variance $sigma^2(R)$ for a spherical window of radius $R$. To complement the known direct-space representation of the coefficient $B$ in terms of the total correlation function $h({bf r})$, we derive its corresponding Fourier representation in terms of the structure factor $S({bf k})$, which is especially useful when scattering information is available experimentally or theoretically. We show that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio $B/A$, the hyperuniformity index $H$ and the direct-correlation function length scale $xi_c$, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. We analyze equilibrium hard rods and sticky hard-sphere systems in arbitrary space dimension $d$ as a function of density. We also examine low-temperature excited states of many-particle systems interacting with stealthy long-ranged pair interactions as the temperature tends to zero. The capacity to identify hyperuniform scaling regimes should be particularly useful in analyzing experimentally- or computationally-generated samples that are necessarily of finite size.
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