Journal articles on the topic 'Network Forming Liquids'

The non-Arrhenius behavior of segmental dynamics in glass-forming liquids is one of the most profound mysteries in soft matter physics. In this article, we propose a dynamically correlated network (DCN) model to understand the growing behavior of dynamically correlated regions during cooling, which leads to the viscous slowdown of supercooled liquids. The fundamental concept of the model is that the cooperative region of collective motions has a network structure that consists of string-like parts, and networks of various sizes interpenetrate each other. Each segment undergoes dynamical coupling with its neighboring segments via a finite binding energy. Monte Carlo simulations showed that the fractal dimension of the DCNs generated at different temperatures increased and their size distribution became broader with decreasing temperature. The segmental relaxation time was evaluated based on a power law with four different exponents for the activation energy of rearrangement with respect to the DCN size. The results of the present DCN model are consistent with the experimental results for various materials of molecular and polymeric liquids.

The Arrhenius crossover temperature, TA, corresponds to a thermodynamic state wherein the atomistic dynamics of a liquid becomes heterogeneous and cooperative; and the activation barrier of diffusion dynamics becomes temperature-dependent at temperatures below TA. The theoretical estimation of this temperature is difficult for some types of materials, especially silicates and borates. In these materials, self-diffusion as a function of the temperature T is reproduced by the Arrhenius law, where the activation barrier practically independent on the temperature T. The purpose of the present work was to establish the relationship between the Arrhenius crossover temperature TA and the physical properties of liquids directly related to their glass-forming ability. Using a machine learning model, the crossover temperature TA was calculated for silicates, borates, organic compounds and metal melts of various compositions. The empirical values of the glass transition temperature Tg, the melting temperature Tm, the ratio of these temperatures Tg/Tm and the fragility index m were applied as input parameters. It has been established that the temperatures Tg and Tm are significant parameters, whereas their ratio Tg/Tm and the fragility index m do not correlate much with the temperature TA. An important result of the present work is the analytical equation relating the temperatures Tg, Tm and TA, and that, from the algebraic point of view, is the equation for a second-order curved surface. It was shown that this equation allows one to correctly estimate the temperature TA for a large class of materials, regardless of their compositions and glass-forming abilities.

Organogelators gelate liquids by forming a network of anisotropic fibres. Hansen solubility parameters can be used to rationalize the effect of the gelator structure: the gelation and solubility domains evolve in opposite directions.

This study concerned a novel super-molecular ionic liquid synthesized by ammonium thiocyanate and caprolactam. The physical characters such as melting point and electric conductivity were investigated. Results showed that the melting point is -12.2°C at the molar ratio of 3:1 (caprolactam/ammonium thiocyanate), which is much lower than raw materials. The electric conductivities of synthesized ionic liquids were close to that of imidazole ILs. The structure of ionic liquid was characterized by IR,1HNMR and quantum chemical calculations. It was shown that the NH4+cation connected with caprolactam organic molecules by hydrogen bonds, leading to the forming of a super-molecular ion. The electrostatic attraction of super-molecular ion with anion was decreased because of the larger volume of super-molecular ion than original cation, thus the melting point decreased. The key properties that distinguish super-molecular ionic liquid from other ILs were the presence of supermolecular ion, which can be used to build up a hydrogen-bonded network. This type ion liquid was named as super-molecular ion liquid.

The nature of excitations in liquids has been a subject of debate for a long time. In liquids, phonons are extremely short-lived and marginalized. Instead, recent research results indicate that local topological or configurational excitations (anankeons) are the elementary excitations in high temperature metallic liquids. Local topological excitations are those which locally alter the atomic connectivity network by cutting or forming atomic bonds, and are directly tied to the atomistic origin of viscosity in the liquid. The local potential energy landscape (PEL) of anankeons represents the probability weighted projection of the global PEL to a single atom. The original PEL is an insightful concept, but is highly multi-dimensional and difficult to characterize or even to visualize. A description in terms of the local PEL for anankeons appears to offer a simpler and more effective approach toward this complex problem. At the base of these advances, is the recognition that atomic discreteness and the topology of atomic connectivity are the most crucial features of the structure in liquids, which current nonlinear continuum theories cannot fully capture. These discoveries could open the way to the explanation of various complex phenomena in liquids, such as atomic transport, fragility, and the glass transition, in terms of these excitations.

We have prepared a series of pyridinium-based gemini amphiphiles. They exhibit thermotropic liquid–crystalline behavior depending on their alkyl chain lengths and anion species. By adjusting the alkyl chain lengths and selecting suitable anions, we have obtained an ionic amphiphile that exhibits a normal-type bicontinuous cubic phase from 38 °C to 12 °C on cooling from an isotropic phase. In the bicontinuous cubic liquid–crystalline assembly, the pyridinium-based ionic parts align along a gyroid minimal surface forming a 3D continuous ionic domain while their ionophobic alkyl chains form 3D branched nanochannel networks. This ionic compound can form homogeneous mixtures with a lithium salt and the resultant mixtures keep the ability to form normal-type bicontinuous cubic phases. Ion conduction measurements have been performed for the mixtures on cooling. It has been revealed that the formation of the 3D branched ionophobic nanochannels does not disturb the ion conduction behavior in the ionic domain while it results in the conversion of the state of the mixtures from fluidic liquids to quasi-solids, namely highly viscous liquid crystals. Although the ionic conductivity of the mixtures is in the order of 10–7 S cm–1 at 40 °C, which is far lower than the values for practical use, the present material design has a potential to pave the way for developing advanced solid electrolytes consisting of two task-specific nanosegregated domains: One is an ionic liquid nano-domain with a 3D continuity for high ionic conductivity and the other is ionophobic nanochannel network domains for high mechanical strength.

Two topics are described for structure analyses of glass and liquid using a combination of conical nozzle levitation (CNL) technique and diffraction experiments. The structure of high-purity bulk forsterite (Mg2SiO4) glass synthesized by a CNL technique has been determined by a combination of high-energy x-ray, neutron diffraction, and reverse Monte Carlo (RMC) modeling technique. The 3-dimensional atomic configuration derived from RMC modeling revealed that unusual network structure. In order to study structures of high-temperature and undercooled liquids, a CNL system has been developed and integrated with the two-axis diffractometer for glass, liquid, and amorphous materials at SPring-8, which is one of the third-generation synchrotron source. High-energy x-ray diffraction experiments were performed to obtain reliable diffraction data for the liquid phase of metallic glass-forming Zr-Cu binary alloys.

Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different “order parameters” including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local–nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply supercooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.

Recent developments in machine learning have enabled accurate predictions of the dynamics of slow structural relaxation in glass-forming systems. However, existing machine learning models for these tasks are mostly designed such that they learn a single dynamic quantity and relate it to the structural features of glassy liquids. In this study, we propose a graph neural network model, “BOnd TArgeting Network,” that learns relative motion between neighboring pairs of particles, in addition to the self-motion of particles. By relating the structural features to these two different dynamical variables, the model autonomously acquires the ability to discern how the self motion of particles undergoing slow relaxation is affected by different dynamical processes, strain fluctuations and particle rearrangements, and thus can predict with high precision how slow structural relaxation develops in space and time.

Li-ion batteries are currently considered promising energy storage devices for the future. However, the use of liquid electrolytes poses certain challenges, including lithium dendrite penetration and flammable liquid leakage. Encouragingly, solid electrolytes endowed with high stability and safety appear to be a potential solution to these problems. Among them, ionic liquids (ILs) packed in metal organic frameworks (MOFs), known as ILs@MOFs, have emerged as a hybrid solid-state material that possesses high conductivity, low flammability, and strong mechanical stability. ILs@MOFs plays a crucial role in forming a continuous interfacial conduction network, as well as providing internal ion conduction pathways through the ionic liquid. Hence, ILs@MOFs can not only act as a suitable ionic conduct main body, but also be used as an active filler in composite polymer electrolytes (CPEs) to meet the demand for higher conductivity and lower cost. This review focuses on the characteristic properties and the ion transport mechanism behind ILs@MOFs, highlighting the main problems of its applications. Moreover, this review presents an introduction of the advantages and applications of Ils@MOFs as fillers and the improvement directions are also discussed. In the conclusion, the challenges and suggestions for the future improvement of ILs@MOFs hybrid electrolytes are also prospected. Overall, this review demonstrates the application potential of ILs@MOFs as a hybrid electrolyte material in energy storage systems.

Knowledge of pressure-induced structural changes in glasses is important in various scientific fields as well as in engineering and industry. However, polyamorphism in glasses under high pressure remains poorly understood because of experimental challenges. Here we report new experimental findings of ultrahigh-pressure polyamorphism in GeO2 glass, investigated using a newly developed double-stage large-volume cell. The Ge–O coordination number (CN) is found to remain constant at ∼6 between 22.6 and 37.9 GPa. At higher pressures, CN begins to increase rapidly and reaches 7.4 at 91.7 GPa. This transformation begins when the oxygen-packing fraction in GeO2 glass is close to the maximal dense-packing state (the Kepler conjecture = ∼0.74), which provides new insights into structural changes in network-forming glasses and liquids with CN higher than 6 at ultrahigh-pressure conditions.

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

We investigate the jamming transition observed in vibrated granular systems composed of millimeter size glass beads. When a granular system is submitted to vibrations with decreasing intensity, it evolves in a way similar to glass-forming liquids: from a low viscosity, liquid-like state, it evolves into an amorphous jammed state. This evolution is observed by the means of an immersed oscillator acting as a torsion pendulum in forced mode. The complex susceptibility of the oscillator is measured as a function of the probe forcing frequency and of the vibration intensity. Focusing on the strongly vibrated states, we observe that there are two different dynamic regions. The first is a high fluidization regime, where the internal friction is found to be proportional to the ratio between the pulsation and the vibration intensity: . In this region, the system shows an apparent viscous friction . In the second, low fluidization, regime, we observe a more complex behavior, and the measured internal friction appears to be well described by a relation of the form: . In this second case, the key role is played by a critical breakaway stress, σcr, needed to break the network of chains of forces that form between the grains. Finally, if vibration intensities are still reduced, we also observe that onset of jamming is clearly distinguishable: we observe a sharp increase in the apparent dynamic modulus together with a peak in internal friction. This transition presents important similarities to those observed in glasses, and it leads to the second (low vibrations) regime, where the key role is played by the square root of the vibration intensity.

Yielding behavior in amorphous solids has been investigated in computer simulations using uniform and cyclic shear deformation. Recent results characterize yielding as a discontinuous transition, with the degree of annealing of glasses being a significant parameter. Under uniform shear, discontinuous changes in stresses at yielding occur in the high annealing regime, separated from the poor annealing regime in which yielding is gradual. In cyclic shear simulations, relatively poorly annealed glasses become progressively better annealed as the yielding point is approached, with a relatively modest but clear discontinuous change at yielding. To understand better the role of annealing on yielding characteristics, we perform athermal quasistatic cyclic shear simulations of glasses prepared with a wide range of annealing in two qualitatively different systems—a model of silica (a network glass) and an atomic binary mixture glass. Two strikingly different regimes of behavior emerge. Energies of poorly annealed samples evolve toward a unique threshold energy as the strain amplitude increases, before yielding takes place. Well-annealed samples, in contrast, show no significant energy change with strain amplitude until they yield, accompanied by discontinuous energy changes that increase with the degree of annealing. Significantly, the threshold energy for both systems corresponds to dynamical cross-over temperatures associated with changes in the character of the energy landscape sampled by glass-forming liquids.

In this letter, we propose a novel neuro-inspired low-resolution online unsupervised learning rule to train the reservoir or liquid of liquid state machines. The liquid is a sparsely interconnected huge recurrent network of spiking neurons. The proposed learning rule is inspired from structural plasticity and trains the liquid through formating and eliminating synaptic connections. Hence, the learning involves rewiring of the reservoir connections similar to structural plasticity observed in biological neural networks. The network connections can be stored as a connection matrix and updated in memory by using address event representation (AER) protocols, which are generally employed in neuromorphic systems. On investigating the pairwise separation property, we find that trained liquids provide 1.36 [Formula: see text] 0.18 times more interclass separation while retaining similar intraclass separation as compared to random liquids. Moreover, analysis of the linear separation property reveals that trained liquids are 2.05 [Formula: see text] 0.27 times better than random liquids. Furthermore, we show that our liquids are able to retain the generalization ability and generality of random liquids. A memory analysis shows that trained liquids have 83.67 [Formula: see text] 5.79 ms longer fading memory than random liquids, which have shown 92.8 [Formula: see text] 5.03 ms fading memory for a particular type of spike train inputs. We also throw some light on the dynamics of the evolution of recurrent connections within the liquid. Moreover, compared to separation-driven synaptic modification', a recently proposed algorithm for iteratively refining reservoirs, our learning rule provides 9.30%, 15.21%, and 12.52% more liquid separations and 2.8%, 9.1%, and 7.9% better classification accuracies for 4, 8, and 12 class pattern recognition tasks, respectively.

A quantum spin-liquid is a spin disordered state of matter in which spins are strongly correlated and highly entangled with low-energy excitations. It has been often found in two-dimensional S = ½, highly frustrated spin networks but rarely observed in three-dimensional (3D) frustrated quantum magnets. Here, KSrFe2(PO4)3, forming a complicated 3D frustrated lattice with a spin moment S = 5/2, is investigated by thermodynamic, neutron diffraction measurements and electronic structure calculations. Despite the relatively sizable Curie–Weiss temperature θCW = −70 K, a conventional magnetic long-range order is confirmed to be absent down to 0.19 K. The magnetic heat capacity data follow the power-law behavior at the lowest temperature region, supporting gapless excitations in a 3D spin-liquid state. Strong geometrical spin frustration responsible for the spin-liquid feature is understood as originating from the almost comparable five competing nearest-neighbor antiferromagnetic exchange interactions, which form the complicated 3D frustrated spin network. All these results suggest that the compound KSrFe2(PO4)3, representing a unique 3D spin frustrated network, could be a rare example of forming a gapless spin-liquid state even with a large spin moment of S = 5/2.

It has been studied whether machine learning interatomic potentials parameterized with only disordered configurations corresponding to liquid can describe the properties of crystalline phases and predict their structure. The study has been performed for a network-forming system SiO2, which has numerous polymorphic phases significantly different in structure and density. Using only high-temperature disordered configurations, a machine learning interatomic potential based on artificial neural networks (DeePMD model) has been parameterized. The potential reproduces well ab initio dependences of the energy on the volume and the vibrational density of states for all considered tetra- and octahedral crystalline phases of SiO2. Furthermore, the combination of the evolutionary algorithm and the developed DeePMD potential has made it possible to reproduce the really observed crystalline structures of SiO2. Such a good liquid–crystal portability of the machine learning interatomic potential opens prospects for the simulation of the structure and properties of new systems for which experimental information on crystalline phases is absent.

NFs (neurofilaments), the major cytoskeletal constituent of myelinated axons in vertebrates, consist of three different molecular-mass subunit proteins, NF-L (low), NF-M (medium) and NF-H (high), assembled to form mature filaments with protruding intrinsically disordered C-terminal side-arms. Liquid crystal gel networks of side-arm-mediated NF assemblies play a key role in the mechanical stability of neuronal processes. Disruptions of the NF network, due to NF overaccumulation or incorrect side-arm interactions, are a hallmark of motor neuron diseases including amyotrophic lateral sclerosis. Using synchrotron small-angle X-ray scattering and various microscopy techniques, we have investigated the role of the peptide charges in the subunit side-arms on the structure and interaction of NFs. Our findings, which delineate the distinct roles of NF-M and NF-H in regulating NF interactions, shed light on possible mechanisms of disruption of optimal mechanical network properties.

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated in a way that allows a description of the transition from the initial equilibrium state to the final metastable state without considering any kinetic processes. The RFOT and its applications for real molecular systems (multicomponent liquids with various intermolecular potentials, gel systems, etc.) are widely represented in English-language sources. However, these studies are practically not described in any Russian sources. This paper presents an overview of the studies carried out in this field. REFERENCES 1. Sanditov D. S., Ojovan M. I. Relaxation aspectsof the liquid—glass transition. Uspekhi FizicheskihNauk. 2019;189(2): 113–133. DOI: https://doi.org/10.3367/ufnr.2018.04.0383192. Tsydypov Sh. B., Parfenov A. N., Sanditov D. S.,Agrafonov Yu. V., Nesterov A. S. Application of themolecular dynamics method and the excited statemodel to the investigation of the glass transition inargon. Available at: http://www.isc.nw.ru/Rus/GPCJ/Content/2006/tsydypov_32_1.pdf (In Russ.). GlassPhysics and Chemistry. 2006;32(1): 83–88. DOI: https://doi.org/10.1134/S10876596060101113. Berthier L., Witten T. A. Glass transition of densefluids of hard and compressible spheres. PhysicalReview E. 2009;80(2): 021502. DOI: https://doi.org/10.1103/PhysRevE.80.0215024. Sarkisov G. N. Molecular distribution functionsof stable, metastable and amorphous classical models.Uspekhi Fizicheskih Nauk. 2002;172(6): 647–669. DOI:https://doi.org/10.3367/ufnr.0172.200206b.06475. Hoover W. G., Ross M., Johnson K. W., HendersonD., Barker J. A., Brown, B. C. Soft-sphere equationof state. The Journal of Chemical Physics, 1970;52(10):4931–4941. DOI: https://doi.org/10.1063/1.16727286. Cape J. N., Woodcock L. V. Glass transition in asoft-sphere model. The Journal of Chemical Physics,1980;72(2): 976–985. DOI: https://doi.org/10.1063/1.4392177. Franz S., Mezard M., Parisi G., Peliti L. Theresponse of glassy systems to random perturbations:A bridge between equilibrium and off-equilibrium.Journal of Statistical Physics. 1999;97(3–4): 459–488.DOI: https://doi.org/10.1023/A:10046029063328. Marc Mezard and Giorgio Parisi. Thermodynamicsof glasses: a first principles computation. J. of Phys.:Condens. Matter. 1999;11: A157–A165.9. Berthier L., Jacquin H., Zamponi F. Microscopictheory of the jamming transition of harmonic spheres.Physical Review E, 2011;84(5): 051103. DOI: https://doi.org/10.1103/PhysRevE.84.05110310. Berthier L., Biroli, G., Charbonneau P.,Corwin E. I., Franz S., Zamponi F. Gardner physics inamorphous solids and beyond. The Journal of ChemicalPhysics. 2019;151(1): 010901. DOI: https://doi.org/10.1063/1.5097175 11. Berthier L., Ozawa M., Scalliet C. Configurationalentropy of glass-forming liquids. The Journal ofChemical Physics. 2019;150(16): 160902. DOI: https://doi.org/10.1063/1.509196112. Bomont J. M., Pastore G. An alternative schemeto find glass state solutions using integral equationtheory for the pair structure. Molecular Physics.2015;113(17–18): 2770–2775. DOI: https://doi.org/10.1080/00268976.2015.103832513. Bomont J. M., Hansen J. P., Pastore G.Hypernetted-chain investigation of the random firstordertransition of a Lennard-Jones liquid to an idealglass. Physical Review E. 2015;92(4): 042316. DOI:https://doi.org/10.1103/PhysRevE.92.04231614. Bomont J. M., Pastore G., Hansen J. P.Coexistence of low and high overlap phases in asupercooled liquid: An integral equation investigation.The Journal of Chemical Physics. 2017;146(11): 114504.DOI: https://doi.org/10.1063/1.497849915. Bomont J. M., Hansen J. P., Pastore G. Revisitingthe replica theory of the liquid to ideal glass transition.The Journal of Chemical Physics. 2019;150(15): 154504.DOI: https://doi.org/10.1063/1.508881116. Cammarota C., Seoane B. First-principlescomputation of random-pinning glass transition, glasscooperative length scales, and numerical comparisons.Physical Review B. 2016;94(18): 180201. DOI: https://doi.org/10.1103/PhysRevB.94.18020117. Charbonneau P., Ikeda A., Parisi G., Zamponi F.Glass transition and random close packing above threedimensions. Physical Review Letters. 2011;107(18):185702. DOI: https://doi.org/10.1103/PhysRevLett.107.18570218. Ikeda A., Miyazaki K. Mode-coupling theory asa mean-field description of the glass transition.Physical Review Letters. 2010;104(25): 255704. DOI:https://doi.org/10.1103/PhysRevLett.104.25570419. McCowan D. Numerical study of long-timedynamics and ergodic-nonergodic transitions in densesimple fluids. Physical Review E. 2015;92(2): 022107.DOI: https://doi.org/10.1103/PhysRevE.92.02210720. Ohtsu H., Bennett T. D., Kojima T., Keen D. A.,Niwa Y., Kawano M. Amorphous–amorphous transitionin a porous coordination polymer. ChemicalCommunications. 2017;53(52): 7060–7063. DOI:https://doi.org/10.1039/C7CC03333H21. Schmid B., Schilling R. Glass transition of hardspheres in high dimensions. Physical Review E.2010;81(4): 041502. DOI: https://doi.org/10.1103/PhysRevE.81.04150222. Parisi G., Slanina, F. Toy model for the meanfieldtheory of hard-sphere liquids. Physical Review E.2000;62(5): 6554. DOI: https://doi.org/10.1103/Phys-RevE.62.655423. Parisi G., Zamponi F. The ideal glass transitionof hard spheres. The Journal of Chemical Physics.2005;123(14): 144501. DOI: https://doi.org/10.1063/1.204150724. Parisi G., Zamponi F. Amorphous packings ofhard spheres for large space dimension. Journal ofStatistical Mechanics: Theory and Experiment. 2006;03:P03017. DOI: https://doi.org/10.1088/1742-5468/2006/03/P0301725. Parisi G., Procaccia I., Shor C., Zylberg J. Effectiveforces in thermal amorphous solids with genericinteractions. Physical Review E. 2019;99(1): 011001. DOI:https://doi.org/10.1103/PhysRevE.99.01100126. Stevenson J. D., Wolynes P. G. Thermodynamic −kinetic correlations in supercooled liquids: a criticalsurvey of experimental data and predictions of therandom first-order transition theory of glasses. TheJournal of Physical Chemistry B. 2005;109(31): 15093–15097. DOI: https://doi.org/10.1021/jp052279h27. Xia X., Wolynes P. G. Fragilities of liquidspredicted from the random first order transition theoryof glasses. Proceedings of the National Academy ofSciences. 2000;97(7): 2990–2994. DOI: https://doi.org/10.1073/pnas.97.7.299028. Kobryn A. E., Gusarov S., Kovalenko A. A closurerelation to molecular theory of solvation formacromolecules. Journal of Physics: Condensed Matter.2016; 28 (40): 404003. DOI: https://doi.org/10.1088/0953-8984/28/40/40400329. Coluzzi B. , Parisi G. , Verrocchio P.Thermodynamical liquid-glass transition in a Lennard-Jones binary mixture. Physical Review Letters.2000;84(2): 306. DOI: https://doi.org/10.1103/PhysRevLett.84.30630. Sciortino F., Tartaglia P. Extension of thefluctuation-dissipation theorem to the physical agingof a model glass-forming liquid. Physical Review Letters.2001;86(1): 107. DOI: https://doi.org/10.1103/Phys-RevLett.86.10731. Sciortino, F. One liquid, two glasses. NatureMaterials. 2002;1(3): 145–146. DOI: https://doi.org/10.1038/nmat75232. Farr R. S., Groot R. D. Close packing density ofpolydisperse hard spheres. The Journal of ChemicalPhysics. 2009;131(24): 244104. DOI: https://doi.org/10.1063/1.327679933. Barrat J. L., Biben T., Bocquet, L. From Paris toLyon, and from simple to complex liquids: a view onJean-Pierre Hansen’s contribution. Molecular Physics.2015;113(17-18): 2378–2382. DOI: https://doi.org/10.1080/00268976.2015.103184334. Gaspard J. P. Structure of Melt and Liquid Alloys.In Handbook of Crystal Growth. Elsevier; 2015. 580 p.DOI: https://doi.org/10.1016/B978-0-444-56369-9.00009-535. Heyes D. M., Sigurgeirsson H. The Newtonianviscosity of concentrated stabilized dispersions:comparisons with the hard sphere fluid. Journal ofRheology. 2004;48(1): 223–248. DOI: https://doi.org/10.1122/1.163498636. Ninarello A., Berthier L., Coslovich D. Structureand dynamics of coupled viscous liquids. MolecularPhysics. 2015;113(17-18): 2707–2715. DOI: https://doi.org/10.1080/00268976.2015.103908937. Russel W. B., Wagner N. J., Mewis J. Divergencein the low shear viscosity for Brownian hard-spheredispersions: at random close packing or the glasstransition? Journal of Rheology. 2013;57(6): 1555–1567.DOI: https://doi.org/10.1122/1.482051538. Schaefer T. Fluid dynamics and viscosity instrongly correlated fluids. Annual Review of Nuclearand Particle Science. 2014;64: 125–148. DOI: https://doi.org/10.1146/annurev-nucl-102313-02543939. Matsuoka H. A macroscopic model thatconnects the molar excess entropy of a supercooledliquid near its glass transition temperature to itsviscosity. The Journal of Chemical Physics. 2012;137(20):204506. DOI: https://doi.org/10.1063/1.476734840. de Melo Marques F. A., Angelini R., Zaccarelli E.,Farago B., Ruta B., Ruocco, G., Ruzicka B. Structuraland microscopic relaxations in a colloidal glass. SoftMatter. 2015;11(3): 466–471. DOI: https://doi.org/10.1039/C4SM02010C41. Deutschländer S., Dillmann P., Maret G., KeimP. Kibble–Zurek mechanism in colloidal monolayers.Proceedings of the National Academy of Sciences.2015;112(22): 6925–6930. DOI: https://doi.org/10.1073/pnas.150076311242. Chang J., Lenhoff A. M., Sandler S. I.Determination of fluid–solid transitions in modelprotein solutions using the histogram reweightingmethod and expanded ensemble simulations. TheJournal of Chemical Physics. 2004;120(6): 3003–3014.DOI: https://doi.org/10.1063/1.163837743. Gurikov P., Smirnova I. Amorphization of drugsby adsorptive precipitation from supercriticalsolutions: a review. The Journal of Supercritical Fluids.2018;132: 105–125. DOI: https://doi.org/10.1016/j.supflu.2017.03.00544. Baghel S., Cathcart H., O’Reilly N. J. Polymericamorphoussolid dispersions: areviewofamorphization, crystallization, stabilization, solidstatecharacterization, and aqueous solubilization ofbiopharmaceutical classification system class II drugs.Journal of Pharmaceutical Sciences. 2016;105(9):2527–2544. DOI: https://doi.org/10.1016/j.xphs.2015.10.00845. Kalyuzhnyi Y. V., Hlushak S. P. Phase coexistencein polydisperse multi-Yukawa hard-sphere fluid: hightemperature approximation. The Journal of ChemicalPhysics. 2006;125(3): 034501. DOI: https://doi.org/10.1063/1.221241946. Mondal C., Sengupta S. Polymorphism,thermodynamic anomalies, and network formation inan atomistic model with two internal states. PhysicalReview E. 2011;84(5): 051503. DOI: https://doi.org/10.1103/PhysRevE.84.05150347. Bonn D., Denn M. M., Berthier L., Divoux T.,Manneville S. Yield stress materials in soft condensedmatter. Reviews of Modern Physics. 2017;89(3): 035005.DOI: https://doi.org/10.1103/RevModPhys.89.03500548. Tanaka H. Two-order-parameter model of theliquid–glass transition. I. Relation between glasstransition and crystallization. Journal of Non-Crystalline Solids. 2005;351(43-45): 3371–3384. DOI:https://doi.org/10.1016/j.jnoncrysol.2005.09.00849. Balesku R. Ravnovesnaya i neravnovesnayastatisticheskaya mekhanika [Equilibrium and nonequilibriumstatistical mechanics]. Moscow: Mir Publ.;1978. vol. 1. 404 c. (In Russ.)50. Chari S., Inguva R., Murthy K. P. N. A newtruncation scheme for BBGKY hierarchy: conservationof energy and time reversibility. arXiv preprintarXiv: 1608. 02338. DOI: https://arxiv.org/abs/1608.0233851. Gallagher I., Saint-Raymond L., Texier B. FromNewton to Boltzmann: hard spheres and short-rangepotentials. European Mathematical Society.arXiv:1208.5753. DOI: https://arxiv.org/abs/1208.575352. Rudzinski J. F., Noid W. G. A generalized-Yvon-Born-Green method for coarse-grained modeling. TheEuropean Physical Journal Special Topics. 224(12),2193–2216. DOI: https://doi.org/10.1140/epjst/e2015-02408-953. Franz B., Taylor-King J. P., Yates C., Erban R.Hard-sphere interactions in velocity-jump models.Physical Review E. 2016;94(1): 012129. DOI: https://doi.org/10.1103/PhysRevE.94.01212954. Gerasimenko V., Gapyak I. Low-Densityasymptotic behavior of observables of hard spherefluids. Advances in Mathematical Physics. 2018:6252919. DOI: https://doi.org/10.1155/2018/625291955. Lue L. Collision statistics, thermodynamics,and transport coefficients of hard hyperspheres inthree, four, and five dimensions. The Journal ofChemical Physics. 2005;122(4): 044513. DOI: https://doi.org/10.1063/1.183449856. Cigala G., Costa D., Bomont J. M., Caccamo C.Aggregate formation in a model fluid with microscopicpiecewise-continuous competing interactions.Molecular Physics. 2015;113(17–18): 2583–2592.DOI: https://doi.org/10.1080/00268976.2015.107800657. Jadrich R., Schweizer K. S. Equilibrium theoryof the hard sphere fluid and glasses in the metastableregime up to jamming. I. Thermodynamics. The Journalof Chemical Physics. 2013;139(5): 054501. DOI: https://doi.org/10.1063/1.481627558. Mondal A., Premkumar L., Das S. P. Dependenceof the configurational entropy on amorphousstructures of a hard-sphere fluid. Physical Review E.2017;96(1): 012124. DOI: https://doi.org/10.1103/PhysRevE.96.01212459. Sasai M. Energy landscape picture ofsupercooled liquids: application of a generalizedrandom energy model. The Journal of Chemical Physics.2003;118(23): 10651–10662. DOI: https://doi.org/10.1063/1.157478160. Sastry S. Liquid limits: Glass transition andliquid-gas spinodal boundaries of metastable liquids.Physical Review Letters. 2000;85(3): 590. DOI: https://doi.org/10.1103/PhysRevLett.85.59061. Uche O. U., Stillinger F. H., Torquato S. On therealizability of pair correlation functions. Physica A:Statistical Mechanics and its Applications. 2006;360(1):21–36. DOI: https://doi.org/10.1016/j.physa.2005.03.05862. Bi D., Henkes S., Daniels K. E., Chakraborty B.The statistical physics of athermal materials. Annu.Rev. Condens. Matter Phys. 2015;6(1): 63–83. DOI:https://doi.org/10.1146/annurev-conmatphys-031214-01433663. Bishop M., Masters A., Vlasov A. Y. Higher virialcoefficients of four and five dimensional hardhyperspheres. The Journal of Chemical Physics.2004;121(14): 6884–6886. DOI: https://doi.org/10.1063/1.177757464. Sliusarenko O. Y., Chechkin A. V., SlyusarenkoY. V. The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for manybodydissipative randomly driven systems. Journal ofMathematical Physics. 2015;56(4): 043302. DOI:https://doi.org/10.1063/1.491861265. Tang Y. A new grand canonical ensemblemethod to calculate first-order phase transitions. TheJournal of chemical physics. 2011;134(22): 224508. DOI:https://doi.org/10.1063/1.359904866. Tsednee T., Luchko T. Closure for the Ornstein-Zernike equation with pressure and free energyconsistency. Physical Review E. 2019;99(3): 032130.DOI: https://doi.org/10.1103/PhysRevE.99.03213067. Maimbourg T., Kurchan J., Zamponi, F. Solutionof the dynamics of liquids in the large-dimensionallimit. Physical review letters. 2016;116(1): 015902. DOI:https://doi.org/10.1103/PhysRevLett.116.01590268. Mari, R., & Kurchan, J. Dynamical transition ofglasses: from exact to approximate. The Journal ofChemical Physics. 2011;135(12): 124504. DOI: https://doi.org/10.1063/1.362680269. Frisch H. L., Percus J. K. High dimensionalityas an organizing device for classical fluids. PhysicalReview E. 1999;60(3): 2942. DOI: https://doi.org/10.1103/PhysRevE.60.294270. Finken R., Schmidt M., Löwen H. Freezingtransition of hard hyperspheres. Physical Review E.2001;65(1): 016108. DOI: https://doi.org/10.1103/PhysRevE.65.01610871. Torquato S., Uche O. U., Stillinger F. H. Randomsequential addition of hard spheres in high Euclideandimensions. Physical Review E. 2006;74(6): 061308.DOI: https://doi.org/10.1103/PhysRevE.74.06130872. Martynov G. A. Fundamental theory of liquids;method of distribution functions. Bristol: Adam Hilger;1992, 470 p.73. Vompe A. G., Martynov G. A. The self-consistentstatistical theory of condensation. The Journal ofChemical Physics. 1997;106(14): 6095–6101. DOI:https://doi.org/10.1063/1.47327274. Krokston K. Fizika zhidkogo sostoyaniya.Statisticheskoe vvedenie [Physics of the liquid state.Statistical introduction]. Moscow: Mir Publ.; 1978.400 p. (In Russ.)75. Rogers F. J., Young D. A. New, thermodynamicallyconsistent, integral equation for simple fluids. PhysicalReview A. 1984;30(2): 999. DOI: https://doi.org/10.1103/PhysRevA.30.99976. Wertheim M. S. Exact solution of the Percus–Yevick integral equation for hard spheres Phys. Rev.Letters. 1963;10(8): 321–323. DOI: https://doi.org/10.1103/PhysRevLett.10.32177. Tikhonov D. A., Kiselyov O. E., Martynov G. A.,Sarkisov G. N. Singlet integral equation in thestatistical theory of surface phenomena in liquids. J.of Mol. Liquids. 1999;82(1–2): 3– 17. DOI: https://doi.org/10.1016/S0167-7322(99)00037-978. Agrafonov Yu., Petrushin I. Two-particledistribution function of a non-ideal molecular systemnear a hard surface. Physics Procedia. 2015;71. 364–368. DOI: https://doi.org/10.1016/j.phpro.2015.08.35379. Agrafonov Yu., Petrushin I. Close order in themolecular system near hard surface. Journal of Physics:Conference Series. 2016;747: 012024. DOI: https://doi.org/10.1088/1742-6596/747/1/01202480. He Y., Rice S. A., Xu X. Analytic solution of theOrnstein-Zernike relation for inhomogeneous liquids.The Journal of Chemical Physics. 2016;145(23): 234508.DOI: https://doi.org/10.1063/1.497202081. Agrafonov Y. V., Petrushin I. S. Usingmolecular distribution functions to calculate thestructural properties of amorphous solids. Bulletinof the Russian Academy of Sciences: Physics. 2020;84:783–787. DOI: https://doi.org/10.3103/S106287382007003582. Bertheir L., Ediger M. D. How to “measure” astructural relaxation time that is too long to bemeasured? arXiv:2005.06520v1. DOI: https://arxiv.org/abs/2005.0652083. Karmakar S., Dasgupta C., Sastry S. Lengthscales in glass-forming liquids and related systems: areview. Reports on Progress in Physics. 2015;79(1):016601. DOI: https://doi.org/10.1088/0034-4885/79/1/01660184. De Michele C., Sciortino F., Coniglio A. Scalingin soft spheres: fragility invariance on the repulsivepotential softness. Journal of Physics: CondensedMatter. 2004;16(45): L489. DOI: https://doi.org/10.1088/0953-8984/16/45/L0185. Niblett S. P., de Souza V. K., Jack R. L., Wales D. J.Effects of random pinning on the potential energylandscape of a supercooled liquid. The Journal ofChemical Physics. 2018;149(11): 114503. DOI: https://doi.org/10.1063/1.504214086. Wolynes P. G., Lubchenko V. Structural glassesand supercooled liquids: Theory, experiment, andapplications. New York: John Wiley & Sons; 2012. 404p. DOI: https://doi.org/10.1002/978111820247087. Jack R. L., Garrahan J. P. Phase transition forquenched coupled replicas in a plaquette spin modelof glasses. Physical Review Letters. 2016;116(5): 055702.DOI: https://doi.org/10.1103/PhysRevLett.116.05570288. Habasaki J., Ueda A. Molecular dynamics studyof one-component soft-core system: thermodynamicproperties in the supercooled liquid and glassy states.The Journal of Chemical Physics. 2013;138(14): 144503.DOI: https://doi.org/10.1063/1.479988089. Bomont J. M., Hansen J. P., Pastore G. Aninvestigation of the liquid to glass transition usingintegral equations for the pair structure of coupledreplicae. J. Chem. Phys. 2014;141(17): 174505. DOI:https://doi.org/10.1063/1.490077490. Parisi G., Urbani P., Zamponi F. Theory of SimpleGlasses: Exact Solutions in Infinite Dimensions.Cambridge: Cambridge University Press; 2020. 324 p.DOI: https://doi.org/10.1017/978110812049491. Robles M., López de Haro M., Santos A., BravoYuste S. Is there a glass transition for dense hardspheresystems? The Journal of Chemical Physics.1998;108(3): 1290–1291. DOI: https://doi.org/10.1063/1.47549992. Grigera T. S., Martín-Mayor V., Parisi G.,Verrocchio P. Asymptotic aging in structural glasses.Physical Review B, 2004;70(1): 014202. DOI: https://doi.org/10.1103/PhysRevB.70.01420293. Vega C., Abascal J. L., McBride C., Bresme F.The fluid–solid equilibrium for a charged hard spheremodel revisited. The Journal of Chemical Physics.2003; 119 (2): 964–971. DOI: https://doi.org/10.1063/1.157637494. Kaneyoshi T. Surface amorphization in atransverse Ising nanowire; effects of a transverse field.Physica B: Condensed Matter. 2017;513: 87–94. DOI:https://doi.org/10.1016/j.physb.2017.03.01595. Paganini I. E., Davidchack R. L., Laird B. B.,Urrutia I. Properties of the hard-sphere fluid at a planarwall using virial series and molecular-dynamicssimulation. The Journal of Chemical Physics. 2018;149(1):014704. DOI: https://doi.org/10.1063/1.502533296. Properzi L., Santoro M., Minicucci M., Iesari F.,Ciambezi M., Nataf L., Di Cicco A. Structural evolutionmechanisms of amorphous and liquid As2 Se3 at highpressures. Physical Review B. 2016;93(21): 214205. DOI:https://doi.org/10.1103/PhysRevB.93.21420597. Sesé L. M. Computational study of the meltingfreezingtransition in the quantum hard-sphere systemfor intermediate densities. I. Thermodynamic results.The Journal of Chemical Physics. 2007;126(16): 164508.DOI: https://doi.org/10.1063/1.271852398. Shetty R., Escobedo F. A. On the application ofvirtual Gibbs ensembles to the direct simulation offluid–fluid and solid–fluid phase coexistence. TheJournal of Chemical Physics. 2002;116(18): 7957–7966.DOI: https://doi.org/10.1063/1.1467899

Polyethylene under femtosecond low-dose deposition forms defects, whereas at high doses hydrogens detach from carbons, forming hydrogen liquid and complex carbon networks, also changing electronic structures.