scholarly journals Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3014
Author(s):  
Pai-Yi Hsiao
Keyword(s):  
Volume Fraction ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Stage Model ◽  
Nucleation Time ◽  
Ejection Time ◽  
Scaling Properties ◽  
Initial Volume Fraction ◽  
Starting Point ◽  
Dynamics Simulations

A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m−z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν−1)−1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.

scholarly journals Molecular-dynamics simulations of urea nucleation from aqueous solution

2014 ◽  
Vol 112 (1) ◽  
pp. E6-E14 ◽  
Author(s):  
Matteo Salvalaglio ◽  
Claudio Perego ◽  
Federico Giberti ◽  
Marco Mazzotti ◽  
Michele Parrinello
Keyword(s):  
Aqueous Solution ◽  
Free Energy ◽  
Molecular Simulations ◽  
Finite Size ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Science And Engineering ◽  
Finite Size Effects ◽  
Dynamics Simulations ◽  
Insight Into

Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

Dissolution and Growth Kinetics of Small Crystals in Liquids

1991 ◽  
Vol 238 ◽  
Author(s):  
Michael J. Uttormark ◽  
Michael O. Thompson ◽  
Paulette Clancy
Keyword(s):  
Molecular Dynamics ◽  
Melting Point ◽  
Driving Force ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Equilibrium Melting Point ◽  
Small Crystals ◽  
Dynamics Simulations ◽  
Kinetics Of ◽  
Nucleation Phenomenon

ABSTRACTMolecular Dynamics simulations of the melting of small crystalline clusters (≃800 atoms) in the liquid have been performed at various temperatures above the equilibrium melting point. The melting rates as functions of size and temperature are derived and compared to that predicted by Classical Nucleation Theory. It is found that the driving force for the melting of clusters does not follow the form assumed in the theory, and that this difference is most apparent for clusters containing less than 300 atoms. The implications of these findings on nucleation phenomenon and possible sources for the discrepancies are discussed.

scholarly journals Nucleation and supersaturation in porous media (revisited)

2014 ◽  
Vol 78 (6) ◽  
pp. 1437-1447 ◽  
Author(s):  
M. Prieto
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Interfacial Tension ◽  
Induction Time ◽  
Reactive Transport ◽  
Theoretical Calculations ◽  
Transport Processes ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Nucleation Time

Supersaturation-Nucleation-Time (S-N-T) diagrams are shown to be a useful tool to predict nucleation during reactive-transport processes in porous media. Such diagrams can be determined experimentally or estimated from theoretical calculations based on classical nucleation theory. With this aim, a ‘pragmatic’ understanding of the nucleation rate equation is adopted here and the meaning and magnitude of the interfacial tension and induction time discussed. Theoretical diagrams and experimental data are shown to match fairly well as long as there is an appropriate choice of the ‘relevant’ volume for induction-time calculations.

scholarly journals Molecular dynamics simulations of liquid silica crystallization

2018 ◽  
Vol 115 (21) ◽  
pp. 5348-5352 ◽  
Author(s):  
Haiyang Niu ◽  
Pablo M. Piaggi ◽  
Michele Invernizzi ◽  
Michele Parrinello
Keyword(s):  
Free Energy ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Free Energy Surface ◽  
X Ray Diffraction ◽  
Collective Variables ◽  
Atomic Simulations ◽  
The Difference ◽  
Dynamics Simulations ◽  
Good Agreement

Silica is one of the most abundant minerals on Earth and is widely used in many fields. Investigating the crystallization of liquid silica by atomic simulations is of great importance to understand the crystallization mechanism; however, the high crystallization barrier and the tendency of silica to form glasses make such simulations very challenging. Here we have studied liquid silica crystallization to β-cristobalite with metadynamics, using X-ray diffraction (XRD) peak intensities as collective variables. The frequent transitions between solid and liquid of the biased runs demonstrate the highly successful use of the XRD peak intensities as collective variables, which leads to the convergence of the free-energy surface. By calculating the difference in free energy, we have estimated the melting temperature of β-cristobalite, which is in good agreement with the literature. The nucleation mechanism during the crystallization of liquid silica can be described by classical nucleation theory.

Homogeneous nucleation of NaCl in supersaturated solutions

2021 ◽  
Author(s):  
Cintia Pulido Lamas ◽  
Jorge R. Espinosa ◽  
María Martín Conde ◽  
Jorge Ramirez ◽  
Pablo Montero de Hijes ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Homogeneous Nucleation ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Approximate Approach ◽  
Seeding Method ◽  
Dynamics Simulations ◽  
Supersaturated Solutions

The Seeding method is an approximate approach to investigate nucleation that combines molecular dynamics simulations with classical nucleation theory. This technique has been successfully implemented in a broad range of...

scholarly journals Application of the Nucleation Theorem to Crystallization of Liquids: Some General Theoretical Results

2019 ◽  
Author(s):  
Jürn W.P. Schmelzer
Keyword(s):  
Surface Tension ◽  
Liquid Phase ◽  
Thermodynamic Description ◽  
Heterogeneous Systems ◽  
Chem Phys ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Starting Point ◽  
Component Systems ◽  
Nucleation Theorem

Different aspects in applying the nucleation theorem to the description of crystallization of liquids are analyzed. It is shown that, by employing the classical Gibbs' approach in the thermodynamic description of heterogeneous systems and assuming that the basic assumptions of classical nucleation theory commonly employed in application to crystallization hold, a general form of the nucleation theorem can be formulated valid not only for one-component but generally for multi-component systems. This result is taken then as the starting point for the derivation of particular forms of this theorem for the cases that the deviation from equilibrium is caused by variations of either composition of the liquid phase, temperature, or pressure. In this procedure, recently developed by us expressions for the curvature dependence of the surface tension, respectively, the dependence of the surface tension on pressure and/or temperature are employed. It is shown that the formulation of the nucleation theorem as proposed by Kashchiev [J. Chem. Phys. 76, 5098-5102 (1982)] holds also for multi-component systems as far as mentioned above assumptions are fulfilled. In the application of classical nucleation theory to crystallization processes it is assumed as one of its basic ingredients that the bulk properties of the critical clusters are widely identical to the properties of the newly evolving crystal phase. This assumption is, however, in general, it is not true. This limitation of the theoretical description can be overcome by the application of the generalized Gibbs approach for the specification of the dependence of the properties of critical crystal clusters on the degree of metastability of the liquid phase. Applying this method, it is demonstrated that a similar formulation of the nucleation theorem as derived based on classical nucleation theory holds true also in cases when a dependence of the state parameters of the critical clusters on the degree of deviation from equilibrium is appropriately accounted for.

scholarly journals Unbiased atomistic insight in the competing nucleation mechanisms of methane hydrates

2019 ◽  
Vol 116 (39) ◽  
pp. 19305-19310 ◽  
Author(s):  
Arjun ◽  
Thom A. Berendsen ◽  
Peter G. Bolhuis
Keyword(s):  
Rare Event ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Methane Hydrates ◽  
Crystal Formation ◽  
Transition Path Sampling ◽  
Polymorph Selection ◽  
Nucleation Mechanisms ◽  
Experimental Resolution ◽  
Dynamics Simulations

Methane hydrates have important industrial and climate implications, yet their formation via homogeneous nucleation under natural, moderate conditions is poorly understood. Obtaining such understanding could lead to improved control of crystallization, as well as insight into polymorph selection in general, but is hampered by limited experimental resolution. Direct molecular dynamics simulations using atomistic force fields could provide such insight, but are not feasible for moderate undercooling, due to the rare event nature of nucleation. Instead, we harvest ensembles of the rare unbiased nucleation trajectories by employing transition path sampling. We find that with decreasing undercooling the mechanism shifts from amorphous to crystalline polymorph formation. At intermediate temperature the 2 mechanisms compete. Reaction coordinate analysis reveals the amount of a specific methane cage type is crucial for crystallization, while irrelevant for amorphous solids. Polymorph selection is thus governed by kinetic accessibility of the correct cage type and, moreover, occurs at precritical nucleus sizes, apparently against Ostwald’s step rule. We argue that these results are still in line with classical nucleation theory. Our findings illuminate how selection between competing methane hydrate polymorphs occurs and might generalize to other hydrates and molecular crystal formation.

scholarly journals A general theory of polymer ejection tested in a quasi two-dimensional space

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Pai-Yi Hsiao ◽  
Wei-Yei Chen
Keyword(s):  
Volume Fraction ◽  
Dimensional Space ◽  
Outer Space ◽  
Three Dimensional ◽  
Pore Channel ◽  
Escape Time ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Dynamics Simulations ◽  
Three Dimensional Space

AbstractA general ejection theory of polymer is developed in a two- and three-dimensional space. A polymer is confined initially in a cavity and ejects spontaneously to the outer space through a nanopore channel without the help of any external stimulus. A reflective wall boundary is set at the pore entrance to prevent the falling of the head monomer of chain into the cavity. Three stages are distinguished in a process: (1) an entering stage, in which the head monomer enters the pore to search for a way to traverse the pore channel, (2) a main ejection stage, in which the chain body is transported from the cavity to the outer space, (3) a leaving stage, in which the tail monomer passes through and leaves the pore channel. Depending on the number of the monomers remaining in the cavity, the main ejection stage can be divided into the confined and the non-confined stages. The non-confined stage can be further split into the thermal escape and the entropic pulling stages. The Onsager’s variational principle is applied to derive the kinetics equation of ejection. The escape time is calculated from the corresponding Kramers’ escape problem. Extensive molecular dynamics simulations are then performed in a quasi two-dimensional space to verify the theory. The variation of the ejection speed is carefully examined. The decreasing behavior of the number of monomers in the cavity is studied in details. The scaling properties of the spending time at each processing stage are investigated systematically by varying the chain length, the cavity diameter, and the initial volume fraction of chain. The results of simulation support firmly the predictions of the theory, cross-checked in the studies of various topics. In combining with the previous investigations in the three-dimensional space, the generalized theory is very robust, able to explain the two seemly different phenomena, polymer ejection and polymer translocation, together under the same theoretical framework in the two space dimensions.

scholarly journals Dynamic Surface Tension Enhances the Stability of Nanobubbles in Xylem Sap

2021 ◽  
Vol 12 ◽  
Author(s):  
Stephen Ingram ◽  
Yann Salmon ◽  
Anna Lintunen ◽  
Teemu Hölttä ◽  
Timo Vesala ◽  
...  
Keyword(s):  
Surface Tension ◽  
Surface Composition ◽  
Xylem Sap ◽  
Dynamic Surface Tension ◽  
External Pressure ◽  
Nucleation Theory ◽  
Classical Nucleation Theory ◽  
Dynamic Surface ◽  
Biologically Relevant ◽  
Dynamics Simulations

Air seeded nanobubbles have recently been observed within tree sap under negative pressure. They are stabilized by an as yet unidentified process, although some embolize their vessels in extreme circumstances. Current literature suggests that a varying surface tension helps bubbles survive, but few direct measurements of this quantity have been made. Here, we present calculations of dynamic surface tension for two biologically relevant lipids using molecular dynamics simulations. We find that glycolipid monolayers resist expansion proportionally to the rate of expansion. Their surface tension increases with the tension applied, in a similar way to the viscosity of a non-Newtonian fluid. In contrast, a prototypical phospholipid was equally resistant to all applied tensions, suggesting that the fate of a given nanobubble is dependent on its surface composition. By incorporating our results into a Classical Nucleation Theory (CNT) framework, we predict nanobubble stability with respect to embolism. We find that the metastable radius of glycolipid coated nanobubbles is approximately 35 nm, and that embolism is in this case unlikely when the external pressure is less negative than –1.5 MPa.

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