Nucleation Threshold Research Articles

Dislocation nucleation in Al single crystal at shear parallel to (111) plane: Molecular dynamics simulations and nucleation theory with artificial neural networks

We develop the theory of homogeneous nucleation of dislocations, which predicts plasticity incipience in FCC single crystal using material properties at elastic stage. In contrast to previous nucleation theories, we show that the work of shear stress is compensated by variation of the generalized stacking fault (GSF) energy during the loop formation. As a result, the energy barrier of nucleation includes only the line defect energy of the critical loop, which radius is defined by balance between all three contributions including the work of shear stress, the surface defect energy of the GSF and the line defect energy. This distinction is consequence of the difference between the mechanisms of the initial loop formation consisting in gradual shear along the proto-loop area and the following growth by slip of bordering dislocation line. Calculation of the energy barrier requires material properties at elastic stage such as stress-strain relationship, the GSF and shear modulus. These data are determined from molecular dynamics (MD) simulations and approximated in the form of artificial neural networks (ANNs). We perform direct MD simulations of the dislocation nucleation for simple shear in different directions parallel to (111) plane in Al single crystal at initial pressures from −3 to +3 GPa. MD simulations show complex and nonlinear evolution of stresses at simple shear deformation even at elastic stage before the dislocation nucleation. Predictions of ANN-informed theory are in accordance with our MD simulations and with the literature data. The calculated nucleation threshold for shear along the Burgers vector of partial Shockley dislocation in [112¯] direction at zero initial pressure varies from 2.03 to 2.16 GPa at the strain rate increase from 1 to 109 s−1. The conditions for homogeneous nucleation are close to the states of matter in thin metal films under powerful sub-picosecond laser irradiation. It is shown that twins are nucleated at angles less or equal to 7.5° between the shear direction and [112¯] direction. Perfect dislocation loops formed by leading and trailing partial dislocations arise at larger angles. In spite of change in the final form of nucleated defect, the energy barrier of nucleation is well-described by the same theoretical expression. It is explained by the fact that the initial defect in both cases is the loop of leading partial dislocation with the stacking fault over the entire loop area. The formation of twin or perfect dislocation occurs after the nucleation and does not influence the nucleation threshold. The ANNs reveal themselves as an efficient tool for approximation of the complex and non-obvious dependencies, while one should be careful with using them for data extrapolation. The paper is supplemented by files with the parameters of the trained ANNs and description of their structure so that one can use them within the nucleation model or separately.

Evaluation of void nucleation, growth, and coalescence parameters for HCP-Zr at extreme strain rates

Void nucleation, growth, and coalescence at extreme strain rates in ductile metals with weak mechanical anisotropies, e.g., copper, iron, and aluminum, have been extensively investigated. However, the atomic-scale fracture properties of strongly anisotropic metals, especially hexagonal close-packed (HCP) metals, at ultrahigh strain rates have rarely been studied. We have investigated the nucleation, growth, and coalescence of voids in HCP-Zr under isotropic-triaxial tension using molecular dynamics (MD) and void nucleation and growth (NAG) models. The effects of temperature were also examined by MD. The void evolution predicted by MD corresponded to that predicted by the NAG model and is divided into three stages, i.e., an initial nucleation stage, an exponential growth stage, and a linear stage. The nucleation threshold Pn0 is very sensitive to temperature, while the growth threshold Pg0 decreases slightly with increasing temperature. The initial NAG parameters were evaluated by an improved optimized genetic algorithm. In addition, we adjusted the NAG parameters until the history of the void volume fraction calculated by these parameters was exactly the same as that calculated by MD. This study predicts comprehensive NAG parameters for HCP-Zr under extreme conditions, providing a valuable reference for future studies of dynamic damage in HCP materials.

Triaxial tension-induced damage behavior of nanocrystalline NiTi alloy and its dependence on grain size

This study focused on the effect of grain size (GS) on dynamic damage performance of nano-crystalline nickel titanium (NC NiTi) alloy. Molecular dynamics simulations were conducted to triaxially expand it at a high strain rate (4 × 109 s−1), while the temperature and initial pressure remained 300 K and 0 bar, respectively. It was discovered that the superelastic NiTi alloy exhibited the similar damage response as ductile metallic materials, which was vividly characterized by void nucleation, growth, and coalescence. The stress-strain curves demonstrated that the void nucleations always occurred near the start of the strain softening region at various grain sizes. Interestingly, it was discovered that the void evolution was characteristic of an almost double-linear behavior, and the piecewise linearity became more prominent for the void volume fraction increase at larger grain size. More importantly, the fracture behavior was found to be strongly dependent upon the grain size in the NC NiTi alloy. For small grain size, the existing voids propagated along the grain boundaries and in the grains, leading to intergranular and transgranular fracture. Contrarily, the intergranular-dominated fracture was responsible for the void propagation in the large grain. In addition, the starting time, ending time, and threshold of void nucleation were found to be weak sensitivity to GS, and a reverse effect was appropriate to the void growth. The results highlighted that as the GS increased, more complete stress relaxation and shorter duration time were produced, leading to larger void volume fraction and faster growth rate.

Overview of Secondary Nucleation: From Fundamentals to Application

Secondary nucleation can bring the crystallization process into a more easily controlled state, and it is playing an important role in controlling crystal size distribution, polymorphism, and chirality of the crystal products, no matter whether in a batch or continuous crystallizer. Therefore, in this review, we revisit the research of secondary nucleation in the past 30 years to understand the fundamentals and application of secondary nucleation. First, we summarize the sources of secondary nuclei, that is, how secondary nucleation occurs. Then, we discuss the secondary nucleation threshold from the perspective of the metastable zone widths which are associated with the nucleation mechanism. Furthermore, we discuss how to employ secondary nucleation to regulate the properties of crystalline products (particle size distribution, crystal polymorphism, chirality, etc.). More importantly, we also discuss how polymorphism and chirality can act as a probe to explore the origin of secondary nucleation. Finally, we give conclusions and outlooks, mainly on the molecular nucleation mechanism and crystal growth dead zone of the current topic of secondary nucleation.

Data-driven modeling of electron recoil nucleation in PICO C3F8 bubble chambers

The primary advantage of moderately superheated bubble chamber detectors is their simultaneous sensitivity to nuclear recoils from WIMP dark matter and insensitivity to electron recoil backgrounds. A comprehensive analysis of PICO gamma calibration data demonstrates for the first time that electron recoils in C$_3$F$_8$ scale in accordance with a new nucleation mechanism, rather than one driven by a hot-spike as previously supposed. Using this semi-empirical model, bubble chamber nucleation thresholds may be tuned to be sensitive to lower energy nuclear recoils while maintaining excellent electron recoil rejection. The PICO-40L detector will exploit this model to achieve thermodynamic thresholds as low as 2.8 keV while being dominated by single-scatter events from coherent elastic neutrino-nucleus scattering of solar neutrinos. In one year of operation, PICO-40L can improve existing leading limits from PICO on spin-dependent WIMP-proton coupling by nearly an order of magnitude for WIMP masses greater than 3 GeV c$^{-2}$ and will have the ability to surpass all existing non-xenon bounds on spin-independent WIMP-nucleon coupling for WIMP masses from 3 to 40 GeV c$^{-2}$.

Quantitative Link between Secondary Nucleation and Mixing Hydrodynamics in Batch Cooling Crystallization: A New Approach in Process Development

Precise control of a crystallization process requires a clear understanding of nucleation kinetics. Interpreting secondary nucleation threshold (SNT) of a given crystallization process under optimized hydrodynamic conditions can highlight the impact of critical process variables on product particle size distribution (PSD). In this work, a new approach is proposed in industrial crystallization process development in which a quantitative link was developed between batch cooling crystallization and fluid turbulent shear stress (TSS). The experiments involve solution crystallization of paracetamol in isopropanol. A novel method was adopted in which a large single seed crystal of paracetamol was held stationary in an agitating reactor. Using particle imaging velocimetry, a constant TSS was obtained across different scales which resulted in a constant SNT because of crystal nuclei breeding. This led to better control over the crystallization process which eventually resulted in a consistent PSD, independent of ...

Unusual Crystal Growth Kinetics of (RS)‐Ibuprofen from Ethanolic Solutions

AbstractThe solubility, secondary nucleation threshold, and growth kinetics of (RS)‐ibuprofen have been studied in an aqueous ethanol solvent. The metastable zone for secondary nucleation is very narrow at lower temperatures in this range, but greatly enlarged at higher temperatures. The crystal growth kinetics not only display significant dispersion of growth rates, but also a dead zone that is dependent on the growth rates of the crystals. Faster growing crystals display almost no dead zone, whereas the smallest crystals have a large dead zone. The size of the dead zone is largely responsible for the dispersion of crystal growth rates, perhaps due to differences in the thermodynamic stability of the different crystals. The mechanism of growth rate dispersion relates to that of the dead zone.

The counterdiffusion of HCl and NH3: An experimental and modeling analysis of topochemistry, diffusion, reaction, and phase transitions.

Vapor-phase ammonia, NH3(g), and hydrochloric acid, HCl(g), undergo a series of complex reactions, including nucleation and growth, to form solid ammonium chloride, NH4Cl(s). The counterdiffusional experiment, whereby HCl(g) and NH3(g) diffuse from opposite ends of a tube and react to form spatiotemporally complex patterns, has a rich history of study. In this paper, we combine experimental data, molecular simulations, and analysis and simulations of a partial differential equation model to address the questions of where the first unobserved vapor product NH4Cl(g) and visually observable precipitate NH4Cl(s) form and how these positions depend on experimental parameters. These analyses yield a consistent picture which involves a moving reaction front as well as previously unobserved heterogeneous nucleation, wall nucleation, and homogeneous nucleation. The experiments combined with modeling allow for an estimate of the heterogeneous and homogeneous nucleation thresholds for the vapor-to-solid phase transition. The results, synthesized with the literature on this vapor-to-particle reaction, inform a discussion of the details of the reaction mechanism, including the role of water, which concludes the paper.

Secondary Nucleation from Nuclei Breeding and Its Quantitative Link with Fluid Shear Stress in Mixing: A Potential Approach for Precise Scale-up in Industrial Crystallization

The development of robust process scale-up involves a clear understanding of mixing hydrodynamics in crystallization. In the present work, particle imaging velocimetry (PIV) was used to determine the fluid turbulent shear stress (TSS) as a function of scale-up involving cooling crystallization experiments at different agitation rates. At a given scale, with increased agitation rate from 300 to 370 rpm, the secondary nucleation threshold (SNT) and product mean particle size were observed to decrease due to increased TSS. In nuclei breeding, the nucleated crystals at the seed surface are readily sheared off by the increased fluid shear stress. This catalytic process enhanced the rate of secondary nucleation, and hence a decrease in SNT. The SNT and mean particle size increased with scale size due to a decrease in average turbulent dissipation rate which resulted from a decrease in TSS. Secondary nucleation due to nuclei breeding was found to have a quantitative link with TSS. This resulted in a constant SNT...

Extreme spikes in DMS flux double estimates of biogenic sulfur export from the Antarctic coastal zone to the atmosphere

Biogenic dimethylsulfide (DMS) is a significant contributor to sulfur flux from the oceans to the atmosphere, and the most significant source of aerosol non sea-salt sulfate (NSS-SO42−), a key regulator of global climate. Here we present the longest running time-series of DMS-water (DMSW) concentrations in the world, obtained at the Rothera Time-Series (RaTS) station in Ryder Bay, West Antarctic Peninsula (WAP). We demonstrate the first ever evaluation of interseasonal and interannual variability in DMSW and associated flux to the atmosphere from the Antarctic coastal zone and determine the scale and importance of the region as a significant source of DMS. Impacts of climate modes such as El Niňo/Southern Oscillation are evaluated. Maximum DMSW concentrations occurred annually in January and were primarily associated with sea-ice break-up. These concentrations resulted in extremely high (up to 968 µmol m−2 d−1) DMS flux over short timescales, which are not parameterised in global-scale DMS climatologies. Calculated DMS flux stayed above the aerosol nucleation threshold of 2.5 µmol m−2 d−1 for 60% of the year. Overall, using flux determinations from this study, the total flux of DMS-sulfur from the Austral Polar Province (APLR) was 1.1 Tg sulfur yr−1, more than double the figure suggested by the most recent DMS climatologies.

The effects of ultrasound pressure and temperature fields in millisecond bubble nucleation

A phenomenological implementation of Classical Nucleation Theory (CNT) is employed to investigate the connection between high intensity focused ultrasound (HIFU) pressure and temperature fields with the energetic requirements of bubble nucleation. As a case study, boiling histotripsy in tissue-mimicking phantoms is modelled. The physics of key components in the implementation of CNT in HIFU conditions such as the derivation of nucleation pressure thresholds and approximations regarding the surface tension of the liquid are reviewed and discussed. Simulations show that the acoustic pressure is the ultimate trigger for millisecond bubble nucleation in boiling histotripsy, however, HIFU heat deposition facilitates nucleation by lowering nucleation pressure thresholds. Nucleation thus occurs preferentially at the regions of highest heat deposition within the HIFU field. This implies that bubble nucleation subsequent to millisecond HIFU heat deposition can take place at temperatures below 100 °C as long as the focal HIFU peak negative pressure exceeds the temperature-dependent nucleation threshold. It is also found that the magnitude of nucleation pressure thresholds decreases with decreasing frequencies. Overall, results indicate that it is not possible to separate thermal and mechanical effects of HIFU in the nucleation of bubbles for timescales of a few milliseconds. This methodology provides a promising framework for studying time and space dependencies of the energetics of bubble nucleation within a HIFU field.

Molecular dynamics simulation of effect of temperature on void nucleation and growth of single crystal iron at a high strain rate

In this work, we investigate the triaxial deformation of single crystal iron at a strain rate of 5 × 10<sup>–9</sup> s<sup>–1</sup> by using molecular dynamics simulation through the embedded atomic method, and thus study the temperature effect on the void nucleation and growth, and we also discuss the applicability of nucleation and growth (NAG) model in single crystal iron. The molecular dynamics model size is 28.55 nm × 28.55 nm × 28.55 nm and contains 2 × 10<sup>6</sup> atoms. The results show that the maximum tensile stress of single crystal iron decreases with temperature increasing. The maximum tensile stress reduces 35.9% when temperature rises from 100 K to 1100 K. We find that at 100−700 K temperatures, there are two peaks in the tensile stress-time profile. To ascertain the origin of the double-peak in the stress-time profile, we compute the void volume fraction evolution. In addition, we conduct the dislocation analysis, radial distribution function analysis and common neighbor analysis. The analysis results show that the relaxation of tensile stress in the first peak of stress-time profile takes place through the structural change and the body-centered cubic crystal structure transforming into face-centered cubic crystal structure, hexagonal close packed crystal structure and other structures. We find that there are no voids’ nucleation in the first peak of stress-time profile. The second-peak of stress-time profile proceeds through the nucleation and growth of voids. And the rapid increase of the void volume fraction corresponds to the rapid decline of the tensile stress. The void volume evolution can be divided into three stages. With the increase of temperature, the double peak characteristic of the tensile stress-time profile disappears at 900−1100 K. While at 900−1100 K the nucleation and growth of voids are the only way to release the built-up stress. It is shown that the nucleation and growth of voids are more preferred at high temperature than at low temperature. The nucleation and growth of voids in single iron under high strain rate follow the NAG model. We calculate the best-fit NAG parameters at 100−1100 K, and analyze the sensitivity of NAG parameters to temperature. It is shown that the nucleation and growth threshold of the single crystal iron are much higher than those of mild steel. The results can be useful for developing the fracture models of iron at high strain rate to describe the dynamic damage on a continuum length scale.

Experimental Evaluation of Fluid Shear Stress Impact on Secondary Nucleation in a Solution Crystallization of Paracetamol

Cooling crystallization experiments were performed at 300 and 370 rpm over a range of saturation temperatures for the measurements of the metastable zone width (MSZW) using a large seed of paracetamol crystal in propan-2-ol solution. Particle imaging velocimetry (PIV) was used to quantify the fluid shear stress at each agitation rate employed, which was found to be 0.07 and 0.11 N/m2 respectively. A decrease in MSZW and growth only zone (GNZ) was observed with increasing shear stress, and the secondary nucleation threshold (SNT) was determined with a relative supersaturation ratio (Sr) of 1.17 at 0.07 N/m2 and 1.08 at 0.11 N/m2. Focused beam reflectance measurement (FBRM) displayed an increase in particle counts as nucleation progressed, with total counts increased by 25% at a higher fluid shear as more nuclei were being sheared off from the seed surface. Crystal nuclei breeding is proposed as a mechanism of secondary nucleation, where the surface of a seed crystal served as a nucleation site for the pre-...

Predicting fretting fatigue in engineering design

The progress in fretting fatigue understanding and predictability is reviewed, with engineering applications in mind. While industrial assessments often relies on simple empirical parameters, research in fretting fatigue should allow the design engineer to improve confidence in the fretting fatigue analysis.Fretting fatigue cracks often form in multiaxial stress fields with severe gradients under the contact area, and are inherently difficult to predict.By describing the fretting stress gradients using comparisons with the mechanical fields surrounding cracks and notches, crack nucleation threshold conditions and finite life can efficiently be determined. Also, non-local stress intensity multipliers provide promising tools for the industrial finite element analysis, often involving complex geometries and loading conditions.The use of multiaxial fatigue criteria to determine fretting fatigue nucleation life is also reviewed. Researchers have shown that critical plane calculations with some stress-averaging method can predict fretting fatigue crack initiation. However, the frictional interface causes non-proportional loading paths, and the application of critical plane methods is not straight forward.

Hybrid Materials with Controlled Precipitation Pattern of Nanoparticles

Hybrid materials with ordered patterns are important to control their functionality. Such ordered structure can be spontaneously formed in nature by self-organization under far from equilibrium, where energies or substances within the system is always dissipated (dS / dt ≠ 0). Although formation mechanism of self-organized patterns in nature are complex and hard to control, development of various materials that mimic self-organization in nature (e.g. bio-mimetics and bio-inspired) have been developed remarkably in recent years. Formation of various patterned structures with useful function by self-organization lead to further development of material chemistry based on mimic of these structures. In the present study, we focused on Liesegang pattern found by R. E. Liesegang in 1896. Liesegang pattern has gained a lot of interests due to several features; simple procedure of the pattern formation, diversity of the pattern morphology and no selection of materials. In fact, Liesegang pattern can be formed by contact between a gel containing an inner electrolyte and an aqueous solution containing an outer electrolyte. Thus, the formed patters consisted of precipitates which is a reaction product between inner and outer electrolytes, has spatial periodicity with geometric series formulated by spacing law (xn +1/xn = 1+p), where xn +1, xn , and p are the position of two consecutive (n+1st and n th) bands measured from the junction point of the electrolytes and spacing coefficient, respectively. Therefore, Liesegang pattern can be applied for patterning technologies because periodic patterns are easily formed. However, control of the periodicity in Liesegang pattern has not been achieved for a long time. Therefore, it is necessary to control periodicity to apply patterning technologies in micro-nanotechnologies. For this purpose, we examined the influence of experimental parameters on the geometry of pattern formation. We focused on the nucleation rate as one of the parameter, whose effect on the pattern formation has not been clarified yet. In this study, we applied the strategy of surface chemistry to control the nucleation rate. Liesegang pattern formation was discussed based on the nucleation and growth model, where the particle is produced through the production of nuclei (solid state) by nucleation of a certain precursors (molecular state) and the growth of nuclei. To occur the nucleation process, it is necessary to bring the energy state in this system unstable to exceed the energy barrier (ΔG). To achieve this process, the concentration of the precursor should exceed the nucleation threshold (C*). Therefore, ΔG governs the nucleation rate and can be considered C* in the model. can be reduced by the coordination of an appropriate ligand for the decrease of surface free energy. Cysteine was used as the ligand for Agn nuclei and/or Ag nanoparticles in the present system to reduce their surface free energy and thus ΔG. In the system without cysteine, the periodic concentric ring pattern (Liesegang pattern) with the interring distance of about 100−200 μm was formed (Figure 1a), where the interring distance increased further away from the edge of agarose stamp. On the other hand, in the system with cysteine, the periodic concentric ring pattern (Liesegang pattern) with the interring spacing of below 100 μm was formed (Figure 1b), meaning that the ring periodicity was almost half that of the pattern formed without cysteine. Thus, the addition of cysteine that is corresponding to the decrease of induced the Liesegang pattern with the finer periodic structures. To prove this relationship between the decrease ofΔG and the finer structures, we used reaction-diffusion simulation with lowered C*. As a result, Liesegang pattern became finer with the lowering C*. Furthermore, to demonstrate the effect of the lowering and C* on a miniaturization of Liesegang pattern in more detail, we compared the spacing coefficient as a measure of the periodicity of patterns. As a result, both lowering and C* gave smaller spacing coefficient (i.e., finer periodic patterns) (Figure 2). Therefore, it was suggested that the lowering induced the lowering C*. Then, the smaller spacing coefficient at lowered C* was discussed in terms of a slower rate of Ostwald ripening. Similar control of C* through surface chemistry can be applied to various precipitation systems to control the periodicity in these systems. In his study, we propose that the approach based on the surface chemistry enable us to control the periodicity of Liesegang patterns by the controlling C*. Figure 1

Nanoindentation tests of heavy-ion-irradiated Au foams—molecular dynamics simulation

Irradiation by light ions may change the mechanical properties of nanofoams. Using molecular-dynamics simulation, we study the effect of irradiating a Au foam (porosity, 50%, and ligament diameter, 3 nm) with heavy ions: here, 10 keV Au ions up to a dose of 4 × 1016 m−2. We demonstrate that in consequence, the ligament morphology changes in the irradiated region, caused by local melting. The changes in mechanical properties are monitored by simulated nanoindentation tests. We find that the foam hardness is only around 1/3 of the hardness of a bulk Au crystal. Irradiation increases the hardness of the foam by around 10% in the central irradiated area. The plastic zone extends to only 1.5 ac, where ac denotes the contact radius; this value is unchanged under irradiation. The hardness increase after irradiation is attributed to two concurring effects. To begin with, irradiation induces melting and annealing of the ligaments, leading to their coarsening and alleviating surface stress, which in turn increases the dislocation nucleation threshold. In addition, irradiation introduces a stacking fault forest that acts as an obstacle to dislocation motion.

Micro-cavitation on demand via the nanoparticle mediated interaction of light and sound

The safe utilization of controlled cavitation for HIFU therapy and ultrasound assisted drug delivery requires nucleation sites for bubble formation. We consider the potential for nucleating transient vapor cavities using laser-illuminated gold nanoparticles combined with high-intensity focused ultrasound. An transparent polyacrylamide gel phantom was seeded with 82-nm diameter gold particles and exposed to 20 ns pulses from a 532 nm Nd:Yag laser. Laser firing was synchronized with the arrival of a burst of 1.1 MHz focused ultrasound. Acoustic emissions from ensuing inertial cavitation were detected passively using a 15 MHz focused transducer. At a laser energy of 0.10 mJ/pulse, the resulting inertial cavitation nucleation threshold pressure (peak-negative focal pressure) was as low as 0.92 MPa. In comparison, a peak-negative focal pressure of 4.50 MPa was required to nucleate detectable cavitation without laser illumination (nano-particles were present in both cases). Experimental results agree well with a simple model for transient heating and cavity formation. Since the particles are durable, one can re-activate them as needed, essentially yielding cavitation nuclei “on demand.” [Work supported by the Dept. of the Army (Award No. DAMD17-02-2-0014) and the Center for Subsurface Sensing and Imaging Systems (NSF ERC Award No. EEC-9986821).]

Nucleation and stabilization of cavitation nuclei in liquids

The presence of cavitation nuclei are normally required in order to induce cavitation in water-based fluids, as the homogeneous nucleation threshold is beyond the range of most acoustic-pressure generation systems (a notable exception is the “intrinsic threshold” achieved by some histotripsy devices). There are a number of potential models for these nuclei, but one that continues to receive favor is the “crevice model,” in which a pocket of gas is contained in a crack or crevice in a contaminating particle and then stabilized against diffusion by the geometry of the crevice. This presentation will describe this model in some detail, present some (old) data that support the model, and some new data that imply that such activatable nuclei exist in mammalian tissue.

Role of Nuclei in Liesegang Pattern Formation: Insights from Experiment and Reaction-Diffusion Simulation

Many types of periodic patterns can spontaneously form in nature across wide spatiotemporal scales. Construction of a chemical model that mimics these periodic patterns are of considerable interest from both scientific and technological viewpoints. The Liesegang phenomenon is one of the chemical models to form periodic patterns with well-defined periodicity. However, the parameters that influence the mechanism and resultant pattern geometry are not completely known. In this study, we use surface chemistry methods to evaluate the influence of nucleation threshold on the geometry of Liesegang patterns. Cysteine was used as an additional ligand for the precursors (Agn nuclei and/or Ag nanoparticles in the present system) to reduce their surface free energy and thus the nucleation free energy. As a result, the formed Liesegang patterns had smaller spacing coefficient (i.e., finer periodic patterns), a phenomenon that was also reproduced using reaction-diffusion simulation with lowered nucleation threshold. Th...

Matched asymptotic solution for crease nucleation in soft solids

A soft solid subjected to a large compression develops sharp self-contacting folds at its free surface, known as creases. Creasing is physically different from structural elastic instabilities, like buckling or wrinkling. Indeed, it is a fully nonlinear material instability, similar to a phase-transformation. This work provides theoretical insights of the physics behind crease nucleation. Creasing is proved to occur after a global bifurcation allowing the co-existence of an outer deformation and an inner solution with localised self-contact at the free surface. The most fundamental result here is the analytic prediction of the nucleation threshold, in excellent agreement with experiments and numerical simulations. A matched asymptotic solution is given within the intermediate region between the two co-existing states. The self-contact acts like the point-wise disturbance in the Oseen’s correction for the Stokes flow past a circle. Analytic expressions of the matching solution and its range of validity are also derived.