A thermodynamic approach to mechanical stability of nanosized particles

Open Physics ◽  
2003 ◽  
Vol 1 (2) ◽  
Author(s):  
Vladimir Samsonov ◽  
Nikolay Sdobnyakov
Keyword(s):  
Surface Tension ◽  
Free Energy ◽  
Stability Condition ◽  
Mechanical Stability ◽  
Noble Gas ◽  
Stability Limit ◽  
Gas Clusters ◽  
The Stability ◽  
The Second Variation ◽  
Nonpolar Organic

AbstractThermodynamic stability conditions for nanoparticles (resulting from non-negativity of the second variation of the free energy) have been analyzed for two cases: (i) a nonvolatile nanosized particle with the size-dependent surface tension; (ii) the limiting case of larger objects when the surface tension takes its macroscopic value. It has been shown that the mechanical stability of a nanoparticle, i.e. its stability relative to the volume fluctuations, is defined by an interplay between the excess (“surface”) free energy and the volumetric elastic energy. According to the results obtained, noble gas clusters and metal nanoparticles satisfy the mechanical stability condition. At the same time, water nanodrops, as well as nanoparticles presented by nonpolar organic molecules, correspond to the stability limit. Among the investigated systems, the stability condition is not carried out for n-Pentane clusters.

DIFFUSION IN MULTICOMPONENT METALLIC SYSTEMS: VI. SOME THERMODYNAMIC PROPERTIES OF THE D MATRIX AND THE CORRESPONDING SOLUTIONS OF THE DIFFUSION EQUATIONS

1963 ◽  
Vol 41 (12) ◽  
pp. 2166-2173 ◽  
Author(s):  
J. S. Kirkaldy ◽  
D. Weichert ◽  
Zia-Ul- Haq
Keyword(s):  
Free Energy ◽  
Thermodynamic Properties ◽  
Stability Condition ◽  
Stable Solution ◽  
Positive Definite ◽  
Diffusion Equations ◽  
Second Law ◽  
Isothermal Diffusion ◽  
Gibb’S Free Energy ◽  
The Stability

The second law requirement that the Onsager L matrix for isothermal diffusion in a stable solution be positive definite and the stability condition for such a solution that the Hessian of the Gibb's free energy be positive definite impose on the diffusion D matrix the condition that it always have real and positive eigenvalues. This condition ensures that solutions of the differential equations for diffusion will always relax in a nonperiodic way.

scholarly journals Ion-Size Effects in the Growth Sequences of Metal-Ion-Doped Noble Gas Clusters

1997 ◽  
Vol 17 (2) ◽  
pp. 109-122 ◽  
Author(s):  
Christian Lüder ◽  
Dimitris Prekas ◽  
Michalis Velegrakis
Keyword(s):  
Metal Ion ◽  
Mass Spectra ◽  
Noble Gas ◽  
Magic Number ◽  
Sphere Packing ◽  
Cluster Ions ◽  
Magic Numbers ◽  
Gas Clusters ◽  
The Stability ◽  
Ion Size

We have studied the stability and the structure of doped noble gas cluster ions of the type M+Xn, (M=In, Al, Na, X=Ar, Kr, Xe) by systematically changing the composition M/X and observing changes in the magic number patterns appearing in the mass spectra. When the metal ion radius is comparable to the radius of the noble gas atom, the mass spectra show the familar icosahedral magic numbers n+ 1=13,19,23,26,29,32, 46, 55,... In constrast, for metal ions with radii significantly smaller than the noble gas atoms, we observe a new series of magic numbers n + 9, 11, 17, 21,24, 26,... This series converts into the icosahedral one for larger clusters. Using a simple hard sphere packing model, we show that this new series of magic numbers is consistent with a cluster growth sequence which is based on a capped square antiprism (CSA) geometrical structure of the clusters.

Convective instability in liquid pools heated from below

1971 ◽  
Vol 47 (4) ◽  
pp. 779-787 ◽  
Author(s):  
Harvey J. Palmer ◽  
John C. Berg
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Stability Analysis ◽  
Convective Instability ◽  
Temperature Drop ◽  
Stability Limit ◽  
Liquid Pool ◽  
Silicone Oils ◽  
Liquid Pools ◽  
The Stability

The linear hydrodynamic stability analysis of liquid pools heated from below combining surface tension and buoyancy effects as presented by Nield (1964) is confirmed by experiment for a series of silicone oils. The experimental method used is an adaptation of the Schmidt–Milverton technique, in which the stability limit is located by the change of slope in the plot of heat flux versus temperature drop across the liquid pool.

Variational Principle and Stability of Nonmonotonic Vlasov-Poisson Equilibria

1987 ◽  
Vol 42 (10) ◽  
pp. 1115-1123 ◽  
Author(s):  
P. J. Morrison
Keyword(s):  
Free Energy ◽  
Variational Principle ◽  
Poisson Equation ◽  
Negative Energy ◽  
Variation Principle ◽  
Sufficient Condition ◽  
Second Variation ◽  
Constants Of Motion ◽  
The Stability ◽  
The Second Variation

The stability of nonmonotonic equilibria of the Vlasov-Poisson equation is assessed by using nonlinear constants of motion . The constants of motion make up the free energy of the system , which upon variation yields nonmonotonic equilibria. Such equilibria have not previously been obtainable from a variation principle, but here this is accomplished by the inclusion of a passively advected tracer field. Definiteness of the second variation of the free energy gives a sufficient condition for stability in agreement with Gardner’s theorem [5], Previously, we have argued that indefiniteness implies either spectral in stability or negative energy modes, which are generically unstable when one adds dissipation or nonlinearity [6]. Such is the case for the nonmonotonic equilibria considered.

Initial post-buckling analysis of a fixed–fixed strut

2019 ◽  
Vol 24 (11) ◽  
pp. 3403-3409
Author(s):  
M Jin ◽  
HY Qi
Keyword(s):  
Potential Energy ◽  
Critical Load ◽  
Stability Limit ◽  
Positive Definite ◽  
Second Variation ◽  
Buckling Mode ◽  
Lateral Deflection ◽  
Post Buckling ◽  
The Stability ◽  
The Second Variation

In this paper, the initial post-buckling of a fixed–fixed strut in compression at the first bifurcation point is analyzed. Using the Fourier series of the lateral deflection, the second variation of the potential energy is proved, analytically, to be semi-positive definite when the compression is equal to the Euler critical load. The fourth variation of the potential energy is positive when the disturbance of the lateral deflection matches the buckling mode. Based on Koiter’s initial post-buckling theory, the equilibrium of the straight state of the strut is stable at the stability limit; when the compression slightly exceeds the Euler critical load, the curved shape at initial post-buckling is stable.

On the stability limit of charged droplets

1989 ◽  
Vol 422 (1863) ◽  
pp. 319-328 ◽  
Keyword(s):  
Surface Tension ◽  
Particle Size ◽  
Light Scattering ◽  
Stability Limit ◽  
Prolate Spheroid ◽  
Charged Droplets ◽  
Electric Stress ◽  
The Stability ◽  
Stability Limits

Single, highly charged droplets of dioctylphthalate and sulphuric acid of radius between 1 and 10 μm are suspended in vacuum in a quadrupol trap. As the droplets evaporate their radius is monitored continuously by light scattering and their charge is determined periodically by weight balancing. The droplets break when the electric stress exceeds that of surface tension. The largest fragment remains trapped allowing a determination of the change in volume and charge. The fraction of volume and charge lost is found to be independent of particle size and sign of charge and is variable. The oil drops lose (15.0 ± 3.9)% of their charge on breakup and (2.25 ± 0.96)% of their mass. The acid droplets lose (49.4 ± 8.3)% of their charge and less than 0.1% of their mass. The acid results are compared with those from a model of field emission based upon prolate spheroid deformation and the formation of Taylor cones. For both oil and acid droplets the stability limits are in agreement with those predicted by Lord Rayleigh.

The Effect of Thermo-Solutal Capillary Transport on the Dynamics of Liquid Bridge

Volume 1 ◽  
2004 ◽  
Author(s):  
Fre´de´ric Joly ◽  
Wei Shyy ◽  
Ge´rard Labrosse
Keyword(s):  
Surface Tension ◽  
Liquid Bridge ◽  
Soret Effect ◽  
Stability Limit ◽  
Solute Concentration ◽  
Transport Dynamics ◽  
Separation Ratio ◽  
Prandtl Numbers ◽  
The Stability ◽  
Pseudo Spectral Method

The transport dynamics and stability limit of the axisymmetric steady flow driven by a surface tension variation in a liquid bridge configuration is studied numerically. The surface tension variation results from both thermal and solutal gradients, and varies linearly with both temperature and solute concentration. The pseudo-spectral method is employed to investigate the solutions under different combinations of Marangoni, Prandtl and Lewis numbers, and separation ratio. Steady bifurcations for low Prandtl numbers are observed. The Soret effect has important influence on the stability of the basic flow, as it can change the symmetry of the most destabilizing perturbations and affect the threshold for 3D convection. It is also shown that for large Prandtl number, the Hopf bifurcation observed for pure fluid is replaced by a steady one for negative separation ratio.

An analysis of the transport properties and mechanical stability of rapidly solidified Al-Sb alloy

2015 ◽  
Vol 10 (2) ◽  
pp. 2663-2681
Author(s):  
Rizk El- Sayed ◽  
Mustafa Kamal ◽  
Abu-Bakr El-Bediwi ◽  
Qutaiba Rasheed Solaiman
Keyword(s):  
Mechanical Properties ◽  
Thermal Conductivity ◽  
Melt Spinning ◽  
Elastic Moduli ◽  
Mechanical Stability ◽  
Microstructural Analysis ◽  
Alloy System ◽  
Antimony Content ◽  
The Stability ◽  
Rapidly Solidified

The structure of a series of AlSb alloys prepared by melt spinning have been studied in the as melt–spun ribbons  as a function of antimony content .The stability  of these structures has  been  related to that of the transport and mechanical properties of the alloy ribbons. Microstructural analysis was performed and it was found that only Al and AlSb phases formed for different composition.  The electrical, thermal and the stability of the mechanical properties are related indirectly through the influence of the antimony content. The results are interpreted in terms of the phase change occurring to alloy system. Electrical resistivity, thermal conductivity, elastic moduli and the values of microhardness are found to be more sensitive than the internal friction to the phase changes. 

scholarly journals A pH-Responsive Foam Formulated with PAA/Gemini 12-2-12 Complexes

2021 ◽  
Vol 5 (3) ◽  
pp. 37
Author(s):  
Hernán Martinelli ◽  
Claudia Domínguez ◽  
Marcos Fernández Leyes ◽  
Sergio Moya ◽  
Hernán Ritacco
Keyword(s):  
Surface Tension ◽  
Dynamic Surface Tension ◽  
Foam Formation ◽  
Ph Responsive ◽  
Dynamic Surface ◽  
X Ray ◽  
Equilibrium Surface Tension ◽  
Potential Applications ◽  
The Stability ◽  
Air Interfaces

In the search for responsive complexes with potential applications in the formulation of smart dispersed systems such as foams, we hypothesized that a pH-responsive system could be formulated with polyacrylic acid (PAA) mixed with a cationic surfactant, Gemini 12-2-12 (G12). We studied PAA-G12 complexes at liquid–air interfaces by equilibrium and dynamic surface tension, surface rheology, and X-ray reflectometry (XRR). We found that complexes adsorb at the interfaces synergistically, lowering the equilibrium surface tension at surfactant concentrations well below the critical micelle concentration (cmc) of the surfactant. We studied the stability of foams formulated with the complexes as a function of pH. The foams respond reversibly to pH changes: at pH 3.5, they are very stable; at pH > 6, the complexes do not form foams at all. The data presented here demonstrate that foam formation and its pH responsiveness are due to interfacial dynamics.

Examining sharp restart in a Monte Carlo method for the linearized Poisson–Boltzmann equation

2020 ◽  
Vol 26 (3) ◽  
pp. 223-244
Author(s):  
W. John Thrasher ◽  
Michael Mascagni
Keyword(s):  
Monte Carlo ◽  
Free Energy ◽  
Monte Carlo Algorithm ◽  
Significant Bias ◽  
Poisson Boltzmann ◽  
Electrostatic Free Energy ◽  
Poisson Boltzmann Equation ◽  
The Stability ◽  
Potential Methods ◽  
The Individual

AbstractIt has been shown that when using a Monte Carlo algorithm to estimate the electrostatic free energy of a biomolecule in a solution, individual random walks can become entrapped in the geometry. We examine a proposed solution, using a sharp restart during the Walk-on-Subdomains step, in more detail. We show that the point at which this solution introduces significant bias is related to properties intrinsic to the molecule being examined. We also examine two potential methods of generating a sharp restart point and show that they both cause no significant bias in the examined molecules and increase the stability of the run times of the individual walks.

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