scholarly journals Surface Energy of Au Nanoparticles Depending on Their Size and Shape

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 484 ◽  
Author(s):  
David Holec ◽  
Phillip Dumitraschkewitz ◽  
Dieter Vollath ◽  
Franz Dieter Fischer
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Complex Structure ◽  
Characteristic Size ◽  
Bulk Crystals ◽  
Size And Shape ◽  
Nanoparticle Shape ◽  
Universal Power Law ◽  
Atomistic Study ◽  
Surface Facet

Motivated by often contradictory literature reports on the dependence of the surface energy of gold nanoparticles on the variety of its size and shape, we performed an atomistic study combining molecular mechanics and ab initio calculations. We show that, in the case of Au nanocubes, their surface energy converges to the value for ( 0 0 1 ) facets of bulk crystals. A fast convergence to a single valued surface energy is predicted also for nanospheres. However, the value of the surface energy is larger in this case than that of any low-index surface facet of bulk Au crystal. This fact can be explained by the complex structure of the surface with an extensive number of broken bonds due to edge and corner atoms. A similar trend was obtained also for the case of cuboctahedrons. Since the exact surface area of the nanoparticles is an ill-defined quantity, we have introduced the surface-induced excess energy and discuss this quantity as a function of (i) number of atoms forming the nano-object or (ii) characteristic size of the nano-object. In case (i), a universal power-law behaviour was obtained independent of the nanoparticle shape. Importantly, we show that the size-dependence of the surface energy is hugely reduced, if the surface area correction is considered due to its expansion by the electronic cloud, a phenomenon specifically important for small nanoparticles.

Size and shape dependency of the surface energy of metallic nanoparticles: unifying the atomic and thermodynamic approaches

2018 ◽  
Vol 20 (31) ◽  
pp. 20575-20587 ◽  
Author(s):  
Bastiaan Molleman ◽  
Tjisse Hiemstra
Keyword(s):  
Surface Energy ◽  
Metallic Nanoparticles ◽  
Size Dependency ◽  
Size And Shape ◽  
Surface Of Tension

We identify the surface of tension for faceted, metallic nanoparticles, revealing the thermodynamically consistent size dependency of the surface energy.

scholarly journals Decoupling the Contribution of Surface Energy and Surface Area on the Cohesion of Pharmaceutical Powders

2014 ◽  
Vol 32 (1) ◽  
pp. 248-259 ◽  
Author(s):  
Umang V. Shah ◽  
Dolapo Olusanmi ◽  
Ajit S. Narang ◽  
Munir A. Hussain ◽  
Michael J. Tobyn ◽  
...  
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Pharmaceutical Powders

Using visual image analysis to describe pig growth in terms of size and shape

2004 ◽  
Vol 79 (3) ◽  
pp. 415-427 ◽  
Author(s):  
A. B. Doeschl-Wilson ◽  
C. T. Whittemore ◽  
P. W. Knap ◽  
C. P. Schofield
Keyword(s):  
Surface Area ◽  
Imaging System ◽  
Shape Change ◽  
Growth Curves ◽  
Live Weight ◽  
Large Surface Area ◽  
Random Regression ◽  
Linear Measure ◽  
Size And Shape ◽  
Feeding Station

AbstractRandom regression models were used to analyse the daily growth data for a total of 25 pigs of two commercial crossbred types between 75 and 140 days of age. A visual imaging system placed above a feeding station provided daily the plan area and length measurements of different body parts. Daily live-weight measurements of the pigs were obtained from a platform balance integrated into an electronic feeding station. Growth curves associated with different measures, pigs and types were compared. Significant differences in the age growth curves between the pig types could only be found in the ham width measurements (P < 0.05). The linear measure of ham width showed the greatest difference between the two types, and the lowest coefficient of variation among individual animals. Size measures were shown to be a more consistent indicator of pig performance during growth than live weight: pigs with a relatively large surface area or ham width at the early growth stage also have relatively large surface area or ham width at later stages and the between-animal variation in these measurements remains constant with age. Gain in live weight relative to increase in size differed significantly between the two pig types (P < 0.05). Pigs of the two types had significantly different shapes, but the change of shape during growth did not differ significantly between them. The allometric relationships between surface area and ham width1.85and between body length and ham width0.85indicate that the ham widths of pigs increase faster in proportion to full body measures. Variations between individual animals in size increase and shape change are significant (P < 0.05). The analysis suggests that VIA size and shape measurements provide valid descriptors of pig growth.

scholarly journals Thermodynamics of manganese oxides: Sodium, potassium, and calcium birnessite and cryptomelane

2017 ◽  
Vol 114 (7) ◽  
pp. E1046-E1053 ◽  
Author(s):  
Nancy Birkner ◽  
Alexandra Navrotsky
Keyword(s):  
Surface Energy ◽  
Surface Area ◽  
Oxidation State ◽  
Manganese Oxides ◽  
Lower Surface ◽  
Surface Energies ◽  
Surface Areas ◽  
Bulk Thermodynamics ◽  
Lower Surface Energy

Manganese oxides with layer and tunnel structures occur widely in nature and inspire technological applications. Having variable compositions, these structures often are found as small particles (nanophases). This study explores, using experimental thermochemistry, the role of composition, oxidation state, structure, and surface energy in the their thermodynamic stability. The measured surface energies of cryptomelane, sodium birnessite, potassium birnessite and calcium birnessite are all significantly lower than those of binary manganese oxides (Mn3O4, Mn2O3, and MnO2), consistent with added stabilization of the layer and tunnel structures at the nanoscale. Surface energies generally decrease with decreasing average manganese oxidation state. A stabilizing enthalpy contribution arises from increasing counter-cation content. The formation of cryptomelane from birnessite in contact with aqueous solution is favored by the removal of ions from the layered phase. At large surface area, surface-energy differences make cryptomelane formation thermodynamically less favorable than birnessite formation. In contrast, at small to moderate surface areas, bulk thermodynamics and the energetics of the aqueous phase drive cryptomelane formation from birnessite, perhaps aided by oxidation-state differences. Transformation among birnessite phases of increasing surface area favors compositions with lower surface energy. These quantitative thermodynamic findings explain and support qualitative observations of phase-transformation patterns gathered from natural and synthetic manganese oxides.

scholarly journals The Size and Shape of Yagya Kund: Mathematical and Spiritual aspects

2020 ◽  
Vol 3 (1) ◽  
pp. 08-14
Author(s):  
Jairam Motlani
Keyword(s):  
Surface Area ◽  
Mathematical Knowledge ◽  
Study Analysis ◽  
Successful Completion ◽  
Size And Shape ◽  
Vedic Literature ◽  
Area And Volume ◽  
Ancient Texts

The size and shape of the Yagya Kund is one of the important aspects for successful completion of Yagya. Vedic literature describes in details about their types, size, shapes and constructions. Yagya Kund size and shape helps in construction of the Kund for specific spiritual or materialistic outcomes which require specific mathematical measurements of Yagya Kund. The shape of the Yagya Kund is decided based on the purpose of the Yagya, while the size is decided based on the total offerings given to the fire. The spiritual and mathematical aspects on size and shape of the Kund are presented in the study. During the study analysis, it was observed that Vedic texts used mathematical knowledge from various streams such as astrology, trigonometry, geometry, etc in the construction of Yagya Kund. The size of Yagya Kund is directly propositional to the number of offerings to be done. In addition, during the construction of any Yagya Kund, first of all a circle is made whose parameter is fixed to the number of offerings to be done, then a particular Yagya Kund is to be constructed. Regardless of the shape, the construction of Kund based on the diameter given in the ancient texts resulted in the same surface area and volume for particular number of offerings, opening a gate for further study of fine mathematics involved in the Yagya Kund construction.

The Habit Plate Shift and the Morphology of ∝" Nitride Precipitate in ∝-Fe*

1982 ◽  
Vol 40 ◽  
pp. 728-729
Author(s):  
Y. C. Shih ◽  
J. W. Morris
Keyword(s):  
Surface Energy ◽  
Habit Plane ◽  
Elastic Strain ◽  
Strain Energy ◽  
Lattice Mismatch ◽  
Parent Phase ◽  
Elastic Strain Energy ◽  
Size And Shape ◽  
Linear Elastic ◽  
New Phase

A new phase which precipitates from a parent matrix has a size and shape which reflects its difference from parent phase. If the lattice mismatch is significant, the elastic strain energy is more important than the surface energy in determining the morphology and the preferred habit plane. The preferred habit of a tetragonal inclusion in a cubic matrix has been predicted by minimizing the elastic strain energy as from the Ktachaturyan linear elastic formula.

Atomistic Study on the Structural Stability and Site Preference of Rh7-xTxB3 (T = Fe, Cr and Mn)

2013 ◽  
Vol 739 ◽  
pp. 47-50
Author(s):  
Xiao Xu Wang ◽  
Ping Qian ◽  
Zhi Wei An ◽  
Zhen Feng Zhang ◽  
Jiang Shen ◽  
...  
Keyword(s):  
Structural Properties ◽  
Atomistic Simulation ◽  
Complex Structure ◽  
Inversion Method ◽  
Site Preference ◽  
Cell Parameters ◽  
Pair Potentials ◽  
Temperature Disturbance ◽  
Global Deformation ◽  
Atomistic Study

An atomistic simulation of the structural properties of the Rh7-xTxB3 series, where T is Fe, Cr, Mn, has been carried out using interatomic pair potentials based on the lattice inversion method. Calculated results show T atoms can stabilize Rh7-xTxB3 with Th7Fe3-type structure, and T atoms substitute for Rh with a strong preference for the 2b sites. The phase stability of the intermetallics Rh7-xTxB3 is tested by many means including random atom shift, global deformation and high temperature disturbance under the control of the pair potentials. Calculated unit-cell parameters for Rh7-xTxB3 agree with the experimental data very well. All the above results indicate that the potentials are valid for studying the structural properties of these kinds of complex structure of transition metal boride.

The influence of carrier size and shape in the moving bed biofilm process

2000 ◽  
Vol 41 (4-5) ◽  
pp. 383-391 ◽  
Author(s):  
H. Ødegaard ◽  
B. Gisvold ◽  
J. Strickland
Keyword(s):  
Surface Area ◽  
Municipal Wastewater ◽  
Specific Area ◽  
Moving Bed ◽  
Size And Shape ◽  
Biofilm Reactors ◽  
Biofilm Process ◽  
Surface Area Loading Rate ◽  
Carrier Size ◽  
Very High

The moving bed biofilm process is based on plastic carriers on which biomass attaches and grows. The original Kaldnes carrier was made of high-density polyethylene (density 0.95 gcm−1) that could be used in filling fractions (volume of carriers in empty reactor) up to 70% that gives a specific area of 350 m2m−3. Lately there has been an interest in the use of larger carrier elements, especially when using the process for upgrading of activated sludge plants. This paper analyses the influence of the carrier size and shape on performance, especially related to highly loaded plants working on municipal wastewater. The results demonstrate that moving bed biofilm reactors should be designed based on surface area loading rate (g COD/m2d) and that shape and size of the carrier do not seem to be significant as long as the effective surface area is the same. The results indicate that very high organic loads can be used in order to remove soluble COD but that the settleability of the sludge is negatively influenced at high loading rates.

Retraction of large liquid strips

2015 ◽  
Vol 778 ◽  
Author(s):  
Cunjing Lv ◽  
Christophe Clanet ◽  
David Quéré
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Surface Area ◽  
Driving Force ◽  
Large Scale ◽  
Horizontal Surface

We study the behaviour of elongated puddles deposited on non-wetting substrates. Such liquid strips retract and adopt circular shapes after a few oscillations. Their thickness and horizontal surface area remain constant during this reorganization, so that the energy of the system is only lowered by minimizing the length of the contour (and the corresponding surface energy); despite the large scale of the experiments (several centimetres), motion is driven by surface tension. We focus on the retraction stage, and show that its velocity results from a balance between the capillary driving force and inertia, due to the frictionless motion on non-wetting substrates. As a consequence, the retraction velocity has a special Taylor–Culick structure, where the puddle width replaces the usual thickness.

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