2713:
31:
2688:. This is an essential requirement for pigment dispersions; for wetting to be effective, the surface tension of the pigment's vehicle must be lower than the surface free energy of the pigment. This allows the vehicle to penetrate into the interstices of the pigment aggregates, thus ensuring complete wetting. Finally, the particles are subjected to a repulsive force in order to keep them separated from one another and lowers the likelihood of
1530:
2414:
4803:
1550:
4827:
1011:
2168:
4839:
4815:
1828:
622:
2709:. This crowding effect is accompanied by a decrease in entropy, whereby the number of conformations possible for the polymer molecules is reduced in the adsorbed layer. As a result, energy is increased and often gives rise to repulsive forces that aid in keeping the particles separated from each other.
2683:
The chief purpose of pigment dispersion is to break down aggregates and form stable dispersions of optimally sized pigment particles. This process generally involves three distinct stages: wetting, deaggregation, and stabilization. A surface that is easy to wet is desirable when formulating a coating
2671:
New surfaces are constantly being created as larger pigment particles get broken down into smaller subparticles. These newly-formed surfaces consequently contribute to larger surface energies, whereby the resulting particles often become cemented together into aggregates. Because particles dispersed
1284:
In order to determine the pairwise intermolecular energy, all intermolecular forces in the material must be broken. This allows thorough investigation of the interactions that occur for single molecules. During sublimation of a substance, intermolecular forces between molecules are broken, resulting
149:
There are several different models for calculating the surface energy based on the contact angle readings. The most commonly used method is OWRK, which requires the use of two probe liquids and gives out as a result the total surface energy as well as divides it into polar and dispersive components.
2704:
is a phenomenon used to describe the repelling effect when adsorbed layers of material (such as polymer molecules swollen with solvent) are present on the surface of the pigment particles in dispersion. Only certain portions (anchors) of the polymer molecules are adsorbed, with their corresponding
2663:
offer great potential in modifying the application properties of a coating. Due to their fine particle size and inherently high surface energy, they often require a surface treatment in order to enhance their ease of dispersion in a liquid medium. A wide variety of surface treatments have been
2436:
is based on thermodynamic principles and is used to describe changes in vapor pressure caused by liquids with curved surfaces. The cause for this change in vapor pressure is the
Laplace pressure. The vapor pressure of a drop is higher than that of a planar surface because the increased Laplace
1006:
To estimate the surface energy of a pure, uniform material, an individual region of the material can be modeled as a cube. In order to move a cube from the bulk of a material to the surface, energy is required. This energy cost is incorporated into the surface energy of the material, which is
79:
required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces. There is "excess energy" as a result of the now-incomplete, unrealized bonding between the two created surfaces.
1486:
2437:
pressure causes the molecules to evaporate more easily. Conversely, in liquids surrounding a bubble, the pressure with respect to the inner part of the bubble is reduced, thus making it more difficult for molecules to evaporate. The Kelvin equation can be stated as:
2409:
As a result of the surface tension inherent to liquids, curved surfaces are formed in order to minimize the area. This phenomenon arises from the energetic cost of forming a surface. As such the Gibbs free energy of the system is minimized when the surface is curved.
2386:, wet chemical treatment, including grafting, and thin-film coating. Surface energy mimicking is a technique that enables merging the device manufacturing and surface modifications, including patterning, into a single processing step using a single device material.
1251:
157:
In general, as surface energy increases, the contact angle decreases because more of the liquid is being "grabbed" by the surface. Conversely, as surface energy decreases, the contact angle increases, because the surface doesn't want to interact with the liquid.
317:
2559:
456:
1646:
1108:
989:
of two contacting bodies. The relative surface energy can be determined by detaching of bodies of well defined shape made of one material from the substrate made from the second material. For example, the relative surface energy of the interface
186:
is the surface energy density of the liquid). However, such a method cannot be used to measure the surface energy of a solid because stretching of a solid membrane induces elastic energy in the bulk in addition to increasing the surface energy.
981:
For a slab, we have two surfaces and they are of the same type, which is reflected by the number 2 in the denominator. To guarantee this, we need to create the slab carefully to make sure that the upper and lower surfaces are of the same type.
475:
2716:
Dispersion
Stability Mechanisms: Charge Stabilization and Steric or Entropic Stabilization. Electrical repulsion forces are responsible for stabilization through charge while steric hindrance is responsible for stabilization through
2302:
1371:
Using empirically tabulated values for enthalpy of sublimation, it is possible to determine the pairwise intermolecular energy. Incorporating this value into the surface energy equation allows for the surface energy to be estimated.
771:
In the deformation of solids, surface energy can be treated as the "energy required to create one unit of surface area", and is a function of the difference between the total energies of the system before and after the deformation:
2695:
Dispersions may become stable through two different phenomena: charge repulsion and steric or entropic repulsion. In charge repulsion, particles that possess the same like electrostatic charges repel each other. Alternatively,
1366:
2046:
Surface energy comes into play in wetting phenomena. To examine this, consider a drop of liquid on a solid substrate. If the surface energy of the substrate changes upon the addition of the drop, the substrate is said to be
1933:
70:
than the bulk of the material (that is, the atoms on the surface must have more energy than the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material by
2111:
937:
153:
Contact angle method is the standard surface energy measurement method due to its simplicity, applicability to a wide range of surfaces and quickness. The measurement can be fully automated and is standardized.
839:
91:
means that the energy consumed by the cutting process will be equal to the energy inherent in the two new surfaces created. The unit surface energy of a material would therefore be half of its energy of
1381:
2025:
3521:
Rosales, J. I.; Marshall, G. W.; Marshall, S. J.; Wantanabe, L. G.; Toledano, M.; Cabrerizo, M. A.; Osorio, R. (1999). "Acid-etching and
Hydration Influence on Dentin Roughness and Wettability".
1651:
695:
1154:
1833:
While these quantities can vary between each component, the sum within the system remains constant. At the interface, these values may deviate from those present within the bulk phases. The
2374:. High-energy substrates are more easily wetted than low-energy substrates. In addition, more complete wetting will occur if the substrate has a much higher surface energy than the liquid.
2676:, they exhibit a strong affinity for other pigment particles nearby as they move through the medium and collide. This natural attraction is largely attributed to the powerful short-range
1604:
224:
2443:
2705:
loops and tails extending out into the solution. As the particles approach each other their adsorbed layers become crowded; this provides an effective steric barrier that prevents
1823:{\displaystyle {\begin{aligned}U&=U_{\alpha }+U_{\beta }+U_{\sigma }\\N_{i}&=N_{i\alpha }+N_{i\beta }+N_{i\sigma }\\S&=S_{\alpha }+S_{\beta }+S_{\sigma }\end{aligned}}}
340:
2346:
The energy of the bulk component of a solid substrate is determined by the types of interactions that hold the substrate together. High-energy substrates are held together by
3564:
Khan, H.; Fell, J. T.; Macleod, G. S. (2001). "The influence of additives on the spreading coefficient and adhesion of a film coating formulation to a model tablet surface".
2397:, can be used to increase the surface energy of the substrate. Additives can also be added to the liquid to decrease its surface tension. This technique is employed often in
1021:
1504:
model and the
Guggenheim model. In order to demonstrate the thermodynamics of an interfacial system using the Gibbs model, the system can be divided into three parts: two
617:{\displaystyle V=\pi r^{2}l{\text{ is constant}}\quad \implies \quad \delta V=2\pi rl\delta r+\pi r^{2}\delta l=0\quad \implies \quad \delta r=-{\frac {r}{2l}}\delta l~.}
2245:
2171:
Contact Angles: non-wetting, wetting, and perfect wetting. The contact angle is the angle that connects the solid–liquid interface and the liquid-gas interface.
1553:
Gibbs model. The Gibbs model assumes the interface to be ideal (no volume) so that the total volume of the system comprises only the alpha and beta phases.
3042:"ISO 19403-2:2017. Paints and varnishes — Wettability — Part 2: Determination of the surface free energy of solid surfaces by measuring the contact angle"
2668:
on the surface of a molecule in the presence of polar groups, monolayers of polymers, and layers of inorganic oxides on the surface of organic pigments.
1295:
170:(which increases the surface area and hence the surface energy). In that case, in order to increase the surface area of a mass of liquid by an amount,
731:) and liquids, isotropy is a good approximation for many other materials. In particular, if the sample is polygranular (most metals) or made by powder
1843:
1500:
influences generally all thermodynamic parameters of a system. There are two models that are commonly used to demonstrate interfacial phenomena: the
3457:"Surface Energy Mimicking: Simultaneous Replication of Hydrophilic and Superhydrophobic Micropatterns through Area-Selective Monomers Self-Assembly"
83:
Cutting a solid body into pieces disrupts its bonds and increases the surface area, and therefore increases surface energy. If the cutting is done
3916:
2057:
4536:
3637:
Auschra, C.; Eckstein, E.; Muhlebach, A.; Zink, M.; Rime, F. (2002). "Design of new pigment dispersants by controlled radical polymerization".
2684:
that requires good adhesion and appearance. This also minimizes the risks of surface tension related defects, such as crawling, cratering, and
1014:
Cube model. The cube model can be used to model pure, uniform materials or an individual molecular component to estimate their surface energy.
4580:
4255:
879:
4722:
846:
84:
1289:
can be useful in determining the pairwise intermolecular energy. Enthalpy of sublimation can be calculated by the following equation:
3494:
Sakata, I.; Morita, M.; Tsuruta, N.; Morita, K. (2003). "Activation of Wood
Surface by Corona Treatment to Improve Adhesive Bonding".
4880:
4870:
3221:
3082:
1127:
are coordination numbers corresponding to the surface and the bulk regions of the material, and are equal to 5 and 6, respectively;
778:
2420:
of flat and curved surfaces. The vapor pressure of a curved surface is higher than the vapor pressure of a flat surface due to the
75:. The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the
4663:
998:" is equal to 0.03 N/m. Experimental setup for measuring relative surface energy and its function can be seen in the video.
758:. The surface energy of the facets can thus be found to within a scaling constant by measuring the relative sizes of the facets.
146:
of the liquids, the surface energy can be calculated. In practice, this analysis is done automatically by a contact angle meter.
3854:
Lipsett, S. G.; Johnson, F. M. G.; Maass, O. (1927). "The
Surface Energy and the Heat of Solution of Solid Sodium Chloride. I".
853:) is an alternative approach to measurement. Surface energy is estimated from the following variables: width of the d-band, the
1481:{\displaystyle \gamma \approx {\frac {-\Delta _{\text{sub}}H\left(z_{\sigma }-z_{\beta }\right)}{a_{0}N_{\text{A}}z_{\beta }}}}
4843:
4673:
1545:. Guggenheim takes into account the volume of the extended interfacial region, which is not as practical as the Gibbs model.
1980:
3889:
1246:{\displaystyle a_{0}=V_{\text{molecule}}^{\frac {2}{3}}=\left({\frac {\bar {M}}{\rho N_{\text{A}}}}\right)^{\frac {2}{3}}}
633:
4203:
4021:
30:
4762:
3909:
2712:
138:
experiments. In this method, the contact angle of the surface is measured with several liquids, usually water and
4668:
4526:
4188:
4133:
4113:
4108:
2955:
Marshall, S. J.; Bayne, S. C.; Baier, R.; Tomsia, A. P.; Marshall, G. W. (2010). "A review of adhesion science".
1834:
870:
850:
751:
312:{\displaystyle \delta F=-P~\delta l+\gamma ~\delta A=0\quad \implies \quad \gamma =P{\frac {\delta l}{\delta A}}}
4875:
4865:
4597:
3941:
2554:{\displaystyle RT\ln {\frac {P_{0}^{K}}{P_{0}}}=\gamma V_{m}\left({\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}\right)}
1563:
451:{\displaystyle A=2\pi r^{2}+2\pi rl\quad \implies \quad \delta A=4\pi r\delta r+2\pi l\delta r+2\pi r\delta l}
3299:
Kern, K.; David, R.; Palmer, R. L.; Cosma, G. (1986). "Complete
Wetting on 'Strong' Substrates: Xe/Pt(111)".
2188:), which is the angle connecting the solid–liquid interface and the liquid–gas interface (as in the figure).
4757:
4742:
4138:
4118:
2742:
1286:
109:
72:
4270:
4166:
4093:
4083:
3964:
3902:
2925:
2615:
211:
88:
4210:
4001:
2701:
1497:
327:
215:
190:
The surface energy of a solid is usually measured at high temperatures. At such temperatures the solid
76:
2991:
1103:{\displaystyle \gamma ={\frac {\left(z_{\sigma }-z_{\beta }\right){\frac {1}{2}}W_{\text{AA}}}{a_{0}}}}
4658:
4631:
4609:
4516:
4449:
4198:
4128:
4073:
3810:
3762:
3688:
3308:
3273:
3176:
2685:
2351:
93:
3016:
104:" model just implied above. They are found to be highly dynamic regions, which readily rearrange or
4737:
4680:
4602:
4575:
4260:
4123:
4098:
3679:
Rhee, S.-K. (1977). "Surface energies of silicate glasses calculated from their wettability data".
2677:
2649:
2367:
858:
191:
167:
63:
55:
4826:
3342:
Becker, H.; Gärtner, C. (2007). "Polymer microfabrication technologies for microfluidic systems".
4819:
4717:
4695:
4685:
4521:
3704:
3546:
3476:
3402:
3367:
3202:
Zisman, W. (1964). "Relation of the
Equilibrium Contact Angle to Liquid and Solid Constitution".
3142:
2935:
2869:
2425:
755:
96:, all other things being equal; in practice, this is true only for a surface freshly prepared in
3884:
1609:
All extensive quantities of the system can be written as a sum of three components: bulk phase
4619:
4444:
4305:
4265:
4235:
4220:
4193:
4103:
4006:
3946:
3936:
3581:
3538:
3437:
3420:
Rastogi (2010). "Direct
Patterning of Intrinsically Electron Beam Sensitive Polymer Brushes".
3359:
3324:
3217:
3078:
2972:
2930:
2830:
2383:
1278:
105:
67:
4778:
4752:
4747:
4727:
4712:
4553:
4543:
4323:
4250:
3986:
3863:
3818:
3770:
3731:
3696:
3646:
3573:
3530:
3503:
3468:
3429:
3394:
3351:
3316:
3281:
3246:
3207:
3184:
3111:
2964:
2817:
2804:
2421:
2394:
2390:
2371:
854:
4807:
4788:
4702:
4469:
4384:
4240:
4230:
4215:
4173:
4078:
4028:
3979:
3456:
2920:
2882:
2856:
2843:
2791:
2673:
2596:
2433:
2297:{\displaystyle \gamma _{\text{s-g}}=\gamma _{\text{s-l}}+\gamma _{\text{l-g}}\cos \theta }
724:
720:
143:
39:
3385:
Mansky (1997). "Controlling
Polymer-Surface Interactions with Random Copolymer Brushes".
985:
Strength of adhesive contacts is determined by the work of adhesion which is also called
194:
and even though the surface area changes, the volume remains approximately constant. If
3814:
3766:
3722:
Dundon, M. L.; Mack, E. (1923). "The Solubility and Surface Energy of Calcium Sulfate".
3692:
3312:
3277:
3237:
Owens, D. K.; Wendt, R. C. (1969). "Estimation of the Surface Free Energy of Polymers".
3180:
1148:
Surface area can be determined by squaring the cube root of the volume of the molecule:
4783:
4732:
4707:
4511:
4476:
4409:
4399:
4315:
4295:
4275:
4245:
4225:
4183:
4161:
4143:
4043:
4033:
3969:
3164:
2697:
2579:
2417:
1501:
175:
3650:
3577:
4859:
4831:
4690:
4650:
4614:
4570:
4496:
4459:
4377:
4300:
4068:
4063:
4016:
3996:
3708:
3480:
3406:
3100:"Strength of adhesive contacts: Influence of contact geometry and material gradients"
2915:
2363:
2359:
2355:
2347:
2181:
991:
139:
135:
101:
34:
Contact angle measurements can be used to determine the surface energy of a material.
3371:
4587:
4531:
4481:
4464:
4285:
4058:
3991:
3550:
2706:
2689:
2607:
1361:{\displaystyle \Delta _{\text{sub}}H=-{\frac {1}{2}}W_{\text{AA}}N_{\text{A}}z_{b}}
17:
3398:
3801:
Gilman, J. J. (1960). "Direct Measurements of the Surface Energies of Crystals".
3534:
2968:
4592:
4558:
4432:
4422:
4365:
4348:
4333:
4280:
4178:
3320:
2623:
1928:{\displaystyle N_{i\sigma }=N_{i}-c_{i\alpha }V_{\alpha }-c_{i\beta }V_{\beta }}
1505:
1375:
The following equation can be used as a reasonable estimate for surface energy:
1285:
in a change in the material from solid to gas. For this reason, considering the
3507:
3250:
3212:
1529:
4626:
4548:
4486:
4454:
4394:
4088:
3355:
3285:
3188:
3132:
3116:
3099:
2665:
1522:
and an infinitesimally thin boundary layer known as the Gibbs dividing plane (
1261:
743:
113:
954:
is the total energy of surface slab obtained using density functional theory.
4636:
4563:
4437:
4417:
4389:
4328:
2413:
2389:
Many techniques can be used to enhance wetting. Surface treatments, such as
2338:
is the contact angle between the solid–liquid and the liquid–gas interface.
2106:{\displaystyle S=\gamma _{\text{s}}-\gamma _{\text{l}}-\gamma _{\text{s-l}}}
739:
732:
3585:
3542:
3472:
3441:
3363:
3328:
2976:
3041:
4372:
4353:
4338:
4038:
716:
3867:
3735:
2051:. The spreading parameter can be used to mathematically determine this:
1549:
4506:
4048:
3775:
3750:
3700:
3137:
2895:
2660:
2236:
2048:
2036:
995:
59:
3822:
3626:(3rd ed.). Florida: Taylor and Francis Group. pp. 31-6–31-7.
3433:
1010:
932:{\displaystyle \gamma ={\frac {E_{\text{slab}}-NE_{\text{bulk}}}{2A}}}
166:
The surface energy of a liquid may be measured by stretching a liquid
4053:
3974:
3925:
2779:
2767:
2627:
2401:
formulations to ensure that they will be evenly spread on a surface.
700:
The surface energy density of the solid can be computed by measuring
97:
3075:
Contact Mechanics and Friction: Physical Principles and Applications
2167:
3163:
Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. (2009).
1974:
which allows us to describe the number of molecules per unit area:
27:
Excess energy at the surface of a material relative to its interior
3131:
Dept. of System Dynamics and Friction Physics (December 6, 2017).
2755:
2711:
2428:
of the droplet causing it to vaporize more than it normally would.
2412:
2398:
1548:
1528:
1009:
873:, surface energy can be calculated from the following expression:
747:
728:
2334:
is the interfacial energy between the liquid and gas phases, and
4427:
4360:
4343:
4011:
3898:
3608:(3rd ed.). New York: Wiley Interscience. pp. 435–441.
3045:
834:{\displaystyle \gamma ={\frac {1}{A}}\left(E_{1}-E_{0}\right)}
2325:
the interfacial energy between the substrate and the liquid,
2147:
the interfacial energy between the substrate and the liquid.
198:
is the surface energy density of a cylindrical rod of radius
2316:
is the interfacial energy between the solid and gas phases,
2180:
A way to experimentally determine wetting is to look at the
754:
growth conditions) is related to the surface energy by the
3455:
Pardon, G.; Haraldsson, T.; van der Wijngaart, W. (2016).
3264:
De Gennes, P. G. (1985). "Wetting: statics and dynamics".
2382:
The most commonly used surface modification protocols are
627:
Therefore, the surface energy density can be expressed as
3894:
3834:
3832:
1967:
It is beneficial to define a new term interfacial excess
1837:
of molecules present at the interface can be defined as:
738:
In the case of single-crystal materials, such as natural
134:
The most common way to measure surface energy is through
100:. Surfaces often change their form away from the simple "
108:, so that energy is often reduced by such processes as
3751:"Grain Boundary Effect in Surface Tension Measurement"
3617:
3615:
3206:. Advances in Chemistry. Vol. 43. pp. 1–51.
861:
of atoms at the surface and in the bulk of the solid.
3796:
3794:
3792:
3790:
3788:
3786:
2446:
2248:
2060:
2020:{\displaystyle \Gamma _{i}={\frac {N_{i\alpha }}{A}}}
1983:
1846:
1649:
1566:
1384:
1298:
1157:
1024:
882:
781:
636:
478:
343:
227:
142:. Based on the contact angle results and knowing the
206:
at high temperature and a constant uniaxial tension
4771:
4647:
4495:
4408:
4314:
4154:
3955:
3599:
3597:
3595:
2350:, while low-energy substrates are held together by
1136:is the surface area of an individual molecule, and
723:orientations. While this is only strictly true for
690:{\displaystyle \gamma ={\frac {Pl}{\pi r(l-2r)}}~.}
3666:Adhesion & Adhesives: Science & Technology
3098:Popov, V. L.; Pohrt, R.; Li, Q. (September 2017).
2553:
2296:
2105:
2019:
1927:
1822:
1598:
1480:
1360:
1245:
1102:
931:
833:
689:
616:
450:
311:
2239:relates the contact angle to interfacial energy:
719:, meaning the surface energy is the same for all
2231:, the liquid does not wet the substrate at all.
865:Surface formation energy of a crystalline solid
3133:"Science friction: Adhesion of complex shapes"
2157:, the liquid partially wets the substrate. If
735:(most ceramics) this is a good approximation.
465:) of the rod remains constant, the variation (
3910:
8:
2164:, the liquid completely wets the substrate.
2672:in liquid media are in constant thermal or
2591:is the vapor pressure of the flat surface,
2199:, the liquid completely wets the substrate.
960:is the number of atoms in the surface slab.
3917:
3903:
3895:
3839:Butt, H.-J.; Graf, Kh.; Kappl, M. (2006).
2680:, as an effect of their surface energies.
2342:Wetting of high- and low-energy substrates
1533:Guggenheim model. An extended interphase (
715:This method is valid only if the solid is
573:
569:
511:
507:
386:
382:
278:
274:
3774:
3211:
3115:
2538:
2529:
2518:
2509:
2498:
2480:
2470:
2465:
2459:
2445:
2279:
2266:
2253:
2247:
2097:
2084:
2071:
2059:
2003:
1997:
1988:
1982:
1952:represent the concentration of substance
1919:
1906:
1893:
1880:
1867:
1851:
1845:
1810:
1797:
1784:
1757:
1741:
1725:
1708:
1694:
1681:
1668:
1650:
1648:
1590:
1577:
1565:
1469:
1459:
1449:
1432:
1419:
1401:
1391:
1383:
1352:
1342:
1332:
1318:
1303:
1297:
1232:
1219:
1201:
1199:
1180:
1175:
1162:
1156:
1092:
1081:
1067:
1056:
1043:
1031:
1023:
912:
896:
889:
881:
820:
807:
788:
780:
643:
635:
587:
550:
501:
492:
477:
360:
342:
289:
226:
3856:Journal of the American Chemical Society
3724:Journal of the American Chemical Society
3606:Organic Coatings: Science and Technology
3204:Contact Angle, Wettability, and Adhesion
2725:
2166:
1621:. Some examples include internal energy
1599:{\displaystyle V=V_{\alpha }+V_{\beta }}
29:
3624:Coatings Materials and Surface Coatings
2947:
1145:is the pairwise intermolecular energy.
1002:Estimation from the heat of sublimation
4537:Integrated gasification combined cycle
3566:International Journal of Pharmaceutics
3344:Analytical and Bioanalytical Chemistry
3061:The Chemical Physics of Solid Surfaces
2656:Surface modified pigments for coatings
2366:are much stronger than forces such as
2138:the surface energy of the liquid, and
66:, surfaces must be intrinsically less
4581:Radioisotope thermoelectric generator
4256:Quantum chromodynamics binding energy
2992:"How To Measure Surface Free Energy?"
2129:the surface energy of the substrate,
750:. The shape of the crystal (assuming
7:
4814:
2722:Surface energies of common materials
4838:
4723:World energy supply and consumption
3841:Physics and Chemistry of Interfaces
3017:"Surface Free Energy: Measurements"
1557:The total volume of the system is:
3496:Journal of Applied Polymer Science
3239:Journal of Applied Polymer Science
1985:
1398:
1300:
469:) of the volume is zero, that is,
25:
1625:, the number of molecules of the
4837:
4825:
4813:
4802:
4801:
1526:) separating these two volumes.
1268:corresponds to the density, and
334:is the surface area of the rod:
3145:from the original on 2021-12-12
2664:previously used, including the
746:in the surface energy leads to
574:
568:
512:
506:
387:
381:
279:
273:
54:) quantifies the disruption of
1206:
845:Calculation of surface energy
675:
660:
570:
508:
383:
275:
1:
3668:. London: Chapman & Hall.
3651:10.1016/s0300-9440(02)00048-6
3578:10.1016/s0378-5173(01)00789-x
3461:Advanced Materials Interfaces
3399:10.1126/science.275.5305.1458
3059:Woodruff, D. P., ed. (2002).
855:number of valence d-electrons
3890:Surface Energy and Adhesion
3885:What is surface free energy?
3681:Journal of Materials Science
3639:Progress in Organic Coatings
3535:10.1177/00220345990780091001
2969:10.1016/j.dental.2009.11.157
2120:is the spreading parameter,
971:is the bulk energy per atom.
3321:10.1103/physrevlett.56.2823
210:, then at equilibrium, the
4897:
3803:Journal of Applied Physics
3523:Journal of Dental Research
3508:10.1002/app.1993.070490714
3251:10.1002/app.1969.070130815
3213:10.1021/ba-1964-0043.ch001
2034:
4797:
4527:Fossil fuel power station
4189:Electric potential energy
4134:Thermodynamic temperature
4114:Thermodynamic free energy
4109:Thermodynamic equilibrium
3932:
3356:10.1007/s00216-007-1692-2
3286:10.1103/revmodphys.57.827
3266:Reviews of Modern Physics
3189:10.1103/revmodphys.81.739
3169:Reviews of Modern Physics
3117:10.1007/s40544-017-0177-3
3063:. Vol. 10. Elsevier.
2996:blog.biolinscientific.com
1537:) divides the two phases
871:density functional theory
851:density functional theory
4881:Area-specific quantities
4871:Condensed matter physics
4598:Concentrated solar power
461:Also, since the volume (
4139:Volume (thermodynamics)
4119:Thermodynamic potential
4022:Mass–energy equivalence
3664:Kinloch, A. J. (1987).
3622:Tracton, A. A. (2006).
3301:Physical Review Letters
3165:"Wetting and Spreading"
2743:Polytetrafluoroethylene
2582:of the curved surface,
2393:, plasma treatment and
2378:Modification techniques
1287:enthalpy of sublimation
987:relative surface energy
68:energetically favorable
48:interfacial free energy
4094:Quantum thermodynamics
4084:Laws of thermodynamics
3965:Conservation of energy
3843:. Weinheim: Wiley-VCH.
3473:10.1002/admi.201600404
2926:Sessile drop technique
2718:
2616:universal gas constant
2555:
2429:
2298:
2210:, high wetting occurs.
2172:
2107:
2021:
1929:
1824:
1600:
1554:
1546:
1482:
1362:
1247:
1104:
1015:
933:
835:
691:
618:
452:
313:
89:conservation of energy
35:
4211:Interatomic potential
4002:Energy transformation
3604:Wicks, Z. W. (2007).
2715:
2556:
2416:
2299:
2221:, low wetting occurs.
2170:
2108:
2022:
1930:
1825:
1601:
1552:
1532:
1508:liquids with volumes
1502:Gibbs ideal interface
1483:
1363:
1248:
1105:
1013:
934:
847:from first principles
836:
692:
619:
453:
328:Helmholtz free energy
314:
218:vanishes and we have
216:Helmholtz free energy
33:
4659:Efficient energy use
4632:Airborne wind energy
4610:Solar thermal energy
4517:Electricity delivery
4129:Thermodynamic system
4074:Irreversible process
3021:biolinscientific.com
2678:van der Waals forces
2444:
2246:
2058:
1981:
1844:
1647:
1617:, and the interface
1564:
1382:
1296:
1155:
1022:
977:is the surface area.
880:
779:
634:
476:
341:
225:
56:intermolecular bonds
4681:Energy conservation
4603:Photovoltaic system
4576:Nuclear power plant
4261:Quantum fluctuation
4124:Thermodynamic state
4099:Thermal equilibrium
3868:10.1021/ja01403a005
3815:1960JAP....31.2208G
3767:1951JOM.....3a..63U
3736:10.1021/ja01664a001
3693:1977JMatS..12..823R
3393:(5305): 1458–1460.
3313:1986PhRvL..56.2823K
3278:1985RvMP...57..827D
3181:2009RvMP...81..739B
3023:. Biolin Scientific
2998:. Biolin Scientific
2475:
2424:that increases the
2405:The Kelvin equation
2042:Spreading parameter
1496:The presence of an
1260:corresponds to the
1190:
859:coordination number
182:, is needed (where
64:solid-state physics
58:that occurs when a
52:surface free energy
18:Surface free energy
4718:Sustainable energy
4696:Energy development
4686:Energy consumption
4522:Energy engineering
3776:10.1007/BF03398958
3701:10.1007/BF00548176
3077:. Springer. 2017.
2936:Wulff Construction
2870:Potassium chloride
2719:
2702:entropic repulsion
2650:radii of curvature
2648:are the principal
2551:
2461:
2430:
2426:chemical potential
2294:
2173:
2103:
2017:
1925:
1820:
1818:
1636:, and the entropy
1596:
1555:
1547:
1492:Interfacial energy
1478:
1358:
1243:
1171:
1100:
1016:
929:
831:
756:Wulff construction
687:
614:
448:
309:
36:
4853:
4852:
4620:Solar power tower
4266:Quantum potential
4104:Thermal reservoir
4007:Energy transition
3823:10.1063/1.1735524
3749:Udin, H. (1951).
3730:(11): 2479–2485.
3434:10.1021/nn901344u
3307:(26): 2823–2826.
2931:Capillary surface
2907:
2906:
2831:Calcium carbonate
2544:
2524:
2486:
2384:plasma activation
2282:
2269:
2256:
2100:
2087:
2074:
2015:
1476:
1462:
1404:
1345:
1335:
1326:
1306:
1279:Avogadro constant
1264:of the molecule,
1240:
1226:
1222:
1209:
1188:
1178:
1098:
1084:
1075:
927:
915:
899:
796:
683:
679:
610:
600:
504:
503: is constant
307:
260:
245:
16:(Redirected from
4888:
4841:
4840:
4829:
4817:
4816:
4805:
4804:
4779:Carbon footprint
4713:Renewable energy
4554:Hydroelectricity
4544:Geothermal power
3987:Energy condition
3919:
3912:
3905:
3896:
3872:
3871:
3851:
3845:
3844:
3836:
3827:
3826:
3798:
3781:
3780:
3778:
3746:
3740:
3739:
3719:
3713:
3712:
3676:
3670:
3669:
3661:
3655:
3654:
3634:
3628:
3627:
3619:
3610:
3609:
3601:
3590:
3589:
3572:(1–2): 113–119.
3561:
3555:
3554:
3529:(9): 1554–1559.
3518:
3512:
3511:
3502:(7): 1251–1258.
3491:
3485:
3484:
3452:
3446:
3445:
3417:
3411:
3410:
3382:
3376:
3375:
3339:
3333:
3332:
3296:
3290:
3289:
3261:
3255:
3254:
3245:(8): 1741–1747.
3234:
3228:
3227:
3215:
3199:
3193:
3192:
3160:
3154:
3153:
3151:
3150:
3128:
3122:
3121:
3119:
3095:
3089:
3088:
3071:
3065:
3064:
3056:
3050:
3049:
3038:
3032:
3031:
3029:
3028:
3013:
3007:
3006:
3004:
3003:
2987:
2981:
2980:
2957:Dental Materials
2952:
2818:Lithium fluoride
2805:Calcium fluoride
2726:
2652:of the surface.
2647:
2638:
2621:
2613:
2605:
2594:
2590:
2577:
2576:
2575:
2560:
2558:
2557:
2552:
2550:
2546:
2545:
2543:
2542:
2530:
2525:
2523:
2522:
2510:
2503:
2502:
2487:
2485:
2484:
2474:
2469:
2460:
2422:Laplace pressure
2391:corona treatment
2372:hydrogen bonding
2337:
2333:
2324:
2315:
2303:
2301:
2300:
2295:
2284:
2283:
2280:
2271:
2270:
2267:
2258:
2257:
2254:
2230:
2220:
2209:
2198:
2187:
2163:
2156:
2146:
2137:
2128:
2119:
2112:
2110:
2109:
2104:
2102:
2101:
2098:
2089:
2088:
2085:
2076:
2075:
2072:
2026:
2024:
2023:
2018:
2016:
2011:
2010:
1998:
1993:
1992:
1973:
1964:, respectively.
1963:
1959:
1955:
1951:
1944:
1934:
1932:
1931:
1926:
1924:
1923:
1914:
1913:
1898:
1897:
1888:
1887:
1872:
1871:
1859:
1858:
1829:
1827:
1826:
1821:
1819:
1815:
1814:
1802:
1801:
1789:
1788:
1765:
1764:
1749:
1748:
1733:
1732:
1713:
1712:
1699:
1698:
1686:
1685:
1673:
1672:
1639:
1635:
1628:
1624:
1620:
1616:
1612:
1605:
1603:
1602:
1597:
1595:
1594:
1582:
1581:
1544:
1540:
1536:
1525:
1521:
1514:
1487:
1485:
1484:
1479:
1477:
1475:
1474:
1473:
1464:
1463:
1460:
1454:
1453:
1443:
1442:
1438:
1437:
1436:
1424:
1423:
1406:
1405:
1402:
1392:
1367:
1365:
1364:
1359:
1357:
1356:
1347:
1346:
1343:
1337:
1336:
1333:
1327:
1319:
1308:
1307:
1304:
1276:
1267:
1259:
1252:
1250:
1249:
1244:
1242:
1241:
1233:
1231:
1227:
1225:
1224:
1223:
1220:
1210:
1202:
1200:
1189:
1181:
1179:
1176:
1167:
1166:
1144:
1135:
1126:
1119:
1109:
1107:
1106:
1101:
1099:
1097:
1096:
1087:
1086:
1085:
1082:
1076:
1068:
1066:
1062:
1061:
1060:
1048:
1047:
1032:
976:
970:
959:
953:
938:
936:
935:
930:
928:
926:
918:
917:
916:
913:
901:
900:
897:
890:
840:
838:
837:
832:
830:
826:
825:
824:
812:
811:
797:
789:
725:amorphous solids
721:crystallographic
712:at equilibrium.
711:
707:
703:
696:
694:
693:
688:
681:
680:
678:
652:
644:
623:
621:
620:
615:
608:
601:
599:
588:
555:
554:
505:
502:
497:
496:
468:
464:
457:
455:
454:
449:
365:
364:
333:
325:
318:
316:
315:
310:
308:
306:
298:
290:
258:
243:
209:
205:
201:
197:
185:
181:
174:, a quantity of
173:
21:
4896:
4895:
4891:
4890:
4889:
4887:
4886:
4885:
4876:Surface science
4866:Forms of energy
4856:
4855:
4854:
4849:
4793:
4789:Waste-to-energy
4767:
4703:Energy security
4649:
4643:
4499:
4491:
4470:Natural uranium
4404:
4385:Mechanical wave
4316:Energy carriers
4310:
4150:
4079:Isolated system
3957:
3951:
3928:
3923:
3881:
3876:
3875:
3853:
3852:
3848:
3838:
3837:
3830:
3800:
3799:
3784:
3748:
3747:
3743:
3721:
3720:
3716:
3678:
3677:
3673:
3663:
3662:
3658:
3636:
3635:
3631:
3621:
3620:
3613:
3603:
3602:
3593:
3563:
3562:
3558:
3520:
3519:
3515:
3493:
3492:
3488:
3467:(17): 1600404.
3454:
3453:
3449:
3419:
3418:
3414:
3384:
3383:
3379:
3341:
3340:
3336:
3298:
3297:
3293:
3263:
3262:
3258:
3236:
3235:
3231:
3224:
3201:
3200:
3196:
3162:
3161:
3157:
3148:
3146:
3130:
3129:
3125:
3097:
3096:
3092:
3085:
3073:
3072:
3068:
3058:
3057:
3053:
3040:
3039:
3035:
3026:
3024:
3015:
3014:
3010:
3001:
2999:
2989:
2988:
2984:
2954:
2953:
2949:
2944:
2921:Surface tension
2912:
2883:Barium fluoride
2857:Sodium chloride
2844:Sodium chloride
2792:Magnesium oxide
2736:
2735:Surface energy
2724:
2674:Brownian motion
2658:
2646:
2640:
2637:
2631:
2619:
2611:
2610:of the liquid,
2604:
2600:
2597:surface tension
2592:
2589:
2583:
2574:
2571:
2570:
2569:
2565:
2534:
2514:
2508:
2504:
2494:
2476:
2442:
2441:
2434:Kelvin equation
2407:
2380:
2344:
2335:
2332:
2326:
2323:
2317:
2314:
2308:
2275:
2262:
2249:
2244:
2243:
2225:
2214:
2203:
2193:
2185:
2178:
2158:
2151:
2145:
2139:
2136:
2130:
2127:
2121:
2117:
2093:
2080:
2067:
2056:
2055:
2044:
2039:
2033:
1999:
1984:
1979:
1978:
1972:
1968:
1961:
1957:
1953:
1950:
1946:
1943:
1939:
1915:
1902:
1889:
1876:
1863:
1847:
1842:
1841:
1817:
1816:
1806:
1793:
1780:
1773:
1767:
1766:
1753:
1737:
1721:
1714:
1704:
1701:
1700:
1690:
1677:
1664:
1657:
1645:
1644:
1637:
1634:
1630:
1626:
1622:
1618:
1614:
1610:
1586:
1573:
1562:
1561:
1542:
1538:
1534:
1523:
1520:
1516:
1513:
1509:
1494:
1465:
1455:
1445:
1444:
1428:
1415:
1414:
1410:
1397:
1393:
1380:
1379:
1348:
1338:
1328:
1299:
1294:
1293:
1275:
1269:
1265:
1257:
1215:
1211:
1195:
1194:
1158:
1153:
1152:
1143:
1137:
1134:
1128:
1125:
1121:
1118:
1114:
1088:
1077:
1052:
1039:
1038:
1034:
1033:
1020:
1019:
1007:quantified by:
1004:
974:
969:
963:
957:
952:
946:
919:
908:
892:
891:
878:
877:
867:
816:
803:
802:
798:
777:
776:
769:
764:
709:
705:
701:
653:
645:
632:
631:
592:
546:
488:
474:
473:
466:
462:
356:
339:
338:
331:
323:
299:
291:
223:
222:
207:
203:
199:
195:
183:
179:
171:
164:
144:surface tension
132:
127:
122:
62:is created. In
40:surface science
28:
23:
22:
15:
12:
11:
5:
4894:
4892:
4884:
4883:
4878:
4873:
4868:
4858:
4857:
4851:
4850:
4848:
4847:
4835:
4823:
4811:
4798:
4795:
4794:
4792:
4791:
4786:
4784:Jevons paradox
4781:
4775:
4773:
4769:
4768:
4766:
4765:
4760:
4755:
4750:
4745:
4740:
4735:
4730:
4725:
4720:
4715:
4710:
4708:Energy storage
4705:
4700:
4699:
4698:
4688:
4683:
4678:
4677:
4676:
4671:
4666:
4655:
4653:
4645:
4644:
4642:
4641:
4640:
4639:
4634:
4624:
4623:
4622:
4617:
4607:
4606:
4605:
4600:
4590:
4585:
4584:
4583:
4578:
4568:
4567:
4566:
4561:
4556:
4546:
4541:
4540:
4539:
4534:
4524:
4519:
4514:
4512:Electric power
4509:
4503:
4501:
4493:
4492:
4490:
4489:
4484:
4479:
4474:
4473:
4472:
4462:
4457:
4452:
4447:
4442:
4441:
4440:
4435:
4430:
4420:
4414:
4412:
4410:Primary energy
4406:
4405:
4403:
4402:
4397:
4392:
4387:
4382:
4381:
4380:
4370:
4369:
4368:
4358:
4357:
4356:
4351:
4341:
4336:
4331:
4326:
4320:
4318:
4312:
4311:
4309:
4308:
4303:
4298:
4293:
4288:
4283:
4278:
4273:
4268:
4263:
4258:
4253:
4248:
4243:
4238:
4233:
4228:
4223:
4218:
4213:
4208:
4207:
4206:
4196:
4191:
4186:
4181:
4176:
4171:
4170:
4169:
4158:
4156:
4152:
4151:
4149:
4148:
4147:
4146:
4141:
4136:
4131:
4126:
4121:
4116:
4111:
4106:
4101:
4096:
4091:
4086:
4081:
4076:
4071:
4066:
4061:
4056:
4051:
4046:
4044:Entropic force
4041:
4034:Thermodynamics
4031:
4026:
4025:
4024:
4019:
4009:
4004:
3999:
3994:
3989:
3984:
3983:
3982:
3972:
3967:
3961:
3959:
3953:
3952:
3950:
3949:
3944:
3939:
3933:
3930:
3929:
3924:
3922:
3921:
3914:
3907:
3899:
3893:
3892:
3887:
3880:
3879:External links
3877:
3874:
3873:
3846:
3828:
3782:
3741:
3714:
3687:(4): 823–824.
3671:
3656:
3645:(2–3): 83–93.
3629:
3611:
3591:
3556:
3513:
3486:
3447:
3428:(2): 771–780.
3412:
3377:
3334:
3291:
3272:(3): 827–863.
3256:
3229:
3222:
3194:
3175:(2): 739–805.
3155:
3123:
3110:(3): 308–325.
3090:
3083:
3066:
3051:
3033:
3008:
2982:
2963:(2): e11–e16.
2946:
2945:
2943:
2940:
2939:
2938:
2933:
2928:
2923:
2918:
2911:
2908:
2905:
2904:
2901:
2898:
2892:
2891:
2888:
2885:
2879:
2878:
2875:
2872:
2866:
2865:
2862:
2859:
2853:
2852:
2849:
2846:
2840:
2839:
2836:
2833:
2827:
2826:
2823:
2820:
2814:
2813:
2810:
2807:
2801:
2800:
2797:
2794:
2788:
2787:
2784:
2782:
2776:
2775:
2772:
2770:
2764:
2763:
2760:
2758:
2752:
2751:
2748:
2746:
2739:
2738:
2733:
2730:
2723:
2720:
2657:
2654:
2644:
2635:
2602:
2587:
2580:vapor pressure
2572:
2562:
2561:
2549:
2541:
2537:
2533:
2528:
2521:
2517:
2513:
2507:
2501:
2497:
2493:
2490:
2483:
2479:
2473:
2468:
2464:
2458:
2455:
2452:
2449:
2418:Vapor pressure
2406:
2403:
2379:
2376:
2364:metallic bonds
2343:
2340:
2330:
2321:
2312:
2305:
2304:
2293:
2290:
2287:
2278:
2274:
2265:
2261:
2252:
2237:Young equation
2233:
2232:
2222:
2211:
2200:
2177:
2174:
2143:
2134:
2125:
2114:
2113:
2096:
2092:
2083:
2079:
2070:
2066:
2063:
2043:
2040:
2035:Main article:
2032:
2029:
2028:
2027:
2014:
2009:
2006:
2002:
1996:
1991:
1987:
1970:
1956:in bulk phase
1948:
1941:
1936:
1935:
1922:
1918:
1912:
1909:
1905:
1901:
1896:
1892:
1886:
1883:
1879:
1875:
1870:
1866:
1862:
1857:
1854:
1850:
1831:
1830:
1813:
1809:
1805:
1800:
1796:
1792:
1787:
1783:
1779:
1776:
1774:
1772:
1769:
1768:
1763:
1760:
1756:
1752:
1747:
1744:
1740:
1736:
1731:
1728:
1724:
1720:
1717:
1715:
1711:
1707:
1703:
1702:
1697:
1693:
1689:
1684:
1680:
1676:
1671:
1667:
1663:
1660:
1658:
1656:
1653:
1652:
1632:
1607:
1606:
1593:
1589:
1585:
1580:
1576:
1572:
1569:
1518:
1511:
1493:
1490:
1489:
1488:
1472:
1468:
1458:
1452:
1448:
1441:
1435:
1431:
1427:
1422:
1418:
1413:
1409:
1400:
1396:
1390:
1387:
1369:
1368:
1355:
1351:
1341:
1331:
1325:
1322:
1317:
1314:
1311:
1302:
1273:
1254:
1253:
1239:
1236:
1230:
1218:
1214:
1208:
1205:
1198:
1193:
1187:
1184:
1174:
1170:
1165:
1161:
1141:
1132:
1123:
1116:
1111:
1110:
1095:
1091:
1080:
1074:
1071:
1065:
1059:
1055:
1051:
1046:
1042:
1037:
1030:
1027:
1003:
1000:
979:
978:
972:
967:
961:
955:
950:
940:
939:
925:
922:
911:
907:
904:
895:
888:
885:
866:
863:
849:(for example,
843:
842:
829:
823:
819:
815:
810:
806:
801:
795:
792:
787:
784:
768:
767:Deformed solid
765:
763:
760:
698:
697:
686:
677:
674:
671:
668:
665:
662:
659:
656:
651:
648:
642:
639:
625:
624:
613:
607:
604:
598:
595:
591:
586:
583:
580:
577:
572:
567:
564:
561:
558:
553:
549:
545:
542:
539:
536:
533:
530:
527:
524:
521:
518:
515:
510:
500:
495:
491:
487:
484:
481:
459:
458:
447:
444:
441:
438:
435:
432:
429:
426:
423:
420:
417:
414:
411:
408:
405:
402:
399:
396:
393:
390:
385:
380:
377:
374:
371:
368:
363:
359:
355:
352:
349:
346:
320:
319:
305:
302:
297:
294:
288:
285:
282:
277:
272:
269:
266:
263:
257:
254:
251:
248:
242:
239:
236:
233:
230:
163:
160:
131:
128:
126:
123:
121:
118:
44:surface energy
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4893:
4882:
4879:
4877:
4874:
4872:
4869:
4867:
4864:
4863:
4861:
4846:
4845:
4836:
4834:
4833:
4828:
4824:
4822:
4821:
4812:
4810:
4809:
4800:
4799:
4796:
4790:
4787:
4785:
4782:
4780:
4777:
4776:
4774:
4770:
4764:
4763:United States
4761:
4759:
4758:South America
4756:
4754:
4751:
4749:
4746:
4744:
4741:
4739:
4736:
4734:
4731:
4729:
4726:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4697:
4694:
4693:
4692:
4691:Energy policy
4689:
4687:
4684:
4682:
4679:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4660:
4657:
4656:
4654:
4652:
4646:
4638:
4635:
4633:
4630:
4629:
4628:
4625:
4621:
4618:
4616:
4615:Solar furnace
4613:
4612:
4611:
4608:
4604:
4601:
4599:
4596:
4595:
4594:
4591:
4589:
4586:
4582:
4579:
4577:
4574:
4573:
4572:
4571:Nuclear power
4569:
4565:
4562:
4560:
4557:
4555:
4552:
4551:
4550:
4547:
4545:
4542:
4538:
4535:
4533:
4530:
4529:
4528:
4525:
4523:
4520:
4518:
4515:
4513:
4510:
4508:
4505:
4504:
4502:
4498:
4497:Energy system
4494:
4488:
4485:
4483:
4480:
4478:
4475:
4471:
4468:
4467:
4466:
4463:
4461:
4458:
4456:
4453:
4451:
4450:Gravitational
4448:
4446:
4443:
4439:
4436:
4434:
4431:
4429:
4426:
4425:
4424:
4421:
4419:
4416:
4415:
4413:
4411:
4407:
4401:
4398:
4396:
4393:
4391:
4388:
4386:
4383:
4379:
4378:Hydrogen fuel
4376:
4375:
4374:
4371:
4367:
4364:
4363:
4362:
4359:
4355:
4352:
4350:
4347:
4346:
4345:
4342:
4340:
4337:
4335:
4332:
4330:
4327:
4325:
4322:
4321:
4319:
4317:
4313:
4307:
4304:
4302:
4299:
4297:
4294:
4292:
4289:
4287:
4284:
4282:
4279:
4277:
4274:
4272:
4269:
4267:
4264:
4262:
4259:
4257:
4254:
4252:
4249:
4247:
4244:
4242:
4239:
4237:
4234:
4232:
4229:
4227:
4224:
4222:
4219:
4217:
4214:
4212:
4209:
4205:
4202:
4201:
4200:
4199:Gravitational
4197:
4195:
4192:
4190:
4187:
4185:
4182:
4180:
4177:
4175:
4172:
4168:
4165:
4164:
4163:
4160:
4159:
4157:
4153:
4145:
4142:
4140:
4137:
4135:
4132:
4130:
4127:
4125:
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4100:
4097:
4095:
4092:
4090:
4087:
4085:
4082:
4080:
4077:
4075:
4072:
4070:
4069:Heat transfer
4067:
4065:
4064:Heat capacity
4062:
4060:
4057:
4055:
4052:
4050:
4047:
4045:
4042:
4040:
4037:
4036:
4035:
4032:
4030:
4027:
4023:
4020:
4018:
4017:Negative mass
4015:
4014:
4013:
4010:
4008:
4005:
4003:
4000:
3998:
3997:Energy system
3995:
3993:
3990:
3988:
3985:
3981:
3978:
3977:
3976:
3973:
3971:
3968:
3966:
3963:
3962:
3960:
3954:
3948:
3945:
3943:
3940:
3938:
3935:
3934:
3931:
3927:
3920:
3915:
3913:
3908:
3906:
3901:
3900:
3897:
3891:
3888:
3886:
3883:
3882:
3878:
3869:
3865:
3861:
3857:
3850:
3847:
3842:
3835:
3833:
3829:
3824:
3820:
3816:
3812:
3808:
3804:
3797:
3795:
3793:
3791:
3789:
3787:
3783:
3777:
3772:
3768:
3764:
3760:
3756:
3752:
3745:
3742:
3737:
3733:
3729:
3725:
3718:
3715:
3710:
3706:
3702:
3698:
3694:
3690:
3686:
3682:
3675:
3672:
3667:
3660:
3657:
3652:
3648:
3644:
3640:
3633:
3630:
3625:
3618:
3616:
3612:
3607:
3600:
3598:
3596:
3592:
3587:
3583:
3579:
3575:
3571:
3567:
3560:
3557:
3552:
3548:
3544:
3540:
3536:
3532:
3528:
3524:
3517:
3514:
3509:
3505:
3501:
3497:
3490:
3487:
3482:
3478:
3474:
3470:
3466:
3462:
3458:
3451:
3448:
3443:
3439:
3435:
3431:
3427:
3423:
3416:
3413:
3408:
3404:
3400:
3396:
3392:
3388:
3381:
3378:
3373:
3369:
3365:
3361:
3357:
3353:
3350:(1): 89–111.
3349:
3345:
3338:
3335:
3330:
3326:
3322:
3318:
3314:
3310:
3306:
3302:
3295:
3292:
3287:
3283:
3279:
3275:
3271:
3267:
3260:
3257:
3252:
3248:
3244:
3240:
3233:
3230:
3225:
3223:0-8412-0044-0
3219:
3214:
3209:
3205:
3198:
3195:
3190:
3186:
3182:
3178:
3174:
3170:
3166:
3159:
3156:
3144:
3140:
3139:
3134:
3127:
3124:
3118:
3113:
3109:
3105:
3101:
3094:
3091:
3086:
3084:9783662530801
3080:
3076:
3070:
3067:
3062:
3055:
3052:
3047:
3043:
3037:
3034:
3022:
3018:
3012:
3009:
2997:
2993:
2986:
2983:
2978:
2974:
2970:
2966:
2962:
2958:
2951:
2948:
2941:
2937:
2934:
2932:
2929:
2927:
2924:
2922:
2919:
2917:
2916:Contact angle
2914:
2913:
2909:
2902:
2899:
2897:
2894:
2893:
2889:
2886:
2884:
2881:
2880:
2876:
2873:
2871:
2868:
2867:
2863:
2860:
2858:
2855:
2854:
2850:
2847:
2845:
2842:
2841:
2837:
2835:(1010) plane
2834:
2832:
2829:
2828:
2824:
2821:
2819:
2816:
2815:
2811:
2808:
2806:
2803:
2802:
2798:
2795:
2793:
2790:
2789:
2785:
2783:
2781:
2778:
2777:
2773:
2771:
2769:
2766:
2765:
2761:
2759:
2757:
2754:
2753:
2749:
2747:
2744:
2741:
2740:
2734:
2731:
2728:
2727:
2721:
2714:
2710:
2708:
2703:
2699:
2693:
2691:
2687:
2681:
2679:
2675:
2669:
2667:
2662:
2655:
2653:
2651:
2643:
2634:
2629:
2625:
2617:
2609:
2598:
2586:
2581:
2568:
2547:
2539:
2535:
2531:
2526:
2519:
2515:
2511:
2505:
2499:
2495:
2491:
2488:
2481:
2477:
2471:
2466:
2462:
2456:
2453:
2450:
2447:
2440:
2439:
2438:
2435:
2427:
2423:
2419:
2415:
2411:
2404:
2402:
2400:
2396:
2392:
2387:
2385:
2377:
2375:
2373:
2369:
2368:van der Waals
2365:
2361:
2357:
2353:
2349:
2341:
2339:
2329:
2320:
2311:
2291:
2288:
2285:
2276:
2272:
2263:
2259:
2250:
2242:
2241:
2240:
2238:
2228:
2223:
2218:
2212:
2207:
2201:
2196:
2191:
2190:
2189:
2183:
2182:contact angle
2176:Contact angle
2175:
2169:
2165:
2161:
2154:
2148:
2142:
2133:
2124:
2094:
2090:
2081:
2077:
2068:
2064:
2061:
2054:
2053:
2052:
2050:
2041:
2038:
2030:
2012:
2007:
2004:
2000:
1994:
1989:
1977:
1976:
1975:
1965:
1920:
1916:
1910:
1907:
1903:
1899:
1894:
1890:
1884:
1881:
1877:
1873:
1868:
1864:
1860:
1855:
1852:
1848:
1840:
1839:
1838:
1836:
1835:concentration
1811:
1807:
1803:
1798:
1794:
1790:
1785:
1781:
1777:
1775:
1770:
1761:
1758:
1754:
1750:
1745:
1742:
1738:
1734:
1729:
1726:
1722:
1718:
1716:
1709:
1705:
1695:
1691:
1687:
1682:
1678:
1674:
1669:
1665:
1661:
1659:
1654:
1643:
1642:
1641:
1629:th substance
1613:, bulk phase
1591:
1587:
1583:
1578:
1574:
1570:
1567:
1560:
1559:
1558:
1551:
1531:
1527:
1507:
1503:
1499:
1491:
1470:
1466:
1456:
1450:
1446:
1439:
1433:
1429:
1425:
1420:
1416:
1411:
1407:
1394:
1388:
1385:
1378:
1377:
1376:
1373:
1353:
1349:
1339:
1329:
1323:
1320:
1315:
1312:
1309:
1292:
1291:
1290:
1288:
1282:
1280:
1272:
1263:
1237:
1234:
1228:
1216:
1212:
1203:
1196:
1191:
1185:
1182:
1172:
1168:
1163:
1159:
1151:
1150:
1149:
1146:
1140:
1131:
1093:
1089:
1078:
1072:
1069:
1063:
1057:
1053:
1049:
1044:
1040:
1035:
1028:
1025:
1018:
1017:
1012:
1008:
1001:
999:
997:
993:
992:acrylic glass
988:
983:
973:
966:
962:
956:
949:
945:
944:
943:
923:
920:
909:
905:
902:
893:
886:
883:
876:
875:
874:
872:
864:
862:
860:
856:
852:
848:
827:
821:
817:
813:
808:
804:
799:
793:
790:
785:
782:
775:
774:
773:
766:
761:
759:
757:
753:
749:
745:
741:
736:
734:
730:
726:
722:
718:
713:
684:
672:
669:
666:
663:
657:
654:
649:
646:
640:
637:
630:
629:
628:
611:
605:
602:
596:
593:
589:
584:
581:
578:
575:
565:
562:
559:
556:
551:
547:
543:
540:
537:
534:
531:
528:
525:
522:
519:
516:
513:
498:
493:
489:
485:
482:
479:
472:
471:
470:
445:
442:
439:
436:
433:
430:
427:
424:
421:
418:
415:
412:
409:
406:
403:
400:
397:
394:
391:
388:
378:
375:
372:
369:
366:
361:
357:
353:
350:
347:
344:
337:
336:
335:
329:
303:
300:
295:
292:
286:
283:
280:
270:
267:
264:
261:
255:
252:
249:
246:
240:
237:
234:
231:
228:
221:
220:
219:
217:
214:of the total
213:
193:
188:
177:
169:
162:Other methods
161:
159:
155:
151:
147:
145:
141:
140:diiodomethane
137:
136:contact angle
130:Contact angle
129:
124:
119:
117:
115:
111:
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4588:Oil refinery
4532:Cogeneration
4465:Nuclear fuel
4290:
4271:Quintessence
4059:Free entropy
3992:Energy level
3956:Fundamental
3859:
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3809:(12): 2208.
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2887:(111) plane
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2861:(110) plane
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2809:(111) plane
2796:(100) plane
2732:Orientation
2707:flocculation
2694:
2690:flocculation
2682:
2670:
2659:
2641:
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2608:molar volume
2584:
2566:
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102:cleaved bond
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4844:WikiProject
4664:Agriculture
4593:Solar power
4559:Tidal power
4433:Natural gas
4423:Fossil fuel
4366:Latent heat
4334:Electricity
2990:Laurén, S.
2686:orange peel
2624:temperature
762:Calculation
752:equilibrium
202:and length
125:Measurement
110:passivation
73:sublimation
4860:Categories
4627:Wind power
4549:Hydropower
4500:components
4455:Hydropower
4445:Geothermal
4395:Sound wave
4306:Zero-point
4236:Mechanical
4221:Ionization
4194:Electrical
4089:Negentropy
3970:Energetics
3862:(4): 925.
3149:2018-01-28
3027:2019-12-31
3002:2019-12-31
2942:References
2666:adsorption
1506:immiscible
1262:molar mass
857:, and the
744:anisotropy
120:Assessment
114:adsorption
85:reversibly
4738:Australia
4674:Transport
4669:Computing
4637:Wind farm
4564:Wave farm
4438:Petroleum
4418:Bioenergy
4390:Radiation
4329:Capacitor
4251:Potential
3761:(1): 63.
3709:136812418
3481:138114323
3407:136525970
2729:Material
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2277:γ
2264:γ
2251:γ
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2095:γ
2091:−
2082:γ
2078:−
2069:γ
2008:α
1986:Γ
1921:β
1911:β
1900:−
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1885:α
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1856:σ
1812:σ
1799:β
1786:α
1762:σ
1746:β
1730:α
1696:σ
1683:β
1670:α
1592:β
1579:α
1498:interface
1471:β
1434:β
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1421:σ
1399:Δ
1395:−
1389:≈
1386:γ
1316:−
1301:Δ
1213:ρ
1207:¯
1058:β
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903:−
884:γ
814:−
783:γ
740:gemstones
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717:isotropic
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384:⟹
373:π
354:π
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293:δ
281:γ
276:⟹
262:δ
256:γ
247:δ
238:−
229:δ
212:variation
4808:Category
4373:Hydrogen
4339:Enthalpy
4241:Negative
4231:Magnetic
4216:Internal
4174:Chemical
4039:Enthalpy
3958:concepts
3586:11564545
3543:10512390
3442:20121228
3422:ACS Nano
3372:13813183
3364:17989961
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2661:Pigments
2356:Covalent
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1177:molecule
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168:membrane
94:cohesion
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4507:Biomass
4477:Radiant
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4226:Kinetic
4204:Binding
4184:Elastic
4167:Nuclear
4162:Binding
4049:Entropy
3947:Outline
3937:History
3811:Bibcode
3763:Bibcode
3689:Bibcode
3551:5807073
3387:Science
3309:Bibcode
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3177:Bibcode
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2737:(mJ/m)
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2031:Wetting
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326:is the
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4753:Mexico
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