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Surface energy of solids

  • Jacob J. Bikerman
Conference paper
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 77)

Abstract

At least five conclusions may be formulated after perusing this review.
  1. 1.

    No method so far suggested for measuring the surface energy or surface tension of solids is satisfactory.

     
  2. 2.

    This failure may be caused, above all, by the fact that solids, contrary to liquids, cannot alter their shape without changing the strain energy in their volumes. The changes in strain energy are so much greater than those in surface energy that the latter remain unrecognized.

     
  3. 3.

    Solids possess an energy unknown in typical liquids. This cuticular energy exists because the surface region of innumerable solids has a chemical composition, a frequency of lattice defects, and so on, different from those in the bulk.

     
  4. 4.

    Small solid particles obtained by cooling of vapors, by grinding, or many other methods, usually have a less perfect lattice and more impurity than have bigger crystals of nominally identical composition. Hence, the cuticular energy of the former exceeds that of the latter.

     
  5. 5.

    Cuticular energy implies no tendency of the surface to contract, i.e., no surface tension. The theoretical calculations of the difference in energy between a broken and an unbroken crystal, if correct, afford a quantity which is related to cuticular energy and, like this, causes no contractile tendency.

     

Keywords

Surface Tension Contact Angle Surface Energy Capillary Pressure Rupture Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols

A

Surface area; a constant

Am

Area of surface or interface per molecule

A, As, Asl

Areas of vapor-liquid, vapor-solid, and liquid-solid interfaces

A1

Combined area of grain boundaries

A0, A1

Surface areas of a large and a minute crystal

A1, A2, A3

Areas of different crystal faces

a

The longer half-axis of an ellipse; lattice parameter

B

A constant

b

The shorter half-axis of an ellipse

C, C1, C2

Solubilities

C.E.

Cuticular energy

c

Depth or half-length of scratch

D

Grain diameter; diffusion coefficient

E

Modulus of elasticity; intensity of electrostatic field

E0

Internal energy of a bar

E1

Internal energy of a broken bar

e

Charge of an electron

F

Helmholtz free energy

Fo

Free osmotic energy

Fs

Free surface energy

f

Force; number depending on crystal structure

G

Shear modulus; arbitrary constant; temperature gradient

H

Amount of heat evolved

h

Planck's constant; half-thickness or thickness of a slice or a ribbon; depth of scratch

h0

Initial depth of scratch

K

Modulus of compressibility; proportionality constant

k

Boltzmann's constant; coordination number of atoms in bulk; compressibility

ks, kv

Number of atoms in two-dimensional and three-dimensional unit cells

Δk

Number of broken bonds per atom

L

Length; thickness of a crystal

Ll, Ls

Heat of vaporization or sublimation

l

Length; length of a “roof”; variable length of a filament

l0

Initial length of a filament

l1, l2

Edges of two cubes

M

Molecular weight; atomic mass

MW

Molecular weight

m

Mass of an atom; mass of hydrogen atom; mass

N

Number of atoms in unit cell; Avogadro number

n

Number of grain boundaries in a wire; number of molecules in unit volume

n+, n

Number of cations or anions on unit area

P

Gas pressure

Pc

Capillary pressure

Po

Vapor pressure above a plane surface

P1, P2

Pressure in gas, in liquid

Q

Heat content

Qo, Qp, Q

Heat of solution of large and powdered solids, and solids with zero surface

q

Number depending on crystal structure; surface density of electric charge

q0, q1

Heat of solution of unit mass

R

Radius of curvature; gas constant

R1, R2

The principal radii of curvature

R

Distance at which deformation becomes negligible

R

Radius of wires; distance from an atom or ion; cube root of molecular volume; radius of a void

r0

Radius at the bottom of a groove; radius at zero time

r1, r2

Radius of wire before and after elongation

S. E.

Strain energy

T

Absolute temperature

Tb, Tm

Boiling and melting points

Tl

Melting point of plate of thickness l.

Tmr

Melting point of drop of radius r

Tt

Temperature of treatment

t

Time

U

Interatomic potential

Ul, Us

Total surface energy of a liquid, a solid

u

Height of a ridge point

u1, u2

Displacement of neighboring atoms

V

Volume of unit cell; specific volume of a liquid; volume; molecular volume

V1, V2

Gas and liquid volumes

W

Load; breaking load

W0

Equilibrium load on a filament

Ww

Breaking load of wires

W

Work of extending a rod

Wf

Fracture energy

Wm

Work spent on macroscopic deformation

w

Width; distance between two ridges

x

Variable depth of crack

Y

Plate thickness

Z

Valency of an ion; effective number of electrons per ion

α

Angle on a crystal surface; numerical constant; an angle

β

Contact angle at the edge of a solid

γ

Surface tension of a liquid

γc

“Critical surface tension”

γs

Specific surface energy or surface tension of a solid

γs*

Specific free energy of an interface between UC and U vapor

γsl

Specific energy or tension of a liquid-solid interface

γsv

Surface tension of a solid in a foreign vapor

γ1

Surface tension of a grain boundary

γ12, γ13, γ23

Tensions along boundaries between fluids 1 and 2, 1 and 3, and 2 and 3

“γ”

Specific fracture energy

Δ

Thickness of a line on which facts

δ

Thickness of surface layer; an angle

0

Maximum strain

η

Viscosity

θ

Contact angle

θ0

The characteristic (Debye) temperature

λ

Wave length of disturbances; heat of melting

λ1; λs

Internal heat of vaporization, sublimation

ν

Number of free valence electrons per atom; Poisson's ratio

ξ

Cohesion of a solid

ρ1, ρ3

Density of a solid

ρ1, ρ2

Density of a gas, a liquid

σ0

Average stress

σm

Local stress

τ

Thickness of surface layer

ϕ

Potential energy of a crystal

ϕ

Work of removing an atom from its neighbor; work function; half the dihedral angle in a liquid medium; electric potential

ϕ1

Energy of valency electrons at the Fermi level

ψ

Half the dihedral angle in a gas

ψ*

Dihedral angle in a foreign vapor

Ω

Volume of a molecule or atom

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Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jacob J. Bikerman
    • 1
  1. 1.Dept. of Chemical EngineeringCase Western Reserve UniversityClevelandUSA

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