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Critical surface tension (Zisman)

Pronunciation: /ˈkrɪtɪkəl ˈsɜːrfɪs ˈtɛnʃən, ˈzɪzmən/

Critical surface tension, γc, is the surface tension a liquid would need to just spread completely on a given solid. It is found with a Zisman plot: cos θ for a series of liquids is plotted against their surface tension and extrapolated to cos θ = 1.

Also called

Zisman critical surface tension γc Zisman plot method

Related terms

Surface free energy (SFE) van Oss-Chaudhury-Good method OWRK method

Topics

Surface energy Wetting Zisman plot
Book a 15 minute demo Read the surface energy measurement guide

At a glance

What critical surface tension tells you, and what it does not.

What it is

W. A. Zisman and coworkers found in the 1950s that, for a series of liquids on one low energy solid, cos θ falls roughly in a straight line as liquid surface tension rises.

  • Extrapolate the line to cos θ = 1 (θ = 0°)
  • The surface tension there is γc
  • Liquids with γL below γc spread; liquids above it form a finite angle

Worked example

Two points from a series on a hypothetical fluoropolymer, 20 °C: hexadecane (27.5 mN/m) at 40°, diiodomethane (50.8 mN/m) at 80°.

  • cos 40° = 0.7660; cos 80° = 0.1736
  • Slope = (0.7660 − 0.1736) / (50.8 − 27.5) = 0.5924 / 23.3 = 0.0254 per mN/m
  • γc = 27.5 − (1 − 0.7660) / 0.0254 = 27.5 − 9.2 = 18.3 mN/m

A real Zisman plot uses five or more liquids, not two.

Expert view

“Place a drop and just read it and you get an apparent angle: a value somewhere between advancing and receding that isn't much use. Zisman settled that in the fifties.”

Dr. Alidad Amirfazli, Co-founder and Scientific Advisor, Droplet Lab

What the terms mean

How a liquid behaves relative to the critical surface tension of a solid.

γL < γc

The liquid spreads completely and no finite contact angle forms. This is why low tension oils and solvents wet most plastics.

γL = γc

The threshold of complete wetting, cos θ = 1. This is the point the Zisman plot extrapolates to.

γL > γc

The liquid forms a finite contact angle, and the angle grows as γL rises further above γc. Water on PTFE is an extreme case.

Liquid values used across our model pages, 20 °C: hexadecane about 27.5 mN/m, diiodomethane 50.8 mN/m, water 72.8 mN/m.

γc Critical surface tension of the solid, mN/m
γL Surface tension of a test liquid, mN/m
θ Contact angle of that liquid on the solid, degrees (advancing angle preferred)
b Slope of the Zisman line, per mN/m

Key equations

The Zisman line and how γc is read from it.

Equation: cos θ = 1 − b (γL − γc)

Variable legend:

  • θ: contact angle of each liquid (°)
  • γL: liquid surface tension (mN/m)
  • γc: critical surface tension (mN/m)
  • b: slope of the line (per mN/m)

Interpretation: Each liquid gives one point. The line through the points crosses cos θ = 1 at γL = γc.

When to use: Use it for low energy solids such as polymers and fluorinated coatings with a series of similar liquids.

Assumptions:

  • The points fall on a straight line
  • Liquids do not dissolve, swell or react with the solid

Common mistakes:

  • Fitting a straight line through curved data from polar liquids
  • Extrapolating far beyond the measured range

Equation: γc = γL1 − (1 − cos θ1) / b

Variable legend:

  • b = (cos θ1 − cos θ2) / (γL2 − γL1)
  • Subscripts 1 and 2: the lower and higher tension liquids

Interpretation: The same straight line written for hand calculation. Software fits all points by least squares instead.

When to use: Use it to check a fitted result or for a quick estimate.

Assumptions:

  • Same as the Zisman relation

Common mistakes:

  • Reporting a two point estimate as if it were a full Zisman plot

How to read it

What a γc value means and how it relates to surface energy.

γc is close to, but not the same as, the surface free energy of the solid. It is a wetting threshold that depends on which liquids you use. Our note on reproducible surface energy calculation from contact angles explains why the liquid set must be fixed and reported, and our article on surface tension vs surface energy untangles the two terms.

Reading a Zisman result

If you see It usually means Check next
γc around 18 to 20 mN/m A fluorinated surface similar to PTFE Whether a release or nonstick coating is intact
γc around 31 mN/m A polyolefin surface such as polyethylene Whether treatment is needed before printing
Points curve instead of lying on a line Polar or hydrogen bonding liquids in the series Use a homologous series, or a component model
γc changes when you change the liquid series γc is a property of solid and liquid set together Report the liquids with the value

Common misconceptions

Where critical surface tension is most often misread.

γc is the surface free energy of the solid

It is an empirical wetting threshold, usually a little below the surface free energy found by component models. Compare γc only with other γc values. Reference tables such as our surface free energy of common polymers and substrates state which method each value comes from.

Any set of liquids gives the same answer

Polar liquids such as water and glycols often bend the plot away from a straight line, and the extrapolated γc shifts. Zisman got his cleanest lines with homologous series such as the alkanes. For polar surfaces, a multi liquid model like those in experiment 6 on surface free energy with multiple liquids tells you more.

Dyne pens and Zisman plots measure the same thing

They share the idea of a wetting threshold, but a dyne ink test reads whether a liquid film breaks up, not a contact angle. Contact angle instruments report angle based values instead, which you can turn into surface energy with our surface free energy calculator. Expect related but not identical numbers.

γc only matters for plastics

It is most reliable on low energy solids, but the threshold idea applies wherever you need to know which liquids will spread. On glass and oxides, as in a fused silica surface energy case study, most liquids spread, so other methods are more informative.

Related terms

Where critical surface tension sits among surface energy ideas.

Broader term

  • Surface free energy (SFE)
  • Surface free energy models

Related terms

  • Wetting tension
  • Contact angle
  • Equation of State (SFE model)

Often confused with

  • Surface free energy (SFE)
  • OWRK method
  • van Oss-Chaudhury-Good method

FAQ

Short answers to the questions people ask most about critical surface tension.

What is a Zisman plot?

A graph of cos θ against liquid surface tension for a series of liquids on one solid. For many low energy solids the points lie close to a straight line. Extending that line to cos θ = 1 gives the critical surface tension γc. It is named after W. A. Zisman, who developed it with Fox in the 1950s.

What is the critical surface tension of PTFE?

About 18 mN/m, from Fox and Zisman's original work with alkanes and other liquids, and commonly quoted in the range 18 to 20 mN/m. Any liquid with a lower surface tension, such as many fluorinated solvents, will spread on PTFE. Water, at 72.8 mN/m, sits far above it and beads up.

Is critical surface tension the same as surface energy?

No. γc is a wetting threshold read from a plot, while surface free energy is a thermodynamic property found with a model such as OWRK. For nonpolar solids the two are often close. For polar solids they can differ widely, and γc also depends on which liquids were used.

References

Primary sources and further reading.

1. Fox, H. W., and Zisman, W. A. (1950). The spreading of liquids on low energy surfaces. I. Polytetrafluoroethylene. Journal of Colloid Science, 5(6), 514 to 531. https://doi.org/10.1016/0095-8522(50)90044-4
2. Zisman, W. A. (1964). Relation of the equilibrium contact angle to liquid and solid constitution. In Contact Angle, Wettability, and Adhesion, Advances in Chemistry 43, American Chemical Society, 1 to 51. https://doi.org/10.1021/ba-1964-0043.ch001
3. Kwok, D. Y., and Neumann, A. W. (1999). Contact angle measurement and contact angle interpretation. Advances in Colloid and Interface Science, 81(3), 167 to 249. https://doi.org/10.1016/S0001-8686(98)00087-6
4. Surface energy measurement guide
5. Surface free energy (SFE)
6. OWRK method
7. van Oss-Chaudhury-Good method