Effect of Temperature and Pressure on Surface Tension of Liquids - Surface and Colloid Chemistry: Principles and Applications - page 234

Further, extrapolation of γ to zero surface tension in the data given in Figure A.1
gave values of Tc that were 10-25% lower than the measured values (Birdi, 1997,
2002). This deviation was recently analyzed in much detail (Birdi, 1997, 2002).
The surface tension, γ, of any liquid would be related to the pressure, P, as follows:

(dγ/dP)A,T = (dV/dA)P,T (A.12)

Since the quantity on the right-hand side would be positive, the effect of pressure
should be to give an increase in γ. Preliminary analyses indicates that the term (d γ/dP)
is positive and dependent on the alkane chain length (Birdi, 1997). These consider-
ations are important in many systems where high pressure is present, for example,

Oil reservoirs found at 100-200 atm pressure
High-pressure technologies
Car tires exerting high pressure on the roads
Teeth in the mouth exerting considerable high pressure
Shoes (e.g., soles) exposed to high pressures.
Building structures

The following relationship relates γ to density (Birdi, 1997):

γ (M/ρ) 2/3 = k ( Tc − T − 6) (A.13)

where M is the molecular weight, and ρ is the density (M/ρ = molar volume). The
quantity (γ [M /ρ]2/3) is called the molecular surface energy . It is impor tant to notice
the correction term 6 on the right-hand side. This is the same as found for n -alkanes
and n -alkenes in the estimation of Tc from γ versus temperature data (Birdi, 1997).
Calculated γ [from Equation A.8] and measured values of different n -alkanes at
various temperatures are as follows:

n -alkane temperature (°c) measured calculated

C 5 0 18.23 18.25

50 12.91 12.8

C 6 0 20.45 20.40

60 14.31 14.3

C 7 30 19.16 19.17

80 14.31 14.26

C 9 0 24.76 24.70

50 19.97 20.05

100 15.41 15.4

C 14 10 27.47 27.4

100 19.66 19.60

C 16 50 24.90 24.90

C 18 30 27.50 27.50

100 21.58 21.60