Methods for surface and interfacial tension measurements

Each material has a specific surface energy equivalent to the surface tension. This quantity is equal to the energy needed to create a new surface of a unit area. While liquids such as alkanes have quite a low surface tension, more polar liquids exhibit much higher tensions. The situation with solid materials is similar: there are those with low and with high surface tension. The tensions between two condensed materials are typically much smaller and can even approach values near zero which leads to fascinating phenomena. This is for example the case when oil is brought into contact with an aqueous surfactant solutions. When the interfacial tension (the tension between the two liquids) is close to zero a spontaneous emulsification is observed and no mechanical energy is needed to disperse one phase into the other [[i]]. Another example is the process of wet grinding. While large input of energy would be required to grind a number of materials in air, the energy input for grinding suspended in a liquid can be orders of magnitude lower (Rehbinder effect, see [[ii]]). There is quite a number of methods for measuring the surface tension of a liquid or the interfacial tension between two immiscible liquids. Table 1 gives an overview of methods dedicated to surface tension measurements of liquid interfaces. As one can see, most of these methods are based on concepts with single drops or bubbles, as it was extensively described in a recently published book (R. Miller and L. Liggieri (Eds.),Bubble and Drop Interfaces, Vol. 2, Progress in Colloid and Interface Science, Brill Publ., Leiden, 2011, p. 195-222; ISBN 978 90 04 17495 5).

Table 1: Methods for measuring surface and interfacial tension of liquid interfaces; according to [3]

Method	Liquid/Liquid	Liquid/Gas	Comm. Set-up
Capillary Rise Technique	possible	good	no
Capillary Wave Damping	possible	good	no
Drop Volume Method	good	good	yes
Growing Drops and Bubbles	good	good	no
Inclined Plate Method	bad	good	no
Maximum Bubble Pressure	bad	good	yes
Oscillating Jet	bad	good	no
Pendent Drop Method	good	good	yes
Plate Tensiometry	possible	good	yes
Ring Tensiometry	possible	good	yes
Sessile Drop Method	possible	possible	yes
Spinning Drop Technique	good	possible	yes
Static Drop Volume Method	good	good	available

Some methods are based on dynamic principles and are thus suitable to measure the tension as a function of time. Others are static or quasi-static methods and yield dynamic tensions as well but also allow to approach the equilibrium state of a liquid interface and hence are able to measure the equilibrium tension. While dynamic methods require theories for data interpretation that take the dynamic character into consideration, the data from static methods can be understood more easily. To overcome this problem Joos developed a theory which reduces the data from dynamic methods to a so-called effective lifetime of the interface, which is equivalent to the time needed at a static interface to reach the adsorption state [[i]]. In this way measurement results from all experimental techniques can be directly compared. Each of the given methods has advantages and drawbacks. Actually, none of these methods can provide all the possibilities needed in practice and only a proper selected number of measuring techniques can satisfy the requirements in a surface science laboratory. The most important criterion for users is certainly the availability of commercial set-ups which is particularly marked in the Table 1. Using interfacial methods one comes across the problem of sample purity. Small amounts of surface active components in a liquid can cause dramatic changes in the surface tension. Thus, the correct functioning of a method cannot be simply obtained by measuring an arbitrary liquid. It is rather recommended for such test measurements to use a liquid system with well-known properties and high purity. When the respective measuring value for the chosen standard sample is reached within a certain limit of accuracy, the user can conclude about the functioning of the instrument as well as the quality of the samples. There are few samples useful for such test measurements only. Table 2 provides important data for a number of such liquids. These values are confirmed by various authors and methods and can serve as standard.

Table 2: Surface tension and density of some standard liquids

Liquid	Temp [°C]	Density [g/cm³]	Viscosity [mPa·s]	ST [mN/m]
Water	15	0.9991	1.139	73.5
	20	0.9982	1.002	72.75
	21	0.9980	0.978	72.6
	25	0.9971	0.890	72.0
	30	0.9957	0.798	71.2
	35	0.9940	0.719	70.5
	40	0.9923	0.653	69.6
	45	0.9902	0.596	68.9
	50	0.9881	0.547	68.0
	55	0.9857	0.504	66.9
	60	0.9832	0.467	66.2
Hexane	20	0.660	0.326	18.4
Heptane	20	0.684	0.409	19.7
Octane	20	0.703	0.542	21.6
Nonane	20	0.718	0.711	22.9
Decane	20	0.730	0.92	23.9
Dodecane	20	0.751	1.35	25.4
Tetradecane	20	-	-	26.7
Hexadecane	20	0.7733	-	27.6
Ethylen Glycol	21	-	-	47.7
Methanol	21	-	-	22.3
Ethanol	20	0.789	-	22.0
Hexanol	20	0.814	-	25.8
Octanol	20	0.827	-	27.5
Decanol	20	0.830	-	-
Benzene	20	0.877	0.652	28.9
Chloroform	15	1.489	-	27.2
Toluen	20	0.867	0.59	28.5
Dioxane	20	1.034	-	35.4

Note, that in general the interface between two liquids is affected by surface active impurities most strongly, and the interfacial tension measured is not a reliable value. This even holds although the surface tensions of the two liquids used have correct values. Besides the correct surface tension value for a liquid as criterion of purity, there should also be no change of g with time. This behaviour should be tested over the time interval of interest. In Table 3 values are given for the interfacial tension between two liquids, both mutually saturated in order to avoid effects caused by the matter transfer across the interface. Note, that all liquids have a certain solubility in a second liquid. The solubility limits at room temperature are also given in Table 3.

Table 3: Interfacial tensions g between water and a second liquid and mutual solubility

Substance	Temp [°C]	Solubility in Water [mol-%]	Solubility of Water [mol-%]	mN/m
Hexane	20	3x10^-4	0.043	51.0
Heptane	20	5x10^-5	0.070	51.2
Octane	20	1x10^-5	0.060	51.3
Decane	20	2x10^-7	0.057	51.8
Dodecane	20	4x10^-8	0.061	52.1
Tetradecane	20	good	-	52.4
Chloroform	15	0.15	0.517	36.1
Hexanol	20	0.1	29.0	6.8
Octanol	20	0.06	19.4	8.5
Benzene	20	0.04	0.25	35.0
Toluene	20	0.01	0.24	36.1

For many liquid systems the interfacial rheology yields very important information. Thus, the stability of foams or emulsions is mainly controlled by the elasticity and viscosity of the interfaces [[i]]. Interfacial layers of surfactants or polymers are able to change the mechanical behaviour of liquid interfaces strongly. In contrast to bulk rheology, where essentially the shear rheology is of importance, interfaces have a remarkable dilational rheology [[ii]]. The response to transient and harmonic perturbations can be used to determine the two quantities dilational elasticity and viscosity. There are few methods available only for studies of the interfacial rheology. Most of these methods do exist as laboratory set-ups but commercial instruments are not on the market. In Table 4 some of the techniques used for interfacial rheological studies are summarized. As one can see, the drop and bubble shape method allow measurements of the dilational rheology of interfacial layers, at liquid/gas as well as liquid/liquid interfaces. The software of PAT-1M offers particular time functions for such studies as will be demonstrated further below.

Table 4: Methods for measuring surface and interfacial rheology of liquid interfaces; according to [[iii]]

Method	Liquid/Liquid	Liquid/Gas	Commercial Set-up
Interfacial Shear Methods
Torsion Shear Rheometry	possible	good	yes
Canal Surface Vescosimeter	impossible	possible	no
Deep Channel Surface Viscosimeter	impossible	possible	no
Interfacial Dilation Methods
Capillary Wave Damping	possible	good	no
Longitudinal Wave Damping	possible	good	no
Oscillating Drops and Bubbles	good	good	yes
Drop and Bubble Shape	good	good	yes
Elastic Ring Method	impossible	possible	no
Oscillating Cylinder Method	impossible	possible	no

For studies on solid surfaces, no direct methods for measuring the surface tension exist and indirect procedures must be applied. Most common are combined contact angle and surface tension measurements. Other techniques have been described, for example, by Rusanov and Prokhorov [[i]]. The surface energy of a solid can be calculated from the contact angle and the respective surface tension of the used liquid by applying a respective theory. For users intending to determine the surface energy of solids it seems interesting to have again some reference values. This, however, is not so trivial like for liquids. The reason is that solid material cannot be provided in a standard form like it is the case for liquids and the surface properties can therefore vary from sample to sample (cf. Table 5).

Liquid	Solid	Temp [°C]	mN/m	Contact Angle [°]
Water	Polystyrene	22	47.0	60.0
Water	PTFE	20	20.0	104.0
Water	Polyethylene	20	30.3	87.1
Water	PETP	20	35.8	79.1
Diethylen Glycol	PETP	20	35.6	41.2
Ethylen Glycol	PETP	20	35.1	47.5
Formamid	PETP	0.15	35.4	61.5
Glycerol	PETP	20	35.5	68.1

Methods for surface and interfacial tension measurements

Table 1: Methods for measuring surface and interfacial tension of liquid interfaces; according to [3]

Table 2: Surface tension and density of some standard liquids

Table 3: Interfacial tensions g between water and a second liquid and mutual solubility

Table 4: Methods for measuring surface and interfacial rheology of liquid interfaces; according to [[iii]]

Table 5: Contact angle and surface energy of some selected liquids, according to [[ii]]

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