|
|
|
 |
This theoretical text provides you with a short description of the measurement principles used by the KRÜSS Tensiometers and their software LabDesk.
1. Surface and interfacial tension measurements
Interactions occur between the molecules of a liquid and those of any liquid or gaseous substance which is not soluble in the liquid; these result in the formation of an interface. Energy is required to change the form of this interface or surface. The work required to change the shape of a given surface is known as the interfacial or surface tension.
Most KRÜSS tensiometers determine the surface or interfacial tension with the help of an optimally wettable probe suspended from a precision balance; this is either a ring or a plate. A height-adjustable sample carrier is used to bring the liquid to be measured into contact with the probe. A force acts on the balance as soon as the probe touches the surface. If the length of the probe is known (circumference of ring or length of plate) the force measured can be used to calculate the interfacial or surface tension. A further requirement is that the probe must have a very high surface energy. This is why a platinum-iridium alloy is used for the ring and roughened platinum for the plate.
1.1 The ring method
Historically the ring method was the first to be developed; this is why many of the values for interfacial and surface tension given in the literature are the results of the ring method.
In the ring method the liquid is raised until contact with the surface is registered. The sample is then lowered again so that the liquid film produced beneath the ring is stretched.
The following illustration shows the change in force as the distance of the ring from the surface increases.
The calculation is made according to the following equation:
|
F max - F V
|
||
| s | = |
|
|
L • cos q
|
(s= surface or interfacial tension; F max= maximum force; F V= weight of volume of liquid lifted; L= wetted length, q= contact angle)
The contact angle q decreases as the extension increases and has the value 0° at the point of maximum force, this means that the term cos q has the value 1.
The film breakage shown in Figure 2 is avoided during the measurement in most cases. Nevertheless, the point of film breakage can also be measured with the “Ring-Tear-off”-Method.
1.2 Correction calculations for the ring method
The weight of the volume of liquid lifted beneath the ring, expressed by the term FV, must be subtracted from the measured maximum force as it also affects the balance.
A solution must also be found for a further problem: the curve of the film is greater at the inside of the ring than at the outside. This means that the maximum force (at which the contact angle _ = 0°is reached at different ring distances for the inside and outside of the ring; as a result the measured maximum force does not agree exactly with the actual value.
The correction methods available apply to different ranges of values. You must select the suitable correction method for your application; with the K11 or K100, the calculation is carried out automatically. The three possible correction methods are:
Harkins & Jordan:
Harkins & Jordan have drawn up tables of correction values by determining different surface tensions with rings of different diameters. This comprehensive program of measurements also provides the basic data for the corrections according to Zuidema & Waters and Huh & Mason.
The Harkins & Jordan correction offers the greatest accuracy, but it is possible to imagine liquid systems which are outside the range of validity for the Harkins & Jordan method. However, in practice such a case is extremely rare.
Zuidema & Waters:
Zuidema & Waters needed correction values for small interfacial tensions. For this reason they carried out interpolation calculation on the data from Harkins & Jordan in order to cover the range of small interfacial tensions more accurately. However, the Zuidema & Waters corrections have the greatest deviation range of all corrections and should only be used for comparative measurements with values given in the literature.
Huh & Mason:
Huh & Mason have used mathematical methods to increase the range of application of the correction calculation; this means that this correction method has the largest range of validity while still possessing sufficient accuracy. This is why we have chosen this correction method as the standard one. If you want to make measurements with the greatest possible accuracy you should change to the Harkins & Jordan correction method but keep its range of validity in mind.
1.3 The plate method
In the plate method the liquid is raised until the contact between the surface or interface and the plate is registered. The maximum tension acts on the balance at this instant; this means that the sample does not need to be moved again during the measurement.
|
F
|
||
|
s
|
= |
|
|
L • cos q
|
q = contact angle).
The plate is made of roughened platinum and is optimally wetted so that the contact angle is virtually 0°. This means that the term cos q has a value of approximately 1, so that only the measured force and the length of the plate need to be taken into consideration.
Correction calculations are not necessary with the plate method.
1.4 Ring and plate methods in comparison
With the KRÜSS tensiometers the ring and plate measurement are available as standard procedures for surface and interfacial tension measurements. This section provides you with a list of advantages of both methods. This should make the choice between the methods for the respective purpose more easy.
Advantages of the ring method
- Many values in the literature have been obtained with the ring method. This means that in many cases the ring method should be preferred for comparison purposes.
- The wetted length of the ring exceeds that of the plate by the factor 3. This leads to a higher force on the balance and accordingly to a better accuracy. This effect doesn’t influence the results of surface tension measurements, but small interfacial tensions can be carried out more accurately with the ring method.
- Some substances, e.g. cationic surfactants, show poor wetting properties on platinum. In such cases the surface line between a ring and the liquid is more even than that of a plate.
Advantages of the plate method
- Unlike the ring method, no correction is required for measurement values obtained by the plate method.
- With the plate method, the densities of the liquids don’t have to be known as they have to be with the ring method.
- In an interfacial tension measurement the surface is only touched and not pressed into/pulled out of the other phase. This avoids the phases becoming mixed.
- With the ring method the surface or interface is renewed permanently due to the movement of the ring. If the ring is moving with high velocity, but also if solutions of large molecules or with high viscosities are to be measured, the maximum force is obtained when the diffusion equilibrium at the surface or interface is still not reached. The measurement failure caused by this effect does not occur with the plate method. The plate method is a static measurement, i.e. the plate does not move after the surface or interface has been detected.
2. 2 Critical micelle concentration (CMC)
An important measure for the characterization of surfactants is the critical micelle concentration (CMC). Surfactants consist of a hydrophilic "head" and a hydrophobic "tail". If a surfactant is added to water then it will initially enrich itself at the surface; the hydrophobic tail projects from the surface. Only when the surface has no more room for further surfactant molecules will the surfactant molecules start to form agglomerates inside the liquid; these agglomerates are known as micelles. The surfactant concentration at which micelle formation begins is known as the critical micelle formation concentration (CMC).
Micelles are spherical or ellipsoid structures on whose surface the hydrophilic heads of the surfactant molecules are gathered together whereas the hydrophobic tails project inwards. The washing effect of surfactants is based on the fact that hydrophobic substances such as fats or soot can be stored within the micelles.
2.1 Standard procedure
The critical micelle formation concentration (CMC) can be determined by carrying out surface tension measurements on a series of different surfactant concentrations. Surfactants exhibit a specific surface tension curve as a function of the concentration. Initially the surfactant molecules increasingly enrich themselves at the water surface. During this phase the surface tension decreases linearly with the logarithm of the surfactant concentration. When the CMC is reached, i.e. when the surface is saturated with surfactant molecules, a further increase in surfactant concentration no longer has any appreciable influence on the surface tension.
This means that in order to determine the CMC the two linear sections formed by the measuring points obtained from the series of different concentrations must be determined. The CMC is obtained from the intersection of the straight lines for the linear concentration-dependent section and the concentration-independent section.
In the K100 and K12 the CMC is determined by using the CMC Add-In of the LabDesk software. The concentration series is generated automatically with a computer-controlled Dosimat, so that only a surfactant stock solution needs to be made up. The measurements and their evaluation are carried out automatically.
2.2 Reverse CMC measurement
For reverse CMC measurements not the solvent but the parent solution is first put into the sample vessel and then diluted with the solvent step by step.
One case in which the reverse CMC measurement should be chosen is when the concentration of the sample is above the clouding point. Such a solution can’t be dosed homogeneously, but it can be diluted homogeneously by adding the solvent.
Another application for reverse CMC measurements is the case that the CMC is expected at a low concentration of the surfactant. With standard CMC measurements the region of interest is also the region where only small amounts of the sample solution are dosed and where therefore the largest error by means of dosing inaccuracy would occur. With reverse CMC measurement low concentrations are reached with large amounts of the solvent and so this error is reduced to a minimum.
Another advantage is that the dosimat only gets in contact with the pure solvent and can run in continuous operation. This makes the reverse CMC measurement an ideal method for routine measurements.
Since the end volume exceeds the initial volume by many times a cone shaped sample vessel is used.
2.3 Extended CMC-Method
For the K100 the „Extended CMC“ method is available. The software LabDeskTM does not control one but two dosing units. The second unit substracts the amount of liquid previously added by the first one. Thus the accessible concentration range is increased many times over.
Measuring the contact angle between a liquid and a solid is the domain of our optical Drop Shape Analysis intruments (DSA). Nevertheless, contact angles can also be measured using tensiometrical measurements.
3.1 Contact angles of solid bodies
The theoretical principles of the plate method also apply to the determination of the contact angle between a liquid and a solid surface. In this method liquids with a known surface tension are used and a plate made of the material to be investigated is used instead of the platinum plate. The wetted length of the plate must be measured; it is obtained from the following equation:
L = 2 x length + 2 x thickness
The height of the plate does not matter.
The plate is suspended from the balance by using a sample holder. The liquid is moved upwards. As soon as a contact is registered the measurement of the force is started. By using the equation for the plate method the contact angle q can be calculated from the surface tension of the liquid, the wetted length and the measured force:
|
F
|
||
| cos q |
=
|
|
|
L • s
|
3.2 Contact angles of powders: Sorption measurements using the Washburn method
Sorption measurements are used for determining the surface energy of a powder-form solid. The powder to be measured is filled into a glass tube with a filter base and this is suspended from the balance. After the vessel has contacted the liquid the speed at which the liquid rises though the bulk powder is measured by recording the increase in weight as a function of time.
|
l 2
|
sl • r • cos q
|
|
|
|
=
|
|
|
t
|
2h
|
The capillary radius r for bulk powder must be replaced by a quantity which describes the orientation of the microcapillaries c and the mean radius. As a result r is replaced by the constant (c • 
), this applies to a particular powder.
|
l 2
|
=
|
(c •
) • sl • cos q |
|
|
|
|
|
t
|
2h
|
As the flow front cannot be determined directly, it must be calculated from the measured increase in weight, the liquid density and the tube diameter. The viscosity and surface tension of the liquid are known, only two unknown quantities remain: the required advancing angle (contact angle) and the material constan (c •
).
This is why a measurement with an optimally wetting liquid (e.g. hexane, whose advancing angle is virtually 0° , is carried out first; this gives a value for cos q of approximately 1.
When the term
|
l 2
|
|
| 2η |
|
|
sl
|
) i.e. the required constant. For measurements with other liquids this constant can be inserted into the Washburn equation, so that the advancing angle q can be determined for other liquids.
From the contact angle data the surface energy of a solid can be calculated. In the contact angle add-in of the LabDeskTM tensiometer software various methods for calculating the surface energy have been included, the program also includes a database containing the physical data of numerous liquids which is required for this.
4. Density measurement
Apart from the measurement of interfacial and surface tension, the K11 and K00 also provide an accurate method for determining the density of liquids.
The measurement makes use of the fact that as a result of the buoyancy of a solid in a liquid the measured weight in a liquid is less than that measured in air. The mass of the volume of liquid displaced by the measuring probe corresponds exactly to the difference in weight. If the density of the measuring probe is known then the density of the liquid can be obtained by differential weighing.
The equation for the calculation is:
|
|
• G MKA - G MKL
|
|
rL = r MK
|
|
|
G MKA
|
(rL= density of liquid; r MK= density of measuring probe; G MKA= weight of measuring probe in air; G MKL= weight of the measuring probe in the liquid).
5. Measuring the behavior of sediments
5.1 Sedimentation measurement
Sedimentation measurements with the K100 and K12 permit the investigation of the sedimentation speed of suspensions. A crater-shaped measuring probe suspended from a balance is immersed in the suspension to be investigated while this is being stirred. When the stirrer is switched off the suspended particles sink to the bottom. The measuring probe catches the sinking particles and records their weight as a function of time; this allows the sedimentation speed to be determined.
The bulk density of sediments can be checked by penetration measurements. A cone-shaped measuring probe is suspended from a balance. The sample with the sediment is slowly moved upwards. As the height increases the resistance of the sediment to the penetration by the measuring probe also increases. The necessary force is measured as a function of the distance and is used as a measure of the bulk density.
