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Contact angle can also be considered in terms of the thermodynamics of the materials involved. This analysis involves the interfacial free energies between the three phases and is given by:

σ

whereσ

lv cosθ

=σsv -σsl

lv ,σsv andσsl refer to the interfacial energies of the liquid/vapor,

solid/vapor and solid/liquid interfaces. How is contact angle measured?

Two different approaches are commonly used to measure contact angles of non-porous solids, goniometry and tensiometry. Goniometry involves the observation of a sessile drop of test liquid on a solid substrate. Tensiometry involves measuring the forces of interaction as a solid is contacted with a test liquid. Both techniques are described below with comments on the choice of either technique for particular research applications.

In the case of porous solids, powders and fabrics another approach is commonly used. This technique involves using a tensiometer, such as the KSV Sigma 70, and the Washburn method. It is the method of choice when your sample contains a porous architecture which absorbs the wetting liquid. It is described briefly below and more completely in Application Note # 104. Goniometry

Analysis of the shape of a drop of test liquid placed on a solid is the basis for goniometry. The basic elements of a goniometer include a light source, sample stage, lens and image capture. Contact angle can be assessed directly by measuring the angle formed between the solid and the tangent to the drop surface.

The production of drops with advanced and receded edges involves one of two strategies. Drops can be made to have advanced edges by addition of liquid. Receded edges may be produced by allowing sufficient evaporation or by withdrawing liquid from the drop. Alternately, both advanced and receded edges are produced when the

stage on which the solid is held is tilted to the point of incipient motion. Using an instrument with high speed image capture capabilities shapes of drops in motion may banalyzed.

KSV Instruments supplies two instruments for goniometry, the CAM100and CAM 200. The CAM100 uses a 50mm USB camera for image capture. The CAM200 instruments uses a high speed CCD camera for image capture. The images are analyzed with computer software. Advantages

Goniometry can be used in many situations where tensiometry cannot. You can use a great variety of solid substrates provided they have a relatively flat portion for testing and can fit on the stage of the instrument. Substrates with regular curvature, such as contact lenses are also easily analyzed.

Testing can be done using very small quantities of liquid. It is also easy to test high temperature liquids such as polymer melts. Limitations

The assignment of the tangent line which will define the contact angle is a factor which can limit the reproducibility of contact angle measurements. Conventional goniometry relies on the consistency of the operator in the assignment of the tangent line. This can lead to significant error, especially subjective error between multiple users. KSV Instruments’ CAM 200 and CAM100 remove this problem by using c

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analysis of the drop shape to generate consistent contact angle data.

The conditions which produce advanced and receded angles are sometimes difficult to reproduce. Although drops in motion can produce data on dynamic contact angles the velocity of motion cannot be controlled. It is also less suited, when

compared to tensiometry, to analysis of the effects of wetting on changes in contact a

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In addition the amount of surface sampled for each measurement is limited and multiple measurements should be used to characterize a surface. Fibers are not easily studied by goniometry. Tensiometry

The tensiometric method for measuring contact angles measures the forces that are present when a sample of solid is brought into contact with a test liquid. If the forces of interaction, geometry of the solid and surface tension of the liquid are known the contact angle may be calculated. The user first makes a measurement of the surface tension of the liquid using either a Wilhelmy plate or DuNouy ring. The sample of the solid to be tested is then hung on the balance and tared. The liquid is then raised to contact the solid. When the solid contacts the liquid the change in forces is detected and your Sigma70 registers this elevation as zero depth of immersion. As the solid is pushed into the liquid the forces on the balance are recorded. The forces on the balance are

Ftotal = wetting force + weight of probe - buoyancy

Your Sigma70 has tared the weight of the probe and can remove the effects of the buoyancy force by extrapolating the graph back to zero depth of immersion. The remaining component force is the wetting force which is defined as:

Wetting force = σ

whereσ

LV P cosθ

?

is

LV is the liquid surface tension, P is the perimeter of the probe andθ

the contact angle. Thus at any depth data is received which can be used to calculate contact angle. This contact angle, which is obtained from data generated as the probe advances into the liquid, is the advancing contact angle. The sample is immersed to a set depth and the process is reversed. As the probe retreats from the liquid data collected is used to calculate the receding contact angle.

Advantages

The use of tensiometry for measurement of contact angle has several advantages over conventional goniometry. At any point on the immersion graph, all points along the perimeter of the solid at that depth contribute to the force measurement recorded. Thus the force used to calculate ? at any given depth of immersion is already an averaged value. You may calculate an averaged value for the entire length of the sample or average any part of the immersion graph data to assay changes in contact a

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length of the sample.

This technique allows the user to analyze contact angles produced from wetting over an entire range of velocities from static to rapid wetting. Because the contact angles are determined from the forces measured by the instrument there is no p

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subjective error.

The graphs produced by this technique are very useful in studying hysteresis. Variations of contact angles, both advancing and receding, for the entire length of the sample tested is visualized on the same graph. In addition variations generated over multiple wetting/dewetting cycles can yield information on changes caused by wetting (such as absorption or surface reorientation).Analysis of fibers, very problematic for goniometry, is handled easily by your tensiometer. Limitations

There are two major limitations for the application of this technique. Firstly the user must have enough of the liquid being tested available so that he can immerse a portion of his solid in it. Secondly the solid in question must be available in samples which meet the following constraints. The sample must be formed or cut in a regular geometry such that it has a constant perimeter over a portion of it’s length. Rods, plates or fibers of known perimeter are ideal. The sample must have the same surface