In materials science, the sessile drop technique is a method used for the characterization of solid surface energies, and in some cases, aspects of liquid surface energies. The main premise of the method is that by placing a droplet of liquid with a known surface energy and contact angle, the surface energy of the solid substrate can be calculated. The liquid used for such experiments is referred to as the probe liquid, and the use of several different probe liquids is required.

Probe liquid

The surface energy is measured in units of joules per square meter, which is equivalent in the case of liquids to surface tension, measured in newtons per meter. The overall surface tension/energy of a liquid can be acquired through various methods using a tensiometer or using the pendant drop method and maximum bubble pressure method.

The interface tension at the interface of the probe liquid and the solid surface can additionally be viewed as being the result of different types of intermolecular forces. As such, surface energies can be subdivided according to the various interactions that cause them, such as the surface energy due to dispersive (e.g. van der Waals forces) and other interactions (e.g. hydrogen bonding, polar interactions, acid–base interactions, etc.). It is often useful for the sessile drop technique to use liquids that are known to be incapable of some of those interactions (see table 1). For example, the surface tension of all straight alkanes is said to be entirely dispersive, and all of the other components are zero. This is algebraically useful, as it eliminates a variable in certain cases and makes these liquids essential testing materials.

The overall surface energy, both for a solid and a liquid, is assumed traditionally to simply be the sum of the components considered. For example, the equation describing the subdivision of surface energy into the contributions of dispersive interactions and polar interactions would be

where σS is the total surface energy of the solid, σSD and σSP are respectively the dispersive and polar components of the solid surface energy, σL is the total surface tension/surface energy of the liquid, and σLD and σLP are respectively the dispersive and polar components of the surface tension.

In addition to the tensiometer and pendant drop techniques, the sessile drop technique can be used in some cases to separate the known total surface energy of a liquid into its components. This is done by reversing the above idea with the introduction of a reference solid surface that is assumed to be incapable of polar interactions, such as polytetrafluoroethylene (PTFE).

Contact angle The contact angle is defined as the angle made by the intersection of the liquid/solid interface and the liquid/air interface. It can be alternately described as the angle between solid sample's surface and the tangent of the droplet's ovate shape at the edge of the droplet. A high contact angle indicates a low solid surface energy or chemical affinity. This is also referred to as a low degree of wetting. A low contact angle indicates a high solid surface energy or chemical affinity, and a high or sometimes complete degree of wetting. For example, a contact angle of zero degrees will occur when the droplet has turned into a flat puddle; this is called complete wetting.

Measuring contact angle

Goniometer method

The simplest way of measuring the contact angle of a sessile drop is with a contact angle goniometer, which allows the user to measure the contact angle visually. A droplet is deposited by a syringe which is positioned above the sample surface, and a high resolution camera captures the image from the profile or side view. The image can then be analyzed either by eye (with a protractor) or more often is measured using image analysis software. This type of measurement is referred to as a static contact angle measurement.

The contact angle is affected not only by the surface chemistry but also by the surface roughness. The Young equation, which is the basis for the contact angle, assumes a homogeneous surface with no surface roughness. In case surface roughness is present, the droplet can be in Wenzel state (homogeneous wetting), Cassie-Baxter state (heterogeneous wetting) or in an intermediary state. The surface roughness amplifies the wetting behavior caused by the surface chemistry.

In order to measure the contact angle hysteresis, the sessile droplet can be increased gradually in volume. The maximum possible contact angle is referred to as the advancing contact angle. The receding contact angle can be measured by removing volume from the drop until dewetting occurs. The minimum possible contact angle is referred to as the receding contact angle. The contact angle hysteresis is the difference between the advancing and receding contact angle.

Advantages and disadvantages The advantage of this method, aside from its relatively straightforward nature, is the fact that with a large enough solid surface, multiple droplets can be deposited in various locations on the sample to determine heterogeneity. The reproducibility of particular values of the contact angle will reflect the heterogeneity of the surface's energy properties. Conversely, the disadvantage is that if the sample is only large enough for one droplet, then it will be difficult to determine heterogeneity, or consequently to assume homogeneity. This is particularly true because conventional, commercially available goniometers do not swivel the camera/backlight set up relative to the stage, and thus can only show the contact angle at two points: the right and the left edge of the droplet. In addition to this, this measurement is hampered by its inherent subjectivity, as the placement of the lines is determined either by the user looking at the pictures or by the image analysis software's definition of the lines.

Wilhelmy method

An alternative method for measuring the contact angle is the Wilhelmy method, which employs a sensitive force meter of some sort to measure a force that can be translated into a value of the contact angle. In this method, a small plate-shaped sample of the solid in question, attached to the arm of a force meter, is vertically dipped into a pool of the probe liquid (in actuality, the design of a stationary force meter would have the liquid being brought up, rather than the sample being brought down), and the force exerted on the sample by the liquid is measured by the force meter. This force is related to the contact angle by the following equation:

where F is the total force measured by the force meter, Fb is the force of buoyancy due to the solid sample displacing the liquid, I is the wetted length, and σ is the known surface tension of the liquid.

Advantages and disadvantages The advantage of this method is that it is fairly objective and the measurement yields data which is inherently averaged over the wetted length. Although this does not help determine heterogeneity, it does automatically give a more accurate average value. Its disadvantages, aside from being more complicated than the goniometer method, include the fact that sample of an appropriate size must be produced with a uniform cross section in the submersion direction, and the wetted length must be measured with some precision. In addition, this method is only appropriate if both sides of the sample are identical, otherwise the measured data will be a result of two completely different interactions.Christopher Rullison, "A Practical Comparison of Techniques Used to Measure Contact Angles for Liquids on Non-Porous Solids". Kruss Laboratories technical note #303.

Strictly speaking, this is not a sessile drop technique, as we are using a small submerging pool, rather than a droplet. However, the calculations described in the following sections, which were derived for the relation of the sessile drop contact angle to the surface energy, apply just as well.

Determining surface energy

While surface energy is conventionally defined as the work required to build a unit of area of a given surface,Oura K, Lifshits V G, Saranin A A, Zotov A V, and Katayama M (2001). Surface Science: An Introduction. Springer-Verlag: Berlin, 233 when it comes to its measurement by the sessile drop technique, the surface energy is not quite as well defined. The values obtained through the sessile drop technique depend not only on the solid sample in question, but equally on the properties of the probe liquid being used, as well as the particular theory relating the parameters mathematically to one another.

There are numerous such theories developed by various researchers. These methods differ in several regards, such as derivation and convention, but most importantly they differ in the number of components or parameters which they are equipped to analyze. The simpler methods containing fewer components simplify the system by lumping surface energy into one number, while more rigorous methods with more components are derived to distinguish between various components of the surface energy. Again, the total surface energy of solids and liquids depends on different types of molecular interactions, such as dispersive (van der Waals), polar, and acid/base interactions, and is considered to be the sum of these independent components. Some theories account for more of these phenomena than do other theories. These distinctions are to be considered when deciding which method is appropriate for the experiment at hand. The following are a few commonly used such theories.

One-component theories

The Zisman theory

The Zisman theory is the simplest commonly used theory, as it is a one-component theory, and is best used for non-polar surfaces. This means that polymer surfaces that have been subjected to heat treatment, corona treatment, plasma cleaning, or polymers that contain heteroatoms do not lend themselves to this particular theory, as they tend to be at least somewhat polar. The Zisman theory also tends to be more useful in practice for surfaces with lower energies.

The Zisman theory simply defines the surface energy as being equal to the surface energy of the highest surface energy liquid that wets the solid completely. That is to say, the droplet will disperse as much as possible, i.e. completely wetting the surface, for this liquid and any liquids with lower surface energies, but not for liquids with higher surface energies. Since this probe liquid could hypothetically be any liquid, including an imaginary liquid, the best way to determine the surface energy by the Zisman method is to acquire data points of contact angles for several probe liquids on the solid surface in question, and then plot the cosine of that angle against the known surface energy of the probe liquid. By constructing the Zisman plot, one can extrapolate the highest liquid surface energy, real or hypothetical, that would result in complete wetting of the sample with a contact angle of zero degrees.

Accuracy/precision