# Contact angle

The instrument of choice to measure contact angles and dynamic contact angles is Theta optical tensiometer. Sigma 700/701force tensiometers can also be used. Both optical and force tensiometers enable static and dynamic contact angle measurements.

**What is contact angle?**

Contact angle ,θ , is a quantitative measure of the wetting of a solid by a liquid. It is defined geometrically as the angle formed by a liquid at the three phase boundary where a liquid, gas and solid intersect as shown below:

It can be seen from this figure that a low values of contact angle (θ) indicates that the liquid spreads, or wets well, while a high contact angle indicates poor wetting. If the angle θ is less than 90 degrees the liquid is said to wet the solid. If it is greater than 90 degrees it is said to be non-wetting. A zero contact angle represents complete wetting.

The measurement of a single static contact angle to characterize the interaction is no longer thought to be adequate. For any given solid/ liquid interaction there exists a range of contact angles which may be found. The value of static contact angles are found to depend on the recent history of the interaction. When the drop has recently expanded the angle is said to represent the ‘advanced’ contact angle. When the drop has recently contracted the angle is said to represent the ‘receded’ contact angle. These angles fall within a range with advanced angles approaching a maximum value and receded angles approaching a minimum value.

If the three phase (liquid/solid/vapor) boundary is in actual motion the angles produced are called Dynamic Contact Angles and are referred to as ‘advancing’ and ‘receding’ angles. The difference between ‘advanced’ and ‘advancing’, ‘receded’ and ‘receding’ is that in the static case motion is incipient in the dynamic case motion is actual. Dynamic contact angles may be assayed at various rates of speed. Dynamic contact angles measured at low velocities should be equal to properly measured static angles.

*Hysteresis*

The difference between the maximum (advanced/advancing) and minimum (receded/receding) contact angle values is called the contact angle hysteresis. A great deal of research has gone into analysis of the significance of hysteresis. It has been used to help characterize surface heterogeneity, roughness and mobility. Briefly, for surfaces which are not homogeneous there will exist domains on the surface which present barriers to the motion of the contact line. For the case of chemical heterogeneity these domains represent areas with different contact angles than the surrounding surface. For example when wetting with water, hydrophobic domains will pin the motion of the contact line as the liquid advances thus increasing the contact angles. When the water recedes the hydrophilic domains will hold back the draining motion of the contact line thus decreasing the contact angle. From this analysis it can be seen that, when testing with water, advancing angles will be sensitive to the hydrophobic domains and receding angles will characterize the hydrophilic domains on the surface.

For situations in which surface roughness generates hysteresis the actual microscopic variations of slope in the surface create the barriers which pin the motion of the contact line and alter the macroscopic contact angles. There has been a great deal of research investigating the significance of hysteresis.

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:

γ_{LV} . cos θ = γ_{SV} - γ_{SL}

where γ_{LV} ,γ_{SV} and γ_{SL} 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, optical tensiometry (goniometry) and force tensiometry. Optical tensiometry involves the observation of a sessile drop of test liquid on a solid substrate. Force ensiometry 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 Attension Sigma 700/701, 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 here.

*Optical tensiometry*

Analysis of the shape of a drop of test liquid placed on a solid is the basis for optical tensiometry (goniometry). The basic elements of an optical tensiometer (also called contact angle meter) include 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 be analyzed.

Attension supplies two instruments for optical tensiometry, the Theta and Theta Lite. The images are analyzed with computer software.

*> Advantages*

Optical tensiometry can be used in many situations where force tensiometry cannot. You can use a great variety of solid substrates provided they have a relatively flat portion for testing. 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 optical tensiometry 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. Theta and Theta Lite remove this problem by using computer 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 force tensiometry, to analysis of the effects of wetting on changes in contact angle. In addition the amount of surface sampled for each measurement is limited and multiple measurements should be used to characterize a surface.

It is challenging to deposit a drop of water on a thin object like a fiber. It is adviced to use a picoliter liquid dispenser to study fibers. The meniscus technique can also be used to measure the contact angle of a single fiber.

A video of contact angle measurement can be found below:

* *

*Force tensiometry*

The force 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 Du Noüy ring. The sample of the solid to be tested is then hung on the balance and tarred. The liquid is then raised to contact the solid. When the solid contacts the liquid the change in forces is detected and your Sigma 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:

F_{total} = wetting force + weight of probe - buoyancy

Your Sigma has tarred 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 = γ_{LV} . P . cos θ

where γ_{LV} is the liquid surface tension, P is the perimeter of the probe and θ is 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. The process will appear as follows:

The graph of force/wetted length vs depth of immersion will appear as follows:

1 - The sample is above the liquid and the force/ length is zeroed.

2 - The sample hits the surface. For the sample as shown, with a contact angle < 90°, the liquid rises up causing a positive force.

3 - The sample is immersed, buoyant force increases causing a decrease in force on the balance. Forces are measured for advancing angle.

4 - After having reached the desired depth the sample is pulled out of the liquid. Forces are measured for receding angle.

*> Advantages*

The use of force tensiometry for measurement of contact angle has several advantages over conventional optical tensiometry. 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 θ 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 angle along the 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 possibility of 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 are 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 force tensiometer. A single fiber can also be analyzed with an optical tensiometer. You can find more information about fiber wettability here.

*> 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 its length. Rods, plates or fibers of known perimeter are ideal. The sample must have the same surface on all sides which contact the liquid. The sample must also be small enough so that it can be hung on the microbalance of your Sigma force tensiometer.

It is also more difficult to use this technique in systems which are measured at high temperatures. Temperatures at or below 100 ° C are easily handled but for measurements above this range goniometry is recommended.

A dynamic contact angle measurement using Sigma 700/701 force tensiometer is available below:

**Washburn Method**

This method is chosen when the solid sample to be tested contains a porous architecture which leads to absorption of the wetting liquid. The solid is brought into contact with the testing liquid and the mass of liquid absorbed into the solid is measured as a function of time. The amount absorbed is a function of the viscosity, density and surface tension of the liquid, the material constant of the solid, and the contact angle of the interaction. If the viscosity, density and surface tension of the liquid are known the material constant and contact angle can be solved for. Attension Sigma force tensiometers can be used to determine contact angles via the Washburn technique. You can find more information on the powder wettability page.

**Utilization of Contact Angle Data**

The primary focus of contact angle studies is in assessing the wetting characteristics of solid/liquid interactions. Contact angle is commonly used as the most direct measure of wetting. Other experimental parameters may be derived directly from contact angle and surface tension results. Some examples are:

Work of Adhesion: defined as the work required to separate the liquid and solid phases, or the negative free energy associated with the adhesion of the solid and liquid phases. Used to express the strength of the interaction between the two phases. It is given by the Young-Dupre equation as:

W_{a} = γ . (1 + cos θ)

Work of Cohesion: defined as the work required to separate a liquid into two parts, it is a measure of the strength of molecular interactions within the liquid. It is given by:

W_{c} = 2 γ

Work of Spreading: the negative free energy associated with spreading liquid over solid surface. Also referred to as Spreading Coefficient it is given as:

W_{s} = γ . ( cos θ - 1)

Wetting Tension: a measurement of force/length defined as:

Τ = F_{w} / P = γ_{LV .} cos θ

This value, wetting force normalized for length, also represents the product of the cosine of the contact angle and the surface tension. It allows for a characterization of the strength of the wetting interaction without separate measurement of surface tension. This is most helpful in situations, such as multi-component systems, where surface tension at interface may not equal equilibrium surface tension. It is also referred to as Adhesion Tension or Work of Wetting.

**Characterization of the Solid Surface**

Measurements of surface tension yield data which directly reflect thermodynamic characteristics of the liquid tested. Measurement of contact angles yield data which reflect the thermodynamics of a liquid/solid interaction. If you wish to characterize the wetting behavior of a particular liquid/solid pair you only need to report the contact angle. It is possible to characterize the wettability of your solid in a more general way. Various methods are used but the same basic principle applies for each. The solid is tested against a series of liquids and contact angles are measured. Calculations based on these measurements produce a parameter (critical surface tension, surface free energy, etc) which quantifies a characteristic of the solid which mediates wetting. Two basic approaches are covered here.

*Critical Surface Tension*

Using a series of homologous liquids of differing surface tensions a graph of cos θ versus γ is produced. It will be found that the data form a line which approaches cos θ = 1 at a given value of γ. This is the maximal surface tension of a liquid which may completely wet your solid. This value, called the critical surface tension, can be used to characterize your solid surface.

*Surface Free Energy*

Another way to characterize a solid surface is by calculating surface free energy, also referred to as solid surface tension. This approach involves testing the solid against a series of well characterized wetting liquids. The liquids used must be characterized such that the polar and dispersive components of their surface tensions are known. The relevant equation is given by Owens and Wendt as:

γ_{l} (1 + cos θ) / (γ_{ld})^{1/2} = (γ_{sp})^{1/2} . [(γ_{lp})^{1/2} / (γ_{ld})^{1/2}] + (γ_{sd})^{1/2}

where θ is the contact angle, γ_{l }is liquid surface tension and γ_{s} is the solid surface tension, or free energy. The addition of d and p in the subscripts refer to the dispersive and polar components of each. The form of the equation is of the type y = mx + b. You can graph (γ_{lp})^{1/2} / (γ_{ld})^{1/2} vs γ_{l} (1 + cos θ) / (γ_{ld})^{1/2} . The slope will be (γ_{sp})^{1/2} and the y-intercept will be (γ_{sd})^{1/2}. The total free surface energy is merely the sum of its two component forces.

More complete information can be found on the surface free energy page.

Sigma 700 and 701 are state-of-the-art tensiometers, providing highly accurate measurements of surface and interfacial tension, dynamic contact angles, surface free e…

Theta Lite is a compact and accurate optical tensiometer for simple contact angle and surface free energy measurements. It can also measure surface and interfacial te…