contact angle measurement in practice (1) - cmi · keywords: methods, sample preparation, contact...

KRÜSS Technical Note TN311e | http://www.kruss.de

KRÜSS GmbH � Borsteler Chaussee 85-99a � 22453 Hamburg

Tel.: +49 (40) 51 44 01 - 0 � Fax: +49 (40) 51 44 01 - 98 � eMail: [email protected] � http://www.kruss.de

Contact angle measurement in practice (1)Technical note: TN311eIndustry: all sectorsAuthor: FTDate: 04/2007

Methods: Contact Angle MeasuringInstrument DSA100

Processor TensiometerK100

With care to accuracy: preparations and general conditions forcontact angle measurements

Keywords: methods, sample preparation, contact angle, sessile drop, plate

This is the first of a series of articles on practical contact angle measurement. In this and the followingissues we will cover a wide range of topics concerning drop shape analysis: from preparations for themeasurement through drop deposition conditions and up to the choice of the methods used for analyzingthe drop shape and calculating the surface free energy.This first installment answers questions about the correct handling of the samples and test liquids as wellas suitable ambient conditions.

The wettability of a solid by a liquid candramatically alter even if there is only a slightmodification to the chemical or physicalproperties of the surface. This fact makes thecontact angle a sensitive quantity in surfaceanalysis. However, the contact angle also reactsvery sensitively to unwanted alterations in theparticipating phases.Some easy-to-follow tips about samplepreparation and information about »pitfalls« incontact angle measurement should ensure thatthis method produces reliable results.

Sample contaminationEach solid surface has its own particular history.This is why a »spoilt« surface usually can nolonger be saved � after cleaning it is no longerthe same surface as before the contamination.This is why unwanted alterations to the surfaceare to be avoided. Normally the greatest effectsare seen when the surface comes into contactwith fats and grease or surface-activesubstances. We focus on these two cases below.Contamination by fatsThe first important rule for contact anglemeasurement: never touch the surface with your

fingers. Even the slightest traces of grease willhave an effect on the contact angle results.

Fig. 1: Water contact angles on a polycarbonate sampleAn often unexpected source of contaminants iscompressed air produced by a compressor � ifyou want to dry a surface or remove dustparticles by blowing them off with compressed airthen it is essential that you use purified air.Degreasing a sampleIn many cases samples must not be cleanedbefore the measurement. In quality assurancethe wettability of a material before the nextprocess step is often important � cleaning it toprepare it for a laboratory measurement wouldalter the conditions.




Degreasing is advisable when the contact angleor surface free energy is to be determined as aproperty of the material. In this case cleaningshould always be carried out under identicalconditions � uniformly for all samples, and notjust when the sample is obviously contaminated.In many cases the acetone used in the lab forcleaning purposes frequently has proved to beunsuitable, as it does not evaporate withoutleaving residues. Acetone used for rinsing shouldtherefore be very clean. Furthermore, the samplemust be dried thoroughly since acetone adsorbsstrongly to many surfaces. A solvent that can beused al an alternative is, for example,isopropanol. Cleaning should be carried out in anultrasonic bath, so that the solvent can reacheven microscopically small gaps and cracks.During the measurement itself always measurethe contact angle at a »fresh« position and neverat one that has previously been wetted � evenwhen the test liquid has already evaporated.Surface-active substancesNever use surfactants for cleaning purposes. Onmany surfaces surfactants form tenaciousadsorption layers, which in many cases cannotbe removed by rinsing but only by mechanicalmeans. And surface-active substances have adual effect: not only do they alter the samplesurface, they also reduce the surface tension ofwater, the most frequently used test liquid.As many laboratories contact angle measure-ments and surfactant determinations go hand inhand, scrupulous cleanliness must be ensured. Ifpossible, contact angle measurements andtensiometric work on surfactants should becarried out in separate laboratory rooms.It is less well known that cigarette smoke is alsounhealthy for contact angle measurements. Thenicotinic acid contained in the smoke is verysurface-active. Although smoking is not allowedin laboratories anyhow, even cigarette smokefrom a neighboring office can have ademonstrable effect.Irrespective of the ambient conditions, thesample should always be stored and transportedin a clean and airtight container (e.g. adesiccator) and measured as soon as possibleafter sample preparation.

Static electricityThe next »trap« looms when the cleaned sampleis dried. For plastics in particular, rubbing themdry produces electrostatic charges. As a resultthe deposited drops are deformed; in extreme

cases they actually burst on the surface and formsatellite drops. This is why it is better to dry thesamples in a drying oven.

Fig. 2: The effects of static electricity on water(photo: mariospla.net)

For the same reason samples should not betransported or mailed in plastic containers orbags. Aluminum foil is better suited for this.However, with some materials electrostaticcharges can hardly be avoided. For suchsamples ionization blowers are available on themarket; these can be used to neutralize charges.Such an ionizer is already incorporated in theKRÜSS Tensiometer K100.

Test liquidsThe same purity considerations as for thesamples also apply to the test liquids. Thesurface tension of water reacts most sensitivelyto contaminants. This is why KRÜSSrecommends the use of water in HPLC quality orbidistilled water. In order to avoid the influence ofplasticizers water should not be stored in plasticcontainers.Special rules apply for the standard test liquidsdiiodomethane and ethylene glycol. The firstdecomposes in time due to the effects of light �this is why it is stored in amber glass bottles; itshould no longer be used when a yellow-browncoloration can be clearly seen. In contrast,ethylene glycol � just like other diols or glycerol �is strongly hygroscopic; its surface tension altersas the amount of water it contains increases.Such substances should be stored under dryconditions an in airtight containers.The containers used for all test liquids shouldnever be left open for a long time. In instrumentswith built-in storage reservoirs, for example theDSA100, the test liquids should be replaced afterlonger periods of use � after one week at thelatest.

Ambient conditionsThe chemical structure of solids is different at thesurface from that in the interior. For example,




under ambient conditions most metalsimmediately form an oxide layer. Above all, high-energy surfaces also shield themselves with agas adsorption layer consisting primarily of airand water vapor. As this layer forms athermodynamic equilibrium with the surroundingair this means that the atmospheric humidity alsoinfluences the measurement. Strong variations inthe room climate should therefore be avoided.The same applies for the ambient temperature,which also has an influence on the surface freeenergy and, in particular, on the surface tensionof the test liquids. If the measurements are tohave an extremely good reproducibility then theinstrument should be set up in a temperature andhumidity-controlled laboratory (but not with theinstrument exposed to an air stream). In addition,various environmental chambers are availablefrom KRÜSS for measurements under definedconditions of temperature, pressure andhumidity.

SummaryA prerequirement for the reliable use of thecontact angle method is the careful preparationand execution of the measurements. Some of thebasic rules for the most important stations andgeneral conditions have been collected anddescribed. In sample preparation the primary aimis to avoid contaminant by substances such asfats / greases and surface-active substances.Cleaning procedures are also described. Furthermain topics are the avoidance and elimination ofelectrostatic charges and the proper use of thetest liquids. Finally the importance of the ambientconditions in the laboratory is mentioned.

KRÜSS Technical Note TN312e | Page 1 http://www.kruss.de



Practical Contact Angle Measurement (2)

Technical note: TN312e Industry: all Author: F. Thomsen, C. Bilke-KrauseDate: 07/2007

Method:

Contact angle measuring instrument DSA100

Measurement with nicely deposited drops Keywords: methods, sample preparation, contact angle, sessile drop, plate

In the second part of our practical series on contact angle measurement we are concentrating on drop deposition. What is the difference between static and dynamic contact angles? What influence does the drop volume have? How can the drops be deposited on the sample? The clarification of such questions helps to exactly match the deposition conditions to the particular problem and the functional range of the sample, and how to deal with some of the problems that occur in practice. Contact angle instruments with computer-controlled sample tables and multi-dosing systems offer a wide range of drop deposition possibilities. The way that a drop is generated and makes contact with the sample can be matched exactly to suit the particular problem.

Fig.1: Drops with dosing capillary

Dynamic or static measurement According to Young the contact angle describes the relationship between the surface tension of the liquid and that of the solid as well as the interfacial tension between the phases. From this relationship the Young contact angle θ is used to describe the wetting processes:

l

sls

σγσθ −=cos ,

where sσ and lσ represent the surface tensions of the solid and liquid and slγ is the interfacial tension. The contact angle can be determined with either a constant or a varying drop volume. In the first case we are concerned with a static contact angle, in the second case with a dynamic one, with a differentiation being made between an advancing (with increasing drop volume) and a retreating (with decreasing drop volume) contact angle � the rarely measured retreating angle is not covered in this article. On a theoretical, ideal solid surface neither chemical nor topographical inhomogeneities exist, so that the contact angle of a liquid is identical at all positions. A further requirement for the formation of an ideal Young contact angle is that no chemical reaction between the components occurs at the phase contact points. In an ideal system the static contact angle does not differ from the dynamic one; in both cases an equilibrium contact angle is formed, as is described in the Young equation. However, systems which occur in practice vary to a greater or lesser degree from the ideal state: roughness




affects the wettability, the surface may be chemically inhomogeneous, or soluble components may diffuse from the solid surface into the solution � depending on the nature of the system such influences could increase or decrease the real contact angle. Differences in energy between neighboring positions could also result in the occurrence of energy barriers which cause resistance to the wetting process and therefore produce a contact angle that does not correspond to the equilibrium value of the Young equation. This does not mean that the contact angle is "wrong" � it is just this sensitivity to inhomogeneities that makes the contact angle such a useful tool for checking surface quality. However, it means that conditions under which a measurement is made must be evaluated in order to be able to interpret the contact angle and its variations in a reasonable manner. Consistency should be observed when making comparisons between different samples: static values should not be compared with dynamic ones and the same applies for the surface free energies calculated from contact angle data. In the advancing angle the drop is �forced� to wet a neighboring position by the increase in deposition volume. When measuring the advancing angle it can frequently be observed that as the volume increases the contact angle initially increases, without any change in the contact area. When a limiting contact angle has been achieved then this angle no longer changes; instead the drop borderline moves outward with a constant contact angle � it is only in this region that we talk about an advancing angle. In an online measurement of the advancing angle this is recorded at very many closely adjacent positions so that a meaningful mean value is obtained. For this reason, and because the angle is always measured at a �fresh� contact line, the advancing angle method is frequently used. If an inhomogeneous surface is to be determined by static contact angles then a large number of single drop measurements is usually required to obtain a reliable mean value. However, with dynamic contact angle measurements the number of evaluation methods available is reduced. Some methods, in particular the Young-Laplace method, which is the most accurate from a scientific viewpoint, include the whole of the drop shape in the analysis. In a dynamic measurement the deposition needle is still located in the upper part of the drop, so that the contour is pierced and

only the contact area of the drop can be evaluated. An important criterion for deciding between static and dynamic contact angles is the technical wetting process the samples are involved in. If the process itself is dynamic, such as applying coatings to moving surfaces, then dynamic measurements provide a better model of reality. For the evaluation of quasi-static processes, e.g. bonding in semiconductor technology, static contact angles are often more meaningful. Static measurements are also usually appropriate when inhomogeneities are not to be statistically eliminated but to be determined on the contrary. Mapping the sample � measuring the static contact angle at many sample positions � helps to provide a meaningful correlation between position and wettability. For the choice of method the following, seemingly paradoxical, rule also applies: if the dynamics of the interface formation are to be investigated then static contact angle measurements are appropriate. For example, during absorption processes a reduction of the contact angle with time is observed after surface contact; this can be quantified by using a high-speed camera. Surface-active substances also lead to the variation of the static contact angle with time � we described an interesting application from the dental sector [hyperlink] in the last issue of this Newsletter. To sum up briefly: many users prefer the dynamic contact angle because of its lower susceptibility to scattering. At the same time there are also reasons for preferring the static contact angle � arising from the problem to be solved or from practical measuring considerations.

Drop volume There is no �golden rule� for choosing the drop volume. In theory the Young contact angle is not dependent on the drop volume � at least in the macroscopic range. Only with very small drops, e.g. in condensation processes, does �line tension� come into play; this is related to the excess energy of the phase-contact line compared to the surface free energies of the individual phases. This parameter is so small that it can be neglected for drop dimensions such as occur in contact angle measurements � even in micro-depositions as encountered with the DSA100M the line tension plays no part.




As described above, a dynamic measurement can result in a minimum volume above which the contact angle no longer increases; it can then be measured as the advancing angle. With ideal, completely homogeneous surfaces measurements are possible with small drops of virtually any size. In the opposite direction the drop volume is limited by the weight of the liquid itself, this causes drop shape distortions. The surface tension σ of the liquid and the volume-dependent drop weight g⋅ρ determine the maximum drop radius which is represented by the capillary length κ-1:

g⋅=−

ρσκ 1

For water this results in a maximum radius of 2.7 mm; above this value a considerable influence of the weight on the drop shape is to be expected. Kranias1 � was able to show that in a volume range between 1 and 10 μl no influence of the volume on the water contact angle could be demonstrated. At higher densities or smaller surface tensions the chosen volume should not be too large; this applies in particular for the standard test liquid diiodomethane with a

1−κ value of 1.2 mm.

Deposition speed The deposition speed plays a role in dynamic contact angle measurements in particular. If too high a speed is selected the drop shape will also be determined by the volume flow � the correct contact angle will not be measured. With low-viscosity test liquids such as water or diiodomethane a speed of 100 μl/min should not be exceeded. The speed should be considerably reduced for high-viscosity liquids whose ultimate drop shape is only achieved after a certain time. If dynamic measurements are essential then test measurements should be made at different speeds in order to determine the speed-independent range.

Type of surface contact In computer-controlled dosing systems and sample tables many possible ways are available for the liquid to contact the sample: the drop can be generated on the sample, picked up from the sample, deposited on the sample and finally

1 Kranias, Spiridon: Effect of drop volume on static contact angles. KRÜSS Technical Note TN310e.

dropped onto the sample. In theory the contact angle value does not depend on the type of phase contact � once again practical considerations determine the planning of the measurement. For a dynamic measurement there is no choice regarding drop contact � as the volume is continuously altered during the measurement, drop deposition takes place on the sample and within the field of view of the camera. In static measurements the drop frequently cannot be generated on the sample directly � when the needle is removed the drop may retreat, so that the contact angle is measured at a surface that has already been wetted. This can be counteracted by carefully picking up or depositing a sufficiently large drop suspended from the dosing needle. As the sample table movement can be set to very slow on the DSA100 from KRÜSS, picking up the drop is the most gentle phase contact method. This method is also recommended for small contact angles, for which each mechanical input of energy will lead to an unwanted stronger wetting of the sample. However, picking up has the disadvantage that the table must first be moved back to the measuring position � the first drop formation phase cannot be observed. If work has to be carried out quickly then a more rapid deposition of the drop on a sample that is already at the measuring height is suitable. In extreme cases, such as in adsorption processes, the drops can be dropped onto the sample from a low height in order to be able to record the first milliseconds of drop contact � however, a stronger mechanical influence on the drop shape must be accepted. Extremely large contact angles, e.g. encountered with water drops on ultra-hydrophobic samples, require special treatment. It is often difficult to bring the drop onto the sample, because the cohesive forces of the liquid and the adhesion to the needle are far larger than the adhesion of the liquid to the sample. It frequently helps to first generate a small drop and then bring it into contact with the sample by moving the needle or sample table. The dosing volume can then be slowly increased until the drop is large enough to part from the needle when the distance is increased. Help is also provided by the use of special needles with a Teflon insert to which the drop adheres less strongly.




Summary In this second part of our series on contact angle measurement we are concerned with drop deposition. There is no single type of drop deposition that is suitable for all cases, on the contrary a decision must be taken between static and dynamic contact angles, the drop volume and deposition speed must be selected together with the type of surface contact with the solid and liquids used � all these must be matched to the particular problem. Some criteria for the choice of deposition conditions are given in this article.





Technical note: TN313e Industry: all Author: F. Thomsen Date: 12/2007

Method:

Contact Angle Instrument DSA100

The eye also measures Keywords: methods, contact angle, sessile drop,

The optical system with illumination, camera and video image evaluation is the heart of a contact angle measuring instrument. Its increasing precision is primarily due to advances in video technology and drop shape analysis. This third part of our series on practical contact angle measurement helps you to utilize the possibilities of the optics to the full and measure accurately and reproducibly. In comparison to dosing, in which the volume and volume flow together with the dosing procedure can be exactly controlled, setting the optical parameters is apparently concerned with more subjective criteria: The drop image should be �well� illuminated and �sharp� and �as large as possible�. In fact the optical parameters can also be controlled exactly and matched to suit the measuring task.

Preparations The creation of optimal optical conditions starts with the selection of the measuring location. External light influences negatively affect the shadow image of the drop created by using the instrument illumination. The result is a broader gray level distribution of the drop shape and the surrounding white region; this affects the accuracy of contour recognition. In extreme cases � for example direct sunlight � light reflexes can result in the drop not being recognized at all. The objective or prism and the glass panel in front of the light source should not be touched with the fingers and never with sharp-edged objects. If marks are seen on optical components these should be carefully removed using a solvent-impregnated (e.g. isopropanol), lint-free cotton swab.

All adjustable optical components should have been adjusted before the dosing process; afterwards only minor corrections at the most should be made so that as little time as possible elapses between the drop contacting the sample and the measurement itself. Otherwise incorrect results could be obtained, for example as a result of evaporation of the liquid.

Illumination �Bright lights cast dark shadows� � this saying only has a limited validity for drop shapes, as the drop liquid is normally light-permeable, so that a bright illumination increases the gray levels not only outside but also inside the drop and possibly produces an unfavorably broad gray level distribution. In addition, if the illumination is too bright then diffraction effects can make the shape appear smaller � the drop is �over-illuminated�. When you have gained some experience in measuring contact angles you will realize that a drop image that is optimal for evaluation frequently seems to be too dark. The gray level values of the image can easily be read off in all three in KRÜSS programs for Drop Shape Analysis � DSA1, DSA2 and DSA3. The value for the current video image position of the mouse cursor is shown in the information bar at the lower margin of the program window.




Fig.1: Gray level measurement for a contact angle standard For the optical drop shape standards, which can be acquired for drop shape calibration, KRÜSS gives gray level guide values of max. 40 for the interior of the drop shape and 170-200 for the outer region. With real drops the value should be measured as close to the drop margin as possible.

Image size Drop shape analysis increases in reliability as the number of pixels that the shape image contains increases � this means that the drop image must not be too small. The width of the drop should amount to between 2/3 and 3/4 of the total image width. In automatic measurement procedures it must be remembered that the middle of the drop is not always exactly beneath the needle, but is frequently slightly displaced to the left or right of the dosing position. This means that in order for every drop to be shown completely some space must remain at the left and right-hand image margins.

Fig. 2: Drop too small; adequately sized drop Please also remember that the contact angle itself makes a contribution to the drop width � smaller contact angles result in broader drops. As a result, for example, if the zoom is set for water drops then a diiodomethane drop could extend beyond the image limits. In order to take this alteration into consideration either the dosing volume must be reduced or the programmed

zoom adapted to suit the corresponding test liquid.

Image sharpness The sharpness is the only truly subjective factor in the optical adjustments � which does not really have to present a problem. The eye is extremely reliable in assessing the sharpness and is better at this than the resolution of current cameras and monitors � this means that there is no �concealed� unsharpness. In addition, a slight degree of unsharpness frequently has no effect at all or only a slight one on the precision of the contact angle measurement. In principle, focusing can be carried out on the needle or drop image. For non-programmed single measurements, which involve or demand adjustment of the optics for each drop, focusing should take place on the drop image. In contrast, with automatic measurement focusing should be carried out on the needle. The same applies as for the horizontal position: the center of the drop may be slightly in front of or behind the needle. On average � assuming a Gaussian distribution of the position inaccuracy � focusing on the needle results in the smallest variation from the maximum sharpness. The positioning error often results from electrostatic charges on the sample � which is why sample preparation (see part 1 of this series) can also influence image sharpness.

Baseline The baseline � the border between drop shape and sample surface � is a sensitive factor in shape recognition. A slight displacement of its height can result in an alteration of the measured contact angle by a few degrees. In order to avoid systematic errors during multiple measurements on a drop the baseline should be determined not just once, but separately for each drop shape analysis. The DSA programs determine the baseline automatically by using the peak or inflection points in the drop shape. These are formed by either the termination of the drop shape line itself or � with reflecting drops � by the transition between the drop image and its mirror image. The second case is the more favorable one. If the surface provides a clear mirror image of the drop shape then the baseline will be recognized exactly.

max. 40 170-200




With non-reflecting samples a max. 4° observation angle can be set for easier recognition of the baseline. At this angle the distortion of the shape is so small that it hardly affects the measured value; the transition between the drop shape and the sample is much clearer. The DSA100 is equipped with specially constructed prism optics allowing the inclination angle to be adjusted. If the video system uses a frame-grabber then the contrast can be additionally increased by using the software; this also makes it easier to recognize the border region.

Fig. 3: Drop with baseline In principle the user should make use of automatic baseline recognition wherever possible. The baseline should only be set manually when no recognition is possible after the measures described above. Setting the baseline becomes even more difficult when the sample not only reflects poorly, but is also inhomogeneous. In this case a large number of measured values with a manually set baseline is frequently necessary. In such a case it is better not to measure online, but to make the measurements on stored drop images or videos.

Small contact angles With small contact angles and correspondingly flat drops the light meets the drop at an obtuse angle. The result is total reflection of the light from the upper part of the light source, the drop shape may then be impossible to recognize. For this reason the illumination of the DSA100 is fitted with a sliding diaphragm with which the upper part of the illumination can be covered. On the basic instruments the user can tape over this region, but should avoid contaminating the light source.

Summary The optical components of a contact angle measuring instrument provide many different ways of influencing the quality of the results obtained and of standardizing the measuring procedure. By making good preparations and selectively setting the illumination, zoom,

sharpness and observation angle the reproducibility of the drop shape analysis can be improved and even difficult samples mastered.


KRÜSS GmbH • Borsteler Chaussee 85-99a • 22453 Hamburg

Tel.: +49 (40) 51 44 01 - 0 • Fax: +49 (40) 51 44 01 - 98 • eMail: [email protected] • http://www.kruss.de

Practical contact angle measurement (4)

Technical note: TN314e Industry: all Author: F. Thomsen Date: 05/2008

Method:

Contact Angle Measuring Instrument DSA100

Measuring with method – but with which one? Keyword: methods, contact angle, sessile drop,

For computer-supported drop shape analysis mathematical models are used which describe the optically determined shape. The DSA software from KRÜSS provides various methods with different application and validity ranges for this. This fourth part on practical contact angle measurement gives an overview of the methods and mentions the criteria for selecting the most suitable method. The user of the historical goniometer for contact angles was not plagued by the choice of method: by using a scaled rotating disk a tangent was aligned to the drop shape by hand. Today the optical evaluation is carried out by camera and software, which on the one hand represents a great step toward high-resolution and reproducibility, while on the other hand requires more know-how from the user.

Selecting the drop type Before carrying out the drop shape analysis the drop type must be selected in the DSA software. The drop type describes the arrangement of sample and drop in the image. The type to be selected therefore inevitably depends on the measuring setup used.

Sessile Drop

The sessile drop is the standard arrangement for contact angle measurement. A drop lying on the solid surface forms a characteristic contact angle with the surface at the three-phase contact point.

Fig.1: Sessile drop: a drop lying on the solid sample

Captive bubble

With high-energy surfaces the user faces the problem that with each liquid a very small, hardly measurable contact angle is formed. It may also happen that the sample can only be measured when it is immersed in a liquid – soft contact lenses, for example. In such cases the captive bubble method is the classical method: instead of a drop an air bubble is deposited beneath a solid sample surrounded by a liquid phase. The angle measured within the bubble shape is not yet the contact angle between solid and liquid that we are looking for. This results from the difference between 180° and the bubble angle. The DSA programs carry out this calculation automatically.

Fig.2: Captive bubble: an air bubble sitting beneath a solid sample




Pendant drop

The pendant drop is not used for contact angle measurements. In this setup a drop (as large as possible) hangs from a needle. If the image scale is known then the pendant drop shape can be used to calculate the surface tension of the liquid.

Fig.3: Determining the surface tension on a pendant drop

Shape analysis and baseline All the KRÜSS drop shape analysis programs determine the contact angle in two steps. In the first step the drop image is subjected to a gray level analysis. The result is an optically determined contour line around the phase boundary in the drop image. In the second step this drop contour is described mathematically. The contact angle is obtained from the angle between this drop contour function and the sample surface, whose projection in the drop image is known as the baseline (see Fig. 4). The mathematical description of the baseline depends on its shape: a straight-line equation for a flat surface, a circular function for rounded substrates.

Fig.4 Contour analysis on a flat and a curved sample surface For the analysis of the drop shape several models are available.

Models for contour analysis The drop contour is a curved line for whose mathematical description several models are implemented in the KRÜSS drop shape analysis programs (DSA). The more that the actual contour follows the requirements of the model, the more suitable the model is for analyzing the contour. For this reason the DSA programs show both the optically determined and calculated contour lines. The agreement of these two lines is an important criterion for the quality of the contour analysis.

Circle method

In the circle method a drop shape in the form of a circular arc is assumed. This requirement is only fulfilled to a large extent by very small contact angles and drop volumes. A version of this method is the height-width method, in which the height and width of the rectangle enclosing the arc are determined.

circular arc

enclosing rectangle

Fig.5 Circular and height-width methods: drop shape as arc A disadvantage of the height-width method is that instead of the whole contour only a few pixels at the point of inflection and at both sides are used. The measurement is therefore more susceptible to interference in these areas.

Conic section method

In this model an elliptical drop shape is assumed. The conic section method or tangent method 1 fits a general conic section equation to the drop shape. The contact angle is determined as the angle between the baseline and the tangent at the conic section curve at the three-phase contact point.

Polynomial method

The polynomial method or tangent method 2 only evaluates the phase contact region. Basically there is no geometrical requirement for the contour shape: the polynomial adapts itself to

Contour line Baseline (substrate)

Contour line Baseline (substrate)

θ θ




any curve that can be thought of at the three-phase contact point.

Young-Laplace method

The Young-Laplace fit is particularly suitable for symmetrical drop shapes that are not affected by interferences such as sample tilting or contact with the deposition needle. The Young-Laplace method takes the charac-teristic drop shape under the influence of gravity into account with a sophisticated iteration method. It is also used for determining the surface tension from the shape of a pendant drop (see above).

Choice of a suitable model The criteria described in this section should help with the selection of the suitable model for the contour fit for the particular drop.

Small or large contact angle?

With small contact angles, particularly in combination with small volumes, the contour can be well described as an arc. For the lower measuring range up to 10° the circle method provides the most accurate results. From about 20° the contour assumes a more and more elliptical shape, which it finally varies from at large contact angles.

Fig.6: left: circle method, right: conic section method. For the same drop contour the contact angle measured on the left is about 6° too small. The circle or height-width methods should accordingly only be used for angles up to 20° and the conic section method only up to about 100°. The polynomial method and the Young-Laplace fit can be used throughout the whole measuring range above 10°. In the captive bubble measurement the angle between the air bubble and the solid is normally very large. For this reason only the polynomial method and the Young-Laplace fit come into question for this method.

Small or large drops?

With larger drops there is also a greater variation of the drop contour from the circular or elliptical shape. Its own weight causes the drop to flatten noticeably. This influence is particularly marked with the test liquid diiodomethane, in which a low surface tension occurs together with a high density. For liquids with such properties the polynomial method or the Young-Laplace fit should be used for drops of more than 3 μl.

Dynamic or static drops?

This criterion is not related to the drop shape itself, but with the deposition method: in measurements using advancing or retreating angles the deposition volume changes continuously; the needle tip is also located within the drop. This means that only methods can be used that are largely insensitive to the contact between drop and needle – the two tangent methods, conic section and polynomial. In each case care should be taken that the distortion of the drop shape by contact with the needle does not stretch out to the three-phase contact point. This is why larger drop volumes are recommended for measurements with advancing and retreating angles than for static drops. If the adhesion of the liquid to the needle distorts the drop too much then the use of a PTFE deposition needle can provide help.

Symmetrical or asymmetrical drops?

Contact angle measurements are frequently used to study the homogeneity of a sample. If the sample surface is inhomogeneous then it is often not just the contact angles of various drops that differ. Individual drops can also be deformed, so that the contact angles at the left-hand and right-hand sides differ. The same applies to measurements on a tilted table, on which the drops are deformed by the inclination.

Fig.7: Polynomial fit with a tilted table measurement. The drop shown is located on an inclined surface.




The circle method and Young-Laplace method cannot be used with such drops: they produce a single contact angle which is either inaccurate or completely nonsensical for asymmetrical drops. In such cases only the two tangent methods can be used, as they can detect differences between the left-hand and right-hand contact angles. With very asymmetrical drops only the polynomial method produces reliable values.

Robustness

Up to now it could be assumed that the polynomial method can be used for any shape and size of drop as well as for dynamic drops, so why not always use this method? The answer is that although the polynomial fit can analyze any imaginable curve shape in the contact region, it also reacts to interferences more sensitively than other methods. If the drop image is not flawless, then a "vertical flip" of the tangents can be observed sporadically – the measured angle bears no relationship to the actual value. The polynomial method requires a clean, high-contrast drop shape image to a greater extent than other methods. The Young-Laplace fit is the model of choice if a symmetrical, disturbance-free drop contour is present - and if the longer calculation time for this fit is acceptable. A symmetrical drop is mathe-matically represented exactly by the Young-Laplace model, so that the best agreement between the theoretically and optically deter-mined contours can be expected. A further advantage is that if the image scale is known the real drop dimensions – volume and wetted area – can be determined.

Summary There is no universally suitable model for the drop shape analysis of all shapes and sizes of drops. The size of the contact angle and the drop, the deposition method and the symmetry of the drop are important criteria for selecting the suitable measuring method. The following table provides an overview of the selection guidelines given in this article.

Circle Conic section

Poly-nomial

Young-Laplace

Measuring range

0-20°

10-100°

100-180°

Drop weight (volume∗density)

Low

High

Very high

Deposition

Static (contour without needle)

Dynamic (contour with needle)

Contour shape

Symmetrical

Slightly asymmetrical

Very asymmetrical





Technical note: TN315e Industry: all Author: Dr. F. Thomsen Date: December 2008

Method:

Contact angle instrument DSA100

Custom-made models: from contact angle to surface free energy Keywords: methods, contact angle, sessile drop, surface free energy, interfacial tension

The determination of the surface free energy (SFE) of a solid is the ultimate in contact angle measuring techniques. The method provides the user with important information about the material surface, such as its wettability and adhesiveness. In order to plan a measurement and draw the correct conclusions from the results a good knowledge of the scientific models upon which these are based is useful. In this final part of the Newsletter series on contact angle measurement the most important models for determining the surface free energy (SFE) are described; these are used in practice (and in KRÜSS software). In addition to the proper use of the models, it is also concerned with the practical aspects of SFE determination: selection of suitable test liquids, suitable ambient conditions and the consequences arising from the properties of the solid surface.

About models The keyword �model� may perhaps have a sobering effect on one reader or the other: an SFE value obtained from contact angle data is not knowledge about a solid that is carved in stone, but rather an interpretation of its behavior within the framework of the model used. Strictly speaking, this applies to any scientific statement. However, many formulations from the natural laws are so familiar to us that we are now no longer aware of their model character.

Fig.1: Copernicus� model of the solar system � since �relativized� by Einstein The measure for the meaningfulness of a model is its consistency, the possibility of explaining observed phenomena in as simple a way as possible and of making predictions that can be confirmed empirically. This means that it is a good idea for users of the contact angle measuring technique to familiarize themselves with the theory � and limitations � of the models used.




Surface tension and surface free energy Surface tension (ST in the following text) and SFE are equivalent physical terms; the first is conventionally used for liquids and the second for solids. In a liquid the surface tension results from the fact that a molecule at the surface is in contact with fewer neighboring molecules that it can interact with than in the bulk of the liquid. Remaining at the surface is less attractive for molecules of a (pure) liquid. This is why liquids attempt to achieve as small as surface area as possible; work is required to increase a surface.

Fig. 2: Forces between molecules in the condensed phase and at the boundary In principle the same applies to the SFE of solid phases. However, it is hardly possible to directly measure the amount of work required to increase a surface, as it is difficult to differentiate this work from the work of deformation of the bulk phase. The SFE of a solid can be measured indirectly by using its wettability by liquids. This is where the contact angle enters the picture.

Contact angle and surface free energy As long ago as 1805 Young established a relationship between the contact angle θ and the ratio of the ST of the liquid ( lσ ) and solid phase ( sσ ). Young�s basic equation for the contact angle was:

θσγσ cos⋅+= lsls . If the contact angle is measured and if the ST of the liquid is known there are still two unknown quantities: the SFE of the solid ( sσ ) and the interfacial tension between the phases ( slγ ). Various models were drawn up to explain the relationship between these two quantities. In them the interfacial tension (IFT) was usually derived from molecular interactions between the

phases. In principle the following applies: the greater the interactions occurring at the phase boundary, the lower the IFT.

Zisman

Zisman [13] plotted the cosine of the contact angle against the surface tension of the corresponding liquid. He defined the extrapolated value for cosθ=1 (θ=0°) as the critical ST ( cσ ). This quantity was supposed to correspond to the ST of a liquid in which complete wetting is just taking place. Zisman himself regarded the critical ST as being only a measure of the SFE of the solid, but did not give these two quantities the same value � in contrast to many subsequent users of the Zisman plot. In actual fact,

cσ and sσ are only practically the same for non-polar solids and liquids, and the greater the distance between the extrapolated value for cσ and the test liquid with the smallest ST, the more inaccurate the result. Today test inks still work according to the critical surface tension concept: the liquid selected from a series of liquids with defined surface tensions is that liquid which just wets the solid completely.

Fowkes and Owens-Wendt-Rabel-Kaelble (OWRK)

Fowkes [2] assumed that various types of interaction are responsible for the ST of a phase � disperse and non-disperse (polar) interactions. On this basis Fowkes first determined only the disperse fractions of the ST. Owens and Wendt [9] as well as Rabel [10] and Kaelble [5] used Fowkes as a basis and determined the disperse and polar fractions of the ST of liquids and the SFE of solids. In the two-component model according to Fowkes and OWRK the IFT lsγ is obtained as the sum of the STs of the individual phases, reduced by the disperse (D) and polar (P) interactions between the phases. These interactions are calculated as geometric mean values:

)(2 Ps

Pl

Ds

Dlslls σσσσσσγ ⋅+⋅−+=

In the DSA software this equation forms the basis for both the Fowkes and the OWRK method; the methods differ only in the calculation path. With OWRK the polar and disperse fractions are obtained from a graphical evaluation. In the two-component model the IFT depends on whether the polar and disperse fractions can




enter into interactions with the corresponding fractions in the bordering phase. For example, the IFT becomes smaller against the polar liquid water when the solid is also polar. In contrast, if the polar fraction of the solid is low then the square root term P

sPl σσ ⋅ assumes a smaller

value. The polar interactions then only make a small contribution to lowering the IFT; this corresponds to poor wetting � a large contact angle. In the following illustration the various types of interaction are symbolized by hands � only similar hands can grasp each other.

---------------------------------------------------------------------------------

Fig. 3: Schematic diagram of phase contact in the two component model Rabel used the model for studies on polyethylene surface treatments � it has actually proved to be workable, particularly for the activation and coating of plastics. Even when working with only two test liquids the empirical findings for wettability and adhesion often correlate well with the ST values calculated according to OWRK and the polar and disperse fractions � although Good has produced theoretical objections to the method used for calculating the polar fraction (see below). The two-component model has far-reaching consequences for the interpretation of wettability. An IFT of 0 mN/m leads to a contact angle of 0°; conversely the IFT can be larger than zero for a contact angle of 0°. For practical coating applications, for example, this means that even for an optimally wetting liquid the adhesion can be destabilized by a residual IFT.

Fowkes (extended)

In a more recent paper [1] a three-component model has been developed in which the polar fraction has been further split up into a hydrogen

bridge bonding fraction ( Hσ ) and a fraction for

dipole-dipole interactions ( Pσ ). The above equation has been extended by a further square root term:

)(2 Hs

Hl

Ps

Pl

Ds

Dlslls σσσσσσσσγ ⋅+⋅+⋅−+= .

Accordingly this means that at least three test liquids are required for determining the SFE. This method, which is included in the DSA software as �Extended Fowkes�, is rarely used for material testing. However, it is valuable for estimating the adhesion between two phases, as hydrogen bridge bonds have greater bonding energies when compared with disperse and dipole-dipole interactions. The wettability of a solid by water depends to a great extent on the ability of the solid to form hydrogen bridge bonds.

Wu

Wu [11;12] stated that for a low SFE the harmonic mean between the particular fractions (disperse and polar) often provided more reliable values than the geometric mean. The use of the harmonic mean corresponds to the following equation:

)(4 Ps

Pl

Ps

Pl

Ds

Dl

Ds

Dl

slls σσσσ

σσσσσσγ

+⋅+

+⋅−+=

The empirical basis for this is provided by interfacial tension measurements between polymer melts, i.e. materials with a predominantly low surface tension for the individual phases. Accordingly the Wu method is mostly used for SFE calculations for polymers with low surface free energies (up to 30-40 mJ/m2).

Acid-base model as per Oss and Good

The authors Oss and Good [3; 4; 8] adopted the definition of the disperse fraction from Fowkes, but split the polar fraction into an electron acceptor (acid, +σ ) and an electron donor

fraction (base, −σ ). The objection to Fowkes, OWRK and Wu is that not all the polar interactions can be set in relationship to one another � a Lewis base, for example, can only enter into interactions with the acidic components of a bordering phase and not with the basic components. Accordingly the opposing components for the polar interactions are gathered together in the square root terms in the equation:

)(2 +−−+ ⋅+⋅+⋅−+= lslsDl

Dslssl σσσσσσσσγ




Despite the compelling theoretical nature of this approach it is currently little used in practice. This could be because the choice of test liquids with known basic and acidic fractions is relatively limited. In addition, other models such as OWRK or Wu have proven themselves many times in practice and require less measuring data than the acid-base method. Negative IFT values, which are possible in the acid-base model, are not easy to interpret.

Equation of state

The methods mentioned up to now have been linked historically and systematically to one another: after the influence of non-disperse interactions became known, its components were described by using various models. The work Neumann et al [6;7] was carried out in a different field; their theory entered the SFE determination as an �Equation of State�. According to the thermodynamic approach of Neumann, breaking down the ST into interactive components does not hit the target. The not undisputed [see 4,32] theory does not need any differentiation of interactive components and requires only one liquid with a known ST � the advantage lies in the rapid access to an SFE value. As Neumann has mainly derived his equation from results for non-polar solids with low surface free energies, his approach can primarily be used in this field. For such solids the results tend to agree with those obtained by evaluations according to Zisman or OWRK.

Selecting the liquids Some standard test liquids were mentioned in part 1 of this Series and their use for measuring contact angles was described. The liquids that are suitable depend on the requirements of the particular model for the evaluation.

Number of test liquids

The fact that the reliability of the result increases with the number of test liquids used applies to all models. For Zisman, Fowkes, Extended Fowkes and OWRK this means that more data are used for the linear regression; in other methods more individual equations can be used to calculate an arithmetical mean SFE value.

Test liquid properties

In the multi-component models the values of the liquid components should be spread as widely as possible. For example, for Fowkes and OWRK liquids with both the largest and smallest polar fractions should be included in the selection. Water and diiodomethane is a frequently used pairing with only two liquids. Diiodomethane is ideal, because as a purely disperse or � for some authors � slightly polar liquid it has a relatively high ST and therefore forms easily measurable contact angles with many solids. In contrast, non-polar liquids which spread on almost any solid (e.g. n-hexane), are not suitable for the measurement. In the Extended Fowkes and the Acid-Base method the choice of liquids is limited, as to date only a few substances have been characterized with regard to the relevant components. Water should always be used for both methods because of its marked hydrogen bridge formation and its amphoteric character (Lewis acid and base at the same time) unless it chemically changes the solid surface. Mixtures of liquids should not be used, because the liquids have different affinities to the solid and form a different (and unknown) mixing ratio at the interface from that in the bulk phase.

Consistency of selection

The more similar the measuring conditions, the more meaningful is the comparison between the SFE data of different samples � this also applies to the number and selection of the test liquids. As far as possible solids whose SFE values are to be compared should be measured with the same test liquids. The databases of the KRÜSS software products contain several entries for many liquids whose data is provided by different authors. For comparative measurements the liquid data should always be taken from the same source. For two-component models with the geometric mean of the components (Fowkes, OWRK), KRÜSS recommends using the data from Ström, which are based on the geometric mean. For many liquids data has additionally been provided by the authors Fowkes, Owens or Rabel. In the Wu evaluation the required consistency cannot be completely achieved, as no liquid data exist with which the harmonic mean values of the components have been calculated. This is why the same liquid data is usually used for Wu as for Fowkes or OWRK.




Sample preparation and ambient conditions Many solid surfaces have much higher surface free energies than liquids. For this reason they tend toward passivation, e.g. by the formation of oxidation or gas and vapor adsorption layers. This is why the SFE of solids depends more strongly on the chemical surroundings than the ST of liquids (e.g. air or inert gas, air pressure, relative humidity). There are special methods for the measurement on high-energy samples, e.g. contact angle measurement at the interface between two liquid phases instead of in air as in the Schultz method, or measurement under inert gas. However, the contact angle is usually measured at the three-phase point liquid/solid/air. Ideally the solid sample should be stored at the intended relative humidity and temperature for a long time before the measurement � it is important that the selected standard conditions are kept the same for all samples. Vapors of organic liquids should be avoided at all costs, as they form stable adsorption layers on many samples. In this case the contact angle with water will then be larger and the calculated SFE value lower than on an uncontaminated surface. For the same reason spreading liquids with a high vapor pressure are not suitable � within a large area around the deposited drop the sample is spoiled for measurements with other, poorly wetting liquids.

Properties of the solid In contrast to liquids, hardly any molecules change places in a solid; this means that the surface free energy describes a static condition of the solid and not a dynamic equilibrium between mobile particles. As a result, the SFE of a chemically inhomogeneous solid may depend on the place of measurement. In addition, the macroscopic structure of the surface influences the contact angle.

Roughness

Young�s equation can describe ideal solids that are smooth, flat and chemically homogeneous. The roughness of the material should be taken into consideration in every measurement: the rougher the solid the harder it is to correlate the measured values with the chemical properties of the surface. Nevertheless, an SFE calculation for a rough solid is not without value. For example, an

evaluation according to OWRK still describes the behavior of the solid toward differently polar liquids with different surface tensions. However, the user should be clear that the framework of the model has been exploded. The calculated values are only empirical quantities. As such they are still useful; however, differences between a smooth and a rough sample should not be interpreted as differences in polar and disperse interactions.

Chemical inhomogeneity

Strictly speaking, the SFE is a property of exactly that surface position at which the measurement was made. Before the measurement a decision must be taken as to whether a global value for the surface is being sought for, or whether local differences in the SFE are to be determined. In the first case drops of each liquid should be deposited as far away from each other as possible and a mean value for the contact angle obtained for each liquid across the whole sample. In the second case one drop of each test liquid should be deposited as close to one another as possible. The SFE can then be calculated for the corresponding position by using such a group of drops of different test liquids.

Literature 1. Chen Jie-Rong; T. Wakida, Studies on the

Surface Free Energy and Surface Structure of PTFE Film Treated with Low Temperature Plasma. In: Appl. Poly. Sci 63,13 (1997), S. 1733-1739.

2. F. M. Fowkes, Attractive Forces at Inter-faces. In: Industrial and Engineering Chemis-try 56,12 (1964), S. 40-52.

3. R. J. Good; C. J. van Oss, The Modern Theory of Contact Angles and the Hydrogen bond Components of Surface Energies. In: G. I. Loeb; M. E. Schrader (Hrg.): Modern approaches to wettability. 1992, S. 1-27.

4. R. J. Good, Contact Angle, Wetting and Ad-hesion: a Critical Review. In: K. L. Mittal (Hrg.): Contact Angle, Wettability and Ad-hesion. Festschrift in Honor of Professor Robert J. Good. Utrecht 1993, S. 3-36.

5. D. H. Kaelble, Dispersion-Polar Surface Ten-sion Properties of Organic Solids. In: J. Adhesion 2 (1970), S. 66-81.

6. D. Li; A. W. Neumann, Equation of State for Interfacial Tensions of Solid-Liquid systems.




In: Advances in Colloid and Interface Sci-ence 39 (1992), S. 299-345.

7. E. Moy; A. W. Neumann, Solid/Liquid Inter-facial Tensions from contact Angle Data and Direct Force Measurements. In: J. Coll. Interf. Sci. 119,1 (1987), S. 296-297.

8. C. J. van Oss; M. K. Chaudhury; R. J. Good, Interfacial Lifschitz-van der Waals and Polar Interactions in Macroscopic Systems. In: J. Chem. Rev. 88 (1988), S. 927-941.

9. D. Owens; R. Wendt, Estimation of the Sur-face Free Energy of Polymers. In: J. Appl. Polym. Sci 13 (1969), S. 1741-1747.

10. W. Rabel, Einige Aspekte der Benetzungs-theorie und ihre Anwendung auf die Unter-suchung und Veränderung der Ober-flächeneigenschaften von Polymeren. In: Farbe und Lack 77,10 (1971), S. 997-1005.

11. S. Wu, Calculation of Interfacial Tensions in Polymer Systems. In: J. Polym. Sci. 43 (1971), S. 19-30.

12. S. Wu, Polar and Nonpolar Interaction in Ad-hesion. In: J. Adhesion 5 (1973), S. 39-55.

13. W. A. Zisman, Relation of the Equilibrium Contact Angle to Liquid and Solid Consti-tution. In: Advances in Chemistry 43 (1964), S. 1-51.

contact angle measurement in practice (1) - cmi · keywords: methods, sample preparation, contact...

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