Is There A Correlation Between Contact Angle And Stain Repellency?

By Daniel J. Mania | July 14, 2016

Architectural coatings are becoming increasingly robust as we move into the 21st century.  Consumers demand that coatings be more stain repellent or easy-to-clean.  To meet this demand, paint companies advertise highly cleanable, stain repellent paints.  Many people believe that if a material beads on a surface, it will either not stain or the stain will be easy to remove.  In some instances, stain repellency or ease of cleaning may occur; however, there are times when beading will concentrate the stain in a small area, making the stain more noticeable or harder to remove.

Three basic starting point interior flat paint formulations were used in this study.Various binder chemistries were used including all-acrylic, vinyl-acrylic, and ethylene-vinyl acetate.  Additionally, 18 commercial paints were also evaluated.  Four different stain repellent additives were included (either included in the formulated paints or post-added to the commercial paints).  The stain repellent materials were added to approximately 80% of these samples to increase stain repellency performance variability.  Two main output variables were used to determine if a correlation exists: (1) contact angle as measured by goniometer, and (2) stain repellency as determined by a standard coating stain repellency test method, measured using a colorimeter for absolute change in the L* value in the L*a*b* color space.

No correlation was found to exist between the contact angle of water or dodecane and stain repellency to nine different household chemicals.  Within a very small set of samples, slight correlations were found to exist between diiodomethane and several of the household chemicals.  However, this set was less than 10% of the total sample set of 171 samples, thus it may not be statistically relevant.  This suggests that contact angle should not be used as a developmental predictive tool for stain repellency testing.

Adhesion is a very important concept for many industries and applications.  A simple Merriam-Webster definition of adhesion is “the act of sticking or attaching something”. 1
More precisely, according to Kinloch2, there are four main components or mechanisms of adhesion: mechanical interlocking, diffusion theory, electronic theory, and adsorption theory.  Depending upon the type of system involved, one or more of these mechanisms can apply.

Since this paper involves correlating contact angle with stain repellency (or lack of adhesion), we will focus on adsorption theory starting with the Dupre equation, also known as the Work of Adhesion equation3:

WA = γs   +   γlv   -   γsl  (1)


WA - sum of free energies
γs - surface free energy of the solid phase
γlv - surface free energy of the liquid phase
γsl - interfacial free energy

The issue with the Dupre equation is that it contains components that are difficult if not impossible to measure, specifically, the interfacial free energy. Young2,3 developed an equation to describe the relationship between interfacial energy and contact angle:

γs   -  γsl = γlvcosθ  (2)

where θ is the contact angle of the liquid on surface s.

Combining equations 1 and 2 yields the Young-Dupre equation:

WA = γlv (1 + cosθ)  (3)

The Young-Dupre equation allows for predictability of adhesion based upon the surface free energy of the liquid in question and the contact angle of the liquid upon the surface in question.  In this case, the smaller the contact angle (θ), the better are the chances of good adhesion.

When θ ≥ 90°, cosθ ≤ 0, which should indicate lack of adhesion.
Under normal circumstances, we would be evaluating adhesion by attempting to find a polymeric material that has a low contact angle on a substrate so as to increase chances of successful adhesion.   However, here we are looking to do the opposite.  We are attempting to establish stain repellency, by either ease of cleaning or a lack of adhesion, which in this case would be equal to a lack of adhesion, which in turn would be equal to a high contact angle.

To determine if a correlation exists, we need to measure the contact angle and calculate the surface free energy, in addition to determining stain repellency.  Multiple methods exist to determine stain repellency4-8, some of which utilize a colorimeter to measure the color difference in a given color space between an un-stained/soiled area, and a stained/soiled and cleaned area.  We used the light-dark (L*) value in the L*a*b* color space for this work.

Surface energy analysis can be accomplished in multiple ways9-14, e.g., Fowkes, Owens-Wendt, Wu, Schultz, Oss-Good, extended Fowkes, Zisman, and the Neumann Equation of State to name a few.  All these methods involve some type of measurement and a calculation.  We chose the method of Wu because it requires only two liquids of known and disparate polar and dispersive components.  Additionally, the Wu method is suitable to determine the surface energy of polymeric materials with values up to 40 mN/m.9  We chose water as a mostly polar liquid and either diiodomethane or dodecane as our mostly dispersive liquid.  The values for the surface free energy of each liquid used in this study are listed in Table 1.

We used the sessile drop technique16,17 with a goniometer to measure the contact angle, which was then used to calculate the surface free energy.  Surface energy can be calculated from contact angles using various formulae as mentioned previously.  We focused on the Wu method since it is useful for calculating surface energies in the expected range of our samples (< 40 mN/m).  Water and dodecane were tried with every sample, but in about 10% of the samples, dodecane completely wet the surface too quickly for us to measure the contact angles.  In those cases, we used diiodomethane.  Using these solvents’ known free energies, the contact angles, and the following equation (calculated using Kruss Advance Drop Shape software), we were able to calculate the dispersive, polar, and total surface free energy of each substrate.

where superscripts D and P represent the Dispersive and Polar component, respectively.  A correlation coefficient analysis data tool pack within Microsoft Excel® was used to determine correlation coefficients between the variables listed in Table 2.

Methods and Materials
A total of 171 paint samples, including formulated and commercial coatings, were used in this evaluation.  Eighteen different commercial paints from six different paint manufacturers were used as part of this study.  These paints were used as is, and four additional samples per paint were prepared using four different stain repellent post-add additives.  Commercial paints accounted for 89 of the test samples.  The remaining 82 samples were produced from six different internally developed paint formulations using the same post-add stain repellent additives.  The testing formulation variables were:

• RhoplexTM 585 (all-acrylic)
• RovaceTM 9900 (vinyl-acrylic)
PVC (%):
• 47
• 57
Stain repellent additive:
• None
• Variant 1
• Variant 2
• Variant 3
• SILRES® BS 6500 A
WACKER Developmental Stain repellent additive concentration (%):
• 0.75
• 1.50

Test panels were prepared according to ASTM D3450 - Standard Test Method for Washability Properties of Interior Architectural Coatings5, using a 10-mil square draw-down bar.  The panels were allowed to air dry for seven days prior to stain testing.  The staining agents were compiled from the following sources:

• ASTM D1308 – Standard Test Method for Effect of Household Chemicals on Clear and Pigmented Organic Finishes4
• ASTM D3450 – Standard Test Method for Washability Properties of Interior Architectural Coatings5
• ASTM D4828 – Standard Test Method for Washability of Organic Coatings6
• Ceramic Tile Institute of America, Inc., CTIOA Field Report T-72 (R-02)7.
• Stain Repellency Testing of Cementitious Grouts8
• Grout Market Survey15

The stains used were:
• Mustard
• Ketchup
• Red wine
• Red lipstick
• Coffee
• Vegetable (soybean) oil
• Soy sauce
• Cola
• ASTM stain media

Stains were applied in lines across the surface of the paint samples so that all the stains could be cleaned using a linear wash/abrasion machine.  Various test methods stipulate stain residence times varying from 15 minutes to 24 hours.  We chose one hour so that none of the liquids had sufficient time to completely dry, and we would have a wide range of performance from good to bad.

After the one hour stain residence time, the panels were blotted dry with a paper towel, and quickly rinsed off under running water.  The panels were then clamped into the stainless steel tray of the abrasion testing machine.  Standard ASTM sponges were pre-wetted and 25 mL of pre-prepared cleaning solution (3 g of water to 2 g of ASTM non-abrasive scrub media) were applied to the sponge according to ASTM D3450 (100 back-and-forth scrub cycles).  The panels were rinsed again and allowed to dry for 24 hours prior to determining stain repellency.

Stain repellency data was collected using a colorimeter with L* from the L*a*b* color space as the evaluation parameter.  The unstained control value was measured on an unstained and clean area, while values were also measured at each of the stained and cleaned areas.

For example, the L* value for sample 1 was 96.51, and the L* for the red wine stained and cleaned area for the same sample was 94.53.  The difference of 1.98 was used for the stain repellency data.  The lower the number, the closer the actual L* value is to the original unstained area equating to better stain repellency.  Conversely, the higher the L* value, i.e., further away from the value for the original unstained area, the worse is the stain repellency.

A Kruss DSA30 Drop Shape Analysis System was used to measure the contact angle of the liquids.  Using the sessile drop technique, water and dodecane were used to measure contact angles, However, dodecane spread too quickly and flat to be read over 13 of the samples so diiodomethane was used for those 13 samples as the second required contact angle measurement used to calculate surface energy.  An average of three readings was used to determine the contact angle for each liquid over each sample.  The two solvent method of Wu was used to calculate surface dispersive, polar, and total surface free energies.

The data was entered into an Excel® spreadsheet and analyzed using a correlation coefficient data analysis tool pack included in the software.  We evaluated for correlations between all contact angles, all surface energy calculated values, and all L* absolute values for each staining agent to determine what, if any, correlation existed.

• 10 mil stainless steel, 4 inch wide, drawdown square
• Black vinyl scrub charts
• Goniometer – Kruss DSA30 with Advance Drop Shape Software
• Colorimeter – Byk Spectro Guide Sphere

Results and Discussion
Given the magnitude of the data generated from this work with 171 samples, this discussion is focused upon selected data to highlight specific information and with summarized data to highlight trends.
Table 3 shows the stain repellency data for one set of commercial paints.  The stain repellency performance range exhibited minimum values of L* around 0.2, which may not be discernible to the human eye, while other stains resulted in L* values > 5.0, which are clearly noticeable and do not appear to have been either repelled or easily removed.  Table 3 exemplifies the range in stain repellency performance for the commercial paints in this study.

A similar example is shown in Table 4 for a set of the formulated paints.  The performance for the formulated paints is even broader showing a drastic disparity in stain repellency values. Tables 3 and 4 highlight the broad range of stain repellency data found in this study that is better for determining correlations since small differences are not magnified.

The samples shown in Tables 3 and 4 are also shown in Tables 5 and 6, respectively, except that these tables highlight the contact angles and subsequent calculated surface energy values used to determine if any correlation to stain repellency exists.  The range of values for contact angle and surface energy are not as different within each set of paint samples.

However, Table 7 shows the complete range of data for contact angle measurements and calculated surface energy data.  Again, the broad range indicates a good spread of data for determining whether a correlation exists.

The sheer volume of data and the broad range of data should have the effect of reducing variation errors in the correlation coefficient calculations.  Correlation coefficients were calculated for diiodomethane, however, the information is of spurious value since only a small number of very similar samples were measured using this solvent.

The summarized stain repellency data shown in Table 8 represents a very broad range of data with the minimum values for most stains at or below L* of 0.5 or less, and maximum values in excess of 10, and in some cases in excess of 20.

The ASTM black stain media, red lipstick, and red wine were the most deleterious stains and should be considered as being very aggressive for stain repellency testing.  Conversely, while ketchup, soybean oil and cola all have average L* values > 1.0, they show the lowest average staining with values < 2.0.  Thus, in some cases, these materials may either not stain or be easy to clean even though the test substrate may not be very stain repellent.

Since contact angle of a liquid correlates to its surface energy, a relationship is expected between the chemistry of the staining agents and the surfaces to which they are applied.  A discussion of the chemical nature of the staining agents is needed to understand why staining or attraction (adhesion) occurs.  Coffee contains over 20 different chemicals but the more common components are acidic, and thus polar (caffeic acid, chlorogenic acid, and quinic acid).18,19

The main ingredients in tomato ketchup are ascorbic acid, acetic acid, sugars, and lycopene, some of which are polar and others are non-polar.19,20 Soy sauces contain many chemicals as well but primarily are comprised of multiple amino acids and peptides, both of which have polar character.21  Red wine is a veritable cornucopia of chemicals containing alcohol, tannic acid18, and various anthocyanins, again mostly polar species.22  Cola typically contains phosphoric acid, tannins, caffeine and flavonoids23, most of which are polar materials.  Mustard contains vinegar (acetic acid), mustard seeds, and salt, thus making it partially polar.  Soybean oil is a triglyceride of long chain fatty acids, and is essentially non-polar in character.  Red lipstick contains mostly oils and waxes as well as red dyes which are mostly non-polar materials.24 The ASTM staining media is comprised of carbon black dispersed in non-polar oils and solvents.

Correlation coefficients are useful tools to determine first if a correlation exists and second to determine whether the correlation is a positive or negative relationship.  Table 9 lists ranges of correlation coefficients and the subjective descriptors for that particular range.

The descriptive values in Table 9 were used to determine if any correlation exists between the staining agent and contact angle.  Table 10 shows the data for water contact angle.  The only stain that shows any significant correlation with water contact angle is the ASTM black stain media with a value of 0.61 making it a positive and weak correlation at best.

Correlation coefficients were also calculated between all the contact angle measurements and the subsequently calculated surface energy values to determine if a correlation coefficient is a suitable calculation to determine mathematical relationships between stain repellency and contact angle.  The more polar a surface, the greater is its interaction with a polar solvent like water.  This translates to a lower contact angle.  Conversely, the less polar a surface, lesser is the interaction between it and water, and should lead to a higher contact angle.  The data in Table 13 bears this out with a correlation coefficient of -0.89 between increasing water contact angle and decreasing polar component of surface energy.  Similarly, dodecane having almost exclusively dispersive energy should exhibit a total lack of correlation with its contact angle and the contact angle of water, which is the case with a correlation coefficient of 0.12.  However, as previously shown, the correlation between surface energy and contact angle does not extend to stain repellency even upon considering the chemical nature of the staining agents.

While not perfect or absolute, the data suggests that correlation coefficient is not an adequate tool to describe whether a relationship exists between contact angle or surface energy and stain repellency.  The fact that some subjectivity exists in all of the test methods could explain the less than perfect relationships.  For example, while the contact angle is determined using precision equipment, the choice of where to place the interpretative lines is decided by an operator.  Additionally, there does exhibit some variation in the stain removal.  An average of multiple values recorded over a range of the area of the cleaned stains and the choice of where to take the readings with a colorimeter are determined by an operator.  This does not mean that the testing in this study is flawed, rather that it is imperfect due to inherent human error.

Summary and Conclusions
This study evaluated 171 samples for stain repellency, contact angle with at least two different solvents, and calculated surface energy to determine if a correlation exists between stain repellency, contact angle, and surface energy.  This was done in an attempt to determine if a staining agent is more repelled (shows less staining), or easier to clean if the staining agent exhibited a higher contact angle (beading behavior).  Had this been the case, stain repellency development work might be done more expeditiously since no stain testing would have to be done.  However, the opposite was found to be true, at least with respect to contact angles with water and dodecane.  With the exception of a weakly positive correlation between ASTM black stain media and water contact angle, no other relationship was shown to exist within the context of the staining agents used and the chemical agents used to measure contact angle.

No correlation was noted between the chemical nature of the staining agents and the contact angles of any test liquid or subsequently calculated surface energies.   Hansen Solubility Parameters (HSP) may provide a key to establishing a link between staining/stain repellency, the chemical nature of the substrate (coating), and the chemical nature of the staining agents.

HSP values can be estimated25 from surface energy data but the calculations are estimates at best, especially given the limited number of solvents used in this study.  The surface energy analysis only determines the dispersive (Van der Waals) surface energy contribution and the total polar contribution (which in HSP is split into hydrogen bonding and polar components).  Additionally, neither this study nor HSP adequately describes acid-base contributions.

This study, while not being comprehensive of all factors potentially involved (e.g., HSP, contact angle, surface energy, acid-base), does show convincingly the lack of correlation between contact angle and stain repellency.  The problem is more complex and should be investigated further.

This work shows that while determination of contact angle and surface energy is suitable for some applications like adhesive bonding (a long term or permanent effect), it is not appropriate as a predictive tool for determining stain repellency in coatings.

As a result of the comprehensive study we were able to develop a new stain repellent additive for interior architectural coatings that improves stain repellency to household chemicals in most paints at concentrations ranging from 1.0 to 3.0%.  This product is SILRES® BS 6500 A, for more information contact WACKER.

Future Work
Several other components of surface properties could be investigated to determine if they have any impact upon stain repellency and correlating other surface measurements to stain repellency. 

• Contact angle hysteresis might possibly show a correlation to stain concentration or to staining on non-horizontal surfaces.
• As contact angle spread rate is kinetically driven, it may be important to determine if a correlation exists between this and stain repellency at time intervals. 
• For stain repellent material development work, dispersion of the additive throughout the film and on the film surface would be important to determine the efficacy of the stain repellent agents and any correlation between their film locations and stain repellency properties.
• HSP values of surfaces and staining agents should be studied to determine how this affects stain repellency.

1. www.merriam-webster.com
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3. Pocius, A.V. Adhesion and Adhesives Technology: An Introduction, 3rd ed.; Hanser Publications, Cincinnati, OH, 2012.
4. ASTM D1308 – 02 (Reapproved 2013) Standard Test Method for Effect of Household Chemicals on Clear and Pigmented Organic Finishes.
5. ASTM D3450 – 00 (Reapproved 2010) Standard Test Method for Washability Properties of Interior Architectural Coatings.
6. ASTM D4828 – 94 (Reapproved 2012) Standard Test Method for Practical Washability of Organic Coatings.
7. Ceramic Tile Institute of America (CTIOA), CTIOA Field Report T-72 (R-02) Subject: Stain Test
8. Mania, D.J. Stain Repellency Testing of Cementitious Grouts, 4th Annual American Drymix Mortar Council Encyclopedia, 2014, 54-65.
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11. Hansen, F.K. The Measurement of Surface Energy of Polymers by Means of Contact Angles of Liquids on Solid Surface – A Short Overview of Frequently Used Methods, University of Oslo, 2004.
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13. Duncan, B.; Mera, R.; Leatherdale, D.; Taylor, M.; Musgrove, R.; NPL Report DEPC MPR 020 – Techniques for Characterizing the Wetting, Coating and Spreading of Adhesives on Surfaces, National Physical Laboratory, Middlesex, UK, 2005.
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15. Unpublished internal market survey of cementitious tile grout performance by Daniel J. Mania, Wacker Chemical Corporation.
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19. Presentation from BASF by Nicholas Foley, Ph.D. at a Canadian Coatings Symposium in November 2015.
20. Sharoba, A.M.; Senge, B.; El-Mansy, H.A.; Bahlol, H.E.; Blochwitz, R. Chemical, sensory and rheological properties of some commercial German and Egyptian tomato ketchups. Eur. Food Res. Technol. 2005, 220, 142-151.
21. Gao, X.; Cui, C.; Ren, J.; Zhao, H.; Zhao, Q.; Zhao, M. Changes in the chemical composition of Chinese-type soy sauces at different stages of manufacture and its relation to taste. Int. J. Food Sci. Technol. 2011, 46, 243-249.
22. Kennedy, J.A. Chapter 13, The Chemistry of Red Wine Color, ACS Symposium Series, Washington D.C., 2008, 168-184.
23. Akaninwor, J.O.; Wegwu, M.O.; Nwaichi, E.O. Physico chemical properties and the anti-nutrient status of a non-alcoholic beverage (coke). J. Appl. Sci. Environ. Management 2008, 12(3), 11-13.
24. Website: http://www.dailymail.co.uk/sciencetech/article-2728711/Whats-really-lipstick-From-chillies-insects-bizarre-ingredients-perfect-pout.html
25. Hansen, C.M. Hansen Solubility Parameters: A User’s Handbook, 2nd Edition, CRC Press, Boca Raton, FL, 2007.

Many people contributed to the work in this study and paper and I would like to extend a heartfelt thank you to all of them:
• Wacker Chemical Corporation in Adrian, MI - Lucas Madison, Matthew Luethold, Donald Stephens, and Rick Coffey prepared paint samples, drawdowns and performed stain testing and data collection; Amanda Andrews, Jerry Havens, Andrew Pearson, and Jim Greene for technical discussions; Mark Westfall and Jim Greene for editing the manuscript.
• Wacker Chemie AG, in Burghausen, Germany - Dr. Stefan Altmann and Stefan Diwisch for contact angle measurements and surface energy data.
• The University of Southern Mississippi - Dr. Sarah Morgan for supplying technical articles and information.
• The Waterborne Symposium and The University of Southern Mississippi for allowing me to publish and present this work after the 43rd Annual Waterborne Symposium.
• The American Coatings Show for allowing me to publish and present this work at ACS 2016.

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