On the Use of Probe Liquids for Surface Energy Measurements

To assess the surface energy of solids, normally a set of probe liquids comprising polar and apolar compounds is used. Here we survey the surface tension of some frequently used probe liquids as given in the literature, for which a significant scatter appears to be present, and compare them with experimentally determined values. We discuss the influence of the liquid purity as well as the contact angle between the liquid and the Wilhelmy plate, which is commonly used for surface tension measurements. For hygroscopic polar probe liquids such as dimethyl sulfoxide, ethylene glycol, and formamide, water impurities appear to be of limited importance. Similarly, the amount of halogen impurities is of minor importance for diiodomethane and 1-bromonaphthalene, which decompose under the influence of light. Conversely, the influence of the contact angle for liquids that do not fully wet the plate, such as diiodomethane, is large in many cases, rendering a rather accurate determination of the contact angle necessary. Some discrepancies in the literature are indicated, and brief recommendations for future studies using such liquids are given.


SI-1: Contact angles
For all liquids the contact angle on the Wilhelmy plate was determined.Figure S1 shows a schematic of the setup and an image of the actual setup.Except for diiodomethane, full wetting of the plate was observed.Consequently, a value of 0 was used for the contact angle W.The data for diiodomethane are given in Table S1.The data show more than average scatter as usual for contact angle measurements.
Nevertheless, for all data measured directly after glowing and after wetting the plate with diiodomethane prior to measuring and discarding the measurements for which the difference in contact angle was more than 2, the average is virtually the same as the complete set (Table S1).As the surface tension measurements are performed by first immersing the plate in the probe liquid, the contact angle of the prewetted plate should be used.In the main text we therefore used  = 20.7.

SI-2: Correcting for condensation on the Wilhelmy plate
To determine the contribution of condensation on the overestimation of the surface tension, the weight of condensed material was measured over time by hanging the Wilhelmy plate just above the water surface.The weight was noted every two minutes during three consecutive measurements (Figure S2).The surface tension is normally determined via: in which F represents the force on the balance of the tensiometer due to the surface tension, l represents the wetted length of the Wilhelmy plate and θW is the contact angle.
In the case of condensation on the plate, a higher weight is registered by the balance in the tensiometer.This additional gravitational force should be subtracted from the force that is exerted on the balance by the surface tension to obtain the corrected surface tension: in which F, l, and θW are defined as above, and Fz corresponds to the additional gravitational force.This gravitational force can be calculated for each time point via: in which m represents the mass of the condensed material and g represents the gravitational constant.The weight gain caused by condensation of water on the platinum iridium plate was recorded every 2 minutes.Three measurements were performed (grey symbols), after which the average weight gain was determined (blue circles).Using a linear fit on the average weight gain Fz (light blue line), the contribution of condensation on the Wilhelmy plate was determined, as calculated from the slope a and intercept b for the fit of the average weight gain (Figure S1).Both non-corrected and corrected surface tension data are shown in Figure 1B (main text).

SI-3: Effect of argon flow on the surface tension measurements
For the hygroscopic liquids, an argon flow was applied to prevent the uptake of water.To investigate the influence of the argon flow on the results, the surface tension of water was measured under large and small argon flows (Figure S3).As can be seen in Figure S3, a large argon flow leads to more scatter of the data, possibly because the argon flow is causing slight movements in the plate that affect the measurement.A smaller argon flow does not show such scatter.For the large flow a temperature decrease of about 2 C was observed.However, even a small argon flow leads to a temperature decrease of the water of 1 about C, resulting in a higher surface tension value.Hence, more systematic measurements using a more quantitatively measured flow using a Brooks R2-15-B (Porter Instrument Company) flow meter were done as well.A similar temperature decrease of more than 2 C results for the maximum flow applied (150 mm sphere height corresponding to 4.6 standard liter per minute flow).Positioning the thermocouple as close as possible to the Wilhelmy measuring position without affecting the curvature near the Wilhelmy plate is thus advised.

SI-4: Drying hygroscopic liquids
For drying, mol sieves were used that were first activated by heating at 380 °C for 8 h.Ethylene glycol was dried using 3 Å mol sieves (CAS # 1318-02-1, MERCK) and dimethyl sulfoxide using 4 Å mol sieves (CAS # 1318-02-1, MERCK).Liquid was poured over the mol sieves until it just covered the mol sieves and were let drying for 2 weeks.Thereafter the mol sieveliquid mixture was sieved to retrieve the dried liquid.The amount of water was determined with Karl-Fischer titration [1][2] using a Metrohm 899 with a generator electrode without diaphragm under an argon atmosphere.CombiCoulomat fritless (MERCK) was used as titration liquid.
The detection limit was 10 μg ± 0.5 %.Table S2 shows the water content as determined.

SI-5: Surface tensions measured
For all liquids examined, below the experimentally determined surface tension data are given.
In the tables given below n indicates the total number of measurements comprising both repeated immersions and new samples.

SI-6: Accuracy of data
Accepting that a Gauss distribution represents the outcome of measurements properly, all relevant characteristics can be calculated once the expectation value for the mean  of the parent distribution or the average x ̅ , the expectation value for the parent distribution standard deviation  or the sample standard deviation s and the number of measurements n are given [3] .
To be explicit, using E() for expectation value, V() for variance and S() = [V()] 1/2 for standard deviation, we have where n is the nth central moment of the parent distribution.For a Gauss distribution with  = 0, 4 = 2 2 = 3 4 and 2 =  2 .Although m2 = n −1 j(xj−x ̅ ) 2 is an estimator for the moment n, it is biased, while s 2 is a (nearly) unbiased estimate.They are related by s 2 = nm2/(n−1).
To estimate the standard deviation of s, we use that for a function f(x) of x [4] , For a Gauss distribution therefore V(s 2 ) becomes 24 ( ) 2 /( 1) V so that for the standard deviation S(s) of s we have

S
where in the last step we replaced  by s, because clearly the exact value of  is unknown.A more precise and complex analysis, using that the variance has a  2 -distribution, leads to

S
Table S10 provides some numbers from which we conclude that S(s) is sufficiently accurate.
For a typical surface tension measurement, we have x ̅ = 40 mN m −1 , s = 0.5 mN m −1 and n = 5.Hence, s ̅ x  0.5/5 1/2 mN m −1 = 0.22 mN m −1 or s ̅ x/x ̅ = 0.028.Similarly, S(s)  [1/24) 1/2 0.5 = 0.18 mN m −1 or S(s)/s = 0.36.Their relative values thus differ by a factor of about 10.Hence, it is probably fair to say to that while the average and its associated standard deviation are rather well determined by a relatively small number of measurements, the sample standard deviation and its associated standard deviation are not so well determined.It should also be kept in mind that because the distribution for s 2 is a  2 -distribution, which is a skewed distribution.

SI-7: Literature data for the surface tension of water
In order to be able to assess the variability of surface tension data for the liquids examined, we provide plots of the surface tension as a function of temperature, including the data measured.
The data are largely from Landolt-Börnstein [5] and the associated supplements [6][7] .Individual references are given ion the various captions.The reference values and the corresponding abbreviations are taken from Wohlfahrt [5] and the later supplements [6][7] .Note that reference 94I2 [8] is considered the reference standard according to the International Association for the Properties of Water and Steam (IAPWS).References: A. 2011BEG1 [9] , 2011BLA1 [10] , 2011RAF2 [11] , 2011RAY1 [12] , 2011SUA1 [13] , 2011KEL1 [14] ; B. 2011MAN1 [15] , 2010MOH1 [16] , 2010SAD1 [17] , 2009ROM1 [18] , 2008ALV1 [19] , 2008GAR1 [20] ; C. 2006ROM1 [21] , 2007END1 [22] , 2007ROM1 [23] , 2007LAM1 [24] , 2007LIJ2 [25] , 2007MAR1 [26] ; D. 2005BEL1 [27] , As mentioned in the main text, the data from Ramsay and Shields are systematically lower as compared to the IAPWS data.Shifting their values up by 2 mN m −1 reduces the average deviation with the IAPWS data to about 0.15 mN m −1 .For other liquids their data do not deviate as much as for water, but generally also have a negative deviation: Figure S5 shows data on diethyl ether, methyl formate, ethyl acetate, carbon tetrachloride and ethanol.From the comparison as given in Figure S5, we suggest that the value given by Ramsay and Shields for methyl formate at 70 C contains a typographic error.From their (detailed) experimental description no clear reason could be distilled what is the possible reason for these discrepancies.Noteworthy is that most researchers measure the surface tension of a liquid against air while Ramsay and Shields measured against the saturated vapor.This effect is, however, small for the pressure involved, that is, about 1 bar.Nevertheless, the striking resemblance after shifting and the, so it seems, generally negative deviation suggest some systematic error.

SI-9: Chromatography paper experiments
As partial wetting of the platinum-iridium plate was obtained for diiodomethane, chromatography paper was used as an alternative, as suggested, amongst many others, by Partridge et al. [125] To make the paper plates, a roll of chromatography paper (2 cm × 100 m, 1 CHR, Whatman) with a measured thickness of 0.18 mm was used.From this roll, rectangles with a length between 10 and 17 mm were cut as straight as possible using a paper cutter.These pieces of paper were then soaked in the liquid of interest for at least 10 min.Before data acquisition, the paper plate was hung above the liquid surface, with the cut edge facing the liquid using a clamp that was cleaned with ethanol and MilliQ water.
As an initial test for the reliability of this method, measurements with water were performed (Figure S16).For both the measurements that were performed at 25 °C as well as those performed at 45 °C, the measurements that were executed with chromatography paper display quite some deviation between the individual measurements.The measurements that were executed with the platinumiridium plate, however, do show a great deal of overlap between separate measurements.Filter or chromatography paper is often advocated, in particular for non-wetting liquids but seems to be much less effective for wetting fluids.In any case, because of the swelling of the paper, the method will need a calibration with a liquid with a well-known surface tension.

SI-10: An explanation for the diiodomethane data discrepancy
In his overview Jasper [56] states that for diiodomethane the maximum bubble pressure method was used.Checking the original reference (Grzeskowiak et al. [126] ) it appeared that, most likely, the capillary rise method was employed.These authors refer to an earlier paper in which it was stated that only for those liquids which did not appear to wet glass (and for those cases where an independent check was required, whatever that means) the maximum bubble pressure method was employed.Grzeskowiak et al. [126] do not mention that diiodomethane did not wet the glass capillary.Körösi et al. [79] (81K1) (capillary rise) report 50.88 mN m −1 at 20 C, note the large difference with the Jasper data and state that diiodomethane decomposes above 40 C.They also stated clearly that diiodomethane wets the capillary (Pyrex glass).A similar (but independently determined) value of 51.4 mN m −1 is reported by Fletcher and Nichols [109] .It appears that for thoroughly baked out fused silica the contact angle  for diiodomethane is about 0, but that exposure to (humid) air induces a non-zero contact angle converging to  ~ 40 given sufficient time, typically ~3 h (Schrader [127] ).Similarly, for (non-specified) glass slides and non-specified storage conditions  ~ 49 was reported (Ozkan [128] ) as well as advancing and receding angles of ~56 and 29 (Comte [129] ) and ~48 and ~43 (Chibowski [130] ).Grzeskowiak et al. [126] indicated that they did dry their glassware at 100 C for 1 h, but that is certainly insufficient to obtain  = 0.Therefore, it seems likely that  in their case was not zero.Assuming  = 41.2 would bring their value of  = 66.7 mN m −1 to  = 50.88mN m −1 (the Körösi et al. [79] value), while  = 39.6 results in  = 51.4mN m −1 (the Fletcher and Nichols [109] value).

SI-11: Data for the surface tension calculation of solutions
In Table S11 the necessary data for the calculation of the surface tension of solutions of diiodomethane with iodine and 1-bromonaphthalene with bromine according to the considerations of Kaptay [131][132] are given.The interchange energy  is given by where vapHj and Vj are the enthalpy of vaporization and molar volume of component j, respectively, and RT has its usual meaning.In Figure S17 and Table S11 the results for the diluted regime are plotted.The molar surface area  is calculated as  = NA 1/3 (Vm) 2/3 with NA Avogadro's number and Vm the molar volume.For the references referring to the surface tensions, see the main manuscript.Thermodynamic data are varying somewhat in the literature, are mainly taken from the NIST Chemistry WebBook and, if necessary, extrapolated to room temperature.
Table S11: Data for the surface tension calculation according to Kaptay.

Figure S1 :
Figure S1: A) Schematic of the Wilhelmy plate setup; B) Image of the actual setup showing the Wilhelmy plate, the temperature sensor and the environmental chamber.

Figure S2 :
Figure S2: Condensation of water on the Wilhelmy plate at T = 45 °C.

Figure S3 :
Figure S3: Fluctuations in surface tension resulting from an argon flow during measurement.Surface tension (A) and temperature (B) with different argon flows applied during the measurements.Different colors indicate different measurements.Colors used in the temperature plot correspond to those used in the surface tension plot.

(V
with xj the j-th measurement.The variance V(x ̅ ) of the average x ̅ and the variance V(s 2 ) of the variance s 2 are given by

Figure S6 :
Figure S6: Surface tension of dimethyl sulfoxide (DMSO).Examples of surface tension measurements (grey) and temperature (blue) as a function of time at (A) 25 °C and (B) 45 °C.The linear fit to determine the surface tension is given as a red dashed line.The measurements were performed under argon flow to prevent uptake of water.

Figure S7 :
Figure S7: Surface tension of ethylene glycol.Examples of surface tension measurements (grey) and temperature (blue) as a function of time at (A) 25 °C and (B) 45 °C.The linear fit to determine the surface tension is given as a red dashed line.The measurements were performed under argon flow to prevent uptake of water.

Figure S8 :
Figure S8: Surface tension of formamide.Examples of surface tension measurements (grey) and temperature (blue) as a function of time at (A) 25 °C and (B) 45 °C.The linear fit to determine the surface tension is given as a red dashed line.The measurements were performed under argon flow to prevent uptake of water.

Figure S12 :
Figure S12: Surface tension measurements of diiodomethane at T = 44.2°C. A. Surface tension measurements as function of time.B. Corresponding temperature profiles.

Figure S15 :
Figure S15: Surface tension measurements of 1-bromonaphthalene at T = 44.7 °C. A. Surface tension measurements as function of time.B. Corresponding temperature profiles.

Figure S16 :
Figure S16: Use of chromatography paper to determine the surface tension.The surface tension was measured as a function of time at (A) 25 °C and (B) 45 °C.Each color represents a new measurement.The solid lines indicate the measurements that were performed with chromatography paper, the dashed lines indicate the measurements that were performed with the platinum-iridium plate.Note that the measurements with the platinum-iridium plate overlap.

Table S2 :
Water content analysis.

Table S3 :
Surface tension data for water.

Table S4 :
Surface tension data for dimethyl sulfoxide.

Table S5 :
Surface tension data for ethylene glycol.

Table S6 :
Surface tension data for formamide.

Table S7 :
Surface tension data for diiodomethane.

Table S9 :
Surface tension data for n-hexadecane.

Table S10 :
Relative standard deviations S(s) and S(s) of the sample standard deviation s of n data.