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Surface Elasticity and Viscosity from Oscillating Bubbles Measured by Automatic Axisymmetric Drop Shape Analysis
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
207, 97–105 (1998)
CS985745
Surface Elasticity and Viscosity from Oscillating Bubbles Measured by Automatic Axisymmetric Drop Shape Analysis Rolf Myrvold and Finn Knut Hansen1 Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway Received March 9, 1998; accepted July 8, 1998
under dynamic conditions. The surface shear viscosity and elasticity, the 2-dimensional equivalents to ordinary bulk rheology, have been shown to be closely correlated with the stability of emulsions and foams (1). However, probably more important for these processes are the surface dilatational viscosity and elasticity that are often several orders of magnitude higher that the shear parameters (3). These properties are, however, less readily measurable, except for the Gibbs elasticity, which is the static limit of the latter. Several methods have been developed for the measurement of the surface dilatational properties (1–3). The Langmuir surface balance may be used both in static mode to measure Gibbs elasticity and in oscillating mode for the measurement of the complex surface dilatational viscosity. Because of limitations in the barrier movements and the problem of liquid drag, this method can only be used for low frequencies (,0.2 s21). In a similar way, the elastic ring method has been developed (1). Surface waves also have been used to measure these properties, including both transverse and longitudinal waves (4, 5), as well as dynamic light scattering methods (1). The maximum bubble pressure method and the oscillating bubble are methods that use bubbles at the end of a capillary to measure the changes in surface tension due to variations in the surface area. The oscillation bubble method developed by Lunkenheimer and Kretzschmar (6) can measure surface dilatational elasticity at quite high frequencies by relating the pressure change in the process to the height of the bubble cap. The instrument has been used to calculate the surface viscosity effect due to diffusional transport between the interface and the subphase. There is no readily available instrument of this type. A similar but somewhat different instrument based on the pressure detection principle has been developed by Nagarajan and Wasan (7) for surface relaxation studies. The use of the pendant drop method based on numerical analysis of the drop shape for the measurement of surface tensions has been known for some time; for instance, the program Axisymmetric Drop Shape Analysis (ADSA) developed by Neumann and co-workers (8) is well known. In this laboratory we have developed an instrument using computerbased video image analysis that can calculate the surface tension of sessile or pendant drops or bubbles in a very short
The pendant drop/sessile drop instrument developed by our group and based on video image analysis has been enhanced to measure oscillating drops and bubbles at a rate up to 25 pictures per second. Data analysis has been developed to analyze the results from sinusoidal oscillations in terms of dilatational surface elasticity and viscosity. The polymers ethylhydroxyethyl cellulose (EHEC) and two different poly(oxyethylene)–poly(oxypropylene) ABA block copolymers (PE6200 and PE6800) have been investigated at the air–water interface regarding rate of adsorption and surface dilatational properties. The polymers give surface pressures in the region 20 –30 mN m21, the surface elastic moduli are between 4 and 30 mN m21, and the viscous moduli are generally low, from 0 to 6 mN m21. The elastic moduli increase with increasing frequency, but both the slope and the concentration dependency vary. For the most water-insoluble polymer, EHEC, the modulus increases with polymer concentration, the relatively hydrophobic polymer PE6200 shows the opposite behavior, and the most water-soluble polymer, PE6800, shows a maximum in the equilibrium elasticity. These observations can be explained by the changes in the molecular orientation in the surface layer as reflected in p vs A isotherms. The PE6200 polymer also shows a higher viscous modulus, which may be explained by diffusional transport between surface and bulk. © 1998 Academic Press Key Words: surface tension; oscillating bubble; image analysis; monomolecular films; polymer adsorption.
INTRODUCTION
The equilibrium values of surface tension and adsorption are often used to describe the effect of surface-active materials on phenomena connected to colloidal stability. In many instances, when dealing with liquid– gas or liquid–liquid interfaces, these properties alone have been shown to be insufficient for correlation of the macroscopic behavior to fundamental microscopic phenomena. These observations are relevant to many practical applications of emulsification and foaming. In these systems it is often the dynamic properties of the interfaces that are important as a result of surface tension gradients and surface mobility. The Marangoni effect and the surface rheological parameters are used as a measure of the surface’s properties 1
To whom correspondence should be addressed. 97
0021-9797/98 $25.00 Copyright © 1998 by Academic Press All rights of reproduction in any form reserved.
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time. Details of this (DROP) instrument and the calculation procedures have been published elsewhere (9, 12). Recently, this technique has been steadily improved by the continuous development of both new hardware and new software (9 –12), and commercial instruments of this type have now emerged. By oscillating the drop and simultaneously measuring the surface area and surface tension, one may determine the surface dilatational moduli. Most existing instruments of this type can presently only measure pendant drops and the time for calculations is of the order of seconds. Recently, our instrument has been improved by new hardware and software modifications to further increase speed and usefulness. A drop control unit has been added consisting of a dispenser and a motor-driven oscillating syringe in series. By this unit, both relaxation and oscillation experiments may be performed. The computer side has been improved and makes it possible to measure video pictures in real time, i.e., 25 frames per second (CCIR). By this system sinusoidal oscillating drops and bubbles can be produced and this makes it possible to calculate simultaneously the viscous and elastic parts of the complex surface dilatational module. In this paper we present the background for this method and results for a selection of surfactants and surface-active polymers. THEORY AND DATA ANALYSIS
The theoretical foundation for the measurement of surface rheological properties is well established (1, 2). The analysis of surface dilatational elasticity and viscosity has for instance, been reviewed by Lucassen-Reynders (3). In this framework, we now outline the necessary theoretical background for the methods utilized in this work. The surface elasticity, E, follows the definition given by Gibbs,
E5
dg . d ln A
d ln A , dt
E* 5 E9 1 iE0,
[3]
where E9 is the storage modulus and E0 the loss modulus. The storage modulus will be equal to the pure elastic contribution, and E0 proportional to the viscous contribution. In an oscillatory experiment the surface area is varied with time, t, according to the function D ln A , exp~i v t!,
[4]
where v is the angular rate. In this case the loss modulus will be E0 5 vh d
[5]
and E9 will be equal to E 0 when v 3 0. The surface dilatational viscosity, hd, therefore corresponds to the dynamic viscosity, h 9 5 G0/ v , in an ordinary (bulk) oscillatory rheology experiment (G0 is the bulk loss modulus). It is implied here that the surface area amplitude is sufficiently small to ensure operation in the linear viscoelastic regime. The foregoing analysis can be used with experiments such as surface waves and oscillating drops and bubbles. For an oscillating bubble, we vary the surface area according to Eq. [4] by pulsating the bubble volume in a sinusoidal manner, and provided that the volume change is small, this results in a corresponding sinusoidal variation in the bubble surface area:
[1] DA 5 A 2 A 0 5 A asin~ v t!.
Here g is the surface tension and A the surface area. The term surface elasticity infers that E is a property of pure elastic surfaces. It turns out, however, that many surfaces contain both an elastic component and a viscous component, and the term “surface dilatational modulus” has been used for this more general case. The contributions of the elastic and viscous terms depend on the different types of relaxation processes that occur on the surface layer and on the interaction of the surface with its surroundings, i.e., the bulk liquid(s). The equilibrium (Gibbs) surface elasticity, E 0 , will then usually be different from E. The surface dilatational viscosity, hd, has been defined according to the equation
Dg 5 hd
where Dg is the surface tension difference of a constantly (logarithmically) expanding surface compared to that of the equilibrium surface. The parameter hd will only represent a true Newtonian type of surface viscosity, however, if the elasticity is zero. In other cases, a complex surface dilatational modulus may be written as
[2]
[6]
Here A a is the area amplitude and A 0 is the equilibrium surface area. The response in the surface tension variation can then be described by the function D g 5 g 2 g 0 5 g asin~ v t 1 d !,
[7]
where ga is the measured amplitude, g0 is the equilibrium surface tension, and d is the phase angle. In the usual manner, Eq. [7] may be written D g 5 g asin~ v t!cos d 1 g acos~ v t!sin d
[8]
By using Eq. [1] for E*, we see that the (complex) surface dilatational modulus is then expressed by
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
E* 5 E9 1 iE0 5 uEucos d 1 iuEusin d ,
[9]
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a result of a surface pressure change even at constant surface area.
where EXPERIMENTAL
ga uEu 5 A a/A 0
[10]
The loss modulus E0 represents a combination of internal relaxation processes and relaxation due to transport of matter between the surface and the bulk. The latter process will be important especially in the case of soluble monolayers and in nonequilibrium situations and will be more dominant at lower frequencies because of the time involved in the diffusion process. Several theories have been developed that describe the latter process (2, 3), and it is predicted that in this case the phase angle, d, will be 45° and the elasticity will approach zero at low frequencies (3). The interested reader is referred to refs 2 and 3 for in-depth discussion of this topic. Often, the response function, Eq. [7], is determined from the experimental data by means of a Fourier transform. The transformed time function should ideally only contain the main harmonic component; however, noise in the experimental data will usually also give rise to higher harmonics content, which may complicate the analysis. It will also be important to consider the boundary problem. Another method of analysis is to fit Eq. [7] directly to the experimental data. A nonlinear curve-fitting procedure is able to obtain the universally best results even from noisy data; it is, however, necessary to use good initial parameter estimates if this strategy will succeed. Such parameters may be obtained by preanalyzing the data in a proper way. For the zero values ( A 0 , g 0 ) the arithmetic means can be used, and the amplitudes ( A a, ga) may be calculated from the standard deviations when it is observed that for a sine function
SOD
2 Amplitude 5 N
N
y
2 i
1/ 2
[11]
i5l
Here y i are the experimental data and N the number of measurements. The frequency and phase angle relative to the start measurement time may be estimated by simply counting the data points below and above the mean in each period. By using these initial values in a nonlinear least-squares curve-fitting procedure, it is usually quite easy to obtain a good fit of the sine function to experimental data. It should be stressed that this method for the determination of the surface dilatational modulus is based on the analysis of the drop image only and that an additional determination of the capillary pressure as in earlier published methods (6, 7) is not necessary. This is so because the surface tension is determined from the bubble’s shape (together with the size) and that the shape may change as
Instruments As mentioned in the Introduction, the first DROP instrument has been described earlier. Because of essential modifications from the initial construction, it will be described briefly here. An illustration of the instrument is shown in Fig. 1. It consists of a goniometer (Rame´-Hart) fitted with a macro lens and autobellows (Olympus) and a CCD video camera (Sony). The video frames are captured by a DT3155 frame grabber (Data Translation) in a Pentium 200 PC (Dell Computer). The drop control unit is a Microlab M dispenser (Hamilton) and a specially designed oscillation unit consisting of a syringe with an excenter-mounted piston that is motor driven. The dispenser is controlled by the PC. The dispenser and oscillation units are mounted in series with stainless steel pipes that are filled with distilled water. The drops and bubbles are extended from the tip of a small Teflon tube into a quartz cuvette inside a thermostated and water-filled environment chamber with glass windows. The Teflon tube contains an air pocket toward the water in the steel pipe. The DROP computer program has been rewritten for the MS-Windows platform. On this platform, the program can control the new frame grabber through the manufacturer’s supplied drivers and software libraries (DLLs) and can use all available RAM for picture storage. This means that, if necessary, the program can capture pictures directly to RAM in real time and calculate the results later. A maximum capture rate of 25 Hz in CCIR video is therefore possible. The rate of calculation on this system is ca. 0.2 s per picture. The program has many facilities for different measurement strategies and is also able to keep the drop or bubble volume constant during a long period of time by means of a feedback method. This is very important when measuring adsorption in highly elastic films, where small deviations in volume (i.e., area) may cause significant measurement errors. The results that are calculated are the surface tension, shape factor (b), radius of curvature (R 0 ), the drop volume, height, and width, the surface area, and the contact angle with the horizontal plane. A description of the instrument and the program may be found at http://www. uio.no/;fhansen/dropinst.html. An automatic Langmuir surface balance (Minithrough, KSV Instruments Ltd., Finland) was used to record the p vs A isotherms. The trough is made from a single block of PTFE and has a surface area of approximately 250 cm2. The surface tension of the monolayers is measured by means of a Wilhelmy plate.
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MYRVOLD AND HANSEN
FIG. 1.
DROP instrument for the measurement of interfacial tension and surface dilatational rheologic parameters.
Chemicals The ethylhydroxyethyl cellulose (EHEC) polymer was manufactured by Akzo Nobel and purified by B. Lindmans group at the University of Lund. The molecular weight of the polymer is ca. M w 5 80,000 and the degrees of substitution of ethyl and hydroxyethyl groups are 0.6 – 0.7 and 1.8, respectively. The polymer has been described elsewhere (16). The poly(oxyethylene)–poly(oxypropylene) (POE–POP–POE) block copolymers were commercial products (Pluronics) produced by BASF. The molecular weight of the POP block is 1750 and the PE6200 and PE6800 polymers contain 20 and 80% of POE in the molecule, respectively (total molecular weights ca. 2500 and ca. 8500, respectively). The polymers were used as received. All water was ion exchanged followed by distillation. Its surface tension was 72 6 0.5 mN m21 (25°C). In the Langmuir surface balance the surface was checked for purity by affirming that surface compression led to a pressure p , 0.5 mN m21. Procedure A small amount of air (ca. 150 mL) was sucked into the tip of the Teflon tube. The tip was dipped into ca. 10 mL of the polymer solution in the cuvette and fixed to the environmental chamber. The temperature in the chamber was
24.5°C in all experiments. The computer was programmed to increase the bubble volume instantly, with immediate start of surface tension measurements. The formation of a 50-mL bubble took ca. 0.5 s. The surface tension was measured as a function of time until a near equilibrium was reached (with many substances, true equilibrium was never reached). In most experiments, this time was ca. 10,000 s. During most of these measurements, the bubble volume was kept constant by the program (60.5 mL). The bubble was oscillated around the equilibrium position with an amplitude of ca. 2.5 mL and a frequency between 0.2 and 2 Hz. This amplitude was found to be in the linear viscoelastic regime. At each frequency 3 periods were measured and the surface tension data stored. The measurements were finally analyzed by means of a nonlinear gradient expansion method (Marquardt method) (14) by fitting the surface area and surface tension data to sine functions as described earlier. Because the measurements start at some arbitrary time during an oscillation, the value of d is determined as the difference between the experimental phase angles of the surface area and surface tension functions. The value of uEu was determined from the measured amplitudes and the mean surface area by means of Eq. [10] and the moduli from uEu and d as shown in Eq. [9]. For each sample the oscillation measurements were repeated 3–7 times.
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SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
FIG. 2. Example of measurement of a sinusoidal oscillation at the highest video rate.
The p vs A isotherm was obtained from monolayers spread on water according to a procedure developed for water-soluble biopolymers (15). RESULTS AND DISCUSSION
It was found that the surface area and surface tension data could be easily fitted by means of the method described in the
preceding section. An example of such a fit is given in Fig. 2. These data were collected at the highest possible video rate of 25 Hz. The drawn curves in the figure are fitted sine functions. It is seen that the area is very well described by the sine function. The surface tension is also well measured by this method. Small deviations from the sine curve have little influence on the fitted curve; usually the fit is even better at lower frequencies. An error analysis of the oscillation data is represented in Table 1. For each sample, the standard deviation is calculated from the repeated measurements and a total standard deviation is calculated from all the measurements, under the hypothesis that all standard deviations represent the same population. The total standard deviation on the sample mean is calculated using an average of six repetitions per sample; these are 0.21 and 0.40 mN m21 for E9 and E0, respectively. We see that there are no significant differences between these average standard deviations and the individual estimates for each sample; an F-test shows that the difference is not significant at the 95% confidence level. We may therefore conclude that these values represent the errors inherent in the applied method and that preferably at least four repeated measurements should be used. It may be noted that the error in E0 is approximately double that in E9 and together with the generally low values of E0 makes the relative error in this parameter quite high. This is a consequence of the low phase angle, d, of the measured samples and the uncertainty in the determination of d. When d is higher, and E9 and E0 thus more equal, the error in these parameters will also be more equal. We will therefore in this discussion use an error estimate of 60.4 and 60.8 (52s) in E9 and E0, respectively. The results for the EHEC polymer are presented in Figs.
TABLE 1 Error Analysis of Surface Rheology Measurements For each measurement
System EHEC
PE6200
PE6800
Sum of squares Variance s per measurement s of sample mean s of s (per measurement)
Concentration (ppm) 10 40 100 1 10 100 1000 1 10 100 1000
Number of measurements 6 6 3 6 6 6 6 7 6 4 5 (11) (6)
For the means
s (E9) (mN m21)
s (E0) (mN m21)
s (E9) (mN m21)
s (E0) (mN m21)
0.25 0.57 0.66 0.51 0.58 0.55 0.41 0.49 0.49 0.46 0.48 2.812 0.256 0.51 0.21 0.15
1.1 0.77 1.4 1.3 1.1 0.90 0.44 0.71 0.81 0.61 1.15 10.411 0.946 0.97 0.40 0.28
0.10 0.23 0.38 0.21 0.24 0.22 0.17 0.19 0.20 0.23 0.21
0.45 0.31 0.79 0.53 0.45 0.37 0.18 0.27 0.33 0.31 0.51
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FIG. 3. Dynamic surface tension of EHEC solutions as a function of time measured by the sessile bubble method.
3–5. In Fig. 3 the surface tension as a function of time is shown. These results are similar to those measured by Nahringbauer (17) by the pendant drop method, except that our measurements are extended to much shorter times and may also be extended to very long times. The surface tension is seen to decrease at a lower rate at long times, but a true equilibrium adsorption is not reached in the measured time interval. The curve at 1000 ppm shows a downward dip above ca. 2000 s. This is a consequence of a decreasing bubble volume, and the curve was kept to illustrate this point; in all other experiments the volume was kept constant by the computer. The decreased surface area leads to an increase in surface pressure as in the corresponding p vs A isotherm. This is typical of insoluble surface films and shows that there is no (or very little) desorption in these systems in the time scale of these experiments. The adsorption kinetics and mechanism of this polymer have been discussed by others and will not be discussed further here. We only want to stress that in order to evaluate the kinetics of adsorption properly, the surface tension (pressure p) should be converted to surface concentration (G) by measuring the p vs A isotherm separately in a Langmuir balance as previously done in the adsorption of HSA (13). The measured surface dilatational modulus of the EHEC polymer is presented in Fig. 4. There are several interesting features with these results: First it is noted that the elastic modulus, E9, is much higher than the viscous modulus, E0, meaning that the surface area and surface tension oscillations are almost in phase, as shown in Fig. 2. Second it is seen that both moduli increase with increasing frequency. The absolute increase is approximately linear and is stronger (in absolute terms) for the elastic than for the viscous modulus. The extrapolation of the elastic modulus to zero frequency gives a
finite value which is expected to be equal to the equilibrium Gibbs elasticity, E 0 . The straight line that fits the viscous modulus extrapolates to zero (within experimental errors), which is well in line with the observation that these films behave like insoluble films, as a higher value at low frequencies can be interpreted as a result of desorption (2, 3). The slope of the line, E0/ v , is equal to the dynamic, or surface dilatational, viscosity, hd, as shown in Eq. [5]. It can therefore be concluded that hd may be measured by this method but that the modulus for EHEC is quite low, ca. 0.25 mN s m21 at the highest polymer concentration. The elastic modulus, E9, increases to a certain degree with increasing polymer concentration but the increase in not very strong. This is a consequence of the fact that the surface tensions, and thus the surface concentrations, are not very different at the measured time (10,000 s). A compression of the surface, as a result of bubble shrinkage, results in an increase in elasticity. This means that the p vs A isotherm must be curved upward in this region. We also find that the elasticity, E9, increases with frequency; the slope of the highest curve is 0.57 mN s m21. This is characteristic of insoluble monolayers and has been observed previously by using the small oscillating bubble (2). The limiting elasticities as v 3 0 may be compared to those calculated form the p vs A isotherms measured by the Langmuir balance. This isotherm for EHEC is shown in Fig. 5, where also the elasticity E 0 is calculated by means of Eq. [1]. We see that the elasticity goes through a maximum of 18.8 mN m21 at a surface pressure of 8.4 mN m21 and becomes quite low again at surface pressures around 20 mN m21. At higher surface pressures it seems that E 0 may increase again, but we were not able to compress the film further in the Langmuir balance. Such a behavior is often observed with monolayers of both synthetic
FIG. 4. Surface dilatational moduli of the EHEC solutions: upper points, E9; lower points, E0.
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
103
FIG. 5. p vs A isotherm of EHEC measured by the Langmuir surface balance. Also plotted is the surface elasticity calculated by Eq. [1].
and natural polymers (13, 18, 19). We see that the surface pressures at long times for the adsorbed films measured by this oscillating bubble method are around 20 mN m21 and higher and that the extrapolated elasticity therefore may be expected to increase with increasing concentrations, as observed. Results for the block copolymer PE6200 are shown in Figs. 6 and 7. Figure 6 shows the adsorption vs time behavior and
Fig. 7 the surface rheological moduli. The dynamic surface tension curves are somewhat similar to those with EHEC, but adsorption from corresponding concentrations is much faster, mainly as a result of the much lower molecular weight. The curves also seem to flatten more at longer times, except for the one for 1000 ppm, which curves downward again, an observation that is believed to be due to impurities in the commercial
FIG. 6. Dynamic surface tension of PE6200 solutions as a function of time measured by the sessile bubble method.
FIG. 7. Surface dilatational moduli of the PE6200 solutions: upper points, E9; lower points, E0.
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FIG. 8. Dynamic surface tension of PE6800 solutions as a function of time measured by the sessile bubble method.
polymer. The almost constant surface tension at long times indicates that these polymers have reached near-equilibrium adsorption; i.e., that there also may be desorption from the surface. The surface elastic modulus, as shown in Fig. 7, is considerably higher than for EHEC and decreases with increasing concentration, except for the highest concentration, 1000 ppm, which is equal to that at 100 ppm. This result cannot be explained by a diffusional relaxation mechanism, because the viscous modulus should then be closer to the elastic modulus (tan d 3 1) (3). It is rather probable that the elasticity decreases with increasing surface pressure because of a configuration change in the surface layer, leading to a decreasing slope of the p vs A isotherm in the same way as observed for EHEC (Fig. 5). The fact that the elasticities for the two highest concentrations are almost identical may be explained by the fact that these two concentrations are close to the minimum in E (we do not know if there is a minimum here; E 0 may as well stay constant). Even if the surface elasticity is higher than for EHEC, the frequency dependency is lower; the slope for the 1 ppm data is 0.36 mN s m21. The viscous modulus is also here very low, on the order of 1–2 mN m21, but does not seem to change much with frequency. If the loss modulus is solely due to viscous friction, it should increase with frequency, as is the case with EHEC; if the loss is due to diffusional exchange with the bulk, the opposite frequency dependency is expected (3). Therefore, the reason for a near-constant value may be a combination of these effects. However, the experimental errors in these data are of the same magnitude as the change in the data itself, and it is therefore difficult to make any decisive conclusions. Results for the more hydrophilic block copolymer PE6800 are presented in Figs. 8 and 9. The adsorption of this polymer
clearly proceeds more slowly than that of PE6200 because of the higher molecular weight and the resulting surface tension is higher, probably because of the more hydrophilic nature of this polymer. The polymer seems to reach near-equilibrium adsorption close to the far end of our measured data (70,000 s). The reason for the “bumps” on the surface tension curves for 1 and 10 ppm is uncertain but may be caused by uneven molecular weight distribution of the polymer. The surface rheological moduli shown in Fig. 9 (measured at 10,000 s) show a still more complex behavior than for PE6200. The elastic modulus, E9, is seen to increase from the curve at 1 ppm to that at 10 ppm, but then it decreases again. At the same time the slope of the curve is increasing with concentration. At 100 and 1000 ppm the curves do not seem to be straight lines anymore but have a tendency to bend downward at low frequencies. This tendency may be present also in the results for PE6200, but the significance of those data is uncertain. At the same time as the elastic modulus decreases, the viscous modulus increases. It is probable that this now may be explained by diffusional transport between the bulk and the surface because of the higher water solubility of this polymer. Especially the data at 100 ppm clearly show that E0 is decreasing with increasing v. At 1000 ppm, E0 is mostly constant again, but this may be a result of a decrease in both moduli with a simultaneous increase in the phase angle, which is expected in the case of diffusional exchange (3). The maximum in E9 possibly has the same explanation as the increase for EHEC and the decrease for PE6200: The difference between the “equilibrium” surface tensions for the different concentrations of the polymer PE6800 is larger than for either of the other two polymers; the
FIG. 9. Surface dilatational moduli of the PE6800 solutions: upper points, E9; lower points, E0.
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
surface pressures are both below and above the bend in the p vs A isotherm, and the elasticity may go through a maximum in the same way as shown for EHEC (Fig. 5). However, the increase in diffusional interchange will also decrease E9 and may be a part of the explanation. To make any further conclusions about the exact mechanism, the p vs A isotherms should be measured; however, the Pluronics polymers are too water soluble to be measured easily by the Langmuir balance. CONCLUSION
It may be concluded that the new method of oscillating bubble with full profile image analysis is well suited to measure dynamic surface elasticity and viscosity of adsorbing polymers from low frequencies up to a few hertz. Interesting features of the polymer films are observed that are due to both viscoelastic properties of the adsorbed polymers and diffusional transport between the surface and the bulk. REFERENCES 1. Edwards, D. A., Brenner, H., and Wasan, D. T., “Interfacial Transport Processes and Rheology.” Butterworths-Heinemann Publishers, Oxford, 1991.
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2. Dhukin, S. S., Kretzschmar, G., and Miller, R., “Dynamics of Adsorption at Liquid Interfaces.” Elsevier, Amsterdam, 1995. 3. Lucassen-Reynders, E. H., Surfactant Sci. Ser. 11, 173 (1991). 4. Lucassen-Reynders, E. H., and Lucassen, J., Adv. Colloid Interface Sci. 2, 347 (1969). 5. Hansen, R. S., and Ahmed, J., Prog. Surf. Membr. Sci. 4, 1 (1971). 6. Lunkenheimer, K., and Kretzschmar, G., Z. Phys. Chem. (Leipzig) 256, 593 (1975). 7. Nagarajan, R., and Wasan, D. T., J. Colloid Interface Sci. 159, 164 (1993). 8. Rotenberg, Y., Bouvka, L., and Neumann, A. W., J. Colloid Interface Sci. 93, 169 (1983). 9. Hansen, F. K., and Rødsrud, G., J. Colloid Interface Sci. 141, 1 (1991). 10. Miller, R., Policova, Z., Sedev, R., and Neumann, A. W., Colloids Surf. 76, 179 (1993). 11. del Rı´o, O. I., and Naumann, A. W., J. Colloid Interface Sci. 196, 136 (1997). 12. Hansen, F. K., J. Colloid Interface Sci. 160, 209 (1993). 13. Hansen, F. K., and Myrvold, R., J. Colloid Interface Sci. 176, 408 (1995). 14. Bevington, P. R., and Robinson, D. K., “Data Reduction and Error Analysis for the Physical Sciences.” McGraw-Hill, New York, 1992. 15. Sta¨llberg, S., and Teorell, T., Trans. Faraday Soc. 35, 1413 (1939). 16. Thuresson, K., Nystro¨m, B., Wang, G., and Lindman, B., Langmuir 11, 3730 (1995). 17. Nahringbauer, I., J. Colloid Interface Sci. 176, 318, (1995). 18. Myrvold, R., and Hansen, F. K., Colloids Surf. 117, 27 (1996). 19. Ahluwalia, A., Stussi, E., and Domenici, C., Langmuir 12, 1416 (1996).
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CS985745
Surface Elasticity and Viscosity from Oscillating Bubbles Measured by Automatic Axisymmetric Drop Shape Analysis Rolf Myrvold and Finn Knut Hansen1 Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway Received March 9, 1998; accepted July 8, 1998
under dynamic conditions. The surface shear viscosity and elasticity, the 2-dimensional equivalents to ordinary bulk rheology, have been shown to be closely correlated with the stability of emulsions and foams (1). However, probably more important for these processes are the surface dilatational viscosity and elasticity that are often several orders of magnitude higher that the shear parameters (3). These properties are, however, less readily measurable, except for the Gibbs elasticity, which is the static limit of the latter. Several methods have been developed for the measurement of the surface dilatational properties (1–3). The Langmuir surface balance may be used both in static mode to measure Gibbs elasticity and in oscillating mode for the measurement of the complex surface dilatational viscosity. Because of limitations in the barrier movements and the problem of liquid drag, this method can only be used for low frequencies (,0.2 s21). In a similar way, the elastic ring method has been developed (1). Surface waves also have been used to measure these properties, including both transverse and longitudinal waves (4, 5), as well as dynamic light scattering methods (1). The maximum bubble pressure method and the oscillating bubble are methods that use bubbles at the end of a capillary to measure the changes in surface tension due to variations in the surface area. The oscillation bubble method developed by Lunkenheimer and Kretzschmar (6) can measure surface dilatational elasticity at quite high frequencies by relating the pressure change in the process to the height of the bubble cap. The instrument has been used to calculate the surface viscosity effect due to diffusional transport between the interface and the subphase. There is no readily available instrument of this type. A similar but somewhat different instrument based on the pressure detection principle has been developed by Nagarajan and Wasan (7) for surface relaxation studies. The use of the pendant drop method based on numerical analysis of the drop shape for the measurement of surface tensions has been known for some time; for instance, the program Axisymmetric Drop Shape Analysis (ADSA) developed by Neumann and co-workers (8) is well known. In this laboratory we have developed an instrument using computerbased video image analysis that can calculate the surface tension of sessile or pendant drops or bubbles in a very short
The pendant drop/sessile drop instrument developed by our group and based on video image analysis has been enhanced to measure oscillating drops and bubbles at a rate up to 25 pictures per second. Data analysis has been developed to analyze the results from sinusoidal oscillations in terms of dilatational surface elasticity and viscosity. The polymers ethylhydroxyethyl cellulose (EHEC) and two different poly(oxyethylene)–poly(oxypropylene) ABA block copolymers (PE6200 and PE6800) have been investigated at the air–water interface regarding rate of adsorption and surface dilatational properties. The polymers give surface pressures in the region 20 –30 mN m21, the surface elastic moduli are between 4 and 30 mN m21, and the viscous moduli are generally low, from 0 to 6 mN m21. The elastic moduli increase with increasing frequency, but both the slope and the concentration dependency vary. For the most water-insoluble polymer, EHEC, the modulus increases with polymer concentration, the relatively hydrophobic polymer PE6200 shows the opposite behavior, and the most water-soluble polymer, PE6800, shows a maximum in the equilibrium elasticity. These observations can be explained by the changes in the molecular orientation in the surface layer as reflected in p vs A isotherms. The PE6200 polymer also shows a higher viscous modulus, which may be explained by diffusional transport between surface and bulk. © 1998 Academic Press Key Words: surface tension; oscillating bubble; image analysis; monomolecular films; polymer adsorption.
INTRODUCTION
The equilibrium values of surface tension and adsorption are often used to describe the effect of surface-active materials on phenomena connected to colloidal stability. In many instances, when dealing with liquid– gas or liquid–liquid interfaces, these properties alone have been shown to be insufficient for correlation of the macroscopic behavior to fundamental microscopic phenomena. These observations are relevant to many practical applications of emulsification and foaming. In these systems it is often the dynamic properties of the interfaces that are important as a result of surface tension gradients and surface mobility. The Marangoni effect and the surface rheological parameters are used as a measure of the surface’s properties 1
To whom correspondence should be addressed. 97
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time. Details of this (DROP) instrument and the calculation procedures have been published elsewhere (9, 12). Recently, this technique has been steadily improved by the continuous development of both new hardware and new software (9 –12), and commercial instruments of this type have now emerged. By oscillating the drop and simultaneously measuring the surface area and surface tension, one may determine the surface dilatational moduli. Most existing instruments of this type can presently only measure pendant drops and the time for calculations is of the order of seconds. Recently, our instrument has been improved by new hardware and software modifications to further increase speed and usefulness. A drop control unit has been added consisting of a dispenser and a motor-driven oscillating syringe in series. By this unit, both relaxation and oscillation experiments may be performed. The computer side has been improved and makes it possible to measure video pictures in real time, i.e., 25 frames per second (CCIR). By this system sinusoidal oscillating drops and bubbles can be produced and this makes it possible to calculate simultaneously the viscous and elastic parts of the complex surface dilatational module. In this paper we present the background for this method and results for a selection of surfactants and surface-active polymers. THEORY AND DATA ANALYSIS
The theoretical foundation for the measurement of surface rheological properties is well established (1, 2). The analysis of surface dilatational elasticity and viscosity has for instance, been reviewed by Lucassen-Reynders (3). In this framework, we now outline the necessary theoretical background for the methods utilized in this work. The surface elasticity, E, follows the definition given by Gibbs,
E5
dg . d ln A
d ln A , dt
E* 5 E9 1 iE0,
[3]
where E9 is the storage modulus and E0 the loss modulus. The storage modulus will be equal to the pure elastic contribution, and E0 proportional to the viscous contribution. In an oscillatory experiment the surface area is varied with time, t, according to the function D ln A , exp~i v t!,
[4]
where v is the angular rate. In this case the loss modulus will be E0 5 vh d
[5]
and E9 will be equal to E 0 when v 3 0. The surface dilatational viscosity, hd, therefore corresponds to the dynamic viscosity, h 9 5 G0/ v , in an ordinary (bulk) oscillatory rheology experiment (G0 is the bulk loss modulus). It is implied here that the surface area amplitude is sufficiently small to ensure operation in the linear viscoelastic regime. The foregoing analysis can be used with experiments such as surface waves and oscillating drops and bubbles. For an oscillating bubble, we vary the surface area according to Eq. [4] by pulsating the bubble volume in a sinusoidal manner, and provided that the volume change is small, this results in a corresponding sinusoidal variation in the bubble surface area:
[1] DA 5 A 2 A 0 5 A asin~ v t!.
Here g is the surface tension and A the surface area. The term surface elasticity infers that E is a property of pure elastic surfaces. It turns out, however, that many surfaces contain both an elastic component and a viscous component, and the term “surface dilatational modulus” has been used for this more general case. The contributions of the elastic and viscous terms depend on the different types of relaxation processes that occur on the surface layer and on the interaction of the surface with its surroundings, i.e., the bulk liquid(s). The equilibrium (Gibbs) surface elasticity, E 0 , will then usually be different from E. The surface dilatational viscosity, hd, has been defined according to the equation
Dg 5 hd
where Dg is the surface tension difference of a constantly (logarithmically) expanding surface compared to that of the equilibrium surface. The parameter hd will only represent a true Newtonian type of surface viscosity, however, if the elasticity is zero. In other cases, a complex surface dilatational modulus may be written as
[2]
[6]
Here A a is the area amplitude and A 0 is the equilibrium surface area. The response in the surface tension variation can then be described by the function D g 5 g 2 g 0 5 g asin~ v t 1 d !,
[7]
where ga is the measured amplitude, g0 is the equilibrium surface tension, and d is the phase angle. In the usual manner, Eq. [7] may be written D g 5 g asin~ v t!cos d 1 g acos~ v t!sin d
[8]
By using Eq. [1] for E*, we see that the (complex) surface dilatational modulus is then expressed by
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
E* 5 E9 1 iE0 5 uEucos d 1 iuEusin d ,
[9]
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a result of a surface pressure change even at constant surface area.
where EXPERIMENTAL
ga uEu 5 A a/A 0
[10]
The loss modulus E0 represents a combination of internal relaxation processes and relaxation due to transport of matter between the surface and the bulk. The latter process will be important especially in the case of soluble monolayers and in nonequilibrium situations and will be more dominant at lower frequencies because of the time involved in the diffusion process. Several theories have been developed that describe the latter process (2, 3), and it is predicted that in this case the phase angle, d, will be 45° and the elasticity will approach zero at low frequencies (3). The interested reader is referred to refs 2 and 3 for in-depth discussion of this topic. Often, the response function, Eq. [7], is determined from the experimental data by means of a Fourier transform. The transformed time function should ideally only contain the main harmonic component; however, noise in the experimental data will usually also give rise to higher harmonics content, which may complicate the analysis. It will also be important to consider the boundary problem. Another method of analysis is to fit Eq. [7] directly to the experimental data. A nonlinear curve-fitting procedure is able to obtain the universally best results even from noisy data; it is, however, necessary to use good initial parameter estimates if this strategy will succeed. Such parameters may be obtained by preanalyzing the data in a proper way. For the zero values ( A 0 , g 0 ) the arithmetic means can be used, and the amplitudes ( A a, ga) may be calculated from the standard deviations when it is observed that for a sine function
SOD
2 Amplitude 5 N
N
y
2 i
1/ 2
[11]
i5l
Here y i are the experimental data and N the number of measurements. The frequency and phase angle relative to the start measurement time may be estimated by simply counting the data points below and above the mean in each period. By using these initial values in a nonlinear least-squares curve-fitting procedure, it is usually quite easy to obtain a good fit of the sine function to experimental data. It should be stressed that this method for the determination of the surface dilatational modulus is based on the analysis of the drop image only and that an additional determination of the capillary pressure as in earlier published methods (6, 7) is not necessary. This is so because the surface tension is determined from the bubble’s shape (together with the size) and that the shape may change as
Instruments As mentioned in the Introduction, the first DROP instrument has been described earlier. Because of essential modifications from the initial construction, it will be described briefly here. An illustration of the instrument is shown in Fig. 1. It consists of a goniometer (Rame´-Hart) fitted with a macro lens and autobellows (Olympus) and a CCD video camera (Sony). The video frames are captured by a DT3155 frame grabber (Data Translation) in a Pentium 200 PC (Dell Computer). The drop control unit is a Microlab M dispenser (Hamilton) and a specially designed oscillation unit consisting of a syringe with an excenter-mounted piston that is motor driven. The dispenser is controlled by the PC. The dispenser and oscillation units are mounted in series with stainless steel pipes that are filled with distilled water. The drops and bubbles are extended from the tip of a small Teflon tube into a quartz cuvette inside a thermostated and water-filled environment chamber with glass windows. The Teflon tube contains an air pocket toward the water in the steel pipe. The DROP computer program has been rewritten for the MS-Windows platform. On this platform, the program can control the new frame grabber through the manufacturer’s supplied drivers and software libraries (DLLs) and can use all available RAM for picture storage. This means that, if necessary, the program can capture pictures directly to RAM in real time and calculate the results later. A maximum capture rate of 25 Hz in CCIR video is therefore possible. The rate of calculation on this system is ca. 0.2 s per picture. The program has many facilities for different measurement strategies and is also able to keep the drop or bubble volume constant during a long period of time by means of a feedback method. This is very important when measuring adsorption in highly elastic films, where small deviations in volume (i.e., area) may cause significant measurement errors. The results that are calculated are the surface tension, shape factor (b), radius of curvature (R 0 ), the drop volume, height, and width, the surface area, and the contact angle with the horizontal plane. A description of the instrument and the program may be found at http://www. uio.no/;fhansen/dropinst.html. An automatic Langmuir surface balance (Minithrough, KSV Instruments Ltd., Finland) was used to record the p vs A isotherms. The trough is made from a single block of PTFE and has a surface area of approximately 250 cm2. The surface tension of the monolayers is measured by means of a Wilhelmy plate.
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FIG. 1.
DROP instrument for the measurement of interfacial tension and surface dilatational rheologic parameters.
Chemicals The ethylhydroxyethyl cellulose (EHEC) polymer was manufactured by Akzo Nobel and purified by B. Lindmans group at the University of Lund. The molecular weight of the polymer is ca. M w 5 80,000 and the degrees of substitution of ethyl and hydroxyethyl groups are 0.6 – 0.7 and 1.8, respectively. The polymer has been described elsewhere (16). The poly(oxyethylene)–poly(oxypropylene) (POE–POP–POE) block copolymers were commercial products (Pluronics) produced by BASF. The molecular weight of the POP block is 1750 and the PE6200 and PE6800 polymers contain 20 and 80% of POE in the molecule, respectively (total molecular weights ca. 2500 and ca. 8500, respectively). The polymers were used as received. All water was ion exchanged followed by distillation. Its surface tension was 72 6 0.5 mN m21 (25°C). In the Langmuir surface balance the surface was checked for purity by affirming that surface compression led to a pressure p , 0.5 mN m21. Procedure A small amount of air (ca. 150 mL) was sucked into the tip of the Teflon tube. The tip was dipped into ca. 10 mL of the polymer solution in the cuvette and fixed to the environmental chamber. The temperature in the chamber was
24.5°C in all experiments. The computer was programmed to increase the bubble volume instantly, with immediate start of surface tension measurements. The formation of a 50-mL bubble took ca. 0.5 s. The surface tension was measured as a function of time until a near equilibrium was reached (with many substances, true equilibrium was never reached). In most experiments, this time was ca. 10,000 s. During most of these measurements, the bubble volume was kept constant by the program (60.5 mL). The bubble was oscillated around the equilibrium position with an amplitude of ca. 2.5 mL and a frequency between 0.2 and 2 Hz. This amplitude was found to be in the linear viscoelastic regime. At each frequency 3 periods were measured and the surface tension data stored. The measurements were finally analyzed by means of a nonlinear gradient expansion method (Marquardt method) (14) by fitting the surface area and surface tension data to sine functions as described earlier. Because the measurements start at some arbitrary time during an oscillation, the value of d is determined as the difference between the experimental phase angles of the surface area and surface tension functions. The value of uEu was determined from the measured amplitudes and the mean surface area by means of Eq. [10] and the moduli from uEu and d as shown in Eq. [9]. For each sample the oscillation measurements were repeated 3–7 times.
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SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
FIG. 2. Example of measurement of a sinusoidal oscillation at the highest video rate.
The p vs A isotherm was obtained from monolayers spread on water according to a procedure developed for water-soluble biopolymers (15). RESULTS AND DISCUSSION
It was found that the surface area and surface tension data could be easily fitted by means of the method described in the
preceding section. An example of such a fit is given in Fig. 2. These data were collected at the highest possible video rate of 25 Hz. The drawn curves in the figure are fitted sine functions. It is seen that the area is very well described by the sine function. The surface tension is also well measured by this method. Small deviations from the sine curve have little influence on the fitted curve; usually the fit is even better at lower frequencies. An error analysis of the oscillation data is represented in Table 1. For each sample, the standard deviation is calculated from the repeated measurements and a total standard deviation is calculated from all the measurements, under the hypothesis that all standard deviations represent the same population. The total standard deviation on the sample mean is calculated using an average of six repetitions per sample; these are 0.21 and 0.40 mN m21 for E9 and E0, respectively. We see that there are no significant differences between these average standard deviations and the individual estimates for each sample; an F-test shows that the difference is not significant at the 95% confidence level. We may therefore conclude that these values represent the errors inherent in the applied method and that preferably at least four repeated measurements should be used. It may be noted that the error in E0 is approximately double that in E9 and together with the generally low values of E0 makes the relative error in this parameter quite high. This is a consequence of the low phase angle, d, of the measured samples and the uncertainty in the determination of d. When d is higher, and E9 and E0 thus more equal, the error in these parameters will also be more equal. We will therefore in this discussion use an error estimate of 60.4 and 60.8 (52s) in E9 and E0, respectively. The results for the EHEC polymer are presented in Figs.
TABLE 1 Error Analysis of Surface Rheology Measurements For each measurement
System EHEC
PE6200
PE6800
Sum of squares Variance s per measurement s of sample mean s of s (per measurement)
Concentration (ppm) 10 40 100 1 10 100 1000 1 10 100 1000
Number of measurements 6 6 3 6 6 6 6 7 6 4 5 (11) (6)
For the means
s (E9) (mN m21)
s (E0) (mN m21)
s (E9) (mN m21)
s (E0) (mN m21)
0.25 0.57 0.66 0.51 0.58 0.55 0.41 0.49 0.49 0.46 0.48 2.812 0.256 0.51 0.21 0.15
1.1 0.77 1.4 1.3 1.1 0.90 0.44 0.71 0.81 0.61 1.15 10.411 0.946 0.97 0.40 0.28
0.10 0.23 0.38 0.21 0.24 0.22 0.17 0.19 0.20 0.23 0.21
0.45 0.31 0.79 0.53 0.45 0.37 0.18 0.27 0.33 0.31 0.51
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FIG. 3. Dynamic surface tension of EHEC solutions as a function of time measured by the sessile bubble method.
3–5. In Fig. 3 the surface tension as a function of time is shown. These results are similar to those measured by Nahringbauer (17) by the pendant drop method, except that our measurements are extended to much shorter times and may also be extended to very long times. The surface tension is seen to decrease at a lower rate at long times, but a true equilibrium adsorption is not reached in the measured time interval. The curve at 1000 ppm shows a downward dip above ca. 2000 s. This is a consequence of a decreasing bubble volume, and the curve was kept to illustrate this point; in all other experiments the volume was kept constant by the computer. The decreased surface area leads to an increase in surface pressure as in the corresponding p vs A isotherm. This is typical of insoluble surface films and shows that there is no (or very little) desorption in these systems in the time scale of these experiments. The adsorption kinetics and mechanism of this polymer have been discussed by others and will not be discussed further here. We only want to stress that in order to evaluate the kinetics of adsorption properly, the surface tension (pressure p) should be converted to surface concentration (G) by measuring the p vs A isotherm separately in a Langmuir balance as previously done in the adsorption of HSA (13). The measured surface dilatational modulus of the EHEC polymer is presented in Fig. 4. There are several interesting features with these results: First it is noted that the elastic modulus, E9, is much higher than the viscous modulus, E0, meaning that the surface area and surface tension oscillations are almost in phase, as shown in Fig. 2. Second it is seen that both moduli increase with increasing frequency. The absolute increase is approximately linear and is stronger (in absolute terms) for the elastic than for the viscous modulus. The extrapolation of the elastic modulus to zero frequency gives a
finite value which is expected to be equal to the equilibrium Gibbs elasticity, E 0 . The straight line that fits the viscous modulus extrapolates to zero (within experimental errors), which is well in line with the observation that these films behave like insoluble films, as a higher value at low frequencies can be interpreted as a result of desorption (2, 3). The slope of the line, E0/ v , is equal to the dynamic, or surface dilatational, viscosity, hd, as shown in Eq. [5]. It can therefore be concluded that hd may be measured by this method but that the modulus for EHEC is quite low, ca. 0.25 mN s m21 at the highest polymer concentration. The elastic modulus, E9, increases to a certain degree with increasing polymer concentration but the increase in not very strong. This is a consequence of the fact that the surface tensions, and thus the surface concentrations, are not very different at the measured time (10,000 s). A compression of the surface, as a result of bubble shrinkage, results in an increase in elasticity. This means that the p vs A isotherm must be curved upward in this region. We also find that the elasticity, E9, increases with frequency; the slope of the highest curve is 0.57 mN s m21. This is characteristic of insoluble monolayers and has been observed previously by using the small oscillating bubble (2). The limiting elasticities as v 3 0 may be compared to those calculated form the p vs A isotherms measured by the Langmuir balance. This isotherm for EHEC is shown in Fig. 5, where also the elasticity E 0 is calculated by means of Eq. [1]. We see that the elasticity goes through a maximum of 18.8 mN m21 at a surface pressure of 8.4 mN m21 and becomes quite low again at surface pressures around 20 mN m21. At higher surface pressures it seems that E 0 may increase again, but we were not able to compress the film further in the Langmuir balance. Such a behavior is often observed with monolayers of both synthetic
FIG. 4. Surface dilatational moduli of the EHEC solutions: upper points, E9; lower points, E0.
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
103
FIG. 5. p vs A isotherm of EHEC measured by the Langmuir surface balance. Also plotted is the surface elasticity calculated by Eq. [1].
and natural polymers (13, 18, 19). We see that the surface pressures at long times for the adsorbed films measured by this oscillating bubble method are around 20 mN m21 and higher and that the extrapolated elasticity therefore may be expected to increase with increasing concentrations, as observed. Results for the block copolymer PE6200 are shown in Figs. 6 and 7. Figure 6 shows the adsorption vs time behavior and
Fig. 7 the surface rheological moduli. The dynamic surface tension curves are somewhat similar to those with EHEC, but adsorption from corresponding concentrations is much faster, mainly as a result of the much lower molecular weight. The curves also seem to flatten more at longer times, except for the one for 1000 ppm, which curves downward again, an observation that is believed to be due to impurities in the commercial
FIG. 6. Dynamic surface tension of PE6200 solutions as a function of time measured by the sessile bubble method.
FIG. 7. Surface dilatational moduli of the PE6200 solutions: upper points, E9; lower points, E0.
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FIG. 8. Dynamic surface tension of PE6800 solutions as a function of time measured by the sessile bubble method.
polymer. The almost constant surface tension at long times indicates that these polymers have reached near-equilibrium adsorption; i.e., that there also may be desorption from the surface. The surface elastic modulus, as shown in Fig. 7, is considerably higher than for EHEC and decreases with increasing concentration, except for the highest concentration, 1000 ppm, which is equal to that at 100 ppm. This result cannot be explained by a diffusional relaxation mechanism, because the viscous modulus should then be closer to the elastic modulus (tan d 3 1) (3). It is rather probable that the elasticity decreases with increasing surface pressure because of a configuration change in the surface layer, leading to a decreasing slope of the p vs A isotherm in the same way as observed for EHEC (Fig. 5). The fact that the elasticities for the two highest concentrations are almost identical may be explained by the fact that these two concentrations are close to the minimum in E (we do not know if there is a minimum here; E 0 may as well stay constant). Even if the surface elasticity is higher than for EHEC, the frequency dependency is lower; the slope for the 1 ppm data is 0.36 mN s m21. The viscous modulus is also here very low, on the order of 1–2 mN m21, but does not seem to change much with frequency. If the loss modulus is solely due to viscous friction, it should increase with frequency, as is the case with EHEC; if the loss is due to diffusional exchange with the bulk, the opposite frequency dependency is expected (3). Therefore, the reason for a near-constant value may be a combination of these effects. However, the experimental errors in these data are of the same magnitude as the change in the data itself, and it is therefore difficult to make any decisive conclusions. Results for the more hydrophilic block copolymer PE6800 are presented in Figs. 8 and 9. The adsorption of this polymer
clearly proceeds more slowly than that of PE6200 because of the higher molecular weight and the resulting surface tension is higher, probably because of the more hydrophilic nature of this polymer. The polymer seems to reach near-equilibrium adsorption close to the far end of our measured data (70,000 s). The reason for the “bumps” on the surface tension curves for 1 and 10 ppm is uncertain but may be caused by uneven molecular weight distribution of the polymer. The surface rheological moduli shown in Fig. 9 (measured at 10,000 s) show a still more complex behavior than for PE6200. The elastic modulus, E9, is seen to increase from the curve at 1 ppm to that at 10 ppm, but then it decreases again. At the same time the slope of the curve is increasing with concentration. At 100 and 1000 ppm the curves do not seem to be straight lines anymore but have a tendency to bend downward at low frequencies. This tendency may be present also in the results for PE6200, but the significance of those data is uncertain. At the same time as the elastic modulus decreases, the viscous modulus increases. It is probable that this now may be explained by diffusional transport between the bulk and the surface because of the higher water solubility of this polymer. Especially the data at 100 ppm clearly show that E0 is decreasing with increasing v. At 1000 ppm, E0 is mostly constant again, but this may be a result of a decrease in both moduli with a simultaneous increase in the phase angle, which is expected in the case of diffusional exchange (3). The maximum in E9 possibly has the same explanation as the increase for EHEC and the decrease for PE6200: The difference between the “equilibrium” surface tensions for the different concentrations of the polymer PE6800 is larger than for either of the other two polymers; the
FIG. 9. Surface dilatational moduli of the PE6800 solutions: upper points, E9; lower points, E0.
SURFACE ELASTICITY AND VISCOSITY FROM OSCILLATING BUBBLES
surface pressures are both below and above the bend in the p vs A isotherm, and the elasticity may go through a maximum in the same way as shown for EHEC (Fig. 5). However, the increase in diffusional interchange will also decrease E9 and may be a part of the explanation. To make any further conclusions about the exact mechanism, the p vs A isotherms should be measured; however, the Pluronics polymers are too water soluble to be measured easily by the Langmuir balance. CONCLUSION
It may be concluded that the new method of oscillating bubble with full profile image analysis is well suited to measure dynamic surface elasticity and viscosity of adsorbing polymers from low frequencies up to a few hertz. Interesting features of the polymer films are observed that are due to both viscoelastic properties of the adsorbed polymers and diffusional transport between the surface and the bulk. REFERENCES 1. Edwards, D. A., Brenner, H., and Wasan, D. T., “Interfacial Transport Processes and Rheology.” Butterworths-Heinemann Publishers, Oxford, 1991.
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2. Dhukin, S. S., Kretzschmar, G., and Miller, R., “Dynamics of Adsorption at Liquid Interfaces.” Elsevier, Amsterdam, 1995. 3. Lucassen-Reynders, E. H., Surfactant Sci. Ser. 11, 173 (1991). 4. Lucassen-Reynders, E. H., and Lucassen, J., Adv. Colloid Interface Sci. 2, 347 (1969). 5. Hansen, R. S., and Ahmed, J., Prog. Surf. Membr. Sci. 4, 1 (1971). 6. Lunkenheimer, K., and Kretzschmar, G., Z. Phys. Chem. (Leipzig) 256, 593 (1975). 7. Nagarajan, R., and Wasan, D. T., J. Colloid Interface Sci. 159, 164 (1993). 8. Rotenberg, Y., Bouvka, L., and Neumann, A. W., J. Colloid Interface Sci. 93, 169 (1983). 9. Hansen, F. K., and Rødsrud, G., J. Colloid Interface Sci. 141, 1 (1991). 10. Miller, R., Policova, Z., Sedev, R., and Neumann, A. W., Colloids Surf. 76, 179 (1993). 11. del Rı´o, O. I., and Naumann, A. W., J. Colloid Interface Sci. 196, 136 (1997). 12. Hansen, F. K., J. Colloid Interface Sci. 160, 209 (1993). 13. Hansen, F. K., and Myrvold, R., J. Colloid Interface Sci. 176, 408 (1995). 14. Bevington, P. R., and Robinson, D. K., “Data Reduction and Error Analysis for the Physical Sciences.” McGraw-Hill, New York, 1992. 15. Sta¨llberg, S., and Teorell, T., Trans. Faraday Soc. 35, 1413 (1939). 16. Thuresson, K., Nystro¨m, B., Wang, G., and Lindman, B., Langmuir 11, 3730 (1995). 17. Nahringbauer, I., J. Colloid Interface Sci. 176, 318, (1995). 18. Myrvold, R., and Hansen, F. K., Colloids Surf. 117, 27 (1996). 19. Ahluwalia, A., Stussi, E., and Domenici, C., Langmuir 12, 1416 (1996).