© Copyright 1997 American Chemical Society
JULY 23, 1997 VOLUME 13, NUMBER 15
Letters Influence of Surface Aging on the Drainage of Foam Films Stabilized by Aqueous Solutions of Ethyl Hydroxyethyl Cellulose E. Poptoshev, Suh-Ung Um, and R. J. Pugh* Institute for Surface Chemistry, Box 5607, S-114 86 Stockholm, Sweden Received March 18, 1997X The drainage times of microscopic horizontal foam films stabilized by dilute aqueous solutions of ethyl hydroxyethyl cellulose (EHEC) was shown to be dependent on the aging effects (configuration changes of the adsorbed macromolecules) occurring in the freshly created air/solution interface. At low polymer concentration (5 ppm), the films drained fairly rapidly from thicknesses of about 400 to 300 nm with drainage times about 5 to 6 times greater than theoretical values calculated using the Reynolds equation. However, at higher polymer concentrations (100 ppm) at extended surface aging (15-180 min) the film drainage times were shown to increase drastically giving values 50 times greater than theoretical values. Although these aging effects could not be directly related to surface tension data, diffusion coefficients were calculated from interfacial tension profiles using classical diffusion theory. As the concentration of polymer increased, the diffusion coefficients were shown to decrease and were considerably smaller than previously reported experimentally values determined in bulk solution by NMR. This difference between experimental and theoretical results endorsed a kinetic rather than a diffusion or mass transport model for the transfer of EHEC molecules to the interface. The increase in drainage times with extended aging times could be explained by the gradual formation of a steric energy barrier caused by configuration changes of the adsorbed polymer. This probably involved the progressive extension of the EHEC tails into the aqueous phase increasing the disjoining pressure, decreasing the drainage rate, and producing thick stable films.
Introduction The dynamic interfacial properties of surface active polymers are of great research interest because of their wide practical use in numerous colloidal systems. Recently, the dynamic surface tensions of different cellulose ethers have been determined for relatively short aging times (from 0.15 to 2.5 s) using the maximum bubble pressure method.1 These results were compared to data obtained over longer time scale (from 30 s to over 17 h) by Nahringbauer2 using the pendant drop technique. From * Corresponding author. E-mail:
[email protected]. X Abstract published in Advance ACS Abstracts, July 1, 1997. (1) Um, Suh-Ung; Poptoshev, E.; Pugh, R. J. Aqueous Solutions of Ethyl (Hydroxyethyl) Cellulose and Hydrophobic Modified Ethyl (Hydroxyethyl) Cellulose Polymer; Dynamic Surface Tension Measurements J. Colloid Interface Sci., in press. (2) Nahringbauer, I. J. Colloid Interface Sci. 1995, 176, 318.
S0743-7463(97)00292-8 CCC: $14.00
these studies, it was suggested that the adsorption process includes two consecutive or concurrent stages: a slow diffusion of the macromolecules from the bulk phase to the subsurface region proceeded by adsorption of polymer segments at the interface. Also, it was proposed that these processes were followed by configuration changes in the molecules. Initially, in bulk solution, the macromolecules are coiled, but on diffusing to the interface the polymer backbone starts to entangle after a critical time. A model was proposed involving unfolding or spreading of the adsorbed molecules followed by attachment of the polymer segments from the subsurface to the surface.2 This leads to an increase in the number of adsorbed polymer segments causing a reduction of the surface tension. The rearrangement of the adsorbed polymer segments between the surface and the subsurface occurred over an extended time scale. Further, it was shown that the kinetic isotherms relating © 1997 American Chemical Society
3906 Langmuir, Vol. 13, No. 15, 1997
surface tension to the aging time followed a sigmoidal pattern. From these data it was possible to assign separate consecutive regions: an induction period at low surface aging times followed by a region of increasing surface coverage. Finally, at high aging times a mesophase region is formed. In the mesophase region, slow equilibration occurred which involved a progressing ordering of the polymer segments within the surface layer. The time scales of such conformation changes were found to be greatly extended. In fact, a constant steady state equilibrium interfacial tension value could not be fully achieved, although measurements were made over time scales prolonging over 17 h. In the literature, studies on free liquid films stabilized by aqueous solution of polymers have been reported infrequently. In fact, of the few experiments carried out, these were mostly concerned with characterizing the equilibrium state of the foam films which has been shown to be strongly dependent on the polymer type, the ionic strength of the aqueous solution, and the concentration of surfactant. Generally, such studies have enabled the interaction forces, the diffuse electrical layer, and the general thermodynamic properties of the films to be quantified. In the present paper, we report dynamic surface tension and drainage results for thin films stabilized by a high molecular weight ethyl hydroxyethyl cellulose (EHEC) polymer in aqueous solution. This is as an alternative to the equilibrium approach and emphasizes the importance of surface aging (conformation changes of the adsorbed polymer) on the drainage kinetics. Materials and Methods Materials. The EHEC polymer (molecular weight 100 000 g/mol) was manufactured and supplied by Berol Nobel AB, Stenungsund, Sweden. The degree of substitution of the ethyl was expressed in terms of DSethyl (average number of ethyl groups per anhydroglucose unit of the polymer), and the molecular substitution (MSEO) referred to the average number of hydroxyethyl groups per anhydroglucose unit of the polymer. Values given by the manufacturer were DSethyl ) 0.6-0.7 and MSEO ) 1.8. Purification of the polymer (dialysis to remove electrolyte) and freeze drying was carried out, as previously reported by the Department of Physical Chemistry, Lund University, Sweden.3 The polymer was then stored in a desiccator prior to the preparation of a stock solutions. All working solutions were prepared by dilution of stock solution (1 wt %) and stirred for several hours before starting the measurements. Milli-Q water was used throughout the experiment work. Surface Tension Measurements. Surface tension was measured for a range of EHEC concentrations using Kru¨ss K-12 tensiometer and K-122 version 2.14 a software. This equipment is based on the Wilhelmy method. A standard platinum plate with perimeter 40.2 mm was used. The polymer solutions were introduced into the sample vessel, and after an initial aging time of 2 min (which is the shortest time required for starting the equipment) data for surface tension were taken in intervals of 60 s. The precision of the technique was checked by measuring the surface tension of Milli-Q water over the same time scale as the polymer solutions. A mean value of 72.45 mN/m with standard deviation of 0.08 was obtained. Film Drainage. The microinterferometric method was used to obtain the data for drainage times of microscopic horizontal foam films. This technique, pioneered by Scheludko and Mysels, is described in detail in numerous publications.4-6 The film is formed between the tips of the menisci of a biconcave drop held in a vertical cylindrical glass tube. The amount of the liquid in the biconcave drop and the film radius are controlled by sucking (3) Thuresson, K. PhD Thesis, Solution Properties of Hydrophobic Modified Polymers; Lund University, Sweden, 1996. (4) Scheludko, A. Adv. Colloid Interface Sci. 1967, 1, 391. (5) Manev, E. D.; Pugh, R. J. Langmuir 1991, 7, 2253. (6) Radoev, B.; Scheludko, A.; Manev, E. J. Colloid Interface Sci. 1983, 95, 254.
Letters the liquid out of the drop. The cell is placed on the stage of a inverted microscope (IM-35 “Carl Zeiss-Jena”). Reflected light from a small portion of the film (450 µm2) is received by a fiber optic probe mounted in the microscope eyepiece. The light signal is then passed through a monochromatic interference filter λ ) 546 nm, converted into a photocurrent, and finally recorded as photocurrent versus time strip chart interferogram. This allows the thickness of the film at any instant of time to be measured. To investigate the dependence of drainage times on the film surface age, we used the follow procedure: Initially the biconcave drop (i.e., formation of a fresh liquid-gas interface) was formed in the horizontal cell. This was allowed to age for a predetermined period of time (the surface aging time). After this period was complete, the thickness of the film was reduced by sucking, so that the film thickness came within the range of capillary forces causing drainage. The time of film thinning (drainage time) for each film within a specific thickness range (i.e., between initial and final thicknesses ca. 400-300 nm) was determined. After the drainage process was complete, stable thick films were produced. Experiments were repeated with different aging times and EHEC concentrations. This enabled a plot of drainage time versus surface aging time to be constructed. For a circular, horizontal, model foam film, assuming its thickness to be much smaller than its radius R (this condition is always fulfilled in the experiment), Scheludko4 has derived the following expression for the rate of thinning
VRE ) -
dh 2h3∆P ) dt 3µR2
(1)
Here µ is the dynamic viscosity, ∆P ()Pc - P) is the driving force per unit area, where Pc is the capillary pressure and P is the disjoining pressure, and h is the thickness. Equation 1 is analogous to the expression derived by Reynolds in 1886 for the rate of thinning of a liquid film formed between two rigid disks and is known as “Reynolds’ law” or Reynolds’ equation. On integration eq 1 gives
∆t )
(
3µR2 1 1 4∆P h 2 h 2 f i
)
(2)
where for the present experiment R ) 2 × 10-4 m, µ ) 8.9 × 10-4 PaS, ∆P ) 2γ/Rc, where Rc is the radius of the capillary (2 × 10-3 m) and γ is the surface tension, and hi and hf are the initial and final film thicknesses, respectively. Drainage was measured between the interference peaks corresponding to hi ) 4.08 × 10-7 m and hf ) 3.06 × 10-7 m. Usually, throughout this thickness range, the steric components of the disjoining pressure are considered to be small. Also from eq 2 it can be seen that the film drainage is weakly dependent on surface tension compared to such factors as film radius and the thickness range which are depicted as squares.
Results and Discussion The results for dynamic surface tension measurements are presented in Figure 1. The overall shapes of the curves as well as the rate of approach to the equilibrium surface tension values after extended aging, show a strong dependence on the bulk polymer concentration. Generally, these surface tension versus time isotherms follow a sigmoidal pattern and are in agreement with the previous studies with EHEC determined by the pendant drop technique.2 At low polymer concentrations (5 ppm), the isotherms show a induction time extending up to several minutes. This is followed by the fast reduction of the surface tension or so-called fast fall region. Finally, the meso equilibrium state begins at surface tension values less than 60 mN/m, and this is characterized by the slow approach to equilibrium values. For concentrations g13 ppm, the induction period is considerably reduced and at surface tension values about 53-57 mN/m begin to approach equilibrium values after an aging time of about 30 min. The systems with higher bulk concentrations
Letters
Figure 1. Surface tension versus surface age for aqueous solutions of EHEC (determined by Wilhelmy plate technique).
Langmuir, Vol. 13, No. 15, 1997 3907
the experimental aging rates increase from about 30 to 50 times greater than the theoretical values as the aging times increase. At this higher polymer concentration, the surface tension remains fairly constant. Many theoretical models have been proposed to describe the adsorption of surfactant at a freshly formed interface. Earlier theories are based on the premise that the surface transfer process was purely a mass transfer diffusion controlled process. Ward and Tordai7 showed that for a clean interface without convection, the diffusion of the solute toward the subsurface could be treated by applying the classical diffusion equation. By considering short aging time (assuming that the subsurface concentration was negligible and that the equilibrium between the surface and subsurface is established instantaneously), they showed that the surface concentration after time t (where t ) 0 for initial surface formation) could be expressed by
Γ ) 2C0(Dt/π)1/2
(3)
where Γ is adsorption, C0 is the bulk concentration, and D is the diffusion coefficient of polymer molecules. This equation indicates the surface concentration increase as the square root of time. In addition, for the more general case, they showed that when the subsurface concentration can be no longer neglected and Γ can be extended to give a modified form of eq 3 to include an expression for back diffusion
Γ ) 2(D/π)1/2{C0t1/2 -
Figure 2. Drainage time (from film thickness 408-306 nm) versus surface age for aqueous solutions of EHEC.
show more rapid approaches to equilibrium. In Figure 2, the thin film drainage time is plotted versus the aging time enabling a comparison to be made between the drainage and interfacial dynamic interactions. At low concentrations (5 ppm), the drainage remains fairly constant over extended aging times. However, at higher EHEC concentrations, although the drainage time increases with polymer concentration. At all concentrations, the curves are characterized by an induction aging period of about 10 min. Beyond this point a drastic increase results. In fact, after an aging time of 190 min the drainage time between the 5 and 100 ppm polymer concentration was found to differ by a factor of 10. Table 1 shows a comparison between the experimentally determined drainage times and theoretical values (calculated using eq 2). From previous studies it was shown that there was no significant difference in viscosity of the aqueous polymer solutions throughout this concentration range.1 Also the surface tension results shown in this table were taken from Figure 1. At a very low concentration of EHEC (5 ppm), the experimental drainage times are shown to be between 5 and 6 times greater than those of the theoretical predictions and do not increase significantly over the aging period. This result indicates that even at low polymer concentrations, and relatively high thickness, a positive disjoining pressure contribution is present which can be explained by a steric interaction. In addition, from Table 1 it can be seen that the reduction in surface tension caused by an increase in aging does not appear to have a significant influence on the experiment or theoretical values at this low polymer concentration. However, in the case of the higher polymer concentration,
∫0t
1/2
φ(z)d[(t - z)1/2]}
(4)
In this equation, z is a dummy variable and φ(z) is the subsurface concentration. Providing the surface excess is known then the diffusion coefficient can be calculated from eq 4. Hence, graphical determination of the back diffusion integral (from zero to t1/2) enables a mean value of the diffusion coefficient to be calculated. This can be achieved following the procedure described by Ward and Tordai.7 Essentially, the method may be summarized as follows; from a plot of the equilibrium surface tension against concentration, together with a isotherm of the dynamic surface tension as a function of time (for a range of bulk surfactant concentrations) the variation of the subsurface concentration with time can be calculated. Values for Γ could be calculated from the surface tension data determined under equilibrium conditions. However, it is important to note that theory is based on the assumption that there is an instantaneous equilibrium between surface and subsurface (the surface adsorption is a function of the surface tension for both dynamic and equilibrium conditions). According to Nahringbauer2 the polymer will initially adsorb with an extended conformation with most of the segments within the flat chains and few in the form of loops and tails. With increase in time, conformation changes will occur initially involving spreading and unfolding of the adsorbed molecules. This will be followed by attachment of segments from subsurface to surface and then rearrangements of adsorbed segments between surface and subsurface. The number of segments in contact with the surface will increase with time and this will result in a gradual increase in the thickness of the polymer film. In fact, as the aging time increases, a large portion of segments of adsorbed molecules will extend into solution but a considerable amount of time will be needed to complete this process. Also, the transfer step would be complicated by the size and the polydispersity (7) Ward A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453.
3908 Langmuir, Vol. 13, No. 15, 1997
Letters
Table 1. Comparison of Theoretical (Using Equation 2) and Experimental Drainage Times (Thickness Range from 408 to 306 nm) of Single Foam Films Stabilized by EHEC 5 ppm EHEC
100 ppm EHEC
td (s)
surface age (min)
surface tension (mN/m)
calcd (eq 4)
exptl
6 14 28 35 65
69.2 61.6 57.5 57.1 55.9
1.8 2.1 2.2 2.2 2.3
11.4 12.1 12.3 11.8 13.8
td (s)
td (exptl)/td (calcd)
surface tension (mN/m)
calcd (eq 4)
exptl
td (exptl)/td (calcd)
6.33 5.76 5.59 5.36 6.00
52.4 52.3 52.1 52.0 51.9
2.4 2.4 2.4 2.4 2.4
74.5 76.0 103.0 106.0 122.0
31.04 31.67 39.62 44.17 50.83
of the EHEC. Hence, values of the diffusion coefficient calculated from the above equation will represent a complex quantity, dependent on both diffusion and the crossing of a dynamic energy barrier between the subsurface and the surface. In the literature, values calculated by this method are usually referred to as the apparent diffusion coefficient Da. Generally, Da values are less than D (the bulk value) and the difference between these values gives an estimate of the energy barrier of the kinetically controlled process. Only in cases where Da and D are in close agreement can a diffusion process be regarded as the main step in the interfacial transfer process. However, it is of interest to calculate Da and compare the values to D obtained from bulk measurements. In Figure 3, Da values are presented and can be seen to decrease with concentration. The Da value for 5 ppm EHEC is about 6.8 × 10-11 m2 s-1 or about 400 times greater than for the values at 100 ppm (1.7 × 10-13 m2 s-1). Experimentally determined mean values of the diffusion coefficient (D) obtained in bulk solution by NMR gives considerably higher values in the range of 8 × 10-11 m2 s-1.8 This result confirms the presence of a fairly large energy barrier which increases with polymer concentration. With a high molecular weight EHEC polymer, infinitely long chains consisting of hundreds of segments are involved and the configuration step can involve a relatively high value of the activation energy. Also, the gradual extension of the macromolecules into the aqueous solution will eventually result in the evolution of a strong steric interactions between the interfaces causing an (8) Thuresson, K., private communication, Lund University, Sweden, 1996.
Figure 3. Apparent diffusion coefficient calculated from eq 4 versus concentration of EHEC.
increase in disjoining pressure. From this study, it can be generally concluded that for a complete understanding of the drainage of foam film stabilized with surface active polymers, the effect of the surface aging should be taken into account. In fact, the adsorption step cannot be solely considered as a simple surface enrichment process since a complex dynamic conformation step is involved which can increase the drainage time and effect the stability of the film. Acknowledgment. The authors thank the Swedish Institute for a research award to E. Poptoshev and T.F.R. for a research fellowship for Suh-Ung Um. LA970292Q
