1379
Langmuir 1990, 6, 1379-1388
Dynamic Interfacial Properties of Poly(ethylene oxide) and Polystyrene at Toluene/Water Interface Kenichi Ito,+ Bryan B. Sauer,i Randy J. Skarlupka, Masahito Sano,S and Hyuk Yu* Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 Received May 15, 1989. I n Final Form: August 31, 1989 An experimental technique called electrocapillary waves diffractionhas been implemented to investigate viscous polymeric liquid-liquid interfaces. The instrument constructed recently in our laboratory has been calibrated with several standards, the static surface tensions and interfacial tensions of air/water, air/ hydrocarbon, and hydrocarbon/water. The results on surface tensions and interfacial tensions are in good agreement with the literature values in the static limit, and they are confirmed to remain the same over a wide range of frequencies (0.1-5 kHz). Next, we have examined the solutions of poly(ethy1ene oxide) (PEO) and polystyrene (PS) in various interfacial configurations: (1)toluene/PEO in water, (2) PEO in toluene/water, (3) spread films of PEO at toluene/water, (4) PS in toluene/water, (5) PS and PEO in toluene/water, and finally (6)PS in toluene/PEO in water. The interfacial tensions at the surface saturation limit are found to be the same at 19 mN/m in the first three cases, indicating that PEO is highly interface active and its adsorbed state is independent of the path by which it reaches the interface of toluene and water. In the fourth case, PS in toluene/water, the static limit of the interfacial tension is shown to be the same as that for pure toluene/water(without any polymer in either phase) at 36 mN/m, which may be taken as evidence for a depletion layer of PS at the interface. Further, the interfacial tension u is shown to be insensitive to frequency if the PS concentration is less than or equal to 2% in toluene whereas it is sensitive to frequency if the concentration is at about 8%. In the fifth case of PS and PEO in toluene/ water, u decreases from 36 to 19 mN/m while its frequency dependence is somewhat similar to the fourth case. In the last case of PS in toluene/PEO in water, u is found to remain constant at 19 mN/m regardless of PS concentration up to 14% in toluene. These results are used to surmise that the interfacial properties of toluene/water are predominantly controlled by PEO while being somehow affected by the viscoelastic properties of the toluene phase if the PS concentration exceeds a certain threshold.
Introduction
dispersion equation of surface waves6
To investigate surface properties, electrocapillary wave diffraction (ECWD)has been employed by Sohl et al.,l Stenvot and L a n g e ~ i n , ~ Nagarajan et a1.,2Miyano et and Vogel and MObius,5 all to examine surface tensions or interfacial tensions of simple liquids, with or without amphiphilic surfactants. Here we report an application of the technique to interfaces of polymer solutions. The method relies on a difference of dielectric constants across the interface, and upon application of an intense ac electric field over a small area on the interface, one can generate surface capillary waves, which propagate over the interface and can be probed spatially relative to the point of field application by optical diffraction of a laser beam. The wave propagation characteristics, i.e., the spatial wave vector k and the corresponding damping coefficient p, are used to deduce the surface tension y or interfacial tension u and the bulk shear viscosity of one liquid phase 7, through a t Research Center, Japan Synthetic Rubber Co., Ltd., 25 Miyukigaoka, Tsukuba 305, Japan. t Central R & D Department, Bldg. 356, Experimental Station, E. I. du Pont de Nemours & Co., Wilmington, DE 19898. 4 Kunitake Molecular Architecture Project, Research Development Corp. of Japan, Fukuoka 818, Japan. (1)Sohl, C. H.; Miyano, K.; Ketterson, J. B. Reo. Sci. Instrum. 1978,
49, 1464. (2) Nagarajan, N.; Webb, W. W.; Widom, B. J. Chem. Phys. 1982, 77, 5771. (3) Miyano, K.; Abraham, B. M.; Ting, L.; Wasan, D. T. J. Colloid Interface Sci. 1983, 92, 297. (4) Stenvot, C.; Langevin, D. Langmuir 1988, 4, 1179. (5) Vogel, V.; Mobius, D. Langmuir 1989,5, 129.
0743-7463/90/2406-1379$02.50/0
[iq(k*+ m ) + iqo(k* + mo) + ( t * / ~ ) k * ~ ] [ i+~m) ( k *+ iqo(h*+ mo)+ ( o / ~ ) k+*g(p ~ - p o ) / w - w ( p + pO)/k*]+ [V(k* - m) - qO(k* - m0)12= o (1) where k* = k - ip, with k as the spatial capillary wave vector, p as the spatial capillary wave damping coefficient, and i = -1112; m = [k*2 ( i w p / q ) ] 1 / 2and mo = [ k * 2 (iwpo/ TO)]^/^; 9 and qo are the shear viscosities of lower and upper phases, respectively; p and po are the densities of lower and upper phases, respectively; g is the gravitational constant; w is the angular frequency of the capillary wave; u is the interfacial tension; and t* is the dynamic modulus of the surface dilational wave, t * = t - i u , with t as the surface dilational elastic modulus and K as the surface dilational viscosity. It is generally assumed that eq 1 is applicable when both phases are Newtonian fluids, and the value of k should be large enough that tanh (kd)i= 1,where d is the depth of fluid from the interface. It should be noted t h a t this technique has some advantages over that of surface light scattering (SLS), which we have been using for some time.'-1° The SLS technique in the propagating wave regime has a fairly low viscosity limit (-5 cP); the power spectrum of scattered light, induced by thermal surface phonons, broadens so
+
+
(6) Lucassen-Reyners, E. H.; Lucassen, J. Adu. Colloid Interface Sci. 1969, 2, 347.
(7) Sauer, B. B.; Kawaguchi, M.; Yu, H. Macromolecules1987,20,2732. (8)Sauer, B. B.; Yu, H.; Tien, C.-F.;Hager, D. F.Macromolecules1987, 20, 393. (9) Kawaguchi, M.; Sano, M.; Chen, Y.-L.; Zografi, G.; Yu, H. Macromolecules 1986, 19, 2606. (10) Chen, Y.-L.; Kawaguchi, M.; Yu, H. Langmuir 1987, 3, 31.
0 1990 American Chemical Society
Zto et al.
1380 Langmuir, Vol. 6, No.8. 1990
I P0.W
Amplifier
I
r7 VAX 8500
Figure I. Rlock diagram ofthe experimental setup for the elecfrocapillary wave8 diffraction technique.
much at such a limit of viscosity that it is no longer detectable with any precision. On the other hand, the theoretical upper limit of viscosity for ECWD in the same regime is a few poise, so we can access the interfacial properties of relatively viscous liquids. Although the SLS technique covers only a few discrete wave vectors at a highfrequencyrange (510 kHz), ECWD can continuouslycover a wide range of frequency from 10 to 6000 Hz. The technique is also regarded as noninvasive because ratios of amplitude to wavelength of induced capillary waves are of the order of IO-'. Parenthetically, we should note that SLS can be applied to a much higher viscosity range if one probes the capillary waves in the damped reb'lime as opposed to the propagating regime, which we deal with here. In that event, one deduces just the ratio of surface tension to viscosity, and the viscosity can be as large as lo3 P as reported by Langevin et al." in 1972. Experimental Method Instrumentation. The experimental method is based on surface wave generation by electrocapillarity'z and detection by diffraction, i.e., harmonic deflection of a specularly reflected laser beam, from the surface wave.13 A block diagram of the apparatus is shown in Figure 1. The initial instrument design, construction, and performance characteristics were described by Sano." The sample cell is made of stainless steel (11 cm x 11 cm X 5 cm in depth) with a quartz window on the cell wall, and the thicknesses of the two liquids are kept at about 2 cm. The output of a frequency generator (Wavetek, Model 21) is amplified 10-fold by a voltage amplifer (Kepko, BOP lOO-lM),giving an oscillating electric field at a needle placed in the center of the sample cell, which is used to generate the surface capillary waves. The radius of the curvature of the needle tip is estimated to be around 10 pm from scanning electron micrographs of the needle. The gap between the needle tip and the interface is adjusted to be around 40 pm by visual monitoring through the cell window with a cathetometer. I. Optics. A beam from a 5-mW He-Ne laser (Melles Criot, 05-LHP-1'71) is directed perpendicular to the (11) Langevin, D.:Meunier. J.: Bouchiat, M..A. Opt. Commun. 1972.
6.427. (12) Jackson. J. D. In Clossicol Eleetrodynomics: Wiley: New
York.
,of? ."I_.
(13) Leiderer. P. Phys. Rev. B. 1919,20,4511. (14) Sam. M. Ph.D. Thesis. 1987, University of WimominMadison.
interface through a cubic beam splitter and a converging lens. The reflected beam a t the interface traces back to the beam splitter and then to a position-sensitive detector (PSD) (Hamamatsu, S1545). The focal spot of the beam a t the interface is calculated to be about 120 pm. In order to avoid the reflected laser beam from the surface of upper phase, an optical flat is placed on top of the surface and inclined slightly with respect to the surface of the liquid. The signal from the PSD is then fed into a lock-in amplifier (Stanford Research Systems) together with the output of the same frequency generator, after passing through a frequency doubler, as the reference. The complete optics are mounted on a translation stage which can be moved by a stepping motor (Superior Electric Co.) controlled by a microcomputer or manually, and the optical table is vibration isolated by floating on a set of air pillows (Newport). 2. Capillary Wave Generation. A more detailed picture of the wave generation process is as follows. An intense electric field produced by a sinusoidal voltage applied to a needle causes surface deformations due to a difference in the dielectric constants across the interface. The time dependence of force F(t) acting on the interface, when a harmonic potential
V ( t )= v, cos (4 (2) is applied to the tip of the needle, can be shown as F(t) a v,z (fa- f ) cos (2wt) (3) where t o and t are dielectric constants of the upper and lower phases, respectively. To detect the wave at a distance perpendicular to the needle point axis on the surface, a small portion of a focused laser beam is reflected. The angle of t h e reflected beam is modulated by t h e propagating wave with the same frequency as that of the surface wave, with an amplitude proportional to that of the surface wave. In all previous with the ECWD technique, a razor blade or a wire has been used to generate plane waves, whereas we use a needle point. Basically the needle and blade methods are the same in terms of determining the wave vector and damping coefficient, although the waves generated by a needle point damp faster than those by a blade. On the other hand, the needle point method has several technical advantages, and they may be enumerated as follows: (1)we can avoid possible edge effects of the razor blade, (2) we can prevent dealing with nonplanarity of the generated wave in cases where the blade axis is not perfectly parallel with the interface, and (3) we can eliminate errors prone t o determinations of t h e displacement distance x from the source axis by placing the laser beam scanning axis off perpendicular to the razor blade line. The modeling function of the damped circular wave profile is represented by the zeroth-order circular Bessel function (4)
where r(n+l) is the r function, and it can be approximated by a Hankel function (exponential decay) H , ( X ) = (2/ax)-"2cos ( x - */4)
(5)
under the condition of a large distance away from the source point. The errors involved in the amplitude calculations by the approximation have been evaluated to be less than 0.05% if the distance is larger than the first three wave peaks and less than 0.7% even if the distance
Langmuir, Vol. 6, No. 8,1990 1381
Polymer Interfacial Properties at Toluene1Water
is at the first valley of the wave. Thus, we use the Hankel function t o represent the spatial profiles of the generated capillary waves that are free from the damping due to the viscous contribution. Once the damping constant p is included, the expression of the amplitude envelope in eq 5 can be written in the exponential form
1001
8
'
P
I
' I '
8
'
,8
'
I
80
u
e f P
H,(x)a x-lI2 exp(-px) (6) If p is larger than 0.007 (0.7%))the value obtained from eq 6 is correct to within experimental error of O.O07/p, and for most cases, fl is larger than this mathematical approximation, e.g., p = 0.24 (f = 200 Hz) for water having the smallest damping constant. Thus the approximation can be regarded as safe in all cases. If the excitation is represented by eq 2, then the output from the PSD due to the oscillating reflected laser beam has the form
'
60 40
s a 20
0 -20
U.0
0.2
0.4
0.6
0.8
1.0
1.2
0.8
1.0
1.2
dcm
s = S(x) cos ( k x + 2 w t )
(7) at a radial distance x from the source point, Le., the tip of the needle. Inputting the two signals, represented by eqs 2 and 6, into the lock-in amplifier, we obtain phase difference = kx wave amplitude = S(x)
a
x-1/2 exp(-px)
(8)
(9)
where p is the spatial wave damping coefficient. By scanning along a radial axis from the tip of the needle, sets of the phase difference and amplitude at different distances x are obtained. By plotting the phase difference and natural logarithm of the corrected amplitude, In [x1/2S(x)], against x, one obtains straight lines whose slopes are exactly k and 0, respectively. Examples of such plots are shown in Figure 2 for the test system of toluene (T)/ water (W). The expected linearity between phase difference and x, and that between In [xl/W(x)] and x, is well borne out for five frequencies. We call attention to the fact that we probe mainly the capillary waves instead of the longitudinal ones because the latter damp out very fast, and any coupling between the two kinds of waves is not efficient under our experimental conditions. Thus the situation confronts us with some difficulties in deducing t* because the wave vector and damping coefficient for capillary waves turn out to be fairly insenstive to t* value. In other words, t* values calculated by using the experimental wave vector and damping coefficient for capillary waves are fairly inaccurate for small t* value. We therefore sometime assume that t * = 0, calculate u and 7 values upon inputting p , p o , and to,and compare them in different interfacial systems. When t* values become large enough and vary significantly from one system to another, then we compute them under the assumption that u = ust(constant), where the static limit of the interfacial tension ustis that of u in the low-frequency limit and remains the same over the entire frequency range. Once t* values are so calculated, they are compared among different systems. 3. Calibration. We have calibrated the instrument by determining the surface tensions of water (Millipore water) and cyclohexane (Aldrich, HPLC grade) and the interfacial tension of toluene (Aldrich, HPLC grade)/water. The results are all tabulated and compiled as supplementary material with this report; the surface tensions u and steady shear viscosity of the lower phase, i.e., water, are collected in Table 1(A),those of the cyclohexanein Table 1(B),and the interfacial tension of toluene (T)/water (W) and steady shear viscosity of the upper phase, toluene, in Table 1(C) of the supplementary material. They are seen to be in good
U.0
0.2
0.4
0.6
dcm Figure 2. (A) Plots of phase angle difference between the excitation field and capillarywave against a radial distance x from the field source point, the needle tip, and (B)plots of natural against x for logarithm of the corrected amplitude, In [~1/2S(r)], the test system of T/W, both at different excitation field frequences f. Both graphs show good straight lines for the five frequencies. The wave vector and damping coefficient are deduced from the slopes of these lines.
agreement with literature values16 within experimental error ( 1 ~ 3 % for the surface or interfacial tension and =lo% for the viscosity). For the A/W and T / W system, we have determined CT and q values by making use of a razor blade instead of a needle at a low-frequencyregion (1800 Hz) and found that the results are the same as those obtained by the needle system within experimental errors. We should emphasize here that no frequency dependence is observed in any of the three test systems of simple liquids, as would be expected. These results are thus taken as the successful calibration of our instrument and evidence for validation of the technique relative to the test systems chosen.
Materials and Systems Polymers used here are PEO (Toyo Soda, M , = 148 OOO, Mw/ M, = 1.04) and PS (Dow Styron, M, = 360 000, M,jM, = 1.8). The polystyrene sample was purified further before use by precipitation twice from a toluene solution into methanol and drying in vacuo (10-5 Torr) for a week at room temperature. The use of the polydisperse polystyrene sample was necessitated by the large quantity requirement in 8% solution(see below), although this is somewhat mitigated by apparent invariance on molecular weight of the interfacial properties we have investigated here. Concentrations of polymer solutions are all in weight to volume percent, represented here simply as % for short. Solutions are filtered through O.2-gm membrane filters. ECWD measurements were started after waiting for 1 day to allow the interfaces to equilibrate, and the temperature was 22.0 f 0.5 "C. Steady shear viscosity measurements of PS solu(15) Girifalco, L.A.; Good, R. J. J. Chem. Phys. 1967,61,904. Weast,
R. C., Ed. In Handbook Raton, FL, 1972.
of Chemistry and Physics, 53rd ed.; CRC:
Boca
1382 Langmuir, Val. 6, No. 8, 1990
Ita et ai.
A. PEO at T/W
I
22,
--P
PEO s read lilm
PEO Toluene
Toluene
water
water
Tol~ens WBIM
E . z . E
E O
0
(31
17 0
PS Toluene
C. PEO and PS al TMI
PS
PS c/PEO
--
TOIYBIIB
h_
Water
E O (5)
16)
Figure 3. Schematicrepresentation of the interfaces examined here: shaded areas stand for polymer solutions in indicated solvents, PEO with an arrow indicates mean spread films on the prepared interfacesin cases 3 and 5, and thick curves at interfaces indicate spontaneously adsorbed PEO either from solutions or by spreading with chloroform solutions. tions in toluene were all performed with a Cannon-Fensketype viscometer at 22.3 & 0.1 "C. The viscoelastic measurements of 8 % solution of PS were kindly performed in the laboratory of Prof. Eric J. Amis with their multiple-lump resonator (MLR) system at 22.00 OC. When we make references to overall hiphasic liquid-liquid systems, we use dashes, such as X-Y, whereas we use slashes, e.&,X/Y, to designate the interfaceof two liquid phases, X and Y. Three different kinds of polymeric interfaces have been examined. In order to make ready references to different interfaces, we adopt the following shorthand notations for the interfaces: (a) T/W denotes the pure toluenewater interface without any polymer in either phase; (b) T/W(PEO:y) and T(PS:x)/W stend. respectively, for the interfaces of pure toluene over PEO solution in water at a concentration of y and of PS solution in toluene at concentration of x over pure water; and (c) T(PS:x)/W(PEOy) denotes the interface of PS solution in toluene at a concentration of x over PEO solution in water at concentration of y. The first system we have examined is PEO at the T/W, (1) T/W(PEO:y), (2) T(PEOx)/W, and (3) spread film of PEO at the T/W, by applying a small amount of chloroform solution of PEO (0.1% , 4 uL). Small amountsof Dure chloroform (UD to 50 rL) had no effect on the interfacial tension or viscosityin blank tests.
The second system is PS at the T/W (4) T(PS:x)/W. The last system is for competition trials between PS and PEO a t the T / W (5)chloroform solution of PEO (0.1%,46 uL) spread on T(PS:x)/W and (6)T(PSx)/W(PEO80 ppm), meaning that the concentration of PS in toluene in the upper phase is varied while the PEO concentration in the lower water phase is kept constant at 80 ppm. In order to clarify the individual cases, we have represented them schematically in Figure 3 along with their respective designation numbers.
Results
PEO at T/W.
3
4
5
6
Figure 4. Apparent interfacial tension vs frequency for m e 1. T/W(PEO:y), at different concentrationsof PEO in water: y = 0.19 ppm (open circles),y = 1.87 ppm (filled circles),y = 10.0 ppm (open triangles), and y = 82.7 ppm (open squares).
(4)
walel
2
fkHz
water
Toluene
1
1. Adsorption from Water. We deal first with case 1 in Figure 3. The results concerning the
interfacial tension u deduced from the ECWD experiment are shown in Figure 4, while the steady shear viscosity data are compiled as a part of the supplementary material since they are essentially the pure water values. The error bar on each datum is represented by one standard deviation of determinations of k and 0 from the slopes of plots in Figure 2. The decrease in interfacial tension to around 19 mN/m from 36 mN/m for such dilute PEO solutions is a clear indication of an interface activity of the polymer. At the lowest concentration of 0.19 ppm, the u value remains almost constant relative to frequency. At an intermediate concentration of 1.87 ppm, it shows a slight increase with frequency, which we would tentatively attribute either t o the viscoelastic properties or to the adsorption-desorption kinetics of the adsorbed PEO film. Upon an increase of the concentration by 5-fold, to 10ppm, again almost no frequency dependence of the interfacial tension is observed while the u values are seen to decrease. At the highest concentration of 82.7 ppm, the frequency dependence seems almost abolished, with no further decrease in u. A t this concentration, a substantial time dependence of u is also observed; its value, though not shown here, was around 19 mN/m 1day after the interface was formed, and subsequently it decreased to about 18 mN/m 3 days afterwards as shown in the figure, which could he taken as an indication of an increase in the surface concentration of PEO film due to a slow adsorption a t the interface.I6 All the tabulated values of the interfacial tension at the four concentrations are made available as a part of the supplementary material. The lower phase viscosity values show that of water as stated earlier, and they remain constant relative to frequency as is expected for the very low concentration of PEO in water, which is equal to or less than 82.7 ppm. 2. Adsorption from Toluene. The results from case 2 are presented here. The interfacial tension value of a very dilute solution (1 ppm) of PEO in T/W is determined to be 19.1 f 0.2 mN/m and the steady shear viscosity of the lower phase liquid, water, as 0.95 f 0.09 cP. Table I summarizes the values collected for a frequency range 0.5-5 kHz. The u values are again 19 mN/m and remain constant relative to frequency, and the same holds true for the water-phase viscosity. The results suggest that the adsorption state of PEO at T/W adsorbed from the toluene phase is the same as that adsorbed from the water phase. 3. Spread Film. We now present the results from case 3. Three surface concentrations, 0.4, 0.8, and 4.0 mg/ m2, have been examined which correspond to a surface (16) Sauer. B. B.;Yu, ti. Mncromolecules 1989.22,786.
Langmuir, Vol. 6, No. 8, 1990 1383
Polymer Interfacial Properties at Toluene1Water Table I. Summary of the ECWD Results on Interfacial Tension of T(PEO1 ppm)/W and Viscosity of Water. f , Hz k, cm-l 8, cm-1 u, mN/m q , CP 4.65 f 0.01 19.31 f 0.01 1.02 f 0.01 500 101.84 f 0.01 1000 162.81f 0.02 8.67 f 0.03 19.16f 0.01 1.05 f 0.01 1502 214.69 f 0.04 11.29 k 0.03 18.88f 0.01 0.80f 0.01 2000 261.48 f 0.05 16.02f 0.05 18.75 f 0.01 1.03 f 0.01 2500 302.99 f 0.10 18.79 f 0.09 18.87f 0.02 0.94 f 0.01 3000 340.32 f 0.73 22.03 i 0.26 19.26f 0.13 0.98 i 0.02 3500 379.80f 0.20 25.08f 0.27 18.90f 0.03 0.93f 0.03 4000 412.82 0.25 26.49 f 0.26 19.19 0.03 0.81 f 0.02 4400 439.49 f 0.29 30.20 f 0.44 19.35f 0.04 0.93f 0.04 4900 473.70f 0.47 34.35 f 0.60 19.25f 0.06 1.00f 0.05 avg 19.09 f 0.22 0.95 f 0.09 =Errors on the individual entries stand for one standard deviation, whereas the errors on the average values are one standard deviation of the mean values. ~~~
~~~
*
1
. z E
E
\
0
1 0
1
2
3
4
5
6
fkHz Figure 5. (A) Apparent interfacial tension vs frequency for case 3, T/ W with spread film of PEO from chloroform solutions, at the calculated final surface concentrations of 0.4,0.8,and 4.0 mg/ m*,(B)The same graph with an expanded ordinate scale for the largest concentration case, 4.0 mg/m*.
coverage of about 70%, loo%, and 500%, respectively, as obtained from the relationship between surface pressure and surface concentration of PEO at A/W.' In the first two instances, the surface is expected to be covered by a monolayer of PEO with very little PEO left in the bulk liquids, whereas a t the last concentration there should be some PEO molecules dissolved in both the water and toluene to some extent. Figure 5A shows the frequency independence of u for PEO spread at the T/W, while the magnitude of u depends on surface coverage, i.e., 25 mN/m at 70% coverage and 19 mN/m at 100% coverage; u shows an intermediate value between 36 mN/m for pure T / W and 19 mN/m for the surface saturation limit. At the higher concentrations of 0.8 and 4.0 mg/m2, u again turns out to be around 19 mN/m, which is the same as in the adsorption from either water or toluene. If the highest concentration is closely examined, u shows a slight frequency dependence as seen in Figure 5B, which is the
same tendency as the adsorption case from water (1.87 ppm). The viscosity of both phases remained the same as in pure toluene and water, and no frequency dependence emerges for one or the other. Again, all tabulated results for u and r) are compiled in the supplementary material. Summarizing from these results, we can state with confidence that PEO at the interface of toluene and water gives a u value of 19 mN/m a t the surface saturation limit for all three cases. We may surmise from these findings that the adsorption state of PEO at the T/ W is the same, independent of the path by which PEO molecules reach the interface. The same conclusion was drawn by Glass as early as 1971 for PEO adsorption on the benzene/ water interface, examined by the pendant drop method." At a surface concentration exceeding that of the saturation limit, u shows a frequency dependence similar to the adsorption case from water at a dilute concentration of 1.87ppm. PS at T/W. Determinations of u are carried out for three PS concentrations in toluene, 0.048%, 2.1 % , and 8.0%, whereas the water is kept intact. This is case 4 in Figure 3. First of all, we have calculated u and the viscosity of the toluene phase qo by assuming e* = 0 in eq 1. Parts A and B of Figure 6 show the plots of u and r)O versus frequency f where the data for pure T/ W and for solutions of 2.1% and 8.0% are plotted; those for the solution of O.Q48% are not included since they are indistinguishable from the 2.1% case. Tables I1 and I11 show summaries of the results. A literature value of u = 36 mN/m for T/W16 is represented by a dashed horizontal line in Figure 6A. The steady shear Viscosity values of the PS solutions in toluene, measured by capillary viscometry, and a literature value of pure toluenels are indicated by dashed horizontal lines in Figure 6B. We should note several aspects of the results shown in Figure 6. Firstly, u values in the low-frequency limit, at around 10 Hz,are the same for all three, 35-36 mN/m, whereas qo values are different for the three at the same frequency limit. Secondly, there are well-delineated frequency dependences for u and r)O for the 8.0% solution while the other two show no dependence u p t o 5 kHz. Thirdly, the onset of the frequency dependence for either u or qo takes place at the same frequency region, around 100 Hz. Deferring to later a detailed discussion of these results, we briefly remark here that the coincidence of u values for all four cases(only three are shown in Figure 6) at the low-frequency limit might be attributed to a depletion layer of PS at T/ W similar to the case of air/T(PS).18Je On the other hand, this point is not unanimous in the literature; Uberreiter et aLZoconcluded that PS has an adsorption layer at the benzene/water interface. We now turn t o a comparison of the viscosity of the highest concentration case (8%)as obtained by dynamic mechanical measurements to that deduced by ECWD. Filled squares and open squares in Figure 6B stand for the viscosity values obtained by the dynamic mechanical (MLR) and ECWD methods, respectively;the filled squares are obtained from the dynamic loss modulus G", as shown in Figure 6C (r)' = Gf'/27rf). The chained curve drawn over the filled squares and made to merge with a dashed line in Figure 6B represents a possible frequency profile with our capillary viscometry value indicated at 10 Hz. Despite the slight difference in the frequency profiles of the two, (17)Glass, J. E.J . Polym: Sci., Part C 1971,34, 141. (18)Ober, R.;Paz, L.; Taupm, C.; Pincus. P.; Boileau, S. Macromolecules 1983, 16,50. (19)de Gennes, P.-G.Mocromolecules 1981,14,1637. (20) Uberreiter, K.;Morimoto, S.; Steulmann, R. Colloid Polym. Sci. 1974,252, 273.
1384 Langmuir, Vol. 6, No. 8, 1990
Zto et al.
Table 11. Summary of the ECWD Results on Interfacial Tension of T(PS:2.l%)/Wand Viscosity of the Toluene Phase. ___ k, cm-1 8, cm-I u, mN/m f, Hz % cp ~~~
'.
50.0 100 200 200 200 500 500 500 1000 1000 1000 1502 2000 2000 2500 2990 3010 3490 3500 4000
avg
17.74 f 0.03 28.51 f 0.02 44.82 f 0.07 45.07 f 0.07 45.39 f 0.08 83.45 f 0.02 83.70 f 0.18 83.86 f 0.10 133.21 f 0.07 132.68 f 0.58 133.74 f 0.04 175.25 f 0.05 212.11 f 0.10 211.60 f 0.11 247.89 f 0.21 277.52 f 0.49 281.11 f 0.36 309.07 f 0.33 309.98 f 0.47 339.39 f 1.46
0.38 f 0.09 1.18 f 0.03 3.16 f 0.13 2.42 f 0.15 2.80 f 0.14 5.54 f 0.04 5.93 f 0.04 5.72 f 0.03 10.17 f 0.03 10.73 f 0.42 10.50 f 0.06 14.65 f 0.05 18.49 f 0.05 18.71 f 0.10 23.58 f 0.19 26.29 f 0.20 27.22 f 0.27 29.83 f 0.27 29.97 f 0.47 33.34 f 0.27
34.45 f 0.20 34.90 f 0.09 36.94 f 0.18 35.94 f 0,18 35.41 f 0.20 36.05 f 0.02 35.84 f 0.23 35.59 f 0.13 35.94 f 0.05 36.47 f 0.41 35.57 f 0.03 35.93 f 0.03 36.10 f 0.05 36.38 f 0.06 35.58 f 0.09 36.32 f 0.19 35.47 f 0.14 35.92 f 0.11 35.82 f 0.16 35.73 f 0.46
4.42 f 0.53. 2.61 f 0.17 6.25 f 0.46 3.54 f 0.52 4.68 f 0.49 3.67 f 0.05 4.16 f 0.05 3.83 f 0.04 3.57 f 0.02 4.05 f 0.31 3.74 f 0.04 3.57 f 0.02 3.43 f 0.02 3.56 f 0.04 3.64 f 0.06 3.40 f 0.05 3.47 f 0.06 3.27 f 0.06 3.27 f 0.10 3.17 f 0.05
35.82 f 0.54
3.76 k 0.74
a Errors on the individual entries stand for one standard deviation, whereas the errors on the average values are one standard deviation of the mean values.
the two solid lines. Clearly, the low-frequency regime must be lower than 100 Hz. As frequency increases, the slopes of G' and G" change from 0.89 to 0.65 and 1.6 to 0.85, respectively, in the frequency range examined. 1°1/ Considering only the static values of viscosity for solutions in different PS concentrations, we can compare those deduced in the low-frequency region (f 5 100 Hz) Figure 6. (A) Apparent interfacial tension vs frequency for case from ECWD to the values obtained by a capillary vis4, T(PSx)/W: x = 0% (open circles),2.1% (open triangles),and cometer and also to literature values.22 The results, 8.0% (open squares). The dashed horizontal line represents a static interfacial tension value for pure T/W from the 1iterat~re.l~ designated by open circles, are in reasonable agreement over a wide range of concentrations, as shown in Figure (B)Apparent shear viscosity of toluene phase vs frequency,with the same set of symbols as in A for the three concentrationvalues. 7. Dashed horizontal lines represent the steady shear viscosity values PEO and PS at T / W . Since P E O is extremely obtained by capillary viscometry. The data for C"/27rf from interface active (while PS is active toward the T / W in a dynamic mechanical measurements by MLR of 870 PS solution negative sense such that it gives rise to a depletion layer), in toluene are also plotted by filled squares, and a chained curve the interfacial tension is expected to be dominated by PEO is drawn over the data to smooth the frequency profile by forcing if the two polymers are allowed to compete with each other it to merge with the correspondingdashed line. (C) Storage shear modulus C' and loss shear modulus G" vs frequency obtained relative t o their access t o t h e interface even if the by MLR with the expected limiting slope drawn in for each case. concentrations of the two are highly skewed toward PS. We have tested this in two different ways. The first is to t h e general agreement is remarkable indeed. T h e allow PEO to compete with PS a t 8% in the same phase difference, however, may be accounted for by the manner by spreading a dilute PEO solution in chloroform onto the with which the ECWD values are deduced, namely, under interface from the toluene side, and the second is to let the assumption of e* = 0 whereby we neglected completely PEO approach the interface from the other side, Le., the any viscoelastic effects of the interface layer. We defer water phase, by adding a dilute aqueous solution of PEO. to later an alternative analysis by relaxing the assumption These are cases 5 and 6, respectively, in Figure 3. t* = 0 and deducing the surface dilational elasticity and Figure 8A shows the results for case 5, where a plot of viscosity instead of resorting to the shear viscosity of the u vs f with PEO and PS (at 8%)in toluene is compared bulk solution of the upper phase. to that with PS (at 8%) alone; we emphasize once again that u values are calculated under the assumption of e* The behavior of the storage shear modulus G' and loss modulus G" of the PS solution, as shown in Figure 6C, is = 0 in eq 1. The final amount of PEO in the toluene phase not particularly different from others.21 In the logarithmic was 0.25 ppm, which amounts to a surface concentration plots of G' and G" - u t sagainst frequency (where t sis of 4 mg/m2 if all were to come to the interface; this surface solvent viscosity), both should increase with frequency in concentration value exceeds the surface saturation limit, the low-frequency limit with a slope of 2 and 1for G' and as we have indicated earlier for PEO a t T/W. It is far too G" - uvs,respectively. Also, they should both have a slope apparent that the low-frequency limiting value of u of 1/2-213 for an intermediate frequency range. We see decreases from the pure T / W value (36 mN/m) to that both these trends in Figure 6C, although the lowof the PEO-saturated T / W value (19 mN/m). In addition, frequency limits are not reached for both as indicated by it shows a frequency dependence which is much more sensitive than that observed for PEO alone a t the T/W, (21) Ferry, J. D. Viscoelastic Properties of Polymers, 3rd. ed.;Wiley:
f
'
New York, 1980.
(22) Streeter, D. J.; Boyer, R. F. Ind. Eng. Chem. 1951,43,1790.
Langmuir, Vol. 6, No. 8, 1990 1385
Polymer Interfacial Properties at ToluenelWater Table 111. Summary of the ECWD Results on Interfacial Tension of T(PS:8.0%)/W and Viscosity of the Toluene Phase
f, Hz 10.0 10.0 10.0 20.0 20.1 20.1 50.0 50.0 100 100 100 100 101 200 200 20 1 249 250 303 303 498 498 498 501 750 750 801 1002 1002 1002 1250 1250 1502 1502 1502 1502 1749 1749 2000 2000 2000 2000
k, cm-l 6.01 f 0.01 6.07 f 0.01 6.00 f 0.01 9.72 f 0.01 9.72 f 0.01 9.73 f 0.02 17.79 f 0.01 17.82 f 0.01 28.08 f 0.04 28.08 f 0.04 28.01 f 0.01 28.24 f 0.03 28.19 f 0.01 43.54 f 0.02 43.54 f 0.04 44.02 f 0.03 49.96 f 0.05 50.37 f 0.05 56.39 f 0.07 55.85 f 0.11 77.42 f 0.08 76.81 f 0.05 77.20 f 0.10 76.97 f 0.12 98.73 f 0.09 100.10 f 0.05 102.77 f 0.08 122.14 f 0.07 120.04 f 0.10 121.97 f 0.39 136.83 f 0.13 139.22 f 0.30 157.16 f 0.13 156.96 f 0.13 156.92 f 0.14 158.72 f 0.67 170.97 f 0.19 173.68 f 0.67 183.44 f 0.28 181.98 f 1.93 184.91 f 0.30 191.46 f 0.86
8, cm-l 0.89 f 0.01 0.84 f 0.01 0.82 f 0.01 1.52 f 0.01 1.61 f 0.01 1.69 f 0.01 3.64 f 0.01 3.70 f 0.01 6.86 f 0.02 6.61 f 0.04 6.92 f 0.01 6.92 f 0.02 7.00 f 0.01 12.25 f 0.02 11.97 f 0.04 12.04 f 0.02 15.22 f 0.05 14.20 f 0.06 16.36 f 0.05 16.30 f 0.11 23.31 f 0.08 24.21 f 0.07 22.84 f 0.09 23.53 f 0.10 30.72 f 0.10 30.72 f 0.10 32.25 f 0.11 34.50 f 0.11 35.53 f 0.14 38.18 f 0.41 42.24 f 0.17 39.55 f 0.54 47.38 f 0.22 47.28 f 0.18 46.40 f 0.19 44.38 f 0.69 49.40 f 0.23 49.52 f 0.71 56.52 f 0.34 57.28 f 2.13 56.60 f 0.26 51.21 f 0.81
u, mN/m 34.75 f 0.19 33.88 f 0.19 35.16 f 0.09 35.20 f 0.05 35.55 f 0.07 35.36 f 0.26 36.83 f 0.04 36.60 f 0.08 37.14 f 0.14 37.39 f 0.14 37.36 f 0.04 36.51 f 0.11 36.99 f 0.05 38.78 f 0.05 39.02 f 0.10 38.21 f 0.06 38.79 f 0.10 39.18 f 0.11 40.69 i 0.13 42.31 f 0.21 42.09 f 0.12 42.32 f 0.08 42.71 f 0.14 43.09 f 0.17 45.56 f 0911 43.99 f 0.05 45.93 f 0.09 44.61 f 0.07 46.24 f 0.10 43.18 f 0.35 47.88 f 0.12 46.86 f 0.27 46.17 f 0.10 46.36 f 0.10 46.70 f 0.11 45.98 f 0.51 49.38 f 0.14 47.34 f 0.48 51.08 f 0.20 51.85 f 1.37 50.03 f 0.21 47.14 f 0.56
V0, cp 52.25 f 0.46 47.22 f 0.37 47.63 f 0.31 45.25 f 0.15 49.02 f 0.11 52.06 f 0.27 49.20 f 0.11 49.97 f 0.13 49.19 f 0.18 47.14 f 0.29 50.13 f 0.08 48.85 f 0.16 50.02 f 0.09 47.87 f 0.09 46.71 f 0.18 45.71 f 0.09 49.03 f 0.13 44.79 f 0.19 44.62 f 0.13 46.42 f 0.30 40.35 f 0.13 42.81 f 0.10 39.89 f 0.16 41.67 f 0.17 38.54 f 0.11 37.00 f 0.11 38.29 f 0.11 30.54 f 0.10 33.17 f 0.12 33.89 f 0.33 33.16 f 0.12 29.49 f 0.41 29.50 f 0.13 29.55 f 0.11 29.03 f 0.11 26.79 f 0.43 27.82 f 0.13 26.57 f 0.38 29.43 f 0.16 30.52 f 1.02 28.77 f 0.12 23.34 f 0.39
a Errors on the individual entries stand for one standard deviation, whereas the errors on the average values are one standard deviation of the mean values.
literature
c= . ._
P
h
*
g
.-n>
10' p
A
0
d
P 10
-
10-11 ' 10''
i """"
10''
'
""."' 100
'
""""
'
10'
'.,-I
t
10'
(21%
Figure 7. Concentration dependence of viscosity of toluene phase for cases 4 and 6 deduced by ECWD (open circles and open squares, respectively) together with those deduced by capillary viscometry and from the literature.22
as shown in Figure 4. Thus, the more sensitive frequency dependence needs to be attributed to the presence of an 8% solution of PS in the upper phase. Since the added amount of PEO is minute indeed at 0.25 ppm, no significant effect of PEO on the PS solution viscosity qo should be expected, and this is confirmed as
Ail
i
0 wloPEO wl PEO
10
10'
IO'
10'
10'
f/Hz
30
t
20 10'
0 '
'
" ~ " "
10'
'
'
"""'
'
10'
'"".
10'
f/Hz
Figure 8. (A) Apparent interfacial tension vs frequency for case 4 at 8% PS without PEO (open circles) and case 5 a t 8% PS with spread film of PEO at a calculated surface concentration of 4 mg/ m2 (filled circles). Dashed horizontal lines are drawn to indicate the static interfacial tension values for pure T/W (upper) and PEO-saturated T/W (lower). (B) Frequency dependence of apparent shear viscosity of the toluene phase deduced by ECWD with the same symbols as in A. Dashed horizontal line stands for the steady shear viscosity of 8% PS solution in toluene.
shown in Figure 8B by similar frequency profiles of the viscosity with and without PEO in the toluene. A slight increase in viscosity at the low-frequencylimit, with PEO added, is attributed to the concentration increase in the toluene phase by its evaporation during the experimental period. To test further the dominant interface activity of PEO over that of PS at T/W, we have examined how u and qo for the T(PS)-W(PE0) system vary with PS concentration in the upper phase while the PEO concentration is kept constant at 80 ppm; the range of PS concentrations was from 0.12% to 14.6%. This is case 6 in Figure 3. Table IV shows a summary of the results. Independent of the PS concentration in toluene, the apparent u values remain constant at 19 mN/m, as in all of the previous cases described so far, indicating again that PEO is dominant at the interface and PS is not able to displace PEO even at 14.6% . In addition to a razor blade being used instead of a needle for the generation of surface waves in this case, the accessible ranges of frequency were limited since we had not yet fully automated the apparatus when these measurements were made, whereby we could only show a narrow range for each concentration. Nevertheless, we establish a crucial point that the low-frequency limiting value of u remains practically constant while the viscosity of the upper phase covers over 2 orders of magnitude. Notwithstanding large error ranges in the viscosity determination by ECWD, we can show that the values we deduce for the system, represented by open squares in Figure 7, are indeed in accord with those obtained by other steady shear methods.
1386 Langmuir, Vol. 6, No. 8, 1990
Ito et al.
Table IV. Summary of the ECWD Results on Interfacial Tension of T(PS)/W(PEO:80ppm) and Viscosity of the Toluene Phase PS conc, wt r;~ f , Hz k, cm-l &cm-l u, mN/m 70, CP 0 0.12 0.59
5.2
11.8 14.6
300 400 74 200 70 74 400 600 700 26 80 180 180 302 800 22 22 92 14 20 26 50
71.2 89.0 28.2 56.1 27.9 27.8 91.5 119.9 135.5 14.8 30.3 52.9 53.1 76.5 134.6 10.0 11.0 19.6 5.93 7.46 7.24 11.34
4.1 4.6 0.9 18.3 1.3 4.7 6.9 6.2 2.1 4.4 9.1 9.2 13.2 29.4 5.2 5.1 15.5 4.2 5.0 6.3 9.5
20.1 18.4 19.5 18.3 18.1 20.4 17.3 17.5 16.6 17.6 19.4 18.8 18.7 17.6 22.5 23.0 20.0 19.0 22 27 16 22
1.9 0.9 0.5 4.9 2.2 1.o 1.1 0.5 22.7 16.7 15.7 15.9 12.6 14.0 142 114 135 240 220 250 210
Discussion
PEO at T/W. The results of adsorbing PEO onto the T/W in three different ways may be taken to conclude that the polymer's adsorbed state is invariant to the adsorption path, which by itself is not surprising in view of the interface activity of PEO. Nevertheless, it needs to be established for the sake of completeness. When we starve the system relative to full coverage, the u value lies at an intermediate value between 19 (full coverage) and 36 mN/m (no coverage), and in such a case we would expect that all chain segments are in the train state with no loops or tails into the water or toluene phase. Before turning to discuss the results shown in Figure 4, we should note a general feature of modemode coupling at any oil/water interface. As stated in the Experimental Section, the mode coupling between transverse capillary waves and longitudinal dilational waves is not efficient, which is a natural consequence of the dispersion equation when two liquids of a comparable density form an interface. Hence, the complex wave vector k* is dominated by the capillary wave mode, whereby t* we deduce through the dispersion equation and is subject to a large error. In addition, we need to input a precisely known value of u since t * values are critically dependent on u values: the low-frequency limiting value obtained by ECWD is not precise enough. It turns out that the t value we have so deduced for each PEO concentration is about the same at 3 mN/m, which is a rather small value and of doubtful precision. A similar observation is made with respect to the other component of e*, namely, W K . Thus, we turn to interpret the PEO adsorbed layer behaviors in terms of frequency dependence of u and avoid altogether the option of analyzing them in terms of the viscoelastic parameters of the mode-coupled longitudinal waves in this adsorption case. We now discuss the results shown in Figure 4 in two respects: (1) the concentration dependence of the lowfrequency limiting value of u and (2) the onset of a frequency dependence at a concentration of 1.87 ppm. As the interface concentration is increased from pure T/W, the polymer chains gradually pack each other, but the monolayer state of chain segments a t the interface, i.e., all in the train state, remains until it reaches the saturation
limit.7 Because of a small collapse pressure of PEO at A/W, chain looping and tailing toward the water phase are likely to take p l a ~ e when ~ J we ~ further ~ ~ ~increase ~ ~ ~ the concentration in bulk solution, and there should be a substantial number density of polymer molecules in the vicinity of the interface, which have no segment adsorbed to the interface. Hence, the low-frequency limit of u should reflect not just the PEO monolayer covered T/ W but PEO loops and tails, large and small, mixed with free PEO chains in the vicinity of the interface. This would explain the monotonic decrease of u relative to the bulk concentration of PEO in water. Such a concentration dependence of u was earlier observed by Glass.'7 With respect to the frequency dependence that is detectable only at the 1.87 ppm case, we put forth our speculation as follows. At a bulk concentration of about 1order (=2 ppm) over that necessary to attain the full train state ( ~ 0 .ppm), 2 the interface concentration is about right to give rise to an instantaneous decrease of the train segments in certain time scales within our frequency range of observation since there are not enough other segments near the interface to quickly fa the looped sites. This gives rise to the frequency-dependent increase in u since a transient reduction in the segment density due to the looping should increase with frequency, which in turn results in the increase in u toward the 36 mN/m value. Further, the kinetics of desorption-adsorption must be related to a frequency dispersion range of u,and there must be a plateau beyond which u should no longer vary with f at higher frequencies. It is problematical, however, whether we can reach the high-frequencyasymptote of u(f, with our instrument by somehow tuning the desorptionadsorption kinetics. Finally, we propose an explanation for the frequency threshold at around 2-3 kHz where u starts to depend on f. Generally, PEO is known to make aggregats in many Despite a organic ~ o l v e n t s 2 ~as- ~well ~ as in ~ater.~&3O lingering controversy surrounding the issue,25,31,32 surface force measurements indicate stickiness between the chains when molecules are compressed in contact with each other. Although the aggregation mechanism is yet to be fully delineated, it is clear that PEO aggregates easily in bulk solution.33 G l a d 7 in fact has suggested that the interfacially adsorbed PEO is better ordered than PEO in bulk solution state. It is therefore expected that adsorbed PEO molecules aggregate easily, giving rise to a higher segment density of PEO at the interface in equilibrium with a lower segment density in solution. T h u s it seems t h a t cooperative motions of the chain segments would result in a low-frequency range for the threshold, whereas the critical frequency for local segmental motions in dilute solution in an organic solvent such as benzene is higher by many orders of magnitude, 140 GHz.34*35 T(PS or PS+PEO)/W.We finally come to the results displayed in Figure 6. The crucial issues are as follows: (23) Sauer, B. B.; Yu, H.; Kim, M. W. Langmuir 1989,5,278. (24) Kuzmenka, D. J.; Granick, S. Macromolecules 1988, 21, 779. (25) Mana, J.; Hair, M. L.J. Colloid Interface Sci. 1988, 125,552. (26) Elias, H.-G.; Lys, H. Makromol. Chem. 1966,92, 1. (27) Maxfield, J.; Shephard, I. W. Polymer 1975,16, 505. (28) Brown, W. Polymer 1985,26, 1647. (29) Brown, W. Macromolecules 1984,17,66. (30) Polik, W. F.; Burchard, W. Macromolecules 1983, 16, 978. (31) Israelachvili,J. N.; Tandon, R. K.; White,L. R. J.ColloidInterface Sci. 1980, 78, 430. (32) Kein, J.; Luckham, P. F. Macromolecules 1984, 17, 1041. (33) Tsuchida, E.;Abe,K. Adv. Polym. Sci. 1982,45, 1. (34) Davies, M.; Williams, G.; Loveluck, G.D. 2.Elektrochem. 1960, 64, 575. (35) Stockmayer, W. H.; Yu, H.; Davis, J. E. ACSPolym. Prep. 1963, 4 (2), 132.
Langmuir, Vol. 6, No. 8,1990 1387
Polymer Interfacial Properties at Toluene1 Water 0
I
0 0
6
a
Qe
20tio3
10'
10'
f/Hz
f/Hz Figure 9. Comparison of 7' and 7'' deduced by ECWD with and without PEO to those determined by MLR, where 9' and 7'' determined by MLR are calculated from G" and G', respectively.
(1) How can we account for the frequency-dependent increase of u over 36 mN/m for the case of T(PS:8%)/ W? (2) What comparison we can make for the viscoelastic parameters determined by the MLR measurements and those deduced by ECWD? (3) What sort of a viscoelastic film might be present in T(PS:8%)/W? 1. Frequency-Dependent Interfacial Tension. Clearly, for T(PS:8%)/W at high frequencies the apparent u becomes larger than that for T / W at 36 mN/m. At the risk of repetition, we emphasize that u values are calculated from the dispersion equation under the assumption that t * = 0; hence, these values are subject to a model dependency, and that is why we call them the apparent interface tension. Even with this provision in mind, we cannot account for the observed increment in u since any interface concentration of PS would decrease or not affect the interfacial tension. Suppose that, as the frequency increases, some of the PS molecules come to the interface by some fluctuation mechanism; then a t the highest frequency, u would approach that of solid PS/W, which can be calculated to be around 36 mN/m or less by using Wu's equation36 at 20 OC. The apparent u value at the highest frequency is seen as 52 mN/m; hence, the frequency dependence cannot be ascribed to the situation where a bare surface of solid like PS is being exposed to water. 2. Comparison of ViscoelasticParameters. We must offer a caveat for all of the foregoing analysis. The dispersion equation represented by eq 1 is generally understood to apply only to the interfaces of Newtonian liquids, whereas the 8% solution of PS has been shown to be viscoelastic. Hence, we attempt to take into account the viscoelasticity of the upper phase by replacing 70 by s* (=$ - is") in eq 1 and deduce q' and 7" from the observed k and /3 by assuming t* = 0 and u = ust (constant) with uBt= 36 mN/m without PEO and ust = 19 mN/m with PEO at the interface. A comparison of 7' and 7 ' is shown in Figure 9, where the deduced 7' and 9' for the cases with and without PEO are compared with the MLR data. It appears that there is a reasonable agreement for 9' for all three cases, i.e., two ECWD (with and without PEO) and MLR. Slightly larger values in the case of the ECWD with PEO over the other two are attributed to the concentration increase in the upper phase due to solvent evaporation during the measurements. A similar level of (36) Wu,S. J. Polym. Sci., Part C 1971, 34, 19.
.
$ 1t r
20
10
-
0 10'
I
8
8
io3
102
10'
f/Hz
Figure 10. (A) Frequency dependence of the longitudinal elasticity t, deduced by assuming u = uat and inputting 7' and 9" of MLR shown in Figure 9 to eq 1,for case 4 T(PS8%)/W with PEO (open circles) and without PEO (filled circles). (B) Correspondingdependence of the longitudinalviscous component W K with the same symbols as in A.
agreement for 7 ' may be seen only for ECWD without PEO and MLR but not for ECWD with PEO. This indicates that frequency dependence of the apparent u might be attributed wholely to the viscoelasticity of the upper phase. It, however, should be noted that the analysis is still model dependent because only two parameters can be deduced from the experimental parameters of k and 0;hence, the assumptions of e* = 0 and u = ust (constant) are explicitly imbedded in the comparison. The discrepancy in T]" between ECWD with PEO and MLR however could be accounted for by the existence of PEO film at the interface, whereas the fairly good agreement in 7' cannot be explained by the PEO film. 3. Viscoelastic Concentration Layer. We present an alternative analysis by relaxing the assumption oft* = 0. We have calculated e* in the case with PEO upon insertion of q* values from the MLR measurements into eq 1 with the single assumption that u = uat (constant). Each s* value at the frequency corresponding to a given ECWD datum is estimated from the interpolation or extrapolation of discrete MLR data points of q* in Figure 9. The results for t and W K for the cases with and without PEO are shown in parts A and B of Figure 10, respectively. For t, there exist different behaviors between the cases with and without PEO whereas W K shows the same increasing tendency relative to frequency. One can make several points concerning the interfacial structures from these results. In the case with PEO, both t and W K increase with frequency similar to those cases of the dynamic storage modulus G' and the correspondingloss modulus G" in bulk solutions and liquids. This may then be taken as normal interfacial film b e h a ~ i o r .On ~ the other hand, the t values for PEO film at T/W are around 3 mN/m at most whereas for the case of the upper phase being an 8% solution of
1388 Langmuir, Vol. 6, No. 8, 1990
Ito et al.
PS in toluene, it increased 2 or 3 times, indicating some sort of interaction between PEO a t the interface to PS in the upper phase. Also, the W K values for PEO film a t T / W are around 5 mN/m or less while the latter shows much larger values. This again is taken as an indication of certain interactions between PEO film and PS solution. Accepting a PS depletion layer at the interface together with some sort of interaction between PS and PEO to increase the t * values, we may hypothesize a dense layer of PS just above the interface, which we call a concentration layer and its existence is partially supported by another experiment (see below). Contrary to the similar frequency dependences of WK for the cases with and without PEO, the frequency dependences of t for the two cases are in opposite directions in addition to the low-freqency limiting values of t being different; i.e., that without PEO is larger than that with PEO. The case without PEO is anomalous, t decreasing with increasing f , and this might also be attributed to the presence of the PS concentration layer in the upper phase above the depletion layer, although we have for the moment only a very circumstantial piece of evidence to support such a complex structure near the interface. Since the penetration depth of the capillary wave is expected to decrease as the imposed frequency is increased, it seems that the coupling of capillary and longitudinal waves becomes less efficient with frequency, which would result in a decreasing trend of t with frequency. In other words, the decreasing trend o f t with f might be ascribed to the variation in the probing depth, and this will sample different concentrations of the polymer if the depth range coincides with the concentration profile range. Alternatively, if the increasing tendency of 6 with f is correct as seen in the case with PEO, the assumption that u = uSt(constant) may be wrong, and in that event the problem becomes ill posed because we need to obtain three parameters from two observables. In any case, we are inclined to surmise that there must be different structures with and without PEO in the lower phase. Briefly, we describe an experiment which could be taken to lend support to the presence of the PS concentration layer above t h e depletion layer, which we have hypothesized in t h e above. When a toluene ( n o t chloroform) solution of PEO at a comparable concentration to that of the chloroform is gently mixed in the PS solution in toluene without disturbing the interface, the apparent u did not change even after 11 days, meaning that its static value remained the same a t around 36 mN/m, as though the PEO had no effect whatsoever on the interfacial tension. Apparently, translational diffusion of PEO molecules to the interface is somehow blocked. However, we can rule out the possibility of not allowing sufficient time for the diffusion to the interface. We thus come to our proposal for some sort of a barrier layer of PS immediately above the depletion layer at T/W, which blocks the diffusion of PEO molecules to reach the interface. Just how large the concentration of PS in this layer is we cannot estimate, although it must be greater than the bulk concentration of 8 % , since PEO is easily soluble in a PS solution of this concentration. Why and how such an excess concentration layer, adjacent to a depletion layer, should come about must be established in order for the proposal to gain any credence.
conclusions out of the experiments on three different kinds of interfaces. PEO at T/WInterface. (1)Three different adsorption methods have been examined, and in all cases the u values are the same (19 mN/m) a t the surface saturation limit. Thus, PEO assumes the same adsorbed state a t the T/ W independent of the adsorption path. (2) An apparent frequency dependence of u is deduced upon ignoring any surface viscoelastic film contribution, and this occurs only at a surface concentration range greater than the surface saturation limit, which may reflect the adsorptiondesorption kinetics of PEO molecules. PS and PEO at T/WInterface. (3) The apparent u values at the low-frequency limit, under the assumption oft* = 0, are the same as that for pure T/W (36 mN/m) regardless of the concentration of PS in toluene, which is interpreted as a signature of a depletion layer of PS. In the T(PS:x)-W(PE0:y) system for all concentration ranges of PS, the u values at the low-frequency limit are around 19 mN/m, and in the T(PS+PEO)-W system, the u value at the low-frequencylimit is also 19 mN/m, indicating that interfacial properties are dominated by PEO. (4) Large frequency dependences of apparent u and viscosity are observed for 8.0% PS in toluene with and withoug PEO, whereas no frequency dependence is observed for concentrations less than 2.1 5%. (5) Viscosity values a t low frequencies deduced by ECWD are in good agreement with those measured by other static methods for a wide range of PS concentrations in toluene. (6) The q‘ and q” values deduced from ECWD on T(PS:8.0% )/W with and without PEO, assuming t * = 0 and u = ust (constant), show reasonable agreement for q’ from MLR for both cases whereas q” values with PEO were slightly different, indicating perhaps the effect of PEO film a t the interface. (7) E and W K for T(PS:8%)/W with and without PEO, calculated upon insertion of the frequency dependence of q* determined by MLR with the assumption of u = ugt (constant), show similar behavior of WK in both cases while t is totally different. We attribute the behavior of c for the case without PEO to the concentration layer of PS near the interface and for the case with PEO to the interfacial PEO film interfacing with such a concentration layer of PS, giving rise to a large value of t compared to that for the PEO film a t T/W.
Conclusions
diffraction results on the surface tension, interfacial tension, and viscosity of water, cyclohexane, toluene, and the various toluene/ water systems investigated (11pages). Ordering information is given on any current masthead page.
We have examined dynamic properties of polymeric interfaces by the ECWD technique. We can draw several
Acknowledgment. This work is in part supported by the Research Committee of the University of WisconsinMadison, the Polymers Program of the National Science Foundation, and the Japan Synthetic Rubber Co. We thank Mr. Dennis W. Hair and Prof. Eric J. Amis for the determinations of viscoelastic parameters of a polystyrene solution. We also acknowledge the generous gift of the motion control system by the Superior Electric Co. H.Y. recalls with gratitude helpful discussions with Prof. Isaac C. Sanchez and Philip Pincus. Finally, we thank our colleagues, Dr. Hongdoo Kim and Mr. Sanghoon Kim, for their suggestions and advice on the instrument design a t several crucial junctures. Supplementary Material Available: Tables l(A-C), 2(A-D), and 3(A-C)giving a summary of the electrocapillary wave
