Polydimethylsiloxane monolayers at an air-water interface

Polydimethylsiloxane monolayers at an air-water interface

Polydimethylsiloxane Monolayers at an Air-Water Interface YOSUKE KAKIHARA, D. M. HIMMELBLAU, AND R. S. SCHECHTER Deparlment of Chemical Engineering, T...

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Polydimethylsiloxane Monolayers at an Air-Water Interface YOSUKE KAKIHARA, D. M. HIMMELBLAU, AND R. S. SCHECHTER Deparlment of Chemical Engineering, The University of Texas, Austin, Texas 78712

Received September 23, 1968 A part of our studies relating to the dynamics of interfaces has been an investigation of diffusional processes along gasliquid interfaces. These studies are conducted under conditions of uniform surface pressure as contrasted to spreading experiments which are associated with gradients of surface pressure and as a consequence, hydrodynamic flows. The diffusional processes arise from random thermal motions and should partly characterize the interaction of the substrate with the surface molecules. Also, it should be noted that surface diffusion coefficients appear in many formulations of macroscopic transport problems (1) although such coefficients have never been measured. The measurement of surface diffusion coefficients may, in fact, never be achieved owing to the structure exhibited by monolayers. This note describes the strange and largely unexplained observations made during an attempt to study diffusive mixing of polydimethylsiloxane (PMS) monolayers on water. Such monolayers seem to have a structure which is of macroscopic dimensions, and, in a surface diffusion experiment, these structures apparently migrate as a unit. If all monolayers of importance are similarly structured, then the formulations of surface transport based on the concept of a surface diffusion "driven" by variations in surface concentration are likely to be of only academic importance. A secondary result has been the measurement of the bulk diffusivity of a 40 centistoke radioactive PMS in water. This quantity should be of interest in considering the applications of PMS as an antifoamant or as a water repellent (2).

I. SURFACE PRESSURE AND AREA PER MOLECULE To characterize the molecular weights of the PMS molecules used in the experimental work, the correlation given by Barry (3) has been used. This correlation predicts, for example, that the value of n in the structure CH3Si(CH~)~[--O--Si(CH3) ~]n--CH, is 39 for PMS having a viscosity of 40 centistokes. Since very little information regarding the structure of the radioactive PMS was available from the manufacturer, it appeared reasonable to verify this prediction by making surface pressure measurements. Figure 1 shows the surface pressure vs. area curve for the radioactive PMS used in this work. The measurement was made using a torsion wire film balance. Before spreading the PNIS dissolved in an ether solvent, the surface of the distilled water (pH = 6.45) was first swept clean several times and trapped surface impurities were removed with a suction pipet. After a few minutes the first readings were taken and a number of measurements were obtained during both compression and expansion of the film. No hysteresis effects were observed although a small increase (~ dyne) in the surface pressure was observed after 15 hours. The surface pressure measurements were taken within 30 min to avoid the aging problem noted by Fox, Taylor, and Zisman (4). Fox, Taylor, and Zisman (4) have also suggested that at low surface pressures the PMS molecule which has the structure CH3Si(CH~)2[--O--Si(CH3)~]n--CH3 is ar-

Journal of Colloid and ln~erfave ~¢ien~, Vol. 30, No. 2, Juno 196g

200

PMS MONOLAYERS AT AN AIR-WATER INTERFACE 14 f

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There is, however, a somewhat disturbing feature if Fig. 2 is examined more closely. The slope of the line gives an area per monomer of 17.6 A2, which is considerably lower than the areas mentioned above. Adjustment downward of the average molecular weight from the Barry correlation to bring the area per monomer in this study up to 22.7 A 2 would prevent agreement with the data of Jarvis. Thus, although we have characterized the radioactive PMS as having a molecular weight of 3000, there is some uncertainty in this value. II. DIFFUSION INTO THE SUBSTRATE AND SOLUBILITY

0 0

201

16

20

cm2/grom

FIG. 1. Film pressure-area isotherm for radioactive polydimethylsiloxane (40 centistokes/25°C) at 22.5°C. ranged at the air-water interface with all the silicon atoms in line in the same plane and all the hydrocarbon groups on one side of that plane. The silicon and oxygen groups are envisioned as being in the water surface. To calculate the area per monomer, the compression curve is extrapolated back to zero surface pressure as shown in Fig. 1. The area per monomer found by Fox and co-workers was 22.7 A~, and Newing (5) has confirmed this value. Recently, however, Trapeznikov et al. (6) and Noll et al. (7) have obtained a value of 19 A2. Extrapolation of the curve in Fig. 1 gives a value of 1.5 X 107 cm~/gram. To convert this value to the area/monomer, the molecular weight given by Barry's correlation was used. In order to justify the values of the predicted molecular weight and the intercept on the pressure-area curve, the intercept from Fig. 1 in the units of area per molecule was plotted as shown in Fig. 2 together with the data of Jarvis (8), Fox et al. (4), and Noll (9). The areas obtained both for the radioactive PMS and two other samples of silicone oil fall on the extrapolation of the straight line passed through these data, apparently validating the calculated values of the molecular weight and the area/gram.

A. The Model for Diffusion. If it is assumed that the surface-active film is slightly soluble but not so soluble that the presumed equilibrium boundary condition at the liquid interface changes substantially, the dissolution of the surface-active agent from the interface can be modeled by the well-known one-dimensional diffusion equation Oc(y, t) _ D O~c(Y' t) Ot Oy2

[1]

with the following initial and boundary conditions:

c(y, O) = O,

c(co, t) = O,

c(0, t) = c , ,

[21

where c is the concentration, t is the time, y is the direction perpendicular to the interface, and c8 is the saturated bulk concentration. The solution for the model is

c(y, t) = cs erfe ( 2 ~ t

) ,

[3]

where erfc (z) is the complementary error function. The rate of change 1~ of the surface concentration is

0r(t)

_

Ot

D

Oc

O-Y u=o'

and making use of Eq. [3] one obtains ot

-

c, \-Ftt/

"

[41

Journal of Colloid and Interface Science, Vol. 30, No. $, Jeun 1969

202

KAKIHARA, HIMMELBLAU, AND SCHECttTER 900

/ /

Radioactive~tracer

800

700

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o

600

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400 D.

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This work (molecular weight based on Barry c o r r e l a t i o n )

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30

40

Number of monomers

per molecule ,n

FIo. 2. Prediction of Molecular Weight Integration of Eq. [4] yields r(t~)

-

r(t,)

= 2c,

[5]

(v'~ - ~/~).

Thus, by measuring the radioactive counting rate at the interface, which proves to be essentially proportional to F (because of the absorption of beta particles by the substrafe), it is possible to estimate from a statistical analysis the quantity c, x/D. If the surface concentration is proportional to the counting rate of tracer, F(t) = qN(t), then \q/\~

/

'

required for a significant change in concentration at the bottom to occur. If the values of the initial counting rate N(0), the equilibrium counting rate N~, the area A of the radioactive interface, and the volume V of the bulk substrate are known, a material balance on the silicone oil gives c,V = q[N(0) - Ye]A

[7]

or

c, _

IN(0)

q

-

h

Ne]

iS]

'

where h is the height of the substrate. Substituting Eq. [8] into Eq. [6] and solving for the bulk diffusion coefficient gives

[6]

0
D = 7r 2{N

Ne}

'

where m is the slope of the plot of counting rate vs. t"2.

PMS MONOLAYERS AT AN AIR-WATER INTERFACE The saturated bulk concentration c. was ascertained from the decrease in counting rate through use of the material balance between the initial counting rate and the equilibrium counting rate. If Q = qN(O)A is the initial quantity of tracer put on the substrate, an amount sufficient to form a saturated solution is then Q r N(0) - N~.1

c~ = V L

N(~

with water to the height of 1 cm. The cover (which held the counting tube) was placed in position, and the background radioactivity was counted for a few hours at 10-min intervals. To carry out an experiment, the cover was removed, and a measured amount of radioactive silicone oil solution spread on the water surface with an Agla micrometer syringe. The cover and the counting tube were replaced and the counts emitted from the radioactive film recorded in 10-min intervals for lengths of time varying up to 470 hours. After the continuous monitoring of the surface radioactivity was terminated, the background counting rate was again measured to determine if any of the radioactive film had been transported onto the counting tube. Although the background counting rate increased slightly, a negligible amount (less than ~ of 1% by weight of the surface film) was picked up on the window of the counter. Figure 3 represents a typical run. The counting data in the figure have been corrected for a slight decline in the level of the substrate, 0.169 cm in total, during the experiment. The data in Fig. 3 combined with the replicate run at the same temperature gave the bulk diffusion coefficient and the solu-

[9]

"

B. Experimental Study. To obtain the experimental data, radioactive PMS having a viscosity of 40 eentistokes at 25°C and a specific activity of 1.57 ~c/mg (purchased from Tracerlab) was spread on a water substrate in a Petri dish 2.95 cm in diameter. The Petri dish was placed in a Pyrex dish containing water, and both dishes were enclosed in a tight container to prevent light and air from entering the system, and water from evaporating from the substrate. Before each experiment the apparatus was carefully cleaned to remove any residual radioactivity, and the aluminized Mylar foil on the counting table was replaced by new foil to avoid increasing the background counting rate caused by slight contamination of radioactive material from the previous experiment. The Petri dish was filled

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Temperature : 2 6 ° C Surface coverage : Ca. 1 . 6 5 x l O 6 c m 2 / g r a m Initial height of substrate, hi : 1.0 cm change in i n t e r f o c i a l level : 0 . 1 6 9 cm

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Fio. 3. Counting rate (counts per minute) vs. square root of time for the bulk diffusionof polydimethylsiloxane (40 centistokes/25°C) in water substrate. Journal of Colloid and Interface Science, Vol. 30, N o . 2, J u n e 1969

204

KAKIHARA, HIMMELBLAU, AND SCHECHTER

bility of the polydimethylsiloxane at 25 ° as D -- 0.43 ± 0.12 × 10-6 cm2/sec cs = 3.15 :t: 0.44 X 10-~ gm/cm ~ at a confidence level of 90 %. C. Interpretation of the Results on a Molecular Scale. An anomalous phenomenon was observed for the first two or three hours in all the experiments, a rise in counting rate. Whether a nonuniform multilayer film existed at the beginning of an experiment instead of a uniform monolayer, so that some of the beta particles were self-absorbed by the oil, or whether the surfaceactive agent solvent (ether) might have affected the counting rate (also by absorption of beta particles) for an initial period, could not be determined. Another possibility was that the solvent, which is relatively soluble in water, might have carried some of the silicone oil into the aqueous phase, with subsequent diffusion from the bulk to the water surface. Another typical feature shown by the curve in Fig. 3 is the nonlinear trend at long times, presumed to be caused by the change in the boundary condition at infinity. Thus, the first few hours and the tail of the data were not employed in estimating D. The so-called hydrodynamic radius of large molecules such as those in the silicone oil can be calculated from the Stokes-Einstein equation R -

kT 6~D '

[10]

where R is an effective radius of the molecule, ]c is the Boltzmann constant, and is the viscosity. Substituting k = 1.38 × 10-16 (erg) (°K-l), T = 297°K, ~ = 0.90 × 10-2 gm/(em) (sec), and D = 0.43 X 10-6 cm2/sec gives R --___ 55 A. However, the interpretation of R from a theoretical point of view is difficult. Tanford (10), for example, noted that the hydrodynamic radius is related to the volume of solvent more or less permanently associated with the polymer molecule as well as the mean end-to-end distance as suggested by the KirkwoodRiseman (11) equation. The solvation of the dimethylsiloxane polymer molecule in water Journal of Colloid and Interface Science, Yol. 30, No. 2, June 1969

is not easy to estimate, but the mean endto-end distance should not be changed much from the so-called random flight configuration since water is a very poor solvent for PMS (12). The mean end-to-end distance computed from the differing bond angles is about 27 A for a molecular weight of 3000 (13). If we ignore the water of solration, the value of the diffusion coefficient calculated by means of the Kirkwood-Riseman equation is 3.3 × 10-6 cm2/sec, which is a factor of 8 larger than the measured diffusion coefficient. This discrepancy may well be attributed to the water of solvation, which would tend to reduce the diffusion coefficient from the predicted value. It is also possible to compute the projected area of the polydimethylsiloxane molecule CH~ CH3--Si [--O--Si (CH3)2]n--CH~ CH~ on the assumption that each molecule is stretched out in the form of a cylinder of diameter d and length L, with the O atom in the substrate and the Si atoms out of the substrate. The length and diameter can be estimated from a knowledge of bond lengths (3) and angles as follows: Si--O, 1.91 A; Si--C, 1.94 A; C - - H , 1.07 A; H (covalent radii including van der Waals radii), 1.50 A. The tetrahedral angle for the Si and C atoms is about 109 ° . The calculated projected cross-sectional area at the axis of 868 A 2 is in reasonable agreement with the same quantity determined by the method proposed by Adam (14) to estimate the crosssectional area of a molecule of a surfaceactive compound having one hydrophilie end group. On compressing an expanded film, an initial high slope in the pressurearea curve is followed by a plateau and then again a high slope (see Fig. 1). The first high slope is interpreted as the change from the state in which the molecules are widely separated on the substrate to the compact state in which the molecules are in close contact with one another but still lie in the substrate. Under increasing pressure the hydrophobic ends of the molecules rise from the interface. Thus, by compressing the film and ex-

PMS MONOLAYERS AT AN AIR-WATER INTERFACE trapolating the slope of the pressure-area isotherm to zero surface pressure, an estimate of the longitudinal cross-sectional area of a molecule of silicone oil could be made. Table I lists the calculated areas based on this study and the data of Jarvis. The agreement is good except for the longest molecules, but the extrapolation of the linear portion of the pressure-area isotherm is somewhat subjective. III. SURFACE STRUCTURE OF PMS The structure of monolaycrs of PMS at an air-water interface has been the subject of some conjecture by both Fox and coworkers and Trapeznikov and co-workers. The latter investigators have suggested that the P M S molecules may agglomerate on the surface so as to form disks or islands. Such surface structures have been reported for lower molecular surfactants particularly in the range of surface densities which do not lead to close packing. Surface structure has been reported by Bouchet (15), Zocher and Stiebel (16), Harkins and Fischer (17), and Ries and Kimball (18), although the findings of the latter authors have been questioned in a recent note (19). Ries and Kimball studied the structure of a close-packed monolayer using an electron microscope after the monolayer had been "lifted" from the substrate. This technique may introduce spurious structure as evidenced by the recent controversy. Some of the earlier studies were based on measurements of surface potentials, but these results, too, can be questioned since the reproducibility of

/ o s?

205

surface potential measurements is extremely poor. Therefore a different technique was employed here to study the surface structure of PMS monolayers. A . E X P E R I M E N T A L APPARATUS

Radioactive PMS (40 centistokes/25°C) and nonradioactive PMS (20 eentistokes/ 25°C) were spread separately on each side of a double Nylon thread barrier t h a t divided the water surface in a narrow Langmuir trough. The surface pressure read on two calibrated surface balances was adjusted to be the same on each side of the barrier. Refer to Fig. 4. The force could be read to within 2 % on each balance. After removal of the barrier, the radioactivity of a fixed surface area was continuously monitored by an end window proportional counter in order to investigate surface (twodimensional) diffusion. To insure that the counting tube counted TABLE I LONGITUDINAL SECTION AREA OF POLYDIMETHYLSILOXANE MOLECULE~ A 2 n

Asymptote from the first slope

Area calculated from bond lengths

7 11 16 26 39 44

213= 256~ 383~ 537b 790b 822b

195 284 388 596 865 971

Calculated from the data of Jarvis (8). b This work.

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SURFACE BALANCE

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RAIL SUPPORT

FIG. 4. Apparatus for surface diffusion measurement Journal of Colloid and Interface Science, Vol. 30, No. 2, June 1969

206

KAKIHARA, HIMMELBLAU, AND SCHECHTE~

all radioactive surface material moving axially,two ~ inch wide stainless steel rails were fixed onto a ~ 6 inch thick stainless steel plate and placed in the trough. This arrangement reduced the water depth to 0.40 cm and reduced the disturbance caused by removing the barrier. Two Nyoln threads (a crystal Nylon sewing thread and a relatively thick fishing thread) were placed side by side to form a barrier because the single fine thread sometimes permitted leakage of surface-active agent around the [

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barrier. The fine thread was lifted after the thick thread. The counting tube was fixed in a supporting brass frame. Attached to the window of the tube was a 0.5 cm deep stainless steel hood that was designed to shield out the particles emanating from any other r e , o n than the area immediately covered by the window of the counting tube. The supporting frame for the tube could be moved along the trough. The whole assembly was placed in a

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Fro. 5. Counting rate (counts per minute) vs. time for the surface diffusion of 8.5 X 10 e cm~/gram polydimethylsiloxane (40 centistokes/25°C) into 5.0 X 10 6 cmS/gram polydimethylsiloxane (20 eentistokes/25°C). I

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FIG. 6. Counting rate (counts per minute) vs. time for the surface diffusionof 13.6 X 106 cm2/gram polydimethylsiloxane (40 centistokes/25°C) into 13.0 X 106 cm~/gram polydimethylsiloxane (20 eenti~tokes/25°C). Journal of Colloid and Interface Science, Vol. 30, No. 2, June 1969

PMS MONOLAYERS AT AN AIR-WATER INTERFACE

exhibited both periodic fluctuations and a number of peaks. The existence of these fluctuations indicated the nonlmlformity of the surface films. In addition, the peaks are strikingly high compared with the equilibrium counting rate N°. In Fig. 6, for example, the height of peak C is nearly the same as the initial counting rate on the radioactive side of the barrier (about 240 counts per minute) before the barrier was lifted. Thus, it appeared that each peak represented a coherent portion of the radioactive film with the initial surface concentration which

shielded box containing a trough of water of about 1 cm depth in order to retard evaporation from the Langmuir trough. B. ~ , X P E R I M E N T A L

I:~ESULTS

Figures 5 through 8 show typical results; H is the surface pressure, X0 the distance from the thread barrier to the center position of the counting tube, and N, the equilibrium counting rate. Although curves were not reproducible certain common features can be observed. All the curves of the counting rate vs. time I

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70

80

90

FIG. 7. Counting rate (counts per minute) vs. time for the surface diffusion of 20 X 106 cm2/gram polydimethylsiloxane (40 centistokes/25°C) into 20 X 106 cmS/gram polydimethylsiloxane (20 centistokes/25°C). 500

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Fro. 8. Counting rate (counts per minute) vs. time for the surface diffusion of 6.75 X 10e crab/gram polydimethylsiloxane (40 centistokes/25°C) into 5.0 X 10e cm~/gram polydimethylsiloxane (20 centistokes/25°C) using two counters. Journal of Colloid and Interface Science, Vol. 30, No. 2, June 1969

208

KAKIHARA, HIMMELBLAU, AND SCHECHTER

had penetrated the nonradioactive film and passed under the counting tube. Such a high-intensity film section may be called an "island" of radioactive PMS in contact with or surrounded by nonradioactive PMS and must have then traveled a distance of approximately the diameter of the window of the counting tube, i.e., 3.2 cm, in a time equivalent to the width of the peak. To determine if these islands were moving in the same direction, experiments such as those depicted in Fig. 8 were carried out in which the surface radioactivity was monitored at two different axial positions b y two counters. The results clearly show that the islands moved in the same direction, and although the sensitivities of the two counting tubes were different, several of the smaller peaks could be related (A to A ' , B to B', etc.) as well as the large over-all peaks. Thus, the islands represented fairly large identifiable structures which retained considerable integrity during motion. The speed of these floating islands can be estimated as 3.2 V = ~,

[11]

where U = the velocity of the island in centimeters/second, and wp = width of the peak in seconds. The mass of the island can be also estimated by comparing the height of the peak with the equilibrium counting rate (or one half of the initial counting rate on the radioactive side). T h a t is, k = Aw \-~]\T]'

[12]

TABLE II CALCULATED CHARACTERISTICS OF " I S L A N D S " OF SURFACE F I L M Peak

wp (see U ~. X 10-4) (cm/sec) X 104 (grams X 107)

rd (cm)

Shown in Fig. 5

A B C D E

5.04 7.56 10.08 7.20 6.84

A B C D E

1.98 2.16 3.60 1.98 3.96

A B C

1.51 1.66 1.91

0.635 0.423 0.317 0.444 0.468

1.84 5.08 6.47 6.60 7.22

0.706 1.17 1.32 1.34 1.40

Shown in Fig. 6

1.62 1.48 0.889 1.62 0.808

2.71 3.69 5.42 4.06 3.87

1.08 1.26 1.53 1.33 5.29

Shown in Fig. 7

2.12 1.93 1.68

1.59 1.72 2.11

1.01 1.04 1.16

that given initially on the radioactive side of the trough and that the island is in the form of a circular disk, then the size of the island is given by 2

k

7rrd -- - F0

[13]

or

rd

\~F0]

'

[14]

where rd is the radius of the circular island. Substituting Eq. [12] into Eq. [14] gives Aw

Np

1/2

where ), = mass of the island in grams, A w = surface area covered by the window of the counting tube, 8.04 cm ~, N~ = counting rate of the peak in counts per minute, N , = equilibrium counting rate in counts per minute, and r0 = initial surface concentration in the radioactive side in grams/ square centimeter. If it is assumed that the average surface concentration of each island is the same as Journal of Colloid and Interface Science, Vol. 30, No. 2, June 1969

The calculated values of rd for the peaks shown in Figs. 5, 6, and 7 are given in Tables II and indicated that the size of the islands was surprisingly constant. I t is quite clear that the islands were not in pure Brownian motion. I t is then reasonable to speculate on what caused the flow of radioactive material. Several possible causes are: 1) The flow was caused by unequal surface pressures of the nonradioactive and radioactive films due to unequal rates of

PMS

MONOLAYERS

AT

AN

dissolution of each film into the substrate. When the rates of desorption from the surface of the films are different, changes in surface concentrations and/or unequal changes in surface pressures might arise. I t is clear that unequal rates of diffusion into the bulk will give rise to a directed surface flow from the region having smaller rate of dissolution to the region having larger rate. The postulated mechanism was rejected by the following experimentation. The nonradioactive silicone oil having 26 repeating units was replaced by a nonradioactive PMS having 44 repeating units, corresponding to a larger molecular weight than the radioactive PMS. Consequently, the nonradioactive oil should have had a smaller dissolution rate into the water substrate. If unequal dissolution rates were the cause of the observed flow of the islands, then by decreasing the dissolution rate of the nonradioactive PMS, the direction of motion of the islands should be reversed. Experimentation demonstrated that the direction of motion was unchanged. 2) Flow was caused by unequal changes of surface pressures of nonradioactive and radioactive films, respectively, in turn due to different film pressure-area isotherms. Even if the two distinct compounds have the same bulk diffusivity and the same solubility, a difference between the surface pressures of the two films could arise provided the change in surface pressure for a given number of surface-active molecules dissolving in the bulk differs between the two films. This would be the case if the isotherms have a different shape. The shapes of the respective isotherms must be somewhat different because of their different physical properties, although in this case differences were found to be quite small. 3) Nonideal mixing of two films. When two distinct surface films mix with each other, the film pressure of mixed film is not necessarily the same as the original pressure. Since the two distinct compounds used in this study had the same chemical structure differing only in the average molecular weight or the number of monomer units in each molecule, their mixing was probably very nearly ideal.

AIR-WATER

INTERFACE

209

4) Impurities in the film-forming nmterials. One of the original film-forming materials might have contained some impurities giving a lowering of surface tension with time and a changing of the surface pressure to some extent. 5) Heat effect. A difference in surface pressures can arise if the temperature becomes different in the two films. It seemed unlikely that such a difference existed. The observed radioactive islands are different from those found by other investigators in that they were much larger than those found, for example, by Ries and Kimba~ (18), and most probably were not isolated structures but were surrounded by nonradioactive polymers. I t should be noted, however, that previous work on surface structure has been with monolayers having much lower molecular weights than that of PMS. It may be t hat molecular entanglements arising during the formation of a monolayer are much more likely for the larger molecular and disentanglement may at the same time be much slower. The origin of the large islands may possibly be related to the polymeric nature of the PMS studied. This and other aspects of our unusual results are presently being studied in a revised apparatus. IV. CONCLUSIONS The study of the desorption of P~IS from an air-water interface has shown that the solubility of PMS (n = 39) in water is about 3.1 X 10-7 gm / cm 3 and the diffusion coefficient is 0.43 X 10-6 cm2/sec. The diffusion coefficient is about 8 times smaller than that predicted by the Kirkwood-Riseman theory, and the discrepancy is postulated as being due to the water of solvation associated with the polymer molecule. By carrying out surface diffusion experiments between radioactive and nonradioactive PMS, we observed some unusual phenomena related to the structure of monolayers of PMS. The most interesting result was that apparently islands form that are much larger than those observed by other investigators for systems of much smaller molecular weight. The dimensions of the islands were sensitive to surface pressure, Journal of Colloid and Interface Science, Vol. 30, No. 2, June 1969

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KAKIHARA, HIMMELBLAU, AND SCHECHTER

b u t the average radius of an island was r e m a r k a b l y uniform at about 1 cm. A n o t h e r interesting and still unexplained p h e n o m e n o n was the observation of the net motion of trough on the islands. The surface pressures were carefully balanced prior to each experiment and yet the islands of surface-active material were observed to m o v e slowly into the nonradioactive region. T h e speed was not changed significantly when the molecular weight of the nonradioactive P M S was changed. ACKNOWLEDGMENT This investigation was carried out with the support of the National Science Foundation under Grant NSF-G123. REFERENCES 1. LEVICH, V. G., "Physiochemical Hydrody-

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