1182
A. K A T L W K Y A N D I. MILLER
on the adsorbent, waa found to be 1.2. This was done by varying the pH with constant HAd .S and varying the quantity of adsorbent at constant pH. The effect of changing concentrations of chloride ion is not represented in the above and a second mass law expression
K =
y
(CI-)"
(1 - y)(HAd*S*ClJ'
was shown to represent the data obtained on the influence of variations in ammonium chloride concentrations on cobalt adsorption a t constant pH and volume. The authors are pleased to express their sincere gratitude to Professor Edward Mack, Jr., for his continued support of this research. The grant-in-aid of the Industrial Research Foundation received through the Graduate School of The Ohio State University is greatly appreciated by the authors. REFERENCES
(1) BJERRUM. J.: Metal Ammine Formation in Aqueous Solution, pp. 28€-7. P. Haase and Son, Copenhagen (1941). (2) KOLTHOFF, I. M.,A N D ~ ~ O S F L O VB.: I TJ. Z ,Phys. Chem. 41, 629 (1937). L. G.: J. Phys. Chem. 43, 767, 909 (1939). (3) KOLTIIOFF,I. M.,A N D OVERHOLSER, (4) KURBATOV, J. D., KULP,J . L., A N D MACK,E., JR.:J. Am. Chem. SOC.67,1923 (1945). (5) KURBATOV, M.H.: J. Am. Chem. SOC.71,858 (1949). (6) KIJRBATOV, bl. H., A N D KURBATOV, J. D.: J. Am. Chem. SOC. 69,438 (1947). (7) KURBATOV, M.H.,Yu, Fu-CHUN,A N D KURBATOV, J. D.: J. Chem. Phys. 16,87 (1948). (8) NEKRASOV, B. V.: J. Russ. Phys. Chem. SOC.66,207 (1926). R. M.:M . S. Thesis, The Ohio State University, 1949. (9) STEELMAN,
T H E SURFACE ACTIVITY OF POLYMERIC ACIDS I N AQUEOUS SOLUTIONS A. KATCHALSKY
AND
I. MILLER'
Weirmann Insiitufe of Scienccr, Rshocot, Israel
Received July 14, 1060 1. INTRODUCTION
Although the surface behavior of a number of synthetic polymer monolayers has been investigated recently (1, 2, 6, 7), the adsorption phenomena of watersoluble polymers were barely touched. The few attempts to elucidate the regularities governing the activity of po!ymeric glycols (5, 17) are inconclusive nor can they be considered as a guide to the investigation of polyelectrolyte solutions. Surface coagulation and complex time phenomena cause difficulties in the inves1 This article is part of a thesis presented by I. Miller t o the Hebrew University, Jerusalem, Israel, in partial fulfillment of the requirements for the degree of Master of Science, Janusry, 1950.
SURFACE ACTIVITY OF POLYMERIC ACID3
1183
tigation of protein solutions (3, 9, 17). Therefore, the behavior of simpler molecules, of well-defined constitution and known molecular weight, was studied in order to shed some light on the general behavior of long-chain polar molecule3 at the air-water interface. Recently a method for the fractionation and molecular-weight determination of polymethacrylic acid was developed in this Laboratory (14); hence the meaaurements presented here were carried out on well-defined material. This paper deals with the dependence of the surface activity on the molecular weight of the polymer and on the pH and ionic strength of the solution. 11. EXPERIMENTAL
A . Pseparatian of the material For accurate measurements, certain precautions must be taken in the preparation of the polyacids. The polymerization of the methacrylic acid is carried out in aqueous solution a t 50°C. without an organic catalyst, since the latter might exhibit surface activity. In all cases hydrogen peroxide was used as the polymerization catalyst. After polymerization the solution was dialyzed against conductivity water to remove the hydrogen peroxide and unreacted material, and the solution was then evaporated in oacuo. Dissolution in alcohol and subsequent precipitation by ethyl ether is not recommended, as the slightest esterification of the carboxyl groups influences the surface activity to a considerable degree. The final drying of the polymer is carried out at a temperature lower than 50°C. to avoid anhydridization. The resultant polymer is a clear glassy substance. Polymethacrylic acids of the following degrees of polymerization were used: 600, 800, 2600, and 7800; the corresponding molecular weights nvere 51,800, 68,700, 227,500, and 670,000. The molecular weights were determined according to the procedure of Katchalsky and Eisenberg (14).
B. Measurement technique The drop-weight method was found suitable for routine measurements. A stalagmometer with a ground-glass tip was used, and the data were calculated according to Harkins and Brown (9). In order to keep the development of the drops sufficiently low, a Mariotte flask for regulation of the pressure gradient was added to the stalagmometer. The latter was kept a t a constant temperature by means of a water jacket a t 24OC. Under these conditions, the reproducibility of the data waa within 0.1 dyne/cm. It was found that the time effects were not very marked with polymethacrylic acid solutions. After 2-3 min. more than 90 per cent of the surface-tension depression w~ obtained; from 5 min. upwards, no measurable changes in the surface tension could be detected (see figure 1 ) . Measurements by the capillary-rise method show a more pronounced time effect, though the final values agree fairly well with those of the dropweight method.
1184
A. KATCHALSKY AND I. MILLER
I
I
I
-
I
l
i
0
-
I ,
0
-
1I
600 1800
t
MI20
M 160
Y/120
dvncrjcm.
dynerlrm.
dynrrlcm.
3.9 2.2
2.8 1.6 1.3
2.2 1.2 1.0
2650
7800
I
I
I
.If
1
,240
dmerlcm.
1.6
are given in table 1. These results +ow the normal decrease of surface activity with decreasing concentration. However, it is remarkable that the surface activity decreases with increasing molecular weight for each concentration. As seen in figure 2, the surface-tension depression for a given concentration increases linearly with the reciprocal of the square root of the degree of polymerization of the polyacid. This result may be summarized in the formula Au =
constant
-
d-F
SURF.\CE
ACTIVITY O F POLYMERIC ACIDS
1185
the constant being 96 for M/20,68 for MIGO, and 52.7 for M/120 polymethacrylic acid solutions (Mbeing the concentration in base-moles per liter). The dependence of surface activity on concentration is of the usual logarithmic type encountered in more concentrated solutions of substances of low molecular weight. Figure 3 gives the dependence of the sui-face-tension depression on the natural logarithm of the volume fraction o b .
B. Discussion The interpretation of the experimental results presented in Section I11 A follows the simple classical method of Rideal (19). I t is assumed that the solution
1
2
3
4
l/dT x 102 FIG.2. Dependence of surface-tension depression (AU) of 51/20, .1f/60, and .1.1/120 polymethscrylic acid solutions on the reciprocal of the square root of the degree of polymerization (PI. Curve I, M/20; curve 11, .11/60; curve 111, .l1/120.
under investigation may be divided into a bulk phase of volume 2‘6, containing nb polymer molecules of degree of polymerization P , and a surface phase of thickness 6 and area 4 containing n, polymer molecules ?f the same degree of polymerization. If the volume of a single monomerunit bew, then the “free space” in the bulk will be (V - nb.Pw) and in the surface (6A - n,.Pw). The transfer of a polymer molecule from the bulk to the surface is accompanied by a change in the standard free energy (cf. Ward and Torday (20)) of ‘p units per molecule. dn polymer molecules are now added to the system, so that dn. molecules pass dn, = dn. Neglecting any into the surface phase and dna into the bulk: dna interaction in the surface, the ratio of the activities of dna and dn, is determined by the exponent of p / k T and by the ratio of the free spaces available, Le.,
+
1186
A . XATCHALSKY AND I. MILLER
d
nr
dn;,pw 6A-
inb-
=
dnb
V
ev/kT
naPw
Assuming 6 and (p to be independent of concentration, the integration is readily performed and gives:
n&P,ur/Vis the volume fraction of the polymer in the bulk = u b , and similarly n,Pw/AG = v, is the volume fraction of the polymer in the surface phrrse.
I
I
1
-8
-7
-6
-5
In vb
-
FIQ.3. Dependence of surface-tension depression (ACT)on natural logarithm of v o l w A fraction of the polymer, In V b . The surface-tension depression follows the curves Au B In V b . For P = 600:Au 3 9.18 -I-0.9% In V b For P = 1800: Au 5.34 -I-0.55 In V b For P = 2650: Au = 4.58 -k 0.47 In Ob
+
-
In (1 - u,) = In a11 cases of experimental interest
ev/k*
ub
ln(1
- ub)
