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NORIOISEAND TSUNEO OKUBO
Mean Activity Coefficient of Polyelectrolytes.
111. Measurements of
Hydrochlorides of Polyethylenimine and Its Low Molecular Weight Analogs’
by Norio Ise and Tsuneo Okubo Department of Polymer Chemistry, Kyoto University, Kyoto, Japan
(Received February 18, 1966)
The mean activity coefficients of hydrochlorides of polyethylenimine and its low molecular weight analogs such as tetraethylenepentamine, triethylenetetramine, diethylenetriamine, and ethylenediamine have been measured, using a concentration cell with transference and silver-silver chloride electrodes. The single-ion activity coefficient of the gegenions (chloride ions) and the transference numbers of the macroions and low molecular weight polyvalent cations have also been determined. The results show that the mean activity coefficient of the polyelectrolyte cannot be equal to the single-ion activity coefficient of its gegenions. This agrees with the previous conclusion obtained with sodium salts of anionic polyelectrolytes. It is further demonstrated that the discrepancy between two coefficients can be small for the low molecular weight analogs. In the light of MacInnes’ convention assuming the equality of the mean activity coefficient of potassium chloride and the singleion activity coefficient of chloride (or potassium) ion, it is suggested that the discrepancy decreases continuously with decreasing charge numbers of electrolytes and therefore characterizes the transition from polyelectrolytes to simple electrolytes. The logarithm of the mean activity coefficient of the polyethylenimine salt decreases linearly with the cube root of concentration. The slope is -0.86 for this salt, not far from a value of -0.74 previously found for sodium polyacrylate. This cube-root rule is also found to be valid for the low molecular weight imine salts. The slope ranges from -0.60 to - 1.10, the magnitude increasing with rising valency.
Introduction In previous paper^,^^^ mean activity coefficients were measured on sodium polyacrylate (NaPAA) and sodium salts of polyvinyl alcohols partially acetalized with glyoxylic acid (NaPVAG). In the present paper, experimental data are reported on the hydrochlorides of polyethylenimine (PEI), tetraethylenepentamine (TP), triethylenetetramine (TT) , diethylenetriamine (DT), and ethylenediamine (ED). These samples are of interest for three reasons. First, a concentration cell used for measurements of mean activity coefficients can be set up using silver-silver chloride electrodes, since the gegenion is C1-. This electrode has been studied much more intensively than the Na-glass electrodes used for NaPAA and NaPVAG.4 Second, the single-ion activity coefficients of the gegenions of PEI(HCl), and of its low molecular weight analogs have been studied earlier.5 Comparison of their data The Journal of Physical Chemistry
and the mean activity data is a source of useful information. Third, by studying these hydrochlorides, the transition from simple electrolytes to polyelectrolytes can be investigated, as Lapanje, et al., have a ~ s e r t e d . ~ Experimental Section Principles. The method of the determination of mean activity coefficient adopted in this paper was described in the previous paper.2 The galvanic cell with transference was as is shown in (I). (1) Presented in part at the 14th Polymer Symposium, Kyoto, Oct 1965. (2) N. Ise and T. Okubo, J. Phys. Chem., 69,4102 (1965). ( 3 ) N. Ise and T. Okubo, ibid., 70, 1930 (1966). (4) R. G. Bates, “Determination of pH, Theory and Practice,” 1st ed, John Wiley and Sons, Inc., New York, N. Y.,1964, Chapter 9. ( 5 ) 9. Lapanje, J. Haevig, H. T. Davis, and S. A. Rice, J . Am. Chem. SOC.,8 3 , 1590 (1961). Japan,
MEANACTIVITYCOEFFICIENT OF POLYELECTROLYTES. I11
Ag-AgC1 solution of bydrochloride electrode of the polyelectrolyte 2 solution of hydrochloride Ag-AgC1 of the polyelectrolyte 1 electrode ~
~
(1)
The emf of this concentration cell ( E ) can be given as
E =
tZpd In a CYF
where a1 and a2are mean activities of the hydrochloride in the solutions 1 and 2, respectively, R is the gas constant, T the temperature, F the Faraday charge, hP the transference number of macroions, and CY the number of free gegenions dissociated from one macroion. The principle and detail of the transference experiments have been described in a previous paper.6 The polymer concentrations before and after the electrolysis were determined by conductometric titration. The chloride concentration was measured by a conductometric titration with AgN03, using bright platinum electrodes. The single-ion activity coefficient of gegenions 7*ze of the polyethylenimine salt was determined using the following cell.
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a 50% aqueous solution. The molecular weight of the polyimine was estimated to be 4500 using a viscositymolecular weight relationship. lo Purification of the sample was carried out by passing the diluted aqueous solution through columns containing cation- and anion-exchange resins in the hydrogen and hydroxide forms, respectively. Thereafter, hydrochloric acid was added quantitatively. The nitrogen content of the sample was determined by the Kjeldahl method, which agreed with the value from the conductivity method within the limit of experimental error. ED, DT, TT, and TP were commercially available. They were purified by distillation under reduced pressure of nitrogen and by recrystallization. These samples were a.nalyzed with the results shown in Table I. Table I
ED DT TT TP
-CalculatedC
-ObservedC
H
N
40.3 46.4 50.4 51.2
13.9 13.1 12.5 12.2
46.0 40.4 37.1 36.7
40.0 46.1 49.3 50.8
H
N
13.4 13.5 12.3 12.2
46.6 40.4 38.4 37.0
calomel electrode]polymer solution]Ag-AgC1 electrode
(11) The emf of this cell Elg was assumed to be expressed as
Ezg = EZga- (RT/F)In a c l From this equation, we determined Y*
acl-,
and hence
2g.
Electrodes. Ag-AgC1 electrodes were prepared by electrodeposition of silver. The base for the electrodes was a spiral (2-mni diameter) of 4 or 5 turns of a platinum wire. On the base, a layer of silver was electrodeposited and then chloridized by anodizing in a dilute solution of hydrochloric acid.' The standard potential of the silver-silver chloride electrodes (Eoo)against the hydrogen electrode was estimated to be 222.6 mv when use was made of a standard potential value of the saturated calomel electrodes, 242.0 mv.* On the other hand, Harned and Paxtons reported 222.39 mv for Eoo, with which our result is in good agreement. In the emf measurements, a pair of the Ag-AgC1 electrodes was used for 10-15 pairs of solutions; the electrodes were discarded when they failed to show the potential values given by the calibration curve. The electrodes were equilibrated with the cell solutions for an hour or so in order to obtain reliable emf data. Materials* was gift from the Sumitomo Chemical Co., Osaka. The sample was
The degree of neutralization of these samples used for measurements were 0.86, 0.96, 0.98, 0.98, and 0.86 for PEI, TP, TT, DT, and ED, respectively. The concentrations' of all the solutions were determined by conductometry. The emf and transference measurements were carried out at 25 f 0.02 and 25 f 0.1", respectively.
Results and Discussion Calibration oft he Ag-AgC1 electrode was carried out using a cell shown by calomel electrodel KC1 (m)lAg-AgC1 electrode (111) For this type of cell, if the liquid junction potential can be assumed to be negligible, the emf ( E ) is given by
E
=
Eo
- RT - In & I F
where Eo is the standard value of the emf of the above (6) T. Okubo, Y. Nishiaaki, and N. Ise, J. Phys. Chem., 69, 3690 (1966). (7) D. J. G. Ives and G. J. Janz, "Reference Electrodes, Theory and Practice," Academic press h e . , London, 1961, Chapter 4. (8) See ref 7, Chapter 3, p 159, Table V. (9) H.S. Harned and T. R. Paxton, J . Phys. Chem., 57,631 (1953). (10) G.D.Jones, A. Langsjoen, M. M. C . Neumann, and J. Zomlefer, J . o ~ g them., . 9 , 125 (1944).
Volume 70, Number 7 July 1966
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NORIOISEAND TSUNEO OKUBO
\I
I
I
I
-
2oo-xx\
Table I1 : Transference and Activity Coefficient Data of PEI(HCl), a t 25'" m,
1000 g
E,b mv
0.001 0.002 0.005 0.01 0.02 0.05 0.1
43.0 39.3 31.4 28.2 22.1 14.2 10.2
equiv/ 3
- looE
-
X'
G
G
6
\x 0 . 1
I
Figure 1. Calibration curve of silver-silver chloride electrode a t 25": X, observed value; , the Nernstian slope.
-
cell, and acl- is the single-ion activity of C1-. Using the value of the single-ion activity coefficient of C1calculated by MacInnes' convention from the mean activity coefficient data of potassium chloride,ll eq 2 was tested. As is shown in Figure 1, a linearity between E and log a ~ l -was obtained over a wide range of el-. The slope was 59.1 mv between a~l-= 1 and = which was in good agreement with the theoretical value, 59.157 mv at 25". The emf reading varied appreciably immediately after the electrodes were inserted into the solutions. It reached a limiting value which was constant within k O . 1 mv over a 30-min period. The emf value given in this paper is this limiting value. Important data of transference and activity coefficient data of PEI(HCl), are given in Table 11. The first column gives the concentration of solution 2 (equiv/1000 g of water), that of solution 1 being 0.504. The emf's of the cells shown by (I) are given in the second column. The transference numbers, tZp, are given in the third column. In the fourth column, the observed mean activity coefficients, y * , are given. These y* values were determined on the basis of a y*2g value a t m = 0.01 by the same convention as adopted in the preceding paper^.^^^ Column 5 gives the single-ion activity coefficients of gegenions (C1-) in the same solution measured by the Ag-AgC1 electrode and calomel electrode (cell 11). In the last column the pH value of each solution is given. The degree of neutralization of the polymer was chosen so as to reduce hydrolysis to a negligible amount, a t most 1.58% (at m = 0.001). In the present experiments using Ag-AgC1 electrodes, the accuracy of the emf measurement can be claimed to be h O . 1 mv, and the reproducibility was =k1.5%. The error associated with the y* The Journal of Physical Chemistry
t*P
Y*
Y *zg
PH
0.41
0.62 0.45 0.42 (0.302) 0.30 0.29 0.23
0.535 0.488 0.402 0.302 0.233 0.203 0.200
4.80
... 0.35 0.35
... 0.34 0.34
... 4.96 5.14
... 5.50 5.67
a The degree of neutralization is 0.86. * The emf measurementa were carried out with a reference concentration of 0.504 m.
value was smaller than *lo%. The accuracy of the transference number is estimated to be *3%. As is shown in Table 11, the transference number, hP, decreased with increasing concentration. This observation is in agreement with the one on NaPVAG and in disagreement with the one on XaPAA. y*zg of PEI(HC1). decreased with increasing concentration in the range covered. This is in contrast with y*zg of NaPAA2 and NaPVAG3 which was found to be almost independent of concentration. Though the reason for this disagreement is not clear, our finding on PEI(HC1). agrees with the one previously reported by Lapanje, et aL5 Table I1 also shows t,hat the mean activity coefficient, y * , of PEI(HCl), decreased with increasing Concentration, more sharply than y*2g. In other words, y* cannot be always equal to y * 2 g ; ie., we have Y* #
Y*2P
(3)
This conclusion has also been obtained previously on NaPAA and NaPVAG2v3and can now be asserted to be generally valid. The definition of y* Y*l+a
=
Y*263a Y*2p
(4)
indicates that the reason for this disagreement is the single-ion activity coefficient of macroions (y*zp) being extremely large or extremely small. Thus the importance of the contribution of macroions to the thermodynamic solution properties is again clearly demonstrated. In the previous paper,3 it was shown that the logarithm of the mean activity coefficient decreases (11) For MacInnes' convention, see Chapter 3 in ref 4. The mean activity coefficient data of potassium chloride were taken from: H. 9. Harned, J. Am. Chem. Soc., 51,416 (1929); H. 9. Harned and M. A. Cook, ibid., 59, 1290 (1937).
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
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Table III : Transference and Activity Coefficient Data of TP(HCl)6,TT(HCl)d, DT( HCl), and ED( HCl)*a t 250 m, equiv/ Sample"
TP(HC1)s 2 = 5 a = 3.88
TT (HC1)a 2 = 4 a = 3.72
DT(HC1)a 2 = 3 cy = 2.94
ED(HC1)z 2 = 2 a = 1.72
1000 g
E,b mv
1PP
Y*
Y*22
PH
0.001 0 * 002 0.005 0.01 0.02 0.05 0.1 0.2 0.503
64.7 56.9 46.1 39.6 31.5 22.7 16.5 9.1 0
0.39
1.10 1.02 0.97 (0.823) 0.73 0.66 0.55 0.51 0.43
... ...
4.44
0.883 0.823 0.758 0.655 0.589 0.528 0.423
4.14 4.12
0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.502
65.1 57.5 47.7 40.5 33.1 23.5 17.2 10.0 0
0.38
... ...
4.30
0.901 0.844 0.786 0.685 0.607 0.538 0.442
3.73 3.51
0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.502
64.7 57.3 47.8 40.7 33.8 23.6 17.7 10.1 0
0.00095 0.0019 0.00475 0.0095 0,019 0.0475 0.095 0.191 0,476
104.7 92.6 73.6 62.0 50.1 34.6 24.0 14.0 0
... 0.38 0.38 0.37
...
0.37
...
0.37 0.37 0.36 0.36
...
0.35 0.35
...
0.34 0.34
...
0.33 0.32
0.50 0.50
...
0.49 0.48 0.47
1.12 1.04 0.93 (0.844) 0.78 0.71 0.61 0.56 0.53 1.13 1.06 0.95 (0.866) 0.79 0.76 0.64 0.62 0.61 1.06 0.96 0.98 (0.873) 0.79 0.68 0.58 0.48 0.40
...
...
4.26 4.41
...
4.77
...
... 3.28 3.25
...
3.39
... ...
4.21
0.908 0.866 0.813 0.727 0.649 0.566 0.481
3.97 3.94
... ... 0.904 0.873 0.820 0.754 0.683 0.610 0.497
...
4.06 4.15
... 4.41 6.18 ... 6.32 6.38
... 6.54 6.64
... 6.87
a The degrees of neutralization were 0.96, 0.98, 0.98, and 0.86 for TP, TT, DT, and ED, respectively. Ir In the emf measurements, the reference concentration was the highest one for each sample. Y*Z. values were cited from the results of Lapanje, et al.6
linearly with the cube root of Concentration in the concentration range studied. It is interesting to see whether the cube-root rule also holds for PEI(HCI).. Thus log y* of this polyimine was plotted against the cube root of concentration, which is shown in Figure 2. Clearly the plot gives a linearity over a wide range of concentration with a slope of -0.86. The slope of NaPAA was -0.74 and that of NaPVAG was in the range of -3.2 and -1.6, varying with the degree of polymerization and the charge d e n ~ i t y . ~The data of NaPVAG's of various degrees of polymerization show that the magnitude of the slope decreases with increas-
ing degree of polymerization. This variation accounts for the difference in the slopes of NaPAA and PEI(HCI), of nearly equal charge densities, since the degree of the polymerization of the polyacid was 1640 and that of the polybase about 100. In Table 111,the essential data of activity coefficients and transference data of very low molecular weight analogs of the polyethylenimine salt, i.e., TP(HC1)5, TT(HCI)(, DT(HCI),, and ED(HC&, are shown. The number of free gegenions (CY) is given in the first column, with the stoichiometric number of charges, z. In the second column, the concentrations in equiv/1000 Volume 70, Number 7 July 1966
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NORIOISEAND TSUNEO OKUBO
0
I
I
I
I
-
m3 Figure 2. Concentration dependence of the mean activity coefficient of the hydrochloride of polyethylenimine (25’). Vertical bars represent an uncertainty of &lo%.
g are given. The emf values of the concentration cells are given in the third column. The transference numbers of polyvalent cations (fourth column) a t each concentration were obtained using the transference method described already.6 In column 5 the observed mean activity cofficients are given. Column 6 gives the single-ion activity coefficients of gegenions determined by Lapanje, et d 6 In the seventh column the pH values of each solution are given. The highest degree of hydrolysis of the imine salts was 4.2% in the case of T P a t m = 0.001. The accuracy of the transference number data is estimated to be &3%. The error associated with the y * value was about 10% for these imine salts. Table I11 shows that the transference number of polyvalent cation (hp) generally decreases with increasing concentration as was the case for polyethylenimine. As is readily seen from Table 111, hp values of TT(HC1)4 and DT(HCl)a are slightly smaller than those of TP(HC1)5. This may be accounted for by the difference of the degree of neutralization: the degrees of neutralization of TT and DT were larger than that of TP, and the contribution of coexisting hydrogen ions to the conductivity was larger for TT and DT than for TP (compare the pH values of these three imines) , though the experimental condition was always chosen such that the contribution of hydrogen ions was within 10% of the total conductivity. Table I11 shows that, in the case of ED, DT, TT, and TP, which are low molecular weight polyvalent electrolytes, y * can be nearly equal to y*zg,i.e.
creases. This continuous change in the discrepancy appears to characterize the transition from simple electrolytes to polyelectrolytes and must be taken into consideration when thermodynamic properties of electrolyte solutions, polymeric and simple, are to be discussed from a unified standpoint. In Figure 3, log y * of low molecular weight imine salts was plotted against the cube root of concentration. It is seen that the cube-root rule also holds for these salts. The upper limit of concentration, at which the cube-root rule begins to fail, and the slope are summarized in Table IV, together with the data for polyethylenimine salt. It would be plausible that the upper limit goes down a t first with increasing charge
Table IV: The Constants of the Cube-Root Plot
ED(HC1)a DT( HCl)a TT(HCl)( TP(HC1)S PEI (HCl),
Upper limit, equiv/1000 g of water
Slope
0.12 0.064 0.030 0.027 ~0.504
-0.60 -0.86 -0.94 -1.10 -0.86
*
Y* =
Y*ZP
(5)
According to the MacInnes conventi~n,~ we have for potassium chloride Y* (=y**:Rci)
=
(=y*cl- = Y*K+)
~ * z g
(6)
Inspection of eq 3, 5, and 6 reveals that the discrepancy between y * and y*o becomes large as the valency of one ionic species (cationic one in the present case) inThe Journal of Physical Chemistry
1.
m3
Figure 3. Concentration dependence of the mean activity coefficient of hydrochlorides of ED, DT, TT, and T P (25’). Vertical bars represent an uncertainty of *lo%.
MEANACTIVITY COEFFICIENT OF POLYELECTROLYTES
number and then, after passing through a minimum, increases. Thk tendency may be accounted for as follows. As the charge number of the cation increases, the repulsive force between the ionic species becomes large enough to break the local regular structure, which would have been present for electrolytes having a small number of charges and would be responsible for the linearity in the cube root. With a further increase in the charge number, however, the macromolecular properties of the cation become important, resulting in the intermacroion linkage mentioned in the previous paper, so that the upper limit goes up. The magnitude of the slope, as is seen from Table IV, appears to become large
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a t first, as the charge number increases, and then flattens out for the low molecular weight imines. The monotonic increase would be due to increasing electrical potential energy between ions. The comparatively small magnitude of the slope of polyethylenimine is due to the large volume effect of the cation, as was mentioned in the previous paper.a
Acknowledgments. The authors gratefully appreciate Professor Ichiro Sakurada’s encouragement and useful comments. They also express their thanks to the Sumitomo Chemical Co., Osaka, for having kindly furnished the polyethylenimine.
Volume 70,Number 7 July 1966
