1626
P. R. Holyk, J. Szymczak, and P. Ander
Electrical Conductivity of Aqueous Solutions of Polystyrenesulfonate Salts Containing Simple Salts Peter R. Holyk, Janet Srymczak, and Paul Ander' Department of Chemistry, Seton Hall University, South Orange, New Jersey 07079 (Received January 16, 1976) Publication costs assisted by Seton Hall University
Conductance measurements at 25 "C have been performed on aqueous solutions of the alkali metal salts and the ammonium salt of polystyrenesulfonate containing their respective chlorides. Specific conductances plots of these solutions are linear for the whole polyelectrolyte concentration range and are in the order LiCl < NaCl < KCl N NH&l < RbCl = CsC1. The results are discussed in terms of the rodlike model of Manning.
Using a rodlike model for the polyion which has counterions condensed onto,it above a critical charge density and uncondensed counterions and coions interacting with the polyion by Debye-Huckel interactions, Manning obtained expressions for electric conductance for the ionic species in salt-free and salt-containing solution^.^-^ Promising accord between the theoretical predictions for electric transport properties obtained from this model and the experimental results was obtained for salts of DNA,5 sodium carboxymethylcellulose,6 sodium alginate,7 sodium polygalacturonate,7 sodium p~lyacrylate,~ and salts of polystyrenesulfonate.8jg For salt-free solutions of monovalent salts of polystyrenesulfonate (PSS), Kwak and Hayes8 and Szymczak, Holyk, and Anderg found that Manning's conductance equation correctly predicted the dependence on the nature of the counterion, but overestimated the decrease in the conductance with increasing concentration. Kwak and Johnson6 reported excellent agreement between theory and experiment for the conductance of salt-free alkali metal ion salts of carboxymethylcellulose, a more rodlike polyelectrolyte than salts of polystyrenesulfonate. Here, we report the results of conductance measurements obtained at 25 "C for aqueous solutions of alkali metal ion salts and the ammonium salt of polystyrenesulfonate containing the respective chlorides. These results will be compared with those predicted from Manning's theory. Experimental Section The same LiPSS, NaPSS, KPSS, RbPSS, CsPSS, and NH4PSS samples used in a previous studyg were employed here. The acid form of the polystyrenesulfonate has a molecular weight of 70 000 and contains one sulfonate group per monomer unit. All solutions were prepared by weighing the dried polystyrenesulfonate salt in 50-ml class A type volumetric flasks and adding some aqueous salt solution to dissolve the polymer, followed by diluting to the mark with the salt solution. The determination of the specific conductances of these solutions were described earlier.g Results and Discussion The specific conductances K of solutions of LiPSS, NaPSS, KPSS, RbPSS, CsPSS, and NH4PSS were determined at 25 "C over a tenfold polymer concentration range from 0.0010 to 0.010 N in aqueous solutions of their respective simple salt chlorides of concentration 0.0010, 0.0010, and 0.010 N. Table I contains these results.1° For each counterion studied, a t a The Journal of Physical Chemistry, Vol. 80,No. 14, 1976
definite polymer concentration higher specific conductances were obtained for higher simple salt concentrations, as would be expected. Plots of the specific conductances of the solutions against the normality of the polyelectrolyte for the data in Table I were linear over the whole concentration range studied. Figure 1 shows the plot for 0.010 N simple salt; curves for 0.0010 and 0.000 10 N simple salt are similar except that the lines are closer together for these salt solutions. For each simple salt concentration, the trend observed for the specific conductances over the whole polyelectrolyte concentration range is LiCl < NaCl < KC1 E NH4C1< RbCl N CsCl. This is the same order found for the conductances of aqueous solutions of salt-free polystyrenesulfonate solutions? Also, this is the order for the specific conductances of polyelectrolytefree simple salt solutions, indicating the importance of the nature of the counterion on the conductance of polyelectrolyte solutions. A similar order has been reported for DNA in aqueous solutions of LiCl, NaCl, and KCl at 5 For each simple salt concentration the experimental results in Table I are well represented by K
- Ks = 1 0 - 3 ~ $ i ,
(1)
where K and K~ are the specific conductances of the polyelectrolyte-simple salt solution and of simple salt solution in the absence of polyelectrolyte, respectively, N , is the normality of the polyelectrolyte and A, is an empirical coefficient obtained from the slopes of plots of K vs. N,. Values of A , evaluated from linear regression plots of K vs. N , for the data given in Table I and their standard error are given in Table 11. Correlation coefficients of better than 0.996 were obtained for all linear regression plots except for 0.010 N CsCl where the correlation coefficient was 0.990, It is noted from Table I1 that for a given simple salt concentration the experimental values of A, are in the general order LiCl < NaCl < KC1 N NH4C1 < RbCl CsC1, the series found for their specific conductances for one salt concentration. Also, for a definite simple salt the experimental values of A, are approximately the same for the two lowest simple salt concentrations and slightly lower for the highest concentration. Most important is the additivity of the specific conductances of simple salt solutions and salt-free polyelectrolytes solutions suggested by the linearity obtained for all K vs. N , plots. T o compare the values of ApexPt with the values Apadd obtained from additivity, the leastsquare slopes of the lines constructed from the sum of the specific conductances of the salt-free polyelectrolyte solutionsg and the polyelectrolyte-free simple salt solutionsll were de-
1627
Electrical Conductivity of Aqueous Solutions
TABLE 11: Experimental and Theoretical Values of A,, for Several Simple Salt Solutions of Polystyrenesulfonate Salts at 25 "CQ Salt LiCl NaCl KCl RbCl CSCl
NHdCl
0.000 10 N A,exPt
32.6 f 0.9 38.4 f 0.4 45.6 f 0.0 46.0 f 1.6 47.4 f 0.2 46.0 f 0.1
0.0010 N
Apadd
A Ptheo
Apexpt
Apadd
Aptheo
ApexPt
32.8 f 0.1 38.7, f 0.0 46.6 f 0.1 48.6 f 0.6 49.6 f 0.2 47.2 f 0.2
39.6 43.0 49.8 51.0 51.0 49.8
32.9 f 0.3 38.2 f 0.5 45.9 f 0.6 48.6 f 0.4 49.6 f 1.3 45.8 f 0.1
32.8 f 0.1 38.7 f 0.0 46.6 f 39.2 48.6f0.6 49.6 f 0.2 47.2 f 0.2
29.0 32.4 39.2 40.2 40.3 39.2
29.0 f 0.8 33.5 4~ 0.5 40.3 f 0.4 40.6 f 2.0 43.9 f 2.6 42.1 f 0.4
0.010 N A ,add 32.8 f 0.1 38.7 f 0.0 46.6 k 0.1 48.6 f 0.6 49.6 f 0.2 47.2 f 0.2
Aptheo
18.2 21.4 28.1
28.9 29.0 28.1
A , has units of ohm-l cm2equiv-l.
I
A
m
0
* X
4
8
12
16
N, x IO3 Figure 1. The specific conductivity of polystyrenesulfonatesolutions as a function of polyelectrolyte normality in 0.010 N simple salt solutions of (m) LiCI, (0) NaCI, ( A ) KCI, (A)"&I, (0) RbCI, ( 0 )CsCI.
termined. These are listed in Table 11,where it is noted that the values of Apaddand ApexPt are in very good agreement for the 0.000 10 and 0.0010 N simple salt solutions and in fair agreement for the 0.010 N solutions. To evaluate A , from his cylindrical model of a polyelectrolyte, Manning determined the contributions of the specific conductances of the cation, anion, and polyion to the specific conductance giving
where A, is the equivalent conductance of the simple salt in the absence of polyelectrolyte, tA+(') is the transference number of the cation in the absence of polyelectrolyte, = e2/ckTb, a dimensionless polyelectrolyte charge density parameter which depends on the distance b between charges on the polyelectrolyte chain, where t is the dielectric constant of bulk solvent, e is the protonic charge, T i s the absolute temperature, and A, is the equivalent conductance of the polyion given by A, = (F/300)(tkT/3mp)IlnKa( (3) where F is the Faraday, 9 is the viscosity of bulk solvent, K is the Debye screening parameter for the simple salt solution in
the absence of polyelectrolyte, and a is the radius of the polyion. It was shown that the relaxation effect is not important inasmuch as it only adds a second-order term in N , to the specific conductance and that A , is interpreted as a measure of the interaction between the simple salt and the polyelectrolyte. Using literature values or values obtained from Onsager's equations for A, and tA+(S),ll = 2.85, and a = 8.0 X lo-* cm,12 values of A, and A , were calculated from eq 3 and 2, respectively. For 0.000 10, 0.0010, and 0.010 N simple salt solutions, the respective A, values are 93.6, 64.0, and 34.4 ohm-1 cm2 equiv-I. The calculated and experimental values for A , are listed in Table 11, where it is noted that, in general, good agreement is evident between the theoretical and experimental values for each simple salt for the two lowest concentrations of simple salt. At the highest simple salt concentration where coiling of the polyelectrolyte is most pronounced, the theory would be expected to be less applicable. The theory correctly predicts the order of the A, values with respect to the nature of the counterion. Since in eq 2, A, and do not depend on the nature of the monovalent counterion, the order of the interaction parameter A , with respect to the nature of the counterion was found to depend on both the order of the counterions with respect to their t ~ + values ( ~ ) and the order of conductances of the simple salt without polyelectrolyte present. The fairly good agreement between theory and experiment for the most dilute simple salt solutions suggests that the omission of the relaxation effect in calculating A, might be justified. However, it is felt by the authors that the concentration dependence of the equivalent conductance of polyelectrolyte solutions containing simple salt could be experimentally represented in a manner similar to that of simple electrolytes if the salt-polyelectrolyte interactions is taken into account appropriately. Also,.it is felt that the value of A , is not merely an interaction term, but is composed of the equivalent conductance of the polyelectrolyte with a small interaction term in it, Acknowledgment. The authors acknowledge the discussions with Dr. Marie Kowblansky. Supplementary Material Available: A listing of specific conductances of polystyrenesulfonate salts containing simple salts where the polyanion and the simple salt contain the same cation (Table I) (1 page). Ordering information is available on any current masthead page. References a n d Notes (1) G. S. Manning, J. Chem. Phys., 51, 934 (1969). (2) G. S. Manning, Biopolymers, 9, 1543 (1970). (3) D. I. Devore and G. S. Manning, J. Phys. Chern., 78, 1242 (1974).
The Journal of Physical Chemistry, Vol. 80, No. 14, 1976
1628
T. Ohmichi, H. Ohno, and K. Furukawa
(4) G. S. Manning, J. fhys. Chem., 79, 262 (1975). (5) P. D. Ross, R. L. Scruggs, and G. S. Manning, Biopolymers. 14,1991 (1975). (6) J. C. T. Kwak and A. J. Johnson, Can. J. chem., 53, 792 (1975). (7) F. M. Tuffile and P. Ander, Macromolecules,8, 789 (1975). (8) J. C. T. Kwak and R. C. Hayes, J. fhys. Chem., 79, 265 (1975).
(9) J. Szymczak, P. Holyk, and P. Ander, J. fhys. Chem., 79, 269 (1975). ( I O ) See paragraph at end of text regarding supplementary material. (1 1) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions”, 2d ed, Butterworths, England, 1970. (12) S.Oman and D. Dolar, 2.fhys. Chem. (Frankfortam Main), 58, 1 (1967)
Self-Diffusion of Fluorine in Molten Dilithium Tetrafluoroberyllate Toshihiko Ohmichi, Hideo Ohno,* and Kazuo Furukawa Molten Materials Laboratory,Japan Atomic Energy Research Institute, Tokai, lbaraki, Japan (Received April 26, 1976) Publication costs assisted by the Japan Atomic Energy Research lnstitute
The self-diffusion coefficients of fluorine in molten Li2BeF4 have been measured with the capillary reservoir technique, using lsF as a tracer. lsF was prepared in our laboratory. The results can be described with the Arrhenius equation D = 6.53 X lo3 exp[- (30.6 f 3.4) X 103/RT], where D is expressed in cm2 s-l, R in cal mol-l deg-l, and T i n K. An attempt was made to qualitatively explain the high activation energy of fluorine self-diffusion. Possible mechanisms involve the transport of fluorine resulting from the movement of fluoroberyllate anions, the exchange of fluorine between neighboring anions, and ion-pair diffusion.
Introduction A crystalline solid BeFz has a three-dimensional network structure made up of BeFd2- tetrahedra which shares corners, as in crystalline Si02. The anions F- are all bridged between two of the tetrahedrally coordinated central cations Be2+.Its compounds readily form glass, and are highly viscous above the melting point, suggesting that it still has a network structure. The binary molten mixture between BeFz and alkali metal fluoride melts shows a rapidly falling viscosity as the amount of alkali metal fluoride components is increased.l This indicates.the breakdown of the network-type structure of BeF2 melt with addition of alkali fluorides. Our interest centers on how the diffusion behavior of constituent ions, in particular the fluoride ion, in the molten LiF-BeFz system changes with composition of melts. In general, the study of the self-diffusion of fluorine in molten fluorides still remains an unexplored field. This is because, in addition to the difficulty due to corrosion of glass or ceramic vessels in handling fluoride melts, the only applicable isotope of fluorine is limited to lsF whose half-life is inconveniently short (109.7 min) as a tracer in diffusion experiments. Up to now, the only measurement of the self-diffusion coefficient of fluorine in molten fluoride was done by Harari, Lanteine, and Chemla2 in NaF-AlF3 melts by the capillary-reservoir technique using l*F.Though the fluorine self-diffusion coefficient can be measured by the nuclear magnetic resonance method, the application of this method to molten fluoride has not been found in the literature. The present article concerns the measurement of the selfdiffusion coefficient of fluorine in molten LiZBeF4 (congruent melting at 459.1 OC3) and its temperature dependence by the capillary reservoir technique using a tracer lsF. The reason for the selection of this salt composition is connected with the fact that the fluorine could preferably exist in the form of a BeF42- ion as a result of the dissociation reaction: LizBeF4 ~i The Journal of Physical Chemistry, Voi. 80, No. 14, 1976
+
2Li+ B e F P . Another motivation for study of a Li2BeF4 melt arises from its applicability to nuclear reactors: this is the solvent for fissile and fertile components in molten salt thermal breeder reactors and also possibly the blanket medium of D-T nuclear fusion reactors.
Experimental Section Preparation of Radioactive Tracer. Highly purified Li2CO3 powder (100 mg) which was sealed in an evacuated quartz ampoule was irradiated in the JRR-2 (Japan Research Reactor-2) a t a flux of greater than 1013thermal n/cm2.s for 20 min. The fluorine-18 is produced by the following reactions using thermal neutrons:
+ An = BH + ;He BH + g60= bn + i8F
!Li
The presence of lSF was confirmed from a half-life determination using the 0.51-MeV peak in the y spectrum of the irradiated Li2CO3 powder. After opening the irradiated ampoule, Li2C03 powder was treated with aqueous hydrofluoride in a platinum crucible to produce the labeled LiF deposit. This was followed by heating to dryness. Preparation of LideF4. The following chemicals were used in the present work: LiF prepared by Morita Kagaku Kogyo Co., analytical reagent grade; BeFz prepared by Rare Metallic Co., known impurities (in ppm): K Na, 600; Ca, 10; Si, 10; Al, 20; Cr, 30; Fe, 10; Ni, 10. A mixture of the two salts was melted in a nickel container and treated with a HF-Hz mixture at 700 OC and then sparged with He. Apparatus. The technique employed was the “diffusion from the capillary” method. The capillary which was 0.8 mm i.d. and 3-4 cm in length was made of Ni. Figure l a is the cell for filling the radioactive melt into a capillary. The cell which was placed in the furnace was composed of a fused silica tube
+
