Nov., 1959
ELECTROPHORESIS AND SURFACE CHARGE
1809
ELECTROPHORESIS AND SURFACE CHARGE BY DIPTIK. CHATTORAJ~ AND HENRY B. BULL Biochemistry Department, State University of Iowa, Iowa City, Iowa Received Januarzl ,$g, IQdQ
The interfacial tension lowering produced by organic ions adsorbed at a paraffin oil-water interface and the electrophoretic mobility of isoelectric paraffin oil particles in the presence of organic ions have been studied and the charge density a t the interface calculated from the two methods. Agreement is found as the concentration of the organic ion approaches zero. The shift of the apparent pK values of weak acids adsorbed a t solid-paraffin surfaces as determined by electrophoresis have been compared with theory and satisfactory correspondence between theory and experiment is reported.
There has long been an interest in the distribution of counterions adjacent to a charged interface and the relation of this distribution to the potential of the interface. Recently Davies,2 Philips and Rideala and Philips and Haydon4 have considered this problem anew and have published results of their measurements of the potential change at oilwater and air-water interfaces produced by monolayers of ionic detergents. They used the vibrating plate technique for their potential measurements and, accordingly, the total potential change from one phase to the adjacent phase has been determined. They also measured the film pressures exerted by the organic ions and have discussed their results in terms of equations of state of the ionic monolayers. We have concerned ourselves with the potential of the electrical double layer as measured by electrophoresis (the zeta potential) and have thus confined the electrical effects to the water phase only. The interfacial tension lowerings produced by organic ions at oil-water interfaces have been compared under what we think are suitable conditions with the corresponding electrophoretic mobilities of emulsion particles of oil in the presence of solutions of the organic ions. We have also considered the shifts of the apparent pK values of weak acids a t paraffin-water interfaces and the relation of the observed shifts to the electrophoretic mobility of paraffin particles covered with the weak acids. Experimental The hydrocarbon oil was Nujol which was vigorously shaken with .40yq sodium hydroxide and then washed exhaustively with distilled water until the washings were neutral. The solid paraffin wax was from Fisher Scientific Co. It was melted in the and had a melting point of 68-70'. presence of 40% sodium hydroxide, vigorously shaken and washed, while melted, with distilled water until the washings were neutral. The stearic acid was from Eastman Organic Chemicals (lot no. 41) and used without further purification. The octadecylamine was from the Research Division of Armour and Co. (lot no. 4) and used without further purification. The sodium dodecyl sulfate was a special lot from Procter and Gamble Co. and was recrystallized from hot ethanol before use. Interfacial tensions of the Nujol-water systems were measured a t 25" by the drop-weight method. It was found that the time of formation of the drops had to be extended to 5. minutes to achieve constant values for the interfacial tensions. The corrections of Harkins and Brown6 have been applied. (1) Chemistry Department, Jadavpore University, Calcutta, India. (2) J. T. Davies, Proc. Roy. Soc. (London), AZO8, 224 (1951). (3) J. N. Philipa and E. Rideal, ibid., AZSZ, 149 (1955). (4) J. N. Philips and D. A. Haydon, Trans. Faradau Soc., 64, 698 (1958).
Electrophoretic measurements were conducted in a microelectrophoretic cell of flat design.6 Mobilities were observed a t room temperature and corrected to 25" by multiplying the measured mobilities by t8heratios of the viscosities of water at the temperature of the measurement to the viscosity of water a t 25'. The emulsions were manually prepared and the solid paraffin was melted and emulsified at an elevated temperature. The particles were in the neighborhood of 5 p in diameter which a t an ionic strength of 0.05, gives a xr value of about 1,000 ( K is the reciprocal Debye-Hiickel distance and r is the radius of the particle). This value of KT permits the use of the Smoluchowski equation for the calculation of the zeta potential from the electrophoretic mobility.
Results The electrophoretic mobilities of Nujol particles a t an ionic strength of 0.05 have been measured as a function of pH. The aqueous solutions consist of mixtures of sodium chloride and hydrochloric acid. The mobilities of such particles decrease almost linearly with decreasing pH and become zero a t a pH of 1.65. The pH of isoelectric Nujol particles has been adopted as our reference state for both interfacial tension measurements as well as for electrophoretic mobilities in the presence of organic ions. Figures 1 and 2 show plots of the electrophoretic mobgities of Nujol particles as functions of the molar concentrations of octadecylamine and of sodium dodecyl sulfate, respectively. Figures 3 and 4 are plots of the interfacial tension lowering in dynes per centimeter produced by the indicated molar concentrations of octadecylamine and of sodium dodecyl sulfate, respectively, a t the Nujolwater interface. Figures 5 and 6 show the results of the study of the mobilities of various kinds of particles as functions of the pH of the solutions. The pH was adjusted by the addition of the appropriate amounts of hydrochloric acid or of sodium hydroxide and enough sodium chloride added to yield an ionic strength of 0.05. Figure 5 has curves for a suspension of micelies of pure octadecylamine, for paraffin particles containing 0.265 g. of octadecylamine in 25 ml. of the melted paraffin and emulsified at pH 2.0, for Nujol emulsified in 1 X loF4molar octadecylamine at the pH of the experiment. Figure 6 gives plots for micelles of sodium stearate-stearic acid, for paraffin particles containing 0.10 g. of stearic acid dissolved in 25 ml. of melted paraffin and emulsified a t pH 10.5 and for Nujol containing 0.067 -g. stearic acid dissolved in 25 ml. of the oil.In a preliminary study of the mobilities of Nujol (5) W. D. Harkins and F. E. Brown, 3. Am. Chem. SOC.,41, 503 (1919). ( 6 ) H. B. Bull, ibid., 80, 190 (1958).
DIPTIK. CHATTORAJ AND HENRYB. BULL
Vol. 63
r
0 3 4 5 6 c x 106. Fig. 1.-Electrophoretic mobilities of Nujol emulsion particles as a function of the molar concentration of octadecylamine at p H 1.65 and at an ionic strength of 0.05 (NaC1 plus HC1) and a t 25". 0
2
1
q/, , ,
a
0 0
1
, ,
,
2
3 4 5 6 104. Fig. 2.-Electrophoretic mobilities of Nujol emulsion particles as a function of the molar concentration of sodium dodec 1 sulfate at pH 1.65 and at an ionic strength of 0.05 ( NaC plus HCl) and at 25".
cx
2
4
cx
8
6
10
12
104.
Fig. 3.-Interfacial tension lowering of Nujol-water system as a function of the molar concentration of octadecylamine at pH 1.65 and a t an ionic strength of 0.05 (NaC1 plus HC1) and at 25".
r
3 4 5 6 106. Fig. 4.-Interfacial tension lowering of Nujol-water system as a function of the molar concentration of sodium dodec 1 sulfate at pH 1.65 and at an ionic strength of 0.05 (NaCrplus HC1) and at 25". 0
1
2
cx
9
and of paraffin emulsions as a function of the concentrations of octadedylamine and of stearic acid it was found that the amounts of these compounds employed in the experiments described in the paragraph above were sufficient to give the highest mobilities a t a given pH. Discussion Since the radii of the emulsion particles are very much larger than is the thickness of the double layer, the electrical double layer of the non-conducting particles may be treated as a plane plate condenser and the Gouy equation can be used to calculate the electrostatic charge per unit area a t the oil-water interface. For a uni-univalent electrolyte the Gouy equation may be written' (7) H. A. Abramson, L. S. Moyer and M. H. Gorin, "Electrophoresis of Proteins," Reinhold Publ. Corp., New York, N. Y.,1942. See aq. 77, page 133 and substitute the value of Kappa.
c+It
5
w
2
6
4
8
10
PH. Fig. 5.-Electrophoretic mobilities as a function of p H at an ionic strength of 0.05 (NaC1 plus HC1 or NaOH) and at 25"; 0 , Nujol emulsion particles and octadecylamine; 0 , micelles of octadecylamine; 0 , solid paraffin particles and octadecylamine.
Nov., 1959
ELECTROPHORESIS AND SURFACECHARGE
where u is the electrostatic charge per unit area, K the Debye-Huckel reciprocal distances, D the dielectric constant, R the gas constant, E the elementary charge, K the Boltzmann constant and r is the potential of the electrical double layer as obtained from electrophoresis. Gorins applied a small ion correction to the electrophoretic mobilities of spherical particles. The physical basis for this correction lay in the fact that the small ions not being point charges cannot approach the larger colloidal particles closer than . . the radius of the small ion; this has the effect of 2 4 6 8 10 PH. increasing the radius of the colloidal particle by the Fig. 6.-Electrophoretic mobilities as a function of pH at radius of the ion. The Gorin correction has been an ionic strength of 0.05 (NaCl plus HCI or NaOH) and a t discussed by Overbeekg who, apparently, is of the 25'; 0,Nujol emulsion particles and stearic acid; 0 , opinion that the small ion correction is somewhat micelles of stearic acid-stearate; 0 , solid paraffin particles speculative in character. The correction factors and stearic acid. for the finite size of the small ions is
Where f is the ratio of the charge on the spherical particle with the small ion correction to that without the small ion correction, r is the radius of the spherical particle and a is the radius of the small ion. For very large values of Kr such as employed in the present research eq. 2 reduces to (3)
According to this conclusion, the right side of eq. 1 should be multiplied by f and this is the form of eq. 1 that Bateman and Zellner'O use in their calculation of the surface charge of red blood cells. At an ionic strength of 0.05 and at 25" and with a small ion radius of 2.5 X lo-* em., f has the value 0.845 and is, therefore, a significant cgrrection. The electrostatic charge a t the oil-water interface has been calculated from the electrophoretic mobilities of the oil droplets both with the use of uncorrected eq. 1 as well as with the aid of the correction factor for the finite size of the small ion (eq. 3). At pH 1.65 octadecylamine would exist entirely as the ammonium ion and sodium dodecyl sulfate would be completely dissociated. The affinity of these organic ions for the hydrocarbon-water interface must be very much larger than it is for the inorganic ions present. We have, accordingly, assumed that the number of moles of organic ions present at the interface can be calculated directly from the charge per unit area as revealed by eq. 1 and also by a combination of eq. 1and 3. The concentrations of the organic ions in solution have been divided by the corresponding number of adsorbed mole ions ( N e ) and this ratio plotted against the molar concentrations of the organic ion; this is a suitable procedure for linearizing a Langmuir adsorption plot. The best straight lines through the experimental points have been calculated by the method of least squares. ( 8 ) M. H. Gorin, J . Chem. Phys., 7 , 405 (1939). (9) J. Th. G. Overbeek, Advance8 in CoZloid Sci., 8 , 125 (1950).
(IO) J. B. Bateman and A. Zellner, Arch. Biochsm. Biophys., 60, 44 (1956).
I
0
I
2
I
c x
I
4 I 07.
I
-.-.-. I
6
-\
I
Fig. 7.-Ratio of organic ions per unit area from interfacial tension lowering ( N B )to the number calculated from electrophoresis ( N e )as a function of the molar concentration of sodium dodecyl sulfate (NaDS) and of octadecylamine (ODA) at pH 1.65, ionic strength 0.05 and a t 25". Broken lines include small ion corrections.
The interfacial tension lowerings in dynes per centimeter a t the Nujol-water interface have been divided by the corresponding molar concentrations of the organic ions and these ratios have been plotted against the molar concentrations and the least square line calculated. The resulting equations have been differentiated (interfacial tension in respect to concentration). These differentials have been substituted in the Gibbs adsorption equation thus permitting the calculation of the number of moles of adsorbed organic ions (Ne) per unit area as a function of the molar concentration of the organic ions. Combining the least square equations for N , and for N e , the ratio of N , to N e as a function of the concentration of octadecylamine and sodium dodecyl sulfate has been plotted in Fig. 7 both with and without the small ion correction. At zero concentration of octadecylamine the ratio N s / N e extrapolates to 1.053 i 0.081 without the small ion correction and to 1.244 i 0.081 with the small ion correction. The intercept at zero concentration
DIPTIK. CHATTORAJ AND HENRY B. BULL
1812 lo
r
VOl. 63
P K = P K i + - 0.4343el:
A
kT In analogy to the expression for the pH of a weak acid, we can write PH = PK log- N
ODA
+
(7)
where No is the number of mole ions per unit area of the surface of the particle at surface saturation and N is the number of mole ions for intermediate stages of ionization corresponding to the existing pH in solution. Substituting eq. 7 into eq. 6 and introducing numerical values at 25" PH
- log=
N
4
0 1 2 3 4 5 6 Fi 8 Apparent pK as a function of the electrophoretic mob%ti&-of solid paraffin particles with octadecylamine (ODA) and with stearate; ionic strength 0.05 and at 25".
of sodium dodecyl sulfate is 1.16 i 0.31 without the small ion correction and is 1.28 A 0.24 with the correction for the small ions. The results obtained with octadecylamine are much more satisfactory than are those with sodium dodecyl sulfate. The difficulty with the sodium dodecyl sulfate data arises from the erratic electrophoretic results (see Fig. 2). Whereas the interfacial data are certainly statistically consistent with the electrophoretic measurements with sodium dodecyl sulfate, the probable error associated with N , / N , at zero concentration is too large to inspire confidence. Agreement between the techniques is best supported by the octadecylamine data. Here the ratio N , / N , approaches unity fairly closely as the concentration approaches zero with a much smaller probable error and furthermore the ratio remains near unity over an appreciable concentration range of the octadecylamine. It is to be noted that the ratio N,/Ne is closer to unity both for sodium dodecyl sulfate and for octadecylamine if the surface charge is not corrected by including the small ion radii. Hartley and Roe" proposed an equation relating the apparent pK of a weak acid a t an interface to the electrophoretic mobility. This equation has been used and discussed on several occasions and the following simple derivation serves to illustrate the effect being considered. The total free energy of ionization of an acid can be separated into two parts such that AB' = AB'i
+ AFe
(4)
where AFi is the intrinsic free energy change and AFe is the contribution made by the electrostatic interaction. The electrostatic contribution to the free energy change is simply Ape = el:
(5)
where B is the elementary charge substituting eq. 5 into eq. 4, there results per molecule -kT In K = -kT In Ki + er or (11)
G. S. Hartley and J. W. Roe, Trans. Faraday
(l'd40).
Soc., 86, 101
=
#Ki
+ 0.217.5'
(8)
where U is the electrophoretic mobility in microns per second per volt per centimeter. The sign of the last term on the right of eq. 8 will depend on the sign of the electrostatic charge on the particle. For a negative particle the sign is positive whereas if the particle is positive the sign is negative (for the ionization of protons). It is to be noted from Figs. 5 and 6 that the mobility-pH curves for micelles of the organic ions as well as those for Nujol particles have pronounced inflections in them; it is probable that phase changes have occurred in the surface layers in response to changes in state of ionization. The solid paraffin particles, however, appear to exhibit mobility-pH curves resembling titration curves. Assuming that the largest mobility observed corresponds in the case of stearic acid to complete ionization of the stearic acid a t the interface and that the largest mobility for the octadecylamine-paraffin emulsion represents maximal formation of the ammonium ion, we have plotted in Fig. 8 the function pH - log [N/(JVo - N ) ] (the apparent pK) for stearic acid and pH log [ N / ( N o- N ) ] (the apparent pK) for octadecylamine against the electrophoretic mobilities. For convenience of plotting, we have neglected the sign of the electrophoretic mobility. By the nature of the function N / (No - N ) is very sensitive to the value of N owhen N is large and becomes very much less so as N decreases. Omitting the experimental points for large values of N , the least square line through the remaining experimental points give slopes of +0.292 10.017 and -0.224 i 0.041 for stearic acid and for octadecylamine, respectively. The slope according to theory should be 10.217. The intrinsic pK of stearic acid is 4.65 and that for octadecylamine is 9.41. It is clear that the equation of Hartley and Roe is in fairly close agreement with experiment. The maximum charge density for both octadecylamine and for stearate surfaces is surprisingly small and corresponds to an area of about 300 sq. A. per ion. The results described above both in respect to the calculation of the charge density and to the work of charging the electrical double layer as expressed by the equation of Hartley and Roe tend to confirm the reality of the conception of the zeta potential and indicate that the values of the coef-
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Nov., 1959
THERMODYNAMIC PROPERTIES OF SOLID BIBMUTH CHLORIDES
ficient of viscosity and of the dielectric constant in the electrical double layer are not greatly different from what they are in bulk solution.
1813
Acknowledgment.-Financial support for this research was provided by the National Science Foundation for which we wish t o express our thanks.
SOME THERMODYNAMIC PROPERTIES OF SOLID BISMUTH CHLORIDES’ BY A. J. DARNELL AND S. J . YOSIM Atomics International, A Division of North American Aviation, Inc., Canoga Park, California Received February 10, 1969
The thermodynamic stability of solid BiCl with respect to its disproportionation products, Bi( s) and BiC13(g),has been determined from 127 to 242‘. This was accomplished by measuring the pressure of BiCla gas over the solid subhalide and over pure BiC13 by the Knudsen technique. The pressures of BiCla from the sublimation and disproportionation reactions are, respectively, log P B ~ =c (-6200 ~ ~ f 30)/T 9.95 f 0.07 and log PBicla = (-6360 f 60)/T 9.29 f 0.14. These results show that the subchloride is barely stable with respect to its solid disproportionation products. At 298’K. the ma, AFO and AS0 of formation of BiCl(s) are, respectively, -30.4 kcal./mole, -24.0 kcal./mole and -18.0 e.u. New values for AFOtam, ASoformand So of BiCL(s) were calculated and are, respectively, -73.6 kcal./mole, -57.1 and 36.4 e.u.
+
Introduction The bismuth chlorides consist of bismuth trichloride, BiC13, and the subhalide, BiC1.2 The dichloride, BiCl2,*appears to be unstable by disproportionation4 while the existence of the tetrachlorides has not been confirmed. Bismuth trichloride is a colorless salt, melting a t 232’ and boiling at 447”. Bismuth subchloride is not as well known. It was first isolated by Eggink6 who determined the compound to have a chlorine to bismuth ratio of unity. At 320°, the solid subchloride disproportionates to farm two immiscible solutions, a black salt-rich phase with an ’ bismuth and 53 over-all composition of 47 mole % mole % BiC13,and a metal-rich phase consisting of 99 mole yobismuth and 1mole yoBiChS Some of the physical and chemical properties of BiCl have been described by Corbett.’ Recently there has been some question concerning the stability of.BiC1. Brewer4 suggested that if BiCl exists in the solid form, it is just barely stable toward disproportionation and, therefore, has about the same free energy of formation per equivalent as the trichloride. However, Sokolova,8who studied BiCl by X-ray techniques a t room temperature concluded that it was unstable. This was based on the fact that after the compound was formed, predominant lines, which were attributed to BiC1, became quite weak in 20 minutes. Corbett’ determined that BiCl was inert in dry air, and attributed Sokolova’s results t o excessive impurities. Therefore, it was of interest to determine the thermody(1) This paper was supported b y the Atomic Energy Commission. and has been presented in part before the Division of Physical Chemistry at the National Meeting of the ACS in April, 1958. (2) Solid bismuth subchloride is referred to, in this paper, a8 BiCI, although i t is possible that, like HgZC12, the cations of this subhalide are dimerized, or form higher polymers. (3) R. Schneider, A n n . Physik., 96, 130 (1855); R . Weber, ibid., 107, 596 (1859); P. Muir, J . Chem. SOC.,29, 144 (1876). (4) L. Brewer, “The Chemistry and Metallurgy of Miscellaneous Materiala-Thermodynamics,” L. L. Quill, Ed., N N E S IV-19B, McGraw-Hill Book Co., New York, N . Y., 1950. (5) B. G . Eggink, 2. p h y s i k . Chem., 64, 449 (1908). (6) 8. J. Yosim, A. J. Darnell, W. G. Gehman and 8 . W. Mayer, THIS JOURNAL, 63, 230 (1959). (7) J. D . Corbett, J . A m . Chem. SOC.,80, 4757 (1958). (8) M. A. Sokolovrs, G. G. Urazov and V . G . Kuznetsov. Akad. Nauk, X.S.S.R. Inst. Gen. Inorg. Chem., 1, 102 (1954).
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namic stability of BiCl with respect to its solid disproportionation products, Bi and BiCl3. An earlier experiment in this Laboratory showed that the gas phase over solid BiCl was essentially BiCla gas. Thus, by studying the sublimation pressure of BiC13 and the pressure of BiCla over solid BiC1, the stability of BiCl with respect to its solid disproportionation products could be determined. Therefore, a series of vaporization experiments was carried out to determine the thermodynamic stability of BiC1. I n addition to the stability of BiC1, the heat and entropy of sublimation of BiCla and the heat of fusion of BiC13 were obtained. The absolute entropy, the entropy and free energy of formation of solid BiC1S9 are based, in part, on the entropy of fusion of BiCla.lo Since, as will be shown later, this value may be in error, new values for So, AXoformand AF’form of BiCla were calculated from the sublimation data. Experimental Materials .-Reagent grade bismuth was melted under an inert atmosphere and filtered through Pyrex glass wool to remove bismuth oxide. Reagent grade bismuth trichloride was dried under a current of HC1 gas, distilled under HC1 and then under argon. The first and last eighths of the distillate were discarded. The salt had a melting.point of 232.2’. A bismuth and chlorine analysis of the salt showed a 66.2 f 0.1 weight yo bismuth as compared to 66.27% theoretical. Bismuth subchloride, free of BiCla, could not be synthesized simply by direct combination of BiC13with excess bismuth, as was also noted by Corbett.7 Therefore, the excess BiClt was removed by sublimation. The BiCl used in this investigation was prepared from a mixture originally consisting of 80 mole % bismuth and 20 mole % BiC4, heated in a seal:d Pyrex tube with continuous mixing for two days at 305 This process converted approximately 85y0 of the BiC4 into BiC1. Most of the unreacted bismuth “lumps” were mechanically removed. Since one of the products of the reaction studied was solid bismuth, it was not necessary to remove completely the unrescted bismuth. Pressure Measurements .-The vapor pressure of solid BiCIs at the temperatures of interest is in the range where the effusion technique is applicable. The experimental apparatus was similar to that used by Farber and Darnel1,ll in their
.
(9) F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine and 1. Jaffe, “Selected Values of Chemical Thermodynamic Properties,” National Bureau of Standarb, Circular 500, 1952. (IO) K. K. Kelley, IS.8. Bureau of Mines, Bulletin 393, Washington, D. C . (1936). (11) M . Frtrber and A. J. Darnell, THIS JOURNAL, 69, 156 (1955).
