Tsuji, Fukuju

Ueda, Shizuo

Watanabe, Akira

Yasuda, Tokuro

Kyoto University Research Information Repository

TitleStudy on Surface Electricity. (XXI) : On the Structure ofInterfacial Double Layer Considered from the Behaviour of itsCapacitanceAuthor(s)Watanabe, Akira; Tsuji, Fukuju; Yasuda, Tokuro; Ueda,ShizuoCitationBulletin of the Institute for Chemical Research, KyotoUniversity (1956), 34(1-2): 65-73Issue Date1956-03-30URL http://hdl.handle.net/2433/75542RightType Departmental Bulletin PaperTextversionpublisherKyoto University          Study on Surface Electricity.  (XXI)*       On the Structure of Interfacial Double Layer Considered               from the Behaviour of its Capacitance               Akira WATANABE, Fukuju TsUJi, Tokuro YASUDA                            and Shizuo UEDA**                              (Tachi Laboratory)                           Received February 22, 1956     The differential double layer capacities at mercury-0.1 N salt solution interfaces are meas- ured by resonance method using dropping mercury electrodes, and the results are discussed  from the viewpoint of double layer structure.     The capacity behaviours in this case have the same features as in the case of 1 N solu- tions, although they are reduced in magnitudes in all range of polarization. Tendencies of  capacity minima near electrocapillary maximum potentials begin to appear in this case. These  two results are quite in accord with the theory of double layer structure, because the diffuse  double layer capacity, which is in series to the non-diffuse double layer capacity, has the very  property and begins to predominate the whole capacity value as the solution becomes more  dilute.      The humps near electrocapillary maxima become less evident, when the solutions are more  dilute, which suggests that these phenomena of capacity humps are attributed to the property  in the non-diffuse double layer. Contrary to apparent presumption, the capacity values at humps  increase with anionic radii of salts in solutions. These are ascribed to the ionic polarizability  at interfaces.    We have so far measured the differential double layer capacities at various mercury-salt solution interfaces by our resonance method, and many interesting features of their behaviours have been identified. In the foregoing papers were described details of the experimental deviceso and the results of measurements with various 1 N salt solutions as the liquid phases of interfaces2 . In view of the ultimate aim of the present authors, however, extension of our measuring method to more dilute salt solutions is indispensable for clarifying the structure of double layer. With this improvement the behaviours of the differential double layer capacities of mercury-0.1 N salt solution interfaces were determined and their behaviours were discussed from the viewpoint of double layer structure in connection with those at 1 N salt solutions. °k Read before the Semi-annual Meeting of this InstihRe, held June 11, 1955.                               ( (35 )          Akira  WATANABE, Fukuju Tsun, Tokuro YASUDA and Shizuo UEDA 1. EXPERIMENTAL    As the concentration of the solution phase of the interface becomes less, the resis-tivity of the circuit becomes greater and its Q-value smaller. Although the resistance of solution was taken into account in the preceding measurements by using substitution method, we shall discuss here the influence of the resistivity on the resonance phenome-non in detail.    (i) Resonance phenomenon of the circuit including resistivity    The principal resonance circuit used in our measurements is shown in Fig. 1, ----------o  P c,L DMEEc                               R,s R                                Fig. 1. Resonancecircuit.where DME is the dropping mercury electrode, P a potentiometer by which the bias voltage --co is applied to the mercury cathode, L the load inductance, R a small re-sistance to which an alternating voltage E is fed from a CR-valve oscillator and Rs and CS are standard resistance and capacitance boxes used to calibrate the resistance and capacitance values of DME by substitution method.    The Q-value of this circuit, defined as the ratio of the resonance voltage E, and input voltage E, is given by                  Ee__ j(-1/c0C)+R_o  Lx+M             Q—Ej( -1/wC)+(Rt+jwL)-Px+S(1) where L=j, M=Ro, 1'=j, S=Rt+jc,)L and x= —1/(0C.(2) Here the small inner resistance of potentiometer is neglected. Because the interfacial capacitance becomes larger with the growth of mercury drop, we can consider x the variable of this equation. Now, when we put                   L•MP•S _1 (1112 S2v                                        a—.-I.__..            _ P'—                                   2a L P2),    * C and Ro are double layer capacitance and solutionresistance, respectively." Rc=-12 1-R„                              ( 66 )                        Study on Surface Electricity. (XXI)  b=               P.-r,c =,2PSe+pa(3)" we can obtain the condition of maximum Q-value as follows : In case a<0, whenx= -V c -, ,(4)              Q7nax=P.Jl-Vca b.(5) The calculation is simple, giving : When                       1 CJ                                           4R,2               c„C211+• 1+20zL2)(6)                Qniax=2R(1+.4/2,2(7)                  ccJL. These two equations give the resonance conditions of our experimental circuit, which tend to the ordinary resonance conditions as the total resistance R2 becomes zero.    (ii) Experimental method    The method of experiments is the same in principle as that in the foregoing pa-pers,1,2' except that the measuring frequencies are chosen which are far lower, i. e. from 15 to 60 cps, and that the frequency is changed to obtain its value which satis-fies the resonance conditions at the last moment of the drop growth, contrary to the foregoing experiments where the load inductance was changed.    (iii) Results    The differential capacity values of double layer at mercury-0.1 N salt solution in-terfaces, obtained in this experiment, are summarized in Table 1. For brevity, detail-ed experimental conditions are not shown, the outlines of which are as follows: cp=0----2.0 V, W=2.5-4.8 mg, A=0.016—.0.025 cm2, T=2-.4.5 sec, f =15-..60 cps, E=7.4 mV (AC), L=4 h (20012) or 2 h (11012), C=2.11-0.25 PF.                            2. DISCUSSION   The capacity behaviours in the case of 0.1 N solutions have the same features as in the case of 1 N solutions, as were given in the preceding paper in detail.2' Here,   * The letters without dots show the moduli of each complex quantities, and the symbol     shows the scalar product of the two complex quantities.                              ( 67 )                    Akira  WATANABE, Fukuju TSUJ[, Tokuro YASIJDA and Shizuo UEDA                    Table 1. Differential double layer capacities at mercury-0.1N salt solutions. µF/cxn2 ~alts                 KI KBr KCI KF KIO3 NaIO3 KBrO3 NaBrO3 KC1O3 KNO3 co(V)        033.3447.27 56.44 43.58 28.16 -0.151.07 30.6535.38 41.68 29.89 22.60 -0.2 61.87 34.61 28.74 67.13 30.45 31.70 25.60 19.10 -0.3 71.44 46.40 34.36 25.33 51.22 45.54 26.32 29.08 22.49 19.62 -0.4 60.89 45.05 35.83 22.27 39.22 37.38 26.92 28.39 22.56 21.28 -0.5 39.20 35.16 33.11 20.56 33.52 35.19 26.52 27.56 22.97 23.94 -0.6 23.59 24.02 25.41 18.99 27.63 28.59 24.65 26.06 24.41 25.90 -0.7 16.56 18.11 19.86 17.90 22.92 23.15 24.20 23.43 24.25 24.97 -0.8 14.56 15.61 18.39 17.57 20.50 20.09 20.96 20.13 23.00 21.21 -0.9 14.30 14.51 16.38 16.85 19.68 17.72 18.21 17.86 19.69 18.30 -1.0 14.68 13.87 15.84 15.61 17.30 16.71 16.29 16.81 17.33 17.58 -1.1 15.21 14.16 15.57 14.52 15.90 15.59 15. 15 15.69 15.76 14.82 -1.2 15.99 14.45 14.52 14.72 14.88 14.72 14.51 14.02 14.22 14.20 -1.3 17.00 14.59 14.88 14.06 14.0614.00 14.35 14.15 13.96 --1.4 17.87 16.08 14.35 14.5013.29 14.74 13.66 13.48 -1.5 18.94 16.25 14.73 14.8813.53 14.19 14.24 14.15 -1.6 22.63 16.85 15.84 15.3614.25 14.19 14.55 14.17 -1.718.42 16.45 15.4214.60 15.43 15.27 14.79 -1.819.95 17.63 16.5916.70 15.85 15.21 -1.919.03 17.5315.92 15.77 -2.020.60 19.4917.89 15.93 co„tax(V) 0.440 0.410 0.581 0.610 0.860 0.895 0.720 0.740 0.760 0.700       1°C 21 21 22 22 22 22 22 24 22 22 C0-E curves are shown of halide (Fig. 2) and oxy-anion (Fig. 3) solutions, separately.         We shall discuss here also the results by dividing the polarization of mercury electrode         in three regions, i. e. anodic (E>Ea), cathodic (E<0) and zero regions (E=0).2'            (i) Anodic region             The order of the strength of anionic adsorption in this region is shown to be the          same as the strength of the bonds between mercury and corresponding anion in this 75 -                        KB r°                  -KCl                       50 -               U   -KF\)7_\,\„,*                             25 -                                                                          I I I 1 I I                  0.5 0-0.5 -1.0 -1.5                                       E (v)                                             Fig. 2. 0.1N K-halides.                                      ( 68 )                        Study on Surface Electricity. (XXI)           75  K103         50 — KBr0          - KC103       Uc _ ~~1          —KNO3'" -._._~ _ __ e..-           0i , l I, , ,  1 i „1 , , , , I , , i         1.00.50-0.5-1.0                             E (v)                         Fig. 3. 0.1N K-halogenates and -nitrate. case also. This is evident from Figs. 2 and 3, where, for the sake of simplicity, halide and halogenate anions are compared separately. The solubilities of mercurous salts of halogenate are known to be in the order of, IQ,'> BrO33'> C103'.    (ii) Cathodic region    The capacity values in this region have flat minima of about 14-45 ,uF/cm2. This is the same in character as in the case of 1 N solutions, but a little smaller in magnitude than in the latter case, which shall be explained later, where the structure of double layer is discussed.    (iii) Zero region    The characteristic feature in this region is the well-defined hump in capacity-bias voltage curve, although, in the case of iodide and fluoride, it is more or less masked and becomes less well-defined in the more dilute solutions, as is shown in Fig. 4.    This phenomenon of hump was shown in the preceding paper2' to be intimately connected with the dielectric properties of the corresponding anion, because the capacity values at humps Ch are arranged in the order of anionic species, which is the same as the deformabilities of the respective anions.    Now, we shall discuss them by applying Grahame's model of the double layer structure" and making use of the equations derived by Devanathan°'.    The locus of specifically adsorbed (dehydrated) anions is called here "H-plane" and that of the hydrated adsorbed cations (or anions) "G-plane", outward of which stretches the Gouy diffuse double layer. The geometrical surface of mercury is called "M -plane", and the space between M- and H-planes constitutes the so-called non-diffuse layer (Fig. 5). Fig. 6 shows the schematic potential behaviour in the interfacial double layer, where O's are the Grahame's "cavity potential" of the individual planes with reference to that of the bulk of solution phase. We shall designate the integral                             ( 69 )          Akira WATANABE, Fukuji  TsU]r, Tokuro YASUDA and Shizuo UEDA       -1N KBr = K V 50 - —1N      .1N1N 25 -        -0 0               10  l i i ~: l i, I i: i: 1 i i  50- KF — 1N KC1 - 1N 25-— •1N - .1N  0 — 0 o 40- KC103 — KNO3 _ 1N — 1N 25~ 1N 0~ —1N 0 10---------------------------------------------------------                     • — KI 03            40 _ KB103 •*1 Na 103             - NaBr03 .,A:,.1N 25-— 1.0 0.5 0 -0.5 -1.0                                E (v)               ``Fig. 4.                            /--Non -diffuse ioye1 Diffuse layer ---_-'""                                        So1ution                 0 - -plane "- 111.1.,e                  Fig. 5. Double layer model. Small circles without                          any sign stand for water molecules. capacity between M- and H-plane KAI- r with dielectric constant EM-H, that between H- and G-plane Km-0 with Eli-o, and the differential capacity of the Gouy layer CG with Eo, respectively.* * Devanathan did not discriminate between Ear-H and Ell-s.                              ( 70 )                         Study on Surface Electricity. (XXI)                       0xi                                    r-1 ------ KM-N  C4                          7M '                      Fig. 6. Potential course in  the double layer.    According to Devanathan, the total differential capacity of this double layer system is given by --- 1                                        dq                                                                  G C Km-a+\Ka-G+CG)dq)>(8) where q and q0 are the charge densities on the mercury surface and of the diffuse double layer, respectively. The integral and differential capacities are given by the electrostatics and the theory of Gouy, as Kh:-ts = E~t-a/4lrxl,(9) KG-G= fr-G/(4n(x2-xi)),(10) and              1/CG =d0G/dqG =~zeA)101+4A2)A‘(11) where                            A2 = EG k Tn/27r, and in the case of 1-1 salts, CG=19.46 (137.8 c+qo2).(11')    It is evident from eq. (8) that the total capacity becomes less, as the concentration of solution becomes smaller, because the diffuse layer capacity thereby becomes smaller and no longer negligible. Although we cannot say with certainty that qG is zero at electrocapillary maxium (we can only say q=0), we can presume in general that the zero point of qG may lie near this point. At this point CG must have minimum value, as is clear from eq. (11) or (11'), at constant concentration.    This tendency of lowering of the capacity is practically noticeable in the cases of nitrate, fluoride and halogenate solutions of 0.1 N concentration. (Fig. 4) In the cases of 1 N solutions it is masked by the non-diffuse part of the double layer, because CG becomes too large to be effective on the total capacity, cf. eq. (8).    It is noticed by comparing the capacity behaviours at 1 N and 0.1 N solutions in Fig. 4, that the capacity humps are more prominent in the former cases, which suggests that these are due to the behaviours in the non-diffuse part of the double layers. The capacity in this part would be inversely proportional to the ionic radius, as is evident ( 71 )          Akira WATANABE, Fukuju TSUJI, Tokuro YASUDA and Shizuo  UEDA        Table 2. Humps of differential double layer capacities and anionic properties.                                                K-salts. r)c)c) C,`Ionic radius Interatomic (1 F/cm2)distanceIonic shape            1 N 0.1 N r (A)r13 (A) I 75 652.16    Br 60.5 451.95                                                                       Monatomic   Cl 52 371.81 F 32 301.36 IO333.51.83 BrO3271.67Pyramidal C1O3 30 22.51.48   NO3 33.5 26.51.22Planar SO4 481.51Tetrahedral 1.9 1. 8 - 01.6 - INIBr          F p 1.5 -Cl 1.4 --------------------------------------------- 0.15 0.20 0.25 0.30 0.35                              log r(A)                                         Fig. 7.from eq. (9), if the dielectric constants were the same in all solutions. However, this is not the case in our results, as is shown in Table 2. Contrary to our presumption, the larger the ionic radius, the larger is the value of C,,. Fig. 7 shows how C,, depends upon r in the case of halogens, all of which have the same ionic shapes. Plots of log C,, at 1N solutions give a straight line with a slope of 1.7. This slope is, of course, ascribed to the different polarizabilities of the anions, which are nearly proportional to ionic volumes.    We need not mention that the non-linearity in the case of 0.1 N solutions is the more prominent influence of diffuse double layer capacity CG in the more dilute solu-tions.                               ( 72 )                        Study on Surface Electricity. (XXI)           1.7+1N                                         804  1.6 -NO3Jo,                ~,uC10,703        U1.5      toTO ° 1.4 - 1.3 -------------------------------------------------- 0.10 0.15 0.20 0.25 0.30                                  log r,2(A)                                        Fig. 8.    Halogenates seem to have the same tendency with almost the same slope, as is shown in Fig. 8, where log C,, is plotted against log r12, i.e. logarithm of interatomic distance of each ion. Although we shall presumably obtain linearity at 1N solutions, we cannot perform the experiment because of the limited solubilities of these salts.    In the same figure are plotted also log C,, values of other ions. It is not unex-pected that they do not come on the halogenate line, because sulfate is a 2-valent ion and nitrate a plane triangular shaped ion, both of which are supposed to enhance the inner layer capacity values.    In view of the fact that this capacity hump is chiefly ascribed to the polarizability of the anionic species present at H-plane, we can assume that the phenomenon of hump is connected with the dielectric saturation of the adsorbed anions. That is, as the electrical field in the double layer is generally very large, the polarizabilities of the adsorbed anions in the region apart from zero potential have saturated values. How-ever, in zero region, as the field strength becomes less, the polarizabilities tend to have more or less their normal values and the capacity values become larger. In other words, the capacity hump indicates the minimum of dielectric saturation at this poten-tial. As this conclusion is intimately connected with the absolute potential, this is but a bold hypothesis, which must be examined from another evidence other than thermo-dynamic means.    The authors express their gratitude to Prof. I. Tachi for his continued interest and encouragement.                            REFERENCES  (1) A. Watanabe, F. Tsuji and S. Ueda, This Bulletin, 33, 91 (1955).  (2) A. Watanabe, F. Tsuji and S. Ueda, ibid., 34, 1 (1956).  (3) A. Watanabe, F. Tsuji, K. Nishizawa and S. Ueda, ibid., 32, 62 (1954).  (4) D. C. Grahame, Chem. Rev., 41, 441 (1947).  (5) M. A. V. Devanathan, Trans. Faraday Soc., 50, 373 (1954).  (6) L. Pauling, "Nature of Chemical Bond", Cornell Univ. Press, (1939). ( 73 )

Study on Surface Electricity. (XXI) : On the Structure of Interfacial Double Layer Considered from the Behaviour of its Capacitance

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Study on Surface Electricity. (XXI) : On the Structure of Interfacial Double Layer Considered from the Behaviour of its Capacitance

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