Electrokinetic Potentials. X. The Effect of Particle Size on the

X. T H E EFFECT OF PARTICLE SIZE ON T H E POTENTIAL* ELECTROKINETIC POTENTIALS.

BY HENRY B. BULL AND ROSS AIKEN GORTNER

Introduction The present study was an outgrowth of an effort to obtain a standard material for the investigation of electrokinetic phenomena. Much of the work on electrokinetics has been done on ill-defined materials and it has been almost impossible for other workers to repeat each other's results with any degree of precision. It seemed desirable that the different methods for determining the electrokinetic potentials be checked against each other using the same standard material. Accordingly it was decided to use very pure quartz powder for this purpose. Investigation however showed that the situation was not simple because the electrokinetic potential on quartz particles depends upon particle size. Accordingly it was necessary to study the effect of particle size on the potential. Mooney' reports a decrease in cataphoretic mobility of red oil, benzyl chloride, iodobenzene, tribromhydrine and dimethylaniline measured in distilled water as the particle size is decreased. He found the mobility to start decreasing with the decreasing particle size at about 150p. Abramson's and L. MichaelisJ2work on the cataphoresis of protein-covered particles seems to indicate that with such particles the mobility is independent of the size. Experimental Five pounds of pure well-formed quartz crystals were groundt to pass a twenty-mesh sieve, digested with aqua regia for six hours, washed by decantation forty times with distilled water and ten times with condhctivity water, sucked dry on a Biichner funnel, and then heated at 80oOC. for 1 2 hours in a muffle furnace. This quartz was subsequently separated into nine portions by means of different mesh screens. The only electrolyte solutions used in this investigation were I .o X 10-4 N and 2.0 X ro4NNaC1. The NaCl was the purest obtainable. It was dried at 400' before weighing for solution. The water used in making the solution was twice distilled and had a conductance of about 1.5 X IO+ mhos. The volumetric apparatus waa calibrated. The solutions were used the same day they were made. From the Division of Agricultural Biochemistry of the University of Minnesota. Published 88 Journal Series No. 1022. Minnesota Agricultural Experiment Station. 1 J. Phys. Chem., 35, 331 (1931);Phys. Rev., ( 2 ) 23, 396 (1924). * J. Gen. Physiol., 12, 587 (1929). t Thanks are due Dr. C. C. Furnss of the Experimental Station, U. S. Bureau of Minea for grinding this quartz.

H E N R Y B. BULL AND ROSS AIKEN GORTNER

112

The streaming potential method was used for determining the electrokinetic potential on the quartz. The apparatus was the same as that described by Bull and Gortner.s No constant temperature bath was employed but all the work was done in a room the temperature of which was 24.5 0.5'. The conductivity of the salt solution in contact with 4 . 6 ~size quartz was determined in the streaming potential cell. The other conductivities reported are those of the solution in bulk. This is deemed permissible because it was found that the surface conductance of the quartz larger than 4 . 6 ~was small enough so that surface conductance could be neglected. The bulk conductivi-

*

.-e n

0

100

ZOO

E.M.E in Millivolts

300

1

FIQ.I Showing the relation between the streaming potential and the remure, as experimentally determined in our apparatus using a cellu7ose diaphragm and I .o X I 0 - 4 N NaC1, a8 the liquid waa being streamed thru the diaphragm

ties were determined using a conductivity cell described in detail by Washburn' for specific coqlluctances in the range between 10-6 and 104 mhos. The resistance was deterfnined with a Leeds and Northrup alternating current galvanometer. The cell constant was determined with both N/IO and N/roo KC1 using the Kahlrausch values. Head phones tuned to 1000 cycles vibrations were used to determine the cell constant. Since it was our original intention to obtain a standard material for electrokinetic work, and to check the streaming potential method against cataphoretic methods, using this material, we ground some of our quartz in an agate mortar until it remained in suspension when mixed with water. This quartz was packed in a diaphragm and its (--potential determined. The theory demands that there exist a linear relationship between the pressure applied on the liquid streaming thru the diaphragm and the electrical potential observed across the diaphragm as is shown in Fig. I for cellulose and an aqueous solution of 1.0x IO^ N NaCI. J. Phys. Chem., 35, 309 (1931). J. Am. Chem. SOC., 38, 2431 (1916)

ELECTROKINETIC POTENTIALS

113

To our surprise we found no such relationship with our quartz but instead, as is shown in Table I and Fig. 2, where the pressure is the abscissa and the streaming potential is the ordinate, we found a decreasing slope as we increased the pressure. We found the same behavior to hold with 2.0 X IO+ N NaCl and in later work used this concentration. Much time was spent in trying to determine the cause of this deviation from a straight line. I t is one of the fundamental requirements in the derivation of the streaming potential equation for calculating the zeta potential that Poiseuille’s law for the flow of liquids thru capillaries be obeyed. It occurred to us that our difficulty might lie in the failure of this law of flow a t higher pressures. This law states that the volume of liquid passing any cross section of a capillary in unit time is

v = -7rr4 P1-P2 89

1

where 7 =coefficient of viscosity of the liquid flowing r = radius of capillary P1- P2 = difference in pressure between the two ends of the capillary 1=length of capillary.

FIG 2 Showing relation between pressure and the streaming potential with a heterogeneous mixture of quarts particles (sizes between . 5 p and 36p) and 1.0 x 10-4

N NaCl

TABLE I Showing the Relationship between the Streaming Potential and Hydrostatic Pressure for a Quartz Diaphragm through which a 1.0 X 10-4N Solution of NaCl was being streamed, the Quartz Particles being Non-uniform in Size. Presaure (P) Streaming Potential cm. H g (H) mv. 1.0

2.4

5.1 8.7 18.8 33.7 43.9 57.0

19.5 40.5 77.5 124.0

71.7

251.0 423 .o 536.0 670.5 821.0

82.1

928.0

H/P

19.50 16.88 15.20 14.25 13.35 12.55 12.21 11.76 11.45 11.30

Pressure ( P ) cm. Hg

Streaming Potentid (H) mv.

H/P

With decrectsing pressure 77.5 885.0 11.42 66. I 767.5 11.61 49.7 593.0 11.93 37.2 463.0 12.45 12.94 23.5 304.0 15.1 208.0 13.78 9.7 141.5 14.59 5.5 86.5 15.73 3.5 61.5 =747 1.2 25.5 21.25

H E N R Y E. BULL AND ROSS AIKEN GORTNER

1 I4

One test of this law is to determine the relation between the rate of flow of a liquid thru a capillary as a function of the pressure applied. Poiseuille’s law demands that this function be linear and that the volume of the liquid in unit time per unit pressure be a constant. Accordingly the rate of flow thru a quartz diaphragm at different pressures was studied. The quartz diaphragm used was prepared from the same sample of quartz as that employed to obtain the data for Table I. The results shown in Table I1 were obtained. The data in Table I1 show that there is not a sufficient deviation from Poiseuille’s law to explain the lack of linearality between the pressure and the streaming potential .

TABLE I1 Testing Poiseuille’s Law of Flow thru a Quartz Diaphragm made of a Heterogeneous Mixture of Quartz Particles (sizes between .5p and 36p in diameter) with an Aqueous Solution of 2.0 X 104 N NaCl. V/P

Pressure (P) cm. Hg

Rate of Flow (V) grams of solution per nun

V/P

.350 ,786 I . 190

.0437 ,0457

58.4 67.0

2.709 3.126

,0464 ,0466

.0452

1.750

.0468 .046I

75.9 82.3

3.462 3.950

,0456 ,0480

Presaure Rate of Flow (V) (P) cm. grams of solution per min Hg

8.0 17.2

26.3 37.4 48.0

2.260

I t was then decided to investigate the effect of particle size on the streaming potential. To this end that portion of the quartz powder which passed a 2 0 mesh sieve was further separated by sieving into nine portions. The particle size was assumed to be the arithmetic mean between the sieve size it was passed thru and that upon which it was retained. The three smallest sizes, i.e., 4.59p,31.1p, and 74.9Ip were determined by measurement of a number (75-100) of particles with a calibrated microscope and then taking the average of these measurements. The 4 . 5 9 size ~ was packed in a diaphragm 1.1 cm. long and 2 cm.in diameter. The larger sized samples were packed in diaphragms 9.5 cm. long and 2 cm. in diameter. With this arrangement a convenient rate of liquid flow was obtained. Perforated gold electrodes were used a t each end of the diaphragm. With the smaller quartz (98p and below) a thin layer (about I mm.) of 214p quartz was placed at each end of the diaphragm to keep the smaller quarts from washing thru the perforations in the electrodes. The diaphragms were washed with a t least 500 cc. of the solution and were then allowed to remain 1 2 hours in contact with a portion of the electrolyte solution t o be used. This portion was replaced by fresh solution before a measurement was attempted. The values reported and used in the graph of the results are the average of at least six or more readings.

115


Results The results of the electrokinetic studies on the nine different particle sizes of the quartz are given in Table I11 thru Table XI, summarized in Table XI1 and graphed in Fig. 3. TABLEI11 2

X

Preas,me Streaming cm. in Potential in Hg (P) millivolts (H) 2.03 6 1 .o

0.23 1.76 2.70 3.49

10-4

N NaCl and 630p Quartz Pressure in cm. Hg (P)

H/P

80.0

30.06 30.74 28.42 29.65

90.0

25.70

7.0 50.0

0.98 0.57 I .06 0.78

Streaming Potential in millivolts (H)

H/P

28.56 31.82 31. I4 20.0 25.27 Average H/P = 29.04 28.0 18.0 33 .o

TABLEIV 2

Pressure in cm. of Hg (P)

x


0.71

20.0.

1.33 .80

40.0

10-4

N

NaCl and 33op Quartz

H/P

28.29 30.06 31. I4

25.0



I.23 0.90

35.0 25.0

H/P

28.42 27.61

Average H/P = 29.IO TABLEV

2

X IO-^



2.57 2.54 2.71 3.01

80.0

N NaCI and

H/P

31 .OI 29.51 29.51 29.92

75.0

80.0 90.0

214p Quartz Preasure Streaming Potential in in cm. of millivolts (H) Hg (P)

2.90 2.36 3.27

H/P

31.OI 29.65 100.0 30.46 Average H/P = 30. I 5 90.0 70.0

TABLEV I 2

X IO-^



2.93 3 .OB 3.28

90 90

95

N

NaCl and 163p Quartz

H/P


30.76 29.21 28.97

3.31 2.81 2.84


H/P

30.23 80 28.49 80 28.19 Average H/P = 29.3 I IO0

I 16

HENRY B. BULL AND ROSS AIKEN GORTNER

TABLEVI1 X IO-^ NaCl'and 128p Quartz

2

Pressure in cm. of Hg (P) 1.11

2.72

4.61 11.4 20.9


H/P

27.92

31.0 74.0 128.0 293 .o 544.0

27.21

27.77

25.70 26.03


Streaming Potential in millivolts ( H )

I.29 3.57 9.9 17.6 22.9

34.0 99.0 254.0 453 .o 598.0

H/P

26.36 2; '73 25.66 25.74 26.11 Average H/P = 26.62

TABLE VI11 2

Prwure in cm. of Hg (P)

3.86 9.1 21.9 31.4 1.53 4.08 10.6

X IO-^

Streaming Potel-tial in millivolts (H)

104.0 223 .o 545.0

N NaCl and 98p Quartz Pressure in cm. of Hg (P)

H/P

26.94 24.51 24.89 24.68 26.14

775.0 40.0 103 .o

25.25

250.0

23.58


19.5 34.2 I .61 3.57 8.6 18.7 34.0

H/P

23.85 24.27 23.60

465.0 830.0 38.0 84.0 188.0 423 . o 780.0

Average H/P

23.53 21.86 22.62 =

22.94 24.19

TABLE IX 2

x

Preasure in cm. of Hg (P)


1.90 3.97 9.60 18.70 28.40 1.42

40.0 89.0

IO-(

N NaCl and 74.9~Quartz H/P

21.05

431 .O 665.0

22.42 21.88 23.05 23.42

35.5

25.00

210.0



4.06 9.60 19.50 27.60 37.30

97,o 216.0 453.0 635.0 850.0

H/P

23.89 22.50

23 ' 23 23.01

22.79 Average H/P = 22.93


117

TABLE X

x

2

Pressure in cm. of Hg (PI


1.41 3.75 9.20 19.80 29.80 40.40

30.0 78.0 I77 .o

51. IO

1057.0

1310.0

N NaCl and 3 1 . 1 ~Quartz Pressure in em. of Hg (P)

H/P

21.28 20.80 19.24 19.80 20.27 20.45 20.68 20.86 22.56 20.42 18.85 19.44

392.0 604.0 826.0

62.80 1.33 3.77 9.60 19.60

10-4

30.0

77.0 I81 .o 381.o

29.70 40.30 52.50

52. IO

4.50 9.00 20.10

29.00 40.IO 50.60 59.80


H/P

20.03 20.30 20.90 21.09 18.89 IS.50 1.9.30 19.55 19.75 19.88 19.92 Average H /P = 20.12 595.0 818.0 I097 .O 1099.0 85.0 166.5 388.0 567.0 792 .o 1006.0 1191.0

TABLE XI 2

Pressure in cm. of Hg (PI

X


23.0 65.0 116.0 199.0

3.47 11.60 18.40 31.40

IO-(

N NaCl and 4.59 p Quartz

H/P

6.63 5.60 6.30 6.34

Pressure in crn. of Hg (P)

Streamink Potential in millivolts (H)

47.20 62.50 73.50

302.5 392.0 456.0

H/P

6.41 6.27 6.20 Arerage H/P = 6.25

TABLE XLI Summary of Electrokinetic Potentiah at a Quartz-Aqueous2.0 X Interface. Showing the Effect of Particle Size. Particle diameter in

630 330 214 163 I28 68 74.9 31.1 4.59

Kn

p

log

p

2.799 2 * 519 2.330 2.212 2.107

1.991 1.875 1.493 0.662

x

mhos

Ha/P

29.04

28.90

29. IO

28.93

30.I 5 29.31 26.62 24.I9 22.93

28.90 28.90 28.90 28.90 28.90 28.90 35.81

83.93 84.IO 87.I3 84.71 76.93 69.91 66.27

6.25

N NaCl

I@

H/P

20. I2

104

58.15

22.38

logHim/P

1.924 1.925 1.940 I .928 I. 886 1.845 1.821 1.765 1.350

I 18

HENRY B. BULL AND ROSS AIKEN GORTNER

Discussion It is our belief that the deviation from a linear relation between pressure and the streaming potential is due to the fact that the

Electrokinetic Potentials. X. The Effect of Particle Size on the

Recommend Documents