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MICELLE THEORY OF COLLOIDAL ELECTROLYTES 325

solute value of each is a maximum. As the concentration of electrolytes
in the solution is increased, the potential differences between the solu-
tion and the collagen phase, and between the solution and the layer
round the tannin, will decrease, thereby lessening the rate of tanning;
but if the concentration of electrolytes is increased sufficiently, the tannin
must precipitate alone and the collagen shrink to a hard mass. In
alkaline solutions both colloids have negative charges, and consequently
will not combine, whilst in the presence of lime the negatively charged
tannin particles are neutralised by calcium ions and a calcium compound
of the tannin precipitates. This reasoning clears up many points con-
cerning the function of acids in tan liquors, and the important role
played by salts in the process. Analogous effects may be explained in
a similar manner in other processes which involve colloids.

THE MICELLE THEORY OF COLLOIDAL ELECTROLYTES.

(Compare the summarising paper by McBain and Salmon, Jonrn.
Amer. Chem., Soc., 42, 426 (1920), from which the following account is
directly taken.)

Colloidal electrolytes are salts in which an ion has been replaced by
a heavily hydrated polyvalent micelle, consisting chiefly of agglomerated
anions, each micelle carrying an equivalent sum total of electrical charges
and conducting electricity as well or even better than the simple icn
which it replaces. The chief feature of the micelle is its great electrical
mobility, which it possesses in virtue of the numerous charges upon it,
and at the same time its very low mechanical mobility, which it possesses
in virtue of its great mass and hydration, thereby giving rise to marked
viscosity on the part of the solution.

In a measure, the properties of this ionic micelle must apply to all
colloids which possess even slight electrical charges. In the case of
proteins and soaps at high concentration, the undissociated substance is
an ordinary colloid while the organic ion is a micelle. In dilute soap
solutions, on the other hand, the undissociated molecules possess only
the simple formula weight and the ions are also simple. The class called
electrolytic colloids, characterised by the existence of the micelle is
extremely wide, embracing such substances as acid and alkali proteins,
dyes, indicators, sulphonates and soaps. The work of McBain and his
collaborators extending over several years and cited in the paper referred
to, deals mainly with the properties of soap solutions. We shall con-
sider such systems from the standpoint of the micelle.

McBain and Taylor have found that soap solutions are characterised
by possessing high electrical conductivity. This shows that they consist
to a large extent of something other than neutral colloid. The next
step was to show, by two independent methods, namely by the rate of
catalysis and the e.m.f. of the hydrogen electrode, that the hydroxyl
ion present was negligible, its concentration being only about o'ooiN.
Hence the high conductivity was due to the soap itself.

In addition to electrical conductivity measurements a long series of
determinations of the molecular weights of soap solutions have been



326



A SYSTEM OF PHYSICAL CHEMISTRY



carried out, the results of which demonstrate that as the soap solutions
become more dilute there is a gradual transition from colloid to
crystalloid. This refers to the undissociated colloid as well as the
colloidal anion or micelle. A dilute solution of soap is essentially an
electrolyte like sodium acetate. Quite definite and reproducible equili-
bria are set up between the various constituents, colloid and crystalloid.
The experimental method of determining the concentration of the various
constituents in any solution consisted in a modification of the dew-
point method of molecular weight determination first employed by
Gumming (Trans. Chem. Soc., 95, *77 2 ( I 99))- Some details of this
method are given in the next section.

Dew-point Method of Determining the MoleciUar Weight
of a Solute.

In connection with soap solutions it is impossible to use the ordinary
boiling point method owing to the presence of a large amount of air
which does not escape from the bubbles and therefore by its partial
pressure, invalidates the results. This is a criticism of Krafft's well-
known boiling point observations on soap solutions, and equally invalidates



From regulaTed
reservoir.



Warer in



transparent"
Thermosrat-



Thermomerer.
To reyulared



reservoir.



pump.



Silver rube.




FIG. 50 (a).

Smits tensimeter measurements. Correct vapour pressure measure-
ments can be obtained with special precautions.

The dew-point apparatus of McBain is as shown in the Fig. 50 (a).

A highly-polished silver tube with silver bottom is closed with a
cork at the top. Through the cork are inserted a thermometer and two
tubes through which a rapid current of water^is circulated by a pump



MICELLE, THEORY OF COLLOIDAL ELECTROLYTES 327

from and to a thermostat of adjustable temperature. The silver tube is
held in a cork in a glass vessel which contains the solution to be studied.
The top of the glass vessel rises an inch or so above the cork so that
the enclosed space is completely immersed in the water of a thermostat
with glass sides. Further, a capillary glass tube passes through the cork
holding the silver tube and can be connected with a pump and thus
evacuated or the pressure adjusted to any desired value. This tube is
closed by a glass tap.

The principle of the method is as follows. When the silver tube is
cooled by running water through it, just far enough to form a little dew,
the pure water thus formed on the surface of the tub^ is in equilibrium
with the vapour over the solution. The vapour pressure can therefore
be obtained from tables giving the saturated vapour pressure of water as
a function of temperature. But this vapour is also in equilibrium with
the soap solution, which solution is at a somewhat higher temperature,
namely, that of the transparent thermostat. In other words, the differ-
ence of temperature between the silver tube and the soap solution is
the rise in boiling point of water, at reduced pressure, due to the pre-
sence of the solute. The rise predicted for a i -oN of a crystalloid such
as sugar, according to the familiar van J t Hoff formula, RT% is 0-483
at 90 C. Since the latent heat of vaporisation of water is greater at
lower temperatures, and T is less, this rise is slightly less than the rise
of 0*5010 expected in the ordinary Beckmann method at 100. The
values of the constant at lower temperatures are as follows : at 70 C,
0-414; at 45 C, 0-353; at 25 C, 0-303; at 20 C, 0-291.

Reverting to the experimental procedure, the following device was
found to be essential for accurate readings. The silver tube was kept
highly polished, but as it was very difficult to detect the first trace of
dimming, a portion of the tube was so treated that no dew deposited on
it, and thus a contrast between polished and slightly dimmed surface
was obtained. The test of dew formation or disappearance was the
formation of a sharp boundary or its vanishing point. To produce this
effect boiling water was run through the silver tube and the bottom
corner of the tube was dipped once into boiling conductivity water.
The water evaporated, but thereafter no dew would form on this part of
the surface. In this way the boundary line in a dew-point experiment
ran diagonally across the lowest part of the side of the tube. The next
step is to pass practically boiling water through the prepared silver tube
and insert the latter into the glass vessel to about i cm. above the
surface of the soap solution. This prevents (a) condensing large
amounts of water on the silver tube, (b) altering the surface of the
silver, (c) dimming the glass when heavy dew is evaporated, (d) changing
the concentration of the solution. The whole apparatus with the hot
water passing through it is then inserted into the transparent thermostat,
as in Fig. 50 (a). The glass tap is kept open for a few minutes to
equalise pressure outside and inside, since the vapour pressure of the
solution is considerable at 90, which is the temperature to which the
transparent thermostat is adjusted. The tap is then closed.



328 A SYSTEM OF PHYSICAL CHEMISTRY

The determination is now begun by very gradually lowering the
temperature of the water running through the silver tube, noting the
the thermometer contained in it and also the thermometer in the ther-
mostat with its bulb close to the solution tube. On the first sign of
dew formation the two thermometers are read. Immediately the supply
of heat to the adjustable thermostat, which furnishes the water for
heating or cooling the silver tube, is increased so as to raise slowly
the temperature of the running water. The dew disappears and the two
thermometers are again noted. Appearance and disappearance of dew
are thus made use of.

McBain claims that the results are as accurate as an ordinary Beck-
mann determination in dilute solution, and of course the method has
special advantages for soap solution determinations for the reasons
already mentioned. For moderate concentrations of ordinary electro-
lytes the method is more accurate than the Beckmann method. Thus,
from the data given in Landolt and Bernstein's tables, the dissociations
indicated for normal solutions of KC1 and NaCl are 80 per cent, and
94 per cent, respectively, whereas the dew-point method gives 78 pel
cent, and 76 per cent, respectively, in agreement with the results
obtained by the same method for the corresponding acetates, namely.
78 and 74 per cent.

Experimental Results and Deductions from them.

In Concentrated Soap Solutions the only Crystalloidal or Electrolytic
Constituent is the Potassium or Sodium Ion. This means that nearly
half of the current is carried by the negative colloid, which must be as
good a conductor as an ordinary ion. To take a single case, the dew-
point method shows that a i normal solution of potassium stearate
exhibits a rise of boiling point of 0*20 at 90 C. ; hence the total con-
centration of all ions and molecules is o^N. This solution has, at
90, an equivalent conductivity of 113 '4 reciprocal ohms, that of i
normal potassium acetate being 176-9 at the same temperature. It is
evident that at this concentration the stearate conducts about two-
thirds as well as the acetate, and must, therefore, be regarded as a good
conductor.

We have now to consider the concentration of the metallic ion
present. If the negative ion were an ion at all the high molecular
weight of the stearate radicle would lead us to predict that the stearate
ion would not conduct as well as the acetate ion (116 recip. ohms at
90). The mobility of the stearate ion might, in fact, be about 90
reciprocal ohms. This, with a mobility of 188 reciprocal ohms for the
potassium ion, would make the conductivity of potassium stearate 278
when dissociation is complete. Using this result, the concentration of

the potassium ion is given by ^| x roN = o^iN. This equals the

total observed concentration of crystalloidal constituents, o'42N, within
the experimental error as given by the dew point. Hence everything



MICELLE THEOR Y OF COLLOIDAL ELECTRO L YTES 329

else, that is the whole of the stearate including whatever carries the
equivalent of this large amount of electricity, must be colloid and not
simple unpolymerised stearate. Salmon (Trans. Chem. Soc., 117, 530
(1920)) has made a series of determinations of the potassium and
sodium ions concentration or more strictly speaking their activities in
potassium and sodium soap solutions respectively, and also in gels by
means of e.m.f. measurements ; the numerical values agree satisfac-
torily with those calculated by McBain.

The Concept of Highly Mobile Ionic Micelles. Bayliss (Proc. Roy.
Soc., B, 84, 229 (1911)), dealing with the osmotic pressure of Congo red
solutions, makes several alternative suggestions, among which occurs
" the possibility of aggregated simple ions carrying the sum of the
charges of their components". Independently, McBain, in 1913, put
forward the conception of a highly mobile heavily hydrated micelle in
order to remove some of the difficulties in interpreting the properties
of acid and alkali albumens, since it reconciles their enormous viscosity
with their good electrical conductivity. McBain has developed this
idea to a large extent in connection with soap solutions as has already
been pointed out.

According to Stokes' law for a sphere of radius r moving through a
liquid of viscosity 17 the velocity v of the body is given by v F/67rrrj,
where F is the force causing the motion. It is known, in view of
the work of Perrin and others, that this expression applies to par-
ticles of colloidal dimensions. In conductivity experiments the
force is due to the electric charge upon the particle. If this charge
could be varied without other alteration of the ion, the mobility or con-
ductivity would vary in direct proportion to the driving force. If, on
the other hand, a number of ions, say a dozen, were to coalesce, the
resulting particles would be driven by a force of I2F. The velocity
would not be proportionally so great, for the radius of the sphere would
now be increased by r\j~^ = 2-y. The new velocity would be
12/2*3 = 5' 2 #- This five-fold increase in mobility of the aggregate
would, in practice, be counterbalanced by its greatly enhanced electro-
static potential in attracting water molecules and other material, so that
such an aggregate would become a heavily hydrated micelle. The
result would be a colloidal particle of about the same mobility as a
rather slow true ion. The hydration would account for the enormous
mechanical viscosity observed in all the systems mentioned, and also
the fact that it varies with the concentration of other constituents.

In Dilute Soap Solutions the Colloid Breaks up into Simple Ions
and Simple Undissociated Soap Molecules. With the dew-point method
o-2N solutions were the most dilute which could be accurately dealt
with. With potassium palmitate solutions of this concentration at 90
the results were as follows : Lowering of dew point = rise of boiling
point = o'i2. Hence total concentrations of all ions and molecules
present = o^N. The molar conductivity of o'2N potassium palmitate
at 90 is 1 1 1 reciprocal ohms. If the conductivity at infinite dilution is
304, the concentration of potassium ions is o'c^N; if it be 278, the



330



A SYSTEM OF PHYSICAL CHEMISTRY



concentration is o*o8oN. Hydrolysis does not affect this result by
more than about 2 per cent., and this may be neglected for our present
purpose.

Taking the second result, concentration of potassium ions = o'oSoN,
the concentration of total crystalloids being o*25N, leaves a concentra-
tion of (0-25 - 0-08), or o-iyN for crystalloids other than the K+.
The total undissociated soap is 0*200 0-080 = o'i2oN. Thus, even
if all the undissociated soap is in simple crystalloidal form, there is still
a o'ly o'i2 = o*o5N concentration of crystalloid to be accounted for,
and this must be afforded by simple palmitate ions, since the hydroxyl
ions have been shown to be only about o-ooiN. The small balance of
0-03, namely the difference between the K+ (o-o8N) and the simple
palmitate ions 0*05 N, is all that can be colloid. Not more than one-
fourth of the undissociated palmitate nor more than three- eighths of the
palmitate ion can be in the colloidal form. If there be some of each
in the colloidal form this has to be divided up between them so as not
to exceed a total of o'03N.

It is evident that in o*2N soap solution the break down of colloid
has proceeded fairly far, and further dilution would complete it. We
thus have a clear case of transition from colloidal to crystalloidal state
depending upon the concentration. The transition is reversible.

Molecular Weights of Typical Solutions of Soditim Salts of
Fatty Acids at 90 C.

McBain and his collaborators have investigated by the dew-point
method a great number of such cases involving potassium as well as
sodium salts. For purposes of illustration only the sodium salts are
referred to here. The rise in boiling point of these salts as a function
of concentration is shown in the following table. It will be observed
that the data cover simple non-colloidal substances such as the acetate
right up to the behenate.

TABLE I. RISE OF BOILING POINT AT go C. FOR SODIUM SALTS.



ll
















a


Weight
Normalit


Behenate

c 22 .


s .

rt oo

1

w


Palmitate

C 16-




2 ^

r


0)

H s

r




fi

P




D

F


a^>

*!

c-2

<U


O*2


o'og


O'll


0-I 3


o-i 4


0-15


0-17




O'lO


0'5
075
1*0

i '5


O'll

o'og


0-18
0*22
0-23
0-18


0'2O
0*24
0-25
0'22


0*24
0-28

o'2g
0-27


0-28
0-32
0-34

o*33


'37
0-50
0*62


0-45
0-84


o'24
0-36
0-48
072


2'0


o*n


o'ig


O'5O









,


'97


3*o




0-30


I-2 3


~











i'45



MICELLE THEORY OF COLLOIDAL ELECTROLYTES 331



'ABLE II. TOTAL CRYSTALLOIDAL MATTER (IONISED AND OTHERWISE; CALCU-
LATED FROM DATA OF TABLE I.) IN SODIUM SALT SOLUTIONS AT 90 C.
MOLES PER 1,000 GRAMS OF WATER.



Weight
"formality.


Behenate.


Stearate.


Palmitate.


Myristate.


Laurate.


Caprylate.


Acetate.


0'2


0*19


0*23


0-27


0*29


0'33


0'35





'5


0-23


0'37


0-41


0*50


0-58


077


0'93


075





0*46


0'50


0-58


0-66


I'0 4





I'D


o'ig


0*48


0-52


o'6o


0*70


1-28


174


i*5





0'37


0^46


0*56


0-68








2'O


0-23


0-39


1-04














3'




0'62


2'55




~^


~


~



The results given in the two tables show certain interesting
haracteristics. It is evident that the salts fall into two classes. From
le acetate up to the caprate Qo the behaviour is regular, showing
issociation. On the other hand, from the laurate upwards the curve
epresenting rise of boiling point (or calculated solute content) passes
hrough a pronounced maximum at about i normal, and a minimum
t 1*5 normal. Above this concentration the rise of boiling point
T lowering of vapour pressure rapidly increases again.

It may be mentioned that the stearate above i -5 normal is hardly
, solution ; i ^N sodium stearate at 90 is a viscid gum. On the other
land, 2-oN potassium laurate solution with a similarly shaped curve
5 a clear oily liquid. The form of the curve is thus due to the
onstituents in the system and is not due to mechanical effects, e.g.
;el formation, skins on the surface, or other changes of state. The
ffect is also not due to hysterisis, as is the case in the dehydration
>f certain gels, for it is independent of the age or method of preparation
if the soap solution or whether water may have been previously added
>r taken away. It will be pointed out later that the existence of the
ninimum in the boiling point rise is due to dehydration of the colloidal
onstituents, thereby releasing a quantity of solvent which effectively
lilutes the solution and thus produces a diminished rise in the boiling
oint. Were it not for this, the boiling point would rise steadily all the
sray with increase in concentration.

In i-oN Solutions at 90 the total Colloid prese?it equals at least 15
ier cent, in the case of Hexoate, increasing to nearly the whole in the case
f the Higher Soaps, but falling off rapidly with Dilution. In the
receding table have been given the concentrations of the total
brystalloidal matter in any one of these solutions, namely, the sodium
ion, the simple soap ion, such as the palmitate ion P, and the simple
jundissociated soap molecules, such as NaP. McBain next proceeds to
'calculate the concentration of the metallic ions, say the sodium ions,
by conductivity measurements. For the moment we assume that the
jion activities and ionic concentrations are sensibly identical. To
icalculate the concentration of sodium ion in any solution the values
(taken for the mobilities of the negative radicles are : behenate to
Jaurate, 90; caprate, 92; caprylate, 94; caproate, 98; acetate, 116;



332



A SYSTEM OF PHYSICAL CHEMISTRY



and for sodium, 139. The results of the calculation are given in tl
following table :

TABLE III. CONCENTRATIONS OF SODIUM IONS IN SALTS AT 90 C.



Weight
Normality.


Stearate.


Falmitate.


Myristate.


Laurate.


Acetate.


G-2


0-053


0-079


0-085


0-099


0*140


o'5


0*166


0-195


0*2l6


0-239


0-303


075


0-272


0-286


0-324


0-350


0-409


I'O


0-386


0-369


0-405


0-455


0*511


rs


0*553


0*553


0-543


0*615


0*664



By subtracting the corresponding values of Table III. from tho
of Table II., we arrive at the values of crystalloidal constituents oth
than the sodium ions. That is we obtain the values of the simple so;
anions together with the simple undissociated soap molecules whe
such exist. These are given in the following table :

TABLE IV. CONCENTRATIONS OF CRYSTALLOID CONSTITUENTS OTHER THAN
SODIUM IONS AT 90 C.



Weight
Normality.


Stearate.


Palmitate.


Myristate.


Laurate.


Acetate.


0'2
0-5
075


0*18
0*20
0-18


0*19
O*22
0-21


O'2O
0-28
0'26


0-23

0-34
0-31


0-63


I'O


0*09


0*15


O*2O


0-25


1-23


i'5


- 0-20


- O'll


O'O2


0-07


_



The data given in the ab9ve table represent simple organic ion ai
simple molecule of the undissociated soap. By subtracting these valu
from the apparent normality of the solution as given in the first colum
we obtain a quantity which must represent the colloidal part of t
soap. This colloid of course includes ionic micelle and colloic
undissociated soap aggregate. The values are given in the followii
table :

TABLE V. CONCENTRATIONS OF TOTAL COLLOID IN SODIUM SALT SOLUTIONS

AT 90 C.



Weight
Normality.


Stearate.


Palmitate.


Myristate.


Laurate.


Acetate.


0*2


0'02


O*OI


o-oo


- 0-03


_


o'5


0-30


0-28


O-22


+ 0*l6


- 0-13


0-75


0-57


o*54


0-49


0-44





i-o


0*91


0*85


0-80


o*75


- 0-23


i'5


(1*70)


(1-61)


1-48


i'43





It is necessary to consider the validity of this comparison of osmot
with conductivity data. It is undoubtedly the case that the osmot



WflCELLE THEORY OF COLLOIDAL ELECTROLYTES 333

p allies are too high, presumably, as already mentioned on account of the
f ydration of the solute. Thus the dissociation deduced for sodium
iscetate from conductivity is less than the osmotic activity by 20 to 23
|:>er cent. Were all this due to hydration, 7 or 8 moles of water would
pave to be combined with the acetate and its ions, a not improbable
[result. On the other hand McBain concludes that the results of con-
ductivity measurements are too low, on account of the retarding influence
clue to viscosity. It is unknown what the exact viscosity correction
.should be in such cases where the colloid content is large, and the
system consequently heterogeneous. McBain considers that the correc-
tion for viscosity is not a large one, in spite of the actual great viscosity
which is due to aggregates floating in a dilute solution of an electrolyte,
iand we know from Lodge's original determinations of mobility of ions
in a set jelly (where the mechanical viscosity is enormous) that the
:mobility is very little less than that in pure water. In the case of the
Acetates the viscosities of normal solutions at 1 8 C. exceed that of water
by 26 per cent. Although this would be somewhat less at 90 C. it is
ample to account for the divergence between conductivity and osmotic
effect, but probably both viscosity and hydration contribute their share.
It may be pointed out that the divergence between the two different
kinds of measurement, conductivity and osmotic effect, in the case con-
sidered is in the opposite sense to that considered in (Chap. VIII.) deal-
ing with strong electrolytes, in which it was found that the activity of
the ions, as shown by the osmotic effect, is less than their concentration
as shown by conductivity. In the present case the osmotic activity
observed is certainly too great and the conductivity results too small, for
the reasons cited. And yet in concentrated solutions of the higher
soaps the osmotic effect is not enough even for the sodium and potas-
sium ions alone as deduced from conductivity ; compare the results for
sodium stearate and palmitate at i'5N in Tables II. and III. which lead



Online LibraryWilliam C. McC. (William Cudmore McCullagh) LewisA system of physical chemistry (Volume 2) → online text (page 34 of 47)