Adiabatic compressibility of alkyltrimethylammonium bromides in aqueous solutions

Adiabatic Compressibility of Alkyltrimethylammonium Bromides in Aqueous Solutions RYSZARD

Z I E L I l q S K I , *'1 S H O I C H I I K E D A , * H I R O Y A S U AND S H I G E O KATO~"

NOMURA,~

*Department of Chemistry, Faculty of Science, Nagoya University, Nagoya 464, Japan; and "~Departmentof Chemical Engineering, School of Engineering, Nagoya University, Nagoya 464, Japan Received July 1, 1986; accepted December 2, 1986 The adiabatic compressibility of aqueous solutions of octyl-, decyl-, dodecyl- and tetradecyltrimethylammonium bromides has been determined from measurements of ultrasound velocity and density at 25°C. A theoretical treatment giving the adiabatic compressibility as a function of concentration has been developed, and the apparent adiabatic compressibility of a surfactant in the monomeric and micellar forms is derived from the experimental results. The apparent adiabatic compressibility of surfactant in either form is constant, independent of concentration, so that it is identified with the apparent adiabatic compressibility in each form. The adiabatic compressibility in the monomeric form decreases from -0.25 × 10-5 bar-~ for the octyl to -2.52 X 10-5 bar-~ for the tetradecyl derivative, while that in the micellar form increases from 3.41 × 10-5 bar-~ for the octyl to 4.17 × 10-5 bar-1 for the tetradecyl derivative. The former includes the hydration of ionic head group of the surfactant, while the latter is related to the structure of miceUe. If the same treatment is applied to the literature data, the apparent adiabatic compressibility of sodium alkyl sulfate in the monomeric form changes conversely with the alkyl chain length, while that in the micellar form is qualitatively similar. © 1987AcademicPress,Inc. INTRODUCTION S u r f a c t a n t m o l e c u l e s in a q u e o u s solutions exist in the m o n o m e r i c f o r m below the critical micelle c o n c e n t r a t i o n (CMC), while t h e y c a n be in either m o n o m e r i c o r m i c e l l a r forms, if the surfactant c o n c e n t r a t i o n exceeds the C M C . D i s s o l u t i o n o f an i o n i c surfactant in w a t e r below t h e C M C causes a c o n t r a c t i o n o f v o l u m e a n d a decrease in compressibility, owing to the effects ofelectrostriction o f the ionic groups a n d h y d r a t i o n at b o t h ionic groups a n d hyd r o c a r b o n m o i e t y (1). U p o n increasing surfactant c o n c e n t r a t i o n b e y o n d t h e C M C , surfactant m o l e c u l e s associate i n t o micelles, t h u s decreasing h y d r o p h o b i c h y d r a t i o n o r d i s r u p t ing the h y d r a t i o n shell a r o u n d the h y d r o c a r b o n m o i e t y . T h e i n t e r i o r o f a micelle is sup-

1Permanent address: Department of General and Analytical Chemistry, Institute of Commodity Sciences, Academy of Economics, 60-967 Poznafi, Poland.

p o s e d to have a structure similar to t h a t o f l i q u i d h y d r o c a r b o n (2-4), t h u s being c a p a b l e of incorporating various water-insoluble materials therein. V a r i o u s w o r k e r s i n c l u d i n g Shigehara a n d B l o o r et al. ( 5 - 1 5 ) m e a s u r e d ult r a s o u n d velocity o f a q u e o u s s o l u t i o n s o f surfactants a n d o b s e r v e d v a r i o u s effects influencing the a d i a b a t i c c o m p r e s s i b i l i t y o f surfactants in the m o n o m e r i c a n d m i c e l l a r forms. I n the p r e s e n t w o r k we m e a s u r e t h e d e n s i t y a n d u l t r a s o u n d velocity o f a q u e o u s solutions o f a l k y l t r i m e t h y l a m m o n i u m b r o m i d e s having alkyl chains o f octyl, decyl, dodecyl, a n d tetradecyl, a n d derive t h e a p p a r e n t a d i a b a t i c compressibilities o f these surfactants in b o t h m o n o m e r i c a n d m i c e l l a r forms, in o r d e r to elucidate t h e n a t u r e o f h y d r a t i o n o f s u r f a c t a n t ions a n d the structure o f s u r f a c t a n t micelles. We develop a simple theoretical treatment o f the u l t r a s o u n d velocity a n d the a d i a b a t i c c o m p r e s s i b i l i t y o f a q u e o u s s o l u t i o n s o f surfactant a n d a p p l y it to the p r e s e n t results o n

398 0021-9797/87 $3.00 Copyright © 1987 by Academic Press, Inc. All rights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

399

COMPRESSIBILITY OF SURFACTANTS

alkyltrimethylammoniumbromides, to obtain their apparent adiabatic compressibilities in both monomeric and micellar forms, as well as their apparent molar volumes. These quantifies have values essentially equal to their partial quantities. In earlier work (5, 6, 15) on aqueous solutions of surfactant, it has been observed that the ultrasound velocity and the adiabatic compressibility changes linearly with the surfactant concentration, both in monomeric and micellar forms, and that the slope of the straight lines varies with the surfactant species. The present treatment can give a phenomenological insight into these observations. We will apply the same treatment to the experimental data published by other workers (15-17) on aqueous solutions of sodium alkyl sulfates having alkyl chains of methyl, octyl, decyl, and dodecyl, in order to derive their apparent adiabatic compressibilities in both monomeric and micellar forms. We can use the same procedure for treating the observed data on a nonionic surfactant, polyoxyethylene dodecyl ethers having polyoxyethylene chains of different lengths (13), to estimate their apparent adiabatic compressibility in the micellar form. APPARENT ADIABATIC COMPRESSIBILITY OF SURFACTANTS IN AQUEOUS SOLUTIONS

In general, surfactant molecules exist in both monomeric and micellar forms. In a solution of volume, V (cm3), there are Wo g of solvent and w g of the surfactant, of which w~g is in the monomeric form and Wmg is in the micellar form: w=wl+w~a. [1] If the specific volume of the solvent is Vo, and the apparent specific volume of the surfactant in the monomeric form is ~e~,and that in the micellar form is 9m, then the total volume of the solution at constant temperature can be expressed by V - - W0V0 -[- Wl~/1-{- WmVm

and its weight is equal to p V ~- Wo"[- Wl nt- Wm,

where p is the density of the solution. Eliminating w0 from Eqs. [2] and [3], the density of the solution is given by p = p0 + (1 - ¢elp0)q+ ( 1 -

~¢mP0)Cm,

[4]

where p0 is the density of the solvent, and q = W l / V a n d Cm = Wm/Vare the weight concentrations of the surfactant in the monomeric and micellar forms, respectively. For convenience, the apparent molar volume of the surfactant in the monomeric form, 9~, and that in the micellar form, 9m, are introduced by 9, = M]~I [5] 9 m = MlCdrn,

[6]

where Mmis the molecular weight of the surfactant. In order to derive the adiabatic compressibility of the solution, fl (bar-l), as a function of surfactant concentration we differentiate Eq. [4] with respect to pressure, P, at constant entropy, S. The concentrations of monomer and micelle, Caand Cm, change with pressure only through the change in volume of the solution, so that it follows that acl 3P OCm OP

Clfl

[7]

- Croft.

[8]

-

Introducing the adiabatic compressibility of the solvent, 80, we have

t~ = 90 + (d~- ~0)~c~ + (rim-- ~0)~mCm,

[9]

where the apparent adiabatic compressibilities of surfactant in the monomeric and in the micellar forms are defined by dl---- -- l ( O V l /

[10]

I (O~lml

& = - V ~ i T f i ] s.

t l 1~

[2] For convenience, the apparent molar adiabatic compression of the surfactant in the [3] monomeric form, I~l (cm 3 mole -1 bar-l), and Journal of Colloidand InterfaceScience,Vol. 159,No. 2, October 5987

400

ZIELIlqSKI ET AL.

that in the micellar form, I(m, are introduced by I~1 =

X~lll~l

[121

I(m ='Cream.

[13]

The quantity, /~i, is sometimes called the coefficient of adiabatic compressibility of the solute in solution. Correspondingly, the quantity, I(~, is often called the apparent molar adiabatic compressibility of the solute in solution, but we will call it the apparent molar adiabatic compression of the solute in solution, in order to avoid possible confusion with the apparent adiabatic compressibility of the solute in solution. In general, the ultrasound velocity in liquid, including aqueous solutions, u (m s-~), is related to the density of the solution, p, and adiabatic compressibility,/3, by u=

.

[14]

For dilute surfactant solutions Eq. [ 14] can be expanded to the power of concentration, after substituting Eqs. [4] and [9], to give u0+ u° H0 ~

/~m

/)01Cm"

We introduce the total concentration of the surfactant W

c=~.

[161

In the pseudo-phase model of micelle formation the concentrations of monomer and micelle can be approximated by q=c

cm=O

c~
[17]

q=CMC

Cm=C-CMC

c>~CMC.

[18]

In the mass-action model of micelle formation the concentrations of monomer and micelle can be calculated by solving Journal of Colloid and Interface Science, Vol. 119,No. 2, October 1987

q+Cm=C

[19]

Cm = KecT,

[201

where m is the aggregation number of micelle and Ke is the equilibrium constant of miceUe formation. Here it will be relevant to make clear the relation of our apparent molar volumes, Vi, and our apparent molar compressions, I~i, for monomer (i = 1) and micelle (i = m) with the apparent molar quantities of surfactant defined by De Lisi et al. (19) and Vikingstad et al. (9, 11, 12): OV {v= M~w

[211

q~x = Ml O(O~)

[221

From Eqs. [2] and [91 we can readily show that ~ V = CI X~l -1- Crn g m c c CI~

. Cm~

-~.. = - l~l + --

C

[23]

t~m.

[24]

¢

Similar equations were used for volume by De Lisi et al. (19) and Vikingstad et al. (9, 1 l, 12) in the pseudo-phase approximation. As can be seen below, the coefficients of concentration terms in Eqs. [4], [9], and [15] can be regarded as constant, respectively, and the apparent specific or molar volume of the surfactant in the monomeric or micellar form and its apparent adiabatic compressibility are, therefore, equal to its corresponding partial quantities, respectively. EXPERIMENTAL

Materials Special-grade reagents of tetramethylammonium bromide (C1TAB) and dodecyltrimethylammonium bromide (C12TAB) (Nakarai Chemical Co., Ltd.), octyltrimethylammonium bromide (C8TAB), decyltri-

401

COMPRESSIBILITY OF SURFACTANTS

m e t h y l a m m o n i u m bromide (C~oTAB), and tetradecyltrimethylammonium bromide (C14TAB) (Tokyo Kasei Kogyo Co., Ltd.) were used without further purification, but after drying in v a c u o at room temperature for at least 48 h. The purity of the samples was determined by means of thermal decomposition gas chromatography. The composition of the samples based on weight percentage of CNTAB was as follows: CsTAB (C6, 0.11; C8, 99.89), C10TAB (C8, 0.06; C1o, 99.83; C12, 0.11), ClzTAB (C12, 99.90; Cl4, 0.10), and CI4TAB (C12, 0.03; C14, 99.47; unspecified nonquaternary component, 0.50). All solutions were prepared by weight, by dissolving the surfactant in distilled water (which was degassed before use). The surfactant concentrations were converted to grams per cubic centimeter by means of density data.

Measurements

Measurements of density of the solutions were carried out at 25 + 0.01 °C using pycnometers of Ostwald type having 20 em 3 capacity. Pycnometers were calibrated using distilled and degassed water, based on the value of density of water, 0.997047 g c m 3 (20). Densities of the solutions were corrected for the density of air. Uncertainties in the surfactant concentration and measurements of density (mainly in the latter) can produce an error in the density, ca. +5 × 10 -5 g c m -3. Ultrasound velocity was measured at 25 + 0.01°C using an ultrasonic interferometer working at a frequency 5.0 MHz, with an accuracy of+0.15 m s-~. The ultrasound velocity in water at 25°C was found to be 1497.11 m s -1, corresponding to the adiabatic compressibility, 4.475 X 10 -5 bar -1. The errors due to temperature fluctuations during ultrasound velocity measurements were relatively large. Since the temperature coefficient of ultrasound velocity in water is ca. 3 m s -~ K -~ at 25°C, an uncertainty of +0.01 °C in temperature of the solution during measurement produces an error in the ultrasound velocity, ca. +3 X 10 -2 m s -1.

RESULTS

Figures 1-4 show changes in density, Ap = O -- Po, ultrasound velocity, Lxu = u - Uo, and adiabatic compressibility, 4/3 = /3 - 130, of aqueous solutions of alkyltrimethylammonium bromides (CNTAB) as a function of surfactant concentration. Note that the range of surfactant concentration covered differs about sixfold between the octyl (C8) and tetradecyl (C14) derivatives, because of the difference in the CMC and of the accuracy of measurements. Each plot of the density of aqueous solutions ofalkyltrimethylammonium bromides can be divided into two straight line segments, and the CMC appears as a break point on it. The two segments correspond to the monomeric and micellar forms, respectively, and they can be expressed by Eq. [4]. For very dilute solutions the precision of our measurements is not very high, but it is sufficient to draw a straight line with a definite slope at concentrations lower than the C M C , except for tetradecyltrimethyl-ammonium bromide. By using Eq. [4], values of the apparent specific volume of the surfactant in the monomeric and micellar forms, vl and Vr~, can be derived from the slopes of the straight lines. The constant slope of each part, or the constant value of~l or ~m, means that the apparent specific volume is equal to the partial specific volume over the concentration range within experimental errors. Or, more strictly, it can be taken as an average value of the apparent or partial specific volume, to the zeroth approximation. Literature data on various surfactants in solution gave practically no difference in the apparent molar volume or the apparent adiabatic compressibility at infinite dilution and at the CMC (8, 21, 22). Values of the apparent molar volumes of the surfactants in the monomeric and micellar forms, "Vland ~rm, together with those of the CMC, are given in Table I. Values of change in the apparent molar volume due to micelle formation A~rm = ~rm -- Wl Journal of Colloid and Interface Science,

[25]

Vol. 119,No. 2, October1987

402

ZIELI/qSKI ET AL. 60

6I

0

-10 -~

,~40

16

~20

o ~

o to -1 "T

'tn

E 4

L

- 8- -3o~. I

lo

i 1

-40

0

40

0

80

120

CONCENTRATION

0

160

10

20

30

CONCENTRATION

/ g drn-3

40

/ g dm -3

FIG. 1. Changes in ultrasound velocity, adiabatic compressibility, and density of aqueous solutions of octyltrimethylammonium bromide (CsTAB) as a function of concentration at 25°C. Symbols: (©) AU = u -- uo, (O) A# = /~ -- ~o, (i-I) Ap = p -- Po.

FIG. 3. Changes in ultrasound velocity, adiabatic compressibility, and density of aqueous solutions of dodecyltrirnethylammonium bromides (C~2TAB) as a function of concentration at 25°C. Symbols are the same as those in Fig. 1.

are also given in Table I. For comparison, data from the literature are included. Each plot of the ultrasound velocity can also

be divided into two straight line segments, with the intersection at the CMC. The two parts can be assigned to the monomeric and micellar

-00

20

10

16

8

I° -2

!2o 0.s

t~ o

V- 1.5

0.8
> I- ;,,%. E~

7

-I.0 "q tiff

Q 1.0

rl>.

t/')

I I I

i Y

~

o

0 ff

h

n

i

i

i

0

20

40

60

80

100

CONCENTRATION

i_12 u

05

l

0.0 ~'i

/ g dm -3

FIG. 2. Changes in ultrasound velocity, adiabatic compressibility, and density of aqueous solutions of decyltrimethylammonium bromide (CIoTAB) as a function of concentration at 25°C. Symbols are the same as those in Fig. 1. Journal of Colloid and Interface Science,

Vol. 119, N o . 2, O c t o b e r 1987

~0.~ ~

0

,

5

,

,

,

.

o -1.5 ~

,

10 15 20 25 CONCENTRATION / g drn"3

FIG. 4. Changes in ultrasound velocity, adiabatic compressibility, and density of aqueous solutions of tetradecyltrimethylammonium bromides (C,4TAB) as a function of concentration at 25°C. Symbols are the same as those in Fig. 1.

COMPRESSIBILITY OF SUREACTANTS

403

TABLE I Critical Micelle Concentration and Apparent Molar Volume of Alkyltrimethylammonium Bromides in Water at 25°C C~TAB

CIVIC (mole dm-s)

Ref.

"~, (eras mole-~)

CITAB

--

--

115.2

~/'~ (cms mole-~)

A~ (cms mole-I)

Ref.

This work

115.2

(23)"

114.40

(23, 24)

CsTAB

2.93 X 10-1 2.24 X 10-1 2.9 X 10-1

This work (25) (26)

225.0 223.7

228.8 227.5

3.8 3.8

This work (17)

CIoTAB

6.63 × 10-2 5.70 X 10-z 6.4 X 10-2 6.76 X 10-2 6.8 X 10-2 7.0 X 10-2

This work (14)c (26) (27) (28) (25)

255.0 255.4 258.2 --

262.2 262.3 265,0 --

7.2 6.9 6.8 5.07

This work (17) (29) (14)

C12TAB

1.46 X 10-2

This work

1.44 X 10 -2

(25)

1.46 X 10-2 1.48 X 10-2 1.5 X 10-2 1.53 X 10-2

(30) (14) (26) (28)

283.4 287.0 278.1 280.2

296.2 295.5 285.1 298.4

12.8 8.5 7.0 18.2

This work (17) (29) (32)

309.6 320.6 318.5

329.4 331.2 328.0

19.8 10.6 9.5

This work (17) (29)

C14TAB

1.54 X 10 -2

(27)

1.55 X 10-2

(31)

3.72 X 10-3 3.4 X 10-3 3.6 X 10-3 3.79 X 10-3 3.82 X 10-3

This work (25, 26) (25, 33) (27~), (34)c'a (34)c'a

By means of Eq. [4]. bAt infinite dilution. c CMC in moles per kilogram of water. d At 25.2°C. a

forms, a n d they can be represented by Eq, [ 15]. Values o f the a p p a r e n t adiabatic compressibility of a l k y l t r i m e t h y l a m m o n i u m b r o m i d e s i n the m o n o m e r i c a n d micellar forms,/31 a n d /~m, can be estimated from the slopes, a n d their values are t a b u l a t e d i n T a b l e II. T h e plot of u l t r a s o u n d velocity i n a q u e o u s solutions o f the octyl derivative n e a r the C M C deviates from the straight lines. A similar dev i a t i o n c a n be observed o n the plot p u b l i s h e d b y Bloor et al. (15) for s o d i u m octyl sulfate. This suggests that the micelle f o r m a t i o n o f o c tyl derivatives is n o t necessarily cooperative

b u t is s o m e w h a t stepwise, thus the pseudophase a p p r o x i m a t i o n is n o t always valid. Nevertheless, the straight line segments c a n be assigned to the m o n o m e r i c a n d micellar forms. Each plot of the adiabatic c o m p r e s s i b i l i t y is represented b y two parts of the straight lines intersecting at the CMC. T h e straight lines can be described by Eq. [9]. F r o m the slopes o f each part o f the straight lines the a p p a r e n t adiabatic compressibility of a l k y l t r i m e t h y l a m m o n i u m b r o m i d e s i n the m o n o m e r i c a n d m i cellar forms, ¢~ a n d ~m, c a n be evaluated, a n d their values are given i n Fig. 5 a n d T a b l e II. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

404

ZIELIlqSKI ET AL. TABLE II

Apparent Adiabatic Compressibility of Alkyltrimethylammonium Bromides (CNTAB) in Monomeric Form (/~) and in Micellar Form (/~m)at 25°C ~1 ( 10-5 bar-l) C~,TAB

Eq. [9]

Eq. [15]

CITAB

0.08

0.00

CsTAB

-0.17

-0.32

CIoTAB

-0.55

CI2TAB CI4TAB

/3= (10-5 b ar~t) Average

FA1.[91

Eq. [15]

Average

-0.25

3.47

3.35

3.41

-0.60

-0.58

3.78

3.75

3.77 4.03 b

- 1.48

- 1.50

- i .49

4.04

4.04

4.04 4.12 b

-2.62

-2.43

-2.52

4.18

4.16

4.17

0.04 -0.01 a

a Value calculated based on the data of Conway and Verrall (23). b Values taken from the paper of Bloor et al. (15), whose method of calculation is different from ours.

In the case of octyltrimethylammonium bromide, a curvature is observed near the CMC. For comparison, values of/~ and ~m derived from both ultrasound velocity and adiabatic compressibility plots are included in Table II,

z,3

O.5

0.0 ~ -0.5 'rL

to 'o

-10

3.9

u')

'o

Z-t5 3.7

E

-2.0 -2.5

3.5

-3.0

3.3

-3.5

NUMBEROF CARBON ATOMS

FIG. 5. Apparent adiabatic compressibility of alkyltrimethylammonium bromides in the monomeric form (~) and that in the micellar form (~m) as a function of length of the hydrocarbon moiety at 25°C. Symbols: ((3) ~ , (0) /~m. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

together with some data published by other workers. DISCUSSION

We have observed that two straight line segments can be drawn for both density and ultrasound velocity or adiabatic compressibility of aqueous solutions of alkyltrimethylammonium bromides having alkyl chains of octyl, decyl, dodecyl, and tetradecyl, if they are plotted as a function of surfactant concentration. This can be taken as an indication of micelle formation above the intersection of the two straight lines. This kind of linearity was observed on similar plots for density by Scott and Tartar (35) and Bloor et al. (15), and for plots of ultrasound velocity by Shigehara (5, 6) and Bloor et al. (15). Some authors (8-12, 36-38) extrapolate values of apparent quantities such as volume or compression of a solute to infinite dilution, after correcting for Debye-H/ickel terms, in order to obtain a value of the apparent quantity at infinite dilution or the partial quantity there, and they assigned this value to the partial quantity of a solute (surfactant) in the monumeric form. Other authors (26, 33) also extrapolate values of apparent quantities to high

405

COMPRESSIBILITY OF SURFACTANTS

concentrations, in order to obtain the value of the partial quantity of the surfactant in the micellar form. To our approximation, however, the surfactant in the monomeric and micellar forms is regarded as being in the state independent of its concentration. For octyltrimethylammonium bromide two linear segments are curved at the CMC, which can be ascribed to the presence of its smaller micelles and their less sharp formation.

Apparent Molar Volume of Alkyltrimethylammonium Bromides In Table I we can see that the apparent molar volume of alkyltrimethylammonium bromides in both monomeric and micellar forms increases with the increasing number of carbon atoms of alkyl chain. Several authors (37, 39) divided the partial molar volume of electrolytes into contributions of constituent ions based on the additivity principle. The apparent molar volume of a surfactant can be similarly divided into two contributions from the constituent cation and anion, depending on whether it is in the monomeric or micellar form. That is, ~'rl = v~'rl,++ g l , -

Qm ----Qm,+ + Vm,_.

[26] [27]

If the contribution of Br-, 30.9 cm 3 mole -~ (37), is subtracted from the apparent molar volume ofalkyltrimethylammonium bromide, the apparent molar volume of alkyltrimethylammonium ion, CNTA +, in the monomeric form, 91,+, can be obtained as 194.1, 224.1, 252.5, and 278.7 cm 3 mole -1 for the oetyl, decyl, dodecyl, and tetradecyl derivatives, respectively. The increase in the apparent molar volume of CH2 group at micelle formation suggests that the surfactant ion in the micellar form has a structure that is looser than that in the monomeric form, which would mean less effects of hydration and electrostriction. It is interesting to see that the contribution of CHE group to the apparent molar volume of the surfactant in the monomeric form is slightly

lower than the value calculated from the atomic volumes (40, 41), 16.1 cm 3 mole -1. It probably reflects some effects of strong hydration of ionic group as well as, more possibly, hydrophobic hydration of alkyl chain. The apparent molar volume increases more strongly, upon micelle formation, as the alkyl chain is longer. This increase amounts to 2 4 cm 3 mole -1 per CH2 group.

Apparent Adiabatic Compressibility of Alkyltrimethylammonium Bromides Table II and Fig. 5 show values of apparent adiabatic compressibility of alkyltrimethylammonium bromides in both monomeric and micellar forms. They show a nonlinear decrease in ~1 and a linear increase in ~m with an increasing number of carbon atoms ofalkyl chain. Negative values of/~1 must be ascribed to the effect of hydration of the monomer, and the larger decrease in ~{1at longer alkyl chains may be attributed to stronger hydrophobic hydration. The increase in /3m amounts to about 0.13 × l0 -5 bar -1 per CH2 group. It may be assumed that the apparent molar adiabatic compression of alkyltrimethylamm o n i u m bromides, in either the monomeric or the micellar form, can be divided into contributions of constituent ions: I~ 1 ~- I~l, + -[- I~1,I~ m ~" I~m, + "~-I~m,_.

[28] [29]

Actually Eqs. [28] and [29] can be obtained by differentiation of Eqs. [26] and [27] with respect to pressure at constant entropy. Mathieson and Conway (38) assigned numerical values to the partial molar compression of various cations and anions with reference to I?~cl- = - 1 7 0 × 10 -5 cm 3 mole -1 bar -1. They gave a value for Br-, I(Br- = - 9 5 × 10 -5 cm 3 mole -t bar -~. Using this value we can obtain for the contribution of tetramethylammonium ion l~CH94N+ = 100 × 10 -5 cm 3 mole -~ bar -1. In Table III values of the apparent molar adiabatic compression of alkyltrimethylammonium ion, C~¢TA+, are listed for the tooJournal of Colloid and Interface Science,

Vol. 119,No. 2, October1987

406

ZIELIlqSKI ET AL. TABLE III

Apparent Adiabatic Compression and Apparent Adiabatic Compressibility of Alkyltrimethylammonium Cations (CuTA +) in Monomeric and Micellar Forms

fL+ CNTA+

C~TA+ CsTA + Ct0TA + CI2TA ÷ CIaTA+

(10.5 em 3 mole-~ bar-I)

100 40 -50 -330 -690

-

-

880 1080 1290 1470

~%+ (10-5 bar -1)

1.19 0.20 -0.24 -1.30 -2.46

-

-

4.42 4.68 4.87 4.92

nomeric form. If one assumes that the contribution of counterion remains the same in the micellar form as in the monomeric form, the contribution of the surfactant ion in the micellar form can be derived similarly. Their values are also given in Table III. Furthermore, it is defined as in Eqs. [12] and [ 13] that I ~ l , + = "~rl,+~l,+ I~m,+ = ~/-m,+~m,+

[301

Apparent Adiabatic Compressibility of Other Surfaetants (a) Sodium alkyl sulfates. Now we apply our treatment on the ultrasound velocity to the other surfactant homologs, i.e., sodium alkyl sulfates, whose values of the apparent adiabatic compressibility can be estimated from published data on the ultrasound velocity (15, 16), density (16), and partial molar volume (17). The partial molar volume of sodium octyl sulfate was obtained by extrapolation of published data for decyl, dodecyl, and tetradecyl sulfates (17). Figure 6 shows the apparent adiabatic compressibility of sodium alkyl sulfates in both monomeric and micellar forms as a function of the number of carbon atoms of alkyl chain. In contrast to the case of alkyltrimethylammonium bromides, the value of (~1 increases with increasing number of carbon atoms of alkyl chain. The large negative value of/~l reflects strong hydration of the ionic head group. Mathieson and Conway (38) gave the apparent molar adiabatic compression of sodium cat-

[311

in order to determine the apparent adiabatic compressibility of surfactant ion in the monomeric and miceUar forms. By means of the values of apparent molar volume of alkyltrimethylammonium ions derived above, we can estimate values of the apparent adiabatic compressibility in both monomeric and micellar forms, which are also tabulated in Table III. Since there could be counterion binding of Br- on the micellar cation, the apparent adiabatic compressibility of the micellar cation, tim,+, can be evaluated with great difficulty. Nevertheless, the cationic moiety of micelle has an apparent adiabatic compressibility ranging over (4.4-4.9) X 10-5 bar -1 for alkyltrimethylammonium cations. These values are much lower than those for liquid hydrocarbon (8-11) X 10-5 bar -1 (5), and this decrease can be attributed to the contribution of ionic head group. Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

1

40

°! -1

3.9

-2 -3

aa

to

9-5

z~-6

E 3.7

-7 -8 -9

3.6

-10 i

i

i

i

i

I

2 4 6 8 10 12 NUMBER OF" CARBON ATOM5

FIG. 6. Apparent adiabatic compressibility of sodium alkyl sulfates in the monomeric form (/30 and that in the mieellar form (~m) as a function of length of the hydrocarbon moiety at 25°C. Symbols: (O)/~1, (O) ~m- Note: Based on data from Ref. (16) for N = 1 and from Refs. (15, 1 7 ) f o r N = 8, 10, 12.

COMPRESSIBILITY OF SURFACTANTS

ion, I(Na+ = --335 X 10 -5 cm 3 mole -l bar-L The values o f ~ , _ are -1.71 X 10-5 bar -~ for sodium methyl sulfate and range over - 0 . 6 9 × 10 -5, 0.03 X 10 -5, and 0.37 × 10 -5 bar -1 for sodium octyl, decyl, and dodecyl sulfates, respectively. The increase in/~,_ with an increasing number of carbon atoms suggests a decrease in hydration, possibly around the hydrocarbon chain. The values of ~m are positive, similar to those for alkyltrimethylammonium bromides. The values of ~m,- are (5.27, 5.13, and 5.07) X 10 -5 bar -1 for sodium octyl, decyl, and dodecyl sulfates, which may be regarded as independent of the alkyl chain length. The increase in/~m with the increasing length of hydrocarbon moiety is 0.06 X 10-5 bar -1 per CH2 group, which is nearly half of that for alkyltrimethylammonium bromides. (b) Polyoxyethylene dodecyl ethers. Figure 7 shows the apparent molar volume and the apparent adiabatic compressibility of polyoxyethylene dodecyl ethers (abbreviated as C12Ex) in the micellar form, which was cal-

407

culated from the data published by Harada and Nakagawa (13). The apparent molar volumes are 447.1,486.7, and 524.8 cm 3 mole -1 for C12E6, C12E7, and C~2E8, respectively. They increase with the increasing length of polyoxyethylene chain by 38.8 cm 3 mole -1 per CH2CH20 group. The values of ~m are positive and decrease with the increasing length of polyoxyethylene chain. The decrease in/~m amounts to - 0 . 2 1 6 X 10 -5 bar -1 per CH2CH20 group, which corresponds to the limiting value of the apparent adiabatic compression, I( ° = - 1 1 . 7 X 10-5 cm 3 mole -~ bar -1 per CHzCH20 group. The last value is much lower than the value of I{° = - 7 . 5 X 10 -5 cm 3 mole -1 bar -l per CH2CH20 group reported for the polyoxyethylene alkyl ethers having shorter alkyl chains (42). The decrease in /~m with the increasing number of CH2CH20 groups can be interpreted as a result of the increase in hydration around polyoxyethylene groups with the increasing length of hydrophilic moiety. ACKNOWLEDGMENTS

60(

42

550

4O

The authors express their appreciation to Professor Shin Tsuge and his collaborators of Nagoya University for gas chromatography analysis of the samples used in this study. One of us (R.Z.) thanks the Ministry of Education, Science and Culture of Japan for the scholarship. REFERENCES 5-

aQ tt~ 3.8 ' o

E

,'~E500

E

450

3B

400 I

I

I

I

5 6 7 8 NUMBER OF OXYETHYLENE GROUPS

FIG. 7. Apparent molar volume (Vm)and apparent adiabatic compressibility (/3,,) of polyoxyethylene dodecyl ethers in the micellar form as a function of the number of oxyethylene groups at 25°C. Symbols: (O) ~rm, (0) ~m. Note: Based on data from Ref. (13).

1. Conway, B. E., "Ionic Hydration in Chemistry and Biophysics," Elsevier, Amsterdam, 1981. 2. Tanford, C., "'The Hydrophobic Effect," 2nd ed. Wiley, New York, 1980. 3. Kalyanasundaram, K., G~tzel, M., and Thomas, J. K., J. Amer. Chem. Soc. 97, 3915 (1975). 4. MaUiaris, A., Le Moigne, J., Sturm, J., and Zana, R., J. Phys. Chem. 89, 2709 (1985). 5. Shigehara, K., Bull. Chem. Soc. Japan 38, 1700 (1965). 6. Shigehara, K., Bull. Chem. Soc. Japan 39, 2332 (1666). 7. Shigehara, K., Bull. Chem. Soc. Japan 39, 2643 (1966). 8. Brun, T. S., Hoiland, H., and Vikingstad, E., J. Colloid Interface Sci. 63, 89 (1978). 9. Vikingstad, E., Skauge, A., and Hoiland, H., J. Colloid Interface Sci. 66, 240 (1978). 10. Vikingstad, E., J. Colloid Interface Sci. 68, 287 (1979). 11. Vikingstad, E., and Kvammen, O., J. Colloid Interface Sci. 74, 16 (1980). Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

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ZIELIlqSKI ET AL.

12. Vikingstad, E., and Saetersdal, H., J. Colloid Interface Sci. 77, 407 (1980). 13. Harada, S., and Nakagawa, T., J. Solution Chem. 8, 267 (1979). 14. De Lisi, R., Ostiguy, C., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 71, 147 (1979), 15. Bloor, D. M., GromaUy, J., and Wyn-Jones, E., J. Chem. Soc. Faraday Trans. 1 80, 1915 (1984). 16. Koda, S., and Nomura, H., J. Solution Chem. 14, 355 (1985). 17. Corkill, J. M., Goodman, J. F., and Walker, T., Trans. Faraday Soc. 63, 768 (1967). 18. Ueno, M., Nakahara, M., and Osugi, J., Rev. Phys. Chem. Japan 47, 25 (1977). 19. De Lisi, R., Perron, G., and Desnoyers, J. E., Canad. J. Chem. 58, 959 (1980). 20. Schaefer, K., in "Landolt-B6rnstein: Numerical Data and Functional Relationships in Science and Technology" (K. H. HeUwege, Ed.), Vol. 1, Part B, p. 1. Springer-Vedag, Berlin/Heidelberg/New York, 1977. 2 I. Kale, K. M., and Zana, R., J. Colloid Interface Sci. 61, 312 (1977). 22. Musbally, G. M., Perron, G., and Desnoyers, J. E., J. Colloid Interface Sci. 54, 80 (1976). 23. Conway, B. E., and Verrall, R. E., J. Phys. Chem. 70, 3952 (1966). 24. Franks, F., and Smith, H. T., Trans. Faraday Soc. 63, 2586 (1967). 25. Tartar, H. V., J. ColloidSci. 14, 115 (1959). 26. Zana, R., Yiv, S., Strazielle, C., and Lianos, P., J. Colloid Interface Sci. 80, 208 (1981).

Journalof Colloidand InterfaceScience.Vol.119,No. 2, October1987

27. Evans, D. F., Allen, M., Ninham, B. W., and Founda, A., J. Solution Chem. 13, 87 (1984). 28. Phillips, J. N., Trans. Faraday Soc. 51, 561 (1955). 29. Giiveli, D. E., Kayes, J. B., and Davies, S. S., J. Colloid Interface Sci. 82, 307 (1981). 30. Anacker, E. W., Rush, R. M., and Johnson, S. S., J. Phys. Chem. 68, 81 (1964). 31. Roe, J. M., and Barry, B. W., J. Colloid Interface Sci. 94, 580 (1983). 32. Imae, T., Abe, A., Taguchi, Y., and Ikeda, S., J. Colloid Interface Sci. 109, 567 (1986). 33. Lianos, P., and Zana, R., J. Colloidlnterface Sci. 88, 594 (1982). 34. Evans, D. F., and Wightmann, P. J., J. Colloid Interface Sci. 86, 515 (1982). 35. Scott, A. B., and Tartar, H. V., J. Amer. Chem. Soc. 65, 692 (1943). 36. Desnoyers, J. E., and Arel, M., Canad. J. Chem. 45, 359 (1967). 37. Millero, F. J., in "Water and Aqueous Solutions, Structure, Thermodynamics, and Transport Properties" (R. A. Home, Ed.), p. 519. Wiley, New York, 1971. 38. Mathieson, J. G., and Conway, B. E., J. Solution Chem. 3, 455 (1974). 39. Mukerjee, P., J. Phys. Chem. 65, 740 (1961). 40. Edsall, J. T., in "Proteins, Amino Acids and Peptides as Ions and Dipolar Ions" (E. J. Cohn and J. T. Edsall, Eds.), p. 157. Reinhold, New York, 1943. 41. Friedman, E., Gill, T. J., III, and Doty, P., J. Amer. Chem. Soc. 83, 4050 (1961). 42. Harada, S., Nakajima, T., Komatsu, T., and Nakagawa, T., J. Solution Chem. 7, 463 (1978).