3370
J. Phys. Chem. 1991, 95, 3370-3376
ranges from 56 to 63. This decrease in the dielectric constant
agrees with our experimental evidence showing the effect of these
reverse micelles on the crystal violet visible spectrum.
In Table 1 are shown the pseudo-first-order rate constants for
the reverse CTAB/I-BuOH and CTAB/I-OcOH micelles at a
low content of water. From these results it is deduced that the
change of alcohol practically does not affect the crystal violet basic
hydrolysis rate constant for this amount of water. These results
agree with all the experimental evidence showing that the reaction
occurs in the water pool.
Phase Behavlor of Systems of Cationic Surfactant and Anionic Polyelectrolyte:
Influence of Surfactant Chain Length and Polyelectrolyte Molecular Weight
Kyrre Thalberg,*Vt Bjorn Lindman,t and Gunnar Karlstromt
Physical Chemistry 1 and Theoretical Chemistry, Chemical Center, University of Lund. P.O. Box 124,
S-221 00 Lund, Sweden (Received: July 31. 1990)
Phase diagrams for systems of the anionic polysaccharide hyaluronan (Hy) and cationic surfactants of the alkyltrimethylammonium bromide type have been investigated for different alkyl chain lengths of the surfactant. Furthermore,
the influence of the molecular weight of Hy has been studied. As in previous work, a phase separation into one phase concentrated
in polymer and surfactant and one very dilute aqueous solution is observed. It is concluded that the longer the hydrocarbon
chain of the surfactant, the larger is the twephase region in the phase diagram. A reduced molecular weight of the polysaccharide
results in a slightly changed position of the two-phase region, while the size is little affected within the range studied. The
obtained phase diagrams are rationalized by means of a simple theoretical model, based on the Flory-Huggins theory for
polymer solutions. The effects of surfactant chain length and polymer molecular weight are further discussed in terms of
the surfactant-to-polyelectrolyte ratio in the concentrated phase and the effective ionic strength in the systems.
Introduction
Increasing interest has been directed to aqueous systems containing a polyelectrolyte and an oppositely charged surfactant.
Goddard, who pioneered this field, has determined "solubility
diagrams" for a cationic polyelectrolyte with a number of anionic
surfactants.] By the use of surfactant specific electrodes, the
binding of the surfactant to the polyelectrolyte in different systems
has been investigated, especially by Kwak and HayakawaSz The
surfactant binding is seen to start at a rather well-defined surfactant concentration (denoted by cl), which is always below the
critical micelle concentration (cmc) of the surfactant, and it is
often characterized by a marked cooperativity. Attempts have
also been made to unravel the structure of the resulting surfactant-polyelectrolyte complexes, mainly by means of photophysical
t e c h n i q ~ e s and
~ . ~ by N M R meas~rements.~
Polyelectrolyte-surfactant interactions have been reviewed by
Goddard6 and more recently by Hayakawa and Kwak.' The
general picture for the interaction in dilute solution is that the
surfactant forms micelle-like aggregates adsorbed to the polyelectrolyte chains, in close analogy with aqueous systems of an
uncharged water-soluble polymer and ionic surfactant^.^*^
We have focused our work on the polysaccharide hyaluronan
(Hy), which is used as a sodium salt at pH 7. The interaction
of Hy with cationic surfactants of the alkyltrimethylammonium
bromide type (C,,TAB; n indicating the number of carbons in the
alkyl chain) is seen to follow the general pattern with the surfactant
molecules forming micelle-like aggregates on the polyelectrolyte
chains.'O However, phase separation occurs readily in these
systems, which complicates the investigation of the Hy-surfactant
complexes in dilute solution.
In a previous paper," the phase diagram for the system
NaHy-C14TAB-H20 was worked out in the aqueous part (>60%
water). It consists of a droplet-shaped two-phase region, hanging
from the water corner and being totally enclosed in an isotropic
one-phase region (see also Figure 3). The tie lines are roughly
in the direction from the water corner or a water-rich surfactant
'Physical Chemistry I .
'Theoretical Chemistry.
solution toward the C14TAB-NaHy side of the phase diagram;
i.e., hyaluronan and surfactant prefer to separate out and together
form a concentrated phase, when both are present in an initially
dilute sample. (The properties of the concentrated phase are
described elsewhere.'*) The main reason for this phase behavior
is the electrostatic attraction between the polyelectrolyte and the
surfactant. This is inter alia seen by the fact that screening of
the electrostatic attraction by addition of salt may totally prevent
phase separation (ref 10, Figure 9).
In this work, we continue our investigation of the phase behavior
for systems containing NaHy, C,,TAB, and water. Phase diagrams
for cationic surfactants with n equal to 10 and 12 are presented,
and phase diagrams obtained by using Hy of different molecular
weights are compared. The obtained diagrams are discussed
qualitatively with special regard to the surfactant-t~polyelerolyte
ratio and the effective ionic strength in the different systems. The
experimental phase diagrams are also compared with a theoretical
model as described below.
~~
~
(1) (a) Goddard, E. D.; Hannan, R. B. J . Colloid Interface Sci. 1976,55,
73. (b) J . Am. Oil Chem. Soc. 1977, 54, 561.
(2) (a) Hayakawa, K.; Kwak, J. J . Phys. Chem. 1982, 86, 3866. (b)
Hayakawa, K.; Santerre, J. P.; Kwak, J. Mucromolecules 1983,16, 1642. (c)
Hayakawa, K.; Kwak, J. J . Phys. Chem. 1983,87, 506. (d) Santerre, J. P.;
Hayakawa, K.; Kwak, J. Colloids Surf. 1985. 13, 35. (e) Malovikova, A.;
Hayakawa, K.; Kwak, J. J . Phys. Chem. 1984.88, 1930.
(3) Abuin, E. B.; Scaiano, J. C. J . Am. Chem. SOC.1984, 106, 6274.
(4) Chu, D.; Thomas, J. K. J. Am. Chem. SOC.1986, 108,6270.
(5) (a) Gao, 2.;Wasylishen, R. E.; Kwak, J. C. T. J . Colloid Intetface
Sci. 1988,126,371. (b) Macromolecules 1989,22,2544. (c) J. Phys. Chem.
1990,94,773.
(6) Goddard, E. D. Colloids SurJ 1986, 19, 301.
( 7 ) Hayakawa, K.; Kwak, J. In Carionic sutfactants: Physical Chemistry;
Rubingh, D., Holland, P. M., Eds.;Surfactant Science Series;Marcel Dekker:
New York, 1991; p 189.
(8) (a) Cabane, 9. J . Phys. Chem. 1977, 81, 1639. (b) Cabane B.; Duplessix, R. J . Phys. (Lcs Ulis, Fr.) 1982,13,1529. (c) Cabane, B.; Duplessix,
R. Colloids Surf. 1985. 13, 19.
(9) Goddard, E. D. Colloids Sur/. 1986, 19, 255.
(IO) Thalberg, K.; Lindman, B. J. Phys. Chem. 1989, 93, 1478.
(1 1) Thalberg, K.; Lindman, B.; Karlstram, G. J . Phys. Chem. 1990, 94,
4289.
(12) Thalberg, K.; Lindman, B. Langmuir, in press.
0022.365419 112095-3370$02.50/0 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3371
Aqueous Surfactant-Polyelectrolyte Systems
Tbeoretical Model
c12y
In our previous paper," a simple model was introduced in order
to qualitatively account for the observed phase diagram for the
system NaHy-CI4TAB-H20. A detailed description of the model
and a discussion of its approximations and limitations were also
given, and here, the model is more briefly presented.
The basis of the model is the Flory-Huggins theory applied
to a system of two different polymers (A and B) in a common
solvent (water). In our treatment, polymer A represents the
polyelectrolyte and polymer B the surfactant micelles; Le., a
"polymerization number" is given to the surfactant molecules. (It
is clearly indicated that the concentrated phase contains micelle-like aggregates bound to the polyelectrolyte chains.I2) This
polymerization number is not to be considered as an aggregation
number for the micelles; it should merely be regarded as a fitting
parameter chosen to give good agreement with experiment.
Obviously, there exists a relation between the aggregation number
of the micelle and the parameter L3 in the model; i.e., larger
aggregation numbers correspond to larger L3 values. The main
effect introduced by the use of a polymerization number for the
surfactant molecules is a reduced entropy of mixing of the surfactant molecules with water or polymer. Without this assumption,
the experimental and theoretical phase diagrams disagree strongly.
The interaction energy is modeled by one single interaction
parameter wij for each pair of interacting species i and j in the
system. For a system of water (index 1)-polymer A (index
2)-polymer B (index 3), we thus have five parameters that together
determine the phase diagram, Le., the three interaction parameters
w12,~ 1 3 and
,
~ 2 and
3 the two polymerization numbers L2 and L3.
The Helmholz energy is thus given by
A = RTMolQl In
+ ( 0 2 / L 2 )In a2+ (a3/&)In a3]
+
M0~w12ala2
+ w13aIa3
+ w23a2*3)
where Mois the total number of cells and Qi the volume fraction
of component i in the phase. The interaction parameters are
related to the normal Flory-Huggins interaction parameters
through
= X12RT
Phase diagram calculations are performed for a given set of the
five parameters by minimizing the total Helmholz energy, A,,
in the system with respect to the content of the three components
in the different phases. (In principle, three phases may coexist.)
We will in this work pursue the comparisons between experimentally obtained and theoretically modeled phase diagrams, in
order to illustrate how the changes in phase behavior upon changes
in surfactant chain length and polymer molecular weight can be
rationalized.
w12
Experimental Section
Materials. Hyaluronan (Hy) is a linear biological polysaccharide, built of alternating units of glucuronic acid and Nacetylglucosamine, and was provided by Pharmacia AB, Uppsala,
Sweden, in the form of its sodium salt. The weight-average
molecular weight, M,,of the untreated specimen was about 3 X
lo6 as determined by low-angle laser light scattering (LALLS).
The M, was reduced by acid hydrolysis with 0.1 M HCI at 70
OC, followed by neutralization. The M, of the different preparations used in this study was 2.5 X lo5 (three preparations), 9.0
X lo4, 6.0 X IO4, and 2.3 X lo4. All Hy preparations were
extensively dialyzed against pure water to get rid of excess salt
before use. Hy concentrations are expressed in weight percent
or in millimolar of the repeating monovalently charged disaccharide unit (at pH 7, the carboxylate groups are almost fully
dissociated); 1.0 wt 7% of NaHy corresponds to 25 mM of repeating
units.
The cationic surfactants were all of the alkyltrimethylammonium bromide type. The number of carbon atoms in the
alkyl chain, n, was varied between 8 and 14. These surfactants,
denoted C,TAB, were all purchased from Tokyo Kasei Inc., Tokyo,
Japan. All surfactants were used without further purification.
NaBr (suprapur) was from Merck, Darmstadt, G.F.R.
%NaHy
-
NaHY
Figure 1. Experimental phase diagram for the system NaHy (M,2.5
X 10S)C12TAB-H20.The compositions of some samples are indicated.
Open circles refer to the initial sample compositions, and filled circles
connected by tie lines refer to the compositions of the two separated
phases in equilibrium. The dashed part of the phase boundary indicates
a larger uncertainty. The charge neutralization line refers to compositions with equal amounts of surfactant cations and Hy carboxylate
groups.
Determination of Phase Diagrams. Samples with a NaHy
concentration of about 0.9 wt % and a surfactant concentration
in the range 1.0-20 wt 7% were thoroughly mixed and equilibrated
for several days, until macroscopic phase separation into two clear
and neatly separated phases was completed. The viscosity of the
dilute phase (the supernatant) was close to that of pure water,
while the concentrated phase most often was highly viscous. The
two phases of the samples were separated, and their relative
amounts were assessed. Determinations of the content of polyelectrolyte, surfactant cation, and bromide were carried out in
each dilute phase, as described previously." From these results,
the concentration of each of these components in the corresponding
concentrated phase is calculated.
Phase diagrams are presented on the basis of weight. Conversion of the concentrations of surfactant and polyelectrolyte into
weight percent has been done disregarding the distribution of Na+
and Br- in the system. Thus, the NaHy content is calculated from
the Hy- concentration and the C,TAB content from the C,TA+
concentration in each phase. In this way, pseudo three-component
phase diagrams, which are easy to conceive, are obtained. In
reality, however, we deal with four-component systems, and the
compositions of separating phases do not in general fall into the
illustrated plane.
Results
Effect of Surfactant Chain Length. In Figure 1, the pseudo
three-component phase diagram for the water-rich part of the
system NaHy (M,2.5 X 10S)-C12TAB-H20 is shown. A droplet-shaped two-phase region is seen, hanging from the water
corner and the watersurfactant side of the diagram. The tie lines
are in the direction from this corner and toward the NaHysurfactant side of the diagram. This means that NaHy and
C12TABprefer to form a concentrated phase together, separating
out a supernatant solution essentially consisting of water. If an
excess of surfactant is used, surfactant micelles are left in the
supernatant. The behavior of this system is thus analogous to the
system of NaHy, C14TAB,and water as reported earlier."
A similar picture emerges also when C12TABis replaced by
CIoTAB(Figure 2). In this case, however, the two-phase region
is considerably smaller. (Note the difference in scales.) This is
clearly seen in Figure 3 in which all three phase diagrams are
compared.
A difficulty in the investigation of the C,4TAB-NaHy system
was to determine the boundary of the two-phase region toward
high NaHy and relatively low surfactant concentrations (i.e., the
lower right phase boundary). The location of phases arising from
phase-separating samples seldom fall in this part of the diagram,
and direct mixing is difficult, because precipitates tend to form
locally in the sample due to the elevated viscosities of concentrated
3372 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
Thalberg et al.
:j@-\l:
cloy
50
OO
t
10
% NaHy
I
20
) - - - NaHy
30
50
10
20
100 200 300
Surfactant concentration (mu)
400
0
Figure 4. Critical electrolyte concentrations (cec) of NaBr in systems
of NaHy, C14TAB,and H20at two different Hy molecular weights: 6.0
X lo4 (squares) and 3.1 X 106 (circles). Open symbols refer to clear
one-phase solutions and filled symbols to two-phase dispersions. 1 @ and
2@ refer to one-phase and two-phase regions, respectively.
Figure 2. Experimental phase diagram for the system NaHy (M,2.5
X 1O5)-CIoTAB-H20.Symbols, etc., as in Figure I . The squares refer
C127AB
to the phase boundary as determined by direct mixing, as is further
described in the text.
CnTAB
6011‘
%Natty
%NaHy
-
-
Figure 3. Comparison of phase diagrams for systems with NaHy, H20,
and the surfactants CloTAB,C12TAB,or C14TAB(tie lines omitted).
The molecular weight of the Hy preparation used was about 2.5 X lo5
in all the systems.
NaHy solutions. In the case of CloTAB, this part of the phase
diagram is easier to study because of the considerably weaker
interaction between surfactant and polyion and was therefore
studied in more detail. The squares along this side of the two-phase
region in Figure 2 refer to the midpoint of the interval between
where a two-phase behavior first is identified and where no signs
of phase separation could be detected; the width of the intervals
was approximately 0.1 wt % surfactant. It should be noted,
however, that the phase boundary as determined in this way does
not necessarily correspond to the phase boundary traced out by
the phase-separating samples, as the latter do not generally fall
into the plane represented in the figure. (This problem will be
dealt with in a future article.)
Effect of Polymer Molecular Weight. The critical electrolyte
concentration (cec) is defined as the concentration of salt needed
in order to prevent phase separation in systems containing two
oppositely charged colloids. Cec values for NaBr have been
determined previously in systems containing 1 .O mM NaHy and
C,TAB (n equals 10-16; ref 10, Figure 9). In Figure 4, the
influence of the molecular weight of Hy on the cec of NaBr in
samples containing CI4TABand 1.O mM NaHy (0.04 wt %) is
shown. An increase in cec is observed when the molecular weight
of Hy is increased. It is also seen that the C14TABconcentration
needed in order to obtain redissolution in the absence of added
salt is increased from about 350 to 450 mM. Similar results were
obtained with CloTAB and C12TAB.
For the system NaHy-C,,TAB-H,O, the phase diagram was
worked out for Hy of three different molecular weights, namely,
2.5 X IO5 (the phase diagram presented in Figure l), 9.0 X IO4,
and 2.3 X IO4. The phase diagrams are compared in Figure 5a.
Apparently, the difference in polyelectrolyte molecular weight
brings about shifts in the position of the two-phase area, while
its shape and area remain largely constant. Similar findings were
% NaHy
-
Figure 5. Experimental phase diagrams for (a, top) the system NaHy-
C12TAB-H20at three different Hy molecular weights and (b, bottom)
the system NaHy-C,oTAB-H20 at two different Hy molecular weights.
obtained for the systems with CloTAB (Figure 5b) and C14TAB,
which indicates that the shifts are real and not due to experimental
errors in the establishment of the phase diagrams. It is concluded
that a 10-fold decrease in M, of the polyelectrolyte (from 2.5 X
lo5 to 2.3 X 104) only induces relatively small changes in the phase
diagram.
Comparison with the Model
Effect of Surfactant Chain Length. As a starting point in our
attempts to model the observed phase behavior, the theoretically
calculated phase diagram for the system NaHy-C14TAB-water
(Figure 8 in ref 11) was chosen. The effect of a decreased surfactant chain length may be modeled in different ways. First,
the aggregation number for free micelles13as well as for Hy-bound
micellesI4 decreases. In Figure 6, calculated phase diagrams, with
different degrees of ‘polymerization” of the surfactant compound,
are shown. As expected, the two-phase region decreases in size
(13)
(14)
Berr, S. S.J. Phys. Chem. 1987, 91, 4760.
Thalberg, K.;van Stam, J.; Lindblad, C.; Almgren, M.; Lindman, B.
Manuscript in preparation.
The Journal of Physical Chemistry, Vol. 95, No. 8, 1991 3373
Aqueous Surfactant-Polyelectrolyte Systems
Polymer B
Polymer B
/
"20
/
, , , , /
10
20
% Polymer A
30
-- -Polymer
A
40
Figure 6. Theoretically calculated phase diagrams for a system of two
different polymers in a common solvent. Index 1 stands for the solvent
(water), index 2 for polymer A (representing the polyelectrolyte),and
index 3 for polymer B (representingthe surfactant). w12= -200 J/mol,
wI3= IO00 J/mol, ~ 2 =3 -5200 J/mol, and & = 300 in all the diagrams.
The polymerization number for polymer B, L3, is 25, 20, or 15. The tie
lines, which in large agree with the tie lines seen in the experimental
systems, have been omitted. The phase diagram with L3 = 25 is the same
as in our previous work" and may be regarded as representing the phase
diagram Na Hy-C I ,TA B-H20.
% Polymer A
-Polymer A
-
Figure 7. Theoretically calculated phase diagrams for a system of two
,
& are as in Figure
different polymers in a common solvent. w12,~ 1 3 and
6. L3 = 25. The interaction parameter ~ 2 equals
3
-5200, -5000, or
-4700 J/mol.
Poly,mer B
with a decrease in L3, in accordance with the effect seen experimentally (Figure 3).
A second way to model the shorter surfactant chain length is
by making the interaction between the polyelectrolyte and the
surfactant micelles less favorable. This may be rationalized by
the observation that the c,/cmc ratio decreases when the surfactant
chain length is increased.'O The (molar) free energy of micellization, A P , , is to a first approximation equal to R T In cmc, and
the free energy of surfactant binding to the polyelectrolyte may
analogously be written Aceb = R T In cI. For the reaction free
micelle * polyelectrolyte-bound micelle, the change in free energy
per mole of surfactant molecule is given by
AGe(free micelle * bound micelle) = RT In (cl/cmc)
Figure 8. Theoretically calculated phase diagrams for a system of two
3 as in Figure 6, ~ 2 =
3
polymers in a common solvent. w 1 2and ~ 1 are
-5200 J/mol, and L3 = 20. L2, the polymerization number for polymer
A, representing the Hy polyelectrolyte, is set to 600, 300, or 100.
This indicates a decrease in the free energy when the ratio c,/cmc
decreases. The interaction between polyelectrolyte and surfactant
thus becomes less favorable when the surfactant chain length is
decreased. (This can be rationalized from the electrostatics of
surfactant self-assembly (see ref 10) and is further discussed in
the section Effective Ionic Strength below.)
If we assume that the entropy terms for normal micellization
and polyelectrolyte-induced micellization are similar, this effect
can be ascribed to different interaction energies between the
polyelectrolyte and the different surfactants. In the model this
corresponds to an increase in the interaction parameter ~ 2 between
3
the two polymers (it becomes less negative), when the surfactant
chain length is reduced.
Phase diagrams for three different values of ~ 2 are
3 shown in
Figure 7. A reduction of the two-phase region is obtained as Iwz31
is decreased. The effect is in large similar to the one obtained
when L3 is decreased, and we have thus two effects that contribute
to the observed reduction of the two-phase region when the
surfactant chain length is decreased. The two effects are not
completely identical, however, as a change in wz mainly influences
the length of the two-phase region, i.e., the extension in the direction of the tie lines, while a change in L3 has a larger influence
on the width of the two-phase region, Le., in the direction perpendicular to the tie lines. If we examine the experimentally
obtained phase diagrams in Figure 3, a change in the length of
the two-phase region dominates in the system with CloTAB, as
compared to the other systems, while the change in this direction
is less important between the systems with C12TABand CI4TAB.
It thus seems that a reduction of the interaction between polyelectrolyte and surfactant is the major reason for the reduced size
of the two-phase region in the CloTABsystem. The same effect
may explain why phase separation is not seen at all in the system
3
of -4500 J/mol gives no phase separation
with GTAB; a ~ 2 value
in the model, if the other parameters are as in Figure 7.
Effect of Polyelectrolyte Molecular Weight. The effect of a
changed molecular weight of the polyelectrolyte is modeled by
a change in L2. As is seen in Figure 8, the effect of reducing L2
is a slight decrease in the size of the two-phase region. The
reduction is seen to take place mainly at the upper side of the
two-phase region and is different from the effects induced by a
decrease in L3 or ~ 2 3 .
The higher redissolution concentration and the increase in cec
of NaBr when the molecular weight of the polyelectrolyte is
increased (Figure 4) are clearly in accordance with the trend seen
in Figure 8 and are due to the different entropy contributions for
Hy of different molecular weights. Hy of a higher M , contributes
less to the entropy of the system and will thus redistribute more
easily. The concentrated phase is therefore expected to be favored
when the M , of Hy is increased, and more added salt is needed
in order to prevent phase separation.
In the experimentally obtained phase diagrams with Hy of
different molecular weights (Figure Sa,b), some interesting points
emerge. The first is that the two-phase region may be displaced
slightly to the right when the Hy molecular weight is reduced.
The second point is that no significant decrease in the extension
of the two-phase region is detected in the experimental studies,
although the molecular weight of Hy was reduced by a factor of
10. A possible explanation to the latter observation is that the
initial polymerization number L2, representing Hy, was too low
in the model. As it is the inverse Lz value that enters into the
entropy expressions, no significant change is expected in the model
as long as & is large. Only when going to relatively short polymer
molecules is a significant change in the phase behavior expected.
The displacement of the two-phase region to the right when
the Hy molecular weight is reduced, can, however, never be ex-
H20-)-Poylmer
10
20
% Polymer A
30
40
A
3374 The Journal of Physical Chemistry, Vol. 95, No. 8, 1991
plained by the model. The reason for this observation is at present
not clear. Among the facts that may be considered is that the
composition of the supernatant phase differs slightly between
samples with different Hy molecular weights. A lower Hy molecular weight gives more Hy in the supernatant phase. This will
in turn lead to changes in the distribution of the other components
between the two phases. It should be remembered that the systems
in reality are four-component systems, and the experimental phase
diagrams shown are mere projections of the sample compositions
onto ternary systems. Other possible reasons for the discrepancies
between observed and calculated phase diagrams are that there
is an entropy for the pairing of micelles with polyelectrolyte
chains,I5 which may be dependent on the polyelectrolyte chain
length and/or that the interaction energy between the polyelectrolyte and the micelle (per polyelectrolyte segment) may depend
on the length of the polyelectrolyte chain.
Despite these discrepancies between experimentally determined
and theoretically calculated phase diagrams, we believe that the
model gives an adequate insight into the basic physics governing
the behavior of polyelectrolyte-surfactant systems. In view of
the simplicity of the model as compared to the complexity of the
systems (cooperativity, microstructure, chemical structure, etc.,
are features that cannot be taken into account), its use is limited
to qualitative analysis. It is also emphasized that the parameters
of the model are interdependent; Le., the value ascribed to one
parameter depends on the actual values of the others. Thus, more
than one combination of parameters may give the same phase
diagram. However, this reflects the real situation where indeed
different systems, being characterized by different parameters,
may by coincidence give the same phase diagram.
Thalberg et al.
8
K
0
K
0
100
200
300
400
500
Total surfactant concentration (mM)
Figure 9. Ratio between bound surfactant molecules and Hy charges in
the concentrated phase, Rb, and the ratio of excess surfactant molecules
to Hy charges, Re,, in the same phase, plotted as a function of the total
surfactant concentration in the system NaHy-C14TAB-H20.
a common solvent further supports this, and by assuming reasonable values for the parameters in this model a credible, albeit
crude, explanation for the observed phase diagram is provided."
The marked disymmetry in the location of the two-phase region
with respect to the bisector of the water corner can be modeled
by a larger hydrophilicity and/or by a larger size of polymer A,
representing the polyelectrolyte. (See also the discussion on the
effect of polyelectrolyte molecular weight above.) The effect of
a decreased surfactant chain length may also be accounted for,
as discussed above.
While the theoretical model may rationalize the observed phase
behavior of these systems, a further examination of the phase
diagrams and especially of the composition in the concentrated
Discussion
phase may give more information about the nature of the forces
Experimental Phase Diagrams. The dominating interaction,
behind the interaction parameters and about the molecular orwhich will govern the phase behavior of two oppositely charged
ganization in the systems.
colloidal particles in a common solvent, is their favorable interCharge neutralization lines are inserted in Figures 1 and 2. It
action with each other relative to their interactions with the solvent.
is seen that the extension of the two-phase region is not in the
They therefore tend to phase-separate and together form a condirection of charge neutrality between surfactant and polyeleccentrated phase (also called a coacervatei6),in which many more
trolyte. The preferred surfactant-to-Hy ratio in the concentrated
contacts can be formed between colloidal particles of opposite
phase seems instead to be about 3:l (see below). This indicates
charge than in dilute solution. The water content of the conthe presence of other important interactions besides the electrocentrated phase will be determined by the strength of this favorable
static ones in the system, namely, the hydrophobic interaction
interaction, by the size of the particles, and by the hydrophilicity
between surfactant monomers, accompanied by an entropy increase
of the resulting complexes. As long as the two species are large,
for the water molecules released upon surfactant aggregation (the
the gain in interaction energy will largely overcome the loss in
hydrophobic effect). The location of the two-phase region is indeed
entropy for redistributing the molecules and phase separation will
a support for the existence of micelle-like surfactant aggregates
result. Systems of this type have been studied for a long time,
in the concentrated phase. Furthermore, this indicates that the
and a detailed overview has been given by Bungenberg de Jong.16
polyelectrolyte chains are not able to neutralize the surfactant
The mechanism behind the favorable interaction, which is
micelles more than to a minor part, while the major fraction of
referred to as "electrostatic", is not the pure electrostatic interaction
the counterions are bromide ions also in this phase. The reason
between the two species, since counterions are always present close
for the relatively low fraction of polyelectrolyte counterions is at
to charged colloidal species. Therefore, the pure Coulomb energy
present not quite clear. Among the factors that may contribute
is not likely to be significantly changed when an oppositely charged
to this effect are the stiffness of the Hy chain and its low charge
colloid is added. It is instead, we argue, the release of counterions
density and the loss in conformational entropy for a polymer chain
when the two colloids are approached, with a corresponding gain
associated with coiling up around a micelle.
in entropy, that gives the major contribution to the free energy
Surfactant-to-PolyelectrolyteRatio. The ratio between surof interaction between the two species and that should be regarded
factant cations and anionic polyelectrolyte segments in the conas the driving force behind the phase behavior.
centrated phase is a useful parameter in the characterization of
Systems of a polyanion and an oppositely charged surfactant
the phase behavior. We calculate this ratio in two ways; &, is
are seen to largely follow this general behavior, and in particular,
defined as the (molar) concentration of bound surfactant molecules
they show a phase behavior very similar to systems of two op(Le., the surfactant concentration in the concentrated phase minus
positely charged polyelectrolytes in a common ~ o l v e n t . ~This
~ * ~ ~ the free surfactant monomer concentration, c l ) divided by the
indicates that the surfactant molecules behave as a second colloidal
(molar) polyelectrolyte concentration, while the excess surfacspecies in the system. The successful treatment of these systems
tant-to-polyelectrolyte ratio, &, is defined as the excess surfactant
by the Flory-Huggins theory for a mixture of two polymers in
concentration in the concentrated relative to the supernatant phase,
divided by the polyelectrolyte concentration.
Figure 9 relates these parameters to the total surfactant con( I 5 ) Cates, M.E.; Witten, T. A. Macromolecules 1986, 19, 732.
centration in samples of the system C14TAB-NaHy (M,2.5 X
(16) Bungenberg de Jong, H.G. In Colloid Science; Kruyt, H. R.,Ed.;
Elsevier: Amsterdam, 1949 Vol. 11, Chapters 8-1 I; phase diagrams in section
105)-H@. After an initial rise, Rb is seen to level out and then
10:2.
again to increase a t high total surfactant concentrations. The
( I 7) Djadoun, S.;Goldberg, R. N.; Morawetz, H. Macromolecules 1977,
initial increase corresponds to the part in the phase diagram where
10, 1015.
the tie lines change direction, Le., the region where the concen(,18) Frugier, D. Doctoral dissertation, UniversitC Pierre et Marie Curie,
Paris, 1988.
trated phase takes up all surfactant added to the system. The
~
~~~
The Journal of Physical Chemistry, Vol. 95, NO. 8, 1991 3375
Aqueous Surfactant-Polyelectrolyte Systems
6
c
4
51
100
0
200
300
400
500
Total surfactant concentration (mM)
Figure 10. Comparison between R, in systems of NaHy (M,2.5 X 1@),
C,TAB, and water. Squares refer to C14TAB,circles to C,2TAB,and
triangles to Cl0TAB.
6
5
“0
100
200
300
400
Total surfactant concentration (mM)
Figure 11. Effect of Hy molecular weight on Rb (full lines and symbols)
and R, (dotted lines, open symbols) in the system NaHyC12TAB-H20.
Squares refer to M, 2.5 X 10) and circles to M, 9.0 X 10‘.
surfactant concentration in the supernatant is here close to the
cI concentration; therefore, no difference exists between Rb and
Rea. The divergence between the two curves arises when free
surfactant micelles start to appear in the supernatant (at a total
CI4TABconcentration of about 75 mM). Interestingly, Rexremains approximately constant from this point up to the very
highest total CI4TABconcentrations, where a decrease is seen.
(Rta, of course, goes toward zero on approach of the one-phase
region, which is attained at about 480 mM in the present system.)
The leveling out of Re, suggests that the Hy chains become
saturated with CI4TA+at a ratio of between 3 and 4 surfactant
cations per repeating monovalently charged Hy unit. From the
point where this ratio is attained in the concentrated phase, further
added surfactant distributes evenly between the two phases, as
if no polyelectrolyte were present.
The other two surfactants show a similar behavior as is seen
in Figure 10 (Rea values only). The saturation ratio is however
lowered somewhat when the surfactant chain length is decreased
and is about 3:l in the CI2TABsystem and slightly less in the
CloTAB system.
The influence of Hy molecular weight on Rb and Rexin the
C12TABsystem is shown in Figure 11. Both ratios show a slight
decrease when the Hy molecular weight is reduced from 2.5 X
los to 9.0 X IO4; Le., the concentrated phase contains more Hy
per surfactant molecule when the Hy molecular weight is reduced.
This reflects a higher Hy concentration in the concentrated phase
formed at low total surfactant concentrations and a lower surfactant concentration in the concentrated phase formed at high
surfactant concentration when the molecular weight of Hy is
reduced. A similar behavior is seen in the CloTAB-NaHy system.
Effective Ionic Strength. An interesting point is that the
two-phase region of the phase diagram is much smaller for
CloTAB than for the two other surfactants studied (Figure 3).
The same pattern is seen as regards redissolution by salt (ref 10,
Figure 9); Le., the critical electrolyte concentration (cec),of NaBr
is much lower in the system containing CloTAB (plateau level
at 70 mM) than for systems with C12TAB and CI4TAB(plateau
levels of 120 and 140 mM, respectively).
The rather small micelles formed by this surfactant may partly
account for this behavior, but another contribution to this effect
which seems more significant is that the electrostatic interaction
between surfactant and polyion is more screened in the CloTAB
system as compared to the other systems. Clearly, the addition
of salt will screen the electrostatic interaction between polyanion
and an oppositely charged micelle. In the absence of salt, the
electrostatic interactions will be screened only by the free surfactant monomers and their counterions and by the polyelectrolyte
counterions. The free surfactant monomer concentration required
for surfactant binding to the polyelectrolyte to occur, i.e., the c1
concentration, is quite low in the CI4TABand the C12TABsystems
(approximately 0.5 and 5 mM, respectively); in both cases it is
lower than the total NaHy concentration in the system, which
is about 23 mM. In the CloTABsystem, c1is considerably higher,
about 50-60 mM, and will thus give rise to a significant screening
of the electrostatic interaction between micelle and polyion.
Therefore, the interaction between polyelectrolyte and surfactant
is considerably reduced in the case of CloTAB,which in turn leads
to a considerably smaller two-phase region.
The cec for NaBr in the NaHy-CloTAB system a t 1.0 mM
NaHy is about 70 mM. If the contributions from the unassociated
surfactant monomers with their counterions and the added salt
are taken together, an effective cec of about 120 mM is obtained
in this system, which is comparable to the effective cec values
obtained in the CI2TAB(125 mM) and CI4TABsystems (140
mM) at the same Hy concentration. It is concluded that an
effective ionic strength equal to the sum of the free surfactant
monomer concentration and the concentration of added salt is
acting in these systems. (For a complete description, half of the
total polyelectrolyte concentration should also be included.)
The contribution of free surfactant monomers to the effective
ionic strength in the system may also explain why phase separation
does not occur in the system containing C9TAB and Hy.l0 The
cmc for this surfactant has been evaluated to about 140 mM,I9
a concentration of electrolyte that is expected to suppress phase
separation in this system.
Conclusions
Phase diagrams for aqueous systems of NaHy and cationic
surfactants of different chain length have been investigated. The
extension of the two-phase region decreases when the surfactant
chain length is decreased, due to a weaker interaction between
the surfactant micelles and the polyelectrolyte chains as well as
to smaller micelles for surfactants with a shorter chain length.
The considerably smaller size of the two-phase region for the
surfactant CloTAB is explained by the relatively high free surfactant monomer concentration for this surfactant, which screens
the electrostatic interactions. The critical electrolyte concentration
(cec) of NaBr is also considerably lower for this surfactant, but
if the free monomer concentration is taken into account, an effective ionic strength close to that in the other systems is obtained.
The electrostatic screening due to the free surfactant monomer
concentration explains why phase separation is not seen in systems
with a shorter surfactant than CloTAB.
The location of the concentrated phase suggests a structure of
micelle-like surfactant aggregates, adsorbed to the Hy chains. Brstill provides the largest fraction of counterions.
The excess surfactant-to-Hy ratio in the concentrated phase
reaches a plateau level in the concentrated phase, indicating
saturation of the Hy chains with the surfactant. This ratio is
between three and four in the CI4TAB-NaHy system and decreases slightly with a reduced surfactant chain length. Above
the saturation point, further added surfactant distributes evenly
between the two phases.
The Hy molecular weight only slightly influences the phase
diagram, within the range of molecular weights studied. A
tendency for formation of a denser concentrated phase at lower
~~~
(19) Mukerjee, P.; Mysels, K. J. Critical Micelle Concentration of
Aqueous Surfacranr Systems; National Bureau of Standards: Washington,
DC, 1971.
3376
J . Phys. Chem. 1991, 95, 3376-3379
Hy molecular weight is seen. This could not be explained by the
theoretical model.
Acknowledgment. We are grateful to Drs. Bengt Jonsson,
Svante Nilsson, and Mikael Bjorling for fruitful discussions.
Ingegerd Lind is acknowledged for skillful technical assistance
and for drawing most of the figures and Ingela Hillgng, Pharmacia
AB, for performing the molecular weight determinations. This
work was financially supported by Pharmacia AB.
Registry No. NaHy, 9067-32-7; C,,TAB, 2082-84-0 DTAB, 1 1 1994-4; C,,TAB, 1 1 19-97-7.
Turbidity Measurements of Binary Polystyrene Solutions Near Critical Solution Points
Weiguo Shen, Careth R. Smith,+Charles M. Knobler, and Robert L. Scott*
Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90024
(Received: August 27, 1990)
Correlation lengths ( I ) and susceptibilities( x ) for three binary mixtures of methylcyclohexane + polystyrene (M,= 13OO0,
23 OOO, and 29 OOO) at various temperatures near the upper critical solution points have been determined by a series of turbidity
measurements at various wavelengths and temperatures. The critical exponents v and y have been determined from the
temperature dependences of ( and x and are in a reasonably good agreement with the theoretical predictions. The prefactors
p and xo, which have been determined by two methods, are uncertain by more than 20%, but their ratio has been determined
more precisely.
Extensive investigations of light scattering in the critical region
for binary mixtures of cyclohexane with polystyrene samples of
different molecular weights were first carried out by Debye et al.’-3
in order to determine the “molecular force range”. More recent
light-scattering studies of the same systems4s5were used to determine the behavior of the correlation length ( and the susceptibility x in the critical region, where they are expected to diverge
according to
t = t O [ ( T- Tc)/Tcl-”
(1)
x = x O [ ( T -Tc)/Tcl-T
(2)
The prefactors Fo and xo and the critical exponents v and y are
constants, and T, is the critical temperature.
The susceptibility and correlation length can be obtained from
measurements of the angular dependence of the scattered light
or from studies of the turbidity as a function of temperature. This
latter method was employed by Puglielli and Ford6 in an investigation of gas-liquid critical phenomena and, more recently, by
Jacobs and co-workers’~*in studies of binary mixtures.
The relation between the turbidity T , t, and x may be expressed
by an integrated form of the Ornstein-Zernike equation6s9
T = (n3/ Ao4) (8n2/84)’kBTXf(~)
(3)
where A,, is the wavelength of light in a vacuum, kBis Boltzmann’s
constant, n is the refractive index of the solution, and I$ is the order
parameter. The correlation length enters through the function
with a = 2(2nn(/A#.
Jacobs et ala8made a series of measurements of turbidity versus
temperature at a fixed wavelength for the mixture polystyrene
diethyl malonate. They found it necessary to introduce a
background parameter in order to fit the experimental data to
eqs 1-4. The fits are sensitive to this extra scattering, and it was
found that both prefactors and exponents could not be determined.
The least-squares analysis was therefore carried out with y and
v fixed at their theoretical values.
The parameter a can be varied by changing the wavelength,
allowing the susceptibility and correlation length to be determined
+
‘Present address: British Gas Corp., Bristol, England.
from turbidity measurements at a fixed temperature. This is the
procedure that we have employed to study binary mixtures of
polystyrene samples of three different molecular weights with
methylcyclohexane. The critical behavior of such mixtures was
previously investigated by Dobashi et a1.I0 and by Shinozaki et
al.” Our interest in them arises from their connection to the
three-phase equilibria’2 in bimodal mixtures of polystyrene with
methylcyclohexane and the character of tricritical points in such
ternary polymer + solvent systems.I3
Experimental Section
Materials. Methylcyclohexane (>99%) obtained from Aldrich
Chemical Co. was dried and stored over sodium wire. Polystyrene
samples with weight-average molecular weights 13 000,23 000,
and 29000 were purchased from Pressure Chemical Co. The ratias
of the weight-average to the number-average molecular weights
were reported to be 51.06. The polymer samples were dried in
a vacuum desiccator over Pz05for 24 h before use.
Preparation of Mixtures. The critical compositions of the
mixtures were approached by adjusting the proportions of the two
components in order to achieve equal volumes of the two phases.
Mixtures were first prepared in 10 mm i.d. glass tubes provided
with Ace-Thred connections, which allowed them to be sealed with
Teflon caps. Each sample contained about 2 g of polymer. The
loading composition was determined by weight and was reproducible to 0.1%.
Samples were mixed by continuous end-over-end rotation of
the tubes for 72 h while they were simultaneously heated with
(1) Debye, P.; Coll, H.; Woermann, D. J . Chem. Phys. 1968,33, 1746.
(2) Debye, P.; Woermann, D.; Chu, B. J Chem. Phys. 1962, 36, 851.
(3) Debye, P.; Chu, B.; Woermann, D. J . Chem. Phys. 1962. 36, 1803.
(4) Kuwahara, N.; Fenby, D. V.; Tamsky, M.; Chu, B. J . Chem. Phys.
1971, 55, 1146.
(5) Kojima, J.; Kuwahara, N.; Kaneko, M. J. Chem. Phys. 1975,63,333.
(6) Puglielli, V.; Ford, N. C., Jr. Phys. Reo. Lefr. 1970, 25, 143.
(7) Jacobs, D. T. Phys. Reo. A 1986.33, 2605.
(8) Stafford, S.G.;Ploplis, A. C.; Jacobs, D. T. Macromolecules 1990,
23, 470.
(9) Omstein, L. S.;Zernike. F. Proc. K.Ned. Akod. Wer. 1914,17,793.
(IO) Dobashi, T.; Nakata, M.; Kaneko, M. J. Chem. Phys. 1980,72,6685,
6692.
(1 1) Shinozaki. K.; Hamada, T.; Nose, T. J. Chem. Phys. 1982,77,4734.
(12) Dobashi, T.; Nakata, M. J . Chem. Phys. 1986, 84, 5775.
(13) Shen, W.; Smith, G. R.; Knobler, C. M.; Scott, R. L. J. Phys. Chem.
1990, 94, 7943.
0022-3654191 12095-3376%02.50/0 0 1991 American Chemical Society