Sept., 1962
DEKSITY OF MICELLES OF XXSOCIATIOS COLLOIDAL ELECTROLYTES
1733
THE PARTIAL SPECIFIC VOLUME ASD THE DEKSITY OF MICELLES OF ASSOCIATION COLLOIDAL ELECTROLYTES’ BY PASUPATI ~MUKERJEE~ Department of ChPmistry, TJnivprsity of Southern California, Los Angeles 7, California Received M a y 11 1966 ~
Density data of aqueous solutions of association colloidal electrolytes are analyzed. Methods are suggested for deriving the true partial specific volume of the micelles and also the true specific volume and the density. The assumptions involved are examined in detail and the associated probable errors shown to be small. The method is applied to several anionic and cationic association colloidal electrolytes for which precise experimental data are available in the literature and it can be extended readily to other charged colloidal articles. The final results show that little error ( ~ 4 7 is~ made ) on using the experimental partial specific volume for t i e true volume when counterions are small and monovalent. With heavy and highly charged counterions, however, much larger errors are possible. Giant micelles show curious abnormalities.
A knowledge of the density of a charged colloid or macromolecule in solution, aside from its intrinsic importance, provides an important part of the bridge leading from weight concentration and mass to volume fraction and volume. The former are accessible directly and by light scattering, while the latter are of importance in the interpretation of diffusion, ultracentrifugation, viscosity, electrophoresis, and many other methods of study. The estimation of this density involves the typical difficulties associated with all solutes. To obtain the true density of the anhydrous solute from the experimentally accessible partial voIumes,3 allowance must be made for solute-solvent interactions, since the partial volumes can be looked upon as the SUM of the true volumes of the ions themselves and of the associated volume changes of the solvent. The present paper attempts to estimate the true partial specific volume and then the density of micelles of association colloidal electrolytes (ACE’S) from the density of micellar solutnons by the application of our existing knowledge regarding the structure of micelles and some recent investigations on the interaction of small ions with water. ACE’S are one of the simplest and best characterized colloid systems nom available and therefore one of the most tractable. The valueci derived in this paper can be used immediately for a large number of interpretations. The currently accepted picture of micelles in water or salt solutions of not too high concentrations is basically that of Hartley.“.s A large number (30-100) of monomeric ions are aggregated into a compact spheroidal body on the surface of which the charged heads remain exposed to the water. Strong elertrical interactions cause about twothirds of the counterions to be fir,mly bound to the surface of this aggregate, which may be rough.6 The remaining third is in the diffuse double layer surrounding the aggregate. The colloidal kinetic particle consists of the aggregate of the amphipathic (1) This work wag supported in part by the Office of Naval Research and presented a t the 132nd National Meeting of the American Chemical Society in New York, September, 1957. Reproduction in part or in whole for purposes of the U. S. Government is permitted. (2) Departinent of Physical Chemistry, Indian Assaclation for the Cultivation of Science, Calcutta 32, Indla. (3) E. A Guggenheim. “Thermodynamics,” Nbrth-Holland Publishing Co., $msterdam, Third Edition, 1957. (4) G. Sa Hartley, “Aqueous Solutions of Paraffin-chain Salts,” Hermann, Paris 1936. (5) G. 8. Hartley, Ann. Rep. Chilm, Soc., London, 46, a3 (1948). ( 6 ) D,Btigter and IC, Ja Mvselri f . Bhv.9, Chsm., 60, 45 llflirb),
ions, the firmly bound counterions, and the water of hydration. Thus we can distinguish the following entities: (1) the anhydrous and electrically neutral micellar component, Le., the micelle with an equivalent amount of counterions; ( 2 ) the anhydrous micelle, which includes only the firmly attached counterions; and (3) the hydrated micelle, which includes the firmly attached counterions and the firmly attached mater. In this paper we are concerned with the partial volume of the first, the partial and true volume of the second, and the electrostriction of the surrounding water, but not with the volume OT the third one. Method of Calculation A typical plot of specific volumes against concentration of an ACE in water shows a more or less obvious
change of slope a t the critical micelle concentration (c.m.c.1 and an almost linear variation above it (Fig. 1 ) . 7 From the slope above the c.m.c. we get the partial specific volume of the micellar component, Vs, on the assumption that the monomer concentration remains constant. This assumption has frequently been justified theoretically*~gand also experimentally.lO Moreover, the partial specific volume of the 9 C E below the c.m.c. is generally within 5% or less of F8,so that a small variation in the monomer concentration introduces negligible error. From Vs,multiplying by the formula weight, we obtain Fm,the partial molal volume of the micellar component which includes the free counterions. If the degree of dissociation is x and the partial molal volume of the counterions P, then for the micelle proper, the partial volume of 1 mole of am_phipathic_ionsand 1 2 mole of counterions is given by Vm - xV. The corresponding partial specific volume is the quantity truly representative of the micelle. The value of x has been derived to be close to 0.3 for several systems.lOJ1 We use this value and note than an error of 0.1 in it causes an error of less than 1% for our systems. For F valuee v e use some recent estimates a t infinite dilution,12 -5.7 and 22.3 ml./mole for Na+ and C1-, respectively. Two assumptions are involved here: (a) the effect of the finite concentrations in the non-micellar liquid is negligible; and (b) the potential drop in the diffuse double layer contributes nothing t o the volume changes. Considering that only x mole of one ion is involved and that from infinite dilution to 0.1 144 concentration 1:1 electrolytes show a
vm‘, -
vs’
(7) K. A. Wright and H. V. Tartar, J . Am. Chem. Soc., 61, 544 (1939). (8) R. C. Murray and G. S. Hartley, Trans. Faiaday SOC.31, 183 (1935). (9) K. J. Mysels. J . Colloid Scz., 10, 507 (1955). (10) K. J. Mysels and C. I. Dulin, zbzd., 10, 461 (1955). (11) I. M. Kolthoff and W. F. Johnston, J . A n . Chen. Soc., 73, 4563 (1951). (12) P. Muksrjee, d . Rhusn Chsm., 66, 740 (IRBl),
IO0
I
oc
W
3 I
p IO0 0 LL W u)
I oc
I
IO0
025 WEIGHT
050 NORMALITY.
075
Fig. 1.-The variation of specific volume with concentration of aqueous solutions of sodium lauryl sulfonate a t 40” (density data from ref. 7).
1.08
VS*
I
I 0
1 .02
.04
.06
CONCENTRATION
.08
,I
OF N a CL IN
.I2
.14
16
MOLESILITRE.
Fig. 2.-Variation of with concentration of NaCl: 0, sodium lauryl sulfate, 23’; A, dodecylammonium chloride, 30’; V , dodecyltrimethylammonium $loride, 23”; 0 , tetradecyltrimethylammonium chloride, 23
.
change of only about 0.6 ml./mole,13 the concentration effect on Vm‘ values of about 200 ml./mole can be neglected. Assumption ( b ) is hard to evaluate theoretically. Approximately, however, we may note that the double layer potentials involved6 (-100 mv.) correspond to maximum field intensities of about 1 million v./cm. Such a field a t the surface of a monovalent ion in water, assuming the intervening dielectric constant to be unity, requires a radius of 38 A. For a dielectric constant of 80, the distance is about 4 A. Since intermediate values are more likely, the field intensity clearly corresponds t o a fair distance from a monovalent ion, beyond one to several hydration layers, a t which distance any residual electrostriction effects should be small. Stronger support for assumption (b) can be obtained from the experimental density data.’4,’6 In Fig. 2, the com(13) H. S. Harned and €3. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd Edition, Reinhold Publ. Corp., Kew Y o r k , N Y . 1958.
puted p,values of four compounds in water and in various concentrations of sodium chloride are plotted against the salt concentration. The data can be represented by horizontal lines for all the compounds. The average deviations from the straight lines are 0.2% in the case of NaLS, 0.47, in the case of dodecylamine hydrochloride, 0.5% in the case of tetradecyltrimethylammonium chloride, and 0.6% in the case of dodecyltrimethylammonium chloride. Except for the last compound the deviations are random. We can conclude, therefore, that Ve changes very little with salt concentration over the range indicated. Since over this range of concentration the thickness of the double layer decreases by a factor of three to four, and the r-potential, in the typical case of sodium lauryl sulfate, decreases from about 100 to 66 mv.,6 so that the field intensities double, it may be concluded also that the effect of the diffuse double layer on the volume of the system is negligible. This seems to be the first evidence of its kind and is of importance in the study of charged colloids in general. To obtain the true anhydrous specific vohme, Vs’, and the density of the anhydrous micelles from Vm’, ?llowance must be made for micelle-solvent interaction. This is confined to the micelle-water interface and is of three types: (1) the ion-water interaction, (2) the interaction between the hydrated ions, and (3) that between the exposed hydrocarbon surface and water. The first factor causes electrostriction of the solvent, while the second factor influences the extent of it. Both are taken into account if the electrostriction is calculated for the “effective” concentration a t the micelle surface. The electrostriction values a t infinite dilution can be calculated on the basis of a recent study.12JB From geometrical considerations and the variation of Vm with counterions, the “effective” concentration for the lauryl sulfonates has been estimated to be 1-3 M . 1 7 We have used a mean value of 2 z/T and decreased the absolute values of the electrostrictions, calculated a t infinite dilution, by 4 ml./mole, the average value pertaining to 1: 1 electrolytes.13 The third factor is neglected. The partial molal volume of ACE’S increase on micelle formation by about 5% for NaLS and much less for cationic compounds, as estimated from the density data.14~~6A substantial part of this change is due to the decrease in electrostriction on micelle-formation. The reason for the rest is obscure, but even if it were all related to the change in the hydrocarbon area exposed to water,.the residual effect must be small, since only a small fraction, about IO%, of this hydrocarbon area of the monomers remains exposed in the micelles. To obtain the true volume from Vm’ we add to Vm’ th! absolute value of the electrostriction for 1 mole of amphlpathic ions and 1 - z mole of counterion, modified for the concentration effect. Division by the calculated mass now gives the true anhydrous specific volume V,’ and hence the density. For the monovalent counterions involved in our svstems, the electrostriction corrections are 5 ml./mole or less. Uncertainties due to errors in these estimates in the final density figures are expected to be about lY0. The corrections are considerablv larger for multivalent counterions.lZ We have neglected the effect of temperature, which has only a small effect on the partial molal volumes of ordinary electrolytes.’* Error due to this should be significant only in the case of sodium lauryl sulfonate.
Results In Table I the data for several ACE’s are shown. The average u_ncertaintie_s are estimated to be about 0.5% for V,, 1% for V s fand , 1-2% for V,‘ and the anhydrous micellar density. The estimated densities are considerably higher than that of liquid dodecane (0.74 g./ml. a t 25°.)1g (14) L. M. Kushner, B. C. Duncan, and .J. I. Hoffman, J. Res. Natl. Bur. Std , 49, 85 (1962). (16) L. M. Kushner, W. I).Hubbard, and R. A. Parker, i h i d . , 59, 113 (1957). (16) P. Mukerjee, J . Phys. Chem., 65, 744 (1961). (17) P.Mukerjee, i b i d . , 66, 943 (1962). (18) W. Geffken, 2. phynk. Chem., 8155, 1 (1931). (19) F. D.Rossini, et al., “Selected Values of Physical and Tbermodynamic Propertirv of Hydrocarbons and Related Compounds,” American Petroleum Institute, CaInegie Press, 1983.
Scpt., 1962
DESSITY OF ~~ICT!!LLESO F ,kSSOCIAl'IOS
V-OLUMES
AND
1735
COLLOIDAL ELECTROLYTES
TABLE I DENSII'IESOF SOME Aaxocr.4~10~COLLOIDS IN \VATERAND NaCl
SOLUTIONS
souroc I
Temp.,
VS,
-.
V.',
VB',
Anhydrous
of
tnicellar
density
density,
dats.
Substance
Medium
OC.
ml./g.
Ylll./&
n1l./p.
$./L111.
1rf.
Sodium lauryl sulfate 1)odecylamine hydrochloride 1)odecyltriniethylammoniLiin chloride Tetradecyltrimethylammonium ichloride Sodium lauryl sulfonate
Water and NaCl soln. up to 0.12 M PVater and StLC1 soln. up t o 0.15 111
23 30
0.862 1.088
0.889 1.111
0.908 1.132
1.101 0.882
11
Water and KaC1 soln. up to 0.1 M
23
1.095
1.114
1.120
.893
15
Kater and NaCl soln. UD t o 0.1 M Water
23 40 50 60
1.094 0.901 .906 .916 .925
1.111 0.931 .936 .946 .956
1.116 0.950 .956 .966 .975
,896 1.052
15
70
This density has sometimes been assumed for the micelles1' and has been derived from intrinsic viscosity data by neglecting all hydration.lb This point, will be examined in greater detail in a subsequent publication. The difference can be attributed mainly to the contribution of the effectively denser polar heads and counterions, which amounts to 30-60y0 of the total weight for all the compounds except dodecylammonium chloride, for which it is somewhat, less. The rather pronounced difference between the anionic and the cationic electrolytes stems froin the difference in densities between the sulfate or the sulfonate groups and the ammonium or substituted ammonium groups. The decrease in the density of about 3% for sodium dodecyl sulfonate from 40 to 70' corresponds to about 7 ml. in molar volu_me and seems to be real since it is primarily in V,. The small effect of temperature on the partial volumes of ordinary electrolytes1* suggests that only a small part of it is due to the increase in the volume of charged groups. However, the density of dodecane changes over this temperature range by about 3.0%.19 Since about 62% of the weight of this surfactant is hydrocarbon, the contribution from the expansion of this part of the micelle with temperature Fhould be about 275, and this accounts for the major part of the observed change in density. The final density values show that only a snia_ll error is mtade, 3-5%, on using the experimental V, in our systems. Considerably larger errors are possible, however, in the case of dense or highly
1.046
1.035 1.026
16
7 7 7
7
charged counterions. For a quaternary iodide, for example, V,' may differ by 10% from V,. For monovalent counterio_ns the electrost,riction effects are small, and hence V,' is a good approximation for Vs'. For multivalent counterions, however, V,' may differ substantially from Vs', Finally, me note that the general approach of this paper also is applicable to other systems of charged colloids, notably proteins. Density of Giant Micelles.-In high concentrations of sodium chloride, the V8 of dodecyl ammonium chloride from the data of Kushner, et a1.,15 shows appreciable increases. Thus, compared to the average value of 1.088 at low salt concentrations, the values a t 0.25 and 0.30 M salt concentrations are 1.103 and 1.134, respectively. Over this same range, the intrinsic viscosities, the molecular weights of the micelles, and the dissymmetry of the scattering of light all indicate that very large asymmetric micelles are present. Kushner, et aZ.,15 have suggested that in these solutions the first stages of salting-out are evident, especially since the limits of solubility are approached and perhaps even exceeded. The curious decrease in the density suggests, however, that these giant micelles are not more solid-like but rather less so. The organization of the hydrocarbon chains is clearly different from that in ordinary micelles. Acknowledgment.-The author is grateful to Professor Karol J. Mysels, without whose criticism, encouragement, and help this work would not have been possible.
