Sept., 1960
ULTBACENTHIFUGAL
DETERMINATION O F DETERGENT MICELLAR
CHARACTER
1175
T'L7'1IACEKTRIFUGAL DETERMINATION OF THE MICELLAR ('HARACTER OF SOS-TONIC DETERGENT SOLUTTOSSl BY C. I\'. DWIGGINS, .JK., R. J . ROLEXAND H. N.DUNNIXG Petio1Eioii Research C'etifer, Ruieaii of Mines, U . S . Department o j the Interior, Bartlesvzlle, Oklahoma ReceiLed .tlaTch 10, 1960
An analytical ultracentrifuge has been used to determine the micellar molecular weights of micelles in four aqueous nonionic detergent solutions a t 25". Transient state methods have been used eutensively, and capillary synthetic boundary cells were used to determine relative optical concentrations. IIolecular weights were determined for various times and concentrations to ensure accuracy. Three polyosyethylated phenols formed micelles containing 100 to 300 molecules while Pluronic L-G4, a high molecular weight condensate of ethylene and propykne oxide?, does not exhibit micelle formation
Introduction Seyeral properties of aqueous detergent solut,ioiis cease to vary with concentration or change radically a t a concentration characterist'ic of t'he detergent'. This anomalous behavior has been attributed to the formation of micelles. The concentrat,ions a t which such changes occur, critical micelle concentrations, have been st'udied extensively and are usually in the parts-per-million range. 2-4 The st'ruct,ures of detergent and soap solutions have been investigated by several met'hod?, and these studies confirm the format'ion of micelles. Light-scattering methods have been used t o determine the micellar molecular weights of deterg e n t ~ , ~ -and ' X-ray diffraction studies have contributed much to the understanding of micelle formati011.~.~The study of vapor pressure lowering of detergent solutions1o has also furnished valuable data. The theory of micelle formatmionhas been studied, and a st'at'istical mechanical t'heory has been described.I1 The analytical ult,racentrifuge provides a convenient method for the determination of t,he micellar molecular weight>sof det'ergent micelles. The problem of micellar molecular weight determination for lion-ionic detergents is somewhat simpler than for ionic detergent's since ionic materials introduce charge effects t,hat must be suppressed by huff ering or treated t,heoretically.l 2 Transient state ultracentrifuge studies have many of the advantages of true equilibrium methods without the excessive time that, equilibrium methods require.13 I n particular, molecular weights may be obtained from transient state niet~hods without independent' determinations of diffusion coefficients. Synt'heticboundary methods allow the determiiiation of relative optical con(1) Presented beforr the :%th Sational Colloid Syniponiiim. Bethlehem. Pa., .June 16-17, 1960. El. S . Diinning and P.B. Lorenz, T1i1.s JOURX.AL, 60, iizyo, Bull. Chem. Soc., J a p a n , 26, 177 (195.3). R . Bury, J. Chem. Soc., 679 (1929). ( 5 ) A . 11. Jlankowieli, THISJ O U R N ~68, L , 1027 (1954). ((3) P.Debye, J . A p p l . Phys., 16, 338 (1941).
( 7 ) P.Dehye, THISJOCRSAL, 61, 18 (1947). ( 8 ) P. -1.Win?or, ihid.. 6 6 , 391 (1952). (9) J. W.hIcl3ain and S.Ross, J . Am. Chem. Soc., 68, 296 (1946). (10) 1%.Huff, J. K.1fcBain and A . P. Brady, THISJOURNAL, 66, 311 (1951). (11) C . A . ,J. Hoerc and G . C. Benson, ibid., 61, 1149 (1957). (12) T. Svedberg and K. 0. Pedersen. "The Cltracentrifuge," T h e Clarendon Press, Oxford. Reprinted by Johnson Reprint Corp., New York, 1959. (13) H. K. Schaohman, "Ultracentrifugation in Biochemistry," Acedemic Press, h'ew York, 1959, pp, 181-199.
centrations and avoid extremely precise determinatioiis of specific refractive increments. 14 Theoretical The Spinco analytical ultracentrifuge, fitted with Schlieren opt,ics, presents data as a plot of the relative concentration gradient (dc/dz) versus radial distance z in the ultracentrifuge cell. Results of low-speed experiments may be used to calculate apparent weight average molecular weights of sedimentable particles. The equation required for weight-average molecular-weight determination by transientstate methods at the m e n i ~ c u sis' ~
nr,p = ( I -RTP p ) w 2
(dc/dx), TmCm
(1)
\There
LW8p = apparent anhydrous wt. av. mol wt. for :z fixed time and concn.
R
= gas constant, ergs/mole/degree
T w p-
7i c 5
VL
absolute temperature, "K. angular velocity of the centrifuge rotor, radians/sec. density of the soln., g./ml. partial specific vol. of the solute, ml./g. concn. of the solute, g./100 ml. = distance from the axis of rotation to some point in the soln., cm. = meniscus of the liquid = = = = =
The concentration at the meniscus, cIn, that is necessary for solution of equation 1 may be calculated from data obtained with the loss-of-plateau transient -state met hod by
where cg
= initial concentration
b
=
base of liquid column
The term co in the above equation may be determined from the specific refractive increment of the solute and optical constants for the ultracentrifuge, or synthetic boundary methods may be used. The concentration cx a t any point x in the solution may be determined from the equat'ion C,
= ,c
+
s" 5,n
(dc/dz)dz
(3)
(14) 9 . .\I. Klainer and G . Kegelcs. THISJ O U H A - ~ 69, L , 952 (1955). (15) W. .J. Archibald, zbzd., 61, 1204 (1947). (16) 4 . Ginsburg, P. -4ppel and H. K. Schachman, 4rch. Btochem. Biophys., 66, 545 (1956). (17) D. B. Smith, G. C. Wood and P. A . Charlwood, Can. J. Chem., 84, 364 (1956).
T'ol. 64
C. JV. DWIGGINB, J R . , R. J. BOLEX h N D H. Y . DUXXIXG
1176
A synthetic boundary experiment14may be used to determine relative values of the initial concentration that are directly proportional to the colicentration on a weight basis. If the synthetic boundary cell is the same thickness as the cell for the transient-state experiment and if optical constants of the centrifuge are not changed for a given experiment, relative optical concentrations obtained from the following equation may be used to determine molecular weights. CO, rel. =
E:
(dc/dz),dz
(4)
where (dc/tk), = concn. gradient values for a synthetic boundary determination
The same solute concentration should be used for the synthetic boundary and corresponding transientstate experiment. I n practice, initial relative optical concentrations are computed from the synthetic boundary experiment by application of equation 4. The concentration at the meniscus em is calculated from equation 2 using data from the transient-state experiments. Concentrations throughout the cell are then calculated by use of equation 3. Thus a plot of l/sc (dc/dz) against z may be made from which l/xc (dc/dz), may be read. This value may then be used in equation 1 to calculate molecular weights. Experimental The four non-ionic detergents t h a t wrre studied arc described in Table I. All detergents were used as supplied by the manufacturers. The detergents were over 997, pure surfactant according to the manufacturers. Aqueous solutions of them gave a negative silver nitrate test indicating that halides mere absent The detergent solutions were prepared by iwight in freshly redistilled water and stored for only a few days since the solutions sometimes molded after a few weeks storage. h Spinco Model E ultracentrifuge, equipped with a rotor temperature indicator control (RTIC) and phase plate Schlieren optics, was used la It is possible to sense temperatures t o rt 0.02", and excrcise control to =k 0.1' over a range of zero to 40" with the R T I C unit. The temperature-sensing element is a thermistor embedded in the base of the rotor. All ultracentrifuge and density experiments were performed at 25".
Filled-Epon, 2.3", double-sector cells of 12-mm. thickness were used for transient-state studies to allow simultaneous recording of the solvent base line and the transient-state Schlieren patterns. Filled-Epon, 2.5", double sector, capillary-type, synthetic boundary cells of 12-mm. thickness were used for the determination of relative optical concentrations and sedimentation velocity studies. The bottoms of the cells were approximately 7.21 cm. from the center of rotation when the cell? were in the rotors. Eastman Metallographic photographic plates were used for photography of the Schlieren patterns. The coordinates of Schlieren patterns were read directly from the photographic plates with n two-dimensional comparator. Values of the refractive gradient coordinates near the meniscus for transient-state patterns were located reproducible to appI ouimately 1 to 2% for a Schlieren angle of 60". Values of the refractive gradient adjacent to the meniscus were obtained by extrapolation, since opposing, two-directional divergence of sharply defined fringes occurred. Readings taken within (18) Technical Biilletin No. TB 6003B, Spinoo Division Beckmnn Instruments, Ino., Palo Alto, California.
Av. no.
Detergent
RIanrifacturrr
.+nproxlrnates
ethylene oxy-
mol. 1st.
aroiips/ lliolrellle
680 10 3 Igepal CO-710, polyoxr- General Aniline nnd Film Co. eth: lated nonj lphenol G40 9.5 Surfonic ?;-Os, polyoxv- Jefi'erson Chemical Co. eth\ lated nonylphenol 635 9.7 T r i t m X-100, polyoxy- Rohm and Haas ethj lated octylphenol co. 2850 21 I'luronic L-64. ronden- Kyandotte Chemical sate of ethT lene oxide arid propylene o\ide Approximnte molecular wrights are taken from the manufacturers litrrature or the best available sourre.
approximately 0.15 cm. (plate distance) of the meniscus from the bisertor of the proximal peripheral fringes of the rentral shadow could lead to an error of 10% in molecular weight .19 rlppro\imately 0.10 cm. (plate distance) of the image of tlie bottom of the cell was obscured after careful aliqnment of optice, so a short extrapolation also was required a t the cell bottom. The nsual fluids used for bottom liners of the cells such as silicone oils and Kel-F polymer oil could not be used due to interaction of these substances with the detergents. Since thrre is some chance for s!ight convection and other possible disturbances near the bottom of the cells, the refractive gradients a t the cell bottoms were not used for transientstate molecular-m-eight calculations. A planimeter, capable of measuring areas to four signifirant figures, was used for integrations reqiiired for the synthetic boundary euperiments. The numerous integrals reqnired for the transient-state studies vert evaluated by numerical integrations.*" Partial specific rolrimcs were obtained from pycnometsc measurements of solution densities for a series of concentrations.21 The insulated pvcnometer watrr-bath was maintainrd at 25 rfr 0.01". The pvcnometers had a volume of :qqx-o\imately 5 ml. and wew aged for one year. Densities were tletermined in triplicate for a minimum of six detergent solutions for cw.11 drtergent, inrluding those to be ultracentrifuged, in the concentration range of 0 to 3 r 0 detcrgent, and densities were then converted to specific volume. Expanded plots of specific volllme us. conrrntration revealed that these plots were linear, within experimental error, to a few per cent. detergent concentration. A least squares fit of a straight linr to the sperific volume data resulted in an average deviation of f 0.00003in specific volume for a typical case, and the deviations were randomly distributed for various concentrations. However the specific volume ciirves significantly depart from linearity in the range of 30% detergent concentration as might be expected. Thus the lopes of the specific volume us. concentrstion curvcs were casily uhtained for calculation of partial specific volumes in the concentration range of intercst . Partial specific volume of each detergent did not change, within experimental error, Partial lip to a few per cent. detergent concentration. specific volnmrs are listed in Table 11, and were reprodurible to 3 units in the third Fignificant figure. Partial specifir volumes might be expected to change slightly for differrnt batches of the same detergent if the chain-lrngth distrihiitions of tlie detergent polymers changed.
Results and Conclusions The results for transient-state molecular-weight determination at various times of centrifugation and initial concentrations are summarized in (19) R. Trautman and C. F. Crampton, J . A m . Chem. SOC.,81, 4036 (1959). (20) H. IC Schachman. "Methods in Fnrymologp," Vol. I\', Academic Press, h-ew York. N. Y . , p. 51. (21) G. N. Lewis and &I. Randall, "Thermodynamics," McGraw11111 Book Co., New York, N. Y.,1923. 38.
p.
Sept., 1960
ULTRACENTRIFUGAL
DETERMINATION O F DETERGENT MICELLAR
1177
CHARACTER
TABLE I1 PROPERTIES OF NON-IONIC DETERGENT SOLUTIONS A N D MICELLES Detergent
Igepnl co-710
Initial concn., rvt. %
Time of run, min.
Density, 25.00°, g./inl.
0.500 ,6973 .9901 .9901 2.0246
1200 1615 1474 11179 980
0.9975 ,9977 .9981 .9981 .9993
Micellar mol. wt., X 10-4
8.42 8.79 8.24 8.60 8.47
Av. Surfonic N-95
0.4945 .4945 .7297 ,7297 1.0161 1.01Gl
8.50 f 1.8% 16.4 16.6 17.2 16.9 17.4 17.1
0.9976 .9976 .9979 .9979 .9982 .9982
1312 2071 1443 1915 1571 1933
Av. 16.9 =k 1 .8% Triton x-100
.7049
. io19
1,0073 1.00i3
0.9979 .9979 ,9987 .9987
1506 1761 1020 1858
5.96 5.81 6.87 6.59
Av. Pluronic L-64
1.0737 1.0737 I ,0737 1.4957
148 2i6 404 246
6.31 i:6 . 7 %
0.9985 .9985 .9985 .9987
0.277 0.284 0.290 0.270
Av.
125
265
100
1
0.282 f 1 . 6 %
Camera magnification: Cell thickness:
Schlieren angle: 60' Temp. 25
Molecules per micelle
2.146 12.00 mm.
Rotntiona! speeds, r.p.m. T y p e of Run
Igepal CO-710
Transient Synthetic
9341 9341
Rotational speeds, r.p.m. Surfonic N-95
9341 9341
Triton X-100
Pluronic L-64
9341 934 1
47600 47000
0.916
0.890
Partial specific volume, 25', ml./e.
0.914
0.910
Table 11. The various experimental conditions resulted in a wide range of relative optical concentrations at the meniscus. Polydispersity causes the calculated molecular weights to increase with concentrat,ion at the meniscus, while non-ideality effects are in the opposite d i r e ~ t i 0 n . l ~Thus molecular weight determination a t a variety of periods and concentrations should indicate if such effects are significantly influencing the calculated molecular weights. It appears that this is not the case for Igepal CO-710, Surfonic N-95, and Pluronic L-64 within the expected experimental error. It would be desirable to have data for lower concentrations, but error in reading the concentration gradient curves for concentrations lower than those used could introduce much error. Thus the average values of weight-average molecular weights appear to be reasonable values for the true molecular weights of the detergents a t the low concentrations involved. This in no way means that such non-ideality effects may not become important for high concentrations, since experimental conditions were selected so that such effects were suppressed. Concentrations were thus kept as low
as practicable to minimize activity effects, and molecular weights were calculated for times of centrifugation as short as practicable consistent with good precision, to reduce any polydispersity effects. It has been shown that polydispersity effects often do not become apparent until after a reasonably long period of centrifugation in comparison to the attainment of equilibrium, l6 even with considerable polydispersity present. The experimental deviation of the average of molecular weights calculated for Triton X-100 is somewhat higher than for the other detergents. This could mean that there is some dependence of the micellar molecular weight of this detergent on concentration in the concentration range studied. Such a deviation could also result from non-ideality effects or the presence of some unknown contaminant. Hence it is difficult to isolate the contributions of the many possible effects that cause the greater deviation for this detergent. Pluronic L-64 is a quite interesting exception since the calculated micellar molecular weight shows good agreement with the estimated molecular weight of this detergent. This indicates that little
1178
J. TH. G. OVERBEEK
T701. 64
or no micelle formation takes place. Such behavior is not unexpected since light scattering experimentss have shown that a homologous detergent does not form micelles. Therefore light ~ c a t t e r i n g ,and ~ ultracentrifuge data give the same qualitative results. These studies indicate that the number of molecules per micelle is highly dependent on the composition of the detergent. -Although Igepal CO-710 and Surfonic S-95 are qimilar detergentr, the numbers of molecules per micelle are considerably different for the two detergent solutions. This is not unexpected, since the two detergents ha\-e been shown to differ markedly in other respects such as adsorption properties.22
seems t o play a role in ethylene oxide and propylene osidc polymers. K i t h this in mind, it would t)c easier t o accept a value of 2-3 moleculm per micelle rather than t h a t of onr. C. I$'. U n i o c ~ s s JR.-Tht? , l'luronic L-61, dctcrgcrit I\-W foutid t o contain approsimutely 1 molrc.uk per micelle. assuming that thc molecular weight rcyorted for this tic,trryent is correct. Light scattering experiments of .l. 11. Mankowich gave an aggregation Iiumbcr of only slightly greater than I for a similar detergent,. DOKALD G . 1 ) o s a ~(B. F. Goodrich Company).-Could vou comment farther on the great difference in niiniher of molecules per micelle between surfactants of ttpprosimately the same chemical structure and composition? C. It'. DWIGGISS, JR.--At the present state of knowledge i t would be quite difficult to explain this difference since t'here are many possible explanations. Rather weak forces are involved in micelle formation. Variation in DlSCUSSIOS chain length distribution could be partidly responsible, 11. E G n u (LIonsanto Chemical Co.).-Is micellar or possibly slight Contamination of t'he detergent by somr molecii1:u iveight indcp(Andcnt of t n t d ronccntration as a unknoivn material. .is detergents of higher purity a11d narrower chain length distribution heconit. avail:tl)lr, t h ( w grncnl rule, as t h r data siigpest? questions perhaps can he resolved. C. IV. I)WIGGIA\, JR-J,s a general rule, it would not be IRWISH. BILLICR(Em0 Research and Engineering).expected that mic~rllar molrciilar -A eights would be independerit of thri total concentrations. Honever, for the 101% Did you make any nieasurements of t h c crit,ical mirrllo concentrations and cxperimental conditions involved, the concentratiori? dependence appearn to he Ion for thr, non-ionic detergents C. W. DWIGGISS,Jr.-Kot in this 1%-ork. Surface tension studied. It probal)ly n o d d become quite noticeable as studirs by Lun Hsiao, H. 3.Dunning and P. B. Lorenz the concrntrations ncwssary for grl formation are ap- ( J . Phys. Cheni., 60, 657 (1956)) indicate thttt the deterpenk proached or at w'itr t h r critical micelle concentration. studied, with the exception of Pluronic L-64, have critical H. B. KLET'EY.(I
