J. Phys. Chem. 1903, 87, 4548-4553
4548
0.05M
-0.02
I Chg d e n ( c / m 2 )
Flgwe 1. Excess charge adsorption isotherms of a 0.05 M model electrolyte near an electrode. The pdnts &e the MC values and the solM and broken curves give the HNCIMSA and GC values, respectively. The curves are labeled with the ionic valences.
abscissa gives the value of the charge density on the electrode. The units of both the ordinate and abscissa are coulomb/meter.2 The difference between the GC and MC adsorption isotherms is greatest when the divalent ions are the counterions. As stated earlier,l the HNC/MSA isotherms are intermediate between the MC and GC values. Although the MC co-ion adsorption is exceedingly small in magnitude, the co-ions are not adsorbed, except at the largest negative electrode charge densities. This adsorption of co-ions a t large negative electrode charge densities is the result of only of the Coulombic and hard-core forces in the model system considered and does not result from any specific adsorption. Henderson et aL4have shown that the excess ionic adsorption isotherms contain a term kT ap/dp. This term is only partly included in the HNC/MSA. Including the entire term moves the HNC/MSA results in the correct direction but by what appears to be too small a fador. We refrain from displaying thii effect in Figure 1becam there are no fully satisfactory expressions for kT ap/dp available, and, as a result, no really useful statement can be made as to the extent of which this compressibility effect accounts for the difference between the MC and HNC/MSA isotherms.
sorption isotherms are compared in Figure 1. The parameters employed were u = 4.25 A, E = 78.5 (the dielectric constant), T = 298 K, and z1 = 2, z2 = -1 (the valences). The ordinate gives the values of q+ and q-. by q+ and qwe mean the excess charge adsorption of the positive (zl = 2) ions and the negative ions (z2 = -l),respectively. The
Acknowledgment. The authors are grateful to Drs. G. Torrie and J. P. Valleau for sending their Monte Carlo data. J.B. and D.H. were supported in part by NSF Grant CHEBO-01969.
(3) G. Gouy, J. Phys., 9,457 (1910);D.L. Chapman, Phil. Mag.,26, 475 (1913).
(4) D. Hendemon,J. Barojae, and L. Blum, J. Phys. Chem., preceding article in this issue.
Size and Shape of Nonionic Amphiphile (Cl2E6) Micelles in Dilute Aqueous Solutions As Derived from Quasielastlc and Intensity Light Scattering, Sedimentation, and Pulsed-Field-Gradient Nuclear Magnetic Resonance Self-Diffusion Data Wyn Brown,' Robert Johnsen, Peter Stllbe, Institute of Physical Chemlsby, Universw of Uppsale, 5 7 5 1 21 Uppsala, Sweden
and B)6m Llndman phvslcel Chemlsby 1, Chemlml Center, Lund UniversHy, S-220 07 Lund, Sweden (Received: February 18, 1983; In Flnal Form: June 10, 1983)
Aqueous (DzO) solutions of a nonionic surfactant (dodecyl hexa(oxymethy1eneglycol) monoether, ClZE6)have been investigated as a function of concentration and temperature by using dynamic light scattering (QELS), Fourier transform spin-echoNMR self-diffusion,intensity light scattering, and sedimentation. All measurements have been made on the same solutions and the data provide a coherent picture of micelle size as a function of temperature. The micellar mass is constant up to about 20 "C and the apparent shape indicated from these experiments is consistent with monodisperse, spherical particles. At higher temperatures the picture resulting independently from light scattering (QELS and intensity light scattering) and hydrodynamic measurements (PFG-NMR and sedimentation) is that the micelle size increases markedly with increase in temperature in the range 20-35 "C and then more gradually up to the cloud point at about 50 "C. The data thus support the conclusions of earlier workers regarding micelle growth as a function of temperature. While the present data do not preclude perturbations due to critical phenomena as the cloud point is approached, the role of the latter may previously have been overemphasized. Introduction The micelle aggregation number of C12E6,and strutturally related nonionic amphiphiles in aqueous solution, has usually been considered to grow with increasing temperature and rapidly so as the lower critical solution tem0022-3654/83/2087-4548$01.50/0
perature (LCST), frequently termed the "cloud point", is approached. These conclusions have been based, for example, upon measurements of light scattering,'-' diffusion, (1) P. Becher, J . Colloid Sci., 16,49 (1961).
0 1983 American Chemical Society
Nonionic Amphiphile Micelles in Aqueous Solutlons
and sedimentation*l2 although the NMR spectra of solutions have earlier'O been interpreted to reflect a constant micelle size in the region 30-50 "C. In recent years, Corti and Degiorgio13 have proposed that critical concentration fluctuations (critical opalescence) account for the observed increase in turbidity and decrease in the mutual diffitsion coefficient obtained from dynamic light scattering measurements as the LCST (at 50.3 "C in H2013)is approached, rather than reflecting the temperature dependence of the micellar size. The methods used earlier have provided important insight but are unable to unequivocally distinguish between different alternatives. In this paper we present a comparison of diffusion coefficients obtained on the same solutions using quasielastic light scattering (QELS) and Fourier transform pulsed-field-gradient NMR (FT-PFGNMR).The latter method has been developed and refined in recent years and now provides a powerful tool in selective studies of multicomponent (including macromolecules) systems. Since it yields the well-defined self-diffusion coefficient, one can obtain a direct measure of particle size from the infinite-dilution value and information on frictional interactions as a function of concentration without consideration of thermodynamic factors. Data from ultracentrifugation and intensity light scattering were also obtained on the same solutions to give a more comprehensive overview and to provide complementary data concerning micellar size which are independent of possible complications arising from critical opalescence. Deuterium oxide was used as the solvent, partly for lock purposes in the N M R experiments and partly from density considerations in ultracentrifugation. Experimental Section Quasielastic Light Scattering. The experimental arrangement has been described previously14and the main features only are summarized here. The light source was a Coherent Radiation Model CR-4 argon ion laser containing a quartz etalon frequency stabilizer in the cavity to ensure single-mode operation at 488 nm. The detector system comprised an ITT FW 130 photomultiplier, the output of which was digitized by a Nuclear Enterprises amplifier/discriminator system. A Langley-Ford 128-channel autocorrelator was used to generate the full autocorrelation function of the scattered intensity. The correlator was interfaced to a Luxor ABC-80 computer, programmed to calculate the normalized full photon counting time correlation function and the data stored on floppy disks. The solutions in D 2 0 were continuously filtered through a 0.22-pm Millipore filter in (2)J. M. Corkill, J. F. Goodman, and R. H. Ottewill, Trans.Faraday SOC.,57, 1627 (1961). (3)R. R. Balmbra, J. S. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday Soc.,'b8, 1661 (1962);60,979(1964). (4)P. H.Elworthy and C. B. MacFarlane, J. Chem. SOC.,907 (1963). (5)P.H.Elworthy and C. McDonald, Kolloid 2.2.Polym., 195,16 (1964). (6)D.Attwood, J.Phys. Chem., 72,339 (1968). (7)J. M. Corkill and T. Walker, J. Colloid Interface Sci., 39, 621 (1972). (8) R. H.Ottewill, C. C. Storer, and T. Walker, Trans. Faraday Soc., 63,2796 (1967). (9)D. Attwood, P. H. Elworthy, and S. B. Kayne, J.Phys. Chem., 74, 3529 (1970). (10)E. 3.Staples and G. J. T. Tiddy, J.Chem. SOC.,Faraday Trans. 1,74,2530(1978). (11)K.W.Herrmann, J. G. Brushmitter, and W. L. Courchene, J. Phys. Chem., 70,2909 (1966). (12)W. L.Courchene, J.Phys. Chem., 70,2909 (1966). (13)M. Corti and V. Degiorgio, J.Phys. Chem., 85,1442(1981);Opt. Commun., 14,358 (1975);Phys. Rev. Lett., 45,1045 (1980). (14)J. Roots and B. Nystram, Macromolecules, 15,553 (1982).
The Journal of Physical Chemistty, Vol. 87, No. 22, 1983 4549
a closed-circuit flow-cell assembly before transfer to the measuring cuvettes. Aqueous solutions, however, frequently pose special problems in light scattering due to the presence of dust. The absence of the latter was checked by measurement of the angular dependence of the scattering intensity. After the usual angle correction, an angular-independent photon count was obtained. All measurements were made at an angle of 90°, except where otherwise stated. The full photon-counting time autocorrelation function was analyzed by the usual method of cumulants.16 Thus, In (g(2)(7) - 1 I vs. 7 was fitted with appropriate weighting in a linear regression program to a second-order equation. The first coefficient is -2F and the second p2 where f' is the average decay rate (=DmK2where K is the scattering vector, (4rnlX) sin 8/2, and D, is ascribed to the mass diffusion coefficient) and its variance is p 2 / 2 2 . This parameter is frequently used as an indication of polydispersity in polymer solutions. In the present system, the homodyne photocount autocorrelation function was found to closely approximate a single exponential at all temperatures. As pointed out by Phillies16it is most likely impossible to derive information regarding the polydispersity of micelles since each diffuses as an averaged species in the time (D,K2)-'. Intensity Light Scattering. Measurements were made in a laser (He-Ne, 633 nm) light scattering photometer at an angle of 90" on the same solutions as used in dynamic light scattering measurements. The instrument was calibrated with dextran and poly(ethy1ene oxide) chromatography standards obtained respectively from Pharmacia Fine Chemicals (T-70, T-500) and Toya Soda Ltd. (Japan SE-8 and SE-30). Pulsed-Field-Gradient NMR. All measurements were made on protons at 99.6 MHz using an internal D20 lock on a standard JEOL FX-100 Fourier transform NMR spectrometer. The measurement procedure currently employed has been recently described1' in detail. The experimental uncertainty was f1.5% in D at a value of lo-" m2 s-l. It may be noted that, since the cmc is very much lower than the concentrations used here, the values of D will be negligibly affected by monomer diffusion, even at the lowest concentrations employed. In a 10 mM solution the contribution to surfactant diffusion is estimated to be -1%. Sedimentation Coefficients. Sedimentation coefficients were measured at 59 000 rpm in a MSE analytical ultracentrifuge using the Schlieren optical system. Sedimentation coefficients were evaluated by using the position of maximum height method, which agreed well with the second moment calculation. It should be noted that ClzQ micelles are less dense than D20 and the sedimentation coefficients are consequently negative. Partial Specific Volume. These measurements were made with a digital density meter (DMA 60, Anton Paar K. G., Austria) thermostated at 25 "C in the concentration range up to 5% (w/w). The volume V of solution containing 1 kg of water was calculated from the measured density of a solution and its concentration, expressed as kilograms of per kilogram of water and denoted c*. The partial specific volume is obtained as the tangent to a curve of V vs. c* at a particular concentration. The partial specific volume was determined to be independent (15)D.E. Koppel, J. Chem. Phys., 57,4814 (1972). (16)G.D. J. Phillies, J. Colloid Interface Sci., 86,226 (1982). (17)P.Stilbs, J. Colloid Interface Sci., 87,385 (1982).
4550
20
Brown et ai.
The Journal of Physical Chemistry, Vol. 87, No. 22, 1983
0 10.C
~
10
IO
20
LO
30
50
,.lop
Figwe 1. Data from quasielastic light scattering in &lute aqueous @@) solutions of C1& These data are normalized by multiplying by the solvent viscosity at temperature T and dividing by the latter. Concentration is in md of C,.& L-' and dmusion coefficientsare expressed in m2 s-I.
10. 18.
25'
3 5' 4 2' L 0'
10
20
30
50
LO
c
10yM
Figure 2. Data analogous to those in Figure 1 but derived as selfdiffusion coefficients from Fouier transform pulsed-fieldgradlent NMR.
of concentration in the range investigated and to lie in the m3 kg-'. This value is in interval (1.005 f 0.002) X good agreement with the value given by Ottewill and coworkersa (1.O00 f 0.001). The partial specific volume was essentially constant over the temperature range of interest (see Figure 5). Material and Solutions. High-purity CI2E6was obtained in crystalline form from Nikko Chemicals, Tokyo, and used without further purification. Solutions were prepared by weight in deuterium oxide (99.8%) purchased from Stohler Isotope Chemicals, Switzerland, or Norsk Hydro, Rjukan, Norway. The critical micelle concentration for C12E6in H 2 0 is given by Balmbra et al.3 as Co = 8.7 X 10" M at 25 "C. Thus,it is permissible to make concentration plots directly vs c instead of against c - co in all techniques employed in the present paper. Results and Discussion Figures 1 and 2 show the measured diffusion coefficients using NMR and QELS. The D values have been normalized by multiplying by qo/Tto yield a quantity which at infinite dilution is inversely proportional to the hydrodynamically equivalent micellar radius through Stokes's law. The data from the two techniques are of similar magnitude. Below about 20 "C, Dqo/T is essentially independent of concentration. A t infinite dilution this parameter has an average value of -20 x lo-", which corresponds to a hydrodynamic radius of 37 A, in agreement
20
30
LO
50
Flgure 3. Data from Figures 1 and 2 taken at a concentratlon of 0.01 M C,,E,: (X) QELS; (0) PFGNMR.
with the extended molecular length of C12E6(39 A). This observation is thus consistent with a spherical form for the micelles in the lower temperature region. At temperatures below 25 "C, the indicated infinite-dilution values of the normalized diffusion coefficients DoQELsand DoNm are approximately equal as should be the case. At temperatures above 25 "C, however, the infinite-dilution values A possible cause of this is a differ ( D o Q m< DoNMR). difference in sensitivity to polydispersity (which presumably increases strongly with increasing micelle size) since D W is a z-averaged quantity. The nature of the average obtained with PFG-NMR in polydisperse systems depends to a certain degree on the system itself and may also be affected by the measurement conditions and data evaluation procedure but will, in general, be biased toward Mn.l8 At the other extreme in Figure 2, as one moves toward the LCST (=51 "C in D20,see Figure 7), the apparent micellar radius approaches a value of about 100-150 8, at 48 "C, which necessarily corresponds to a form other than spherical. The nature of the concentration dependence in Figures 1 and 2 changes at about 25 "C and this is similar to the situation with the intensity light scattering data in Figure reflects only the frictional behavior while 4. Since Dthe concentration dependence in intensity light scattering is related to thermodynamic factors, it is clear that there is a change in micelle size/shape accompanying the change in the thermodynamic state of the system (see below). At 25 "C and above, DqO/Tdecreases with increasing concentration and, at a given concentration, decreases with increasing temperature. The latter feature is shown in Figure 3 where the, perhaps surprising, similar magnitudes and temperature dependence of D W and DNm are emphasized. This is so since the solutions are nearly ideal at 25 "C, as shown by the concentration dependence of intensity light scattering data (see below) and does not agree with the suggestion13that nonideality effects play (18) von Meerwalllg has recently made a comprehensive analysis of this problem, with particular attention to polymer systems. The polydispersity results in 'nonexponential" echo decays in PFG-NMR experiments on such systems, and consequently the result is strongly dependent on the data evaluation procedure. Micellar systems, however, are dynamic on the time scale in question (milliseconds)and the polydispersity will only manifest itself in the population-weighted averaged self-diffusioncoefficient from the experiment. Apparent D values from PFG-NMR measurements on micellar systems are thus independent of the measurement/evaluationconditions and will effectively be characterized by a relationship of the form D(apparent) = EgiDi, where p i representa the fraction of micelles with a diffusion coefficient Di. Of c o m e , this D(apparent) cannot be explicitly evaluated in terms of polydispersity unless a relationship between micellar aggregation number and D is known (or assumed). Self-diffusion in dynamic systems will, however, always be biased toward the more rapidly moving species and thus toward M,,. (19) E. D. von Meerwall, J . Magn. Reson., 50, 409 (1982).
Nonionic Amphiphile Micelles in Aqueous Solutions
The Journal of Physical Chemistry, Vol. 87, No. 22, 1983 4551
a dominant role at this temperature. We note here that NMR self-diffusion is quite independent of phenomena deriving from critical concentration fluctuations, as the technique inherently monitors purely geometric lateral displacemenb over a time typically of the order of 10-2000 ms (here -200 ms). The mass diffusion coefficient, D,, obtained from QELS may be written20
f
1%
-
Kc
or,
I
/
,Iff I
Dm where p and c are the chemical potential and the concentration and f is the frictional coefficient. Both f and dp/dc are concentration dependent, l/f having a pronounced negative dependence due to increasing hydrodynamic friction, and dp/dc in general a positive dependence on c. In more usual terms20 RT D, = -(1 - 4)(1 + 2AzMc + 3A3Mc2 + ...) ( 2 ) NAf where (1 - 4)(l + 2 A a c + ...) is referred to as the "thermodynamic factor" and includes the volume fraction of solute, 4, the virial coefficients A2 and As, and molar mass, M . The self-diffusion coefficient, D*, is written D* = RT/(NAf*) (3) Assuming f = f* in dilute solutions,2l one usually expects Dm and D* to differ substantially at finite concentrations (although they should coincide at infinite dilution in monodisperse systems) owing to the concentration dependence of the thermodynamic factor in which the virial coefficients describe the binary and higher order interactions between solute particles. The reason for the low contribution of the thermodynamic factor in the present case lies in the closeness of the system to a state which may be considered analogous to that which exists at the Flory temperature20 for polymer solutions. The latter is experimentally defined as that temperature at which the second virial coefficient, A2, becomes zero (in osmotic pressure or intensity light scattering, for example) and corresponds to the critical miscibility temperature in the limit of infinite molecular weight. The second virial coefficient provides a sensitive index ascribed to the delicate balance between the excluded volume (entropic) and enthalpic terms which govern the stability of the polymel-solvent system. (There is frequently a large difference between the Flory temperature and the critical solution temperature for a polymer of small molar mass; for example, for polystyrene (M = 110000) in cyclopentane the critical solution temperature (UCST) is 4 "C while the Flory (0) temperature is 20 "C). Intensity light scattering data as a function of temperature and for an angle of 90° are shown in Figure 4. The usual description at low concentration is Kc/Re = 1/M + 2 A 2 ~+ ... where Re is the Rayleigh ratio at angle B and K is an optical constant. It is observed that a positive value of A2 characterizes the data at the lower temperatures. On plotting the slopes vs. 1/T, one may estimate that A2 = 0 at -21 "C. Thereafter A2 is negative and the reduced scattering intensity becomes nonlinear in c, signifying that the apparent molar mass increases with increasing temperature. (20) H.Yamakawa, "ModernTheory of Polymer Solutions", Harper and Row, New York, 1971. (21)It has been established both theoreticall? and experimentall?" that these friction coefficients are not identical. However, we may for present purposes assume this to be so in these dilute solutions.
I
I
5
10
>
I
20
15
C 1OYM
Figure 4. Intensity light scattering data for &EO in dilute aqueous solutions as a function of temperature and concentration. The second virial coefficient is found by interpolation to be zero at 21.5 "C.
The interpretation of these changes in the second virial coefficient is unclear as a quantitative interpretation must take into account size and shape changes in the micellar system which cannot be clearly evaluated from the present data since the light scattering photometer did not allow determination of the angular dependence of the scattered intensity. The decrease in DO(Le., the value at infiiite dilution normalized by multiplication by Q,,/T) shows that the micelle size (equivalent hydrodynamic radius) increases with increasing temperature and most strongly in the temperature interval 20-35 "C, a conclusion which is in accord with those of earlier workers. This conclusion could also have been derived from the analogous values of D"Furthermore, the similar magnitude of DNMRand D LS at finite concentrations and the overall pattern of the %a using these two techniques strongly suggest that the role of concentration fluctuations is more limited than previously put forward by Corti and Degiorgio13when interpreting QELS and intensity light scattering data for the present system. Were anomalies due to critical opalescence a dominant feature, one would expect substantial qualitative differences in the QELS and NMR data. Balmbra et aL3similarly studied the influence of temperature on the size of C12E6micelles and found that their mass increased exponentially with increasing temperature. Their values of M are of the same magnitude as those corresponding to the intercepts in Figure 4; these yield M 60000 at the lower temperatures and M 600000 at 45 "C. These values are approximately coincident with those found by using a combination of sedimentation/self-diffusion (see below). It may be noted that Balmbra et al.3 also considered the possible role of critical opalescence on their light scattering data and concluded that the increase in turbidity with temperature was not due to this factor. Kjellander22 has recently pointed out that the light scattering data of Corti and Degiorgio13do not necessarily contradict the existence of large micelles at the higher temperatures; he also suggests that the micelles are most likely rod shaped as the LCST is approached. Sedimen-
-
~
-
~
(22)R. Kjellander, J. Chem. SOC.,Faraday Trans.2,78,2025(1982). (23)W. Hess in "Light Scattering in Liquids and Macromolecular Solutions", V. Degiorgio, M. Corti, and M. Giglio, Eds., Plenum Press, New York, 1980; S.Hanna, W.Hess, and R. Klein, Physica A, 111,181 (1982). (24)W.Brown, P.Stilbs, and R. M. Johnsen, J . Polym. Sci., Polym. Phys. Ed., 20, 1771 (1982). (25)W.Brown, R. M. Johnsen, and P. Stilbs, J . Polym. Sci., Polym. Phys. Ed., 21, 1029 (1983).
I
Brown et ai.
The Journal of Fhysical Chemistry, Vol. 87, No. 22, 1983
4552
,*P2] 9.1.
Po s
Id
\
01
I
I
30
LO
It
50
5.10.18 5'
I bl
3 t
I
2t 1-
"
n
0
IO
n
c
20
30
LO
\ L'
. 'X
'\
18 5.C
50 c I0YM
Figure 6. Apparent micellar mass of CIlE6 calculated by combining sedimentation and selfdiffusion coefficients in the Svedberg equation (molar mass expressed in g mol-I).
tation coefficients were determined for C12E6 at a series of concentrations and temperatures. The normalized sedimentation coefficients are shown as a function of concentration in Figure 5. At the lower temperatures (5, 10, and 18.5 "C) the data coincide and are independent of c. A t the higher temperatures there is a maximum in s at about 15 mM C12E6. The sedimentation coefficient is proportional to M and inversely proportional to the frictional coefficient. Thus, the sedimentation increases with increasing concentration (at 25,33, and 40 "C) until the concomitantly increasing friction per unit volume becomes dominant at concentrations exceeding 15 mM. The complex form of the curves thus shows that there is a change in micellar shape a t the higher concentrations/ temperatures. The data suggest that the micelles have a narrow molecular weight distribution and are spherical at temperatures below 20 OC and also at the higher temperatures at the very lowest concentrations approaching the cmc. A nonspherical micelle shape must be assumed at the higher temperatures/concentrations. Figure 6 shows the apparent micellar mass obtained by combining sedimentation and self-diffusion coefficients in the Svedberg equation. At temperatures below 20 O C the molar mass is approximately 65 OOO, both s and D* being independent of concentration in the range of c investigated. These data are of particular relevance in this context since they provide unequivocal evidence, independent of the light scattering data, that the micelle size increases strongly as a function of temperature, both s and D* being
(26) P.-G. N h n , H. Wennerstrom, and B. Lindman, J. Phys. Chem., 87,1379 (1983). (27) J.-E. Ldfroth and M. Almgren in 'Surfactants in Solution",K. L. Mittal and B. Lindman, Ed., Plenum Press, New York, in press.
The Journal of Physical Chem/stry, Vol. 87, No. 22, 1983
Additions and Corrections
“C) and low concentrations (550 mM). Increasing the temperature and/or the concentration is associated with considerable changes in the observed parameters. That self-diffusion coefficients do not exhibit anomalous behavior near critical points has been shown experimentally There is at for low molecular weight present no direct evidence that this is also so in macromolecular solutions. Apparent self-diffusion coefficients have been derived by combining mutual diffusion and osmotic pressure data and no anomalies observed*% near critical conditions. However, the arguments used when evaluating “apparent” self-diffusion coefficients are now known to be i n ~ a l i d . ~ Experimental ~-~~ self-diffusion coefficients however, may be used to deduce information on micellar size and shape and on intermicellar interactions. The NMR self-diffusion coefficients observed here, therefore, provide clear evidence for a growth of CIZEB micelles on increasing the temperature toward the cloud point. The inferred growth of C12E6micelles on increasing the temperature agrees with several studies (cf. above) on various poly(ethy1ene oxide) alkyl ethers. On increasing the temperature there is a clear but slow dehydration of these nonionic surfactant micelles as evidenced by water self-diffusion studies.31 Mitchell et al.rr and N h n et al.,% (28)H. Ha”, C. Hoheisel, and H. Richtering, Ber. Bunaenges. Phys. Chem., 76, 249 (1972). (29)J. C . Allegra, A. Stein, and G. F. Allen, J. Chem. Phys., 56,1716 (1971). (30)J. E. Anderson and W. H. Gerritz, J.Chem. Phys., 53,2584 (1970). (31)J. C. Lang, Jr., and J. H. Freed, J. Chem. Phys., 56,4103(1972). (32)K. Krynicki, S. N. Changdar, and J. G. Powles, Mol. Phys., 39, 773 (1980). (33)R. Bergman and L.-0. SundelBf, Eur. Polym. J., 13,881(1977). (34)J. Roots,B. Nystrijm, L.-0. Sundebf, and B. Porsch, Polymer, 20, 337 (1979). (35)L.-0. SundelBf, Ber. Bunaenges. Phys. Chem., 83, 329 (1979). (36)P.-G. Nilsson and B. Lindman, J.Phys. Chem., in press.
4553
in considering aggregation of C,E, in mixtures with water in general, i.e., in both isotropic and anisotropic solutions, have d i m e d the relationship between micellar shape and the temperature stability of liquid crystalline phases. These authors also find it possible to rationalize general features of micellar growth and of the phase diagrams from simple considerations based on the sizes of the polar and nonpolar parts. The present results cannot directly distinguish between different types of micellar growth. In recent neutron scattering studies, Cebula and 0ttewilPs find support for cylindrical micelles rather than disk micelles whereas Triolo et al.39conclude that their SANS data are best interpreted by the presence of spherical micelles at all temperatures (in the range 14-47 “C). A study3B of water self-diffusion gives an observed obstruction effect which seems inconsistent with large oblate micelles and, therefore, gives good support for prolate or cylindrical micelles. A combined surfactant lH NMR relaxation and self-diffusion study% indicates that surfactant chain and micelle flexibility is much larger than for typical micelles such as those encountered at lower temperatures. Acknowledgment. This work was supported in part by the Swedish Forest Products Research Institute, Stockholm, and in part by the Swedish National Science Research Council. This is gratefully acknowledged. Thanks are due to Stefan Knight and Mikael Jawson for assistance with the light scattering measurements. We also thank Dr. N. Mazer for valuable suggestions on this work. Registry No. CIZEB, 3055-96-7. (37)D.J. Mitchell, G. J. T. Tiddy, L. Waring, T. Bostock, and M. P. McDonald, J. Chem. SOC.,Faraday Trans. 1,79, 975 (1983). (38)D. J. Cebula and R. H. Ottewill, Colloid Polym. Sci., 260, 1118 (1982). (39)R. Triolo, L. J. Magid, J. S.Johnson, Jr., and H. R. Child, J. Phys. Chem., 86, 3689 (1982).
ADDITIONS AND CORRECTIONS 1979, Volume 83
Bruce C. Garrett and Donald G. Truhlar*: Generalized Transition State Theory. Classical Mechanical Theory and Applications to Collinear Reactions of Hydrogen Molecules.
Bruce C. Garrett and Donald G. Truhlar*: Generalized Transition State Theory. Quantum Effects for Collinear Reactions of Hydrogen Molecules. Pages 1079-1112. In Table XVIII, kUS(T= 600 K) should be 4.17 (2). In our original erratum (Volume 84, pp 682-6) Tables XXIIIE-XXVE were left out. They are included here.
Page 1052-1079 and 3058. In eq 47, p x should be pr. In eq 120 and 129, + should be -. Section VD, line 8: model should be mode. Section VIF, line 1 6 + should be =. In Table 111,kCCVT(1500 K, D)should be 2.32 X lo4 (4.0). In K, D)should be 4.46 X lo3 (14). In Table IV, kCCVT(lOOO Table VI, kc(4000 K, D)should be 3.26 X lo3 (8). TABLE XXiIIE: Canonical Rate Constants for C1
+ HD
--f
T,K
* lCVE
CVT/CVE
NVT/CVE
200 300 400 600 1000 1500
2.48 (1) 2.24 ( 2 ) 6.67 ( 2 ) 3.65 ( 3 ) 1.59 ( 4 ) 4.06 ( 4 )
4.77 7.43 (1) 3.52 ( 2 ) 1.95 (3) 9.33 (3) 2.36 ( 4 )
4.76 7 . 4 2 (1) 3.51 ( 2 ) 1.94 ( 3 ) 9.13 (3) 2.26 ( 4 )
ClH
+D MEPVA
MCPVA
1.25 4.00 (1) 2.44 ( 2 ) 1.62 ( 3 ) 8.41 ( 3 ) 2.14 ( 4 )
1.72 4.89 (1) 2.82 ( 2 ) 1.77 ( 3 ) 8.84 (3) 2.20 ( 4 )
QUSIMEP
1.25 3.97 (1) 2.38 ( 2 ) 1.52 ( 3 ) 7.34 ( 3 ) 1.73 (4)
QUS/MCP
1.72 4.85 2.76 1.68 7.77 1.80
(1) (2) (3) (3) (4)
