J . Phys. Chem. 1985, 89. 4390-4395
4390
were prepared and fixed on the grids immediately after sonication. It took longer for the DSC study to be completed. We have not attempted to investigate the fusion of the yolk PC or DPPC vesicles in the presence of the PFC’s. However, it is possible that in the presence of PFTBA the smaller DPPC vesicles had fused into larger ones in the DSC study. Second, the PFTBA emulsions disperse far less evenly than the PFD and PFTPA emulsions or the vesicles alone. With large droplets of PFTBA in the emulsion, this inhomogeneity includes significant variation in both particles sizes and their composition. Energy transport in the sample may be described by the Fourier field equation:33 d T / d t = aV2T where a is the thermal diffusivity. Particle size and shape will affect the Laplacian of the temperature and the composition will affect a. In essence, a homogeneous sample may be treated as a pseudocontinuum while an inhomogeneous one requires a separate equation for each discrete region. The latter case means that there are different temperature profiles with time in the sample chamber. Since a DSC curve records the change in C, with temperature and AH is obtained by integrating the area under the curve, the smaller sizes of the lipid vesicles and the large inhomogeneity in the dispersion in the presence of PFTBA may ~~
~
~
~
~~
~~
(31) Schullery, S. E.; Schmidt, C. F.; Felgner, P.; Tillack, T. W.; Thompson, T. E. Biochemistry 1980, 19, 3919. (32) Schmidt, C. F.; Lichtenberg, D.; Thompson, T. E. Biochemistry 1981, 20, 4792. (33) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. ”TransportPhenomena”; Wiley: New York, 1960; p 353.
cause part or all of the small apparent increases in T , and AH. These increases are nevertheless very small and we do not consider that they are significant with regard to the physical interaction between PFTBA and PC vesicles. In summary, we have observed that in dispersions with phosphatidylcholine perfluorodecalin and perfluorotripropylamine are distributed in two environments, inside the phospholipid bilayers and in the form of tiny droplets up to 0.15 pm in diameter. These two PFC’s do not appreciably change T , and AH of the gel-toliquid crystal transition of the lipid bilayers. On the other hand, perfluorotributylamine does not dissolve in the phosphalipid bilayers. It forms larger droplets up to 8 pm in diameter. In the presence of perfluorotributylamine, phosphatidylcholine vesicles formed by sonication are smaller in diameter and apparently have higher T , and AH, which may be due to the inhomogeneity of the dispersion and the fusion of small vesicles into larger ones. The sizes of biological cells are much larger and are not expected to change in the physical presence of perfluorochemicals. Therefore, we can only speculate that the larger, usually detrimental effects of PFTBA on red and white cells may be due to its interaction with the membrane surface or cytoplasm of the cells rather than affecting the properties of the lipid interior of the membranes. Acknowledgment. This work was supported by the American Heart Association and its Oklahoma Affiliate and PHS Grant HL32640. We thank Dr. Stephen G. O’Neal for helpful discussions and Mr. William F. Chissoe for taking the electron micrographs. Registry No. DPPC, 2644-64-6; N(CF2CF,CF,),, 338-83-0;N(CF2CF2CF2CF,)3,3 1 1-89-7; perfluorodecalin, 306-94-5; cis-perfluorodecalin, 60433-11-6; trans-perfluorodecalin,60433-12-7.
On the CD, Probe Infrared Method for Determlnlng Polymethylene Chain Conformation M. Maroncelli,+H. L. Strauss, and R. G. Snyder* Department of Chemistry, University of California, Berkeley, California 94720 (Received: March 1 1 , 1985; In Final Form: May 28, 1985)
The rocking mode frequency of a CD2group substituted in a polymethylenechain is sensitiveto conformation in the immediate vicinity of the CD, group. This sensitivity forms the basis of a commonly used infrared method for determining site-specific conformation in polymethylene systems. In the present work, the CD2 probe method has been extended and quantified with the use of infrared data on model CD,-substituted n-alkanes. The frequency of the CD, rocking band is determined primarily by the conformation of adjoining CC bonds, Le., by tt, gt, and gg pairs. However, we have found that there are significant frequency shifts associated with other factors. These include the conformation of the next nearest CC bonds, both with the CD, positioned at the end and in the interior of the chain, and chain length. In addition, the ratio of the absorptivities of the tt to gt bands has been established. These results enable the method to provide new details about the conformation of the chains in polymethylene systems and reliable estimates of the concentrations of specific kinds of short conformational sequences.
Introduction The rocking vibration of an isolated CD2 group in a polymethylene (PM) chain is uniquely sensitive to the conformation of the chain in the immediate vicinity of the CD, group. The band associated with this vibration is intense in the infrared spectrum and appears in a frequency region (690-600 cm-’) that is essentially free of other P M bands. For these reasons, the CD, rocking mode provides a convenient sitespecific probe- for studying the conformation of PM chains in a variety of systems. The CD2 probe technique was initially used to study crystalline polyethylene.’ In that study, it was demonstrated that adjoining pairs of C C bonds having the conformations tt and gt could be Current address: Department of Chemistry, University of Chicago, 5735 South Ellis Av., Chicago, IL 60637.
distinguished and the relative concentrations of these pairs estimated. In recent studies on the low-temperature and high-temperature solid phases of n-alkanes, we have used the CD2 method to determine the kind and degree of conformational disorder in the n-alkane chains as a function of position along the chain.*s3 In carrying out this work, it was found necessary to measure the CD2 rocking band for a variety of CD,-substituted n-alkanes and to extend the analysis of this band beyond that reported earlier. As a result, the capability of this technique to detect and measure conformation has been improved significantly. Snyder, R. G.; Poore, M. W. Macromolecules 1973, 6, 708-15. Snyder, R. G.; Maroncelli, M.; Strauss, H. L.; Elliger, C . A,; Cameron, D. G.; Casal, H. L.; Mantsch, H. H. J . Am. Chem. SOC.1983, 105, 133-4. (3) Maroncelli, M.; Strauss, H. L.; Snyder, R. G . J . Chem. Phys. 1985, (1)
(2)
82, 281 1-24.
0022-3654/85/2089-4390$01 .SO10 0 1985 American Chemical Society
The Journal of Physical Chemistry, Vof.89, No. 20, 1985 4391
Polymethylene Chain Conformation
TABLE I: Assignments of CD2 Rocking Modes in the Infrared Spectra of CD,-Substituted Long n-Alkanes (n L 7) and n-Pentane
long n-alkanesO n-CsH1oD2
VOW
band tt
gt
conformation*
liquid
ee et tt
622c 622 622
egt egg tgt ggt
651 650 652 646
solid
location of CD, C
622 622
end
658 -650d 650
end end
interior
conformation ert etg etfe egt
interior
egg egte
vnM.
liquid 622 622 622
location of CD, end end interior
end end
650 643 65 1
interior
interior
“Includes n = 7, 13, 19, 21, 29, 35. bItalicized pairs indicate the bonds adjoining the CD2 group (see text). CGas-phaseCH3CD2CH3(Shimanouchi, T. “Tables of Molecular Vibrational Frequencies. Part 3”; Nat. Stand. Ref. Darn Ser. (US., Narl. Bur. Stand.) 1968. NSRDS-NBS 1 7 ) . dObserved only in the spectrum of the high-temperature form of C2,(*) e Gas. One major finding reported here that extends the potential of the method as a diagnostic for structure is that the CD2 probe frequency is dependent on the conformation of the C C bond or bonds neighboring the tt and gt bond pairs. We have also considered intensities. In utilizing the CD2 method to obtain conformer concentrations from intensities, past workers have assumed the absorptivities of the various CD, rocking modes are equal.’~~9~ We have used CD2 rocking spectra of selected liquid n-alkanes in combination with conformational concentrations estimated from a statistical model to establish the absorptivity from experiment. Thus, a calibration for future work has been provided. In what follows we first discuss the assignments and then the intensity calibration.
660 (CHDI
Phase I 120TI
Phoit
n:
09Tl 660lCHDl
Experimental Procedures
The selectively deuterated samples of n-pentane and n-heptane were obtained from MSD Isotopes. The others were synthesized according to a procedure that has been described previously! For nearly all the samples the concentration of isotopic impurities (mainly CHD) was less than 4 mol %. The infrared spectra were measured with an evacuatable Nicolet Model 8000 FTIR spectrometer equipped with both a TGS and a cooled MCT infrared detector. The resolution used was about 1 cm-’. Sample thicknesses were 0.5-1.0 mm. During the measurement of the infrared spectra, the temperature of the sample was controlled by means of a copper-block assembly through which water or alcohol circulated. The temperature of the circulating liquid was determined by a thermostated bath. The relative integrated intensities of CD2 rocking bands were measured by a combination of techniques that included “se1f-deconvolutionn,7 numerical curve fitting, and curve fitting with an interactive routine.
(iii) In designating the conformational environment of a CD, group, we will italicize the CC bonds that are directly bonded to the CD2. Thus, tg means the CD2 group adjoins a t and g bond. (iv) Finally, in the text and figures we refer to phases I and 11of the solid n-alkanes. Phase I is the low-temperature orthorhombic form, in which the chains are all-trans. Phase I1 is the high-temperature “hexagonal” or “rotator” phase, in which molecules contain a significant number of conformational defects involving gauche bonds. (See ref 2 and 3.)
Notation
Infrared Spectra and Assignments
To aid in the discussion, it is useful to adopt the following notational conventions: (i) All the n-alkanes considered here contain a single CD2 group. An n-alkane that has n carbon atoms and a CD2 group located a t the mth carbon will be designated n-C,H2,D2(m*m)or C i m ) . (ii) We use the standard notation, e.g., gtgtt ..., to define a conformational sequence of gauche (g) and trans (t) bonds. To indicate that a specific conformational sequence occurs at the end of the chain, we will designate the end C C bond by the letter e. Thus, the bond pair “et” indicates an end bond adjoining a trans bond. To a good approximation the end CC bond acts like a trans bond in its effect on the CD2 rocking mode frequency. This enables us to classify the CD2 modes as tt or gt with the understanding that t means either t or e.
To date there have been two studies that have sought to characterize the dependence of the CD2 rocking mode on conformation, the initial investigation of Snyder and Poore’ and the work of Reneker et al! From normal-coordinate calculations and relatively limited experimental data, it was shown that the rocking mode frequency of a CD, group in the interior of a chain is sensitive to the conformation of the two immediately adjacent CC bonds. Specifically, the infrared bands observed near 620 and 650 cm-’ were assigned respectively to the bond pairs tt and gt. It is from this point that we begin. First we consder the infrared spectra of representative model n-alkanes containing a CD2 group and discuss assignments. Then we summarize some of the experimentally determined factors that are found to influence the CD2 rocking frequency and discuss how the influence of these factors compares with the predictions of normal-coordinate calculations. Reprasentative IR spectra in the CD2 rocking mode region are shown in Figures 1 and 2 for CD2-substituted n-alkanes in the solid and liquid states, respectively. Band frequencies are displayed in Figure 3, and assignments are given in Table I. The “tt” band at 622 cm-I dominates the spectra of the solids (Figure 1) and also appears strongly for the liquids (Figure 2).
(4) Reneker, D. H.; Mazur, J.; Colson, J. P.;Snyder, R. G. J . Appl. Phys. 1980,51, 5080-94. ( 5 ) Zerbi, G.; Magni, R.; Gussoni, M.; Holland-Moritz,K.; Bigotto, A,; Dirlikov, S.J . Chem. Phys. 1981, 75, 3175-94. (6) Elliger, C . A. J . Labelled Compd. Radiopharm. 1983, 20, 135-41. (7) Kauppinen, J. R.; Moffatt, D. J.; Mantsch, H. H.; Cameron, D. G. Appl. Spectrosc. 1981, 35, 271-6.
680 665 650 635
620 605
Wavenumbers
Figure 1. Infrared spectra of end and interior CD,-substituted n-alkanes: (a) C13(2) in phases I and 11; (b) CZ1@) in phases I and 11. The CD2 rocking mode assignments are indicated (also see Table I).
4392
The Journal of Physical Chemistry, Vol. 89, No. 20, 1985
Maroncelli et al.
Figure 2. Infrared spectra of various CD2-substituted n-alkanes in the liquid state.
Its shape is uncomplicated, and its frequency is constant to within f l cm-I, irrespective of the position of the CD, group or the state of the sample. The "gt" band near 650 cm-' is more complex. We will limit the discussion of this band mainly to long chains ( n 2 13). The 662-cm-' component is, in fact, not associated with a CD2 group at all, but rather with a C H D impurity, which is present in our samples in low concentrations (usually less than about 4%). As may be seen in Figure 1, this band is essentially the only band in the gt region of the spectrum of the crystal in phase I because the concentration of gauche bonds is very low in this phase.3 For the liquid (Figure 2), however, there are two additional bands. The frequencies of these depend on the position of the CD, group, namely, on whether or not it is a t the chain end. When the CD, is at the end, the bands are at 657 and 650 cm-I, but for any other position the bands are at 652 and 646 cm-I. The assignment of the pair of bands associated with an end CD2 (657 and 650 cm-') and the pair associated with an interior CD2 (652 and 646 cm-I) can be made on the basis of intensities and the temperature dependence of the intensities. The two pairs are similar in these respects: the higher frequency band is the more intense; the intensity of the higher frequency band increases relative to that of its lower frequency companion when the temperature of the sample in the liquid state is lowered (top traces in Figture 2). Quantitatively, the temperature dependence indicates an energy difference such that the conformational sequence associated with the higher frequency component contains exactly one gauche bond more than is associated with the lower frequency component. An assignment consistent with these experimental findings and supported by normal-coordinate calculations involves associating the 657- and 650-cm-' bands (of the end CD,) with the egt and egg conformations, respectively, and the 652- and 646-cm-' bands (of an interior CD2) with tgt and tgg conformations. Finally we note that there should exist a band associated with a gg bond pair. Such a band has not yet been identified with certainty in the case of the n-alkanes. Normal-coordinate calculations indicate that this band has a frequency near 680 cm-l. However, these same calculations also indicate that the gg frequency is sensitive both to variations in the dihedral angles associated with the gg pair and to the conformation of neighboring C C bonds and that this sensitivity will be greater than for either the tt or gt pair.' As a result, the gg band is most likely broad, and this breadth, combined with the low concentration of gg pairs, probably accounts for the difficulty in detection. Recently we have observed the gg band in the infrared spectra of the crystalline CD2-cycloalkancs, C l & I a 2and C,K2D2, in the region 664-657 cm-1,8 If the gg band for the liquid n-alkanes also occurs in this frequency region, it is likely to be masked by the much more
intense gt band. We postpone a detailed consideration of the gg band for a future publication. The factors that influence the frequencies of the tt and gt bands are (i) the position of the CD, groups in the chain, (ii) the chain length, and (iii) the conformation of CC bonds adjacent to a given bond pair. A summary of these effects, based on our observed frequency data (Figure 3) and the assignments indicated in Table I, follows. The tt Bund. The bond pairs tt, et, and ee are all associated with a band at 622 f 2 ~ m - ' . ~The band is not sensitive to CD2 position, chain length, or adjacent conformation. The gt Band. This band is significantly sensitive to all the factors listed above: (i) Positional dependence for long chains ( n > -7): If the CD2 is at the end of the chain, the frequency associated with the eg pair is 4-5 cm-' higher than that associated with an interior gt pair. (ii) Chain length dependence: Chains shorter than about eight carbons must be considered special cases. This is evident in Figure 3 for C5and to a lesser extent for C7. The frequencies of the gt bands for these chains are clearly out of line with those for longer chains. (iii) Dependence on neighboring conformation: For both bond pairs eg and gt, the CD2 rocking frequency depends on the conformation of the C C bond that is once removed from the CD2 group and on the side next to the g bond. The CD2 rocking frequency increases by 6-7 cm-' when the conformation of this C C bond goes from gauche to trans, i.e., from tgt to ggt. Normal-coordinate calculations of CD,-substituted n-alkanes give CD2 rocking mode frequencies that are in good agreement with the above assignments. The computed and observed frequencies along with a description of the modes in terms of L matrix elements and potential energies are given in Table 11. A pictorial representation of the normal modes is provided in Figure 4. For these calculations we used a valence force field previously de-
(8) Shannon, V. L.; Strauss, H. L.; Snyder, R. G., unpublished results.
(9). In the ease of the cycloalkanes, C16H30D2 and C22H42D2, a larger variation (h4 cm-I) has been observed.*
I
660
I
I
I
640 Wovenumbers
I
620
Figure 3. Observed frequencies of CD2 rocking bands in the infrared
spectra of various CD2-substituted n-alkanes in the liquid state. Note that for C$') the frequencies 0 and A designated tgt and ggt, respectively, are actually both egt.
The Journal of Physical Chemistry, Vol. 89, No. 20, 1985 4393
Polymethylene Chain Conformation
TABLE 1I: Calculated Frequencies, Normal Coordinates, and Intensities of CD, Rocking Modes' class of con- conforformers mation' vcalcd C,(Z) er egt egg
615 6151 661 658
rt, rgt, gt9 ggt,
L matrix elements' PCD,
Vobsd
0.214 0.216 0.305 0.291
622
657 650
class of conforconformers mation' Vcalcd c,(~) (rn # 2) rr t,fft, 615 t,rrgt, 6571 rgt t4rgt4 t,g'rgt, 656 rgg t,rggt, 653 t,g'rggt, 6531
1
Vobsd
p,,
p+s
0.500 0.502 0.467 0.455
0.212 0.016 -0.013 0.194 -0.028 -0.016 -0.083 -0.040 -0.006 -0.140 0.171 0.049 L matrix elements' P-, P-, PCD. P,, P,,
P-,
0.015 0.015 652 -0.006 0.070 -0.037 -0.080 646 -0.007 0.063 0.031 -0.062 622
P,,
1:::;;
0.202 0.203 0.321 0.292 0.306 0.277
0.487 0.488 0.418 0.432 0.415 0.427
0.202 0.015 0.185 -0.026 -0.052 -0.031 -0.067 -0.034 -0.112 0.155 -0.127 0.157
potential energy distributiond T R+w r
p, pb
0.916 0.906 0.773 0.829
Are
0.024 0 0.061 1 0.026 0.007 0.054 1.00 0.053 0.117 0.014 0.83 0.050 0.079 0.015 0.82 potential energy distributiond P T R +w r A/
P,, -0.012 -0.015 -0.005 -0.005 0.042 0.042
0.869 0.863 0.719 0.722 0.765 0.769
0.044 0.047 0.098 0.101 0.091 0.093
0
0.006 0.104 0.110 0.075 0.079
0.088 0.083 0.058 0.043 0.055 0.042
1
1.00 0.90 0.89 0.88 0.86
'Calculations are for C,,(') and C,,('). Italicized pairs indicate the bonds adjoining the CD, group (see text). 'fib denotes the CH, in-plane rock of the methyl adjacent to the CD, group; PCD, and Pk denote respectively the methylene rocking coordinate of the CD, group and those of the CH, groups k carbons away. d Potential energy contributions from P + p = rocking, T = methylene twisting, R + w = C-C stretching + LCCC bending, and r = skeletal torsional coordinates. e IR absorptivities calculated from eq 3 relative to the CD, rocking mode of the all-trans chain. The ratio of absorptivities of all-trans C1,(') vs. Cl,(') molecules is A(2,2)/A(7,7) = 1.07. $1
n
et $2
t p t t '2
t
t
observed frequency trends shown in Figure 3, the gt frequencies calculated for C5(2*2) are somewhat lower (-7 f 2 cm-I) than the corresponding frequencies calculated for the longer n-alkanes. For C5(3,3),this difference is significantly smaller (- 1 cm). Intensities We now consider the determination of the relative infrared absorptivities of the tt and gt bands. The quantity we will determine is the absorptivity ratio A,, defined A,
= A(gt)/A(tt)
where A(gt) and A(tt) are gt and tt band absorptivities. The concentration ratio, C, = C(gt)/C(tt), the observed intensity ratio, I, = Z(gt)/l(tt), and A, are related by
''
'2'491
t t
Figure 4. Normal coordinates of CD2rocking modes calculated for end and interior CD2n-alkanes. The arrows are proportional to the L matrix elements of the methylene or methyl rocking coordinates. The dark circles denote the CD2 site.
termined from the observed frequencies of undeuterated n-alkanes for which it was assumed that the gauche dihedral angle was 67".1° In the present calculation, the values of the force constants were not adjusted, and no correction was made for the anharmonicity differences between CH2and CD2. We assumed the above value of the gauche dihedral angle and ignored its probable significant variation between the various conformers. While the calculated frequencies of the tt modes are slightly lower than the observed and the gg modes are slightly higher, the shifts that arise from interior vs. end CD2groups and those from differences in the conformations of the CC bonds adjoining the tt and gt bond pairs are correctly reproduced. W e find that CD2 rocking frequencies are not sensitive to the conformation of CC bonds beyond the next nearest neighbors of the CD2 group. The observed dependence of the CD2 frequencies on chain length also shows up in the calculations. In accord with the (10) Snyder, R.G. J . Chem. Phys. 1967,47, 1316-60.
In what follows, the value of A, is estimated in two ways: (i) from a simple intensity model that utilizes the calculated normal coordinates and (ii) from a combination of intensities derived from the spectra of CD,-substituted n-alkanes in the liquid state and a conformer concentration based on a statistical model. A, from a Group-Moment Model. In this model," which is appropriate for nonpolar molecules, we write for the infrared intensity, A, of normal mode Q
(3) where j2 is the molecular dipole moment, Lj is the eigenvector element associated with the j t h local symmetry coordinate (or group coordinate) S,. The assumptions of the model are that the direction of ap/aSj is determined by the local symmetry of the group and that all chemically similar groups, methylene groups for example, are identical. In the present case, only methylene rocking and methyl out-of-plane rocking coordinates contribute significantly to the intensity of the CD2 rocking mode. It has been shown elsewhere that the values of &i/aS for these two kinds of group coordinates are nearly the same." The calculated values of A, based on this model, which are listed in the last column of Table 11, all fall within the range 0.8-0.9. A, from Observed Intensities. A more direct and reliable way to determine A, is through the use of eq 2 with independently determined values of Z, and,C,. The intensity ratios, I,, can be measured directly from observed spectra. The conformer con(11) Snyder, R. G. J . Chem. Phys. 1965, 42, 1744-63
4394
The Journal of Physical Chemistry, Vol. 89, No. 20, 1985
I
I
500
I
I
I
600
700
800
Maroncelli et al.
0.6
E g (col/molel
Eg (coI/moleI
Figure 5. The absorptivity ratio A, (eg to er) for the end CD2 rocking bands plotted as a function of gauche energy, EB. The A, were obtained from the ratio of the intensity of the 657- and 650-cm-' band pair to the intensity of the 622-cm-' band according to eq 4. Data for C i 2 )with n > 13 are from spectra measured for each sample at one temperature 5 OC above the melting point. For C i 2 )with n C 13, the data represent the average values obtained from spectra recorded at several temperatures. Error bars were derived from the standard deviations in the measurement of band intensities. The dashed curve indicates the average value for the longer chains. The vertical dashed line indicates the preferred value of E,.
-
centrations, C,, are not available from experiment but can be calculated with good accuracy in the case of liquid n-alkanes by using the rotational isomeric state (RIS) model.'* To compute C, from the R I S model, we must assume values for the energy of a gauche bond E, and for the bond pairs E,, and E,,,, all relative to the trans state. These energies contain both intra- and intermolecular contribution^.'^ In keeping with potential energy calculations for n-pentane,12 we have assumed E , = 2E, and E,,, = 3000 cal/mol. The value of the most important parameter, E,, we assume to lie within the range 400-800 cal/mol, a range that includes all previously determined values E, for the liquid n-alkanes. For long chains, in which case we expect E, to be essentially chain length independent, the best estimate of E, for n-alkanes longer than C1,is 508 f 50 cal/mol.14 Intensities were obtained from the spectra with the aid of curve-fitting procedures. Several factors dominate in limiting the accuracy. The CD, rocking bands lie on the tail of the intense 720-cm-I C H 2 rocking band. The 720-cm-' band does not have a simple shape so that its interfering tail could not be entirely eliminated by subtraction. The result is uncertainty in the base line. In addition, the samples contained 2-15% (but usually less than 4%) of the isotopic impurity of CHD, which has a band at 661 cm-l. This band could not always be separated from the CD2 rocking bands. Finally, because the pair of bands at 652 and 646 cm-l (or at 657 and 650 cm-') overlap, it is difficult to accurately measure the intensities of the individual components. However, since our results from group-moment calculations indicate that the components of each pair have nearly the same absorptivity, (12) Flory, P.J. 'Statistical Mechanics of Chain Molecules"; Wiley-Interscience: New York, 1969. (13) See, for example: Robertus, D. W. Berne, B. J.; Chandler, D. J . Chem. Phys. 1979, 70,3395-3400 and references therein. (14) Scherer, J. R.; Snyder, R. G. J. Chem. Phys. 1980, 72, 5798-5808.
Figure 6. The absorptivity ratio A, (gt to t t ) for interior CD2 rocking bands plotted as a function of gauche energy, E,. The A, were obtained from the ratio of the combined intensities of the 652- and 646-cm-I band pair to the intensity of the 622-cm-' band according to eq 5. The dashed curve indicates the average value for the longer chains. The vertical dashed line indicates the preferred value of E,.
we can use the total intensity of the 650-cm-' band to evaluate 1,.
The absorptivity ratios determined from eq 2 are plotted as a function of E, in Figure 5 for C i Z )and in Figure 6 for (2:"). The ratios were calculated for end and interior CD, groups, respectively, according to the relations
and A,(gt) =
+
Z(652) Z(646) P(gt) Z(622) /pot,
(5)
where the Ps are probabilities. The probabilities for the indicated conformational sequences were calculated from the RIS model for values of E , ranging from 400 to 800 cal/mol. For chains longer than C13,the A, were derived from intensity ratios measured for liquid n-alkanes at temperatures about 5 "C above the melting point. For the chains C5 through C13, the A, are averages obtained from the spectra of liquids measured over a series of temperatures. The error bars represent standard deviations estimated in the curve-fitting procedure. In both Figures 5 and 6, the curves for the shortest n-alkanes, C5 and C,, are removed from those for the longer chains. This probably reflects real differences in the values of A,. These differences may arise, as our calculations indicate, from the fact that the normal coordinates of the CD2 rocking modes for the shortest chains are significantly different from those for the longer chains. In the case of the longer n-alkanes, the curves for different n-alkanes should be considered identical within experimental error. We not that their apparent relative disposition shows no obvious correlation with chain length. This is in accordance with the expectation that both E, and the CD, rocking mode normal coordinates are essentially chain length independent for long nalkanes. Most, if not all, of the differences between the curves
J . Phys. Chem. 1985, 89, 4395-4399 probably result from experimental error in measuring the intensity ratios. We have taken as the most probable value of A, an average that excludes Cs and C7. This average is indicated by the dashed lines in Figures 5 and 6. The values A,, based on a value for E, of 508 f 50 cal/m0l,l4 are A,(eg) = 1.14 f 0.08 A&)
= 1.00 f 0.07
These values, which have been estimated by averaging the values for the long chains, are slightly higher than those that were derived soley on the basis of the group-moment model and are, we believe, the more reliable. The indicated errors correspond to an un-
4395
certainty in E, of f 5 0 cal/mol. The intensities of the individual bands of the 650-cm-' pairs are expected to have the above values, Le., A,(egt) = A,(egg) = A,(eg), etc. Acknowledgment. We gratefully acknowledge support by the National Institutes of Health and the National Science Foundation (Grant No. CHE-83-16674). We are indebted to Dr. Carl A. Elliger of the Western Regional Research Center, U S . Department of Agriculture, for synthesizing the deuterium-substituted n-alkanes. Registry No. C5(2),87128-66-3; C T ( ~86369-63-3; ), C13(", 97825-93-9; C19(2),79541-40-5; C21(2),86369-65-5; C Z ~ (97825-94-0; ~), C5"', 5209218-9; C7(4),50674-03-8; C21(4),84010-39-9; C21t6),86369-66-6; CZl('l), 86369-67-7; C29(11),97825-95-1; C35(I8), 97825-96-2.
Intermicellar Interactions in Lithium Dodecyl Sulfate Solutions. Effects of Divalent Counterions YongSheng Chao, Eric Y. Sheu, and Sow-Hsin Chen* Nuclear Engineering Department, 24-209 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received: March 20, 1985; In Final Form: May 16,I985)
Small angle neutron scattering (SANS) has been used to study the growth and interactions of ionic micelles formed from lithium dodecyl sulfate (LDS) in D20. In particular, effective interactions between the micellar aggregates have been studied as functions of the surfactant concentrations and the added salts MgC12 and CaC1,. At low salt concentration [salt] = 0.02 M, the double layer repulsion dominates the intermicellar interaction and we observe an increase in the effective micellar charge but a decrease in the micellar aggregation number as the LDS concentration increases from 1 to 20 g/dL. At high salt concentrations [MgC12] = 0.5 M, the effective intermicellar interaction becomes attractive and the aggregation number increases with the LDS concentration. the extracted fractional surface charge of the micelles at low salt is compared with the recent theory of "dressed micelles" and a moderate agreement is found.
I. Introduction In a series of S A N S experiments on lithium dodecyl sulfate (LDS) solutions,'4 we have measured the small angle neutron scattering intensity distribution (spectra) due to the presence of micelles and their mutual interactions. For solutions without added electrolyte, the SANS spectra show a pronounced interaction peak due to electrical double layer interaction between micelles which is so characteristic of an ionic micellar system with high surface charge density. We have studied the effects of added 1-1 electrolyte (LiCl) on the strength of the double layer interaction. In particular, we have addressed the question of how to interpret an effective surface charge of the micelle which can be determined e~perimentally.'-~ For the model LDS ionic micellar system, we have shown' that the micellar growth as a function of the LDS concentration and added electrolyte is one-dimensional and thus the shape (ellipsoid) and size are determined by specifying the parameter, ri (aggregation number). This simplifying feature, plus a previous experiment' which fixes the average scattering length density of hydrophobic micellar core, allows us to calculate the particle form factor part of the scattering cross section uniquely, once ii is specified. The interparticle structure factor part of the cross section can be computed by the standard liquid theory dealing with interacting spherical particles5 The interaction in this case is the double layer repulsion between micelles, which is of the Yukawa form well-known from the classical DLVO theoryS6 In this theory the only input parameter (1) Bendedouch, D.; Chen, S. H.; Koehler, W. C. J . Phys. Chem. 1983, 87, 2621.
(2) Bendedouch, D.; Chen, S. H. J . Phys. Chem. 1983, 87, 1653. (3) Kotlarchyk, M.; Chen, S. H. J . Chem. Phys. 1983, 79, 2641. (4) Bendedouch, D.; Chen, S . H. J. Phys. Chem. 1984, 88, 648. ( 5 ) Hayter, J. B.; Penfold, J. J . Mol. Phys. 1981, 42, 109.
is the effective charge z*,or equivalently, the fractional surface charge,f= z*/ii. Thus, from a quantitative analysis of the SANS spectrum, one extracts two unique parameters, ii andf; the former gives the growth and the latter the degree of ionization of the micelle. In a recent paper,7 we interpreted the parameter f so extracted according to the thoery of dressed micelles formulated by Evans, Mitchell, and Ninham (henceforth referred to as EMN).* This theory was formulated only for a 1-1 electrolyte solution and comparison of the theory and experiment shows reasonable agreement. We report in this paper an investigation of the LDS micelle growth and the degree of ionization as functions of LDS concentration and added 2-1 electrolytes, MgClz and CaC1,. The case of divalent counterions such as Mg2+and Ca2+is interesting because there is evidence that the traditional Poisson-Boltzmann equation approach to the double layer interaction, which forms J ~ have the basis of the DLVO theory, seems to be i n ~ a l i d . ~ We extended the dressed micelle theory of E M N to the case of mixed 1-1 and 2-1 electrolytes, taking the result from Ohshima, Healy, and White." We discussed comparison of this theory and the experimental results on f in this paper. Besides the fractional surface charge, the main interests of this paper are the observation that the aggregation number of the (6) Verway, E. J. W.; Overbeek J. Th. G. "Theory of the Stability of Lyophobic Colloids"; Elsevier: New York, 1948. (7) Chao, Y. S.;Sheu, E. Y.; Chen, S.H., submitted for publication in J . Phys. Chem. (this paper is referred to as CSC). (8) Evans, D. F.; Mitchell, D. J.; Ninham, B. W. J . Phys. Chem. 1984,88, 6344 (this paper is referred to as EMN). (9) Buldbrand, L.; Jonsson, B.;Wennerstrbm, H.; Linse, P.J. Chem. Phys. 1984, 80, 2221. (10) Lozada-Cassou, M.; Henderson, D. J. Phys. Chem. 1983,87, 2821. (1 1) Ohshima, H.; Healy, T.; White, L. R. J . Colloid Interface Sci. 1982, 90, 17.
0022-3654/85/2089-4395$01.50/00 1985 American Chemical Society
