Self-Diffusion, Dynamical Molecular Conformation, and Liquid

6186

J. Phys. Chem. B 2000, 104, 6186-6194

Self-Diffusion, Dynamical Molecular Conformation, and Liquid Structures of n-Saturated and Unsaturated Fatty Acids Makio Iwahashi,* Yasutoshi Kasahara, and Hideyo Matsuzawa School of Science, Kitasato UniVersity, Sagamihara, Japan 228-8555

Kenichiro Yagi, Kenji Nomura, Hikaru Terauchi, and Yukihiro Ozaki School of Science, Kwansei Gakuin UniVersity, Nishinomiya, Japan 662-8501

Masao Suzuki AdVanced Science and Technology Research Center, Kyushu UniVersity, Kasuga, Fukuoka, Japan 816-8580 ReceiVed: February 17, 2000; In Final Form: April 10, 2000

The translational movement, the dynamical molecular conformation, and the aggregate structure in the liquid state for three kinds of cis-type unsaturated fatty acids (cis-6-, cis-9-, and cis-11-octadecenoic acids), transtype unsaturated acid (trans-9-octadecenoic acid), and n-saturated acid (octadecanoic acid) have been studied through the measurements of density, self-diffusion coefficient, 13C NMR spin-lattice relaxation time, and X-ray diffraction. The magnitude of the self-diffusion coefficient, D, fell in sequence of cis-type unsaturated acids > trans-type acid > saturated acid below 350 K. Above 350 K the value of D for the trans-type acid rose to those for the cis-type acids. On the other hand, the density F for the acids also fell in the order of cis-type acids > trans-type acid > saturated acid; the order of the density is just opposite to that expected from the results of the self-diffusion coefficient and other physical properties such as melting point and heat of fusion. This discrepancy between D and F values for the acids is well explained by the models of the clusters in their liquids.

Introduction Fatty acids are characteristic building-block components of most of lipids such as phospholipids and glycolipids, which construct biomembranes; they play important roles in membrane functions such as flexibility, fluidity, and material transfer. The functions seem to depend mainly on the properties of the liquid, liquid-crystalline, and crystalline phases of the fatty acids in the lipids. Thus, comprehensive understanding of physicochemical properties involved in transformations among the liquid, liquid crystalline, and crystalline phases of fatty acid chain in phospholipid, acylglycerol, and other lipid molecules must be essential. Several superior books reviewing the physicochemical properties of various kinds of alkanes, alcohols, and fatty acids have been published.1-5 In the physicochemical properties, the understanding of the dynamical molecular structures and the aggregate structures in the liquid state is especially important in connection with the crystalline structures of various kinds of alkanes, alcohols, fatty acids, and glycerides, which have been progressively studied.1-8 Namely, their liquid structures are thought to play an important role when the lipids crystallize. There has been plenty of previous research on the physicochemical properties in liquid of long-chain molecules such as n-alkanes, alcohols, fatty acids, and glycerides. Doddrell and Allerhand determined the segmental motion in liquid 1-decanol through the measurement of 13C NMR spin-lattice relation times.9 Levine et al. also measured 13C NMR spin-lattice * To whom correspondence should be addressed: Telephone: 81-42778-9273. Fax: 81-42-778-9369. E-mail: [email protected].

relaxation times for all of the resolved resonances in n-alkanes from C6 to C18 and in n-alkyl bromides from C4 to C15, and determined the dynamical molecular profiles of the long-chain alkane molecule in liquid.10 Brady and Fein studied the aggregation structure of the alkanes (C6-C20) using the X-ray diffraction method.11 Berchiesi et al. studied the viscosities and molar volumes of the fatty acids (C9-C16) as a function of temperature.12 Translational motions in the liquid phases of triglycerides were also measured as a function of temperature using a pulsed field gradient NMR method.13 Concerning the structures of triglycerides in the liquid state, Larsson proposed, based on the results of X-ray diffraction measurements, the existence of the clusters having a liquidcrystalline smectic structure in the liquid of triglycerides.14 Callaghan and Jolky supported the existence of the ordering structure in the liquid state of tristearin by a 13C NMR study.15 By means of an X-ray technique and Raman spectroscopy, Hernqvist also supported Larsson’s model and further proposed the mechanism of the crystallization of a triglyceride melt.16 On the contrary, through small angle neutron scattering experiments, Cebula et al. proposed not the smectic liquid crystal model but the nematic one for the triglyceride melt.17 Larsson made comments on the Cebula’s model.18 Using the timeresolved synchrotron radiation X-ray diffraction method, Ueno et al. have studied the polymorphic crystallization of sn-1,3distearoyl-2-oleoyl glycerol and revealed newer aspects of the polymorphic crystallization and the formation of liquid crystals.19 On the other hand, fatty acids in the liquid state have hitherto been believed not to have order structure;3 the studies of the

10.1021/jp000610l CCC: $19.00 © 2000 American Chemical Society Published on Web 06/10/2000

D Value of n-Saturated and Unsaturated Fatty Acids molecular and liquid structures of fatty acids in their liquid states are fewer than those of the triglycerides. In a previous study,20 mainly through near-infrared spectroscopic measurements, we have revealed that cis-9-octadecenoic acid in its liquid state exists as dimers even at a relatively high temperature. That is to say, the dimers are the units in intra- or intermolecular movement. In addition, through the measurements of ESR, NMR, viscosity, DSC, fluorescence polarization, and X-ray diffraction for cis-9-octadecenoic acid in its liquid state, it has become clear that the dimers aggregate to make clusters possessing the structure of a quasi-smectic liquid crystal below 303 K.21 Furthermore, we assumed additional two types of liquid structures above 303 K for cis-9-octadecanoic acid; however, we did not confirm experimentally the existence of these additional two types of liquid structures. In the present study, the dynamical molecular structures and the assembly structures of the fatty acids such as cis-6octadecenoic, cis-9-octadecenoic, cis-11-octadecenoic, trans9-octadecenoic, and octadecanoic acids in their pure liquids have been studied through the observations of density, 13C NMR spin-lattice relaxation time, self-diffusion coefficient, and X-ray diffraction at various temperatures. Experimental Section Materials. Pure samples (purity greater than 99.9%) of cis6-octadecenoic acid (cis-6), cis-9-octadecenoic acid (cis-9), cis11-octadecenoic acid (cis-11), trans-9-octadecenoic acid (trans9), and octadecanoic acid (stearic acid) were prepared by us. The purity of samples of the acids was confirmed by gas liquid chromatography (Shimazu GC-14A with a capillary column of SP-2560). The samples for NMR measurements were prepared after being fully purged with argon gas. Density. The density, F, of the samples of cis-6, cis-9, and cis-11 in the temperature range 293-343 ( 0.01 K was measured on a vibration-type densimeter (Anton Paar model DMA 58). The density of trans-9 was measured on the same type densimeter at relatively high temperatures, i.e., Anton Paar model DMA 48 for the temperature range 323-353 ( 0.01 K and DMA512 for the range 353-363 ( 0.01 K, respectively. Degassed pure water was used for calibrating the densimeters. NMR Measurements. The self-diffusion coefficient, D, was determined by means of the pulsed-gradient NMR method.22 All of the measurements were made on protons at 399.65 MHz in the temperature range 298-373 ( 0.5 K on an NMR spectrometer (Japan Electron Optics Laboratory (JEOL) model EX-400). The 13C NMR spin-lattice relaxation time, T1, for the samples of the acids was obtained by the inversion recovery method21 employing a 180°-τ-90° pulse sequence, using also the NMR spectrometer in the temperature range 298-373 ( 0.5 K. X-ray Diffraction. X-ray diffraction experiments for all samples were carried out on a X-ray diffraction instrument (Rigaku model RU-300) using MoKR (wavelength λ ) 0.7107 Å) radiation (40 kV × 240 mA) in the temperature range 293393 ( 0.2 K. Samples were set in glass capillary cells with 2-mm diameter and 1/100-mm thickness. Scattering intensities in the range from 0.06 to 2.277 Å-1 or from 0.06 to 6.033 Å-1 in s value (s ) (4π) sin θ/λ, 2θ ) scattering angle) were measured. The intensities were corrected by the subtraction of the background intensity. Deconvolution of the diffraction bands was carried out by assuming a Lorentzian curve for each band and determined the peak positions of the bands.

J. Phys. Chem. B, Vol. 104, No. 26, 2000 6187

Figure 1. Temperature dependence of self-diffusion coefficient, D, for cis-6 (0), cis-9 (O), cis-11 (4), trans-9 ([), and stearic acid (]).

Results and Discussion Self-Diffusion Coefficient. Figure 1 shows the self-diffusion coefficient, D, versus temperature relationships for cis-6, cis-9, cis-11, trans-9, and stearic acid. The D values for the three kinds of cis-type unsaturated acids increase to the same extent with increasing temperature until 333 K; above this temperature the D value for cis-6 (0) or cis-11 (4) rises more considerably than that for cis-9 (O). Namely, the D value follows the order of cis-6 g cis-11 > cis-9 above 333 K. On the other hand, trans-9 exhibits a curious behavior in its self-diffusion profile. Below 353 K the D value for the trans-9 ([) is lower than those for the cis-type acids; the value considerably increases with an increase in temperature and finally exceeds the value for cis-9 at 363 K. Stearic acid (]) always has a low D value compared with those for the unsaturated fatty acids. Clearly, the molecular structures for the acids affect their translational movement. A problem arises concerning the mechanisms which cause such difference in D among the five kinds of fatty acids. One reason for the difference in the D value would be the difference in the degree of the segmental movements in the molecule for each acid. Namely, in the translational diffusion, the acid molecule would move to find a space available for its translational movement (i.e., a rotational movement adopted for a linear-polymer molecule); the segmental movements at the end and near the end of the molecule are probably most important for the fatty acid molecules to find the spaces for their translational diffusion. Thus, we measured 13C NMR spinlattice relaxation times, T1, of different carbon atoms along the chain for the samples of the acids at various temperatures, since T1 is likely to be correlated to the movement of the carbon atoms, i.e., segmental motion22 (specifically rotational tumbling and to a lesser extent translational and internal motion) in the molecule. 13C NMR Spin-Lattice Relaxation Time. In general, 13C NMR spin-lattice relaxation of a protonated carbon is overwhelmingly dominated by dipole-dipole interactions with the attached protons:23 T1 is related to the number of directly bonded hydrogen, N, and the effective correlation time, τc, for the rotational movement of the carbon atoms in the object acid

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Figure 2. Temperature dependence of the reciprocal of the effective correlation time, 1/τc, for the rotational reorientation for the different carbon atoms in cis-9: 303 K (^), 313 K (3), 323 K ([), 333 K (4), 343 K (9), 353 K (O), 363 K (2), and 373 K (]). The movement of the carbon atoms at double bond position are restricted.

Figure 3. Temperature dependence of 1/τc for the rotational reorientation of the different carbon atoms in cis-6: 313 K (3), 323 K ([), 333 K (4), 343 K (9), 353 K (O), 363 K (2), and 373 K (]). The movements of the carbon atoms at double-bond positions are restricted.

molecule. Thus, T1 is approximately given in terms of N and 1/τc24

T1 )

r6CH

()

1 Np2γ2C γ2H τc

(1)

where p is Planck’s constant and γC and γH are the gyromagnetic ratios of 13C and 1H, respectively. Here, rCH is the C-H distance, usually about 0.109 nm, and the reciprocal of the effective correlation time, 1/τc, represents the magnitude of the segmental rotation for the carbon atom at a different position. Figure 2 shows the value of 1/τc at various temperatures for different carbon atoms in a cis-9 molecule. The value of 1/τc for each carbon atom obviously increases with increasing temperature. At any temperature, the rotational movements for the carbon atoms at the second position attached to the carboxyl group and at the double-bonded position are considerably restricted, while those for other carbon atoms increase toward the end of the hydrocarbon chain. That is, the methyl group positioned at the end of the acid molecule moves around most vigorously. Figures 3 and 4 also show the value of 1/τc at various temperatures for the carbon atoms in cis-6 and cis-11 molecules, respectively. For each acid, the rotational movements for the carbon atoms at the double-bonded position are also restricted. Comparison of the values of 1/τc for the carbon atoms at the double bonded positions for cis-6, cis-9, and cis-11 at same temperature shows that the rotational movements for the carbon atoms at the double-bonded position increase slightly in the order cis-6 < cis-9 < cis-11. Interestingly, the value of 1/τc increases almost linearly with an increase of the position of the double bond. Such a relationship also exists for the carbon atoms at the position adjacent to the double bond. Figure 5a,b shows the temperature dependence of the 1/τc value for the carbon atoms at the C17 and C18 positions for cis-6 (0), cis-9 (O), and cis-11 (4), respectively. The magnitude of the rotational movement for the carbon atom at the C17 position is in the order of cis-11 > cis-9 > cis-6; that for the carbon atom at the C18 position is in the order of cis-11 > cis-6 > cis-9. On the other hand, D values for the three kinds of cis-type unsaturated fatty acids were in the order of cis-6 > cis-11 > cis-9 above at 333 K. Thus, the order of the

Figure 4. Temperature dependence of 1/τc for the rotational reorientation of the different carbon atoms in cis-11: 303 K (0), 313 K (3), 323 K ([), 333 K (4), 343 K (9), 353 K (O), 363 K (2), and 373 K (]). The movements of the carbon atoms at double bond position are restricted.

intramolecular movements for the cis-type unsaturated acids seems not directly to affect the order of the D value. Figures 6 and 7 show the 1/τc values at various temperatures for the carbon atoms in trans-9 and stearic acid molecules, respectively. Below 333 K the movements for the carbon atom at double-bonded position of trans-9 are almost same as those for the adjacent carbon atoms; on the whole, all of the segmental movements for trans-9 are gentle compared with those for the cis-type unsaturated acids. On the other hand, the segmental movements for stearic acid seem to be somewhat gentle compared with those for trans-9. To compare the magnitude of the segmental movements for cis-9, trans-9, and stearic acid, we plotted the 1/τc values at 333 and 363 K for the carbon atoms of these acids (see Figure 8a,b). At 333 K the intramolecular movements for cis-9 are obviously larger than those for trans-9. On the other hand, at 363 K, although the intramolecular movements for the C18positioned atom for cis-9, trans-9, and stearic acid are almost equal to each other, the magnitude of the other segmental movements, as a whole, falls in the order of cis-9 > trans-9 > stearic acid. However, as shown in Figure 1, the D values at 363 K for this three kinds of acids are in the order of

D Value of n-Saturated and Unsaturated Fatty Acids


Figure 7. Temperature dependence of 1/τc for the rotational reorientation of the different carbon atoms in the stearic acid molecule: 353 K (O), 363 K (2), and 373 K (]).

Figure 5. (a) Temperature dependence of 1/τc for the rotational reorientation for the carbon atom positioned at C17 in cis-6 (0), cis-9 (O), and cis-11 (4). (b) Temperature dependence of 1/τc for the rotational reorientation of the carbon atom positioned at C18 in cis-6 (0), cis-9 (O), and cis-11 (4).

Figure 8. (a) Comparison of 1/τc at 333 K for the different carbon atoms in cis-9 (O) and trans-9 (9). (b) Comparison of 1/τc at 363 K for the different carbon atoms in cis-9 (O), trans-9 (9), and stearic acid (4). Figure 6. Temperature dependence of 1/τc for the rotational reorientation for the different carbon atoms in trans-9: 323 K ([), 333 K (4), 343 K (9), 353 K (O), 363 K (2), and 373 K (]). The movements of the carbon atoms at double-bond position are slightly restricted.

trans-9 > cis-9 > stearic acid. On the other hand, at 343 K, both D values and the magnitude of the segmental movements for these three kinds of acids are in the order of cis-9 >

trans-9 > stearic acid. Apparently, the segmental movements in the molecule seem to be somewhat related to the translational diffusion of the molecules, especially at low temperatures. However, an exactly direct relationship, as a whole, seems not to exist between the magnitude of the segmental movement and the D value for these fatty acids.


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TABLE 1: Densities at Various Temperatures for cis-6, cis-9, cis-11, trans-9, and Stearic Acid T/ K

cis-6 F/g cm-3

293.1 303.1 313.1

0.87673

323.1

0.86987

333.1

0.86292

343.1

0.85599

348.1 353.1 358.1 363.1 373.1 393.1 413.1 433.1 a

cis-9 F/g cm-3

cis-11 F/g cm-3

0.89067 0.8905c 0.88369 0.8827a 0.87676 0.8761a 0.86990 0.8697a 0.86296 0.8635a 0.85601 0.8567a 0.8530a 0.8503a 0.8470a 0.8440a

0.89056

trans-9 F/g cm-3

Stearic acid F/g cm-3

0.88357 0.87662 0.86975

0.8671

0.86281

0.8602

0.85589

0.8533

0.847b

0.8456

0.8377b

0.8391 0.8247b 0.8117b 0.7988b 0.7856b

Using a Gay-Lussac-type pycnometer. b Ref 2.

Thus, the difference in the D value for the various fatty acids cannot be explained only by the difference in the intensity of the segmental movement in the molecule; we must find the other causes that explain the difference in the D value for the fatty acids. As a possible cause, we may point out the difference in the packing mode of the dimers of the fatty acid in liquid state. Namely, the fatty acid having large D value should have a loose packing mode, while the fatty acid having small D value, a tight packing mode. Thus, we measured the density of cis-6, cis-9, cis-11, and trans-9 at various temperatures. Density of Fatty Acids. Density of the saturated and unsaturated fatty acids at various temperatures is tabulated in Table 1. For stearic acid we listed the density data cited from ref 2 because we could not obtain the satisfactory data on our densimeters due to its high melting point. The apparent molar volume calculated from the density and the molecular weight of the fatty acids is plotted in Figure 9 as a function of temperature. For each acid, a good linear relationship exists between the apparent molar volume and temperature. Interestingly, all of the cis-type unsaturated fatty acids lie on the same line within the experimental error. In other words, the cis-type acids have the exact same molar volumes. Comparison of the molar volumes for all of the acids at the same temperature reveals that the cis-type acids have the smallest molar volume; on the other hand, the saturated fatty acid has the largest molar volume, and the molar volume of the trans-type acid falls in the middle. In other words, the molecules of the cis-type unsaturated fatty acid are most closely packed, while the molecules of the saturated fatty acid are most loosely packed. This is contrary to our simple expectation: As stearic acid has a higher melting point (or crystallization temperature) and a larger heat of fusion2 than the unsaturated fatty acids possessing same number of carbon atoms, the molecular interaction for stearic acid should be stronger than that for the unsaturated fatty acids. In addition, as mentioned before, all of the segmental movements revealed from the 13C NMR T1 experiment for the stearic acid are lower than those for the unsaturated fatty acids. Thus, the molecules of stearic acid having less gauche structures should aggregate easily with each other and orient more tightly than the molecules of the

Figure 9. Temperature dependence of molar volume for cis-6 (0), cis-9 (O), cis-11 (4), trans-9 ([), and stearic acid (]). The molar volumes for cis-type unsaturated fatty acids lie on exactly the same line.

unsaturated fatty acid: Stearic acid should take the most closed packing structure in its liquid. In practice, however, stearic acid in its liquid possesses the lowest density, that is, a large apparent molecular volume compared with the unsaturated fatty acids. To get more direct information explicable for the discrepancy between the density (the apparent molar volume) and the selfdiffusion coefficient (the mobility) among the acids, we carried out the X-ray diffraction experiments for the liquid samples of cis-6, cis-9, cis-11, trans-9, and stearic acid. X-ray Diffraction Measurements. Figure 10 shows the X-ray diffraction spectra for the liquid samples of cis-6, cis-9, cis-11, trans-9, and stearic acid near their melting points. These acids give X-ray diffraction spectra that are similar to each other: In the spectrum for each fatty acid, a broad band exists around 2.8 Å-1 in s value, a large and sharp band exists around 1.4 Å-1, and a small and broad band exists around 0.3 Å-1. The large and sharp band around 1.4 Å-1 is due to the interaction between neighboring molecules and thus gives a measure of the distance between adjacent molecules. The existence of the band around 1.4 Å-1 suggests that the rodlike molecules of the fatty acids, in general, tend to highly aggregate in parallel with each other. The broad band around 2.8 Å-1 would be attributable to the second-order reflection to the band at 1.4 Å-1. The radial distribution function curves obtained through the Fourier transform of other X-ray data obtained for the fatty acids by using AgKR radiation also support the parallel aggregation of the dimer molecules of these fatty acids in the liquid state. On the other hand, the small s region is expected to give the information on the long distance regulation: The small band at the small s value is due to the long distance of the plane made by the aligned molecules. The X-ray diffraction spectra in Figure 10 suggest the presence of the clusters having a lamellar structure in the liquid of the fatty acids. However, as polarization microscopic observations of the samples of the acids did not give any overall macroscopic anisotropy, the size of the clusters of the acids would be small compared with the wavelength of visible light. The obtained values of d spacing for the fatty acids near their melting points are listed in Table 2. The values are 23.8-25.7 Å for a long spacing and 4.57-4.66 Å for a short spacing, respectively.



Figure 10. X-ray diffraction spectra obtained for the liquid samples of five kinds of fatty acids near their melting points: cis-6 at 304 K, cis-9 at 298 K, cis-11 at 298 K, trans-9 at 319 K, and stearic acid at 343 K.

TABLE 2: Short and Long Spacing for cis-6, cis-9, cis-11, trans-9, and Stearic Acid near Their Melting Points cis-6 cis-9 cis-11 trans-9 stearic acid

T/K

short spacing/Å

long spacing /Å

304 298 298 319 343

4.58 4.57 4.57 4.59 4.66

24.2 23.8 24.1 25.0 25.7

The values of the long spacing, which are almost equal to the molecular dimension in the length of the fatty acid containing 18 carbon atoms, however, seem to be small because the molecules of the fatty acid always form a dimer in its pure liquid.20 The incomprehensible value for the long spacing can be explained by assuming an unique arrangement of the dimerized molecules in the clusters (see the schematic drawing A in Figure 11): The dimerized acid molecules arrange longitudinally and alternately to make an interdigitated structure, irrespective of the kinds of fatty acids, i.e., the saturated or the unsaturated fatty acids. The dimerized carboxyl groups in one dimer and the methyl groups at the terminal of the neighboring dimers are aligned alternately in the same lateral plane. If the dimerized acid molecules take this interdigitated structure, the methyl and methylene groups near the ends of the acid molecules are able to move significantly, because the movements of the carboxyl groups in the neighboring dimers are restricted. This structure allows the most compact packing for the dimerized molecules of the fatty acids. In the previous paper,21 we have proposed such a interdigitated lamellar structure for cis-9 in its liquid at room temperature. In this case, the alignment in the longitudinal direction for the acid molecules resembles that for the dodecanoic acid molecules in A-form crystal25,26 and the cis-9 molecules in β1-form crystal.27 In our previous study,10 the X-ray diffraction pattern for the liquid sample of cis-9 at 296 K was obtained on flat photo-

graphic film with Ni-filtered CuKR radiation. From the two diffuse rings on the photographic film, we obtained 4.6 Å as the short spacing and 17.3 Å as the long spacing of cis-9: The former value is closely equal to the short spacing value for cis-9 listed in Table 2, while the latter one is somewhat small compared with the long spacing value for cis-9 listed in the same table. This is probably because of the difficulty in the determination of the peak position from the weak diffuse ring at a small angle. The additional X-ray diffraction observations for the liquid sample of each fatty acid at various temperatures were carried out in the range of 0.06 to 2.277 Å-1 in s value. Figure 12 shows, as typical examples, the temperature dependence of the diffraction spectra for cis-11 and trans-9. The s value of the peak position for the small band around 0.3 Å-1 increases very slightly or seems to be almost constant with an increase in temperature, while that for the large and sharp band around 1.4 Å-1 apparently decreases. The long and short spacings for each fatty acid, calculated from the band positions, are plotted in Figure 13a as a function of temperature. All values for the short spacing lie on the same line and increase slightly with increasing temperature, while the values for the long spacing are scattered. However, the long spacing values are able to be separated into two groups: one group is cis-type unsaturated fatty acids (open symbols) and the other includes trans-9 and stearic acid (closed symbols). The linear fitting curve for each group indicates that the long spacing for trans-9 and stearic acid is larger than that for cistype acids. Both the fitting curves slightly decrease with an increase in temperature. Figure 13b shows the expanded short spacing vs temperature relationship for each fatty acid. The value of short spacing for each fatty acid increases with increasing temperature. Interestingly, trans-9 and stearic acid always have a smaller short


Iwahashi et al.

Figure 11. (A) Cluster model, proposed for the dimers of the fatty acids having 18 carbon atoms, in the liquid state. The cluster takes the structure of a quasi-smectic liquid crystal. This structure allows the most compact packing for the dimer molecules of the fatty acids. (B) Arrangement proposed of the dimers of cis-9 molecules in the cluster. The positions of the double bonds in the neighboring molecules are close to each other. (C) Arrangement proposed for the dimers of cis11 molecules in the cluster. cis-6 Molecules would take a similar cluster structure. The positions of the double bonds in the neighboring molecules are apart from each other.

spacing than the cis-type acids. In other words, trans-9 and stearic acid have a short lateral distance compared with the cistype acids. The remaining X-ray diffraction bands due to the short spacing and the long spacing, at 393 K, reveal that the clusters having the interdigitated lamellar structure still exist in the liquids of the fatty acids even at a high temperature. In the previous paper,21 we assumed that the liquid of cis-9 has additionally two liquid structures depending on temperature: One structure is composed of clusters having a structure of lessordered liquid crystal in temperature range from 303 to 328 K and the other, an isotropic liquid above 328 K. However, the results of the X-ray diffraction measurements at high temperatures did not indicate the existence of the additional two liquid structures. As illustrated in Figure 9 the cis-type unsaturated acids have the same molar volume. Thus the cis-type fatty acids should have almost a same cluster structure and a liquid structure. In fact, the values of the short spacing for cis-6, cis-9, and cis-11 are relatively close to each other and are larger than those for trans-9 and stearic acid; the values of the long spacing for cis6, cis-9, and cis-11 are also close to each other and are smaller than those for trans-9 and stearic acid. Thus, the difference in D among the fatty acids is well explained as follows. (1) The Reason for the Difference in D Value among cisType Fatty Acids. All of the cis-type unsaturated fatty acids in

Figure 12. Temperature dependence of the X-ray diffraction spectra for cis-11 and trans-9. Temperature ranges are 303-393 K and 323393 K for cis-11 and trans-9, respectively; the temperature interval is 10 K for each acid.

the liquid state have the same interdigitated lamellar cluster structure shown in the schematic drawing A in Figure 11. For the liquid of cis-9, as shown in the schematic drawing B in the same figure, a double bond in a cis-9 dimer molecule is favorably located near the double bonds of the neighboring



Figure 13. (a) Temperature dependence of the long and short spacing for all of the fatty acids: cis-9 (O), cis-6 (4), cis-11 (0), trans-9 (9), and stearic acid (1). Dotted line indicates the linear fitting curve for the long spacing data of trans-9 and stearic acid; solid line, the linear fitting curve for the long spacing of cis-type unsaturated fatty acids; dashed line, the linear fitting curve for the short spacing for all fatty acids. (B) Temperature dependence of the short spacing (in an expanded scale) for all the fatty acids: cis-9 (O), cis-6 (4), cis-11 (0), trans-9 (9), and stearic acid (1).

dimer molecules. Therefore, an interaction among the double bonds of the neighboring dimers would serve to slow the translational movement of the cis-9 molecules in inter- or intraclusters. On the other hand, for the liquid of the cis-6 or cis-11 molecules, the double bond of its dimer molecule would have a distance from that of the neighboring dimer molecules as shown in the schematic drawing C. Therefore, the whole interaction between the cis-6 or cis-11 dimer molecules is thought to be weak compared with that for the cis-9 dimer molecules. Thus cis-6 and cis-11 have larger D value than cis-9 at high temperatures. (2) The Reason for the Difference in D Value for cis-Type and trans-Type Unsaturated Fatty Acids and Saturated Fatty Acid. As mentioned before, trans-9 and stearic acid also take the interdigitated lamellar structure in the liquid state as shown in Figure 11a. They have a relatively small short spacing and a large long spacing, compared with the cis-type acids: The lateral distance between molecules for stearic acid or trans-9 is smaller than that for the cis-type acids. Thus, especially for stearic acid, by the strong cohesive interaction between its molecules, the more straight, rodlike molecules of stearic acid having less gauche structures aggregate tightly with each other to make rigid clusters. The rigid clusters aggregate randomly to make a liquid having many spaces in it: The liquid structure may resemble a “house-of-cards” structure found often in the bulky clay.28 The spaces produce a low density and consequently a large apparent molar volume for stearic acid. However, the real distance between the interacting molecules in the cluster of stearic acid is so small that the molecules in the cluster cannot move so easily by the large attractive forces (that is, mainly by van der Waals forces) among the molecules. On the other hand, the flexible molecules of the cis-type unsaturated fatty acid make similar clusters shown in Figure 11. The clusters, which seem to be soft, aggregate randomly with each other to make a liquid. The softness of the clusters would prevent the formation of the spaces among the clusters. Thus, as a whole, the cis-type unsaturated fatty acids seemingly have a large density compared with stearic acid. The interaction between the molecules in the cluster of the cis-type acid is not so strong that the molecules of the cis-type acid can move easily than those of stearic acid.

The D value for trans-9 possessing the middle molar volume increases significantly with increasing temperature and exceeds the D value for cis-9. This is also explained by the cluster model: The extent of the segmental movements in the straight trans-9 molecule is less than that in the cis-type molecule, especially at low temperatures. Thus, at low temperatures, the trans-9, having fewer gauche structures in its molecule, seems to possess a relatively rigid cluster structure which resembles that for stearic acid. The relatively rigid clusters allow the liquid of trans-9 to possess relatively many spaces. Owing to the lesser extent of the segmental movement in the molecule, the value of D at low temperature for trans-9 is small compared with that for the cis-type acids. With rising temperature, the segmental movements of the trans-9 molecule become large (especially for the methyl group at the end of the trans-9 molecule) and the cohesive interaction among the trans-9 molecules becomes weak. Even at high temperatures, however, the many spaces would still remain. Consequently, the molecules of trans-9 are likely to escape easily through the spaces among the clusters at high temperatures. Thus, the D value for trans-9 increases considerably with an increase in temperature and exceeds the value for cis-9 at a high temperature. Acknowledgment. The present study was supported in part by a grant-in-aid for Scientific Research (No. 10640566) from the Ministry of Education, Science and Culture, Japan. References and Notes (1) Raston, A. W. Fatty Acids and Their DeriVatiVes; John Willey & Sons: New York, 1948. (2) Small, D. M. The Physical Chemistry of Lipids; Plenum Press: New York, 1986. (3) Gunstone, F. D.; Harwood, J. L.; Padley, F. B. The Lipid Handbook; Chapman & Hall, New York, 1986. (4) Hamilton, R. J.; Bhati, A. Recent AdVances in Chemistry and Technology of Fats and Oils; Elsevier: Amsterdam, 1987. (5) Gartri, N.; Sato, K., Eds. Crystalization and Polymorphism of Fats and Fatty Acids, Marcel Dekker: New York, 1988. (6) Kobayashi, M.; Kaneko, F.; Sato, K.; Suzuki, M. J. Phys. Chem. 1986, 90, 6371. (7) Sato, K.; Yoshimoto, N.; Suzuki, M.; Kobayashi, M.; Kaneko, F. J. Phys. Chem. 1990, 94, 3180.

6194 J. Phys. Chem. B, Vol. 104, No. 26, 2000 (8) Yoshimoto, N.; Suzuki, M.; Sato, K. Chem. Phys. Lipids 1991, 57, 67. Larsson, K. Fette, Seifen Anstrichm. 1972, 74, 136. (9) Doddrell, D.; Allerhand, A. J. Am. Chem. Soc. 1971, 93, 1558. (10) Levine, Y. K.; Birdsall, N. J. M.; Lee, A. G.; Metcalfe, J. C.; Partington, P.; Roberts G. C. K. J. Chem. Phys. 1974, 60, 2890. (11) Brady, G. W.; Fein, D. B. J. Appl. Crystallogr. 1975, 8, 261. (12) Berchiese, G.; Berchiesi, M. A.; Leonesi, D. J. Therm. Anal. 1976, 9, 455. (13) Callaghan, P. T.; Jolley, K. W. Chem. Phys. Lipids 1980, 27, 49. (14) Larsson, K. Fette, Seifen Anstrichm. 1972, 74, 136. (15) Callaghan, P. T.; Jolky, K. W. J. Chem. Phys. 1977, 67, 4773. (16) Hernqvist, L. Fette, Seifen Anstrichm. 1984, 86, 297. (17) Cebula, D. J.; McClements, D. J.; Povey, M. J. W.; Smith, P. R. J. Am. Oil Chem. Soc. 1992, 69, 130. (18) Larsson, K. J. Am. Oil Chem. Soc. 1992, 69, 835. (19) Ueno, S.; Minato, A.; Seto, H.; Amemiya, Y.; Sato, K. J. Phys. Chem. B 1997, 101, 6847.

Iwahashi et al. (20) Iwahashi, M.; Suzuki, M.; Czarnecki, M. A.; Liu, Y.; Ozaki, Y. J. Chem. Soc., Faraday Trans. 1995, 91, 697. (21) Iwahashi, M.; Yamaguchi, Y.; Kato, T.; Horiuchi, T.; Sakurai, I.; Suzuki, M. J. Phys. Chem. 1991, 95, 445. (22) Farrar, T. C.; Becker, E. D. Pulse and Fourier Transform NMR; Academic Press: New York, 1971. (23) Kuhlmann, K. F.; Grant, D. M.; Harris, R. K. J. Chem. Phys. 1970, 52, 3439. (24) Hertz, H. G. Prog. Nucl. Magn. Reson. Spectrosc. 1967, 3, 159. (25) Lomer, T. R. Acta Crystallogr. 1963, 16, 984. (26) Goto, M.; Ashida, E. Bull. Chem. Soc. Jpn. 1978, 51, 70. (27) Kaneko, F.; Yamazaki, K.; Kitagawa, K.; Kikyo, T.; Kobayashi, M.; Kitagawa, Y.; Matsuura, Y.; Sato, K.; Suzuki, M. J. Phys. Chem. B 1997, 101, 1803. (28) Everett, D. H. Basic Principles of Colloid Science; Royal Society of Chemistry: London, 1988.

Self-Diffusion, Dynamical Molecular Conformation, and Liquid

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