Diffusion of Squalene in n-Alkanes and Squalane

Article pubs.acs.org/JPCB

Diffusion of Squalene in n‑Alkanes and Squalane Bruce A. Kowert,*,† Michael B. Watson,‡ and Nhan C. Dang§ †

Department of Chemistry, St. Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103 Department of Chemistry, Washington University, One Brookings Drive, St. Louis, Missouri 63130 § United States Army Research Laboratory, RDRL-WML-B, Aberdeen Proving Ground, Maryland 21005 ‡

S Supporting Information *

ABSTRACT: Squalene, an intermediate in the biosynthesis of cholesterol, has a 24-carbon backbone with six methyl groups and six isolated double bonds. Capillary flow techniques have been used to determine its translational diffusion constant, D, at room temperature in squalane, n-C16, and three n-C8− squalane mixtures. The D values have a weaker dependence on viscosity, η, than predicted by the Stokes−Einstein relation, D = kBT/(6πηr). A fit to the modified relation, D/T = ASE/ηp, gives p = 0.820 ± 0.028; p = 1 for the Stokes−Einstein limit. The translational motion of squalene appears to be much like that of n-alkane solutes with comparable chain lengths; their D values show similar deviations from the Stokes−Einstein model. The n-alkane with the same carbon chain length as squalene, nC24, has a near-equal p value of 0.844 ± 0.018 in n-alkane solvents. The values of the hydrodynamic radius, r, for n-C24, squalene, and other n-alkane solutes decrease as the viscosity increases and have a common dependence on the van der Waals volumes of the solute and solvent. The possibility of studying squalene in lipid droplets and membranes is discussed.

1. INTRODUCTION Squalene has a 24-carbon backbone with six methyl groups and six isolated double bonds (Figure 1a). An intermediate in the

Einstein limit, in which a common r value would be expected, requires the solute to be much larger than the solvent;4 this is not the case for our solutions. Table 1. Diffusion Constants for Squalene and Squalane SelfDiffusion

Figure 1. Structures of (a) squalene and (b) squalane.

solvent

T (°C)

107D(exptl) (cm2/s)

η (P)

r (Å)a

squalane squalane n-C16 n-C16 n-C16 squalane-self

23.0 22.75 23.0 22.75 22.5 23.0

3.42b 3.27 20.9 21.2 21.0 3.00c

0.303 0.307 0.0316 0.0318 0.0319 0.303

2.10 2.16 3.28 3.22 3.23 2.39

a

Calculated using eq 1. bThe average of two determinations. Calculated from a fit to the data in ref 27 (293 ≤ T ≤ 372 K), which gave log D = −1369/T − 1.902.

c

biosynthesis of cholesterol, it is found in shark liver oil, vegetable oils, alkaliphile membranes, and lipid droplets.1,2 In this work, we report the use of capillary flow techniques to determine squalene’s translational diffusion constant, D, at room temperature in several nonpolar solvents: squalane (Figure 1b), n-C16, and three n-C8−squalane mixtures (n-Ci is used for the n-alkanes n-CiH2i+2). Squalene’s D values will be compared with those for a number of n-alkanes diffusing in n-C6−n-C16. The comparison will use values of the hydrodynamic radius, r, obtained from the Stokes−Einstein relation,3,4 D = kBT /(6πηr )

The n-alkane solutes we consider range from CH4 to n-C32 and include n-C16, n-C18, and n-C24. Their r values also decrease as η increases and are shown to have the same dependence on the relative sizes of the solute and solvent as squalene. Another indication of similarities between the diffusion of squalene and n-alkanes comes from a comparison of their deviations from the Stokes−Einstein model. We (and others)

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where kB is Boltzmann’s constant, T is the absolute temperature, and η is the viscosity. Squalene’s r values decrease as the solvent viscosity increases (Tables 1 and 2). The Stokes− © 2014 American Chemical Society

Received: November 21, 2013 Revised: January 30, 2014 Published: February 14, 2014 2157

dx.doi.org/10.1021/jp411471r | J. Phys. Chem. B 2014, 118, 2157−2163

The Journal of Physical Chemistry B

Article

those for several of the 27 solutes we have studied in n-C6−nC16 and squalane.5,6,10−12 The p values range from 0.537 ± 0.012 for O2 to 0.953 ± 0.020 for rubrene and generally increase as the solute size increases. This is the first systematic study of squalene’s diffusion, and our results may be useful in determining the viscosity in the hydrophobic biological media in which it is found; two such systems, lipid droplets and membranes, are discussed in Section 3.3. Spanova and Daum2 give a review of its biochemistry, molecular biology, and properties. Squalene’s D values also may provide tests of molecular dynamics (MD) computer codes. There is interest in alkanes with 20 or more carbon atoms;13 simulations have been carried out for single n-alkanes and binary mixtures.14,15 There have been calculations for squalene,16−18 but the results were not used to determine D values.

Table 2. Diffusion Constants for Squalene in n-C8−Squalane Mixed Solvents xSa 0.291 0.508 0.508 0.708 0.708

T (°C) 22.5 23.0 22.75 23.0 22.75

107D(exptl) (cm2/s) c

23.6 10.9 11.2d 6.835d 6.445d

η (P)

r (Å)b

0.0297 0.0718 0.0724 0.138 0.139

3.08 2.77 2.67 2.30 2.415d

a xS is the mole fraction of squalane in the mixed solvent. bCalculated using eq 1. cThe average of three determinations. dThe average of two determinations.

have fitted the D values for a given solute in a series of solvents to the modified Stokes−Einstein relation,5−9 D/T = ASE /η p

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where p and ASE are constants; p = 1 for the Stokes−Einstein relation. A value of p = 0.820 ± 0.028 is found for squalene. As shown in Section 3.1, several n-alkanes (n-C16, n-C18, and nC24) have comparable p values. The values of p and log ASE for these n-alkanes and squalene are given in Table 3, along with

2. EXPERIMENTAL SECTION 2.1. Chemicals and Sample Preparation. Squalane (2,6,10,15,19,23-hexamethyltetracosane, 99%) and n-C8 (99+ %) were obtained from Aldrich; n-C16 (99+%) was obtained from Sigma-Aldrich; squalene (2,6,10,15,19,23-hexamethyl2,6,10,14,18,22-tetracosahexaene, ≥98%) was obtained from Sigma. All substances were used as received. Squalene was stored in a cooler at 4 °C; samples were prepared and profiles were taken with the laboratory lights off to minimize the possibility of photo-oxidation.19 Three n-C8−squalane mixed solvents with squalane mole fractions xS = 0.291, 0.508, and 0.708 were prepared; the values of xS and η for a given mixture were calculated using the density and viscosity data in ref 20. The viscosities for squalane are from refs 21 and 22, whereas those for the n-alkanes are from ref 23. The concentration of squalene in our solutions varied from 1.1 to 3.7 mM. 2.2. Profile Acquisition and Analysis. The sigmoidal elution profiles used to determine squalene’s D values (Figures 2 and 3) were obtained as described in ref 10 using a Thermo Separation Products SC100 variable wavelength detector, Chrom Perfect software (Justice Innovations), and a fused silica microcapillary (Polymicro Technology, 76.5 μm i.d.). The detector wavelength was 198 nm.19 The experimental profiles were compared with profiles calculated using Taylor’s equations:24−26

Table 3. Values of p and ASE Obtained from Fits to Eq 2a −logASE

p

solute O2 benzene biphenyl diphenylacetylene n-C16 n-C18 squalene n-C24 coronene triptycene diphenylanthracene tetraphenylbutadiene C60 rubrene

0.537 0.680 0.701 0.730 0.760 0.756 0.820 0.844 0.851 0.861 0.893 0.908 0.924 0.953

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.012 0.009 0.013 0.017 0.010 0.015 0.028 0.018 0.019 0.017 0.014 0.018 0.010 0.020

7.844 8.534 8.749 8.883 9.056 9.097 9.3615 9.390 9.284 9.345 9.498 9.541 9.649 9.731

± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.026 0.022 0.026 0.033 0.023 0.033 0.033 0.040 0.040 0.034 0.027 0.035 0.020 0.040

a

The values of p and log ASE for n-C18, squalene, and n-C24, are from this work; those for n-C16 are from ref 5. The values for the other solutes are from ref 10 and were determined from fits to data in nalkanes and squalane. All fits used D in cm2 s−1 and η in P.

C(t )/C0 = (1/2)(1 − erf{x1/[2(kt )1/2 ]})

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Figure 2. Experimental (squares) and calculated (circles) profiles for squalene in squalane at 23.0 °C. The D values for the calculated profiles in (a) and (b) are 3.00 × 10−7 cm2 s−1 (squalane’s self-diffusion constant) and 3.385 × 10−7 cm2 s−1, respectively. 2158



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Figure 3. Experimental (squares) and calculated (circles) profiles for squalene in the n-C8-squalane mixed solvent with xs = 0.291 at 22.5 °C. A value of D value of 2.34 × 10−6 cm2 s−1 is used for the calculated profile.

x1 = x − Ut

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k = a 2U 2/48D

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Figure 4. Fit to D/T = ASE/ηp of the diffusion constants for squalene in n-C16, (red triangles), squalane (brown circles), and n-C8-squalane mixed solvents (blue x’s); D in cm2 s−1, η in P. Squalane’s self-diffusion constant (black diamond) is shown but was not included in the fit.

the datum for squalane’s self-diffusion (Table 1) but it was not included in the fit. The p value for squalene, with its 24-carbon backbone and isolated double bonds, is reasonably close to those for n-alkanes with chains of 16 or more carbon atoms. It is within the experimental error of p = 0.844 ± 0.018 for n-C24 in n-C6, n-C8, and n-C12.29 A fit for n-C18 in n-C6, n-C8, n-C12,29,30 and n-C8− n-C12 mixed solvents30 gives p = 0.756 ± 0.015, a value marginally smaller than squalene’s as is 0.760 ± 0.010 for n-C16 in n-C6, n-C7, n-C8, n-C12, and itself (self-diffusion).5 Figure 5 shows the colinear data for squalene and n-C24. Also included are the D values for n-C32 in n-C6 and n-C8;29 they are slightly slower than but parallel to those for n-C24.

where t is the time, C0 is the solution concentration, U is the solution’s flow speed through the capillary, a is the capillary radius, and x is the distance between the capillary tip and the detector. The profile intensity ratio, C(t)/C0, increases from 0 to 1 as the solution moves past the detector. Profile acquisition times ranged from ∼160 s for n-C16 and the n-C8-squalane solution with xS = 0.291 to ∼1150 s for squalane. Profiles were taken at room temperature (Tables 1 and 2), which varied by no more than ±0.50 °C during a given acquisition. Squalene’s profiles in squalane were the first to be simulated. The initial estimates of D were based on the self-diffusion constant of squalane, Dself, at the temperature of interest.27 Figure 2a compares an experimental profile in squalane at 23.0 °C with one calculated using Dself = 3.00 × 10−7 cm2 s−1. Differences are seen near the onset and plateau of the profiles. Agreement is obtained for D = 3.385 × 10−7 cm2 s−1 (Figure 2b). The initial estimates for the profiles in n-C16 were based on its viscosity and squalane’s. The initial estimates in the mixed solvents were obtained from of a fit of the results in squalane and n-C16 to eq 2. In Figure 3, an experimental spectrum at 22.5 °C in the mixed solvent with xS = 0.291 is in agreement with one calculated using D = 2.34 × 10−6 cm2 s−1. The D values in the single-component and mixed solvents (their uncertainties are ±10%) are given in Tables 1 and 2, respectively. Taylor stated28 that eqs 3−5 can be used if 4L/a > 690 and Ua/D > 69; L is the capillary length over which C(t)/C0 changes from 0.01 to 0.99 when C(t)/C0 = 0.50 passes the detector. Our squalene profiles meet these requirements. The values for the profile in Figure 2b are 4L/a = 9.60 × 103 and Ua/D = 529; the profile in Figure 3 has 4L/a = 9.27 × 103 and Ua/D = 510.

Figure 5. Plot of log(D/T) vs log η for squalene (blue squares), n-C24, (red triangles), and n-C32 (brown circles); D is in cm2 s−1, η in P. The fit line is for the squalene data.

MD simulations have shown that n-C16, and n-C20 are relatively extended31,32 as are n-C2427 and squalane.27 As reviewed by Desmaële et al.,33 there has been mention of a coiled conformation for squalene in polar media but, like squalane, it is expected to be relatively extended in nonpolar solvents such as the n-alkanes. An MD simulation for squalene in nonpolar CCl4 gave an elongated conformation with a separation of ∼23 Å between carbons 2 and 23.18 This is consistent with the end-to-end distances of the alkanes mentioned above: 14.5 Å (n-C16),31,32 17.0 Å (n-C20),31 20.2 Å (n-C24),27 and 19.1 Å (squalane).27

3. RESULTS AND DISCUSSION 3.1. Values of p. A plot of log(D/T) versus log η for squalene is shown in Figure 4. The viscosities of the mixed solvents with xS = 0.508 and 0.708 bridge the gap between nC16 and squalane; our previous studies10 had no data in this range. A fit to eq 2 gives p = 0.820 ± 0.028. Figure 4 also shows 2159



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Relatively extended solutes should have similar interactions with relatively extended solvents, reducing the solute’s viscosity dependence and giving p < 1.31 It should be noted, however, that it is possible for solutes with dissimilar shapes and sizes to have near-equal p values. Table 3 shows this to be the case for n-C24 (0.844 ± 0.018) and coronene (0.851 ± 0.019). The solute−solvent interactions evidently compensate for the structural differences and bring their p values into coincidence. 3.2. Values of r and Volume-Dependent Analysis. Values of r for squalene were calculated using its D values and eq 1. They are given in Tables 1 and 2 and decrease as the viscosity increases. In our earlier studies,6,10 the r values for a number of solutes in n-C6−n-C16 and squalane also decreased as η increased. The sizes of these solvents increase as their viscosities increase and the r values were discussed using the following: r = R 0/(1 + Vs/Vp)m

Table 4. Solvents and Solutes in Figure 6 solvent n-C6b n-C7c n-C8d n-C10e n-C12f n-C14g n-C16h squalanei self-diffusionj n-C8-squalanek n-C8-n-C12l

i for n-Ci solutesa 32, 24, 18, 16, 12, 10, 8, 7, 5, 3, 2, CH4 16, 14, 12, 10, 8, 3, 2, CH4 32, 24, 18, 16, 14, 12, 10, 7, 3, 2, CH4 7, CH4 24, 18, 16, 10, 8, 7, 6, 2, CH4 8, 7, CH4 12, 8, 7, 6, 3, 2, CH4, squalene squalene 6−14, 16, squalane squalene 18

a The notation i for n-Ci is used for the solutes in this table. bThe data for CH4 are from refs 29 and 41; the rest are from ref 29. cThe data for 16 are from refs 42 and 29; those for 14, 12, 10, and 8 are from ref 42; those for 3, 2, and CH4 are from ref 29. dThe data for 32, 24, 16, 3, 2, and CH4 are from ref 29; those for 18 are from refs 29 and 30; that for 14 is from ref 43; that for 12 is from ref 30; those for 10 and 7 are from ref 48. eThe datum for 7 is from ref 43; that for CH4 is from ref 41. f The data for 24, 2, and CH4 are from ref 29; those for 18 are from refs 29 and 30; that for 16 is from ref 29; that for 10 is from ref 42; those for 8 are from refs 29, 30, and 42; that for 7 is from ref 43; that for 6 is from ref 44; and those for squalene are from Table 1. gThe data for 8 and 7 are from ref 43; that for CH4 is from ref 41. hThe data for 12 are from refs 29 and 45; that for 8 is from ref 29; those for 7, 3, 2, and CH4 are from ref 29; that from 6 is from 43; those for squalene are from Table 1. iData are from Table 1. jThe data for 6−14 are from ref 46; that for 16 is from ref 47; that for squalane is from Table 1. kData are from Table 2. lAll data are from ref 30.

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where R0 is an effective radius, Vp and Vs are the van der Waals volumes of the probe (solute) and solvent molecules, respectively, and m ≈ 1 is a fit parameter; Vs and Vp were estimated using the Bondi-Edward increments.34,35 Equation 6 is consistent with our solvent-dependent results and predicts that r becomes independent of Vs in the Stokes− Einstein limit (Vp ≫ Vs). Zwanzig and Harrison36 characterized r as an effective hydrodynamic radius with the solventdependent values measuring differences in the coupling of the solute motion to the solvent flow. The conditions under which the Stokes−Einstein relation holds have also been discussed in terms of solute−solvent interactions, as well as properties of the solute and solvent; representative results are given in refs 9 and 37−40. In Figure 6, the r values for squalene and n-alkane solutes (CH4−n-C32) in n-alkane solvents (n-C6−n-C16)29,30,41−48 are

mixed solvents, we used (1 + Vs/Vp)mixed = x1(1 + Vs/Vp)1 + x2(1 + Vs/Vp)2, where xi is the mole fraction of solvent i. The values of (1 + Vs/Vp, r) vary from (1.204, 5.36 Å) for nC32 in n-C6 to (10.98, 0.271 Å) for CH4 in n-C16. Self-diffusion, with 1 + Vs/Vp = 2, is a special case; a size independent of chain length is predicted.5,6 The values for the n-alkanes vary from rself = 1.63 Å for n-C6 to 1.91 Å for n-C16 at 25 °C,6,46,47 a relatively small difference given that Vs increases from 113.4 Å3 (n-C6) to 283.4 Å3 (n-C16). The value of rself = 2.39 Å for squalane with its six methyl groups, and Vs = 521.4 Å3 is larger but closer to the average value of r = 2.12 Å for squalene in squalane (Vp = 483.0 Å3, 1 + Vs/Vp = 2.08). The r values for squalene and the n-alkanes (including rself) are in general agreement with eq 6; squalene’s isolated double bonds do not appear to cause a significant difference. The fit to the data in Figure 6 gives R0 = 4.678 Å and m = 1.190. The trend of near-constant values of rself also holds at higher temperatures for n-alkanes with chain lengths longer than nC16. Figure 7 shows a plot of rself versus the number of carbons in the chains of squalane at 23 °C and the following n-alkanes at the indicated temperatures: n-C20 (50.5, 70.5 °C), n-C24 (50.5, 70.5 °C), n-C28 (70.5, 90.5 °C), n-C30 (70.5, 90.5 °C), and n-C32, (70.5, 90.5 °C); the n-alkanes’ D values are from ref 49, squalane’s is from ref 27. Also shown in Figure 7 are the r values for squalene in squalane (Table 1); the values of rself for n-C6−n-C14 at 25 °C;46 the values of rself for n-C16 at 25.0, 30.5, 50.0, and 50.5 °C;47,49 and the r values at 25 °C for the 1-alkenes with 6, 8, 10, 12, and 14 carbon atoms diffusing in n-alkanes with the same number of carbon atoms.5 The values of rself for n-C6−n-C14 and r for the 1-alkenes are somewhat less than 2.0 Å, whereas those for the longer n-alkanes, squalene, and squalane are

Figure 6. Solute r values in the n-alkanes and squalane (including those for self-diffusion) vs 1 + Vs/Vp. With the exception of squalene as a solute, the legend entries are for the solvents. The solute−solvent pairs are given in Table 4. The circles with dots are from the fit to eq 6 (R0 = 4.678 Å, m = 1.190).

plotted versus 1 + Vs/Vp. The solvents and solutes are listed in Table 4; the data (295 ≤ T/K ≤ 304) include values of rself from the self-diffusion constants of n-alkanes and squalane as well as the r values for solutes in two sets of mixed solvents: squalene in n-C8−squalane and n-C18 in n-C8−n-C12.30 For the 2160



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for n-C6, n-C8, n-C12, and n-C14 in Table 5. Given their increased flexibility, it would seem that the values of rself of nC12 and n-C14 should be larger than those for n-C6 and n-C8 but they are essentially the same. The r values for the longer nalkanes in n-C6 (Figure 7) also increase as their chain lengths increase, but all have rself ≈ 2.0 Å. As Harrison and Zwanzig pointed out,36 r is more than a molecular dimension; it is a measure of the interactions between the solute and solvent, as well as their shapes and sizes.37−40 The n-alkanes and squalene may be relatively extended as they move through solution, but their r values are determined by more than the cross section of their hydrocarbon chains. We have considered the n-alkanes’ self-diffusion at or near room temperature (Figure 6), or at the lowest temperatures for which values of Dself for higher n-alkanes were available (Figure 7). It would be worthwhile to see if the n-alkanes’ temperaturedependent self-diffusion data follow eq 2 and if so, what values of p are found. The self-diffusion of water is an example of a system where the solute is not much larger than the solvent, but the D values are in (or near) the Stokes−Einstein limit; p(H2O) = 0.943 for 623 ≥ T/K ≥ 274.52 A smaller value of p(H2O) = 0.668 is found in the supercooled region (273 ≥ T/ K ≥ 238); possible reasons for this transition and similar results in D2O are discussed in refs 8 and 52. 3.3. Squalene in Biochemical Systems. Squalene offers the opportunity to study a naturally occurring component of biological systems. A nonpolar hydrocarbon, it tends to accumulate in lipid storage compartments.2 One such location is the hydrophobic core of lipid droplets.1,2,53 Fluorescence correlation spectroscopy (FCS)54 experiments indicate that it may be possible to use our data to estimate the viscosity in these cytoplasmic organelles.53 Ghosh et al. employed the probe coumarin 153 (C153, Figure 8) to study the lipid droplets of a live Chinese hamster

Figure 7. Values of rself for squalane (black ×) and the n-Ci with i = 6− 14 (blue squares) and i = 16, 20, 24, 28, 30, and 32 (green circles); also included are the r values for (a) squalene in squalane (red triangles), (b) the 1-alkenes with 6, 8, 10, 12, 14 carbon atoms diffusing in n-Ci with the same i (orange diamonds), and (c) the n-Ci, with i = 7, 8, 10, 12, 16, 18, 24, and 32 diffusing in n-C6 (brown inverted triangles).

somewhat larger. However, given the differences in the temperatures and sizes of the diffusants, the variation is relatively small; the r values for squalene in squalane are consistent with the values of rself for n-alkanes with similar chain lengths. Figures 6 and 7 have the same range of ordinate values. This was done to emphasize the relatively small changes in the r values in Figure 7 relative to those in Figure 6. To further emphasize these differences, the r values for n-C7, n-C8, n-C10, n-C12, n-C16, n-C18, n-C24, and n-C32 in n-C6 are included in Figure 7. The data for Figure 7 are given in Tables S1−S4 of the Supporting Information. It has been sugested46 that the near-constant values of rself for the n-alkanes correspond to the cross section associated with faster motion in the direction of their long (backbone) axis, but this does not appear to be the case when the solute and solvent have different chain lengths.5 For example, the values of rself for n-C6 and n-C8 are 1.64 and 1.69 Å, respectively. MD studies have shown that n-C6 rotates as a “nearly rigid object”,50 while the reorientation of n-C8 is31 a “largely rigid body”. This is a result of their chain lengths being less than the n-alkanes’ persistence length (10.5 Å31,32,51). The rigid rotation implies, however, that their r values in other n-alkanes should be the common cross section. Table 5 shows otherwise; the values of r for n-C6 and n-C8 in n-C16 are 0.85 and 1.08 Å, respectively, a factor of ∼1.9 smaller than they are in n-C6. As their chain lengths increase, the n-alkanes show more flexibility and have larger r values in a given solvent. This is seen

Figure 8. The fluorescent probe coumarin 153 (C153).

ovary cell.54 The emission maximum of C153 (502 nm) was identical to that in ethyl acetate, a nonpolar solvent with dielectric constant ε = 6.02. FCS was used to determine 107D(C153) = 1.7 cm2 s−1 at 25 °C. Equation 1 and r(C153) = 3.8 Å gave η = 34 cP.54 This is 23% more viscous than squalane at 25 °C (27.6 cP) but suggests that squalene’s D value might be close to those we have measured. A lower value of η would be found if C153’s diffusion constant, like squalene’s, had a weaker viscosity dependence than predicted by eq 1.55 Additionally, our squalene results may be viable for higher viscosities. At room temperature, where squalane is a factor of ∼9 more viscous than n-C16, the D values for 27 solutes in squalane were found to be within ±25% of the values calculated from the fits of their n-C6−n-C16 data to eq 2.10 Diffusion-ordered NMR spectroscopy (DOSY) has been shown to be useful for studying squalene in complex mixtures, such as those found in lipid droplets. Williard et al. used 1H DOSY to determine the D values of squalene, benzene, triolein, dioleoylglycerols, 1-oleoyl-rac-glycerol, and methyl oleate in the

Table 5. Values of r (in Å) for n-Alkane Solutions at 25 °C.a solute solvent

n-C6

n-C8

n-C12

n-C14

n-C6 n-C8 n-C12 n-C14 n-C16

1.64

2.10 1.69 1.38 1.23 1.08

2.67 2.48 1.70

2.64

1.14 0.848

1.74 1.26

a

The references for the solute−solvent systems are given in Table 4. The values of r are calculated from eq 1. 2161



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same toluene solution.56 The D value for squalene, 7.54 × 10−6 cm2 s−1, is larger than those we have determined but the temperature was not given and toluene57 (at 25 °C) is a factor or 5.5 less viscous than n-C16, our least viscous solvent. In a related study, 1H DOSY was used to determine the D value for squalene and seven other components of olive oil in CDCl3 but here too the temperature was not given.58 There also is evidence for the localization of squalene in the interior of a model phospholipid bilayer membrane.59 Alkaliphile membranes, which contain ∼10% squalene (as well as other isoprenes), were mimicked by incorporating perdeuterated and normal (protonated) squalane into bilayers of dioleoyl phosphatidyl choline doped with dioleoyl phosphatidyl glycerol. Comparison of the neutron diffraction data for the two isotopomers showed that squalane, and by inference squalene, was predominantly in the bilayer center, parallel to the plane of the membrane.59

ASSOCIATED CONTENT

S Supporting Information *

The data for the solutes and solvents in Figure 7 are given in Tables S1−S4. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

(1) Spanova, M.; Zweytick, D.; Lohner, K.; Klug, L.; Leitner, E.; Hermetter, A.; Daum, G. Influence of Squalene on Lipid Particle/ Droplet and Membrane Organization in the Yeast Saccharomyces cerevisiae. Biochim. Biophys. Acta 2012, 1821, 647−653. (2) Spanova, M.; Daum, G. SqualeneBiochemistry, Molecular Biology, Process Biotechnology, and Applications. Eur. J. Lipid Sci. Technol. 2011, 113, 1299−1320. (3) Tyrrell, H. J. V.; Harris, K. R. Diffusion in Liquids; Butterworths: London, 1984. (4) Longuet-Higgins, H. C. Transport Processes in Fluids. Il Nuovo Cim. 1955, 1 (Ser. 10, Suppl. 2), 140−155. (5) Kowert, B. A.; Turner, R. M., II; Caldwell, C. V. C. Diffusion of 1Alkenes and Cyclohexene in Alkane Solvents. Chem. Phys. 2008, 344, 114−120. (6) Kowert, B. A.; Sobush, K. T.; Fuqua, C. F.; Mapes, C. L.; Jones, J. B.; Zahm, J. A. Size-Dependent Diffusion in the n-Alkanes. J. Phys. Chem. A 2003, 107, 4790−4795. (7) Chen, S. H.; Davis, H. T.; Evans, D. F. Tracer Diffusion in Polyatomic Liquids. III. J. Chem. Phys. 1982, 77, 2540−2544. (8) Harris, K. R. The Fractional Stokes-Einstein Equation: Application to Lennard−Jones, Molecular, and Ionic Liquids. J. Chem. Phys. 2009, 131, 054503. (9) Chan, T. C.; Tang, W. K. Diffusion of Aromatic Compounds in Nonaqueous Solvents: A Study of Solute, Solvent, and Temperature Dependence. J. Chem. Phys. 2013, 138, 224503. (10) Kowert, B. A.; Watson, M. B. Diffusion of Organic Solutes in Squalane. J. Phys. Chem. B 2011, 115, 9687−9694. (11) Kowert, B. A.; Dang, N. C.; Sobush, K. T.; Seele, L. G., III Diffusion of Aromatic Hydrocarbons in n-Alkanes and Cyclohexanes. J. Phys. Chem. A 2001, 105, 1232−1237. (12) Kowert, B. A.; Dang, N. C.; Sobush, K. T.; Seele, L. G., III Diffusion of Buckminsterfullerene in n-Alkanes. J. Phys. Chem. A 2003, 107, 1253−1257. (13) Ferguson, A. L.; Debenedetti, P. G.; Panagiotopoulos, A. Z. Stability and Molecular Conformations of n-Alkane Chains in Water. J. Phys. Chem. B 2009, 113, 6405−6414. (14) Makrodimitri, Z. A.; Unruh, D. J. M.; Economou, I. G. Molecular Simulation of Diffusion of Hydrogen, Carbon Monoxide, and Water in Heavy n-Alkanes. J. Phys. Chem. B 2011, 115, 1429− 1439. (15) Makrodimitri, Z. A.; Unruh, D. J. M.; Economou, I. G. Molecular Simulation and Macroscopic Modeling of the Diffusion of Hydrogen, Carbon Monoxide and Water in Heavy n-Alkane Mixtures. Phys. Chem. Chem. Phys. 2012, 14, 4133−4141. (16) Enevoldsen, A. D.; Hansen, F. Y.; Diama, A.; Taub, H.; Dimeo, R. M.; Neumann, D. A.; Copley, J. R. D. Comparative Study of Normal and Branched Alkane Monolayer Films Adsorbed on a Solid Surface. II. Dynamics. J. Chem. Phys. 2007, 126, 104704. (17) Pogliani, L.; Milanesio, M.; Ceruti, M.; Viterbo, D. Conformational and Dynamical Study of Squalene Derivatives. III: Azasqualenes and Solvated Squalene. Chem. Phys. Lipids 1999, 103, 81−93. (18) Guba, W.; Kessler, H. A Novel Computational Mimetic of Biological Membranes in Molecular Dynamics Simulations. J. Phys. Chem. 1994, 98, 23−27. (19) Lu, H.-T.; Jiang, Y.; Chen, F. Determination of Squalene Using High-Performance Liquid Chromatography with Diode Array Detection. Chromatographia 2004, 59, 367−371. (20) Kumagai, A.; Tomida, D.; Yokoyama, C. Measurements of the Liquid Viscosities of Mixtures of n-Butane, n-Hexane, and n-Octane with Squalane to 30 MPa. Int. J. Thermophys. 2006, 27, 376−393. (21) Barlow, A. J.; Erginsav, A.; Lamb, J. Viscoelastic Relaxation of Supercooled Liquids. II. Proc. R. Soc. London, Ser. A 1967, 298, 481− 494. The viscosity for squalane at 25 °C from the fit in this ref differs by 1.4% from that in ref 22, which includes new η data as well as those from earlier work.. (22) Deegan, R. D.; Leheny, R. L.; Menon, N.; Nagel, S. R. Dynamic Shear Modulus of Tricresyl Phosphate and Squalane. J. Phys. Chem. B 1999, 103, 4066−4070.

4. CONCLUSIONS Capillary flow techniques have been used to determine the translational diffusion constant, D, of squalene in squalane, nC16, and three n-C8-squalane mixed solvents. The D values show deviations from the Stokes−Einstein relation. The values of r, squalene’s hydrodynamic radius, decrease as the viscosity increases. The r values for a number of n-alkane solutes diffusing in n-alkane solvents also decrease as η increases. The solutes range from CH4 to n-C32, the solvents from n-C6 to nC16. The r values for squalene and the n-alkanes are found to have a common dependence on Vs/Vp, the ratio of the solvent’s van der Waals volume to that of the solute probe. Squalene’s D values were fitted to the modified form of the Stokes−Einstein relation, D/T = ASE/ηp. A value of p = 0.820 ± 0.028 was found; p = 1 for the Stokes−Einstein relation. The fit suggests that the viscosity and relatively extended structures of squalane, n-C8, and n-C16 are more important for determining squalene’s diffusion than the structure of a given solvent molecule. Relatively extended n-alkane solutes, including n-C24, the n-alkane with the same carbon chain length as squalene, show similar deviations from the Stokes−Einstein relation. Squalene, like these n-alkanes, appears to have a relatively extended conformation, as it diffuses through n-alkanes and squalane.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 314-977-2837; fax: 314-977-2521; e-mail: kowertba@ slu.edu. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The Department of Chemistry, Saint Louis University, supported this research. The data acquisition system and detector were purchased with grants to Dr. Barry Hogan from Research Corp. and the donors of the Petroleum Research Fund, administered by the American Chemical Society. 2162



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(23) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosity of Liquids; Hemisphere Publishing: New York, 1989. (24) Taylor, G. The Dispersion of Matter in Turbulent Flow through a Pipe. Proc. R. Soc. London, Ser. A 1954, 223, 446−468. (25) Birovljev, B.; Måløy, K. J.; Feder, J.; Jøssang, T. Scaling Structure of Tracer Dispersion Fronts in Porous Media. Phys. Rev. E 1994, 49, 5431−5437. (26) Boschan, A.; Auradou, H.; Ippolito, I.; Chertcoff, R.; Hulin, J. P. Miscible Displacement Fronts of Shear Thinning Fluids Inside Rough Fractures. Water Resour. Res. 2007, 43, W03438. (27) Mondello, M.; Grest, G. S. Molecular Dynamics of Linear and Branched Alkanes. J. Chem. Phys. 1995, 103, 7156−7165. (28) Taylor, G. Conditions under Which Dispersion of a Solute in a Stream of Solvent can be Used to Measure Molecular Diffusion. Proc. R. Soc. London, Ser. A 1954, 225, 473−477. (29) Hayduk, W.; Ioakimidis, S. Liquid Diffusivities in Normal Paraffin Solutions. J. Chem. Eng. Data 1976, 21, 255−260. (30) Van Geet, A. L.; Adamson, A. W. Diffusion in Liquid Hydrocarbon Mixtures. J. Phys. Chem. 1964, 68, 238−246. (31) Zhang, Y.; Venable, R. M.; Pastor, R. W. Molecular Dynamics Simulations of Neat Alkanes: The Viscosity Dependence of Rotational Relaxation. J. Phys. Chem. 1996, 100, 2652−2660. (32) Venable, R. M.; Zhang, Y.; Hardy, B. J.; Pastor, R. W. Molecular Dynamics Simulations of a Lipid Bilayer and of Hexadecane: An Investigation of Membrane Fluidity. Science 1993, 262, 223−226. (33) Desmaële, D.; Gref, R.; Couvreur, P. Squalenoylation: A Generic Platform for Nanoparticular Drug Delivery. J. Controlled Release 2012, 161, 609−618. (34) Bondi, A. van der Waals Volumes and Radii. J. Phys. Chem. 1964, 68, 441−451. (35) Edward, J. T. Molecular Volumes and the Stokes-Einstein Formula. J. Chem. Educ. 1970, 47, 261−270. (36) Zwanzig, R.; Harrison, A. K. Modifications of the StokesEinstein Formula. J. Chem. Phys. 1985, 83, 5861−5862. (37) Schmidt, J. R.; Skinner, J. L. Brownian Motion of a Rough Sphere and the Stokes-Einstein Law. J. Phys. Chem. B 2004, 108, 6767−6771. (38) Kurban, M. R.; Peric, M.; Bales, B. L. Nitroxide Spin Exchange Due To Re-Encounter Collisions in a Series of n-Alkanes. J. Chem. Phys. 2008, 129, 064501. (39) Liu, J.; Cao, D.; Zhang, L. Molecular Dynamics Study on Nanoparticle Diffusion in Polymer Melts: A Test of the StokesEinstein Law. J. Phys. Chem. C 2008, 112, 6653−6661. (40) Kravchenko, O.; Thachuk, M. The Effect of Rotational and Translational Energy Exchange on Tracer Diffusion in Rough Hard Sphere Fluids. J. Chem. Phys. 2011, 134, 114310. (41) Evans, D. F.; Tominaga, T.; Davis, H. T. Tracer Diffusion in Polyatomic Liquids. J. Chem. Phys. 1981, 74, 1298−1305. (42) Matthews, M. A.; Akgerman, A. Diffusion Coefficients for Binary Alkane Mixtures to 573 K and 3.5 MPa. AIChE J. 1987, 33, 881−885. (43) Lo, H. Y. Diffusion Coefficients in Binary Liquid n-Alkane Systems. J. Chem. Eng. Data 1974, 19, 236−241. (44) Shieh, J. C.; Lyons, P. A. Transport Properties of Liquid nAlkanes. J. Phys. Chem. 1969, 73, 3258−3264. (45) Matthews, M. A.; Rodden, J. B.; Akgerman, A. High Temperature Diffusion, Viscosity, and Density Measurements in nHexadecane. J. Chem. Eng. Data 1987, 32, 317−319. (46) Iwahashi, M.; Yamaguchi, Y.; Ogura, Y.; Suzuki, M. Dynamical Structures of Normal Alkanes, Alcohols, and Fatty Acids in the Liquid State as Determined by Viscosity, Self-Diffusion Coefficient, Infrared Spectra, and 13C NMR Spin-Lattice Relaxation Time Measurements. Bull. Chem. Soc. Jpn. 1990, 63, 2154−2158. (47) Dymond, J. H.; Harris, K. R. The Temperature and Density Dependence of the Self-Diffusion Coefficient of n-Hexadecane. Mol. Phys. 1992, 75, 461−466. (48) Moore, J. W.; Wellek, R. M. Diffusion Coefficients of n-Heptane and n-Decane in n-Alkanes and n-Alcohols at Several Temperatures. J. Chem. Eng. Data 1977, 19, 136−140.

(49) Von Meerwall, E.; Beckman, S.; Jang, J.; Mattice, W. L. Diffusion of Liquid n-Alkanes: Free-Volume and Density Effects. J. Chem. Phys. 1998, 108, 4299−4304. (50) Budzien, J.; Raphael, C.; Ediger, M. D.; de Pablo, J. J. Segmental Dynamics in a Blend of Alkanes: Nuclear Magnetic Resonance Experiments and Molecular Dynamics Simulation. J. Chem. Phys. 2002, 116, 8209−4304. (51) Zapotoczny, S.; Auletta, T.; de Jong, M. R.; Schoenherr, H.; Huskens, J.; van Veggel, F. C. J. M.; Reinhoudt, D. N.; Vancso, G. J. Chain Length and Concentration Dependence of β-CyclodextrinFerrocene Host-Guest Complex Rupture Forces Probed by Dynamic Force Spectroscopy. Langmuir 2002, 18, 6988−6994. (52) Harris, K. R. The Fractional Stokes-Einstein Equation: Application to Water. J. Chem. Phys. 2010, 132, 231103. (53) Walther, T. C.; Farese, R. V., Jr. Lipid Droplets and Cellular Lipid Metabolism. Annu. Rev. Biochem. 2012, 81, 687−714. (54) Ghosh, S.; Chattoraj, S.; Mondal, T.; Bhattacharyya, K. Dynamics in Cytoplasm, Nucleus, and Lipid Droplet of a Live CHO Cell: Time-Resolved Confocal Microscopy. Langmuir 2013, 29, 7975− 7982. (55) Using η0.80 and C153’s r value in eq 1 gives 26 cP for the droplet’s viscosity at 25 °C. (56) Socha, A. M.; Kagan, G.; Li, W.; Hopson, R.; Sello, J. K.; Williard, P. G. Diffusion Coefficient-Formula Weight Correlation Analysis via Diffusion-Ordered Nuclear Magnetic Resonance Spectroscopy (DOSY NMR) to Examine Acylglycerol Mixtures and Biodiesel Production. Energy Fuels 2010, 24, 4518−4521. (57) Yaws, C. L. Handbook of Viscosity; Gulf Publishing Co.: Houston, 1995; Vol. 2, p 374. (58) Altun, A.; Ok, S. NMR Analyses and Diffusion Coefficient Determination of Minor Constituents of Olive Oil: Combined Experimental and Theoretical Studies. J. Chem. Eng. Data 2012, 57, 2619−2624. (59) Hauss, T.; Dante, S.; Dencher, N. A.; Haines, T. H. Squalane Is in the Midplane of the Lipid Bilayer: Implications for its Function as a Proton Permeability Barrier. Biochim. Biophys. Acta 2002, 1556, 149− 154.

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Diffusion of Squalene in n-Alkanes and Squalane

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