Diffusion of Benzene and Alkylbenzenes in n ... - ACS Publications

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Diffusion of Benzene and Alkylbenzenes in n‑Alkanes Bruce A. Kowert* and Paul M. Register Department of Chemistry, Saint Louis University, 3501 Laclede Avenue, St. Louis, Missouri 63103, United States S Supporting Information *

ABSTRACT: The translational diffusion constants, D, of benzene and a series of alkylbenzenes have been determined in four n-alkanes at room temperature using capillary flow techniques. The alkylbenzenes are toluene, ethylbenzene, 1-phenylpropane, 1phenylpentane, 1-phenyloctane, 1-phenylundecane, 1-phenyltetradecane, and 1-phenylheptadecane. The n-alkanes are n-nonane, n-decane, n-dodecane, and n-pentadecane. Ratios of the solutes’ D values are independent of solvent and in general agreement with the predictions of diffusion models for cylinders and lollipops. For the latter, an alkylbenzene’s phenyl ring is the lollipop’s candy; the alkyl chain is its handle. A model that considers the solutes to be spheres with volumes determined by the van der Waals increments of their constituent atoms is not in agreement with experiment. The diffusion constants of 1-alkene and n-alkane solutes in n-alkane solvents also are compared with the cylinder model; reasonably good agreement is found. The n-alkanes are relatively extended, and this appears to be the case for the alkyl chains of the 1-alkenes and alkylbenzenes as well.

1. INTRODUCTION This paper reports the determination of the translational diffusion constants, D, for benzene (C6D6) and a series of alkylbenzenes in n-nonane (n-C9), n-decane (n-C10), ndodecane (n-C12), and n-pentadecane (n-C15). The alkylbenzenes are toluene, ethylbenzene, 1-phenylpropane, 1-phenylpentane, 1-phenyloctane, 1-phenylundecane, 1-phenyltetradecane, and 1-phenylheptadecane. Capillary flow techniques have been used, as they were in earlier studies of alkenes, alkynes, polyenes, arenes, and C60.1−4 The alkylbenzenes’ diffusion is shown to depend on their shape and size. Ratios of their D values are in general agreement with the predictions of cylinder diffusion5−7 as are the ratios for a number of 1-alkene and n-alkane solutes in nhexane (n-C6), n-heptane (n-C7), and n-octane (n-C8). The agreement for the n-alkanes, with as many as 32 carbon atoms, is consistent with Monte Carlo8 and molecular dynamics5,9 simulations that showed them to be relatively extended; the agreement suggests this is the case for the alkylbenzenes and 1alkenes as well. Another length-dependent model, lollipop diffusion,10 also gives calculated ratios in reasonable agreement with experiment for the alkylbenzenes; the phenyl ring is the lollipop’s candy, the alkyl chain is its handle. A model which considers the solutes to be spheres with volumes determined by the van der Waals increments of the their constituent atoms is not in agreement with experiment. In addition to testing the utility of these models, our data may provide tests of the force fields and computer codes used in molecular dynamics simulations of diffusion constants in nonpolar solvents such as n-alkanes9,11 and supercritical CO2.12 A series of calculations produced general agreement with the D values for benzene and a series of alkylbenzenes in the latter solvent.12 © 2015 American Chemical Society

Benzene and alkylbenzenes have been solubilized in micelles,13,14 and as discussed below, determination of the solubilizates’ D values and a comparison with ours could yield estimates of the micelles’ internal viscosities.15 Our results also may be helpful in separations science. The hydrophobic alkylbenzenes have been used as mobile-phase solutes in studies of the efficiency of reversed-phase chromatographic supports ranging from polybutadiene-coated zirconia16 to immobilized artificial membranes on silica gel.17 Their D values have been included in diffusion constant correlations tested by Carr and co-workers;18 uncertainties in D values can have a significant effect on the interpretation of chromatographic band broadening.

2. EXPERIMENTAL METHODS 2.1. Chemicals and Sample Preparation. n-C9 (99+%), n-C15 (99%), benzene (C6D6, 99.6 atom % D), toluene (99.8%) 1-phenyloctane (98%), 1-phenylundecane (99%), and 1phenylheptadecane (97%) were obtained from Aldrich; n-C10 (99+%) and n-C12 (99+%) were obtained from Sigma-Aldrich; ethylbenzene (99.8%) and 1-phenylpropane (98%) were purchased from Acros Organics; 1-phenylpentane (96%) and 1-phenyltetradecane (97%) were obtained from Alfa Aesar. All substances were used as received. Solutions were prepared by adding two to five drops of the liquid solutes to 6.0−8.0 mL of the solvents. 2.2. Profile Acquisition and Analysis. The elution profiles used to determine the D values in n-C9, n-C10, and nC12 were obtained by first drawing the pure solvent through a fused silica microcapillary (Polymicro Technology, 76.5 μm Received: August 5, 2015 Revised: September 10, 2015 Published: September 29, 2015 12931

DOI: 10.1021/acs.jpcb.5b07610 J. Phys. Chem. B 2015, 119, 12931−12937

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The Journal of Physical Chemistry B i.d.) for several hours via reduced pressure. The pressure was then broken and the capillary was dipped into a solution of the same solvent and the solute of interest for a measured load time τL. The capillary was returned to the pure solvent, the reduced pressure was reset, and the data acquisition was started. The Gaussian profiles were collected using Chrom Perfect software (Justice Innovations) and a Thermo Separation Products SC100 variable wavelength detector. A wavelength of 260 nm was used for all solutes except C6D6 (198 nm). The solutes’ diffusion constants were obtained using1 D = R2t R /[4.328(w1/2)2 ]

Table 1. Diffusion Constants of Benzene and Alkylbenzenes in n-C9 at 24.0 ± 0.25 °C

x1 = x − Ut

(2b)

2

(2c)

2

k = R U /48D

27.5 22.2 17.5 14.3 12.8 10.6 9.71

0.520 0.644 0.817 1.00 1.16 1.35 1.47

solutea

106D (expt), cm2 s−1

D(n-C8Ph)/D(n-CiPh)b

C6D6 ethylbenzene 1-phenylpentane 1-phenlyloctane 1-phenylundecane 1-phenyltetradecane 1-phenylheptadecane

22.0 18.0 13.7 11.4 9.65 8.46 7.42

0.518 0.633 0.832 1.00 1.18 1.35 1.54

a

The D values are the average of two or more determinations for a given solute−solvent pair. bD(n-C8Ph) and D(n-CiPh) are the diffusion constants for 1-phenyloctane and either benzene or an alkylbenzene, respectively.

Table 3. Diffusion Constants of Benzene and Alkylbenzenes in n-C12 at 20.5 ± 0.5 °C solutea




14.6 11.7 8.96 7.40 6.03 5.25 4.66

0.507 0.632 0.826 1.00 1.23 1.41 1.59

a


3. RESULTS AND DISCUSSION 3.1. Results. The diffusion constants for benzene and the alkylbenzenes are given in Tables 1−4 and are plotted versus the number of carbon atoms in their chains in Figure 1. The D values decrease as the chain lengths of the solutes and solvents increase. The motional models we will consider are based on the Stokes−Einstein relation20,21


(3)

where η is the viscosity, T is the absolute temperature, kB is Boltzmann’s constant, and ϕ(r) is a function of the solute’s shape and size. For solutes 1 and 2 in a given solvent at constant temperature, eq 3 predicts a viscosity-independent ratio D(2)/D(1) = ϕ(r )1 /ϕ(r )2



where x is the distance between the capillary tip and the detector, U is the solution’s flow speed, and t is the time; the relative profile intensity ratio, C(t)/C0, increases from 0 to 1 as the solution moves past the detector. These analyses are described in more detail in refs 3 and 4. The uncertainties for the D values are ±8% in n-C15 and ±3% in n-C9, n-C10, and nC12. All profiles were taken at room temperature, which was constant within ±0.50 °C for the 5−7 days needed to acquire the profiles in a given solvent.

D = kBT /[6πηϕ(r )]



where R = 38.25 μm is the capillary’s radius, tR is retention time for the maximum of the profile, and w1/2 is its full width at halfheight. Five profiles were taken for each of the load times τL = 10, 20, and 30 s; the average values of D for the load times were extrapolated to τL = 0 (infinite dilution). See ref 1 for more details. Two or more such determinations of D were made for each solute−solvent pair. The elution profiles used to determine the D values in n-C15 were obtained by drawing the pure solvent through the microcapillary, breaking the pressure, transferring the capillary to a solution of the same solvent and the solute of interest, resetting the pressure, and starting the data acquisition; the detection wavelengths were the same as those used in n-C9, nC10, and n-C12. Diffusion constants were obtained by comparing the sigmoidal experimental profiles with those calculated using3,4,19 (2a)


a

(1)

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

solutea

solutea



C6D6 toluene 1-phenylpropane 1-phenylpentane 1-phenlyloctane 1-phenylundecane 1-phenyltetradecane 1-phenylheptadecane

10.6 9.91 8.08 7.21 5.41 4.32 3.81 3.54

0.510 0.546 0.670 0.750 1.00 1.25 1.42 1.53

a


(4)

Eliminating the viscosity dependence allows us to focus on the role shape and size play in our solutes’ diffusion. 12932


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alkylbenzenes are given in Table 5; data for benzene23−26 in addition to our own were used. Table 5. Values of p and ASE for Benzene and Alkylbenzenes in n-Alkanes C6H6/C6D6 ethylbenzene 1-phenylpentane 1-phenyloctane 1-phenylundecane 1-phenyltetradecane 1-phenylheptadecane

Unless stated otherwise, the ratio D(n-C8Ph)/D(n-CiPh) will be used when comparing the alkylbenzenes’ experimental and calculated diffusion constants; D(n-C8Ph) is the diffusion constant for 1-phenyloctane, and D(n-CiPh) is the D value for either benzene (i = 0) or an alkylbenzene (n-Ci = n-CiH2i+1). 1Phenyloctane was chosen as the reference solute because of its intermediate chain length. Tables 1−4 show that D(n-C8Ph)/ D(n-CiPh) is essentially constant for a given solute in the four n-alkane solvents. The modified Stokes−Einstein relation4,22 D/T = ASE /η

0.711 0.760 0.657 0.709 0.765 0.763 0.730

± ± ± ± ± ± ±

0.008 0.035 0.036 0.034 0.035 0.032 0.029

8.597 8.783 8.679 8.878 9.061 9.120 9.101

± ± ± ± ± ± ±

0.019 0.072 0.073 0.068 0.072 0.065 0.057

Equation 5 with p ∼ 0.73 is not the Stokes−Einstein relation. It does, however, give viscosity-independent ratios at constant temperature and we have assumed the shape and size dependence of the D values and their ratios are given by the functions ϕ(r). The reasonably good agreement found for cylinder and lollipop diffusion in the following sections is encouraging but must to some extent be due to the use of ratios and the cancellation of deviations resulting from the assumptions made in applying the models to the alkylbenzenes. 3.2. Cylinder Diffusion Model. Hansen7 carried out Monte Carlo calculations for the translational diffusion of cylinders; his results give

Figure 1. Experimental D values of benzene and the alkylbenzenes in n-C9, n-C10, n-C12, and n-C15 vs the number of alkyl carbon atoms in the alkylbenzenes’ chains.

p

−log ASE

p

solute

ϕ(r )cyl,i = (3/16)1/3 d i 2/3Li1/3f (ln pi )

(6)

where Li and di are the length and diameter of cylinder i and pi = Li/di. The function f(ln pi) is given by eq 16 of ref 7 and is valid for 0.01 ≤ pi ≤ 100. Equations 4 and 6 give

(5)

also gives viscosity-independent ratios of diffusion constants in the same solvent at constant temperature; p and ASE are constants for a given solute. Values of p ≠ 1 indicate deviations from the Stokes−Einstein limit (p = 1). Figure 2 shows a plot of log(D/T) versus log η for 1-phenylheptadecane, 1-phenyloctane, and C6D6/C6H6in the n-alkanes. The data are in agreement with eq 5 and the fit lines are nearly parallel (with an average value of p = 0.73), indicating a common viscosity dependence. The values of p and ASE for benzene and the

D(2)/D(1) = ϕ(r )cyl,1 /ϕ(r )cyl,2 = (d1/d 2)2/3 (L1/L 2)1/3 [f (ln p1 )/f (ln p2 )] (7)

for solutes 1 and 2 in the same solvent at constant temperature. If the two cylinders have the same diameter di = d, eq 7 becomes D(2)/D(1) = (p1 /p2 )1/3 [f (ln p1 )/f (ln p2 )]

(8)

The alkylbenzenes were assumed to have a common diameter and ni alkyl chain elements of length l. Space-filling molecular models indicated the phenyl ring added three more elements, giving a total of Li = (ni + 3)l and pi = (ni + 3)(l/d). Thus, the ratio of the alkylbenzenes’ diffusion constants depends only on ni and their common ratio l/d, not the individual values of l and d. Figure 3 shows that the calculated ratios are not a strong function of l/d; a value of 1.00 (Figure 3a) does, however, give better overall agreement with experiment than l/d = 0.513 (Figure 3b). To be sure, the alkyl chains are not rigid cylinders. Zhang et al.5 pointed out, however, that there was little change in the length of the basically rodlike n-C8, n-C12, n-C16, and n-C20 between dynamics time steps. The lengths of these n-alkanes are similar to those of the alkylbenzenes’ chains, and a cylinder model6 similar to the one we have employed was used to discuss their translational and rotational motions. These comments regarding chain dynamics also are relevant to the following discussion of the n-alkanes’ diffusion and the lollipop

Figure 2. Plot of log(D/T) versus log η for 1-phenylheptadecane, 1phenyloctane, and C6D6/C6H6 in the n-alkanes. 12933


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Figure 3. Comparison of the experimental diffusion constant ratios D(n-C8Ph)/D(n-CiPh) for benzene and the alkylbenzene solutes with the predictions of Hansen’s cylinder model. The ratios were calculated for l/d = 1.00 in (a); l/d = 0.513 was used in (b).

Table 6. Solutes and Solvents for n-Alkanes and 1-Alkenes Diffusing in n-Alkanes

model where the handle is assumed to be a linear string of elements corresponding to an alkylbenzenes’ chain. In Figure 4, the predictions of the cylinder model are compared with the D-value ratios for n-alkane and 1-alkene

solvent

i for n-Ci solutesa

n-C6b n-C7c n-C8d

32, 24, 18, 16, 12, 10, 8, 7, 6, 5, 3, 2, CH4 16, 14, 12, 10, 7, 3, 2, CH4 32, 24, 18, 16, 14, 12, 10, 8, 7, 3, 2, CH4 i for 1-Ci solutesa

solvent n-C6e n-C8e

14,12, 8, 6, 2 14, 12, 10, 8, 6

a

The notation i for n-Ci and 1-Ci is used for the solutes. bThe D value for the self-diffusion constant of 6 is from ref 27, and the others are from ref 28. cThe D values for the self-diffusion constant of 7 are from refs 29 and30, the value for CH4 is from ref 31, that for 2 is from ref 32, that for 3 is from ref 33, those for 10, 12, and 14 are from ref 34, and that for 16 is from ref 35. dThe D value for the self-diffusion constant of 8 is from ref 27, those for CH4 are from refs 28 and 36, those for 2, 3, 16, 24, and 32 are from ref 28, those for 7 and 10 are from ref 29, that for 12 is from ref 37, that for 14 is from ref 34, and those for 18 are from refs 28 and 37. eThe D value for ethene in n-C6 is from ref 38, while those for the other 1-Ci in the n-Ci were calculated using the data in ref 2.

solutions1−4,39 have values of the Stokes−Einstein size factor ϕ(r) that are smaller than their actual dimensions. As is the case for the alkylbenzenes, these solutes also have p < 1. Zwanzig and Harrison40 pointed out that r is a measure of the coupling between the solute motion and the solvent flow and should be regarded as an effective hydrodynamic radius. The agreement between experiment and the cylinder model suggests that the alkylbenzenes’ diffusion in is similar to that of n-alkanes and 1-alkenes and indicates how this can lead to the lower d value. Experimental41 and computational studies5,8,9,42 have shown that the n-alkanes considered in this paper are relatively extended. The agreement with the cylinder model is consistent with the chains of the 1-alkenes and alkylbenzenes also being relatively extended; they should have similar interactions with the relatively extended n-alkanes, reducing the solutes’ macroscopic viscosity dependence, and giving the smaller values of d and p < 1.5 The alkylbenzenes’ and nalkanes’ D values have a near-equal dependence on viscosity that supports this interpretation; the average value for the alkyl benzenes is p = 0.73; the n-Ci with i = 6, 7, 8, 12, and 16 have 0.70 ≤ p ≤ 0.76 with an average of 0.72.2 3.3. Lollipop Diffusion Model. The lollipop model was developed for macromolecules10 but appears to be useful for smaller systems. An alkylbenzene’s phenyl ring is the lollipop’s

Figure 4. Comparison of the experimental diffusion constant ratios for n-alkanes and 1-alkenes in n-alkanes with the predictions of Hansen’s cylinder model for l/d = 1.00; D(ref)/D(solute) = D(n-C16)/D(n-Ci) for the n-alkanes; D(n-C16)/D(1-Ci) for the 1-alkenes.

solutes. The solutes, with ni carbon atoms, are assumed to have the same diameter with lengths Li = nil and pi = ni(l/d). The nalkane solutes range from CH4 to n-C32 in n-C6,27,28 from CH4 to n-C16 in n-C7,29−35 and from CH4 to n-C32 in nC8.27−29,34,36,37 The 1-alkenes are2,38 1-Ci with i = 2, 6, 8, 12, and 14 in n-C6 and i = 6, 8, 10, 12, and 14 in n-C8. The ratios D(n-C16)/D(n-Ci) and D(n-C16)/D(1-Ci) have been used for the n-alkanes and 1-alkenes, respectively; the references for these D values, all at 25 °C, are given in Table 6. As for the alkylbenzenes, reasonable overall agreement is found for l/d = 1.00. Because of the tetrahedral arrangement of bonds around an sp3 carbon atom, the effective length of a chain element should be less than a carbon−carbon single bond length, 1.54 Å, even for the all-trans conformation. A value of l/d = 1.00 gives an equally small cylinder diameter. This relatively small value can be explained in terms of solute−solvent interactions and is not an isolated result. A number of hydrocarbon solutes in n-alkane 12934


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Figure 5. Comparison of the experimental diffusion constant ratios D(n-C8Ph)/D(n-CiPh) for benzene and the alkylbenzene solutes with the predictions of the lollipop diffusion model. The ratios were calculated for σ1/σ2 = 2.20 in (a); σ1/σ2 = 2.64 was used in (b).

candy; its alkyl chain is the handle. The candy is a sphere with radius σ1; the handle, a linear string of ni spheres with radius σ2, has a length Li = 2niσ2. Garcia de la Torre and Bloomfield10 carried out numerical calculations and reported results for 2 ≤ σ1/σ2 ≤ 10 and Li/σ1 ≤ 16; ϕ(r)loll is given by10 ϕ(r )loll = σ1[1 + ΣiΣjbij(Li /σ1)i (σ1/σ2) j − 1]

(9)

where the values of bij are given in Table 1 of ref 10; both i and j have values of 1, 2, and 3. The double summation in eq 9 and the ratio D(n−C8Ph)/D(n−CiPh) = ϕloll(n−CiPh)/ϕloll(n−C8Ph) (10)

depend only on ni and σ1/σ2 because Li/σ1 = 2niσ2/σ1 = 2ni(σ1/ σ2)−1. We found the best overall agreement between the experimental and calculated ratios for σ1/σ2 = 2.20 although the calculated value is slightly too low for 1-phenylheptadecane (Figure 5a). Decreasing σ1/σ2 to 2.00, the lowest possible value, decreases the degree of agreement for the larger values of ni while a larger value of σ1/σ2 = 2.64 decreases the agreement for the shorter chains (Figure 5b). The ratio σ1/σ2, much like l/d for the cylinder model, is determined by interactions with the solvent as well as being a measure of the relative sizes of the phenyl ring and chain elements. 3.4. Spherical van der Waals Model. The van der Waals volumes, Vp, of benzene and the alkylbenzene also were used to determine ϕ(r). The value of Vp for solute i was calculated using its constituent atoms’ Bondi−Edward increments43,44 and assumed to be the volume of a sphere with radius ri. This gives ϕ(r)vdW,i = ri = (3Vp,i/4π)1/3 and solutes 1 and 2 in the same solvent at constant temperature have

Figure 6. Comparison of the experimental diffusion constant ratios D(n-C8Ph)/D(n-CiPh) for benzene and the alkylbenzene solutes with the predictions of the spherical van der Waals model.

modified Stokes−Einstein relation, eq 5, with near-constant values of p < 1. Representative values are p = 0.84 for benzene, 0.78 for 1-phenylbutane, 0.80 for 1-phenyloctane, and 0.81 for 1-phenyldodecane. The plots of log(D/T) versus log η for these solutes are shown in Figure S1 of the Supporting Information; the values of p and ASE from the fits to eq 5 are given in Table S1. The ratios of D values for a given solute (Table S2) are independent of viscosity, and the analyses based on eq 4 can be applied. The experimental ratios are in approximate agreement with the lollipop model for σ1/σ2 = 2.64 (Figure S2) and, except for benzene and toluene, with the cylinder model for l/d ∼ 0.513 (Figure S3). The values of these fit parameters are not the same as those in the n-alkanes because, as mentioned above, they are indicative of the different solute−solvent interactions in the two types of solvent. 4.2. Alkylbenzenes in Micelles. Benzene and alkylbenzenes have been shown to solubilize in 1-dodecanesulfonic acid13 and sodium cholate micelles.14 Their D values could be compared with ours to estimate the interior’s microviscosity.15,47,48 Diffusion-ordered NMR spectroscopy (DOSY) is a possible means of determining the diffusion constants49−51 but the probe’s internal diffusion must be separated from the diffusion of the micelle as a whole and care must be taken when comparing data in single solvents with those in potentially complex mixtures such as a micelle’s interior.47,48 Additionally, the microviscosities are generally larger than that of n-C15, our most viscous solvent (2.54 cP at 25 °C52), and have been found to be probe and method dependent.47,48

D(n‐C8Ph)/D(n‐CiPh) = r(n‐CiPh)/r(n‐C8Ph) = [V (n‐CiPh)/V (n‐C8Ph)]1/3

(11)

As seen in Figure 6, this model does not give agreement with experiment, which is not surprising since it does not take the shape of the solute into account.

4. RELATED WORK 4.1. Alkylbenzenes in Supercritical CO2. The diffusion constants for benzene and alkylbenzenes ranging from toluene to 1-phenyldodecane have been determined in supercritical CO2 at 40, 50, and 60 °C for pressures ranging from15.0 to 35.0 MPa.45,46 The D values for a given solute follow the 12935


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The Journal of Physical Chemistry B For example, values of 19 and 30 cP53 were determined for cetyltrimethylammonium bromide (CTAB) at 27 °C using the fluorescence depolarization of perylene and 2-methylanthracene, respectively; higher values have been obtained using other methods.47,54 If our D values were to be used to address these issues, it would be desirable to determine them in alkanes with higher viscosities. Pristane (2,6,10,14-tetramethylpentadecane) and squalane (2,6,10,15,19,23-hexamethyltetracosane) are two such solvents; they have η(25 °C) = 6.71 cP (pristane55) and 27.6 cP (squalane56). It also would be interesting to see if the alkylbenzenes’ diffusion in these methyl-substituted alkanes is in agreement with the models we have considered. Isocetane (2,2,4,4,6,8,8-heptamethylnonane) is another candidate; it has η(25 °C) = 3.30 cP.55

Society. We thank Dr. Ryan McCulla for his gift of C6D6 and Dr. Michael Lewis for his gifts of ethylbenzene, 1-phenylpentane, and 1-phenyloctane.

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5. SUMMARY AND CONCLUSIONS The diffusion constants of benzene and a series of alkylbenzenes have been determined in n-C9, n-C10, n-C12, and n-C15 at room temperature using capillary flow techniques. Ratios of the diffusion constants for these solutes are in general agreement with the predictions of a cylinder diffusion model as are the diffusion constant ratios of n-alkane and 1-alkene solutes in n-C6, n-C7, and n-C8. This implies that the diffusion of the alkylbenzenes and 1-alkenes is similar to that of the n-alkanes and that they, like the n-alkanes, are relatively extended in these solutions. The near-equal viscosity dependence of the alkylbenzenes and n-alkanes’ diffusion supports this suggestion. The D values for both types of solutes in n-alkane solvents are in agreement with the modified Stokes−Einstein relation, D/T = ASE/ηp. The alkylbenzenes have values of p ∼ 0.73; the n-Ci with i = 6, 7, 8, 12, and 16 have p ∼ 0.72. The alkylbenzenes’ diffusion constant ratios also have been compared with the lollipop diffusion model; the phenyl ring is the lollipop’s candy while the alkyl chain is its handle. Reasonably good agreement between the experimental and calculated ratios was obtained although a small difference was seen for the longest chain. A model that considered the solutes to be spheres with volumes determined by the Bondi−Edwards increments of their constituent atoms was not in agreement with experiment.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b07610. Results of the analyses of the alkylbenzenes’ data in supercritical CO2 (PDF)

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REFERENCES

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, has supported this research. The data acquisition system and detector were purchased with grants to Dr. Barry Hogan from Research Corporation and the donors of the Petroleum Research Fund, administered by the American Chemical 12936


Article

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