J. Phys. Chem. 1995,99, 5787-5792
5787
ARTICLES Dynamic Structure of Methylcyclohexane and Perfluoro(methylcyc1ohexane) Liquids in Confinement and in Bulk Shu Xu, L. Ballard, Y. J. Kim, and J. Jonas* Department of Chemistry, School of Chemical Science, University of Illinois, Urbana, Illinois 61801 Received: December 19, 1994@
The dynamic behaviors of methylcyclohexane (MCH) and perfluoro(methylcyc1ohexane) (PFMCH) liquids confined to porous silica glasses prepared by the sol-gel process are compared. The NMR spin-lattice relaxation times, T I ,of the MCH and PFMCH liquids in porous silica glasses are reported as a function of pore size in the range from 24 to 96 A over the temperature range from -8 to 45 "C. The pore-size-dependent experimental TI data are analyzed in terms of a general expression obtained from our previous studies, UT1 = 1/Tlb B/R A/R*, where T l b is the relaxation time for bulk liquid, R is the average pore radius, and A and B are two parameters which indicate the relative strength of surface and topological effects on the observed NMR relaxation rates of confined liquids. On the basis of the surface enhancement values, TldTl,, where T I , is the relaxation time of the surface layer liquid, we conclude that the confined PFMCH molecules have a stronger interaction with the glass surface and thus exhibit more hindered molecular motions than the confined MCH molecules. In contrast, topological confinement plays a smaller role in affecting the translational diffusion of PFMCH molecules near the glass surface. In addition to the confinement studies, we have investigated the dynamic structure of bulk PFMCH by analyzing shear viscosity data in terms of the rough-hard-sphere model of liquids in a manner similar to our previous bulk liquid MCH study.
+
+
I. Introduction As part of our systematic experimental and theoretical studies on the dynamic structure of various fluids, including highly viscous fluids such as lubricants and fluids in confined we have become interested in problems related to confinement effects on the dynamic behavior of fluorocarbonbased fluids. The particular chemical and physical properties of fluorocarbons have provided the main motivation of our present s t ~ d y . ~As , ~one knows, the chemical inertness of fluorocarbons leads to much higher thermal and oxidative stability than their parent hydrocarbons. For example, fluorocarbons do not react with concentrated acids, alkali, oxidizing agents, or the majority of chemical reagents and have much higher decomposition temperatures than their parent hydrocarbons. In view of such excellent properties, it is not surprising to find that the peffluorination technique has been applied to make high-quality lubricants or greases used at high temperatures and other extreme conditions.8-10 In this study, we investigate the motional behavior of a perfluorinated liquid, peffluoro(methylcyc1ohexane) (PFMCH), and its parent hydrocarbon liquid, methylcyclohexane (MCH), both confined to porous silica glasses and in bulk. The effect of fluorine on the behavior of these liquids at the liquid glass interface is of particular interest. To the best of our knowledge, no similar experimental studies have thus far been reported. The present microscopic level study contributes toward a better understanding of the dynamic structure of liquids at solidlliquid interfaces. Such improved understanding is important for our long-term research dealing with the dynamic behavior of highly @
Abstract published in Advance ACS Abstracts, April 1, 1995.
viscous fluids, including peffuoropolyether Krytox lubricants, both in bulk and in confined geometries. This is obviously of technological relevance to lubrication processes on solid surfaces and to related problems such as subsurface damage to materials in contact with high-pressure fluids. Several earlier results obtained in our laboratory provide the theoretical background of the present study.11-13 First, our recent progress in NMR relaxation studies of molecular liquids in confined geometries allows us to investigate the molecular motions near solidniquid interfaces." We found that the observed reduction of the nuclear relaxation times of a confined liquid results from two different mechanisms. One mechanism is from interactions between the liquid and the solid surface, which enhances the nuclear relaxation rate by hindering either the translational or the reorientational molecular motions. The effects of the surface interaction on nuclear relaxation have been well interpreted in terms of the two-state, fast-exchange m ~ d e l . ' ~ .The ' ~ other mechanism is from the pure geometric (topological) confinement of the spin-bearing liquid molecules, which enhances the relaxation rate by increasing the probability of molecular reencounters in a confined, low-dimensional ~ y s t e m .Topological ~ confinement changes translational diffusion of confined molecules and thus affects intermolecular dipolar relaxation times. The general expression of the observed spin-lattice relaxation rate, l/Tl, for a liquid confined to pores should include both surface and topological contributions:
where Tlb is the spin-lattice relaxation time for the bulk liquid, T I ,is the relaxation time for the liquid in the surface layer, c is
QQ22-3654/95/2099-5787$09.QQ/Q0 1995 American Chemical Society
5788 J. Phys. Chem., Vol. 99, No. 16, 1995
Xu et al.
TABLE 1: Molecular Properties of MCH and PFMCH Liquids
r (CP) (25 "C)
98.19" 146.5" 374.1" 0.765" 0.683"
P
Ob
350.05" 228.4" 349.5" 1.787' 1.56' od
2.02" 5.74' 2.48e 1.915'
6.71f 1.89 0.62f
M w (g/"l) Tm (K) Tb (K) Q
(g/cm3)(25 "C)
(D) (20 "C) u (A) (25 "C) bp (25 "C) D (x cm%) (25 "C) E
1.Ud
a Taken from ref 17. Taken from ref 18. Taken from ref 6. Taken from ref 19. e Taken from ref 12. fcalculated in this work. For details, see the text. g The coupling constant between rotational and translational motions. For details, see the text.
and in porous silica glasses as a function of temperature. By fitting the experimental data to eq 1, we obtain TI, and A ( o ) of MCH and PHMCH, respectively. Second, on the basis of the surface enhancement values, TldTl,, we want to determine the strength of the surface interaction for both liquids and then further determine the role of the fluorine in modifying the dynamic behavior of liquids at the solidfliquid interface. Third, by analyzing temperature-dependent A(w) data, we want to investigate the effects of topological confinement on nuclear relaxation behavior of both liquids in porous silica glasses in terms of the theoretical model discussed in our previous paper.5 Fourth, in a manner similar to our study of MCH,12 we want to study the dynamic structure of bulk PFMCH by analyzing the shear viscosity data in terms of the rough-hard-sphere model of liquids and then compare the results with those obtained for MCH.
11. Experimental Section
MCH PFMCH Figure 1. Schematic drawing of relative shape and size of methylcyclohexane and perfluoro(methylcyc1ohexane). the thickness of the surface layer liquid, which should be smaller than the pore radius R , and A(w) represents the contribution from the topological confinement. It is important to point out that, by measuring the relaxation time as a function of pore radius and then fitting the experimental data to eq 1, one can determine TlS and A ( w ) and thus separate the effects due to surface interaction and topological confinement. In our earlier studies,12J3 we have carried out systematic studies of the dynamic structure of a variety of bulk molecular liquids. The pressure and temperature dependence of selfdiffusion coefficients, shear viscosities, and densities of the liquids were interpreted in terms of the rough-hard-sphere (RHS) modelI6 of liquids, which yielded the effective-hard-sphere diameter and a parameter reflecting the degree of the coupling between rotational and translational motions. The strength of the coupling was found to be related to the nonspherical shape of liquid molecules.l2 The applicability of the Stokes-Einstein equation was tested by self-diffusion and viscosity data and was shown to be valid for most liquids s t ~ d i e d . ' ~ ? ~ ~ Table 1 summarizes some physical constants of bulk PFMCH and MCH liquids, and Figure 1 shows schematically the spacefilling models of the two molecules. One finds from Table 1 that, as expected, perfluorination increases the density and viscosity of MCH, but does not significantly change the dielectric constants. That the dipole moments of both liquids are close to 0 suggests that the interactions of the liquid with the glass surface are weak, and therefore the topological effects on NMR relaxation rates of confined liquids can be relatively strong and observable. With the absence of molecular dipole moments, nonpolar PFMCH and MCH serve as model liquids for which the topological confinement may dominate the nuclear relaxation. There are several aims of the present study. First, we want to measure the pore-size-dependent 'H and 19F spin-lattice relaxation times for MCH and PFMCH, respectively, in bulk
A. Materials. Both reagents were purchased from Aldrich. Spectrophotometric grade MCH was used without further treatment. PFMCH (90% atom F) was purified by distillation. Purified PFMCH was analyzed by gas chromatography (99% 19F). Both liquids were degassed by repeated freeze-pumpthaw cycles before making NMR samples. The porous sol-gel glasses were prepared following the procedure developed in our l a b ~ r a t o r y . ~Typical glasses prepared by this process have a narrow pore size distribution, a porosity of approximately 70%, a specific surface area ranging from 200 to 400 m2/g, and a high degree of interconnecting pores. The specific surface area, the average pore radius R , and the pore size distribution were determined by the BrunauerEmmett-Teller (BET) method using an Autosorb-1 BET instrument (Quantachrom Corp.). B. Sample Loading. The porous glass was evacuated to Torr at 350 "C for several hours to remove water and other volatile impurities. The degassed liquid was then transferred to the glass under vacuum via the bulb-to-bulb method, allowing the glass to be immersed in, and equilibrate with, the liquid overnight. In the final step, excess liquid was removed by pumping under a vacuum of lo-' Torr, and then the NMR sample was sealed. The pumping rate must be carefully controlled so as to only remove the liquid outside the glass and leave the glass fully filled. C. NMR Measurements. The 'H of MCH and 19F of PFMCH spin-lattice relaxation times were measured at 180 and 169.3 MHz, respectively, on a home-built NMR spectrometer equipped with an Oxford superconducting magnet of 4.2 T. Some TI measurements.for PFMCH were also performed at 376 MHz on a Varian U400 NMR spectrometer, in order to determine the relaxation contribution from chemical shift anisotropy. The standard 18Oo-r-90" pulse sequence was used in the determination of TI. The reproducibility of the experimental data was within f5%. The sample temperature was controlled by a regulated nitrogen stream and measured by a thermocouple located near the sample. Thermal stability was maintained by the use of an MGW Lauda Ultra-Kryomat temperature bath. Temperatures were estimated to be accurate to f 0 . 2 "C.
In. Results and Discussion The 'H and 19F spin-lattice relaxation times of MCH and PFMCH, respectively, were measured as a function of pore radius in the range 24-96 8, over the temperature range -8 to 45 "C. All of the experimental TI values obtained for bulk liquids and the liquids confined to porous silica glasses are
J. Phys. Chem., Vol. 99, No. 16, 1995 5789
Methylcyclohexane and Peffluoro(methylcyc1ohexane)
TABLE 2: Temperature and Pore Size Dependence of Experimental lH TIData of MCH and 19F TIData of PFMCH Bulk Liquids and the Liquids Confined to Porous Silica Glasses Methvlcvclohexane T(T) bulk 96A 60A 438, 30A 24A 3.15 2.74 2.30 3.70 3.57 -8 4.04 3.88 3.40 2.94 2.48 4.52 4.14 0 10 5.16 4.56 4.42 3.82 3.35 2.79 20 6.04 5.31 5.05 4.26 3.77 3.11 6.05 5.65 4.92 4.08 3.42 31 6.78 45 8.13 7.28 6.67 5.71 4.90 4.10
n
0.4 -
w
1
0
-
0.3 -
Q)
m
W
E
0.2
-
\ T4
Perfhoro(methylcyc1ohexane)
T("C)
bulk
-8
3.77 4.44 5.27 6.02 6.37 6.27
0
10 20 31 45 -8 0
10 20 31 45
3.42 3.96 4.53 4.98 4.96 4.63
94A 60A 408, Ring Fluorines 3.39 3.17 2.90 3.19 3.80 3.51 4.32 3.99 3.50 3.83 4.87 4.45 4.19 5.35 4.95 5.64 5.32 4.64 CF3 2.90 3.22 3.08 3.60 3.39 3.15 3.51 4.03 3.80 3.91 4.39 4.18 4.54 4.38 4.17 4.35 4.60 4.55
30A
258,
2.63 2.89 3.12 3.37 3.73 4.09
2.47 2.67 2.88 3.12 3.33 3.70
2.78 2.98 3.22 3.55 3.86 4.15
2.68 3.86 3.07 3.31 3.56 3.83
summarized in Table 2. In contrast to what is observed for bulk liquids, the apparent NMR line widths of the liquids in porous media are usually broad (-lo2 Hz). The line widths occasionally are so large as to produce overlap of the individual NMR resonances. If so, only a broad NMR peak can be observed, and thus the TI data actually represent the average of contributions from all nuclei, as is exactly the case for MCH in porous glasses. However, for PFMCH, the individual resonances of 19F spectra can still be seen because of the large chemical shift differences of different fluorines. In order to make the experimental data comparable between MCH and PFMCH, and between the data in bulk and in pores, the T1 data for PFMCH listed in Table 2 are the weighted average values of ring fluorines. Before proceeding further, we need to consider the mechanisms which contribute to the relaxation rates of MCH and PFMCH liquids. For MCH, the 'H-'H dipolar interaction is usually much stronger than any other interactions and thus provides the main source for 'H relaxation. However, for fluorine relaxation in PFMCH, the chemical shift anisotropy and the spin rotation interactions can also make contributions to the observed nuclear relaxation rate. The contributions from chemical shift anisotropy and spin rotation can be evaluated from the unique signatures of these two interactions: the strength of the anisotropic chemical shift interaction is proportional to the the square of the Laxmor frequency and the spin rotation relaxation time decreases with increasing temperature, in contrast to other mechanisms that lead to increasing T I ' S . Figures 2 and 3 show plots of the relaxation rates, UT', versus 1/T for MCH and PFMCH, respectively. One sees from the figures that 1/T1 of all MCH samples decreases with increasing temperature and has a linear logarithmic dependence on UT, whereas the UT1 of PFMCH shows a different temperature response for the samples in bulk and in larger pore sizes. In fact, the UT1 of bulk PFMCH decreases with increasing temperature in the lower temperature range to reach a minimum and then increases in the high-temperature range due to the spin rotation interactions. If one takes the temperature of the 1/T1 minimum as the point at which 50% of the relaxation rate is
3.2
3.4
3.6
3.8
.,
1000/T (K-l) Figure 2. 'Hspin-lattice relaxation rate, UT', of methylcyclohexane as a function of temperature, UT, in porous silica glasses: 0 , 2 4 A; 0,
30 A;
V,
43 A; V, 60 A; 0, 96 A;
0.4
.
0.3
.
0.2
.
bulk.
n w
'0 Q)
m
-
W 4
I
E
3.2
3.4
3.6
3.0
1000/T (K-I)
3.2
3.4
3.6
3.0
1000/T (K-') Figure 3. I9F spin-lattice relaxation rate, UT', of ring (a) and CFs (b) nuclei of perfluoro(methylcyc1ohexane)as a function of temperature, UT, in porous silica glasses: 0 , 2 5 A; 0 , 30 A; V, 40 A; V,60 A; 0,
94 A; U, bulk. due to the spin rotation, then these temperatures are about 25 "C for the nuclei of the CF3 groups and about 35 "C for the ring nuclei. From Figure 3, one also obtains information on how geometric confinement suppresses the spin rotation relaxation. Since the deviation from a linear dependence of log( 1/ T I )versus 1/T is due to the spin rotation contribution, one may conclude that the effect of the spin rotation interaction is considerably suppressed for the liquid in small pores. In fact, for ring nuclei confined to a pore radius below 40 A, log(l/ Tl)'s have a linear relationship with UT, which provides
Xu et al.
5790 J. Phys. Chem., Vol. 99, No. 16, 1995
O.=
7 PI
n 4
L 0.00 0.01 0.02 0.03 0.04
0.00 0.01 0.02 0.03 0.04
1/R
1/R (A'-')
(A-I)
Figure 4. 'Hspin-lattice relaxation rate, UTI, of methylcyclohexane as a function of pore radius, 1/R, in porous silica glasses. The solid lines are the fitting results using eq 1: 0, -8 "C; 0 , 0 "C; V, 10 "C; V, 20 "C, 0 , 31 "C; W, 45 "C.
0.4 n
* I
evidence that the spin rotation contribution is negligible for these samples. For the nuclei in the CF3 group, this pore radius limit is lowered to 25 A. This suggests that, as expected, the geometrical confinement within the porous glasses affects the molecular overall motion more than the internal rotation of the CF3 group. In order to estimate how much 19F relaxation is due to chemical shift anisotropy, the TI measurement of bulk PFMCH was also performed at 376 MHz at 20 "C. The field-dependent and the field-independent parts of the relaxation rates are separated according to the equation UT1 = av2 b, where v is the Larmor frequency, a is a constant, and b represents the fieldindependent part. Our results show that the anisotropic chemical shift makes a small contribution to the 19Fspin-lattice relaxation of PFMCH. The percentage is about 3% for nuclei of the CF3 group and 7% for ring nuclei. This result, as well as the temperature dependence data discussed earlier, provides additional evidence that 19F- 19Fdipolar interactions represent the dominant spin-lattice relaxation mechanism for PFMCH in small pores and/or at low temperatures. Figures 4 and 5 show the dependence of the relaxation rates, UTI, on the reciprocal of the pore radius, 1/R, at different temperatures for MCH and PFMCH, respectively. According to our previous theoretical and experimental studies,' the UT1 behavior observed for confined liquid as a function of 1/R can be represented by eq 1, which accounts for the effects of both surface interactions and topological confinement. To avoid the complication due to the spin rotation contribution, the UT1 data of the PFMCH sample used in the fitting procedure are restricted to the data in the low-temperature range. Table 3 lists the best fitting results of TI, andA(w) for MCH and PFMCH liquids in porous glasses as a function of temperature assuming that the thickness of the surface layer E is equal to one molecular diameter and is temperatureindependent in the temperature range investigated because of very small d d d T values. The hard-sphere diameters (7 of PFMCH molecules listed in Table 1 were calculated in this work (see the Appendix). In order to compare the data between MCH and PFMCH, the data for PFMCH listed in Table 3 are the weighted average values of CF3 and ring nuclei. We see from Table 3 that, in the temperature range investigated, the spinlattice relaxation times of surface layer liquids are all smaller than corresponding bulk values; both MCH and PFMCH liquids have surface enhancement values TldT1, > 1. At room temperature the TldT1, is about 1.6 for MCH and 2.2 for
+
0
a,
m
v 4
E-r
\
"
Y
0.21,
,
,
,
,
,
j
0.00 0.01 0.02 0.03 0.04
1/R
(A-I)
Figure 5. 19Fspin-lattice relaxation rate, UT,, of ring and CF3 nuclei of perfluoro(methylcyc1ohexane) as a function of pore radius, 1/R, in porous silica glasses. The solid lines are the fitting results using eq 1: 0, -8 "C; 0 , 0 "C; v,10 "C.
PFMCH. These values are quite small if one compares them to TldT1, 11 for the polar liquids pyridine" and acetonitrile,20 which are assumed to be wetting the glass surface and thus have much stronger surface interactions. It is interesting to find that fluorination strengthens the interaction of the confined liquid with the surface. In fact, the surface enhancement TldT1, of PFMCH is about 1.4 times the value,of MCH, indicating much slower molecular motion of PFMCH than MCH due to surface interaction. This may originate from the difference between C-F and C-H bonds of the liquids, where the C-F bond has a much larger local dipole moment, suggesting a stronger local interaction of the PFMCH molecules with the glass surface. In our earlier theoretical studies of confinement effects on dipolar relaxation due to translational diffusion of nonwetting liquids, we obtained expressions for the relaxation rates which depend on the pore sizes. This theory has successfully explained the quadratic pore size dependence of relaxation rates, 1/Ti = l/R2 (i = 1, le, and 2), of nonpolar liquids confined to porous silica glasses. According to this theory, the topological function A ( w ) in eq 1 is given as5
where d, is the nuclear spin density, 6 is the minimal molecular distance assumed equal to the molecular diameter 0,tl is the
J. Phys. Chem., Vol. 99,No. 16, 1995 5791
Methylcyclohexane and Peffluoro(methylcyc1ohexane)
TABLE 3: Surface Layer Relaxation Data TlSand Topological Confinement Function A ( o ) of MCH and PFMCH Liquids at Different Temperature T ("C) T1b.ex.p (S) T1s (SI A(w) (Azs-l) Methylcyclohexane -8 4.04 3.03 88.9 0 4.52 3.24 80.3 10 5.16 3.52 71.3 20 6.04 3.81 63.9 31 6.78 4.14 57.2 45 8.13 4.59 50.3 Perfluoro(methylcyc1ohexane)
-8
3.69 4.34 5.11
0
10
1.68 1.93
-
26.2 22.2 17.3
2.21
For details, see the text.
2.5
1
n
m 4
E
\
50 2.0 -
e
v n
2
25
E
I-
1.5 1.0' 3.0
W
0 '
'
I
3.2
"
3.4
3.6
'
I
the Ea's of zl are 2.6 f 0.3 and 4.5 +c 0.4 kcal/mol for MCH and PFMCH, respectively, which are very close to their bulk values: 2.8 kcal/mol for MCH and 4.2 kcal/mol for PFMCH calculated from the self-diffusion data (for details, see the Appendix). This appears to support our previous argument that pure topological confinement affects the diffusion across the pore but does not change the diffusion in a direction parallel to the pore s ~ r f a c e .The ~ spin density d, = (1 1.5 f 1.2) x 10l6 spins/cm2 found in this study for MCH is in agreement with (9.9 f 0.5) x 10l6 spins/cm2 reported in our earlier study.5 As expected, the spin density of PFMCH is smaller than that of MCH in view of its lower molecular density. A quantitative calculation based on the relation d, 14em(d)? where emis the molecular density and (d) is the equivalent interpianar distance, gives (ds)MCH/(ds)pmCH 1.5, which is comparable to the experimental value of 1.9. In summary, we measured the 'H and 19FNMR spin-lattice relaxation times of MCH and PFMCH liquids, respectively, confined to porous silica glasses prepared by the sol-gel process over the temperature range from -8 to 45 "C. The pore-sizedependent experimental TI data have been analyzed in terms of a general expression which separates the effects from surface interactions and pure topological confinement. We found that both liquids show non-negligible surface effects, despite the absence of molecular dipole moments. On the basis of the surface enhancement values, Tlt,/T1,, we conclude that perfluorinated MCH has a stronger interaction with the glass surface than its hydrogen-containing parent MCH.
"-25
3.0
4.0
.,
1000/T (K-I)
Figure 6. Surface enhancement factor, TdT1, (0,MCH; 0,PFMCH), and the topological function,A(o)(0,MCH; PFMCH), as a function
of temperature, UT. The A(@) data have been fitted using eq 2, which give Ea = 2.6 f 0.3 kcaVmol and d, = 11.5 x lo6 spins/cmzfor MCH (0),E, = 4.5 f 0.4 kcaYmol and d, = 5.9 x lo6spins/cm2for PFMCH .).(
translational correlation time along the solid surface, and all other symbols have their usual meaning. With the goal of providing more quantitative information about the effect of topological confinement on molecular motions, we have fit the A(w) data listed in Table 3 by eq 2. In the fitting, we assume that the spin density d, and the minimal molecular distance 6 (6 x a) are temperature-independent because of the narrow temperature range and very small changes of a and d, compared to z ~ .In our earlier paper we argued that the topological effect does not change the molecular diffusion along the pore s ~ r f a c ez, ~l = zbuk, and z~ is given by the following equation:
where z is related to the self-diffusion coefficient D by the Einstein relation z = a2/6D assuming a jump length equal to a. In the fitting we use the diffusion coefficients at 25 "C as listed in Table 1. The diffusion constant of PFMCH, as detailed in the Appendix, is calculated from the reference shear viscosity data6 according to the Stokes-Einstein relation in the slipping boundary limit. The temperature-dependent A ( o ) values listed in Table 3 have been fit according to eqs 2 and 3 are are shown in Figure 6, taking the spin density d, and the activation energy E, as variables. The fitting results have an accuracy of approximately 10%. From the fitting procedure we find that
Acknowledgment. This work was supported by the Air Force Office for Scientific Research under Grant F49620-931-0241 and the National Science Foundation under Grant NSF CHE-90- 17649. Appendix In this section, the dynamic structure of bulk PFMCH has been investigated by the analysis of the reference viscosity and density data of liquid PFMCH6 in a manner similar to our earlier study of MCH,12 and the results are compared to those of liquid MCH. Hard-Sphere Molecular Diameter. The determination of the effective-hard-sphere diameter, a, of the PFMCH molecule from viscosity data follows the procedure used p r e v i ~ u s l y . ' ~ ~ ' ~ The effective-hard-sphere diameter calculated using the above procedure for PFMCH at 25 "C is about 6.77 A, as listed in Table 1. That is about 1 8, larger than that of MCH. The density at the temperature, eo3 = 0.954, is within the range 0.70 5 eo3 5 0.97, for which Chandler's expression16is valid. As expected, the hard-sphere diameter decreases slightly with increasing temperature. The temperature dependence of a as a k C , linear function of temperature is da/dT = 0.8 x which is larger than 0.4 x & O C for MCH12 and is comparable to -1 x k C reported for CqF8,22CFC13,23 and Another way to obtain the hard-sphere diameters is a graphical procedure based on expressions produced by Hildebrand and LamoureauxZ5which relate fluidity 4 (4 = 1/77) to molecular volume V. If one uses Dymond's definition26of intercept I = 1.384Vo and VO = N d / l / z , where N is Avogadro's number, one obtains VO = 129.8 cm3/mol and a = 6.73 8, for PFMCH molecules, which is in satisfactory agreement with u based on the viscosity data (see Table 1). Coupling of Rotational and Translational Motions. After the hard-sphere diameters are obtained, the experimental viscosity data can be readily examined in terms of the rough-hard-
5792 J. Phys. Chem., Vol. 99, No. 16, 1995
sphere model of liquids.16 This model takes into account the fact that there can be a significant degree of coupling between the rotational and translational motions. This coupling will naturally affect the magnitude of 7 observed for a real liquid. According to Chandler,16 one may write
Xu et al. cyclohexane,28 and even for nonspherical MCH molecules. l 2 In view of the wide applicability of the Stokes-Einstein equation, we feel that it is justifiable to use it in the slipping boundary limit as a reasonable approximation for determining the self-diffusion coefficient of PFMCH.
References and Notes
The experimental viscosity 7 can be best approximated by the , is directly proportional rough-hard-sphere viscosity ~ W Swhich to the 7 ~ fors the smooth-hard-sphere fluid. The proportionality parameter b ( b ? 1) reflects the degree of coupling between rotational and translational motions and is unity for a smoothhard-sphere system. The calculated coupling constant b at 25 "C is equal to 1.85, as listed in Table 1. The main result of the above analysis, though approximate and limited to a narrow range of temperature, is the behavior of the coupling constant b with temperature. In fact, the values of PFMCH are smaller than those of MCH, reflecting that PFMCH has less coupling between rotational and translational motion than MCH. However, in view of the fact that the b values of PFMCH are still quite large, one may conclude that the coupling is still strong and cannot be neglected for PFMCH molecules. As pointed out in our earlier studies,12the strong coupling between rotational and translational motions has its origin in the nonspherical shape of molecules. If one uses these arguments about the coupling constant, one concludes that PFh4CH molecules are closer to a spherical shape than MCH molecules. This is obviously due to the replacement of protons by much larger fluorine atoms. Self-Diffusion Coefficient. Since the shear viscosity of PFMCH is known, the self-diffusion coefficient D can be estimated by using the well-known Stokes-Einstein equation. In our earlier studies, we found that the Stokes-Einstein equation is valid in the slipping boundary for a variety of molecular liquids, such as perfluorocyclobutane,22benzene,27
(1) Jonas, J. In NMR Basic Principles and Progress; High Pressure NMR Vol. 24; Diehl, P., Muck, E., Gunther, H., Kosfeld, R., Seelig, J., Eds.; Springer-Verlag: Heidelberg, 1991; p 85. (2) Jonas, J. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 307. (3) McDaniel, P. L.; Liu, G.; Jonas, J. J . Phys. Chem. 1988, 92, 5055. (4) Liu, G.; Li, Y.; Jonas, J. J . Chem. Phys. 1991, 95, 6892. ( 5 ) Korb, J.-P.; Xu, S.; Jonas, J. J . Chem. Phys. 1993, 98, 2411. (6) Haszeldine, R. N.; Smith, F. J . Chem. SOC.1951, 603. (7) Sianesi. D.; Zamboni, V.; Fontanelli, R.; Binaghi, M. Wear 1971, 18, 85. (8) Jones, W. R., Jr.; Snyder, C. E., Jr. ASLE Trans. 1980, 23, 253. (9) Snyder, C. E., Jr.; Gschwender, L. J.; Cambell, W. B. Lubr. Eng. 1982, 38, 41. (10) Jones, W. R., Jr.; Johnson, R. L. ASLE Trans. 1975, 18, 249. (1 1) Korb, J.-P.; Delville, A.; Xu, S.; Demeulenaere, G.; Costa, P.; Jonas, J. J. Chem. Phys. 1994, 101, 7074. (12) Jonas, J.; Hasha, D.; Huang, S. G. J . Chem. Phys. 1979, 71, 3996. (13) Jonas, J.; Akai, J. A. J . Chem. Phys. 1977, 66, 4946. (14) Brownstein, K. R.; Tam, C. E. J . Magn. Reson. 1977, 26, 17. (15) Liu, G.; Li, Y.; Jonas, J. J . Chem. Phys. 1989, 90, 5881. (16) Chandler, D. J. Chem. Phys. 1975, 62, 1358. (17) CRC Hand Book of Chemistry & Physics, 75th ed.; Lide, D. R., Editor-in-Chief; CRC Press: Boca Raton, FL, 1994. (18) Lange's Hand Book of Chemistry, 12th ed.; Dean, J. A,, Ed.; McGraw-Hill: New York, 1979. (19) Lifanova, N. V.; Usacheva, T. M.; Zhuravlev, V. I. Russ.J. Phys. Chem. 1992, 66, 125. (20) Xu, S.; Kim, Y. J.; Jonas, J. Chem. Phys. Lett. 1994, 218, 329. (21) Alder, B. J.; Gass, D. M.; Wainwright, T. E. J . Chem. Phys. 1970, 53, 3813. (22) Finney, R. J.; Fury, M.; Jonas, J. J . Chem. Phys. 1977, 66, 760. (23) DeZwaan, J.; Jonas, J. J . Chem. Phys. 1975, 62,4036. (24) DeZwaan, J.; Jonas, J. J . Chem. Phys. 1975, 63, 4606. (25) Hildebrand, J. H.; Lamoreaux, R. H. Proc. Natl. Acad. Sci. 1972, 69, 3428. (26) Demond, J. H. J . Chem. Phys. 1974, 60, 969. (27) Parkhurst, H. J., Jr.; Jonas, J. J . Chem. Phys. 1975, 63, 2705. (28) Jonas, J.; Hasha, D.; Huang, S. G.J . Phys. Chem. 1980, 84, 109.
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