The isothermal piezooptic coefficient of n-alkanes, n-alcohols, and some substituted benzenes

M-910 J. Chem. Thermodynamics 1979, 11, 93-99

The isothermal piezooptic coefficient of n-alkanes, n-alcohols, and some substituted benzenes ALFRED J. RICHARD”, KEITH T. McCRICKARD, and PATRICIA B. FLEMING Departmentof PharmaceuticalChemistry,Medical Collegeof Virginia, Virginia CommonwealthUniversity, Richmond,Virginia 23298, U.S.A. (Received3 April 1978; in revisedform 20 July 1978) The isothermal piezooptic coefficients (&r/@), of 27 pure liquids have been measured with an ultracentrifuge equipped with laser optics, in good agreement with available literature values. The isotropic part (RI.) of light scattered by pure liquids has also been calculated. A decrease in RI. has been observed with increasing chain length of n-alkanes. For n-alcohols RI. remains constant at least up to nonanol.

1. IIltroduction The isothermal piezooptic coefficient @n/@)r of liquids has been reported for only a limited number of compounds. U-V In no case has a systematic study of a homologous series of compounds been attempted. In view of the importance of @n/ap), to light scattering workC4) and to the understanding of intermolecular interactions of pure liquids (‘p6) it was decided to measure (&z/ap>T of the normal alkanes from pentane to tridecane, of the normal alcohols from propanol to dodecanol, and of a series of alkyl substituted benzenes. One of the simplest methods of applying pressure to a liquid is by centrifugation; therefore the analytical ultracentrifuge with its refractometric optical systems should readily provide for measurement of (an/ap)r. The schlieren optical system has been used for this purposeC3) giving results for a limited number of compounds that agreed with literature values obtained with a Rayleigh interferometer.(‘) In this laboratory,“’ values of (an/a& calculated by schlieren optics did not agree with literature values, but were generally too high by 4 to 7 per cent. It was not possible to use the interferometer in the ultracentrifuge for those studies, however, as long as the mercury-arc light source provided the illumination, because the refractive index change between a gas phase in one channel of the interferometer cell and that of the liquid in the other channel was so great that coherence, and consequently fringes, were lost. It was therefore decided to equip the ultracentrifuge with laser optics as described by Williams’s’ and to measure “To whom correspondence should be addressed. 0021-9614/79/010093+07 $01.00/O

0 1979 Academic Press Inc. (London) Ltd.

94

A. J. RICHARD,

K. T. McCRICKARD,

AND P.[B. FLEMING

(&z/@)r in the ultracentrifuge by Rayleigh interferometry. The tremendous coherency of laser light should permit the observation of fringes through a very large refractive index change.

2. Experimental All liquids used in this study were obtained in 2 cm3 vials sealed under nitrogen, with purity of 99 moles per cent or better, from the Chemical Samples Corp. A 1.2 cm double-sector aluminium cell with sapphire windows was used. Under a dry nitrogen atmosphere, 0.1 cm3 of liquid was added to one sector and 0.4 cm3 of the liquid to the second. The cell was capped while still in the nitrogen bag, then transferred to the rotor. The centrifuge was accelerated to 500 Hz and held there for about 5 min, following which 30 min runs were made at speeds of 410, 340,254, and 50 Hz. Light was provided by a 4 mW He-Ne laser at 632.8 nm. Photographs were taken on Kodak IV F plates with exposure times not exceeding 1 s, and were taken 30 min after reaching speed at the given temperature to allow for dissipation of any thermal effects of the compression. Figure 1 shows typical interference patterns obtained in this work. In order to calculate (&r/@), the number of fringes displaced between the liquid-to-air meniscus and the liquid-to-liquid meniscus as measured in a two-dimensional microcomparator was plotted against the pressure, given by p = $pw2Ar2, generated at the liquid-toliquid meniscus for each speed. Here, m is the angular velocity, p is the liquid density, and r is the distance from the center of rotation. This line was generally straight with a slope giving @n/ap), and indicating that (%t/ap), was constant at the pressures encountered within the cell. Of course (an/ap)T is known to decrease at elevated

R

A- L

L-L

FIGURE 1. Typical interference pattern obtained at 410 Hz. R, referencepoint from which the distance from the center of rotation is calculated. The air-to-liquid meniscus is at A-L and the liquid-to-liquid meniscusis at L-L. pressures. Ideally, only one centrifugal speed is required to calculate (an/ap)T since each picture is in itself a plot of refractive index against pressure, but several pictures were used to account for any apparent changes in refractive index due to cell-window distortion or to other effects such as slight variability of cell component positions relative to each other in different runs. In several instances it was observed, for example, that even at the lowest speed, 50 Hz, there was an unexplained displacement of from 2 to 4 fringes across the liquid column. If not accounted for, this would introduce a significant error in the (&z/ap)T calculations made on a single photograph. It was assumed for these studies that the densities of the liquids remained constant throughout the cell. Pressures across the liquid column never exceeded 30 x IO5 Pa at the speeds used and sample calculations with pentane, whose isothermal com-

PIEZOOPTIC

COEFFICIENTS

OF PURE LIQUIDS

95

pressibiity is 2180 TPa- ’ at 298.15 K, t9’ showed thad an error of about 0.5 per cent was introduced into (&z/ap)r by ignoring the density change with pressure. Since pentane was by far the most compressible of the liquids in the study, it was considered safe to neglect density changes for all other liquids. The densities of these compounds at the two temperatures were obtained from the literature.(‘o’ Refractive indices of the alcohols were obtained by interpolation on plots of n against 1 from data collected in the review by Wilhoit and Zwolinski.‘“’ Other refractive indices were obtained from the Tables of Selected Thermodynamic Values (API 44)(“) and from the work of Wibaut et a1.03) All of the alcohols were studied in duplicate with the reported value being the average. The variation between runs was never greater than 5 per cent, but for most cases it was 2 per cent or less.

3. Results and dismssion Figure plotted though where

2 shows the (an/a& values at 298.15 K for the n-alkanes and n-alcohols against the number Nc of carbon atoms in each molecule. Very similar, slightly lower results were obtained at 293.15 K, as can be seen in table 1 all the results are collected.

FIGURE 2. The piezooptic coefficient plotted against molecular chain length for n-alkanes and /z-alcohols. 0, literature values; see reference 1.

In the alkane series, the lower molar-mass members have much larger values of (an/Q& than the higher molar-mass members of the series. In fact, the results for the alkanes could be represented linearly as a reciprocal relation between (&/ap)r and Nc. For the alcohols, on the other hand, (an/ap)r decreases only slowly with increasing molecular size presumably because of hydrogen bonding. In figure 2, the literature values of Coumou et al. (‘I have been included as the open circles for comparison. It should be noted that Coumou’s work was done at 296.15 K rather than

96

A. J. RICHARD,

K. T. McCRICKARD,

AND

P. B. FLEMING

298.15 K and that the wavelength used by Coumou was 546.1 nm rather than the 632.8 nm used here. It is perhaps coincidental that agreement is good, because the work of Waxler et ~1.‘~’ which allows a rough calculation of (&z/Q), from tabulated data, shows that (&z/Q), decreases with increasing wavelength while the work of Gottlieb’r4’ shows an increase in (&z/Q), with increasing temperature. Thus the effects may cancel, giving an apparent agreement between the results of Coumou and of this study. At any rate there is enough agreement to substantiate the ultracentrifugal method for determination of (an/ap>,. Table 1 gives the results obtained with all the compounds studied, along with the densities and isothermal compressibilities of these compounds(gP 15) and the refractive index of each at 632.8 nm. TABLE

1. Piezooptic

coefficients

--wwT TPa-1

Hexane Heptane Octane Nonane Decane Undecane Dodecane Tridecane Hexadecane

713 627 551 510 497 461 457 427 419 -

Propanol Butanol Pentanol Hexanol Heptanol cktanol Nonanol Decanol Undecanol

421 402 396 371 356 361 350 333

and isothermal compressibilities lo = 632.8 mn

- K~ TPa-1 293.15 2056 1632 1372 1210 1128 1046 1003 756 o 919” 840” 984 916 851 815 752 741 709 -

nm K 1.3564 1.3735 1.3864 1.3962 1.4041 1.4105 1.4158 1.4208

518 488 459 444 452 464 463

Cyclohexane

475

“Reference “Personal

17. communication

from

918 -

1.3844 1.3980 1.4086 1.4167 1.4228 1.4282 1.4324 1.4357

1.4978

-

Dr

Marc

0.6262 0.6594 0.6838 0.7025 0.7176 0.7300 0.7402 0.7487 0.7564

1.4331

140*

Toluene Ethylbenzene 1 ,ZDimethylbenzene 1,3-Dimethylbenzene 1.4-Dhnethylbenzene

P

__ g cm-3

Lewis,

(wad, Tpa-1

754 659 588 527 500 475 459 439 425 392

of liquids

~~ ma-1 298.15 2180 1706 1427 1273 1172 1074 990

at 0.1 MPa;

40) K 1.3541 1.3712 1.3839 1.3934 1.4018 1.4080 1.4137 1.4186

Go

1.4311

-ALg cm+

0.6214 0.6548 0.6795 0.6985 0.7138 0.7262 0.7366 0.7452 0.7528

0.8038 0.8097 0.8148 0.8198 0.8223 0.8258 0.8280 0.8297 0.8324

439 416 398 381 374 367 353 348 342

1026 941 883 824 778 764 745 -

1.3824 1.3960 1.4066 1.4147 1.4208 1.4262 1.4304 1.4337

0.8000 0.8060 0.8112 0.8162 0.8187 0.8223 0.8247 0.8263 0.8291

0.9982

141

452

1.3312

0.9970

0.8790 0.8669 0.8670 0.8802 0.8642 0.8610 0.8620

524 498 477 432 464 489 473

962 -

1.4948

-

0.8736 0.8623 0.8626 0.8760 0.8599 0.8567 0.8578

0.7786

-

1142

0.7739

Institutes

of Health.

National

PIEZOOPTIC

COEFFICIENTS

97

OF PURE LIQUIDS

It is possible from the values in table 1 to calculate the isotropic part of the Rayleigh quotient in light scattering at a scattering angle of 7r/2, as shown by Parfitt and Wood(4’ using the formula: R is = 2K2kTn2(an/ap)2T/~~ICT,

(1)

where k is the Boltzmann constant, n the refractive index at lo = 632.8 nm, T the temperature, and K~ the isothermal compressibility. Table 2 gives the results of the Ri, calculations for those compounds for which all the quantities are available. Should the Ri, values obtained in this work be consistent with values given in the Iiterature, then from equation (l), it would be possible to show that R,,@z2 remains nearly constant as I is allowed to vary, provided that @n/Q), is only weakly dependent on A..Such was found to be the case with the three compounds for which the calculation could be made. For benzene, hexane, and water the constants were (23.44 & 0.8) x 10w30 m3, (21.87 + 1.1) x 10V3’ m3, and (3.72 + 0.12)x IO-” m3. The data of Par&t and Wood(4) were used for benzene and hexane, but for water it was necessary to refer to work by Cohen and Eisenberg; o*) for agreement with our values.

TABLE

T/K

--

293.15

2. The isotropic part Ri, of scattered light at x/2

T/K

298.15

Pentane Hexane Heptane Octane Nonane Deane

2.26 2.26 2.12 2.09 2.15 2.01

2.42 2.43 2.35 2.15 2.12 2.11

Propaxlol Butanol

1.72 1.72

1.82 1.82

10*Rl./m

Pentanol Hexanol Heptanol Octanol Nom-in01

293.15

298.15

1.82 1.69 1.70 1.79 1.74

1.80 1.79 1.84 1.82 1.73

3.27

3.23

-

0.40

The expected strong dependence of Ri, on wavelength is shown in figure 3 where literature values(4*‘8) of RI, at the wavelengths 435.8 and 546.1 nm and the R,, values of this study at 632.8 nm are plotted against wavelength at 298.15 K; Ri, for all three liquids approaches zero when the wavelength approaches the infrared region. Plots of Ri, at 632.8 nm in homologous series are shown in figure 4. The alkane line converges to a limiting value Of Ri, of about 1.90 x lob4 m- ’ for long-chain molecules. With hexadecane, assuming (an/ap)r not to vary much with wavelength (as shown in figure 2) Ri, can be calculated from the data of Coumou et al.(‘) and is found to be 1.93 x 10m4 m-l, consistent with the idea of a long-chain limiting value. The normal alcohols having more than 12 carbons are solids at the temperatures studied and could not be represented on the graph. However, the shorter-chain alcohols all have a constant R,, of about 1.82 x 10s4 m-l at 298.15 K, very close to the limiting value for alkanes.

98

A. J. RICHARD,

K. T. McCRICKARD,

AND P. B. FLEMING

I

FIGURE

3. The dependence of the isotropic part R,. of light scattering on wavelength 1. 0, This

work; 0, references4 and 18.

2

4

6

8

10

12

14

16

.Yc. FIGURE molecules.

4. The dependence of the isotropic part R1, of light scattering on chain length of the

Kerker(‘@ has pointed out that order in a liquid reduces the amount of light scattered from that liquid because of interference effects. It is therefore reasonable to expect the values of R,, to decrease with increasing chain length of n-alkanes, as seen in figure 4. The presence of hydrogen bonding, however, apparently introduces order into even the short-chain alcohols, giving Ri, comparable to the long-chain alkanes. The authors are grateful to Dr Marc Lewis of the National Institutes of Health for helpful discussions related to laser optics, and for determining (&z/Q), of water at 293.15 K on his centrifuge. This investigation was supported by General Research Support Grant RR-05697 from the General Research Support Branch, Division of Research Facilities and Resources, National Institutes of Health.

PIEZOOITIC

COEFFICIENTS

OF PURE LIQUIDS

99

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. IO. 11. 12. 13. 14. 15. 16. 17. 18.

Coumou, D. J.; Mackor, E. L.; Hijmans, J. Truns. Fur&y Sot. 1964, 60, 1539. Raman, V.; Venkataraman, K. S. Proc. Roy. Sot. @or&n) A 1939, 171, 137. Josephs, R.; Minton, A. P. J. Phys. Chem. 1971, 75, 716. Parhtt, G. D.; Wood, J. A. Trans. Far&y Sot. 1968,64,805. Waxler, R. M. ; Weir, C. E. J. Res. Nat. Bur. Stand. 1963,67A, 163. Waxler, R. M.; Weir, C. E. ; Schamp, H. W., Jr. J. Res. Nat. Bur. Stand. 1964, 68A 489. Richard. A. J. J. Phvs. Chem. 1978. 82. 1265. Williams, R. C. An& Biochem. 1972,48, 164. Sahli, B. R.; Gager, H.; Richard, A. J. J. Chem. Thermodynamics 1976, 8, 179. Dreisbach, R. R. Physical Properties of Chemical Compounds, Adv. in Chem. Ser. American Chemical Society: Washington, D. C. 1%5,15 and 1959,22. Wilhoit, R. C.; Zwolinski, B. J. J. Phys. Chem. Ref. Data 1973, 2, suppl. 1. American Petroleum Institute Project 44 Tables. Thermodynamics Research Center, Texas A & M University, College Station, Texas. Wibaut, J. P. ; Hoag, H. ; Langedijk, S. L.; Overhoff, J.; Smittenberg, J.; Benninga, N. ; Bouman, G. P.; Van Dijk, H.; Gaade, W.; Geldof, H.; Hackmann, J.: Jonker, E. W.: Paap, T.; Zuiderweg, F. J. Rec. Trav. Chim. Pays-&s 1939,58, 329. Gottlieb, M. J. Acoust. Sot. Amer. 1971, 5, 1442. Burkat, R. K. ; Richard, A. J. J. Chem. Thermodynamics 1975, 7, 271. Kerker, M. The Scattering of Light Academic Press: New York, 1%9, Chapter 9. Kartsev, V. N. Russ. J. Phys. Chem. 1976,50,449. Cohen, G.; Eisenberg, H. J. Chem. Phys. 1965,43, 3881.