Effects of Molecular Size and Structure on Self-Diffusion Coefficient and Viscosity for Saturated Hydrocarbons Having Six Carbon Atoms

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1 Journal o Oleo Science Copyright 2007 by Japan Oil Chemists Society Eects o Molecular Size and Structure on Sel-Diusion Coeicient and Viscosity or Saturated Hydrocarbons Having Six Carbon Atoms Makio Iwahashi and Yasutoshi Kasahara School o Science, Kitasato University ( Kitasato, Sagamihara, , JAPAN) Abstract: Sel-diusion coeicients and viscosities or the saturated hydrocarbons having six carbon atoms such as hexane, 2-methylpentane (2MP), 3-methylpentane (3MP), 2,2-dimethylbutane (22DMB), 2,3- dimethylbutane (23DMB), methylcyclopentane (McP) and cyclohexane (ch) were measured at various constant temperatures; obtained results were discussed in connection with their molar volumes, molecular structures and thermodynamic properties. The values o sel-diusion coeicients as the microscopic property were inversely proportional to those o viscosities as the macroscopic property. The order o their viscosities was almost same to those o their melting temperatures and enthalpies o usion, which relect the attractive interactions among their molecules. On the other hand, the order o the sel-diusion coeicients inversely related to the order o the melting temperatures and the enthalpies o the usion. Namely, the compound having the larger attractive interaction mostly shows the less mobility in its liquid state, e.g., cyclohexane (ch), having the largest attractive interaction and the smallest molar volume exhibits an extremely large viscosity and small sel-diusion coeicient comparing with other hydrocarbons. However, a signiicant exception was 22DMB, being most close to a sphere: In spite o the smallest attractive interaction and the largest molar volume o 22DMB in the all samples, it has the thirdly larger viscosity and the thirdly smaller sel-diusion coeicient. Consequently, the dynamical properties such as sel-diusion and viscosity or the saturated hydrocarbons are determined not only by their attractive interactions but also by their molecular structures. Key words: sel-diusion coeicient, density, viscosity, molar volume, hexane, 2-methylpentane, 3-methylpentane, 2,2- dimethyl butane, 2,3-dimethylbutane, cyclopentane, cyclohexane 1 INTRODUCTION Macroscopic properties such as vapor pressure, melting temperature, enthalpy o usion, density and viscosity or the solvents are important or their use in laboratories and industries and have been studied by many investigators 1, 2). On the other hand, sel-diusion coeicient (D), one o the undamental microscopic properties, is also important not only or the theoretical but also or the technical aspects. Thus reliable and precise D values are demanded. In the early stage the D values or various materials were obtained mainly by the radiotracer method 3-8) and now have been obtained by the pulse ield gradient NMR method 9-14). Several data o D or normal alkanes and cyclohexane have been reported 7, 15, 16). Those or the other saturated hydrocarbons having chain branching, however, have not been so much studied irrespective o their scientiic and industrial importance especially as the solvents or the organic synthesis and also or the separation o various materials. In the theoretical aspects, urthermore, it is important to clariy the structure eects o various saturated hydrocarbons possessing chain branching or a cyclic rings on their physicochemical properties such as viscosity and sel-diusion coeicients, since such the physicochemical properties have been generally believed to relate only to the intermolecular attraction among molecules. On the other hand, the intermolecular attractions relate closely to the thermodynamical properties such as the heat o usions and the melting temperatures o the samples. In the present study, we have ocused on the seven kinds Correspondence to: Makio Iwahashi, School o Science, Kitasato University, Kitasato, Sagamihara, , JAPAN maki@kitasato-u.ac.jp Accepted May 15, 2007 (received or review February 26, 2007) Journal o Oleo Science ISSN print / ISSN online 443

2 M. Iwahashi and Y. Kasahara o saturated hydrocarbons having six carbon atoms such as hexane, 2-methylpentane, 3-methylpentane, 2,2-dimethylbutane, 2,3-dimethylbutane, methylcyclopentane and cyclohexane, which are requently used as solvents in many laboratories and industries; we investigated the inluences o their molecular structures to their sel-diusion coeicients and viscosities. 2 EXPERIMENTAL SECTION 2 1 Following samples were purchased rom Wako Pure Chemical Industries, Ltd (Ohsaka, Japan) and used without urther puriication: hexane (99.8% pure), 2-methylpentane (2MP, 98% pure), 3-methylpentane (3MP, >98% pure), 2,2- dimethylbutane (22DMB, >97% pure), 2,3-dimethylbutane (23DMB, >98% pure), methylcyclopentane (McP, 97% pure) and cyclohexane (ch, 99.9% pure). 2 2 The density, r, or the samples in the temperature range (25 40) 0.01 was measured on a vibration-type densimeter (Anton Paar Model DMA 58). Degassed pure water was used or calibrating the densimeter. 2 3 The viscosity or the samples was measured with two Ubbelohde viscometers (Shibata Co. Ltd.) having dierent diameters in a temperature range (25 40) Distilled water was used or calibrating the viscometers. 2 4 The sel-diusion coeicient was determined by means o the pulsed-ield gradient NMR method 17). All the measurements were made on protons at MHz in a temperature range (25 40) 0.5 on an NMR spectrometer (Japan Electron Optics Laboratory (JEOL) Model EX-400). 3 RESULTS AND DISCUSSION The obtained values o sel-diusion coeicient, D, viscosity, h, and density, r, or the seven kinds o saturated hydrocarbons having six carbon atoms at a series o temperature are given in, respectively. also shows the temperature dependence o the D values or the saturated hydrocarbons. The D value or each sample increases with an increase in temperature; at each constant temperature the D values are in the order o 2MP > 3MP > hexane > 23DMB > 22DMB > McP >> ch. The D value o ch is extremely small compared with other Table 1 Sel-diusion Coeicients, Viscosities and Densities or Hydrocarbons Having Six Carbon Atoms. Sel-Diusion Coeicient D/ 10-9 m 2 s -1 Viscosity h / m Pas Density r / g cm -3 Samples ,2-dimethylbutane (22DMB) 2,3-dimethylbutane (23DMB) 2-methylpentane (2MP) 3-methylpentane (3MP) hexane Methylcyclopentane (McP) Cyclohexane (ch) a) a) a) a) a) b) a) 0.29 b) a) a) a) c) a) a) a) J.A. Riddick and W.B. Bunger, Organic Solvents, John Wiley & Sons Inc. (1970). b) D.C. Douglass and D.W. McCall. J. Phys. Chem. 62, 1102 (1958). c) I. Kamal and E. McLaughler. Trans Faraday Soc. 62, 1762 (1966). 444

3 Sel-Diusion Coeicient and Viscosities o Saturated Hydrocarbons Fig. 1 Temperature Dependences o Sel-diusion Coeicients or Various Hydrocarbons Having Six Carbon Atoms. Fig. 2 Temperature Dependences o Viscosity or Various Hydrocarbons Having Six Carbon Atoms. hydrocarbons. On the other hand, as shown in, the h value or each sample decreases with an increase in temperature; at each constant temperature the h values are in the order o 2MP < 3MP < hexane < 23DMB < 22DMB < McP << ch. The h value o ch is also extremely large compared with other hydrocarbons. Namely, the values o the sel-diusion coeicient as a microscopic property are almost inversely proportional to those o the viscosity as a macroscopic property. Thus, the hydrodynamic property such as viscosity is closely correlated to the molecular movements even in a microscale. This would be because, in the general luid, the mean ree paths o the composing molecules are smaller than the size o the molecule. Then, what does determine their orders o the sel-diusion coeicient and viscosity? One o the important actors determining the degree o viscosity or sel-diusion is generally thought to be the attractive interaction among the molecules; the attractive interaction relects the thermodynamic properties such as the boiling point and the enthalpy o evaporation o the sample. shows the boiling points and the two kinds o enthalpy o evaporation or the saturated hydrocarbons at 25 and their boiling points, respectively 1). The boiling Table 2 Samples Boiling Points, Enthalpies and Entropies o Evaporation or Hydrocarbons Having Six Carbon Atoms. Boiling Point Enthalpy o Evaporation at 25.0 DH V / kjmol -1 Enthalpy o Evaporation at Boiling point DH b / kjmol -1 a) J.A. Riddick and W.B. Bunger, Organic Solvents, John Wiley & Sons Inc. (1970). Entropy o Evaporation at Boiling point DS b / J K -1 mol -1 2,2-dimethylbutane a) a) ,3-dimethylbutane a) a) methylpentane a) a) methylpentane a) a) hexane a) a) methylcyclopentane a) a) cyclohexane a) a)

4 M. Iwahashi and Y. Kasahara points and the both enthalpies o evaporation are increasing according to the order o 22DMB < 23DMB < 2MP < 3MP < hexane < McP << ch. This means that the attractive interaction increases according to this intensity order. In addition, the entropies o evaporation calculated rom the enthalpies o evaporation at the boiling points, although they are ully satisying the Trouton s rule 18), increase also according to this order. The gas phases or these hydrocarbons are thought to be in the almost same situations with each other. Thus, the order o the entropies in their liquid would be also determined by the attractive interactions among the molecules. Cyclohexane (ch) in its liquid state has the smallest entropy o the all samples, while 22DMB has the largest entropy. Thus, the attractive interactions among the molecules in the samples seem to ully relate to the sel-diusions and viscosities or the samples. In act, ch and McP having the larger attractive interaction show the larger viscosity and the smaller seldiusion coeicient. However, there are two exceptions, in which the most signiicant exception is 22DMB: It shows the smallest attractive interaction and the largest entropy but the third smaller molecular mobility. The secondly signiicant one is 23DMB, which has the secondly smaller attraction and the medium molecular mobility. In order to clariy the actor determining the dynamical properties o the samples, we calculated the molar volumes or the samples using their densities and molar weights. The obtained molar volumes are plotted as a unction o temperature in. Molar volume or each sample increases with an increase in temperature and, at each constant temperature, the values are in the order o 22DMB > 2MP > hexane > 23DMB > 3MP >> McP > ch. Namely, the smallest ch molecules have the largest attractive interaction and the smallest mobility; the secondly smaller McP molecules, the secondly larger attractive interaction and the secondly smaller mobility. This means that the hydrocarbons being smaller in their sizes have a larger attraction and a smaller mobility. In other words, the hydrocarbons being larger in their sizes have a smaller attractive interaction and a larger mobility. Thereore, 22DMB, having the largest molar volume, should have the smallest attractive interaction and the largest mobility. Surprisingly, however, it has the thirdly smaller ability in its molecular movement. In addition, the relatively small 23DMB has the secondly larger attractive interaction and the medium larger ability in its molecular movements. Then, why the 22DMB molecules having the smallest attractive interaction show the thirdly smaller mobility? For a moving spherical particle being almost equal in size to surrounding solvent molecules under the slip boundary condition, Stokes equation or rictional coeicient,, is given by 19-21) where p is the ratio o the circular constant, h the viscosity o the solvent and a the radius o the spherical particle. Let us apply this equation or a pure hydrocarbon. By assuming a hypothetical sphere, an equivalent radius a 0 or the hydrocarbon is expressed as a = 4πηa 0 3M = 4πρL 1 3 (1) (2) where M is the molar weight o the hydrocarbon, r the density o the hydrocarbon and L the Avogadro number. By substituting a 0 in or a in, the rictional coeicient, 0, or the hypothetical sphere is given by 0 = 4 3M πη 4πρL 1 3 (3) Fig. 3 Temperature Dependences o Molar Volume or Various Hydrocarbons Having Six Carbon Atoms. On the other hand, rom the Stokes-Einstein equation or diusion 22), the rictional coeicient is expressed by = kt / D where k is the Boltzmann constant, T the absolute temperature and D the diusion coeicient. Combining and, we obtain (4) 446

5 Sel-Diusion Coeicient and Viscosities o Saturated Hydrocarbons 0 = kt 3M 4πηD 4πρL 1 3 (5) or the saturated hydrocarbons are determined not only by the attractive interaction but also their molecular structures. The molecular attraction does not always give the perect understanding o the molecular dynamics. The ratio / 0 should be unity when the actual molecule is a sphere. For most rod-shaped or prolate macromolecules including proteins in an organic solvent or in an aqueous solution, the rictional ratio is in general apart rom unity 23). shows the / 0 values or the samples at various temperatures. The values or 22DMB are most close to unity in those or the all samples in this temperature range. Namely, 22DMB is most close to a sphere in its shape in the all samples, while ch molecules most closely packed are most apart rom a sphere. The / 0 values or hexane, 23DMB, 3MP and McP slightly increase with increasing temperature: Their molecular orms slightly approach to a sphere with increasing in temperature. The slight increase in / 0 value probably results rom the increase in the number o molecules having gauche orm and in the rotational molecular movements. The relatively larger viscosity and the smaller sel-diusion coeicient or 22DMB, in spite o its largest molar volume, would results rom not its intermolecular attraction but its steric-bulky structure, which is most close to a sphere. On the other hand, the largest viscosity and the smallest diusion coeicient or ch would result rom the ring structure, having mostly a chair conormation, which are apt to be intertwined each other. Namely dynamical properties such as sel-diusion coeicient and viscosity 4 CONCLUSION Sel-diusion coeicients (D) and viscosities (h) or 2MP, 3MP, 22DMB, 23DMB, McP and ch were measured and discussed in connection with their molar volumes, structures and thermodynamic properties such as melting temperatures and enthalpies o usion. The obtained D values are in the order o 2MP > 3MP > hexane > 23DMB > 22DMB > McP >> ch; contrary to the D results the h values are also in the order o 2MP < 3MP < hexane < 23DMB < 22DMB < McP << ch. Namely, the order o the sel-diusion coeicient as the microscopic property is just inversely proportional to that o the viscosity as the macroscopic property. On the other hand, the attractive interaction is in the order o 22DMB < 23DMB < 2MP < 3MP < hexane < McP < ch, while the molar volume is in the order o 22DMB > 2MP > hexane > 3MP > 23DMB >> McP > ch. The order o their dynamical properties such as viscosity and sel-diusion coeicient seems to almost depend on their molar volumes: The compound having the smaller molar volume seems to have the less molecular dynamical movements. However, an extremely large exception is 22DMB, which has the relatively larger viscosity and the smaller sel-diusion coeicient in spite o its largest molar volume. Thus it is concluded that the dynamical properties such as sel-diusion and viscosity or the saturated hydrocarbons are determined not only by its intermolecular attractions among the hydrocarbon molecules but also by their molecular structures. Fig. 4 Temperature Dependences o Frictional Ratio / 0 or Various Hydrocarbons Having Six Carbon Atoms. 1. Riddick, J.A.; Bunger, W.B. Organic Solvents, John Wiley & Sons Inc. (1970). 2. Dean, J.A. Lange s Handbook o Chemistry, McGraw- Hill, Inc. (1973). 3. Hardt, A.P.; Anderson, D.K.; Rathbun, R.; Mar, B.W.; Babb, A.L. Sel-diusion in Liquids. II. Comparison between Mutual and Sel-Diusion Coeicients. J. Phys. Chem. 63, (1959). 4. Wang, J.H. Sel-diusion and structure o liquid water. I. Measurement o sel-diusion o liquid water with deuterium as tracer. J. Am. Chem. Soc. 73, (1951). 5. Saxton, R.L.; Drickamer, H.G. Diusion in liquid sulur. J. Chem. Phys. 21, (1953). 6. Carman, P.C.; Stein, L.H. Sel-diusion in mixtures. I. 447

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