Structural aspects in the dielectric properties of pentyl alcoholsUdo Kaatze, Ralph Behrends, and Kerstin von Roden Citation: J. Chem. Phys. 133, 094508 (2010); doi: 10.1063/1.3487524 View online: http://dx.doi.org/10.1063/1.3487524 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v133/i9 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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Structural aspects in the dielectric properties of pentyl alcoholsUdo Kaatze,a� Ralph Behrends, and Kerstin von RodenDrittes Physikalisches Institut, Georg-August-Universität, Friedrich-Hund-Platz 1,37077 Göttingen, Germany

�Received 23 June 2010; accepted 17 August 2010; published online 7 September 2010�

At temperatures between 0 and 60 °C densities, shear viscosities and dielectric spectra have beenmeasured for isomers 1-pentanol, 2-pentanol, 3-pentanol, isopentylalcohol, and tert-pentanol, aswell as for mixtures of these alcohols. The density and shear viscosity data are discussed in termsof deviations from ideal mixing behavior. The dielectric spectra are evaluated to yield theextrapolated static permittivity and the relaxation time of the principal �low-frequency� relaxationterm. The former parameter is analyzed in view of dipole orientation correlations, the latter one isdiscussed in terms of the activation enthalpy controlling the relaxation process. A noticeable resultis the effect of isomer structure on both the dipole orientation correlation and the dielectricrelaxation. Especially the dielectric parameters of tert-pentanol deviate significantly from therelevant parameters of the other pentanols. Such deviations are considered in the light of models ofhydrogen network structure and fluctuations. © 2010 American Institute of Physics.�doi:10.1063/1.3487524�

I. INTRODUCTION

During the past decades much attention has been di-rected toward the properties of alcohols, primarily because oftheir widespread use as reaction media in a variety of chemi-cal processes, and also because of their intriguing liquidstructure and molecular dynamics. Since both structural be-havior and dynamical properties can be obtained from thefrequency-dependent complex permittivity of the liquids, di-electric spectroscopy has been intensively used to study di-pole moment orientation correlations and reorientation timesin alcohols and in their mixtures with other liquids.1–24 Fur-ther interest springs from obvious relations between the di-electric spectra of alcohols and the spectrum of water, theomnipresent chemical on our planet. As illustrated by Fig. 1,as an example, the complex dielectric spectra

���� = ����� − i����� �1�

of alcohols and water reveal remarkable similarities. Here ��and �� denote the real and negative imaginary part, respec-tively, of the complex permittivity �, � is the frequency andi2=−1. Both spectra shown in Fig. 1 display one high-frequency dispersion �d�� /d��0�/dielectric loss �������0�region at least, in addition to a dominating relaxation processat microwave frequencies. The relaxation frequency �̂ of thelatter process �Fig. 1�, which will be the focus of interest ofthis paper, is significantly larger for the tetrahedral hydrogenbond network of water than for the chainlike H-bondedstructures of ethanol. In this context �̂ is simply defined bythe maximum in the dielectric loss �d����� /d�=0 andd2����� /d�2�0 at �̂�.

On a first glance, the obviously faster reorientation inwater than in the alcohol is an unexpected feature, sincewater molecules are predominantly connected by four hydro-

gen bonds whereas the degree of association is noticeablysmaller with alcohols. Among other aspects this finding hasled to the conclusion that the dielectric relaxation time�̂= �2��̂�−1 of associating liquids is not only controlled bythe hydrogen bond energy and by the number of hydrogenbonds per dipolar group �or molecule� but that it is also afunction of the probability density for the formation of a newbond.31 A clear tendency of the relaxation time �̂ to increasewith increasing number n of hydrophobic groups per mol-ecule and thus with decreasing density of hydrogen bondingsites is, for example, also reflected by the relaxation times ofthe homologous series CH3�CH2�n−1OH, n=1,2 , . . ., of nor-mal alcohols.31 For these monohydric liquids �̂ increasesfrom 0.057 ns at n=1 �methanol, 20 °C�29 to 2.21 ns atn=10 �n-decanol, 20 °C�.32

In addition to effects related to the density of hydrogenbonding sites, a considerable impact of the molecular struc-ture exists in the dielectric properties of alcohols. The corre-lation of the static permittivity ��0� to the molecular struc-ture of alcohols is known for a long time. We mention octylalcohol isomers as an example.33–36 Whereas for 1-octanol�CH3�CH2�7OH� the static permittivity equals 10.30 at20 °C, it is as small as 5.16 for the structural isomer2-methyl-1-heptanol �CH3�CH2�4CH�CH3�CH2OH� at thesame temperature.37 Similarly, ��0� of 6-methyl-1-heptanol��CH3�2CH�CH2�5OH� amounts to 10.54 at 17.2 °C but ��0�of 3-methyl-1-heptanol �CH3�CH2�3CH�CH3��CH2�2OH� is2.88 only.37 Since the electric dipole moments �g in the gas-eous state of the alcohol isomers are largely independent ofthe configuration of their hydrocarbon groups, the variationin the static permittivity reflects considerable differences inthe structure of the liquids, as, for instance, expressed by theorientation correlation of permanent dipoles.38 Theory,39,40

molecular dynamics simulations,5,41–46 as well as combinednuclear magnetic relaxation and dielectric relaxation data47

suggest the macroscopic �collective� relaxation time �̂ of po-a�Electronic mail: uka@physik3.gwdg.de.

THE JOURNAL OF CHEMICAL PHYSICS 133, 094508 �2010�

0021-9606/2010/133�9�/094508/10/$30.00 © 2010 American Institute of Physics133, 094508-1

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lar liquids to be related via the static �Kirkwood� dipole ori-entation correlation factor g to the relaxation time �� of themolecular electric dipole moment. The simple form of therelation just reads47

�̂ = g��. �2�

Correlations between the molecular structure and the relax-ation behavior of polar liquids have attracted little interest sofar. Qualitatively an influence of steric properties on the di-electric relaxation time is evidenced by the spectra of threebranched alcohols shown in Fig. 2. In conformity with theseries of normal alcohols the relaxation frequency �̂ indeeddecreases when going from isopropanol to tert-butanol.However, �̂ increases significantly at addition of another hy-drocarbon group to tert-butanol. This enhancement in the

relaxation frequency is inconsistent with the reduced densityof hydrogen binding sites in tert-pentanol. It seemed thusinteresting to perform a dielectric spectrometry study of pen-tyl alcohol isomers and of some of their mixtures among oneanother.

II. EXPERIMENTAL

A. Alcohols and their mixtures

The structure of the pentyl alcohols used in this study isshown in Fig. 3 where also an acronym for each isomer isgiven. 1-pentanol �99%, water content 0.1%, CAS no.71-41-0�, ���-2-pentanol �99.5%, CAS no. 6032-29-7�,3-pentanol �99.5%, CAS no. 584-02-1�, isopentylalcohol�99%, water content 0.3%, CAS no. 123-51-3�, and tert-pentanol �99.5%, CAS no. 75-85-4� have been used as sup-plied by the manufacturers �Fluka, Buchs, Switzerland andMerck, Darmstadt, Germany�. Mixtures of 1-P with IP andwith t-P, both series with mole fractions 0.25, 0.5, and 0.75,as well as a 1-P–3-P mixture with mole fraction 0.5 havebeen prepared by weighing appropriate amounts of the con-stituents into suitable flasks. The alcohols were alwayshandled and stored under dry nitrogen in order to avoid wa-ter uptake from the air. The isomer concentrations c1, cI, andct of the mixtures have been calculated using the relation

c1,I,t = �x1,I,t�x1M1 + xI,tMI,t�−1 �3�

with � denoting the density of the mixture, x1, xI, and xt arethe mole fractions �x1=1-xI,t�, and M1, MI, as well as Mt arethe molar weights of 1-P, IP, and t-P, respectively.

B. Complex permittivity measurements

The complex permittivity ���� of the liquids has beenmeasured as a function of frequency � between 4 MHz and18 GHz and of temperature between 0 and 60 °C using twofrequency domain methods. At frequencies below 3 GHz thewavelength of the electromagnetic field within the liquidswas sufficiently large to enable quasistatic approaches atconvenient cell dimensions. The samples were contained incells from the cut-off variety,50 each one essentially consist-ing of a circular/cylindrical waveguide transition. The inputimpedance of the particular cell was determined as a functionof � using a computer-controlled network analyzer �HP

FIG. 1. Log-log plot of the real part �� and negative imaginary part �� of thecomplex permittivity �Eq. �1��, displayed as a function of frequency � forwater �Refs. 25–28� at 19 °C ��� and ethanol �Ref. 29� at 20 °C ���.Dashed lines are graphs of a Debye-type relaxation term with discrete re-laxation frequency �̂. In order to comply with the far-infrared data �Refs. 28and 30� measured at 19 °C, microwave data �Refs. 25–27� for water at20 °C have been corrected by interpolation, utilizing the well-known tem-perature dependence in the dielectric parameters �Ref. 31�.

FIG. 2. Lin-log plot of the complex permittivity spectrum of isopropanol�Ref. 48� ���, tert-butanol �Ref. 49� ���, and tert-pentanol ��� at 25 °C.Arrows mark the relaxation frequency �̂ of the dominating relaxation termin the spectra.

FIG. 3. Acronyms and structures of the pentyl alcohols considered in thisstudy.

094508-2 Kaatze, Behrends, and von Roden J. Chem. Phys. 133, 094508 �2010�

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8753A�, combined with appropriate reflection test set �HP85044A�. Cell parameters were obtained from calibrationmeasurements with the empty cell ������1� and with thecell filled with water or cyclohexane.51–54

At higher frequencies the transfer function of two com-puter controlled double-beam interferometers has been re-corded at continuously varying sample length.55 The interfer-ometers, constructed with waveguide devices, were operatedin the frequency bands of 5.3–8 GHz and 12.4–18 GHz. Thesample cells were circular waveguides, sealed at one end bya polytetrafluorethylene window. The TM11 field mode set upwithin the cell was probed by another circular waveguidewhich was immersed in the liquid and was precisely shiftedalong the direction of wave propagation. The off-balance sig-nal of the interferometer was recorded and was analyzed interms of the sample permittivity by fitting the data to therelevant transfer function.

Use of different cell lengths in the quasistatic input im-pedance measurements and test measurements on liquidswith well-known permittivity spectrum49–52 resulted in rela-tive errors ��� /�� and ��� /��0.01 at ��1 GHz and0.07 at 1 GHz�3 GHz. The relative errors in thedouble-beam interferometer data were 0.02 in both �� and ��.In the complete frequency range of measurement the relativeerror in � was smaller than 0.001. The temperature of thesamples was controlled to within 0.05 K and was measuredwith an uncertainty of less than 0.03 K.

C. Auxiliary measurements

Densities have been measured with a high-precision vi-brating tube densitometer with built-in reference oscillatorand Peltier temperature control �Physica DMA 5000, AntonPaar, Graz, Austria; �� /�5�10−6� and also with a pyc-nometer. Both devices had been calibrated against doublydistilled, degassed, and ultrafiltered water. Temperature fluc-tuations during the measurements were smaller than 0.01 K.Repeated measurements—including cleaning and refillingprocedures as well as samples from different charges—indicated a relative uncertainty �� /� of 10−4 in the vibratingtube data and of 2�10−3 in the pycnometer data. The shearviscosity of the liquids has been determined with the aid ofUbbelohde capillary viscometers �Schott, Mainz, Germany�and additionally with a falling ball viscometer �B/BH,Haake, Karlsruhe, Germany�. The instruments were cali-brated against standard reference liquids. They allowed �s tobe measured to within 2%.

III. RESULTS

A. Densities and viscosities

Deviations of our densities from literature data56–58 arewithin the limits of experimental uncertainty orare only slightly larger. Differences between our viscositiesand data from the literature somewhat exceed theuncertainty limits, e.g., �s= �4.25�0.09� mP s insteadof �s= �4.38�0.02� mP s,57 t-P at 20 °C or�s= �3.35�0.07� mP s instead of �s=3.55�0.02 mP s, t-Pat 25 °C.59,60 These differences, however, are much smallerthan the effects discussed in this paper.

In Fig. 4 the densities of the four pentyl alcohols 1-P,3-P, IP, and t-P are shown as a function of temperature � inCelsius scale. The �-versus-� relations for 2-P as well as the1-P–IP and 1-P–t-P mixtures look similar. Within the limitsof error the temperature dependence in each series of densitydata can be represented by a simple polynomial

� = �0 − �a�̂ − �b�̂2, �4�

where �̂= �T−273.15 K� / �273.15 K� is a reduced tempera-ture. The values of the density �0 at 0 °C and for the coef-ficients �a and �b are given in Table I. The densities of the1-P–t-P system have been also measured at several extramole fractions. At 25 °C the excess densities

�exc = � − �ideal �5�

of this system are displayed in the inset of Fig. 4. Calculatingthe �exc values, the ideal mixture densities �ideal have beenobtained from the relation

�ideal =�M1 − Mt�x1 + Mt

�M1/�1 − Mt/�t�x1 + Mt/�t, �6�

where M1 and Mt denote the �identical� molar weights of 1-Pand t-P and �1 as well as �t are the densities of the purealcohols. Though the excess densities of the 1-P–t-P mix-tures are small ��exc /�5�10−3�, indicating almost idealmixing behavior, a relative maximum emerges at xt=0.7.This maximum exceeds the maximum excess density of the1-hexanol/ethanol mixtures2 at 25 °C still by a factor of al-most 10.

Viscosities of four pentyl alcohol isomers are given in anArrhenius representation in Fig. 5. The slight curvature in the�s-versus-T−1 plots indicates that the temperature depen-dence of the viscosities cannot sufficiently well described bysimple Arrhenius behavior. We also tried to describe the vis-cosities by the frequently used Vogel–Fulcher–Tammann–Hesse relation61–63

FIG. 4. Density � of pentyl alcohols vs temperature � in centigrade: �, 3-P;�, 1-P; �, t-P; �, IP. The inset shows the excess density �exc ��, Eq. �5��of 1-P–t-P mixtures at 25 °C as a function of mole fraction x1 of 1-P. Linesare drawn to guide the eye.

094508-3 Dielectric properties of pentyl alcohols J. Chem. Phys. 133, 094508 �2010�

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�s = A� exp�B��T − T��� . �7�

With some viscosities, however, the deviations between themeasured data and the predictions of Eq. �7� exceed the ex-perimental uncertainty. For that reason the empirical relation

�s = ��0 − 1 + exp�a��̂��exp�− b��̂� �8�

has been used to represent the viscosity data of the liquids.The values of parameters �0, a�, and b�, as resulting from anonlinear least-squares fitting procedure, are also collected inTable I.

Interestingly, the composition dependencies of the vis-cosities of 1-P–t-P and 1-P–IP mixtures, shown in the insetof Fig. 5, reveal more or less pronounced relative maxima atsmall mole fractions x1 of 1-P. The distinct maximum of theformer system is located at x1=0.25, close to the mole frac-tion �x1=0.3� of the maximum in the excess density �Fig. 4�.

B. Dielectric spectra

In correspondence with the complex permittivity datadisplayed in Figs. 1 and 2, the complex dielectric spectra ofthe pentyl alcohols and of their mixtures among one anotherdisplay two relaxation regions within the frequency range ofmeasurements. The low-frequency relaxation term dominatesthe spectra. The amplitude of the high-frequency term is onthe order of 1 throughout. Inspection of microwave permit-tivity spectra of low-weight alcohols, which had been mea-sured up to 89 GHz �Refs. 64 and 65� and had, in somecases, been complemented by far-infrared data,64 has lead toa description in terms of three well-separated relaxation pro-cesses. The relaxation frequency of the fastest relaxation,however, is located distinctly above our measuring range andthe amplitude of this relaxation term is small. Therefore, inthe analytical representation of our spectra that term can beleft out of consideration. We thus represented the spectra bya sum of two Debye-type66 relaxation terms, using the modelrelaxation function

R1��� = ���� +��0� − �1

1 − i��1+

�1 − ����1 + i��2

�9�

with ��0� and ���� denoting the extrapolated low- and high-frequency permittivity, respectively, �1 and �2 are the relax-ation times of the low- and high-frequency Debye term��=2�� , i2=−1�. Since we are interested in the low-frequency �static� permittivity ��0� and the relaxation time �1

of the dominating relaxation term only, we alternatively ap-plied the Davidson–Cole67 relaxation spectral function

R2��� = ���� +��0� − ����

�1 − i��DC��1−�� . �10�

This function reflects an unsymmetrical relaxation time dis-tribution in which the largest relaxation time �DC is the onewith highest weight. Parameter � measures the width of therelaxation time distribution.

Both R1 and R2 have been fitted to the measured spectrausing a Marquardt algorithm68 in a nonlinear least-squaresregression analysis. This algorithm minimizes the reducedvariance

TABLE I. Parameters of the density �Eq. �4�� and shear viscosity �Eq. �8�� relations for the pentyl alcohols andtheir mixtures. With the latter x1 denotes the mole fraction of 1-P.

Alcohol/mixture x1

�0

�g /cm3��a

�g /cm3��b

�g /cm3��0

�mPa s� a� b�

3-P ¯ 0.836 90 0.2205 0.1100 20.0 18.1 18.42-P ¯ 0.825 20 0.2127 0.0870 10.2 13.4 14.6IP ¯ 0.822 94 0.1977 0.0417 8.5 5.4 10.11-P–IP 0.25 0.824 86 0.1965 0.0442 8.6 5.9 9.91-P–IP 0.5 0.829 31 0.1734 0.2130 8.2 8.8 10.91-P–IP 0.75 0.828 21 0.1916 0.0571 8.1 8.1 10.11-P 1 0.829 07 0.1977 0.0417 8.0 7.5 10.11-P–t-P 0.75 0.829 78 0.1982 0.0706 10.8 11.4 13.11-P–t-P 0.5 0.825 00 0.1797 0.0970 13.8 13.3 15.01-P–t-P 0.25 0.831 30 0.2334 0.0773 15.0 16.2 16.9t-P ¯ 0.827 16 0.2424 0.0751 13.3 16.2 17.71-P–3-P 0.5 0.832 17 0.1954 0.0914 12.2 12.2 13.4

FIG. 5. Shear viscosity �s of pentyl alcohols vs inverse temperature T−1: �,3-P; �, t-P; �, 2-P; �, 1-P. For 1-P–t-P ��� and IP–t-P ��� mixtures at0 °C the dependence of the viscosity upon mole fraction x1 of 1-P is givenin the inset.

094508-4 Kaatze, Behrends, and von Roden J. Chem. Phys. 133, 094508 �2010�

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�2 =1

I − J − 1�i=1

I �R1,2� ��i,Pj� − ����i������i�

2

+ R1,2� ��i,Pj� − ����i������i�

2� . �11�

Herein �i=1, . . . , I, denotes the frequencies of measurements,Pj , j=1, . . . ,J, the parameters of the model relaxation spec-tral function, and the inverse experimental errors 1 /�����i�as well as 1 /�����i� are used as weighing factors.

The analysis of spectra in terms of the Davidson–Colefunction R2��� allowed also for a calculation of the relax-ation time �̂ as defined by the maximum in the dielectric lossfunction. It was found that, within the limits of uncertainty��0.03 ns�, the �̂ values agree with the corresponding relax-ation times �1 of the dominating Debye term in Eq. �8�. Weshall therefore restrict the discussion to the �̂ data, which areindependent of the empirical relaxation function used toevaluate the measured spectra. Since the static permittivity ofthe liquids is well defined by the measurements �Figs. 1 and2� the ��0� values from alternative extrapolation by spectralfunctions R1��� and R2��� agree to within 1%, which is again

within the limits of the experimental uncertainty. The ��0�and �̂ values resulting from the regression analysis of spectraare collected in Tables II and III, respectively.

IV. DISCUSSION

A. Volume effects and viscosity interaction parameter

At three temperatures the experimental-to-ideal volumeratio

V/Videal = �ideal/� �12�

of 1-P–t-P mixtures is displayed as a function of mole frac-tion x1 of 1-P in Fig. 6. At all temperatures the data exhibit arelative minimum which is significantly less pronounced asanalogous minima of aqueous systems, such asethanol-water6 and poly�ethylene glycol�-water mixtures.69

In contrast to the 1-hexanol-ethanol mixtures mentionedbefore2 and to the equimolar 1-P–3-P mixture, however, theVideal /V data for mixtures of t-P �and also IP� with 1-P doshow slight deviations from ideal mixing behavior. Obvi-ously, the molar volume decreases when a pentanol withbranched chain is added to normal pentanol and vice versa.

TABLE II. Extrapolated static permittivites ��0� of pentyl alcohols and their mixtures at several temperatures �. The uncertainty in the data is���0� /��0�=0.01.

Alcohol/mixture x1

��°C�

1 10 20 25 30 40 50 60

3-P ¯ 17.1 16.1 14.2 13.3 12.6 11.1 9.8 9.52-P ¯ 17.3 15.6 14.5 13.8 12.8 11.5 10.5 9.7IP ¯ ¯ 16.8 15.6 15.1 14.6 13.5 12.3 ¯

1-P–IP 0.25 18.0 16.7 15.7 15.2 14.6 13.5 12.4 ¯

1-P–IP 0.5 ¯ 16.8 15.7 15.1 14.5 13.5 12.4 ¯

1-P–IP 0.75 17.8 16.6 15.0 15.2 14.6 13.6 12.6 11.81-P 1 ¯ 16.9 15.7 15.1 14.6 13.6 12.5 11.81-P–t-P 0.75 17.4 16.2 15.0 14.4 13.8 12.6 11.5 ¯

1-P–t-P 0.5 16.2 15.3 13.5 12.7 12.3 11.0 9.9 ¯

1-P–t-P 0.25 ¯ 12.5 10.6 10.1 9.7 8.6 7.7 ¯

t-P ¯ ¯ 6.3 6.0 5.7 5.8 5.5 5.5 ¯

TABLE III. Relaxation times �̂ in ns of the dominating low-frequency dielectric relaxation term for pentyl alcohols and their mixtures at temperature �. Theuncertainty in the data is �0.03 ns.

Alcohol/mixture x1

��°C�

1 10 20 25 30 40 50 60

3-P ¯ 2.97 1.70 0.90 0.66 0.50 0.28 0.20 ¯

2-P ¯ 2.37 1.54 0.87 0.66 0.47 0.29 0.21 0.13IP ¯ ¯ 1.47 0.95 0.78 0.62 0.40 0.27 ¯

1-P–IP 0.25 2.11 1.41 0.93 0.75 0.59 0.39 0.27 ¯

1-P–IP 0.5 ¯ 1.37 0.88 0.71 0.58 0.38 0.27 ¯

1-P–IP 0.75 2.00 1.31 0.81 0.69 0.56 0.38 0.30 0.181-P 1 ¯ 1.32 0.86 0.67 0.56 0.37 0.25 0.191-P–t-P 0.75 2.51 1.50 0.97 0.76 0.58 0.36 0.24 ¯

1-P–t-P 0.5 2.51 1.67 0.88 0.70 0.52 0.32 0.21 ¯

1-P–t-P 0.25 ¯ 1.39 0.68 0.50 0.38 0.22 0.15 ¯

t-P ¯ ¯ 0.63 0.31 0.19 0.16 0.08 0.08 ¯

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Hence these mixtures of isomers allow for a denser packingof molecules than the pure pentyl alcohols 1-P, t-P, and IP.The mole fraction x1, at which the relative minimum appears,increases with temperature. With the 1-P–IP system theminima are shifted to somewhat larger x1 values as comparedto the relevant 1-P–t-P mixtures.

As evidenced by the �s–versus-x1 relations in the insetof Fig. 5, the viscosity data of the mixtures of pentyl alcoholisomers likewise indicate deviations from ideal mixing vis-cosity, which is defined as the mole-fraction-weighted mean

�sideal = x1�s1 + xI,t�sI,t. �13�

Here we discuss the deviations in terms of the Grunberg–Nissan relation70

ln��s� = ln��sA� + x1xI,t,3G , �14�

where

ln��sA� = x1 ln��s1� + xI,t,3 ln��sI,t,3� �15�

denotes the logarithm of the Arrhenius viscosity71 �sA of abinary mixture of constituent “1” with constituent I, t, or “3,”respectively. Using the Grunberg–Nissan equation �Eq. �14��the deviation of the experimental viscosity of a mixture fromthe prediction of the Arrhenius relation �Eq. �15�� is ex-pressed in terms of a parameter G which is proportional tothe interaction energy and thus measures the strength of in-teraction between the components.72 G may adopt negativevalues at small interactions and it becomes increasingly posi-tive as the strength of interaction increases.72 In the lowerpart �b� of Fig. 6, G values for the 1-P–t-P mixtures areshown at three temperatures. Strong interactions appear forthis system. The G values are particularly large at mole frac-tion 0.25 of 1-P. In contrast to the V /Videal-versus-x1 curvesalso displayed in Fig. 6, the mole fraction of the extremum inG does not noticeably shift with temperature, rather themaximum G value becomes smaller. Since the maximum is

found at x1=0.25 a favorable configuration appears to existsin the 1-P–t-P system at molar ratio x1 /xt=1:3.

For the equimolar mixtures of 1-P with IP, t-P, and 3-Pinteraction parameter G is displayed as a function of tem-perature between 1 and 60 °C in Fig. 7. Below 30 °C, wherethe structure of the liquids is dominated by hydrogen bond-ing, G evidences large positive values with the 1-P–t-P sys-tem. Opposed to this behavior the mixtures of 1-P with IPand also with 3-P reveal small and even negative G values.At higher temperatures and thus smaller degree of hydrogenbonding of the alcohols, the interaction parameters of thethree binary systems converge and adopt almost identicalvalues at 60 °C.

B. Static permittivity and dipole orientation correlation

According to the Fröhlich theory73,74 the static permittiv-ity of a one-component dipolar liquid is given by the relation

��0� = ���� +4�NA

3kBT

3��0�2��0� + ��

�� + 2

32

g�2c , �16�

where NA and kB denote Avogadro’s and Boltzmann’s con-stants, respectively, � is the dipole moment of molecules inthe gaseous state, g is the Kirkwood dipole orientation cor-relation factor in the liquid,38 c is the concentration of dipolemoments, and �� is a high-frequency permittivity which weshall revisit later. Because of the obvious temperature depen-dence in ��0�, reflecting the fact that alignment of permanentdipole moments competes against thermal agitation, productT��0� of two pentyl alcohol isomers has been plotted againsttemperature in part �a� of Fig. 8. Whereas the T��0� data fort-P, including those from the literature, are independent oftemperature, the data for 2-P monotonously decrease byabout 30% when going from 0 to 60 °C. From the tempera-ture dependence of density, an insignificant temperature de-pendence in c just follows with both pentyl alcohols. Hencewith t-P the high-frequency permittivity �� and the correla-tion factor g obviously are independent of temperature�pointing at ���n2, n=optical refractive index�, while with2-P at least one of these parameters depends strongly upon�. We shall discuss this point with details below when deal-ing with the dipole correlation values. Here we briefly direct

FIG. 6. Experimental-to-ideal volume ratio �a; �Eq. �12��� and interactionparameter G in the viscosity relation �b; �Eq. �14��� of 1-P–t-P mixtures,displayed vs mole fraction x1 of 1-P at 0 °C ���, 25 °C ���, and 60 °C���.

FIG. 7. Interaction parameter G in the Grunberg–Nissan relation �Eq. �14��for the shear viscosity shown as a function of temperature � for equimolarmixtures of 1-P with t-P ���, IP ���, and 3-P ���.

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attention to the composition dependencies in the ��0� data ofthe 1-P–t-P and 1-P–IP mixtures shown in part �b� of Fig. 8.The static permittivity of 1-P and IP are almost identical���0�=16.87�0.17,1-P;��0�=16.85�0.17, IP;10 °C� andtheir mixtures feature a very small minimum only���0�=16.64�0.17,x1=0.75�. In conformity with the sub-stantially smaller static permittivity of t-P���0�=6.30�0.06;10 °C� the data for the 1-P–t-P systemreveal a monotonous increase with x1.

In Eq. �16� the Kirkwood factor g considers the correla-tion between neighboring dipoles of identical molecules. Inbinary liquids, strictly, three orientation correlation factorsshould be taken into account: one for each component toallow for correlations between like molecules, and an addi-tional one to include correlations between unlike molecules.Since we cannot derive three parameters from the static per-mittivity, we take advantage of the similarity of the compo-nents in alcohol mixtures to evaluate the ��0� data of themixtures in terms of an effective orientation correlation fac-tor geff. The literature data for the dipole moment � of 1-P inthe gaseous state �1.65,76 1.68,15,33 1.71,77 1.80 D �Ref. 78��span a range of values which almost includes the � data ofthe other isomers �1.58 D,16 1.66 D,79 2-P; 1.64 D,80 3-P;1.82 D,81 IP; 1.70 D,82 t-P�. We thus apply Eq. �16� in theform

��0� = ���� +4�NA

3kBT

3��0�2��0� + ��

�� + 2

32

geff�2ctot �17�

to calculate the effective correlation factor geff from the totalconcentration of alcoholic –OH groups, thus from the sum ofconcentrations of the components.

A crucial parameter in Fröhlich relation of the static per-

mittivity is the high-frequency permittivity �� which is not apriori known.83 It is evident that �� should adopt a valuebetween the squared optical refractive index n2 and the ex-trapolated high frequency permittivity ���� of the dielectricspectra. As the latter is also insufficiently known from ex-trapolation of the measured permittivity data we employed��=1.1�n2, as proposed by Dannhauser and Bahe84 as wellas D’Aprano et al.59 Also used in the literature has been11

��=1.05�n2. Such smaller �� would scale up the g and geff

values by a small amount, e.g., by about 5% with 1-P at10 °C and by about 7% with t-P at 10 °C.

The g values for the pure alcohols �Eq. �16�� and geff

values for a 1-P–IP mixture and also the 1-P–t-P mixtures�Eq. �17�� are shown as a function of temperature � in Fig. 9.The correlation coefficients have been derived on the as-sumption of �=1.68 D throughout and ��=1.1�n2, using nvalues from Refs. 59 and 60. Except t-P, the g values of thepentyl alcohols and likewise the geff values of the mixtures ofisomers are distinctly larger than 1, thus indicating preferen-tial parallel arrangement of neighboring dipole moments.This clear tendency in the orientation correlation factor isretained if a somewhat different �� is used in the evaluationof static permittivity data. Likewise retained is the trend ofthe correlation factor of all liquids but t-P to decrease withtemperature. Obviously, enhanced thermal motions tend toreduce the preferential parallel ordering of dipoles. The gvalues of t-P as derived on the assumption of ��=1.1�n2

are marginally smaller than 1 �Fig. 9�. They are somewhatlarger than 1 if ��=1.05�n2 is used in the evaluation ofstatic permittivities. Hence the dipole correlation factor oft-P points at an almost random distribution of the dipolar–OH groups. The idea of a random dipole orientation is sup-ported by the finding that, within the limits of uncertainty,the g-values are independent of temperature. Evidently, in-creased thermal motions cannot further randomize the dipoleorientations, since they are already randomly distributed.

FIG. 8. Product T ·��0� vs � �a� for 2-P �inverted triangles� and t-P�squares�. Full symbols refer to these measurements, open �Ref. 59� andhalf-closed �Ref. 75� symbols disclose data from the literature. Static per-mittivity ��0� vs mole fraction x1 of 1-P �b� for mixtures of this alcohol ���with IP �diamonds� and t-P �squares� at 10 °C.

FIG. 9. Kirkwood orientation correlation factor g and effective correlationfactor geff vs temperature � for pentanols �full symbols� and for mixtures of1-P with IP ��; a� and with t-P ��, x1=0.77; �, x1=0.5; �, x1=0.25; b�.

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D’Aprano et al.60 took �=1.70 D for t-P and found g valuessmaller than ours. In conformity with Raman scatteringresults85 they concluded that a mixture of different speciesexists in tert-pentanol: randomly distributed monomers�g=1�, double hydrogen bonded cyclic dimers with mutuallycompensated dipole moments �g=0�, and single hydrogenbonded linear dimers with partly parallel arrangement of di-poles �g�1�. Such model implies, however, that the relativeconcentrations of the different species do not change withtemperature, so that the overall orientation correlation factorremains constant �Fig. 9, part b�.

Another feature of the orientation correlation factors of1-P–t-P mixtures is their nonlinear variation with mole frac-tion xt. A marginal change �g=0.15 �10 °C� emerges whengoing from 1-P to the mixture with xt=0.25 and even whengoing from xt=0.25 to xt=0.5 ��g=0.17,10 °C�, but thevariation is large at higher concentration of t-P ��g=1.27between xt=0.75 and xt=1�. Hence evidently, at high1-pentanol content tert-pentanol is integrated without notice-able disturbances in the alcohol structure. Likely, t-P mol-ecules associate as terminal molecules at chainlike 1-P clus-ters.

C. Dielectric relaxation time and activation energy

In Fig. 10 Eyring plots86,87 of relaxation times of thepentyl alcohols and of the isomolar 1-P–t-P mixture aregiven along with data for ethanol and 1-hexanol from theliterature.2 Except for 2-P and 3-P at high temperatures,where a small curvature emerges, the different series of datadisplay a straight line, thus pointing at an underlying thermalactivation process. The slope of most lines is quite similar.

Ethanol, however, shows a noticeably smaller slope and tert-pentanol a significantly larger one than the other alcohols.We shall return to this point below. Let us first consider therelaxation times in the light of the wait-and-switch model31

of associating liquids. In this model the dominating part ofthe dielectric relaxation time is the period for which a dipolehas to wait until a suitable partner for a new hydrogen bondappears. The virtual reorientation time is on the order of just0.1 ps.88–90 Hence the reorientation itself resembles a switch-ing.

Since the formation of a new hydrogen bond, and thusthe reorientation of the dipolar groups or molecules, is linkedto the availability of a new partner, the wait-and-switchmodel links the dielectric relaxation time to the concentra-tion of H-bond acceptors and donators. In the case of alco-hols �̂ is thus assumed to be controlled by the concentrationof hydroxyl groups. If the fluctuations in the local concen-tration of these groups are assumed to be thermally activated,the dielectric relaxation time, according to

�̂ =h

kBTCf exp��G#/RT� �18�

may be related to an Eyring relation,86,87 with �G#=�H#

−T�S# denoting the Gibbs free energy. Here Cf is a configu-rational factor almost independent of T, R=kBNA is the gasconstant, kB and NA denote Boltzmann’s constant and theAvogadro number, respectively. For the pentanols the valuesof the activation enthalpy �H#, as taken from the slope in the�̂ ·T-versus–T−1 relations �Fig. 10�, are given in Table IV; forthe 1-P–t-P and 1-P–IP mixtures the �H# values are shownin Fig. 11, part a. Also given in the inset �b� of that figure are

FIG. 10. Eyring plot of the dielectric relaxation time for pentanols �fullsymbols; �, 1-P; �, 2-P; �, 3-P; �, IP; �, t-P�, ethanol ��2�, hexanol��2�, as well as the isomolar 1-P–t-P mixture ���.

TABLE IV. Activation enthalpies �H# of pentanols as derived from the relaxation times �̂ �Fig. 10� of theprincipal �low-frequency� dielectric relaxation process.

Alcohol 1-P 2-P 3-P IP t-P

�H#

�kJ/mol� 28.6 34.2 39.7 29.1 45.2

FIG. 11. Activation enthalpy �H# of the principal dielectric relaxation pro-cess �Eq. �18�� shown as a function of mole fraction x1 �a� for mixtures�open symbols� of 1-P ��� with t-P ��� and IP ���. The inset shows �H#

data of a series of normal alcohols CH3�CH2�n−1OH, n=1, . . . ,11, as a func-tion of n �b; �, this paper; �, Ref. 2; �, Ref. 91�. The dashed line repre-sents Eq. �19� with �HCH2

# =3.5 kJ /mol.

094508-8 Kaatze, Behrends, and von Roden J. Chem. Phys. 133, 094508 �2010�

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the activation enthalpies for the series of normal alcoholsfrom methanol to undecanol. The �H# value for 1-P nicelyfits to the literature data, which continuously increase withthe length of the hydrocarbon part of the alcohol molecule.Assuming the activation enthalpy of normal alcohols to becomposed of three terms2

�H# = �HOH# + �HCH2

# + �HCH3

# �19�

a contribution �HCH2

# =3.5 kJ /mol has been found for each–CH2– group at n�8. The significant role of the methylgroups in the activation enthalpy barrier controlling the prin-cipal dielectric relaxation process of normal alcohols hasbeen taken an indication that the whole molecules are in-volved in this process. This view is in line with the wait-and-switch model: the appearance of a partner suitable for a newhydrogen bond is governed by diffusion and thus by the sizeof the polar molecules. Our results for the pentanol isomers�Table IV� show that there is also a considerable effect ofmolecular shape in the activation enthalpy.

Within the series of 1-P–IP mixtures, the data betweenthe almost identical �H# values of both pure pentanols dis-play a light minimum �Fig. 11�, likely suggesting a smalldisturbance in the hydrogen network structure of the mix-tures. In contrast, an almost steplike change arises in theactivation enthalpies of the 1-P–t-P series. This feature cor-responds with the behavior of the dipole orientation correla-tion factor as it likewise reveals that only small variations inthe liquid structure result if small amounts of a componentare added to the other one. Obviously, however, the binary1-P–t-P system undergoes a significant change in the mo-lecular structure at mole fractions x1 between 0.3 and 0.5.

The latter finding may be alternatively discussed assum-ing the principal dielectric relaxation to reflect reorientationof hydrogen-bonded clusters as a whole. The relaxation timeshould then follow the viscosity of the liquid, as predicted,for instance, by the Debye relation66

�� = 4�a3�s/�kBT� �20�

with intrinsic relaxation time92

�� = �̂��� + 2�/���0� + 2� . �21�

In Eq. �20�, parameter a denotes the radius of the clusters,assumed to be spherically shaped and to perform rotationaldiffusive motions in a viscous continuum. The ���s data con-dense indeed on a much narrower range than the dielectricrelaxation times, e.g., 0.04 mm2 /N���s0.06 mm2 /N at10 °C, whereas 0.63 ns�̂1.7 ns. However, the clustervolume 4 /3�a3 following from Eq. �20� is as small as66 Å3, which compares to the volume �V=178 Å3 of asingle 1-P molecule. We mention that relaxation times��= �̂ /g, as following from Eq. �2�, likewise span a some-what smaller range of values �0.42 ns�̂ /g0.65 ns,10 °C� than the �̂ values themselves. Neverthe-less they seem not define a genuine time that could reflect afundamental step in the dielectric relaxation of pentanols.

V. CONCLUSIONS

The principal relaxation term in the dielectric spectra ofpentanols reveals significant differences in the structure andreorientation dynamics of isomers, indicating a substantialeffect of molecular structure on the hydrogen bond networkof alcohols. Since the degree of hydrogen bonding decreaseswith temperature, the differences in the dielectric propertiesof the alcohol isomers become smaller.

The impact of the spatial arrangement of hydrocarbongroups on the hydrogen bond formation of the hydroxylgroups is eminently demonstrated by the dielectric param-eters of t-P which deviate from those of the other pentanolsby a considerable amount, e.g., ��0�=6.3, t-P; ��0�=16.9,1-P; �̂=0.63 ns, t-P; �̂=1.7 ns, 3-P; 10 °C. Evaluation ofthe static permittivity in terms of Kirkwood–Fröhlich theoryyields a dipole orientation correlation factor g close to 1,independent of temperature, thus evidencing an almost ran-dom distribution of dipole orientations. In contrast, g valueson the order of 3 at 10 °C result for the other pentanols,evidencing predominantly parallel alignment of dipoles inchainlike hydrogen bonded structures. In conformity withour idea that hydrogen bonding is reduced by thermal agita-tion the correlation factors of these other pentanols decreasewith temperature �g=2.7,1-P;g=2.1,3-P;60 °C�.

The small dielectric relaxation time �̂, in combinationwith the exceptionally large activation enthalpy �H#

�=45.2 kJ /mol�, of t-P is in accordance with the wait-and-switch model of dielectric relaxation. The finding that, withinthe series of normal alcohols, an additional –CH2– groupadds another 3.5 kJ/mol to �H# has been taken a confirma-tion of the central idea of that model: the dominating part inthe dielectric relaxation time is the period for which hydro-gen bonding site has to wait until a suitable new H-bondpartner occurs. This period depends on the diffusion coeffi-cient and thus not just upon the H-bond enthalpy but also oninteractions between hydrocarbon groups. Obviously, thestructure of the hydrocarbon part of the pentanols is an im-portant factor in determining these interactions. Likely, thesmall relaxation time of t-P is due to a small prefactor Cf inthe Eyring relation �Eq. �18�� of this less associated alcohol.

For 1-P–t-P mixtures parameter G in the Grunberg–Nissan relation of viscosity points at strong interactions be-tween the components of the binary mixtures. As deducedfrom the static permittivity and activation enthalpy data, thevariations in the liquid structure seem to be small when smallamounts of t-P are added to mixtures of high 1-P content.This result suggests that t-P can be rather easily fit into the1-P structure, probably t-P molecules associate as terminalpartners to H-bonded complexes. When 1-P is added to t-P orto mixtures of high t-P content, the static permittivity in-creases substantially but �H# remains almost constant. Theformer finding reveals a significant enhancement in the par-allel alignment of dipoles while, at the same time, stronginteractions between the alcohol molecules impede diffusion.

ACKNOWLEDGMENTS

We are indebted to Gisa Kirschmann-Schröder for helpwith the drawings.

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