ELECTRODILATOMETRY OF LIQUIDS, BINARY LIQUIDS, ANDSURFACTANTS

MANIT RAPPON*, RICHARD M.JOHNS, and SHIH-WEI (ERWIN)LINDepartment of Chemistry, Lakehead University, Thunder Bay,Ontario, P7B 5E1 Canada. *Corresponding author:manit. rappon@lakeheadu. ca

Abstract. When a liquid is subjected to high electric field, its volume change can be increased ordecreased depending upon the liquid under investigation. A new technique has been developed from ourlaboratory to measure the relative volume change per and is known as “Electrodilatometry (ED) ”which may be expressed as:

where R is known as “Electrodilatometric Effect (EDE)”, V and are the

volume of liquid with and without the field, respectively. ED is one of the nonlinear effects such aselectro-optic Kerr effect, the electrostriction, dielectrophoresis, nonlinear dielectric effect (NDE). Ed isfound to be very sensitive to hydrogen-bonded liquids. It has been applied to study pure liquids, binarymixtures, alcohols, and non-ionic surfactants such as Triton X-100. The signs of EDE (R), Kerr constant(B) and NDE are compared and contrasted. A few models have been used to calculate R withlimited success. Not only can ED be used with smaller molecules but it should also be a potential tool to

study polymer solutions and supramolecular assemblies.

1. Introduction

The change in pressure following the impact of high electric field on a liquid isknown in the literature as electrostriction and is the topic of many investigations[1,2]. This method suffers from one drawback i.e. the choice of the referencepressure varies from one laboratory to another [3]. This makes it difficult tocompare experimental results. In order to avoid this, we are investigating theimpact of high electric field on the change in the volume of a liquid. While therewere a couple of reports in the old literature that electric fields were used to studysome liquids as cited in ref.[4], these investigations did not look at the volumechange as we proposed hereunder. To the best of our knowledge, the electric field-induced volume change is a new technique and it is proposed that this newtechnique, originated from our laboratory, be called “Electrodilatometry” (ED).The change in volume was found to vary directly as the square of the externallyappliedelectric field strength Thus, ED is one of the nonlinear methods and is similartothe Kerr effect [5], nonlinear dielectric effect (NDE) [6,7], electrostriction,dielectrophoresis (non-uniform field) [8] and other nonlinear methods [9]. These

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S.J. Rzoska and V.P. Zhelezny (eds.), Nonlinear Dielectric Phenomena in Complex Liquids, 367-377.© 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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methods share one common feature with ED in that application of high electricfields is required. They differ only which physical parameter is used to monitor thechange. For example, for ED it is the volume change; for Kerr effect, the differencebetween refractive indices for NDE , the change in relative permittivityetc. Thus for a given sample of liquid subjected to an applied field, ED can yieldunique information on which may be integrated with information provided byKerr effect and NDE. The presentation is organized in the following manner: thetheories related to ED are presented in section 2, the experimental procedure(section 3), results (section 4), discussion (section 5), and the conclusions are drawnin section 6.

2. Theories

The volume of a liquid is changed when it is subjected to high static electricfield. Such a volume change has been derived. In the case of fluid flow into aregion from the source of constant chemical potential, the volume change is given[10], i.e.

Where V,P,T are the volume, pressure and temperature, respectively; is theliquid volume without the field, and E is the applied electric field. Integration ofequation (1) yields:

Where is the relative permittivity of liquid. Left hand side of equation (2)

may be written as where and V is the volume of liquid

under the applied field. R represents the relative volume change per and it ishenceforward called the “Electrodilatometric Effect ” (EDE). In anotherderivation, attempts are made to include some geometry of a dielectric[1] as shownin equation (3):

Here, 1/K is the compressibility of the liquid, and n is the parameter depending onthe geometry of the dielectric, A model which allows for change in molecularvolume when a dielectric ellipsoid is placed under electric field, has been advanced[11] as shown:

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Where is R evaluated with maximum semi-principal axis (a) parallel to thefield, and is the depolarizing factor of the ellipsoid. is the internal bulkmodulus of the molecule, is the internal permittivity and is the permittivity ofvacuum.

In fact, the observed volume change for some liquids may be due toother contributions, in addition to the classical electrostriction as inequation (5):

Where is the volume change due to interactions; and is thevolume change due to structural interactions. is the volume change due tothe deformation of the dielectric without changing its shape [1], or electrically-induced distortional strain [8]. is calculated from (2) and the netcontribution of this term will be small and negative [4]. is the volumechange due to, e.g. the induced dipole-induced dipole, dipole-induced dipoleinteractions. It has been shown that for the case of ionic interactions involvingcentral metal ion and the surrounding solvent molecules, this term is large andnegative [12]. is the volume change due to structural interactions. It iscaused by molecules with permanent dipole moments, which respond to an externalelectric field by realignment so as to reduce their potential energy, and sometimesknown as orientational polarization [8]. This process may lead to several volumechanges as a consequence, e.g. inter- and intra- steric interactions, forming andbreaking of H-bonds, changes in molecular conformation, etc. For a hydrogen-bonded system, is likely to be large and positive due to the net change in thenumber of hydrogen bonds as the molecules are forced to realign with the field.

3. Experiment

The detailed construction of ED cell and its assembly was provided earlier [13]and is briefly described Two stainless steel cylindrical electrodes, inner one wassolid and the outer one hollow. They were assembled concentrically leaving anelectrode gap of 0.105 cm. They were sufficiently large in order to sink any Jouleheat generated during a measurement. Two electrically insulating plates were usedto cap securely both ends of the electrodes. Liquid sample was introduced throughan inlet port located at the bottom of the cell and it moved up the electrode gap andout through the outlet port at the top of the cell into a connecting line. The latter wasconnected to a glass capillary. The liquid sample partially filled the capillary. Waterjackets were used for the cell and the capillary so that the temperature was keptconstant and controlled to ±0.02K by a circulating bath.

The apparatus was assembled as shown schematically in Figure 1. Laser light(Spectra Physics) at 632.8 nm, passed through a cylindrical lens and was converted

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to a vertical line and focused on to the sample liquid level in the capillary. Theimage of the level was captured by a linear charge-coupled device, CCD (TexasInstruments, TC-104).The output from the board was fed into an A/D board of a PC. Regulated high DCvoltages were generated from a power supply (Bertan, 205A-20R). Typical fieldstrengthused was in the range depending upon the sample used. The

Figure 1. A diagram of ED apparatus (See text for details).

change in pixel number was converted to physical height by calibration. The netchange in height was used to calculate the The system is sensitive to change in

Pure liquids used were of spectroscopic grade and were dried by molecularsieves (heptane and cyclohexane by sodium wire) and filtered. Triton X-100 [TX-100] (t-octylphenoxypolyethoxyethanol)(Aldrich)

with and the water content was0.3% by weight. The reduced form of TX-100 was obtained from the same sourcewhose structure is similar to the regular TX-100, except the phenyl ring washydrogenated to cyclohexyl.

Figure 2. Sample output of cyclohexanol, field off (lower) and on (upper).

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4. Results

Figure 2. shows a typical output of a signal in a measurement in which thepixel number is plotted against the time (arbitrary unit). Figure 3. shows a sampleplot of the difference in pixel number against the square of the applied voltage,Table 1. is a collection of R values for various liquids at 298 K, unless statedotherwise. For some hydrogen-bonded liquids, e.g. some pentanols, the binarymixtures with n-heptane are also shown because of the availability of the Kerrconstants. In addition, the values of calculated R from equation (2) are shown for

some liquids where the data for are available in

the literature. Some data for the Kerr constants (B) and the nonlinear dielectriceffect

Figure 3. Plot of difference in pixel number (arbit.) vs.

are also collected in the same Table for comparison. Table 2. shows thevarious R values at 293 K for each isomer of pentanols mixed with n-heptane atvarious mole fraction (F). Table 3. is a collection of R at 298 K values for a seriesof cyclohexanol mixed with n-heptane. The values of R for TX-100 in cyclohexaneat various concentrations (mole/kg) and at 298 K are collected in Table 4.

5. Discussion

The discussion is divided into 5 sections: 5.1 General aspects, 5.2 Pure andhydrogen-bonded liquids, 5.3 Pentanols and cyclohexanol, and 5.4 Triton-X 100solutions.

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5.1 General aspectsIt may be seen from Figure 3. that the plot of the change in height (hence, the

volume) is directly proportional to This shows that Electrodilatometry (ED) isone of the nonlinear techniques similar to Kerr effect and nonlinear dielectric effect.

5.2 Pure and hydrogen –bonded liquidsFrom Table 1., if the signs are neglected and only the magnitude of R is

inspected by normalizing against the carbon disulfide, the normalized magnitude iscomparable to when the Kerr constant (B) is normalized against its carbon disulfide,for most liquids. However, there are two liquids on the list which do not followsuch a trend, i.e. nitrobenzene and 2-pentanol in n-heptane at F=0.601. Whilenitrobenzene has very large B value, the 2-pentanol mixture has very large R value.It shows that for some hydrogen-bonded systems, ED is a very sensitive technique.

If the attention is now paid to the signs of R (excluding the t-pentanol), it may beseen that the sign of experimental R value is opposite to the sign of B and the sign of

for those liquids (and mixtures) where these values are available. While theexact reasons are not known, only plausible suggestions to this are hereby given.

At this time, only the signs of R and B are discussed first, and the signs ofare to be discussed later. Take the case of a non-hydrogen-bonded liquid, thenegative valueof R suggests that the volume decreases in the presence of the applied field. Theexistence of the high electric field gives rise to high pressure. The latter forces themolecules to be closer, hence the observed volume decrease. This is accompaniedby the B value being positive, which suggests that the refractive indicesOn the other hand, for a hydrogen-bonded liquid, the volume is increased underthe field (R is positive). To account for this, it is plausible that the electric fieldforces the molecules to reorientate and in so doing, the system experiences the netloss of the number of hydrogen bonds. This lessened intermolecular forces, couldtranslate into the observed expansion of the volume under the field. This issimilar to the term “structure breaking effect” which was used in the magneto-optical investigations of associated liquids [19]. This positive R is accompaniedby (B being negative).The sign of NDE is the same as the sign of B, for all the liquids wherethese values are available. While some forms of explanations may be offered toaccount for the sign of R and B, it is, however, more subtle to pin down the originof the sign of NDE. This is because the sign of NDE depends upon an intricatebalance of several

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competing factors [18] which are briefly summarized. (a) At large fieldthe contribution from the higher terms of the Langevin function must be taken intoaccount. This leads to the “normal saturation” and its contribution to isnegative. (b) In an equilibrium, the field shifts the equilibrium in favour of themore polar species. This is called the “anomalous saturation” and makes a positivecontribution to the (c) For species with anisotropic polarizability, the axis ofhighest polarizability is forced to align in the direction of the field (which is relatedto the Kerr effect). Its contribution to the is positive. (d) Contributions fromthe first and second hyperpolarizabilities should also be considered andtheir contributions to can be either negative or positive depending on theparameters and Some of these factors were used to explain the anomalousbehaviour of NDE for solutions of 1-penatnol [20].

For the t-pentanol, R is positive (like other hydrogen bonded liquids) and is thesame sign as B (contrary to other hydrogen-bonded liquids on the list.). This uniquesituation may be due to the unique ability of t-pentanol to form a cyclic trimers (notexcluding higher cyclic multimers). These trimers can also form stacking structurein which one ring stacks on top of another and many rings may be involved. Eachring is staggered from the lower one by about 60°. This facilitates two things; firstly,the formation of inter-ring hydrogen bonds by the bifurcated hydrogen bonds of Oand H atoms; secondly, the bulky t-pentyl groups are displaced further away fromeach other. This structure is consistent with the results of our studies from othertechniques: i.e. Kerr effect [21], viscometry [22], NMR [23], and photochromicreaction probe [24].

The calculated R [from equation (2)] for some liquids and their values areapproximately 2 orders of magnitude lower than the experimental ones. For all theliquids calculated, all of them gives negative sign. This is the same as theexperimental ones, except for chloroform for which the sign is positive. The latter is

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explained in the next section. While the signs of experimental and calculated R[based on equation (4)] are in agreement, the discrepancy in their magnitude has yetto be resolved. The discrepancy in magnitude may be partly due to the contributionto volume change from other factors as shown in equation (5), i.e. and

in addition to

5.3 Pentanol and cyclohexanolFor pentanols in n-heptane as shown in Table 2., all R values are positive, i.e. the

volume is increased under the applied fields. Some of the concentrations could notbe measured due to difficulties in obtaining concordance readings, and for t-pentanol, the changes at low concentrations are too small for the measurements. Atlow concentrations the changes in R values are small and tend to increase withincreasing concentration. This suggests that for 1-, 2- and 3- pentanol, the linearmultimers tend to dominate. However, for 2-pentanol at F=0.800, R= 5305

which is the greatest among the measured values. To account for this, it isnecessary to use the linear model of multimers where O of one molecule isconnected to H of another by H-bond. This situation is repeated to form a chainwhose “pendant” groups are the various alkyl groups of the alcohols, i.e. n-pentyl,

and for 1-,2-and 3-pentanol,respectively. It is likely that the unsymmetrical alkyl groups attached to the C with –OH group, interact with each other by way of the intra- and inter- chain interactionsas the molecules are forced to realign by the field. Such interactions make positivecontribution to the terms A similar contribution for 1- and 2- pentanol isexpected to be smaller. For the case of t-pentanol, only measurements at highconcentrations are obtained and their values are small. This information togetherwith results from other techniques as mentioned earlier, indicates that the cyclicmultimers are dominant. One of the possibilities is the cyclic trimers . However, itdoes not exclude other higher cyclic multimers. For the cyclic trimers, a model maybe visualized by taking the chair form of a cyclohexane and replace all the six Catoms with alternating O and H atoms. Each of the three t-pentyl groups is attachedto each O atom. These rings can form stacking structure as mentioned in section 5.2.To account for such a low magnitude of R, it is plausible that each stacking structureresponds to the applied field as a unit with minimum disruption of the bifurcated H-

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bonds. Consequently, the is small and the volume increase is found to be thesmallest among the pentanols at the same concentrations.

For cyclohexanol, R is positive and small and remains unchanged until F=0.60.This suggests that probably a similar stacking associates may be formed similar tothe case of t-pentanol, except that the t-pentyl group is replaced by a bulkycyclohexyl one. At higher concentrations, R increases with increasing concentrationuntil F=1.0. Such a rapid increase in R implies that a different type of associatesmay be formed.

5.4 Triton X-100ED has been extended to hydrogen-bonded surfactants: Triton X-100 (regular)

and Triton X-100 (reduced) [25]. Due to limited space, only the regular form ofTriton X-100 (TX-100) is hereby given. From Table 4, R values may be divided into3 groups.

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(a) From m=0.2-0.42, here R increases with increasing concentration. It is plausiblethat reverse micelles are formed in this region. When more surfactant is added, moremicelles formed and led to the increase in R. This view is in agreement with QELS[26] and dye probe [27]. (b) In the region m=0.69-1.6, R values are greater thanregion (a) but their values are hardly changed. If the associates were to be of thereverse micellar type as in (a), we should have observed the increase in R withincreasing concentration. It is likely that the associates change to a new type with arod-like structure. This may be formed from a cyclic multimers, which may bestacked together similar to the t-pentanol case. As more surfactant is added, the rodsare extended in a one-dimensional growth. In the presence of a field, only the

and are the major contributions to R. So only small change in Rwith increasing concentration is observed, (c) From m=3.3-12, here R valuesincrease from region (b) but stay more or less the same with increasingconcentration. It is likely that the associates change to an inverted bilayers shape.One possibility would be the association of the –OH groups in one plane with theirtails perpendicular to it. The –OH groups of such a plane can be realigned with –OHgroups of another plane. The growth can be extended in two directions (two-dimensional growth). When the field is applied the dipolar groups such as –OH and

are forced to realign and this should make a positive contribution to thein addition to and

6. Conclusions

It has been shown that the new technique of ED can provide unique andvaluable information on liquids. The information can be used to integrate with othernonlinear techniques such as Kerr effect and NDE in order to enhance ourunderstanding of liquids at the molecular level. ED is particularly sensitive to H-bonded systems. It has been used to investigate simple liquids, binary mixtures andsurfactants. It should also be very useful to study supramolecular assemblies [28]and polymer solutions.

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12. Borsarelli, C.D., Corti,H., Goldfarb, D. and Braslavsky, S.E. (1997) Structural volume change inphotoinduced electron transfer reactions, J. Phys. Chem. A. 101,7718-7724.13. Rappon, M. and Johns, R.M. (1999) Molecular association of pentanols in n-heptane V:electrodilatometric effect, J. Mol. Liquids 80, 65-76.14. Crossley, J., Morgan, B.K. and M. Rujimethabhas (Rappon) (1979) New Kerr cell for low-temperature measurements, Rev. Sci. Instrum. 50, 1400-1402.15. Krupkowski, T., Jones, G.P. and Davies, M. (1974) Permittivity increments in non-dipolar solventsdue to high electric fields, J. Chem. Soc. Faraday Trans. II 70, 1348-1355.16. Rujimethabhas (Rappon), M. and Crossley, J. (1980) Temperature dependence of electro-optic Kerreffect for liquids at 632.8 nm, Can. J. Phys. 58, 1319-1325.17. Piekara, A. (1962) Dielectric saturation and hydrogen bonding, J. Chem. Phys. 36,2145-2150.18. Böttcher, C.J.F.(1973) Theory of Electric Polarization, Vol.1, Elsevia, Amsterdam, pp. 289- 326.19. Dawber, J.G., (1984) Magneto-optical rotation studies of liquid mixtures, J. Chem. Soc. FaradayTrans. I 80, 2133-2144.20. Malecki, J. (1962) Dielectric saturation in aliphatic alcohols, J. Chem. Phys. 36, 2144-2145.21. Rappon, M. and Greer, J. M. (1987) Molecular association of pentanols in n-heptane I: Temperaturedependence of Kerr effect, J. Mol. Liquids 33, 227-244.22. Rappon, M. and Kaukinen, J.A. (1988) Molecular association of pentanols in n-heptane II : Viscositiesas a function of temperature covering the low temperature range, J. Mol. Liquids 38, 107-133.23. Rappon, M. and Johns, R.M. (1989) Molecular association of pentanols in n-heptane III: Temperatureand concentration dependence of proton NMR chemical shift of hydroxyl group, J. Mol. Liquids 40, 155-179.24. Rappon, M., Syvitski, R.T. and Ghazalli, K.M. (1994) Molecular association of pentanols in n-heptane IV: A photochromic reaction probe, J. Mol. Liquids 67, 159-179.25. Rappon, M. Electrodilatometry of Triton X-100 (reduced form), to be submitted for publication.26. Zhu, D.-M. Feng, K.-I. and Schelly, Z.A. (1992) Reverse micelles of Triton X-100 in cyclohexane, J.Phys. Chem. 96, 2382-2385.27. Zhu, D.-M. and Schelly, Z.A. (1992) Investigation of the microenvironment in Triton X-100 reversemicelles in cyclohexane, using methyl orange as a probe, Langmuir 8, 48-50.28. Lehn, J.M. (1995) Supramolecular Chemistry, VCH, Weinhein

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