ORIGINAL CONTRIBUTION

Diffusion properties of liquid crystal-based microemulsions

Alexander Shakhov & Jörg Kärger & Rustem Valiullin

Received: 28 March 2014 /Revised: 20 May 2014 /Accepted: 22 May 2014# Springer-Verlag Berlin Heidelberg 2014

Abstract Microscopic diffusion processes in thermotropic5CB liquid crystals (LC) with imbedded surfactant-stabilizedwater microemulsions are studied using pulsed field gradientnuclear magnetic resonance (PFG NMR). The experimentsare performed in a temperature range around the isotropic-nematic transition temperature of the LC. The temperaturedependence of the diffusivities of the liquid crystal and sur-factant molecules remains almost unchanged in the wholetemperature range studied. With varying water content, thediffusivities of the surfactant molecules are found to be almostinvariable, indicating that the surfactant diffusivities remainessentially unaffected by whether a microemulsion is formedor the surfactant molecules diffuse as individual species. Atthe same time, the formation of the microemulsion is found tobe crucial for the macroscopic separation of the mixture intoLC- and surfactant-rich phases.

Keywords Diffusion . Liquid crystals .Micelles .

Microemulsions . NMR diffusometry

Introduction

Small objects like colloids imbedded in liquid crystals (LC)may exhibit very complex phenomena due to emerging elasticinteractions, resulting from anisotropic orientational fields[1–4]. On the other hand, theymay give rise to a rich structuralbehaviour caused by local disturbances of the director fieldsclose to the colloids surfaces [5, 6]. This topic has attractedsubstantial interest in the last decades, and several interestingphenomena have been described in the literature. Among

them, it has recently been reported that surfactant-stabilizedwater microemulsions dissolved in nematic phases may in-duce the formation of the so-called transparent nematic (TN)phases [7]. In that work, inverse micelles with the size ofseveral nanometres dispersed in a thermotropic liquid crystal(pentylcyanobiphenyl, 5CB) were prepared. The inverse mi-celles were composed of water and didodecyl dimethyl am-monium bromide (DDAB) as a surfactant. With the aid ofdifferential scanning calorimetry, it was shown that the thus-prepared system exhibits, upon cooling from high tempera-tures, two-phase transitions. At high temperatures, above theisotropic-nematic transition temperature for LC (TIN), thesystem was found in the isotropic state. In particular, themicelles were homogeneously distributed in the LC whichalso possessed no orientational order. Upon cooling, the firsttransition occurred around 31 °C. It was associated with theemergence of a nematic order in the close vicinity of themicelles: interaction with the micelle surfaces gave rise tolocal ordering of the LC molecules. At the same time, thesystem appeared to be isotropic on a larger, macroscopic scale.This local ordering was attributed to the existence of a strongdirectional coupling between the LC and the surfactant mol-ecules. This state of the system was referred to as the trans-parent nematic (TN) phase.With further temperature decrease,the second transition was identified near 29 °C, which is closeto the temperature of the isotropic-nematic transition TIN forbulk LC. It was noted that, upon this second transition, thesystem separates macroscopically, within several hours, intotwo phases consisting of a nematic LC phase and a TN phaseconcentrated with the microemulsion.

To provide an independent prove for the existence of theTN phase, the time correlation function of the compositionfluctuations were probed using polarized light scattering. Thediffusion coefficient (10−12 m2 s−1) obtained from the thus-assessed decay rates for the inverse micelles in the tempera-ture range where the TN state exists was found to be of the

A. Shakhov : J. Kärger : R. Valiullin (*)Institute of Experimental Physics I, Faculty of Physics andGeosciences, Leipzig University, Leipzig, Germanye-mail: valiullin@uni-leipzig.de

Colloid Polym SciDOI 10.1007/s00396-014-3288-7

order of the value estimated by using the Stokes–Einstein law.It was anticipated, however, that the dynamics of the micellesin this state may not be diffusive, and further, more detailedstudies were suggested [7].

A series of subsequent work were devoted to the confir-mation of the existence of the TN phase and to establishing thedriving mechanisms for the phase separation [8–12]. Belliniet al. employed static and dynamic light-scattering measure-ments to follow separately the contributions to the signalsmeasured from the paranematic fluctuations and from themicelles [12]. Based on the experimental results thus obtained,it was suggested that the fluctuations in orientational orderingcontribute to the attractive interaction of the micelles which,further on, leads to macroscopic separation. Evidence on theattractive interaction was taken from the observation that theexperimentally determined diffusivities slow down faster withdecreasing temperature than they would decrease followingthe prediction of the Stokes–Einstein equation. This findingwas considered as an indication that the attractive interactionbetween the micelles has a notable effect already at tempera-tures higher than the temperature of the isotropic-nematictransition TIN. These results were further corroborated bysmall-angle neutron and X-ray scattering experiments [8].They, first of all, confirmed the occurrence of thenanometre-sized inverse micelles of spherical shape. Second-ly, the experiments revealed an increase of the paranematicfluctuations upon approaching the isotropic-nematic transitiontemperature TIN. Lebar et al. used deuteron nuclear magneticresonance (DNMR) microimaging and line analyses to obtaininformation on the phase separation and on the alignment ofthe LC molecules [9]. On considering the phase separation, itwas found to proceed extremely slowly, on the time scale ofhours. It was further attempted to directly assess the localnematic orientation based on the line shape, which is largelydetermined by the internuclear magnetic dipolar interactionsand is, therefore, very sensitive to molecular alignments withrespect to the external magnetic field [13]. Molecular diffu-sion, however, gives rise to averaging out of the interactionanisotropy. The resulting line width is thus determined by bothlocal order and the diffusion rate. To assess the local order, onehas to independently know the diffusivities. The authors used,therefore, some reasonable estimates for the diffusion rates ofthe LC molecules. The experimental line width data revealed,however, no peculiarities around the transition temperature,questioning the formation of the TN phase. The latter problemwas further addressed using dielectric spectroscopy [10, 11].This technique has been proven extremely sensitive to molec-ular and collective dynamics in a broad range of frequenciescovering many decades [14]. As a main finding of this work, anew relaxation mode at frequencies of about two orders ofmagnitude lower than those of bulk-like relaxation was de-tected. This mode was anticipated to originate from the LCmolecules effectively confined between the micellar cages.

This finding was considered to be in line with the occurrenceof the TN phase. Notably, analysis of the demixing behaviourimplies knowledge of the diffusion properties of the micelles.

In all these works, particular attention has been paid tounderstanding the microscopic dynamics of the mixture com-ponents and to using this information for a better understand-ing of the structure formation and the system behaviour. Thepulsed field gradient technique of nuclear magnetic resonance(PFG NMR) is known as a most suited experimental methodto probe directly the rates of molecular propagation underequilibrium conditions [15, 16]. Being very sensitive to mo-lecular rearrangements on the time scale from a few to a fewthousands of milliseconds, it may provide information aboutdynamic processes occurring in soft matter, complementary toall experimental techniques referred to in the introduction[17–20]. Its potentials are exploited here to get deeper insightinto the microscopic dynamics of the LC-microemulsion com-plexes. In particular, with this study, we have aimed at probingthe diffusive dynamics of the mixture components upon tem-perature variation. It has been expected that the diffusivities ofthe inverse micelles can reflect tiny changes in the localenvironment due to variations of the local orientational ordergiving thus rise to changes in the viscosity.

Materials and methods

The LC-microemulsion mixture used in this study were com-posed of 4 ′-Pentyl-4-biphenylcarbonitr i le (5CB,CH3(CH2)4C6H4C6H4CN) liquid crystal, surfactantd i d e c y l d ime t h y l ammon i um b r om i d e (DDAB ,[CH3(CH2)9]2N(CH3)2Br) and deuterated water. The LC(98 % purity) and surfactant (98 % purity) were purchasedfrom Sigma-Aldrich (Germany) and used as it is, withoutfurther purification. We quantify the compositions of theLC-microemulsion mixtures used in this work in terms ofthe weight fraction ϕ of DDAB in the micelles and of theweight fractionα of the micellar phase (DDAB +water) in theLC.

In the present work, three different samples with differentcompositions were studied. The formation of the inversemicelles was proven earlier to occur in the range of the weightfractions α between 5 and 15 wt% of DDAB + water in LC[8]. Therefore, we prepared two samples (MD15 and MD6,see Table 1) with weight fractions representing the two limit-ing cases of the range yielding the transparent nematic phaseaccording to the phase diagram reported earlier [7]. One of thesamples, Mx13, contained roughly the same amount ofDDAB as MD15, but no water was added to exclude theformation of micelles. In this way, the transport of individualDDAB molecules in the LC could be probed. With the knownweight fractions, the characteristic radius a of the micelles canbe estimated as a=δ(3−2ϕ)/ϕ, where δ is the length of the

Colloid Polym Sci

surfactant molecule (~1.25 nm). On the other hand, the pa-rameter α defines the inter-micellar distance d, namely, d=a(4π/3α)1/3. The calculated values for a and d are as wellgiven in Table 1. It may also be noted that the length of a 5CBmolecule is about 2 nm. Figure 1 shows the localmesostructure of the samples under study schematically.

It is important to mention that, before measurement, everysample was preliminarily stirred in an ultrasound bath at hightemperatures. As it was shown in [9], simple shaking ofsamples would not suffice to provide reproducible results.Therefore, the same procedure of sample preparation wasrepeated in our experiment every time before any measure-ment was done.

Diffusion properties of the samples used were probed usingthe pulsed field gradient (PFG) technique of NMR. Its variousaspects can be found in numerous textbooks [15–17]. Here,we briefly recapitulate some basics which will be sufficient forthe purposes of this work. The phenomenon of NMR is basedon the occurrence of a precessional motion of nuclear spinsplaced in an external magnetic field. The (Larmor) frequencyω is given as the product of the field strength B0 and thegyromagnetic ratio γ of the nuclei under study. Differentnuclei possess different γ allowing frequency-based signalseparation. In our work, we have performed 1H NMR exper-iments. By using heavy water as a solvent, it was excludedfrom contributing to the signal measured. By bringing the spinsystem into coherence by a resonant radio-frequency (r.f.)field and by letting the system evolve for a time period τ, thespins will acquire a phase γB0τ. The effect of a subsequentlyapplied, second radio-frequency pulse (or series of pulses) isequivalent to inverting the precessional direction so that, attime 2τ, the initial coherence will again be restored. The thus-formed signal is called the (Hahn) spin-echo.

In PFG NMR, the constant magnetic field is superimposedover two short time intervals by an inhomogeneous field(linear in space with the linearity constant g=dB/dz, where zpoints in the direction of the external magnetic field B0), theso-called ‘field gradient pulses’. The two pulses of width δ areseparated by a time interval t, with the latter often referred toas the diffusion time. The effect of the two gradient pulses is topositionally encode and decode the nuclear spins according totheir Larmor frequencies, or, more precisely, by the phasedifferences γgzδ acquired during δ. Thus, if the spins are

hypothetically immobilized in space, the effects of the twopulses compensate each other, and the spin-echo signal inten-sity is only determined by nuclear magnetic relaxation effects.If, however, the spins interchange their positions by Δz duringt, their contribution to the signal will be attenuated by thefactor cos(γgΔzδ). The overall signal appears as the averageover all spins.

S∝Z

P Δz; tð Þcos γgΔδð Þdz; ð1Þ

where P(Δz,t) referred to as the mean propagator, stands forthe probability (density) that an arbitrarily selected molecule(strictly: spin) within the sample will be shifted, during t, overa distance Δz in the direction of the magnetic field gradient[21]. For spins (or molecules, which bear these spins)performing purely stochastic motion, Eq. 1 results in a simpleexponential function.

Table 1 Compositional and structural details of the investigated PFG NMR samples

Sample Mass of liquidcrystal, g

Mass ofsurfactant, g

Mass ofwater, g

DDAB weightfraction, ϕ

Micellar weightfraction, α

Proton fractions of liquidcrystal/surfactant/water

Micellarradius a, nm

Micellardiameter d, nm

MD15 0.1485 0.020 0.0060 0.77 0.15 0.828/0.172/0 2.4 7.2

Mx13 0.1518 0.022 – 1 0.13 0.817/0.183/0 – –

MD6 0.1530 0.008 0.0012 0.87 0.06 0.925/0.075/0 1.8 7.5

Fig. 1 Schematic representation of the structure of the samples studied:(left) containing water and (right) without water

Colloid Polym Sci

S q; tð Þ ¼ S 0; tð Þexp −q2Dt� � ¼ S0exp −

t2T2

−t1T 1

� �exp −q2Dt

� � ð2Þ

with the notation q=γδg and D standing for the diffusivity. S0is proportional to the number of nuclei, T1 and T2 are the spin–spin and spin–lattice relaxation times, respectively, and t1 andt2 are the time intervals during which the respective relaxationmechanisms are effective in the NMR pulse sequence applied.The 1H spin-echo signal intensity recorded in the PFG NMRexperiments is thus seen to result as an integral quantity overall spins of the sample determined by both their displacementsand the experienced nuclear magnetic relaxation.

All 1H diffusion measurements in this work were per-formed using a home-built NMR spectrometer with a workingfrequency of 400 MHz for protons. The maximal value of thegradient pulses applied was 35 T/m. The 13-interval pulsesequence, in which the gradient intensities were varied at fixeddiffusion times t, was used. If not explicitly stated otherwise,all measurements were performed with a 10-ms diffusiontime. Very short rise and fall times of the pulses allowed tokeep the time interval τ, during which (within the pulsesequence) signal attenuation is determined by transverse nu-clear magnetic relaxation, extremely short (τ=1.2 ms). Themeasurements were performed starting from 50 °C towardslower values. After each temperature change, about 30 minwas given for system equilibration. The equilibration wasproven by applying the Hahn spin-echo sequence and byfollowing the signal intensity change with time to excludeany noticeable signal changes. The latter ones were caused bythe spin–spin relaxation processes, which are very sensitive toany local structure variation on the microscopic level.

Experimental results

Diffusion in bulk liquid crystal

Before presenting the results of diffusion studies with thecomplex mixtures, we provide, for comparison, the data ob-tained for the pure LC. It is important to note that withconventional PFG NMR, requiring the incorporation of suffi-ciently long time intervals during which nuclear magneticspin–spin relaxation processes occur, diffusion measurementsare possible in only the isotropic LC phase. Assessment ofdiffusion properties in the nematic phase requires the applica-tion of more advanced NMR methods [22–24]. These limita-tions are caused by the nuclear magnetic relaxation effects.Above TIN, in the isotropic state of the LC, dipole–dipoleinteraction between the protons of the LC molecules is aver-aged out due to irregular molecular tumbling, yielding rela-tively long relaxation times T2,LC and, hence, an observableNMR signal. Local intermolecular order increases by

approaching the isotropic-nematic transition so that this aver-aging becomes more and more incomplete, giving rise to astrong decrease of T2,LC which excludes any meaningful PFGNMR diffusion experiment.

In the covered range of temperatures, the PFG NMR spin-echo attenuation curves (see Fig. 2) are seen to be of expo-nential shape as described by Eq. 2. The diffusivities deter-mined by fitting Eq. 2 to the experimental data are found to bein a good accord with the literature data reported earlier [22].

Diffusion in liquid crystal-microemulsion crystals

Figure 3 shows the PFG NMR spin-echo attenuation curvesmeasured for the sample MD15 at different temperatures. Incontrast to the attenuation functions shown in Fig. 2, theirshapes deviate strongly from the exponential form given byEq. 2. This was observed for all temperatures, including thehighest one where the system is expected to be in a macro-scopically homogeneous state. One has to be aware of the fact,however, that two ensembles of hydrogen atoms contribute tothe NMR signal recorded residing, respectively, in the DDABand LC molecules. The overall signal does thus result as thesum of two components

S q; tð Þ=S 0; tð Þ ¼ PLC 0; tð Þexp −q2DLCt� �

þ PDDAB 0; tð Þexp −q2DDDABt� �

;

ð3Þ

where PLC(0,t)=SLC(0,t)/S(0,t), PDDAB(0,t)=SDDAB(0,t)/S(0,t) and S(0,t)=SLC(0,t)+SDDAB(0,t). Thus, because the diffu-sivities of DDAB and LC are notably different, the shape ofS(q,t)/S(0,t) can reasonably well be approached by the bi-exponential function given by Eq. 3. As discussed in thepreceding section, the weights PLC(0,t) and PDDAB(0,t) arestrongly temperature-dependent. Most notably, in contrast tothe pure LC sample, PFG NMR measurements could now bealso performed at temperatures well below TIN with both

Fig. 2 The normalized spin-echo diffusion attenuations for 5CB in theisotropic phase for selected temperatures as indicated (in °C) in the figure

Colloid Polym Sci

mixture components: The presence of additive molecularspecies with differing properties, which appear as defects inthe original structure, turns out to diminish the local intermo-lecular order and to give rise to an observable NMR signalover also the larger time scale as necessary for PFG NMRdiffusion measurements.

The results of the fitting of Eq. 3 to the experimental dataare shown in Fig. 4a, b, which present the resulting diffusiv-ities D and the relative contribution (P) of the surfactantmolecules to the PFG NMR signal decay. We note that thefaster diffusivities obtained from the fits were assigned to thediffusivities of LCwhile the slower component toDDAB. Thevalidity of this assignment can readily be verified by analyz-ing the fractions PLC(0,t) and PDDAB(0,t) resulting from the fitat high temperatures. At these temperatures, the transverserelaxation times of both mixture components exceed substan-tially the relaxation delays τ used in our experiments. Thus,any relaxation weighting in the contributions to the overallNMR signal can be excluded. The contribution resulting from

the fit for the more slowly diffusing component is found tocoincide with the proton fraction of the surfactant molecules(see Table 1), allowing us to perform such an assignment.

For temperatures above TIN, the diffusivities of 5CB arefound to be slightly, but consistently, lower than those in thepure LC. With solely this observation, this finding might beanticipated to reflect a hindering effect of the micelles expe-rienced by the LC molecules on their diffusion path. Moreremarkably, it may be noted that, upon crossing the isotropic-nematic transition temperature TIN, there is only a minorchange in the temperature dependence: over the whole tem-perature interval considered the activation energyEA, obtainedby approaching the temperature dependence of the diffusivityby the Arrhenius relation D∝exp(−EA/kT) with k denoting theBoltzmann constant, remains essentially identical. Quite un-expectedly, the diffusive behaviour is thus found to remaininsensitive to these transformations, irrespective of all struc-tural changes occurring in the sample, including macroscopicphase separation into two phases with different chemicalcompositions.

To get further insight and to learn whether this behaviour isalso valid for samples with different compositions, a secondsample (MD6), with the water content notably below that ofMD15, was studied. The composition of this sample waschosen to still exhibit macroscopic separation for T<TIN. Thisis as well supported by the experimental results shown inFig. 5, indicating a PFG NMR spin-echo attenuation behav-iour essentially identical with that of sample MD15. Theresulting diffusivities, obtained in analogy to those of sampleMD15, are also shown in Fig. 4.

On comparing the spin-echo attenuation curves in Fig. 5with those in Fig. 3, the contribution PDDAB(0,t) of the slowlydiffusing component is seen to vary, with varying temperature,more strongly in sample MD6 than in sample MD15. Thismay be qualitatively correlated with the lower content of

Fig. 3 The normalized spin-echo diffusion attenuations measured in thesample MD15 for the selected temperatures (in °C). The lines show thebest fit of Eq. 3 to the experimental data

Fig. 4 Arrhenius plot of the diffusivities of 5CB (filled symbols) andof DDAB (open symbols) in MD15 (squares) and MD6 (uptriangles) (a) and relative contribution of the more slowly diffusingcomponent (associated with the surfactant molecules) (b) resultingfrom the fit of Eq. 3 to the spin-echo diffusion attenuations. The data

for the diffusivities of 5CB in bulk (resulting from the PFG NMRattenuation curves shown in Fig. 2) are shown by stars, for compar-ison. The uncertainty of the fit is, in both representations, of theorder of the size of the symbols

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microemulsion in sampleMD6. The latter leads to (1) a higherrelative volume of the LC-rich phase in MD6 compared toMD15 and (2) to a lower relative amount of trace DDABmolecules in the LC-rich phase. Both features give rise to ahigher orientational ordering of the LC molecules at a giventemperature and, hence, to shorter transverse nuclear magneticrelaxation rates in the LC phase. At temperatures substantiallyhigher than TIN, PDDAB(0,t) is predominantly determined bythe mixture composition and to a much lesser extent bynuclear magnetic relaxation weighting. Because the fractionof DDAB in MD6 is smaller than in MD15, for T>TIN inFig. 5, also PDDAB(0,t) is found to be smaller. With decreasingtemperature, however, stronger ordering of the LC moleculesin MD6 gives rise to a notably stronger decrease of PLC(0,t)or, correspondingly, to a stronger increase of PDDAB(0,t), infull agreement with the experimental findings. On the otherhand, the diffusivities of both LC and DDAB do not show(within experimental accuracy) any appreciable dependencyon the system composition for T>TIN. Some minor differ-ences may be noted to occur for T<TIN.

Diffusion in liquid crystal-surfactant mixtures

In order to clarify whether all effects seen with the samplesMD15 andMD6 can be directly associated with the formationof the micelles, the same experimental procedures and analy-ses were applied to a LC-surfactant mixture containing nowater, i.e. to a mixture under preclusion of micelle formation.Figure 6 shows the PFG NMR spin-echo attenuation curvesS(q,t)/S(0,t) of such a sample (Mx13, open symbols) in com-parison with those of the micelle-forming sample MD15 ofsimilar (LC-surfactant) composition, for selected temperaturesaround TIN.

The data were obtained with a diffusion time of t=10 ms.Over the total range of observation times considered (10 ms≤t≤1,000 ms), the attenuation curves S(q,t)/S(0,t) were ob-served to remain essentially unaffected by the diffusion time.

The diffusion processes can therefore be concluded to proceedunder quasi-homogeneous conditions so that the obtaineddiffusivities are anyway independent of the chosen observa-tion time. Although the shape of the attenuation curves of thetwo samples, as resulting from the respective contributions oftwo different molecular species, are qualitatively similar, thereis a notable difference in their contributions to the overallsignal intensity with varying temperature. Opposite toMD15, in Mx13, these contributions do not change apprecia-bly with varying temperature, revealing an only minor struc-tural ordering in the sample with decreasing temperature.Recalling that it was the process of macroscopic phase sepa-ration, which gave rise to the strong ordering of 5CB inMD15, this phenomenon can in fact be ruled out to take placein Mx13. This conclusion is as well supported by visualobservations: while in MD15, two separate regions can beclearly identified, there appears to be only one homogeneousregion in Mx13. Thus, in the temperature range studied,DDAB remains homogeneously dissolved in LC, precludingany strong ordering.

The diffusivities obtained by fitting Eq. 3 to the attenuationcurves of Fig. 6 are shown in Fig. 7. The diffusivities of 5CBin Mx13 are found to be smaller than in MD15. At the sametime, the diffusivities of DDAB in Mx13 are almost identicalto those in MD15. We are going to discuss these remarkablydifferent features in the diffusion behaviour of the two mixturecomponents in the following.

For rationalizing the first observation, namely, the fact thatmicelle formation has an only minor effect upon the transla-tional mobility of the DDAB molecules, there are, essentially,two scenarios to be considered. It might first be explained byappreciating a highly dynamic nature of the individual mi-celles, appearing in retention times of the individual moleculesin the micelles much smaller than the diffusion times (≥1 ms)considered in the PFGNMR experiments. As a second option,the surfactant molecules could be assumed to form verydynamic agglomerates with properties resembling those of

Fig. 5 Normalized spin-echo diffusion attenuations for MD15 (filledsymbols) and MD6 (open symbols) measured at different temperaturesindicated in the figure (in °C)

Fig. 6 The normalized spin-echo diffusion attenuations for the samplesMD15 (filled symbols) and Mx13 (open symbols) for the temperaturesindicated in the figure (in °C)

Colloid Polym Sci

micelles even without water. Although the second option isnot ruled out by direct experimental evidence, it is difficult toexplain, in this way, the absence of macroscopic phaseseparation.

Let us now consider in more detail the first scenario. Theoverall displacements ⟨r2(t)⟩ of the DDAB molecules can,quite generally, be noted as [25]

r2 tð Þ� � ¼ τ ind=tð Þ r2 tð Þ� �ind

þ τmic=tð Þ r2 tð Þ� �mic

; ð4Þ

where τmic and τind denote the total of time spans during whichthe DDAB molecules diffuse as parts of the micelles and asindividual entities in the LC phase. ⟨r2(t)⟩mic and ⟨r2(t)⟩indstand for the respective mean square displacements coveredduring these time intervals. Notably, τind (τmic) is understoodas the sum of the durations of many shorter periods of stay asan individual entity (as part of a micelle) of the DDABmolecules on their trajectory in the LC phase during t. Onwriting Eq. 4, it is reasonably implied that memory effectsbetween such subsequent periods of stay are negligibly small.

By dividing both sides of Eq. 4 by 6t and by introducingPDDAB.LC=τind/t and PDDAB.m=τmic/t, one obtains the effectivediffusivity.

DDDAB;eff ¼ PDDAB;LCDDDAB þ PDDAB;mDmic; ð5Þ

where DDDAB and Dmic denote the diffusivities of singleDDAB molecules in LC (which may be assumed to re-semble those in Mx13) and of DDAB molecules diffusingas part of the micellar units. If Dmic is associated with thediffusivity of a micelle as a single unit, then, according tothe Stokes–Einstein relation, Dmic would be expected tobe notably smaller than DDDAB because the sizes ofDDAB and of the micelles differ notably (where, without

direct experimental evidence, we imply equality between thedynamic viscosity exerted by the surrounding to DDAB andto the micelles). Hence, DDDAB,eff should be found to besmaller than DDDAB. This, however, is not supported by theexperimental results for T>TIN. DDDAB,eff could, on the otherhand, be approached byDDDAB ifDDDAB.m<<DDDAB.LC. Thisscenario does, as well, turn out to be not reasonable. It wouldquestion the formation and integrity of the micelles, the oc-currence of which has been proven by a number of otherexperimental techniques [8]. The experimental resultsshown in Fig. 7a are thus found to require quite gener-ally that DDDAB,LCDDDAB≈DDDAB,mDmic. This conditioncan only be valid if the surfactant molecules, on the timescale of their retention time in the micelles, can bedisplaced by distances large enough for yielding suffi-ciently high values of Dmic. This can provisionally beprovided if the surfactant molecules in the micellar shellsare highly mobile, and if, in addition, their retention timeswithin the micelles are sufficiently short so that their long-term diffusivity may benefit from their high mobility withinthe micelles.

The second experimental observation implies that the 5CBdiffusivity is more strongly impeded by the presence of theDDABmolecules if they are homogeneously distributed withinthe 5CB phase rather than if self-assembled into micelles. Ourassumption that the decrease of the 5CB diffusivities in LC-microemulsion mixtures, in comparison with the pure LC, isdue to a hindering effect by the inverse micelles must thereforebe reconsidered. In fact, it has turned out that the DDABmolecules dispersed in the LC phase have an even larger impacton the LC diffusivities than if they are assembled into themicelles. Following the discussion in the preceding paragraphs,in the LC-microemulsion mixtures, the DDAB molecules arefound in both micelles and the LC phase. Their relative fractionin the LC phase is lower than in Mx13. It is due to this reason

Fig. 7 Diffusivities of 5CB (in bulk (stars), in MD15 (filled squares),and in Mx13 (filled circles)) and of DDAB (in MD15 (open squares) andin Mx13 (open circles)) (a) and relative contribution of the more slowly

diffusing component (associated with the surfactant molecules) to theoverall signal intensity (b) as resulting from the fit. The uncertainty of thefit is, in both representations, of the order of the size of the symbols

Colloid Polym Sci

that the values of the diffusivities of 5CB inMD15 are found tobe between those in the pure LC and in Mx13.

Conclusions

1H PFG NMR has been applied to study the diffusion prop-erties of liquid crystal-microemulsion mixtures. Themicroemulsions were nano-sized inverse micelles which wereformed upon mixing of water and a surfactant in a thermo-tropic liquid crystal. Due to a difference of almost one order ofmagnitude between the diffusivities of the liquid crystal andthe surfactant molecules, their diffusivities could be probed,with high accuracy, separately from each other by applying atwo-phase model to the measured PFG NMR spin-echo dif-fusion attenuation functions. The experiments were performedin a temperature range around the isotropic-nematic transitiontemperature TIN of the liquid crystal.

In the temperature interval above TIN, the diffusivities ofthe liquid crystal and surfactant molecules were found toclosely follow the Arrhenius behaviour, with an activationenergy of about 30 kJ/mol. With the onset of the formationof the transparent nematic phase close to TIN, as anticipated inthe literature, only very minor alterations in the temperaturedependency were registered. Further cooling, leading to theoccurrence of macroscopic phase separation during which thesystem separates into two phases with, respectively, a verylow and a relatively high concentration of micelles in theliquid crystal, did not lead to appreciable variations in thediffusive dynamics. Based on this observation and assumingthat the diffusivities of the surfactant molecules reflect that ofthe micelles, one may question the formation of a transparentnematic phase. This may, however, be related to the fact that it isprimarily the translational dynamics of the individual moleculesrather than that of the micelles which is probed by PFG NMR.

In a series of further experiments, the formation of micelleswas intentionally prohibited by adding only the surfactant andno water to the liquid crystal. Notably, no macroscopic sepa-ration was observed in this case. This finding reveals thatphase separation is intimately related to the existence ofmicelles. On considering the diffusion properties of the liquidcrystal-surfactant mixture, as a most important finding, thediffusivities of the surfactant molecules at temperatures abovethe isotropic-nematic transition were observed to remain al-most unchanged in comparison with those in the liquidcrystal-microemulsion. Notably, in the former case, the sur-factant molecules diffuse as individual species, while in thelatter case, over at least some fraction of time the surfactantmolecules should diffuse as a part of the micelles. In view ofthe different hydrodynamic radii of the two species, it is ruledout by the Stokes–Einstein relation that the micelles diffuse asfast as the surfactant molecules; the surfactant molecules mustbe required to exchange between many micelles during the

time scale of the experiments (≥1 ms). With this scenario, therenewal time of the micelles can be estimated to be evenbelow the experimental diffusion time, being in the range ofmilliseconds. Because the liquid crystal-surfactant mixturesdo not undergo any macroscopic separation, the diffusivity isfound to vary smoothly with varying temperature in the wholetemperature range, without exhibiting any peculiarities fortemperatures below TIN.

Acknowledgments Financial support by the German Science Founda-tion (DFG, FOR 877) is gratefully acknowledged. We dedicate the paperto Professor Friedrich Kremer on the occasion of his 65th birthday andexpress our deep appreciation for a wonderful door-by-door cooperationand for many stimulations, including those leading to a series of jointresearch activities (references 18–20) and to, eventually, the study pre-sented in this communication.

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Alexander Shakhov got his Master’s degree in Physics in 2009 at theNational Research Nuclear University (the former Moscow EngineeringPhysics Institute) with a thesis on the ‘Investigation of Carbon Nano-structures by Raman Spectroscopy’. Since 2011, he is a Ph.D. student inthe Department of Interface Physics at Leipzig University, investigatingstructure–dynamic relationships in complex fluids and nanoporous host–guest systems by the application of various nmr techniques.

Jörg Kärger got his Ph.D. in Physics in 1970 at Leipzig University,followed by the habilitation in 1978. In 1994, he became a Professor ofExperimental Physics and head of the Department of Interface Physics,until his retirement in 2009. His research activities are dedicated todiffusion phenomena quite in general and include the establishment ofthe ‘Diffusion Fundamentals’ Conference Series and Online Journal andthe author-/editorship of textbooks on ‘Diffusion in Nanoporous Mate-rials’ and ‘Diffusion in Condensed Matter’.

Rustem Valiullin got his Ph.D. degree from Kazan State University(Kazan, Russia) in 1997. After 2 years of postdoctoral work in theRoyal Institute of Technology (Stockholm, Sweden), in 2003, hemoved to Leipzig University, Germany, as a fellow of the Alexandervon Humboldt Foundation. From 2008 to 2013, he was a Heisenbergfellow of the German Science Foundation at the Department ofInterface Physics of Leipzig University. Dr. Valiullin’s research in-terests concern phase transitions and molecular dynamics in confinedspaces and in soft-matter systems.

The three of us (RV, JK, AS – from left to right) enjoy the vicinity of our laboratories with those of Professor Kremer’s group. It provided us with the possibility of being straightforwardly pictured in front of Professor Kremer’s group announcements (“Molekülphysik” MOP) with, by the way, the documentation of the fascinating research output of his group. Much more importantly, however, we feel privileged by the possibility of daily contact and of numerous stimulating discussions. Very many thanks indeed, dear Friedrich Kremer, and many happy returns of the day!

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