Calorimetric study of phase transitions in ocylcyanobiphenyl-barium titanatenanoparticle dispersionsKrishna P. Sigdel and Germano S. Iannacchione Citation: The Journal of Chemical Physics 139, 204906 (2013); doi: 10.1063/1.4830430 View online: http://dx.doi.org/10.1063/1.4830430 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/20?ver=pdfcov Published by the AIP Publishing

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THE JOURNAL OF CHEMICAL PHYSICS 139, 204906 (2013)

Calorimetric study of phase transitions in ocylcyanobiphenyl-bariumtitanate nanoparticle dispersions

Krishna P. Sigdela) and Germano S. Iannacchioneb)

Department of Physics, Worcester Polytechnic Institute, Worcester, Massachusetts 01609, USA

(Received 25 August 2013; accepted 1 November 2013; published online 26 November 2013)

High-resolution ac-calorimetry is reported on the weakly first-order isotropic to nematic (I-N) and thecontinuous nematic to smectic-A (N-SmA) phase transitions in the liquid crystal octylcyanobiphenyl(8CB) doped with a ferroelectric nanoparticle barium titanate, BaTiO3 (BT). Measurements wereperformed as a function of BT concentration and over a wide temperature range well above and belowthe two transitions. From the thermal scans of all samples (having BT mass fraction φm = 0.001 to0.014 and pure 8CB), both the I-N and the N-SmA transitions evolve in character. Specifically, thereappears an unusual change of the I-N specific heat peak shape on heating as φm increases. Both thetransitions shift to lower temperature at a different rate for φm < φc

m = 0.002 as compared to that forφm > φc

m. The effective transition enthalpies are essentially constant and similar to that seen in thebulk. Using a simple geometric model, the mean distance between the BT particles at the cross-overφc

m is found to be x̄c ∼ 3 μm, which is consistent with an estimated surface extrapolation length b forthe nematic director. This suggests that the low φm regime is dominated by an impurity/disorder effectwhile for φm > φc

m the mean distance is small enough for the LC to mediate coupling between theBT ferroelectric nanoparticles. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4830430]

I. INTRODUCTION

Liquid crystal (LC) based colloidal suspensions of nano-materials have been of immense technological and scientificinterest in recent years because of the capacity of the LC me-dia to act as a platform for nanomaterial self-assembly.1 Vari-ous nanomaterials of zero-, one-, and two-dimensional shapeshave been dispersed into LC media to enhance the physi-cal properties of resulting composites, to study liquid crys-talline phase behavior of the nanomaterials themselves, andto synthesize novel nanomaterials by using liquid crystals as“templates.”2

Recently, hybrid systems containing a liquid crystal andferroelectric nanoparticles such as barium titanate (BaTiO3)and tin-hypodiphosphate (Sn2P2S6) have attracted great inter-est in experimental3–8 and theoretical research.9–11 These sys-tems are interesting because of observations of new physicalproperties, not observed in the pure LC, due to the elastic me-diated surface interactions between the nano-sized particlesby the anisotropic LC host. The ferroelectric nanoparticlesof size about 20 nm have been observed to alter the phys-ical properties of the liquid crystal without forming defectsor otherwise disturbing the LC nematic director.3 The addi-tion of ferroelectric nanoparticles can also cause an increaseof the isotropic to nematic phase transition temperature,4 in-crease in the dielectric anisotropy,3, 12 higher birefringence,and lower switching voltage.13 However, these observed ef-fects have not been unambiguously explained yet nor consis-tently observed, and remain an open question. For example, astudy3 of a multicomponent liquid crystal ZL4801 doped with

a)Present address: Department of Physics and Astronomy, University ofMissouri, Columbia, Missouri 65211, USA.

b)Electronic mail: gsiannac@wpi.edu

ferroelectric Sn2P2S6 nanoparticles showed that the I-N tran-sition temperature, TIN, remains essentially same as that of thepure LC but a more recent study14 on the same LC (with andwithout the addition of a surfactant) showed a slight decrease(∼2.3%) in the TIN. Similarly, it has been shown that the ad-dition of ferroelectric nanoparticle BaTiO3 in 5CB does notchange the Freedricksz threshold but enhances the dielectricresponse15 while a more recent study6 showed significant de-crease in the Freedricksz threshold. Recent work on 8OCBdoped with BaTiO3 nanoparticles showed significant changesin the thermo-physical behavior, with a decrease in the I-Nphase transition temperature with increasing concentration ofBaTiO3.7 Recently, these results have been replicated usingBaTiO3 doped octyl-oxy-cyanobiphenyl (8OCB) and octyl-cyanobiphenyl (8CB) liquid crystal mixtures.16 Most of thesestudies were focused on multi-component liquid crystal mix-tures (multiple LCs) doped with ferroelectric nanoparticlesand only in the nematic phase.

In this work, we study the phase transition behavior ofsingle-component liquid crystal octylcyanobiphenyl, whichhas nematic and smectic-A phases, doped with ferroelectricnanoparticle barium titanate-BaTiO3 (BT) as a function ofBT concentration. The incorporation of BT into the 8CB hostcauses unique phase ordering behavior as revealed by ac-calorimetry. Both the I-N and the N-SmA transitions evolve incharacter but remain the order of transition as in pure 8CB,namely, the I-N remains first-order and the N-SmA transi-tion remains second-order (or continuous). The I-N�Cp peaksshift toward lower temperature and become broader with in-creasing BT mass fraction (φm). An unusual shift of the I-Nspecific heat peak on heating towards low temperature limit ofthe I+ N coexistence range is observed in contrast to the usualsharp discontinuity of the I-N heat capacity towards the high

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204906-2 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

temperature side of two-phase region. The N-SmA specificheat δCp wings overlay each other consistently for all 8CB+ BT samples with a slight mismatch from that shown in thebulk on the nematic side of the N-SmA transition on heating.Both the I-N and the N-SmA transition temperatures decreasesimilarly as φm increases but at a different rate for higher andlower φm regimes. The I-N and N-SmA ac-enthalpies (effec-tive enthalpies derived from the integrated heat capacities at afixed probing frequency) are essentially constant but, the realac-enthalpy is slightly larger and the imaginary ac-enthalpy isslightly smaller than that of the bulk for the I-N transition. Noimaginary ac-enthalpy is observed for the N-SmA transitionconsistent with it remaining continuous in character.

Our present work is organized as follows: following thisintroduction, Sec. II describes the preparation of the sample,the calorimetric cell, and ac-calorimetric procedure employedin this work. Section III describes the calorimetric results ofthe I-N and N-SmA phase transitions in the 8CB + BT sys-tem. Section IV provides the discussion of the results and con-cludes our work with future directions.

II. EXPERIMENTAL

A. Materials and sample preparation

Ferro-electric nanoparticle dispersions were prepared us-ing a solvent dispersion method.17, 18 Barium titanate nanopar-ticles (with purity 99.9%), purchased from Nanostructuredand Amorphous Materials Inc., were used without furtherpurification or surface treatment. However, the nanoparticleswere degassed under vacuum for about 2 h before using inorder to remove possible moisture or solvent content. Thesenanoparticles, as indicated by manufacturers’ “Certificate ofAnalysis,” have tetragonal structure and verified by XRD withan overall spherical shape of individual particle having a di-ameter of 200 nm as determined using a scanning electronmicroscope (SEM). Tetragonal structured BaTiO3 is ferro-electric in nature and goes to the cubic paraelectric phase ata Curie point of about 403 K.19 Moreover, the tetragonalityat room temperature increases with increasing particle size.20

For this work, we used a well characterized liquid crystal, 4-cyano-4’-octylbiphenyl (8CB), purchased from Frinton Labo-ratory. Pure 8CB has a weakly first-order isotropic to nematicphase transition at T 0

IN = 313.98 K, the continuous nematic tosmectic-A phase transition at T 0

NA = 306.97 K, and stronglyfirst-order crystal to SmA transition at T 0

CrA = 290 K.17

The 8CB was degassed under vacuum in its isotropicphase about 2 h before use. A certain amount of BT and rel-atively large amount of spectroscopic grade (ultra-low watercontent with purity of 99.9%) acetone were mixed in a vial.The mixture was then mechanically mixed in a touch-mixerfor about an hour and sonicated in an ultrasonic bath for about5 h. Then, the desired amount of 8CB was introduced to themixture of BT and acetone and again sonicated for about 10h. After sonication the dispersion was placed on a hot plate toevaporate the acetone slowly out of the mixture and then themixture was degassed under vacuum at 318 K for about 2 h.Different composite samples having φm ranging from 0.001to 0.014 were prepared using the same procedure. Here, φm

= MBT/(MLC + MBT) is the mass fraction of BT, where MBT

and MLC are masses of BT and LC, respectively. The preparedsamples appeared to be homogeneous as verified by visual in-spection and by the homogeneous texture observed under thecrossed-polarizing microscope. No visible sign of phase sep-aration, agglomeration, or sedimentation was observed whilethe suspensions were kept in a transparent vial for severaldays.

When the composite sample was ready it was introducedinto an envelope type aluminum cell of dimensions ∼12× 8× 0.5 mm3 which has a 120 � strain gauge as a heaterand 1 M� carbon flake thermistor preattached in its oppositesides.18 The filled cell was then mounted in the high resolu-tion ac-calorimeter, the details of which can be found in Refs.21–23.

B. Ac-calorimetry

High-resolution ac-calorimetric measurements were car-ried out using a homemade calorimeter at Worcester Polytech-nic Institute (WPI). In its ac mode, ac-calorimetry techniquecomprises an oscillating power P0exp (iωt) applying to a sam-ple + cell arrangement of finite thermal conductivity and de-tecting the temperature oscillations of an amplitude T0 and arelative phase shift between temperature oscillation and inputpower, ϕ = � + π

2 , where � is the absolute phase shift. Theamplitude of the temperature oscillation is given by24

T0 = P0

ωC

(1 + (ωτe)−2 + ω2τ 2

ii + 2Ri

3Re

)−1/2

, (1)

where P0 is the amplitude and ω is the angular frequencyof the applied heating power, C = Cs + Cc is the total heatcapacity of the sample + cell, which includes the heaterand thermistor, and τ e = CRe and τ 2

ii = τ 2s + τ 2

c = (CsRs)2

+ (CcRc)2 are external and internal relaxation times, respec-tively. Here, Ri is the internal thermal resistance that is ap-proximately equal to the thermal resistance of the sample andRe is the external thermal resistance to the bath. The inter-nal time constant, τ ii, is the rms time required for the wholeassembly of sample and cell to reach equilibrium with the ap-plied heat, and the external time constant, τ e, is the time re-quired to reach equilibrium with the bath. The relative phaseshift between the applied power and resulting temperature os-cillations is given by

tan(ϕ) = 1

ωτe

− ωτi, (2)

where τ i = τ s + τ c. If the frequency of the temperature oscil-lation is faster than the external equilibration time and slowerthan the sample internal equilibration time, i.e.,

ωτi � 1 � ωτe. (3)

Then Eq. (1) becomes

C ∼= P0

ωT0≡ C∗. (4)

The plateau observed in log-log scale of the ωTac versus ω

curve is the region where the inequality (3) is valid and givesthe working frequency region for the calorimeter.25

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204906-3 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

With the definition given by Eq. (4), the real and imagi-nary specific heat at a heating frequency ω can be expressedas

Cp = C ′f illed − Cempty

ms

= C∗ cos(ϕ) − Cempty

ms

, (5)

C ′′p = C ′′

f illed

ms

= C∗ sin(ϕ) − (1/ωRe)

ms

, (6)

where C ′f illed and C ′′

f illed are the real and imaginary parts ofthe heat capacity, Cempty is the heat capacity of the empty cell,and ms is the mass of the sample (in the range of 15 mg to 30mg). Equations (5) and (6) need a small correction to accountfor the non-negligible internal thermal resistance as comparedto Re and this was applied to all samples.26 The real part of theheat capacity can be thought of as the normal heat capacity in-dicating storage (capacitance) of the thermal energy whereasthe imaginary part indicates the loss (dispersion) of energy.The temperature regions corresponding to equilibrium, one-phase states exhibit a zero imaginary part of heat capacity,i.e., C ′′

p = 0,17 and the dispersive temperature regions, suchas a two-phase coexistence region where the latent heat is re-leased, have non-zero C ′′

p. In the dispersive temperature re-gions, the evolved latent heat interferes with the pure sinu-soidal applied signal resulting in an appearance of a peak inthe imaginary heat capacity.

The determination of excess specific heat �Cp associatedwith a phase transition can be made by subtracting an appro-priate background CBG

p from total specific heat over a widetemperature range, i.e.,

�Cp = Cp − CBGp . (7)

For the I-N transition,

�Cp = Cp − CBGp . (8)

For N-SmA phase transition,

δCp = Cp(N − SmA) − CBLp , (9)

where CBLp is the baseline or wing below N-SmA Cp phase

transition peak.The evaluation of enthalpy change associated with a

phase transition involves an integration of excess specific heat�Cp:

δH =∫

�CpdT . (10)

For second-order or continuous phase transitions, the limits ofintegration are as wide as possible about �Cp peaks and theintegration gives the total enthalpy change associated with thetransition. But for the first-order transitions, the situation iscomplicated due to the presence of a coexistence region andlatent heat �H. The total enthalpy change is the sum of thepretransitional enthalpy and latent heat �Htotal = δH + �H.An integration of the observed �Cp peak yields an effectiveenthalpy (ac-enthalpy) change δH* which includes a fractionof the latent heat contribution. The integration of the imagi-nary part of heat capacity given by Eq. (6) gives an imaginaryenthalpy (dispersive enthalpy) δH ′′ which is the dispersion

of energy in the sample and is an indicator of the first-ordercharacter of the transition.

III. RESULTS

For pure 8CB, the I-N phase transition occurs at T 0IN

= 313.17 K while the N-SmA transition occurs at T 0NA

= 306.08 K, both are about 1 K lower than the highest val-ues reported in the literature.27 The I-N effective enthalpyδH ∗

IN = 4.50 ± 0.45 J/g, the N-SmA effective enthalpy δHNA

= 0.64 ± 0.06 J/g, and the I-N dispersive enthalpy δH ′′IN

= 0.45 ± 0.05 J/g in pure 8CB are within 10% of the liter-ature value.28 These results are used for comparison to thecomposite results. All data presented here were taken at aheating frequency of 0.196 rad/s and at a thermal scanningrate of 1 K h−1. For all 8CB + BT samples, each heating scanwas followed by a cooling scan and experienced the samethermal history.

The resulting excess specific heat �Cp data for 8CB+ BT samples studied on heating as a function of temperature�TIN = T − TIN are shown in Fig. 1(a). The isotropicto nematic phase transition temperature TIN was taken ashigh temperature limit of I + N coexistence region, whereC ′′

p �= 0 on the isotropic side.29 The I-N and the N-SmA phasetransitions are characterized by a distinct �Cp peak for all8CB + BT samples. The �Cp wings are similar for all 8CB+ BT composite samples and for pure 8CB below andabove the two transitions, revealing that the bulk-like order

FIG. 1. (a) Excess specific heat �Cp on heating as a function of tempera-ture about TIN for all 8CB + BT samples including pure 8CB. (b) Imaginaryspecific heat C′′

p on heating as a function of temperature about TIN. Samesymbols listed in the inset of (a) are used for both (a) and (b) and are for 100× φm.

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204906-4 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

FIG. 2. (a) Excess specific heat �Cp associated with the I-N phase transitionon heating as a function of temperature about TIN for all 8CB + BT sam-ples including pure 8CB. (b) The I-N imaginary specific heat C′′

p on heatingas a function of temperature about TIN. Symbols listed in the inset are for100 × φm and applied for both (a) and (b).

fluctuations are present in the isotropic and smectic-A phases.However, a slight mismatch of the heat capacity wings onthe nematic phase below TIN close to the I-N transition isobserved as φm changes.

The imaginary specific heat C ′′p as a function of temper-

ature about TIN on heating is shown in Fig. 1(b). The C ′′p ex-

hibits a sharp peak associated with the I-N phase transitionand no peak corresponding to the N-SmA phase transition,consistent with the I-N being a weakly first-order and the N-SmA transition being second-order phase transition for all φm.

Expanded views of the I-N excess specific heat �Cp andthe imaginary specific heat C ′′

p on heating as a function oftemperature about TIN are shown in Fig. 2. The �Cp wingsoverlay nicely on the isotropic side for all φm samples but alarger than bulk �Cp is observed for φm = 0.008 and 0.014on the nematic side of the I-N transition. The �Cp peaks pro-gressively shift away from �TIN = 0 (TIN), being ∼ 0.2 Kbelow TIN for φm = 0.001 to ∼ 0.7 K below for φm = 0.014.The �Cp peak also appears broader with increasing φm. The�Cp smoothly decreases from its maximum value as the tem-perature increases from a temperature corresponding to �Cp

peak (i.e., Tp) to TIN (see Fig. 2(a)). Similarly, C ′′p decreases

smoothly as temperature increases from Tp to TIN, as shown inFig. 2(b). In other words, the �Cp and C ′′

p maxima at the I-Nphase transition occur progressively closer to the low temper-ature limit of the I + N coexistence range.

The �Cp and imaginary specific heat C ′′p associated with

the I-N phase transition on cooling are shown in Fig. 3. The

FIG. 3. (a) Excess specific heat �Cp on cooling as a function of temperatureabout TIN. (b) Imaginary specific heat C′′

p on cooling as a function of temper-ature about TIN. The definition of the symbols are given in the inset and arefor 100 × φm.

�Cp behavior on cooling is consistent with the one on heatingin that they are reproducible after multiple thermal cycles andexhibit a distinct �Cp peak associated with the phase transi-tion. However, the relative shift of �Cp peak from �TIN = 0on heating is larger than that in cooling. Also, �Cp rapidly de-creases from its maximum value as the temperature decreasesfrom TIN to Tp in contrast to the �Cp heating behavior. The�Cp peak is widened with increasing φm but the rate of in-creasing the peak width is smaller on cooling as compared tothat on heating. The �Cp wings for all 8CB + BT samplesoverlay each other on the isotropic side of the transition butthis behavior is different in the bulk sample on the nematicside of the transition indicating an enhanced nematic fluctua-tion caused by the addition of BT in 8CB. A similar behaviorof shifting and broadening of the I-N transition C ′′

p peaks areobserved for all φm samples.

The excess specific heat δCp associated with the N-SmAphase transition as a function of temperature about TNA isshown in Fig. 4. The δCp exhibits a sharp and distinct N-SmAtransition peak for all samples. On heating, the δCp wingsoverlay each other for all samples on the SmA side of thetransition but on the nematic side the pure 8CB shows differ-ent wing behavior (see Fig. 4(a)). On cooling, the δCp wingsoverlay each other on both sides of the transition for all 8CB+ BT samples with a small mismatch to the bulk specific heatwing behavior. Since the data in the coexistence region (peakarea) are sparse, no power-law fits were attempted for criticalbehavior analysis. However, a qualitative examination of the

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204906-5 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

FIG. 4. Excess specific heat δCp associated with N-SmA phase transition (a)on heating (b) on cooling as a function of temperature about TNA. Symbolslisted in the inset are for 100 × φm.

critical behavior was performed via a log-log plot of δCp asa function of reduced temperature, |t| = |(T − TNA)/TNA|, andessentially parallel trends of the 8CB + BT and pure 8CB,above and below TNA, indicating no significant change in thecritical exponents, with the amplitude ratio remaining veryclose to 1, was found.

The I-N phase transition temperature TIN is defined asthe lowest temperature of the isotropic phase prior to enter-ing the I + N two-phase coexistence region.29 The N-SmAphase transition temperature TNA is taken as the N-SmA δCp

peak temperature. The value of TIN decreases monotonicallyuntil φm = 0.002, followed by a non-linear decrease as φm

further increases as shown in Fig. 5(a). This indicates two φm

regime behaviors, the low and high-φm regions are partitionedby the vertical dashed line in Fig. 5. The value of TIN on cool-ing is systematically lower than that on heating. The heatingpeaks occur at Tp and are steadily lower than TIN as indicatedby dashed line in Fig. 5(a). The coexistence region, �TI + N

rapidly grows as φm increases in the high-φm region (see Fig.5(b)). The TNA shows a similar behavior as that of TIN, lineardecrease in low-φm regime, followed by a non-linear decreasefor high-φm regime leaving a constant nematic range �TN asa function of φm as shown in Figs. 5(c) and 5(d).

The total enthalpy δH ∗T was obtained by integration of

�Cp over a wide temperature range of ∼300 to 318 K.The effective enthalpy associated with the N-SmA transi-tion δHNA was obtained by integrating δCp over ±3 K aboutTNA. Then, the I-N ac-enthalpy was determined as δH ∗

IN

= δH ∗T − δHNA. The δH ∗

IN increases linearly for φm = 0 toφm = 0.002 and then remains fairly constant with increas-ing φm, as shown in Fig. 6(a). Similar behavior is observed

FIG. 5. (a) The I-N phase transition temperature as a function of φm. Thedashed curve represents the I-N �Cp peak temperature on heating. (b) The I+ N co-existence region as a function of φm. (c) The N-SmA phase transitiontemperatures as a function of φm. (d) The nematic range as a function of φm.All data shown are the average of heating and cooling. The solid and dottedcurves on (a)–(c) represent heating and cooling behaviors, respectively. Thevertical dotted line represents the boundary between low-φm and high-φm

regime.

on δHNA with increasing φm, with linear increase in its valueup to φm = 0.002, followed by φm independent values forhigher φm (see Fig. 6(c)). However, the δH ′′

IN increases veryslightly up to φm = 0.002 and then gradually decreases withincreasing φm, again revealing two BT concentration regimes(Fig. 6(b)).

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204906-6 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

FIG. 6. (a) The integrated �CpI-N enthalpy δH ∗IN as the function of φm. (b)

The imaginary enthalpy δH ′′IN as the function of φm. (c) The integrated δCpN-

SmA enthalpy δHNA as a function of φm. The lines are only the guidance forthe eye. All data are averaged out from heating and cooling data. The verticaldot line represents the boundary between low-φm and high-φm regime.

The differences in transition temperatures between heat-ing and cooling scans, T H

c − T Cc , with increasing φm, are

shown in Fig. 7(a). This transition hysteresis is constant forthe low φm regime followed by a gradual increase in the highφm regime for the I-N phase transition. This is consistentwith the expected behavior of a first-order phase transition.However, the hysteresis for the N-SmA transition decreasessmoothly in the low φm regime then becoming constant for allhigher values of φm. While the uncertainties are large and en-compass T H

c − T Cc = 0 for the N-SmA phase transition with

increasing φm, all the values of the transition temperature dif-ference (T H

c − T Cc ) remain systematically and unexpectedly

negative (Fig. 7(a)).

IV. DISCUSSION AND CONCLUSIONS

The weakly first-order I-N and the continuous N-SmA liq-uid crystal phase transitions of 8CB + BT composite systems

FIG. 7. (a) The I-N (◦) and N-SmA (•) phase transition temperature differ-ence on heating and cooling as a function of φm. The vertical dotted linerepresents the boundary between low-φm and high-φm regime. (b) Mean dis-tance between the BT nanoparticles as a function of φm given by Eq. (12)where arrow indicates the cross-over length x̄c associated with the φc

m deter-mined from Fig. 5.

have been studied using high-resolution ac-calorimetry as afunction of BT content, φm. Multiple heating and cooling cy-cles reproduce each other well for φm ≤ 0.014 while uniformtextures are observed using polarizing microscopy images forall samples studied. Both results support the view that the BTnanoparticles are well-dispersed in these composite samples.

The unusual shift of the �Cp maxima towards the lowtemperature limit of the I + N coexistence range on heatingis in contrast to the expected behavior on cooling, i.e., the�Cp maxima are near the high temperature limit of the I +N coexistence range. This is illustrated as a dashed line forthe Tp behavior in Fig. 5(a). Clearly, the melting and orderingprocesses of the I-N phase transition are driven by differentdynamics. A possible scenario to explain this observed hys-teresis emerges if one assumes coupling of the ferroelectricnanoparticles to the orientational order in the polar LC andthat the LC mediates interactions through this coupling be-tween BT particles. Given this view, entering the I + N coex-istence range on heating would result in a sharp rise in �Cp,followed by a stretched tail as the BT particles “unbind” fromeach other as the nematic phase disappears (see Fig. 2(a)).

Conversely, on cooling into the I + N coexistence rangethere would be a sharp rise in �Cp due to nucleation of Ndomains followed on cooling by a tail as the BT particlesbegin to “bind” to one another. This tail on cooling wouldsmoothly extend into the fully established N phase as shownin the tails of both �Cp and C ′′

p in Fig. 3. This physical pic-ture, which essentially describes a Kosterlitz-Thouless (K-T)

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204906-7 K. P. Sigdel and G. S. Iannacchione J. Chem. Phys. 139, 204906 (2013)

type of transition,30 where the unbinding of vortices is equiva-lent to the unbinding of ferroelectric BT particle pairs, is sup-ported by the observations at the N-SmA transition. Here, theN-SmA δCp appears as a sharp and distinct peak with only aslight mismatch of the wing behavior of the composite sam-ples with that of pure 8CB. Also, the TNA shifts with shiftingof TIN in such a way that the nematic range �TN remains un-changed.

These results indicate that the BT particles are orienta-tionally coupled to each other and to the LC without signifi-cant positional coupling. This is not unexpected for the ferro-electric nature of the BT particles and given that they are notlikely positionally fixed, i.e., forming a gel and pinning theSmA phase locally. This physical picture may also explain theapparent negative Tc hysteresis at the N-SmA phase transition.Here, the smectic domains are much smaller than the nematicdomains and would “cut” coupling between BT particles sothat heating towards and away from the SmA phase would in-volve different dynamics. However, this is not a large effectand the data are not unambiguous.

The rapid and linear change in transition temperaturesfor the low-φm regime, followed by a nonlinear and gradualchange for high-φm, is likely due to a different distributionof BT nanoparticles in LC medium in the two regimes. Forthe low-φm regime, due to the small number of nanoparticles,presumably floating of particles in the LC medium rather pro-duces disorder effects, giving rise to a rapid decrease in tran-sition temperatures. However, for the high-φm, BT nanoparti-cles interact with each other via the LC molecules, producingsomehow an ordering effect, revealed as a gradual change intransition temperature as a function of BT content. Also, the I+ N coexistence region data support the existence of two φm

regimes. The transition enthalpies are essentially constant butthe real parts (δH ∗

IN and δHNA) are slightly larger than that ob-served in the bulk. This may be due to the BT coupling to theLC order that would result in extra energy modes while theslight decrease in the imaginary I-N enthalpy may reflect thecoupling between BT-BT nanoparticles mediated by the LCthat would suppress nematic to isotropic phase conversion.

The existence of two φm regimes is presumably due tothe different degrees of interaction between the nanoparticlesand LC molecules. One measure of this effect could be themean distance between the BT particles, x̄. Previously, a sim-ple model was developed to describe the mean distance be-tween n-hexane molecules in a LC medium in terms of molefraction.29 However, this mixing model of two similar organicfluids is inadequate when one of the components is a solid andof considerably larger size than the LC molecule. Here, an-other model is developed in terms of mass fraction φm. Con-sidering a spherical cell of volume VT with number of BTparticles NBT, we can get volume per particle, v = VT /NBT ,for BT in an LC medium. This can be expressed as

v ={

1

ρBT

+(

1

φm

− 1

)1

ρLC

}mBT , (11)

where ρBT and ρLC are the densities of BT and LC, respec-tively, mBT is the mass per particle of BT, and φm is the massfraction of BT defined earlier. Because of the spherically de-fined cell, the mean distance between particles is simply given

as the diameter of the volume per particle, x̄ = ((6/π )v)1/3.This together with Eq. (11) gives

x̄ =[

6

π

{1

ρBT

+(

1

φm

− 1

)1

ρLC

}mBT

]1/3

. (12)

Taking mBT = 2.45 × 10−14 g, ρBT = 5.85 g/cm3, and ρLC

= 0.966 g/cm3, the φm dependence of x̄ is given in Fig.7(b). Using the φm from Fig. 5 (φc

m = 0.002), the correspond-ing mean distance between BT particles, which representsthe cross-over length, is about x̄c = 2.9 μm. For φm < φc

m,the particle distance is large and only local ferroelectric cou-pling between BT particles and LC molecules occurs, withthe particles acting mainly as an impurity. For φm ≥ φc

m, at ax̄ � 3 μm, the ferroelectric coupling begins to involve multi-ple BT particles and the LC host. This coupling is likely medi-ated by the nematic director and so would be associated withthe nematic extrapolation length (b – which characterizes ne-matic director field distortion caused by the BT particles).31

Interestingly, an estimate of b = K/W , where, K is the aver-age LC elastic constant and W the strength of surface anchor-ing field, can be made using K � 10−11 J/m and a mid-valueof W � 10−5 J/m2 for 8CB, giving b ≈1 μm.32 This estimatefor b is consistent with the cross-over length x̄c (see Fig. 7(b)).

We have undertaken a detailed calorimetric study on theeffect of ferroelectric nanoparticles on octylcyanobiphenyl onthe weakly first-order I-N and the continuous N-SmA phasetransitions. The addition of BT on 8CB causes the change inthe liquid crystal molecular interactions which consequentlygives rise to the evolution of both of the phase transitions. In-teresting effects are observed in the 8CB + BT system includ-ing the unusual shift of the I-N specific heat peaks on heatingtowards the low temperature limit of I + N coexistence range.Continued experimental efforts are needed specifically; prob-ing the structural and ferroelectric behavior of the compositeas a function of BT content, BT size, and temperature wouldbe particulary important and interesting.

ACKNOWLEDGMENTS

We would like to thank Department of Physics at theWorcester Polytechnic Institute (WPI) for its support.

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