DOI: 10.1002/cphc.200900385

From the SmA to the Hexatic, Including the SmC*, SmC*Aand SmC*re Phases: A 2H NMR Relaxation StudyValentina Domenici,* Alberto Marini, Carlo A. Veracini, Corrado Malanga, andRita Menicagli[a]

1. Introduction

Ferroelectric liquid crystals (FLCs) are very fascinating materialsthat have recently experienced a renaissance, with active re-search in both the materials and their technological applica-tions.[1] The ability of a FLC to respond to external fields, suchas electric and magnetic ones, is at the basis of their electro-optical applications, such as spatial light modulators, wave-guides, and telecom devices.[2] In this context, the local mobili-ty and, in particular, the molecular dynamics of FLC systemsplay an important role due to the relationship between molec-ular motions and the macroscopic response to external fields.[3]

Two groups of motions involving single liquid-crystalline (LC)molecules may be identified: “translational diffusion” and “re-orientation” processes, which include overall molecular and in-ternal motions. Moreover, clusters or groups of molecules mayalso experience “collective motions”, in which the spatial aver-age orientation of molecules fluctuates slowly compared tothe much faster reorientation motions.[4, 5] Among these coop-erative motions, order director fluctuations (ODFs), both threedimensional and two dimensional,[6, 7] are typical of the nematicand SmA phases, whereas soft and Goldstone modes[8] arecharacteristic of the ferroelectric LC phases in the low-frequen-cy regime.

Nuclear magnetic resonance (NMR) is an extremely powerfulspectroscopic technique for studying the dynamics of liquidcrystals, not only because it can cover a wide timescale rangefor different nuclei and nuclear interactions, but also for the

possibility of using these different interactions to obtain specif-ic information even localized in particular sites of the molecule.2H represents the nucleus[9] most widely investigated; however,1H, 15N, and 13C nuclei could also give a wealth of informa-tion,[3] even though in these cases the overlapping of resonan-ces coming from the nonequivalent spins in the moleculemakes the analysis of relaxation times not so trivial. Amongthe 2H relaxation times,[9] the two spin–lattice relaxation times,T1Z and T1Q (Zeeman and quadrupolar, respectively), are partic-ularly sensitive to motions with correlation times of the sameorder of magnitude as the inverse of the Larmor frequency,that is, in the range of 10�11–10�7 s in the case of a high mag-netic field (H>5 T).[10] For this reason, 2H NMR spin–lattice re-laxation times have been widely used to obtain detailed infor-mation about overall molecular and internal reorientations inuniaxial LC mesophases formed by uniaxial molecules. In fact,even though relaxation times can also be measured in tiltedsmectic phases, only recently an approximated treatment[11]

has been proposed to link them to the dynamic parameters,thus allowing the study of biaxial phases, such as the ferroelec-

The molecular dynamics of a ferroelectric liquid crystal, denot-ed ZLL 7/*, is investigated by means of 2H NMR relaxation. Thespin–lattice (T1Q and T1Z) and spin–spin (T2) relaxation times oftwo isotopomers of ZLL 7/*, labeled on the phenyl and biphen-yl fragments, are measured and their behavior upon passingfrom the SmA to the hexatic phase, through the ferroelectricSmC*, antiferroelectric SmC*A, and re-entrant ferroelectricSmC*re phases, is discussed. A comparison between the meas-ured T2 and T2*, directly related to the experimental linewidth,provides information on the heterogeneity of the system, thusallowing confirmation of previous hypotheses concerning thestructural and ordering properties of the SmC*A and SmC*re

phases. The possibility to look at different sites of the core ofthe ZLL 7/* smectogen reveals a peculiar sensitivity of thephenyl moiety with respect to the biphenyl fragment, which

may be justified by its vicinity to the chiral centers. Interesting-ly, the trend of the longitudinal relaxation times is character-ized by a minimum that corresponds to the SmC*A and SmC*re

phases, which is reproducible for the two isotopomers and atseveral Larmor frequencies. A quantitative analysis of T1Q andT1Z is performed in the SmA and SmC* phases, for which thenarrowing regime approximation is valid. A multifrequency ap-proach is applied to self-consistently determine the diffusioncoefficients for the overall molecular motions, namely spinningand tumbling, and the internal rotations around the para axesof the phenyl and biphenyl fragments. The effect of the mag-netic field in unwinding the helical structure of the SmC*phase (for H>9 T) allows observation of a sensitive change inthe rotational diffusion coefficients in the frustrated unwoundSmC* phase with respect to the SmC* phase.

[a] Dr. V. Domenici, Dr. A. Marini, Prof. C. A. Veracini, Dr. C. Malanga,Prof. R. MenicagliDipartimento di Chimica e Chimica IndustrialeUniversit� di Pisa, via Risorgimento 35, 56126 Pisa (Italy)Fax: (+ 39) 050-2219260E-mail : valentin@dcci.unipi.it

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tric smectic C phase. This approach allows the quantitativeanalysis of relaxation times in tilted smectic phases by meansof the existing theoretical models, based on the assumption ofa uniaxial distribution of helices taking into account the effectsof the tilt angle on the measured relaxation times.[12, 13]

The analysis of 2H NMR spin–spin relaxation times is muchmore complex.[14] The decay of the transverse magnetizationcomponent, referred to as T2* and directly related to the spec-tral linewidth, depends not only on the low-frequency dynam-ics, but also on the static features of the investigated spinsystem as well as on external conditions (such as field inhomo-geneities). The transverse relaxation time, as measured normal-ly by spin-echo techniques, is usually referred to as T2, and sev-eral definitions exist that are related to different spin coherenc-es refocused by the specific NMR sequences.[14] The main prob-lem of the extraction of dynamic information from T2 concerns,in most cases, the lack of validity of the Redfield theory.[15] Thisapproximation is valid for treating the faster molecular rota-tions, but less useful for motions characterized by much slowerrates. In these cases a slow-motional approach based on theanalytical resolution[16] of the stochastic Liouville equation is re-quired. Nevertheless, the complexity of this model limited itsapplication to a few examples in uniaxial phases, such as nem-atic and smectic A phases, for which angular and/or frequency-dependent measurements were available.[17] In these cases, thespin–spin relaxation rates are mainly determined by collectivemotions, such as ODFs, at the first or second order of approxi-mation.[16, 17] However, in some cases,[18, 19] the slow motions re-sponsible for the measured T2 have been identified in slowmolecular reorientations.

The FLC object of this study is the (S)-2-methylbutyl-[4’-(4’’-heptyloxyphenyl)-benzoyl-4-oxy-(S)-2-((S)-2’)-benzoyl)-propion-yl)]-propionate, denoted ZLL 7/* (see Figure 1). Two isotopom-ers, ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2, labeled on thephenyl and biphenyl moieties respectively, have been synthe-sized with the purpose of investigating the molecular dynam-ics of ZLL 7/* by means of 2H NMR relaxation methods. Detailsof the synthesis of this mesogen and of the two isotopomersare reported in refs. [20] and [21], respectively. The structuraland ordering properties of this smectogen have been previ-ously investigated, by exploiting both 2H[22] and 13C NMR[23]

spectroscopy combined with quantum mechanical calculationsof relevant NMR parameters, such as 13C chemical shieldingtensors. Moreover, a recent 2H NMR study[24] allowed us to in-vestigate the effect of external magnetic fields[25] in unwinding

the supramolecular structure of the chiral SmC* phase of theZLL 7/* mesogen. In the present work, the molecular dynamicsof the ZLL 7/* sample in its smectic phases (Figure 2), from thesmectic A (SmA) to the hexatic (Hex*), through the ferroelectricSmC*, antiferroelectric SmC*A, and re-entrant ferroelectricSmC*re phases, has been investigated by means of 2H NMRspin–spin and spin–lattice relaxation methods.

In the former case, the trends of the measured T2 and T2* re-laxation times in the whole mesophasic range and the ob-served discontinuities at the mesophase transitions are dis-cussed in terms of the dynamic and static components charac-terizing the different mesophases. Hypotheses on different dy-namic mechanisms at the basis of the observed spin–spin re-laxation trends within the different mesophases could also beproposed in view of previous dielectric measurements.[26] Inthe case of longitudinal relaxation times, a multifrequency ap-proach was adopted. As revealed in previous studies,[9, 13] a reli-able analysis of 2H relaxation times needs a large data set toovercome the indetermination of the coefficient for the tum-bling motion, namely D? , and one possibility is to perform amultifrequency study on multiply labeled isotopomers.[9, 13]

Herein, a flat minimum in the trend of the spin–lattice relaxa-tion times corresponding to the SmC*A and SmC*re phases isobserved. The case of the smectogen ZLL 7/*, due to its veryrich mesomorphic behavior, represents a unique opportunityto experimentally observe a well-defined minimum in thetrend of relaxation times as a function of temperature. In fact,few other cases are known that refer to more complex LC sys-tems, such as LC polymers[27] and LC dendrimers.[19, 28] Here, thequantitative analysis of T1Q and T1Z relaxation times was per-formed in the SmA and SmC* phases, for which the narrowingmotional regime approximation is valid.[15] The diffusion coeffi-cients for the overall molecular motions (Dkand D? ) and forthe internal reorientation motions of the phenyl and biphenylfragments (DR_phe and DR_biphe) could be determined in a self-consistent way. Moreover, the contribution to the spectral den-sity J1(w0) of the collective motions, namely the fluctuations ofthe order director, was estimated in both the SmA and SmC*phases. Interestingly, the effect of the magnetic field H in un-winding the helical supramolecular structure of the SmC*phase (for H>9 T) allowed us to obtain the rotational diffusioncoefficients in the frustrated unwound SmC* (uSmC*) phase.These data are compared with those obtained in the SmA andSmC* phases for the ZLL 7/* sample and with those reportedin the literature for other FLCs.[3, 9, 12, 13]

Figure 1. Representation of the smectic mesogen ZLL 7/* with the associat-ed ellipsoid and principal overall molecular diffusion reorientations.

Figure 2. Mesophases shown by the smectogen ZLL 7/*.

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V. Domenici et al.

Experimental Section

Samples and Mesomorphic Behavior: The sample under investiga-tion was (S)-2-methylbutyl-[4’-(4’’-heptyloxyphenyl)-benzoyl-4-oxy-(S)-2-((S)-2’)-benzoyl)-propionyl)]-propionate (ZLL 7/*). Two iso-topomers selectively labeled as indicated in Scheme 1, namelyZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2, were investigated by means

of 2H NMR relaxation spectroscopy at three different values of theexternal magnetic fields. The synthesis, chemical characterization,physical, and orientational properties of the unlabeled ZLL 7/*compound are reported in refs. [20], [23] , and [29]. The physicaland orientational ordering properties of the two labeled isotopom-ers are reported in ref. [22]. The synthesis of the two isotopomersis reported in ref. [21]. HPLC analyses of final products showed asatisfactory and comparable enantiomeric excess (ee), togetherwith high chemical and isotopic purity, as required for comparative2H NMR studies. The mesomorphic behavior of the two isotopom-ers coincides (taking into account some slight changes in the tran-sition temperatures due to the labeling) with that of the non-deu-terated compound (see Table 1); complete experimental details arereported in ref. [22]. The small differences observed can be attrib-uted to a very small isotopic effect. Differences in the transitiontemperatures were also observed depending on the detectionmethod (NMR spectroscopy or differential scanning calorimetry,DSC): this effect was probably due to differences in the heating/cooling rates.

2H NMR Relaxation Measurements: T1Z and T1Q spin–lattice relaxa-tion times : 2H Zeeman (T1Z) and quadrupolar (T1Q) spin–lattice relax-ation times were measured on both deuterated compounds,ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2, by using three NMR spec-trometers working at different magnetic fields: 1) on a 9.40 TVarian Infinity Plus 400 double-channel spectrometer (operating atthe deuterium frequency of 61.38 MHz); 2) on a 7.05 T Varian VXR-300 spectrometer (working at 46.04 MHz for deuterium); and 3) ona 4.70 T Varian Gemini BB-200 spectrometer (operating at the deu-terium frequency of 30.7 MHz). In the latter case, the relaxationmeasurements were performed in the SmC* phase only, every 1 8C.In all cases, the samples were aligned within the magnet by slowlycooling down from the isotropic phase to the LC phases. The lon-gitudinal relaxation times were measured at different temperaturesby applying the broadband version of the Jeener–Broakert pulse

sequence,[30] modified by Wimperis:[31] 900-2 t1-67.5270-2 t1-4590-t1-4590-t2-450-ACQ. The experimental details of the T1 measurementsrecorded at 61.38 MHz are reported in ref. [26]. Relaxation meas-urements at 46.04 MHz were recorded in steps of 1�4 8C and adelay of 10 min was allowed for temperature equilibration (thetemperature was stable within 0.2 8C). The parameters of the NMRsequence were optimized as follows: the value of the delay t1 wasfixed to 12.51 ms, the variable delay t2 ranged from 0.05 to 300 ms,with a relaxation delay of 1 s and a number of scans of 600�900.The 908 pulse was 13.1 ms. T1 relaxation times at 30.7 MHz were re-corded in the whole mesophasic range every 1 8C. The value of thedelay t1 was fixed to 10.0 ms, the variable delay t2 ranged from0.05 to 500 ms, and a relaxation delay of 0.5 s and 400 scans wereused. The 908 pulse was 14.0 ms. In all cases, T1Z and T1Q were ob-tained by fitting the sum and the difference of the integrals ofeach component of the quadrupolar doublet as function of thevariable delay t2. The equations used for the fittings,[32] which differfrom those theoretically predicted[33] for taking into account possi-ble experimental imperfections, are as follows [Eqs. (1), (2)]:

Mþ t2ð Þ ¼ A 1� B exp �t2=T1Zð Þ½ � ð1Þ

M� t2ð Þ ¼ C þ D exp �t2=T1Qð Þ ð2Þ

The theory for the analysis of relaxation times in terms of dynamicparameters is reported in Section 2, while the results of the dynam-ic analysis on ZLL 7/* are presented and discussed in Section 3.

T2 Spin–Spin Relaxation Times: Transverse relaxation times (T2)were measured in the whole mesophasic range of both isotopom-ers, ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2, by using a 7.05 T VarianVXR-300 NMR spectrometer (working at 46.04 MHz for deuterium).The quadrupolar echo (QE) sequence (90x-t-90y-t-ACQ) with theEXORCYCLE phase scheme,[34] with 1H decoupling, was used. Thevariable time delay t ranged from 25 ms to 15 ms (15 values) and1200 scans were acquired for each delay. The T2 values were deter-mined by fitting the QE intensity of the deuterium signal, IACHTUNGTRENNUNG(2 t), byusing the following equation in the case of monoexponentialdecay [Eq. (3)]:

Ið2tÞ ¼ Ið0Þe �2t=T2ð Þ ð3Þ

In the case of biexponential decay, the following equation wasused [Eq. (4)]:

Ið2tÞ ¼ Ae �2t=T2að Þ þ Be �2t=T2bð Þ� �ð4Þ

The values of the transverse relaxation times, T2*, as a function oftemperature were determined from the experimental linewidth de-fined as the width of the 2H NMR signals measured at half height,namely Dnh=2, according to the relationship [Eq. (5)]:

T*2 ¼ ðpDnh=2Þ�1 ð5Þ

Scheme 1. Molecular structure of the two isotopomers ZLL 7/*-phe-D2(X = D, Y = H) and ZLL 7/*-biphe-D2 (X = H, Y = D).

Table 1. Sequence of phases, melting points (m.p.) [oC] on first heating, transition enthalpies DH [J g�1] (shown in square brackets), and phase transitiontemperatures [8C] from DSC measured on cooling at a rate of 5 8C min�1 for the indicated compounds.

m.p. Cr Hex SmC*re SmC*A SmC* SmA Iso

ZLL 7/* 61ACHTUNGTRENNUNG[+17.6]* 54ACHTUNGTRENNUNG[�12.3]

* 65ACHTUNGTRENNUNG[�2.2]* 71ACHTUNGTRENNUNG[�0.06]

* 98ACHTUNGTRENNUNG[�0.04]* 104ACHTUNGTRENNUNG[�0.19]

* 129ACHTUNGTRENNUNG[�5.7]*

ZLL-phe-D2 61ACHTUNGTRENNUNG[+12.5]

* 51ACHTUNGTRENNUNG[�11.6]

* 64ACHTUNGTRENNUNG[�2.0]

* 70ACHTUNGTRENNUNG[�0.05]

* 95ACHTUNGTRENNUNG[�0.03]

* 101ACHTUNGTRENNUNG[�0.18]

* 128ACHTUNGTRENNUNG[�5.6]

*

ZLL-biphe-D2 59ACHTUNGTRENNUNG[+12.9]* 50ACHTUNGTRENNUNG[�9.3]

* 62ACHTUNGTRENNUNG[�2.5]* 69ACHTUNGTRENNUNG[�0.02]

* 93ACHTUNGTRENNUNG[�0.01]* 98ACHTUNGTRENNUNG[�0.15]

* 127ACHTUNGTRENNUNG[�7.2]*

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NMR Relaxation of Liquid-Crystal Mesophases

Details of the static 2H NMR spectra recorded at 46.04 and61.38 MHz are reported in ref. [22] .

Data Analysis : All 2H NMR data acquired at 4.70, 7.05, and 9.40 T(30.7, 46.04, and 61.38 MHz for the 2H resonance, respectively)were processed by using the software of the Varian instrumenta-tion (Vnmrj and SpinSight 4.3.2 software for Sun microsystemworkstation and Varian). The spectral parameters were analyzedmostly by using the Mathematica 5.0 (Copyright 1988–2003 Wolf-ram Research, Inc.) software for PC. The analysis of spin–lattice re-laxation times in terms of dynamic parameters was performed byusing a modified version of the CAGE software.[35]

2. Theory

In this section, a brief summary of the main aspects concern-ing the modeling of the 2H longitudinal relaxation times usedin the following analysis (see Section 3) is reported. For furtherdetails, a comprehensive description of the topic is available inrefs. [3–6, 9] . The quadrupolar (T1Q) and Zeeman (T1Z) spin–lat-tice relaxation times are directly related, through the Redfieldtheory,[15] to the spectral densities of motions Ji ACHTUNGTRENNUNG(iw0) [Eqs. (6),(7)]:

1T1Z¼ J1 w0ð Þ þ 4J2 2w0ð Þ ð6Þ

1T1Q¼ 3J1 w0ð Þ ð7Þ

where w0 is the Larmor frequency. These relationships areindeed valid in the narrowing regime, for which the motionalprocesses responsible for the relaxation obey the w0tc<1 law.Generally, several motional processes may contribute to thespectral densities in this regime. They can be classified as fol-lows:[3] 1) overall reorientations of the whole molecule, whichreduce to the spinning and tumbling motions in the case of auniaxial LC molecule; 2) internal motions of molecular frag-ments, such as conformational or reorientation motions of mo-lecular fragments; and 3) collective motions, such as the ODFstypical of the nematic phase and two-dimensional ODFs, orlayer undulation (LU) motions,[7, 36] characteristic of the smecticphases, which are usually much slower than the overall and in-ternal molecular motions. Due to the complexity of this scenar-io the extraction of the dynamic parameters, such as diffusioncoefficients, requires the use of simplified models linking thespectral densities to these parameters. Herein, the analysis ofthe relaxation data has been carried out by using the Nordiomodel[37, 38] for the overall molecular motions (spinning, Dk , andtumbling, D? ) and the strong collision model[39] for internalmotions (reorientations of phenyl and biphenyl fragments). Onthe basis of the Nordio model, the spectral densities takinginto account both overall molecular and internal motions canbe expressed as [Eq. (8)]:[40]

JmLmLw0ð Þ ¼

3p2 nq

� �2

2

X2

mM¼�2

X2

mR¼�2

cmL mMd2

mR 0 bi;Qi

� �h i2d2

mM mRbM;i

� �h i2

X

j

aðjÞmL mM

tðjÞmL mM

� ��1þx mRð ÞDi

mLw0ð Þ2þ tðjÞmL mM

� ��1þx mRð ÞDi

h i2

ð8Þ

where nq is the quadrupolar coupling constant, drs2 are the re-

duced Wigner matrices, bi;Qiis the angle between the C�D

bond and the axis about which the internal rotation takesplace, bM,i is the angle between this axis and the molecularlong axis, Di is the diffusion coefficient relative to the internalrotation of the fragment considered, and x(mR) is (1�dmR

) inthe strong collision diffusion model.[39] In Equation (8), the cor-relation times, tðjÞmL mM

, are related to the diffusion coefficients forthe spinning (Dk) and tumbling (D? ) motions through the fol-lowing relationship [Eq. (9)]:

1

tjð Þ

mL mM

¼ 6D?

b jð ÞmL mM

þm2M Djj � D?� �

ð9Þ

where the coefficients aðjÞmL mM, bðjÞmL mM

, and cðjÞmL mMhave been calcu-

lated in ref. [40] as a function of the principal molecular orderparameter S for a Maier–Saupe potential. The contribution ofcollective motions in the high-frequency regime is usually verysmall and is limited to a contribution at the first order to thespectral density J1(w0). As reported in the literature for othersmectogens,[3] this contribution is considered additive to thespectral densities arising from overall and internal motions, re-ported in Equation (8). The following relationship can be con-sidered [Eq. (10)]:

JDF;i1 ðw0Þ ¼

3p2

2ðnqÞ2d2

00ðbi;QiÞ2 � d2

00ðbM;iÞ2 � S2zz � T

aDF

wx0

ð10Þ

where x equal to 1=2 corresponds to the frequency dependencepredicted by Pincus[41] and Blinc[42] for the ODFs in the nematicand SmA phases,[43] while x equal to 1 refers to LUs, typical ofsmectic phases, according to the model proposed by Blincet al.[7] In Equation (10) aDF is a coefficient specific to thechosen models, which depends on macroscopic parameterssuch as the average Frank elastic constant and, in the case ofODFs, the viscosity coefficient or, in the case of LUs, the coher-ence length along the layer normal.

3. Results and Discussion

In this section, the dynamic features of the investigated sam-ples are discussed on the basis of :

1) the spin–lattice (T1Q and T1Z) relaxation times;2) the spectral linewidths (Dnh=2) ;3) the spin–spin relaxation times (T2).

While a qualitative discussion of these quantities can be out-lined for all the mesophases, a quantitative determination of

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V. Domenici et al.

dynamic parameters can be performed by applying a GlobalTarget approach[44] to the analysis of the longitudinal relaxationtimes, T1Q and T1Z, only in the SmA and SmC* (uSmC*) phases,for which the Redfield[15] approximation is valid. In Section 3.1we present a qualitative description of the measured T1 and adiscussion of the quantitative analysis of T1 in the higher-tem-perature SmA and SmC* (uSmC*) phases. In Section 3.2 themeasured linewidth, Dnh/2, and the corresponding T2* are re-ported and a deep discussion of the QE intensity decay interms of T2 components is presented together with a hypothe-sis concerning the dynamic processes active in the differentmesophases and influencing the observed T2 decay constants.Moreover, a comparison between the measured T2 and T2* isperformed to reveal the presence of structural heterogeneitiesin some of the mesophases here investigated.

3.1. T1Q and T1Z Relaxation Times

As can be observed in Figure 3, the trend of the spin–lattice re-laxation times is characterized by a flat minimum that corre-sponds with the SmC*A–SmC*re phases (Tmin�338 and �345 Kfor the ZLL 7/*-biphe-D2 and ZLL 7/*-phe-D2, respectively).The relaxation times T1Z and T1Q reported in Figure 3 a and bfor the ZLL 7/*-biphe-D2 and ZLL 7/*-phe-D2, respectively,were measured at w0 = 46.04 MHz. However, a similar behavior(not shown here) has been observed for both isotopomers atthe Larmor frequency of 61.38 MHz.

A first qualitative comment on these trends concerns the oc-currence of three different motional regimes: narrowing, inter-mediate, and slow ones. The first regime is typically found inthe SmA and SmC* phases of calamitic low-molecular-weightliquid crystals :[3, 9] here, the relaxation times decrease by de-creasing the temperature, thus indicating a narrowing regimeof motions (tcw0<1). A second motional regime, characterizedby a minimum in the trend of relaxation times (T1Z and T1Q), af-fects the SmC*A and SmC*re phases. Here, the main motion re-sponsible for the longitudinal relaxation is in the intermediateregime (tcw0�1), thus allowing us to estimate the correspond-ing correlation time, tc = 2.2 � 10�8 and 1.6 � 10�8 s, at 46.04and 61.38 MHz, respectively. A third motional regime, mostlyaffecting the hexatic phase, is characterized by an increase ofthe relaxation times by decreasing the temperature, thusshowing that the motions responsible for the longitudinal re-laxation are in the slow regime (tcw0>1).

In the literature there are few examples of LC systems with aminimum in the trends of the longitudinal relaxation times.For instance, a minimum in the 13C NMR spin–lattice relaxationtimes[45] was observed in another smectogen in its SmC*A

phase, but only recently a minimum in the trend of 2H NMR re-laxation times, T1Q and T1Z, was found in the SmA phase ofmore complex liquid crystals, such as polymers[27] and den-drimers.[19, 28]

As previously anticipated, a quantitative analysis of the relax-ation times of the two ZLL 7/* isotopomers was performed forthe T1Z and T1Q only, in the SmA and SmC* phases, for whichthe narrowing motional regime applies (see Figure 3). More-over, the peculiar behavior of the ZLL 7/* mesogen in the pres-

ence of a magnetic field allowed us to obtain dynamic infor-mation not only in the conventional SmC* phase, but also inthe corresponding unwound phase (uSmC*).

For simplicity, the experimental spectral densities, J1(w0) andJ2 ACHTUNGTRENNUNG(2 w0), as obtained from the longitudinal relaxation timesthrough Equations (6) and (7), are reported in separate figuresfor the three phases (SmA in Figure 4; SmC* in Figure 5, anduSmC* in Figure 6).1 On the other hand, the analysis of thespectral densities in terms of the theoretical models reportedin Section 2 was performed in the three phases by means ofthree separate Global Target[44] fittings. In particular, the overallmolecular and internal diffusion motions were modeled ac-

Figure 3. 2H NMR relaxation times [ms] T1Q (&) and T1Z (&) versus temperature[K] measured at 46.04 MHz relative to the deuterium resonance frequency(corresponding to a magnetic field strength of 7.05 T) in the whole meso-morphic range of the isotopomers: a) ZLL 7/*-biphe-D2 and b) ZLL 7/*-phe-D2.

1 Note that the spectral densities are reported in Figures 4–6 as a function ofthe reduced temperature (T�T*) with T* = 374 K (SmA–SmC* transition).

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NMR Relaxation of Liquid-Crystal Mesophases

cording to the Nordio[37, 38] and strong collision diffusionmodels,[39] respectively, by assuming an Arrhenius trend withinthe temperature for the diffusion coefficients [Eq. (11)]:

DðTÞ ¼ D1e�Ea=RT ð11Þ

In the case of multifrequency studies (in the SmA and SmC*phases), the contribution of the collective motions could alsobe determined as is discussed in the following for each meso-phase.

In the SmA phase, data recorded (17 � 4 data points) for thetwo isotopomers at two Larmor frequencies (61.38 and46.04 MHz) were analyzed in a Global Target fitting by fixingsome parameters according to the previous studies:[22] 1) themolecular principal order parameter S ranges between 0.66and 0.72 by decreasing the temperature; 2) the angle betweenthe biphenyl and phenyl para axes ranges between 2.8 and

6.38 by decreasing the temperature; and 3) the angles be-tween the C�D bonds and the relative para axes are fixed at608. According to previous studies,[22, 23] the long molecular axisis almost coincident with the biphenyl para axis.

Several fitting procedures were performed to take into ac-count rotational diffusion motions as well as collective mo-tions. In particular, both ODF[41, 42] and LU[7] motions were con-sidered, as reported in Section 2, through Equation (10). How-ever, as expected, the contribution to J1(w0) of the collectivemotions is very small, the maximum value found beingJ1

ODF(w0)�4.5 s�1 (aDF = 5 � 10�8 K�1 s1/2 rad�3/2) and J1LU(w0)

�5.4 s�1 (aDF = 1 � 10�3 K�1 rad�3/2) which, on the other hand, isin the error range of the experimental spectral densities (seeFigure 4). As a test, we also tried to fix the contribution of col-lective motions, both ODFs and LUs, to zero in the fitting pro-cedure, and even though the fitting quality is worse as far asthe reproduction of the spectral densities is concerned, the

Figure 4. Experimental (symbols) and calculated (lines) spectral density [s�1]trends versus reduced temperature [K], determined in the SmA phase ata) 46.04 and b) 61.38 MHz relative to the deuterium resonance frequency(corresponding to a magnetic field strength of 7.05 and 9.40 T, respectively).Filled and empty symbols refer to ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2 iso-topomers, respectively. Circles and squares indicate J1(w0) and J2 ACHTUNGTRENNUNG(2 w0), re-spectively.

Figure 5. Experimental (symbols) and calculated (lines) spectral density [s�1]trends versus reduced temperature [K], determined in the SmC* phase ata) 30.71 and b) 46.04 MHz relative to the deuterium resonance frequency(corresponding to a magnetic field strength of 4.70 and 7.05 T, respectively).Full and empty symbols refer to ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2 iso-topomers, respectively. Squares and circles indicate J1(w0) and J2ACHTUNGTRENNUNG(2 w0), re-spectively.

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V. Domenici et al.

values of the diffusion coefficients in the minimum of the qual-ity factor Q2 are approximately the same. This result is not sur-prising, since many detailed studies on collective motions[43,46–48]

show that these processes are not active at frequencies higherthan 10 MHz. Moreover, the other cases of 2H NMR T1Q and T1Z

analysis in the SmA phase confirm that ODFs do not contributemore than 10 % to J1(w0).[3, 13, 49] In the high-frequency regime,at least in the case of ZLL 7/*, there is no difference betweenthe ODFs and LUs. In particular, the values of the diffusion co-efficients, as reported in Table 2 and Figure 7, are not influ-enced by the chosen model for the collective motions. For thisreason, in Table 2 we report the best fitting parameters corre-sponding to the best reproduction of the experimental spec-tral densities, which was obtained by analyzing the experimen-tal data with the additional contribution to J1(w0) due to theODFs only. As shown in Figure 7 the diffusion coefficients de-termined in this analysis are analogous to those found in theliterature for similar FLC compounds in the SmA phase.[3, 5, 6, 9, 13]

This can also be revealed by the values of the correlation timestc evaluated at T = 388 K (in the middle of the mesophase) anddefined as 1/6 D for all diffusion motions (see Table 2). Thefaster motions are the spinning and biphenyl reorientations,whereas the slowest one is the phenyl internal motion.

In the SmC* phase, which is stable at magnetic fields lowerthan 9 T, the longitudinal relaxation times were measured attwo Larmor frequencies (46.04 and 30.71 MHz). The corre-sponding spectral densities, collected for the two ZLL 7/* iso-topomers at these two frequencies (see Figure 5), were ana-lyzed with a Global Target approach[44] (11 � 4 data points) inthe approximation of uniaxiality of the helical supramolecular

structure.[9–13] On the basis of previous results,[22] the order pa-rameter S was fixed in the range 0.68–0.65, the para axes ofthe two fragments are almost parallel, the angles between theC�D bonds and the relative para axes are fixed to 608, and themolecular tilt angle is in the range 12.0–18.58.[22–24] Eventhough, in the SmC* phase, the experimental data are affectedby larger errors (see Figure 5) than in the SmA phase (in partic-ular at the lowest frequency), the fitting is quite good and thebest fitting parameters, also reported in Table 2, are in agree-ment with those found in the SmC* phase of similar FLC sys-tems.[11–13, 49, 50] Concerning the diffusion motions, if no sensitivechanges are observed for the spinning and internal biphenyl

Figure 6. Experimental (symbols) and calculated (lines) spectral density [s�1]trends versus reduced temperature [K], determined in the uSmC* phase at61.38 MHz relative to the deuterium resonance frequency (corresponding toa magnetic field strength of 9.40 T). Full and empty symbols refer to ZLL 7/*-phe-D2 and ZLL 7/*-biphe-D2 isotopomers, respectively. Circles and squaresindicate J1(w0) and J2 ACHTUNGTRENNUNG(2 w0), respectively.

Table 2. Best fitting parameters obtained from the Global Target analysisof the longitudinal relaxation times of the two ZLL 7/* isotopomers in thethree phases: SmA, SmC*, and uSmC*. In particular: pre-exponential diffu-sion coefficients, D1 [s�1] , and activation energies, Ea [kJ mol�1] , for thespinning (k ), tumbling (? ), and internal motions affecting the phenyl (R_phe) and biphenyl (R_biphe) moieties; the coefficient taking into accountthe ODF contribution to J1(w0), aDF [K�1 s1/2 rad�3/2] , where determined. Thecorrelation times, tc [s] , at an intermediate temperature of each meso-phase (at T = 388 K in the SmA and T = 370 K in the SmC* and uSmC*phases) are also reported for all the rotational diffusion motions.

SmA SmC* uSmC*

Dk1 15.0 15.0 15.0

Eak 42.44 42.52 49.42

tck 8.3 � 10�11 1.6 � 10�10 1.6 � 10�9

D?1 15.0 15.1 15.0

Ea? 44.97 46.58 56.60

tc? 2.1 � 10�10 6.7 � 10�10 1.7 � 10�8

DR_phe1 15.0 14.9 15.1

Eaphe 45.87 50.89 49.10

tcphe 2.7 � 10�10 2.4 � 10�9 1.7 � 10�9

DR_biphe1 15.0 15.0 15.0

Eabiphe 42.82 41.99 44.50

tcbiphe 8.3 � 10�11 1.3 � 10�10 3.2 � 10�10

aDF 5.0 � 10�8 2.0 � 10�7 –

Figure 7. Diffusion coefficients Dk , D? , DR_phe, and DR_biphe [s�1] reported on alogarithmic scale versus 1000/T [K�1] for the smectogen ZLL7/* in the SmA,uSmC*, and SmC* phases. The labeling of Di coefficients is shown in thefigure.

2 The quality factor Q is defined asP

i

ðJexpi � Jcalc

i Þ�

Jexpi

� �2 and is the quantityminimized by the fitting procedure.

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NMR Relaxation of Liquid-Crystal Mesophases

motions, a slowdown affects the tumbling motion and, to alarger extent, the rotation of the phenyl ring around its paraaxis (see Figure 7). This is related to the substantial increase ofthe activation energy of this motion from the SmA to theSmC* phases (see Table 2) with respect to the other motions.

The contribution of the collective motions to the spectraldensities J1

ODF(w0) is about 10 % of the largest experimentalvalue of J1(w0) (with the best fitting parameter aDF = 2.0 �10�7 K�1 s1/2 rad�3/2) and a similar result is obtained by using themodel for the LUs instead of ODFs (in particular the maximumJ1

LU(w0) is about 8 % of J1(w0) with aDF = 2.5 � 10�3 K�1 rad�3/2). Inthe case of the SmC* phase, however, fixing the collectivemotion contribution to zero does not give convergence of thefitting. This means that, differently from the SmA phase, thesole rotational diffusion motions are not able to reproduce theobserved spectral densities. This is a clear indication that thecontribution of collective motions (ODFs or LUs) cannot be ne-glected. On the other hand, collective motions such as Gold-stone and soft modes, which are typical of the SmC* phase,should not contribute to T1 since their typical frequency rangeis below the megahertz region.

In the uSmC* phase, the longitudinal relaxation times wererecorded at a single Larmor frequency (61.38 MHz), since theappearance of this phase strictly depends[24] on the magneticfield strength and, in particular, it is stable only at magneticfields higher than 9 T. Experimental spectral densities for thetwo isotopomers (8 � 4 data points) were analyzed in a GlobalTarget fitting and are reported in Figure 6 together with thecalculated spectral densities.

As in the previous two phases, for the analysis of the relaxa-tion data both orientational and structural information need tobe known: the molecular order parameter S ranges from 0.72to 0.75, the angles between the C�D bonds and the relativepara axes are fixed to 608, and the angle between the biphenyland phenyl para axes ranges between 6.4 and 8.78, as deter-mined in previous studies.[22, 23] In this case the contribution ofODF was neglected, due to the fact that a single frequencywas available. However, since the uSmC* phase has a structuremore similar to the SmA than the SmC* phase, due to the lackof a helical supramolecular structure, this approximation is jus-tified. The global fitting analysis obtained by using the Nordiomodel for all the molecular motions and the strong collisionmodel for the internal rotations is quite good, with the best fit-ting parameters reported in Table 2; the values of the diffusioncoefficients for the four motions are displayed in Figure 7. Afirst comment concerns the slowing down of all four diffusionmotions when the system passes from the SmA to the uSmC*phase: this can also be noticed from the sensitive increase ofthe activation energy for all motions. All diffusion motions areinfluenced by this phase transition and, in particular, the corre-sponding diffusion coefficients are all shifted to lower valuesthan in the SmA phase (see Figure 7). As in the SmC* phase,the faster motion is the internal rotation of the biphenyl frag-ment (tc�3.2 � 10�10 s).

The slower motion is the tumbling diffusion, which is shiftedto lower values of about 1.5 orders of magnitude at the SmA–uSmC* transition. However, the spinning motion and phenyl

rotational diffusion are also much slower in the uSmC* than inthe SmA phase. Another aspect is related to the opposite be-havior of the phenyl rotation: while all the other diffusion mo-tions are slower in the uSmC* phase with respect to the SmC*phase, the phenyl ring behaves in the opposite manner. A pos-sible explanation of the different behavior of the phenylmoiety is related to previous observations on the same ZLL 7/*sample.[22–24] These studies in fact show that the relative orderof the two aromatic fragments changes when moving fromthe SmA to the SmC* phase under the different magneticfields. Similarly, some conformational features (such as theangle between the two para axes) change upon decreasingthe temperature. These structural and orientational changesmay be the reason for different local dynamics between thetwo states. As shown in Section 3.2, the phenyl ring is distin-guished by its sensitivity to different dynamics with respect tothe biphenyl moiety.

In summary, what is observed in the case of ZLL 7/* and re-ported above concerning the different trends of diffusion coef-ficients in the SmC* and uSmC* phases is a new phenomenon.These results indicate that the effect of high magnetic fields isnot only evident from the changes in the supramolecularstructure and in the orientational properties, but also, as a nat-ural consequence, in the dynamic processes affecting differentfragments of the LC molecules.

3.2. T2 and T2* Relaxation Times

Additional information can be obtained by looking at thetrends of the experimental 2H NMR spectral linewidths, Dnh/2,as well as by comparing the relaxation times T2* with thosemeasured by means of the QE sequence, namely T2. Figure 8shows the spectral linewidths obtained from the 2H NMR spec-tra recorded at 46.04 MHz for ZLL 7/*-biphe-D2 (Figure 8 a)and ZLL 7/*-phe-D2 (Figure 8 b). It should be noted that similartrends have been observed at the highest frequency(61.38 MHz); however, the case of the lowest frequency(46.04 MHz) seems much more interesting, based on simpleconsiderations concerning the 2H NMR spectral features report-ed in a previous study of the ZLL 7/* mesogen.[22] In particular,Figure 8 gives several interesting clues about the nature of theobserved mesophase transitions, and reveals a substantial dif-ference between the two isotopomers. The experimental line-widths increase upon decreasing the temperature, from about500 ACHTUNGTRENNUNG(250) Hz in the SmA phase up to about 4(3) kHz in the hex-atic phase of ZLL 7/*-biphe-D2 (ZLL 7/*-phe-D2). In both iso-topomers, the almost continuous trend of Dnh/2 from the SmAto the SmC*A phase is separated by an upward jump in corre-spondence to the ferroelectric SmC* phase, similarly to whatwas previously observed for another smectogen.[51] However, ifthe trend of Dnh/2 in the SmC*A phase of the ZLL 7/*-biphe-D2is almost flat (i.e. , a plateau), in the case of ZLL 7/*-phe-D2 theDnh/2 starts to increase rapidly at T�355 K.

It is worth noting that at this temperature a discontinuity of1) the dipolar 2H–1H (see Figure 9 of ref. [22]) and 2H quadrupo-lar splittings (see Figure 7 b of ref. [22]) on the ZLL 7/*-phe-D2and of 2) the 13C chemical shift anisotropy on the phenyl frag-

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V. Domenici et al.

ment of ZLL 7/* (see Figure 5 of ref. [23]) was previously ob-served. Moreover, a different behavior between the two iso-topomers concerns the SmC*A–SmC*re and SmC*re–Hex* phasetransitions: in particular, a continuous (sigma shaped) and adiscontinuous (marked by sudden jumps) increase of the line-width is observed in the ZLL 7/*-biphe-D2 and ZLL 7/*-phe-D2, respectively.

A further step in the analysis of the experimental linewidthsin terms of dynamic features comes from a comparison be-tween the T2* [related to Dnh/2 by means of Eq. (5)] and themeasured T2. As previously mentioned, the spin–spin relaxationtimes were measured through the QE sequence at 46.04 MHzonly, for both isotopomers. The extraction of the characteristicrelaxation decay constants in the different mesophases wasperformed by means of Equations (3) and (4) in the case ofmonoexponential and biexponential decays, respectively. Thecorresponding relaxation times—T2 in the case of the monoex-ponential decay; T2a and T2b in the case of biexponentialdecay—are reported in Figure 9. For convention in this analysisthe subscripts “a” and “b” refer to the faster (with larger T2

component) and slower (with smaller T2 component) dynamic

processes, respectively. A first general comment concerns thefitting of the QE intensity I ACHTUNGTRENNUNG(2 t) in the different mesophases: atypical monoexponential function was found to well reproduceI ACHTUNGTRENNUNG(2 t) only in the Hex* phase in both compounds investigated.In all the other phases, the observed IACHTUNGTRENNUNG(2 t) decay is reproduci-ble only by using a biexponential function for both isotopom-ers, thus indicating a complex dynamic behavior and probablythe presence of more than one motional process affecting thelinewidths in the higher-temperature mesophases. This non-monoexponentiality in the QE decay prevented us from analyz-ing in a quantitative way the observed T2 components interms of dynamic motions; however, several hypotheses con-cerning the main dynamic contributions can be proposed.

In the SmA phase the ratio A/B [A and B being the weightsof the two decay components reported in Eq. (4)] is almostconstant within the phase and it is about 50 and 10 for ZLL 7/

Figure 8. Experimental 2H NMR linewidth Dnh/2 [Hz] versus temperature [K] ,determined at 46.04 MHz, in the whole mesomorphic range of the a) ZLL 7/*-biphe-D2 isotopomer and b) ZLL 7/*-phe-D2 isotopomer.

Figure 9. Spin–spin relaxation times T2 obtained from analysis of the QE in-tensity as described in the text, and T2* obtained from the linewidthsthrough Equation (5), versus temperature [K] , recorded at 46.04 MHz for thea) ZLL 7/*-biphe-D2 isotopomer and b) ZLL 7/*-phe-D2 isotopomer. (*) referto T2*, (&) represent calculated T2 in the monoexponential case [see Eq. (3)] ,and (~) and (~) correspond to T2a and T2b, respectively, in the biexponentialcase [see Eq. (4)] . The errors on T2* are evaluated from the errors in the line-widths (Figure 8), which are evaluated experimentally from the spectra.[22]

The errors on the T2a and T2b components are obtained from the fitting ofthe magnetization decays.

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NMR Relaxation of Liquid-Crystal Mesophases

*-biphe-D2 and ZLL 7/*-phe-D2, respectively. This allows us tostate that the QE decay is dominated by a single T2, which ishere labeled as T2a. Moreover, in the SmA phase the relation-ship T2*�T2a is valid (with T2*�0.5 and �1 ms for ZLL 7/*-biphe-D2 and ZLL 7/*-phe-D2, respectively). This finding indi-cates that the observed spectral linewidths are homogeneousfor both isotopomers, thus determined by dynamic processes,only.

The presence of a small component (T2b), even though itsweight is very small, is due to dynamic heterogeneities,namely the presence of a dynamic motion much slower thanthat affecting the first and most important component (T2a).The origin of such slow motion can be related to the paraelec-tric state,[52] which distinguishes the SmA phase formed by theZLL 7/* from the conventional SmA phase. Here, we can imag-ine clusters of smectic phases with a low molecular tilt (simi-larly to uSmC*) with no azimuthal correlation among the smec-tic planes. A confirmation of this picture comes from thestrong effect of the magnetic field observed directly on the2H NMR quadrupolar splittings: the larger the magnetic fieldthe larger is the quadrupolar splitting, which is related to anincrease of the orientational order.[24] For the ZLL 7/*, in partic-ular at lower magnetic fields, we can expect in the SmA phasethe presence of collective motions typical of the more orderedtilted phases. To summarize, the motions affecting the QE in-tensity decay, with the observed two components, are proba-bly collective motions of different types, such as LUs or ODFsfor the “a” component, with a possible role played by softmodes, as observed by dielectric spectroscopy on the samesample,[26] for the “b” component. On the other hand, theeffect of rotational diffusion motions on the spin–spin relaxa-tion can be excluded in the SmA phase, since they are too fast(see values reported in the previous section) to have any ef-fects on T2.

The scenario is different in the SmC* phases occurring atlower temperatures. In fact, in these mesophases, not only adynamic heterogeneity but also a structural, or static, hetero-geneity exists. The measured T2* is always smaller than T2a,which continues to be the main component of the QE intensi-ty decay, I ACHTUNGTRENNUNG(2 t), in the SmC* for both isotopomers, in the wholeSmC*A for ZLL 7/*-biphe-D2, and at T>355 K (in the middle ofthe SmC*A) for ZLL 7/*-phe-D2. In particular, at T�355 Kchanges in both dynamic and orientational properties, as pre-viously observed (see Figure 9 of ref. [22]), occur only for thesample labeled on the phenyl ring. This is an indication of thehigh sensitivity of the phenyl moiety, which is the closest oneto the chiral lateral wing, to local changes occurring within theSmC*A phase. Moreover, in the ZLL 7/*-phe-D2 sample, for T<355 K the slowest component of the QE intensity decay,namely T2b (ranging from 80 to 100 ms), becomes the most im-portant one (A/B from 0.1 to 0.05). Going down in tempera-ture, in the SmC*re phase the ratio A/B (�0.01) and the relaxa-tion decay T2b (�120 ms) are constant within the mesophase.The comparison between T2* and T2b, also taking into accountthe large experimental error bars (see Figure 8 b), indicatesthat a slowdown in the dynamic processes affecting thephenyl moiety starts to occur in the middle of the SmC*A

phase and then it continues in the SmC*re phase, similarly towhat happens in the sole SmC*re phase for ZLL 7/*-biphe-D2(T2b�70 ms and A/B�0.03; see Figure 8 a). This experimentalfinding suggests that the occurrence of the rare SmC*re phasein the ZLL 7/* mesogen could be related to a change, at a mo-lecular level, in both the dynamics and ordering of the phenylfragment with respect to the biphenyl one.

Concerning the dynamic contribution, a possible explanationis that the phenyl moiety is more influenced by collective mo-tions (which may be associated with the “b” component of thespin–spin relaxation), while the biphenyl moiety, which is alsothe most oriented one, is more influenced by the overall rota-tional diffusion motions, at least in the SmC* and SmC*A

phases. These last motions, in particular the tumbling diffusion,is expected to be quite slow in these phases, based on thetrend of T1 reported in the previous section and in particularon the values of correlation times evaluated in the minimumof T1. Moreover, as observed in another case,[19] slow reorienta-tions may represent an important dynamic contribution to T2

relaxation. For this reason, it cannot be excluded that the “a”component in the SmC* phase is due to slow reorientations.However, the complexity of the supramolecular structure ofthe SmC*, SmC*A, and SmC*re phases introduces additional dy-namic contributions, which are particularly active in the fre-quency region below 1 MHz, such as the Goldstone and softmodes. A previous study[26] based on dielectric spectroscopy isof help in identifying these motions and their typical frequencyin the various mesophases. For instance, in the SmC* phase, aswell as in the re-entrant one, the Goldstone modes with a typi-cal frequency of a few hundreds of hertz represent the maincontribution to the high permittivity of the sample due to thesynclinic supramolecular structure.[8] On the contrary, in theSmC*A phase these modes are appreciably smaller in favor ofthe soft modes, or antiphase modes, typical of the anticlinicstructure, with a frequency of tens of kilohertz. These observa-tions are consistent with the interpretation that the T2 relaxa-tion observed in the SmC* phases of ZLL 7/*, and in particularthe “b” component, is influenced by these kinds of collectivemotions instead of the ODFs or LUs.[53]

In the Hex* phase, for both isotopomers, the QE intensitydecay, I ACHTUNGTRENNUNG(2 t), is well reproduced by a monoexponential func-tion, and the decay constant T2 [evaluated from Eq. (3)] is com-parable with the T2* obtained from the spectral linewidths[Eq. (5)] . The high orientational order found in this phase[22]

and the particular packing among molecules in the layeredstructure (see Figure 2) indicate that the local Hex* domainsare well aligned with respect to the magnetic field and thelocal inhomogeneities are almost negligible. This is confirmedby the fact that T2�T2* for both isotopomers. The values ofthese spin–spin relaxation times in the Hex* phase give an in-dication of the occurrence of a slow molecular motion, whichdramatically affects the spectral linewidths (Figure 8) and isprobably related to local fluctuations or reorientations of theLC molecules around their average position in the hexagonallattice.[54]

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4. Conclusions

A 2H NMR relaxation study, based on the spin–lattice relaxationtimes (T1Q and T1Z), spin–spin relaxation times (T2 and T2*), andlinewidth (Dnh/2) analyses, has been performed on a quite com-plex LC mesogen, namely ZLL 7/*, in its rich variety of meso-phases. In particular, these studies were carried out on two iso-topomers of ZLL 7/*, selectively labeled on the phenyl and bi-phenyl moieties, and at several 2H Larmor frequencies of theorder of tens of megahertz.

Spin–lattice relaxation times show a complex trend by de-creasing the temperature from the SmA to the hexatic phases,for both isotopomers at all the frequencies examined. A mini-mum is observed in correspondence to the antiferroelectricand re-entrant SmC* phases, thus indicating a slowing downof the molecular motions mainly affecting 2H T1. The corre-sponding correlation time, defined in the minimum in the T1

trends as tc�1/w0, is about 10�8 s. Moreover, the phenyl ringseems to be more sensitive to this slowing down than the bi-phenyl moiety. In fact, the minimum of T1 is shifted to highertemperatures for the phenyl than for the biphenyl fragments(Tmin�338 and �345 K for ZLL 7/*-biphe-D2 and ZLL 7/*-phe-D2, respectively). In agreement with these observations, thequantitative analysis of the T1Q and T1Z relaxation times in thehigher-temperature smectic phases, namely the SmA andSmC* phases, indicates that among the rotational diffusionmotions, that is, the spinning and tumbling overall molecularmotions and the two reorientations around the para axes ofthe biphenyl and phenyl moieties, it is the last one which hasthe longer correlation time (tc�1.7 � 10�9 and 2.4 � 10�9 s inthe SmC* and uSmC* phases, respectively). These findings,both qualitative and quantitative, show a significantly differentsensitivity of the two labeled moieties to the dynamic featuresof ZLL 7/*. It is worth noting that the phenyl ring is linked tothe chiral chain, which is chemically responsible for the occur-rence of the chiral phases as well as for the high molecular po-larity, while the biphenyl moiety is less influenced by the chiralchain and is probably less hindered in the reorientationaround its para axis as well as in the internal relative rotationof the two rings.

Interestingly, the possibility of studying the dynamics ofZLL 7/* under different magnetic fields allowed us to observean unexpected difference in the dynamics of the investigatedisotopomers in the unwound SmC* state with respect to thewound SmC*. In particular, the presence of a high magneticfield (H>9 T) produces not only frustration in the supramolec-ular structure of the ferroelectric phase, but also hindrance ofthe molecular diffusion motions. This could be quantified bymeans of a Global Target[44] fitting analysis of the longitudinalrelaxation times in the higher-temperature phases, thanks tothe validity of the Redfield approximation. This hindering isalso expected at lower-temperature phases, for which a quanti-tative analysis is not possible at the moment due to 1) the lackof specific models for these complex smectic phases, namelySmC*A and SmC*re, and 2) the unfeasibility of the Redfieldtheory for the modeling of T1 relaxation times in the case oftcw0�1. However, the expected important role played by

single molecular and internal motions in the low-temperaturemesophases is confirmed by study of the 2H NMR linewidthsACHTUNGTRENNUNG(Dnh/2) versus spin–spin relaxation times (T2), reported here atthe Larmor frequency w0 = 46.04 MHz.

The trends of both Dnh/2 and T2 in the whole mesomorphicrange reflect quite well the transitions among different phases,since discontinuities in the values and/or slopes of these quan-tities are observed for both isotopomers, when cooling thesample from the SmA to the hexatic phase, at the phase transi-tions. The complexity of the dynamic processes affecting thespin–spin relaxation times is confirmed by the failure in fittingthe QE intensity decays by using a monoexponential function,except in the case of the hexatic phase, which is highly or-dered and dominated by a single slow dynamic process, prob-ably related to local fluctuations around the average positionof the LC molecules in the hexatic lattice. In all the other smec-tic phases a biexponential decay applies and, even though it israther difficult to extract dynamic parameters from these data,the comparison between the measured T2* and the decay con-stants obtained by fitting the experimental QE intensity decaysby using a biexponential function (namely T2a and T2b), takinginto account their relative weights (A and B), gives insightsinto 1) the presence or not of phase heterogeneities, 2) theorder of magnitude of the characteristic frequency of the maindynamic motions, and 3) the presence of dynamic heterogene-ities. The most significant findings are summarized as follows:

* In the SmA phase, the QE intensity decay is dominated by asingle component, T2a, which is almost equal to T2*: this ex-cludes any structural or static heterogeneity, as expected inthis high-temperature phase. However, the presence of asmall component, T2b, indicates a dynamic heterogeneity,which can be interpreted as the occurrence of dynamiccontributions due to collective motions of different types,such as order fluctuations and soft modes.

* The non-monoexponential decay of the QE intensity in theSmC*, SmC*A, and SmC*re phases confirms the presence ofat least two dynamic motions at frequencies below 1 MHz.Among these, overall molecular motions or internal rota-tional diffusion of the labeled moieties may play a role inthe T2a component since their characteristic correlationtimes are much larger than in the usual smectic phases, asobtained from the minimum in T1 observed in both iso-topomers. Certainly, the observed QE intensity decays indi-cate a complexity and a heterogeneity in the dynamic fea-tures of the ZLL 7/* in these smectic phases, which is alsoconfirmed by dielectric spectroscopy:[26] Goldstone modesin the SmC* and SmC*re phases, and soft modes in theSmC*A phase, are expected to influence T2b.

* The SmC* for both isotopomers, and the whole SmC*A

phase for the ZLL 7/*-biphe-D2 and part of the SmC*A

phase for the ZLL 7/*-phe-D2, are characterized by a highstatic heterogeneity, T2*<T2a (with “a” the most importantcomponent of the spin–spin relaxation), which could be re-lated to nonhomogeneous distributions of domains as wellas misalignments within each domain.

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* The fact that the ZLL 7/*-phe-D2 shows a change in themiddle of the antiferroelectric phase concerning both thelinewidths (Dnh/2) and the spin–spin relaxation times (T2) isan indication of a high sensitivity of the phenyl fragment tothe changes affecting the supramolecular structure of themesophase. Moreover, this discontinuity in the middle ofthe SmC*A phase is also observed in the dipolar and quad-rupolar splittings,[22] in the order parameter S,[23] and canalso be related to the slowing down of the internal diffu-sion of the phenyl ring observed from the analysis of T1.

* In the SmC*re phase, the increase of the linewidth and thecomplex behavior of the QE intensity decay observed inboth isotopomers give an indication of a slowing down ofthe dynamic motions affecting the spin–spin relaxation andthe presence of both structural and dynamic heterogenei-ties, respectively, which is confirmed by previous studies.[22]

The difficulty in performing a quantitative analysis of thespin–spin relaxation times is due to several reasons: 1) the re-laxation is not monoexponential ; 2) no models are available atthe moment for such complex mesophases; 3) these smecticphases are stable in relatively small temperature ranges so thatthe relaxation data are limited if a temperature dependence ofdynamic parameters has to be modeled; and 4) the observeddiscontinuities, such as that found for the phenyl fragment inthe SmC*A phase, are hardly reproducible, since they probablyreflect correlated effects, such as structural, conformational,and dynamic ones. However, as reported above, the quantita-tive analysis of T2 versus T2* gave important information andallowed us to clearly distinguish different behaviors in the vari-ous mesophases.

An important finding of this work is related to the evidencefor different dynamic behaviors of the two aromatic moietiesin both trends of T1 and T2 relaxation times, which are general-ly sensitive to different frequency regimes of motions. More-over, the dynamic parameters here determined for the two iso-topomers are closely related to the supramolecular structure ofthe mesophases under investigation. In particular, the diffusioncoefficients are very different between the unwound andwound SmC* phases, stable at different strengths of the exter-nal magnetic field.

The role of the internal reorientations in the relaxation proc-esses, however, does not exclude collective motions, such asthe low-frequency soft and Goldstone modes, or other fluctua-tions specific to the frustrated smectic phases, such as theSmC*re phase. In particular, their influence on the spin–spin re-laxation processes is expected to be dominant at least for thesmall component, T2b. 1H NMR relaxometry could give somemore clues, in particular in the region of 10 kHz–1 MHz, inspite of the lack of site specificity.

The present work makes a significant contribution to the un-derstanding of the particularly varied and rich series of chiralsmectic phases shown by the ZLL 7/* LC system in terms of dy-namic features, and it represents a first step in the quantitativeanalysis of this important molecular property.

Acknowledgements

V.D., A.M. , and C.A.V. are grateful to PRIN2005 (Italian MIUR) forfinancial support and to Dr. Alexej Bubnov and Dr. Ing. VeraHamplova for helpful discussions. A.M. is also grateful for finan-cial support to the Young Researcher Project ’07 granted by theScuola Normale Superiore of Pisa. All authors are grateful to Dr.Lorella Marchetti for technical support at the Varian Gemini BB-200 spectrometer.

Keywords: deuterium · liquid crystals · molecular dynamics ·NMR spectroscopy · smectic phases

[1] S. T. Lagerwall in Ferroelectric and Antiferroelectric Liquid Crystals, Wiley-VCH, Weinheim, 1999.

[2] K. K. Kobayashi, J. Phys. Soc. Jpn. 1970, 29, 101.[3] V. Domenici, M. Geppi, C. A. Veracini, Prog. Nucl. Magn. Reson. Spectrosc.

2007, 50, 1.[4] G. R. Luckhurst, C. A. Veracini in The Molecular Dynamics of Liquid Crys-

tals, Kluwer, Dordrecht, 1989.[5] R. Y. Dong, Prog. Nucl. Magn. Reson. Spectrosc. 2002, 41, 115.[6] R. Y. Dong, Nuclear Magnetic Resonance of Liquid Crystals, Springer, New

York, 1997.[7] R. Blinc, M. Luzar, M. Vilfan, M. Burgar, J. Chem. Phys. 1975, 63, 3445.[8] I. Musevic, R. Blinc, B. Zeks, The Physics of Ferroelectric and Antiferroelec-

tric Liquid Crystals, World Scientific, Singapore, 2000.[9] “Dynamics of Liquid Crystals by means of Deuterium NMR relaxation”:

V. Domenici, C. A. Veracini in Nuclear Magnetic Resonance Spectroscopyof Liquid Crystals (Ed. : R. Y. Dong), World Scientific, Singapore, 2009, inpress.

[10] R. R. Vold, “Nuclear Spin Relaxation”, in Nuclear Magnetic Resonance ofLiquid Crystals (Ed. : J. W. Emsley), Reidel, Dordrecht, 1985, p. 253.

[11] V. Domenici, M. Geppi, C. A. Veracini, Chem. Phys. Lett. 2003, 382, 518.[12] V. Domenici, Pure Appl. Chem. 2007, 79, 21.[13] V. Domenici, Ph.D. Thesis, University of Pisa (Italy) 2005.[14] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press,

New York, 1961.[15] A. G. Redfield, Adv. Magn. Reson. 1965, 1, 1.[16] a) D. Frezzato, G. Kothe, G. Moro, J. Phys. Chem. B 2001, 105, 1281; b) D.

Frezzato, G. Moro, G. Kothe, J. Chem. Phys. 2003, 119, 6931.[17] a) G. Althoff, O. Stauch, M. Vilfan, D. Frezzato, G. Moro, P. Hauser, R.

Schubert, G. D. Kothe, J. Phys. Chem. B 2002, 106, 5517; b) D. Frezzato,G. Moro, G. Kothe, J. Chem. Phys. 2003, 119, 6946; c) D. Frezzato, G.Moro, M. Tittelbach, G. Khote, J. Chem. Phys. 2003, 119, 4060.

[18] a) V. Domenici, M. Geppi, C. A. Veracini, A. Lebar, R. Blinc, B. Zalar, J.Phys. Chem. B 2005, 109, 769; b) V. Domenici, D. Frezzato, C. A. Veracini,J. Phys. Chem. B 2006, 110, 24884.

[19] V. Domenici, Phys. Chem. Chem. Phys. 2009, DOI: 10.1039/B902168J.[20] M. Kaspar, V. Hamplov�, V. Novotn�, M. Glogarov�, D. Pociecha, P.

Vanek, Liq. Cryst. 2001, 28, 1203.[21] R. Menicagli, C. Malanga, A. Marini, V. Domenici, C. A. Veracini, unpub-

lished results.[22] D. Catalano, V. Domenici, A. Marini, C. A. Veracini, A. Bubnov, M. Glogar-

ova, J. Phys. Chem. B 2006, 110, 16459.[23] R. Y. Dong, M. Geppi, A. Marini, V. Hamplov�, M. Kaspar, C. A. Veracini, J.

Zhang, J. Phys. Chem. B 2007, 111, 9787.[24] V. Domenici, A. Marini, C. A. Veracini, J. Zhang, R. Y. Dong, ChemPhy-

sChem 2007, 8, 2575.[25] a) D. Catalano, M. Cifelli, V. Domenici, K. Fodor-Csorba, R. Richardson,

C. A. Veracini, Chem. Phys. Lett. 2001, 346, 259; b) V. Domenici, MastersThesis, University of Pisa, 2001.

[26] V. Domenici, A. Marini, R. Menicagli, C. A. Veracini, A. Bubnov, M. Glogar-ova, Proceedings of SPIE—International Conference of Optics and Opto-electronics, 2007, 6587, pp. F1–F13.

[27] M. Geppi, S. Pizzanelli, C. A. Veracini, Chem. Phys. Lett. 2001, 343, 513.[28] V. Domenici, M. Cifelli, C. A. Veracini, V. E. Agina, N. I. Boiko, V. P. Shibaev,

J. Phys. Chem. B 2008, 112, 14718.

2690 www.chemphyschem.org � 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim ChemPhysChem 2009, 10, 2679 – 2691

V. Domenici et al.

[29] V. Novotn�, M. Glogarov�, V. Hamplov�, M. Kaspar, J. Chem. Phys. 2001,115, 9036.

[30] J. Jeener, P. Broekaert, Phys. Rev. 1967, 157, 232.[31] S. Wimperis, J. Magn. Reson. 1990, 86, 46.[32] D. Catalano, E. Ciampi, K. Fodor-Csorba, C. Forte, M. Geppi, D. Imbardel-

li, Liq. Cryst. 1996, 21, 927.[33] R. L. Vold, R. R. Vold in The Molecular Dynamics of Liquid Crystals, Kluwer,

Dordrecht, 1989.[34] Z. Luz, S. Meiboom, J. Chem. Phys. 1963, 39, 366.[35] L. Calucci, M. Geppi, J. Chem. Inf. Comp. Sci. 2001, 41, 1006.[36] J. A. Marqusee, M. Warner, K. A. Dill, J. Chem. Phys. 1984, 81, 6404.[37] P. L. Nordio, P. Busolin, J. Chem. Phys. 1971, 55, 5485.[38] P. L. Nordio, G. Rigatti, U. Segre, J. Chem. Phys. 1972, 56, 2117.[39] P. A. Beckmann, J. W. Emsley, G. R. Luckhurst, D. L. Turner, Mol. Phys.

1986, 59, 97.[40] R. R. Vold, R. L. Vold, J. Chem. Phys. 1988, 88, 1443.[41] P. Pincus, Solid State Commun. 1969, 7, 415.[42] R. Blinc, D. Hogenboom, D. O’Reilly, E. Peterson, Phys. Rev. Lett. 1969,

23, 969.[43] M. Vilfan, M. Kogoj, R. Blinc, J. Chem. Phys. 1987, 86, 1055.[44] R. Y. Dong, Mol. Phys. 1996, 88, 979.[45] K. Hiraoka, T. Seki, K. Miyayama, T. Hiejima, M. Kanekiyo, Ferroelectrics

2004, 310, 37.

[46] R. H. Acosta, D. J. Pusiol, Phys. Rev. E 1999, 60, 021 808.[47] R. C. Zamar, E. Anoardo, O. Mensio, D. J. Pusiol, S. Becker, F. Noack, J.

Chem. Phys. 1998, 109, 1120.[48] A. Carvalho, P. J. Sebastiao, A. C. Rebeiro, H. T. Nguyen, M. Vilfan, J.

Chem. Phys. 2001, 115, 10484.[49] V. Domenici, M. Geppi, C. A. Veracini, A. V. Zakharov, J. Phys. Chem. B

2005, 109, 18369.[50] V. Domenici, M. Geppi, C. A. Veracini, R. Y. Dong, Liq. Cryst. 2006, 33,

479.[51] a) D. Catalano, M. Cavazza, L. Chiezzi, M. Geppi, C. A. Veracini, Liq. Cryst.

2000, 27, 621; b) M. Cifelli, V. Domenici, C. A. Veracini, Mol. Cryst. Liq.Cryst. 2005, 429, 167.

[52] a) M. Skarabot, M. Cepic, B. Zeks, R. Blinc, G. Heppke, A. V. Kityk, I. Mu-sevic, Phys. Rev. E 1998, 58, 575; b) S. Kumari, R. Dhar, M. B. Pandey,I. M. L. Das, R. Dabrowski, J. Phys. Chem. Solids 2009, 70, 316.

[53] P. K. Mukherjee, A. K. Das, Physica B: Condensed Matter 2008, 403, 3089.[54] I. Bikchantaev, J. Szydlowska, D. Pociecha, A. Krowczynski, E. Gorecka,

Mol. Cryst. Liq. Cryst. 1997, 303, 121.

Received: May 21, 2009

Published online on September 2, 2009

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NMR Relaxation of Liquid-Crystal Mesophases