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J. Phys. Chem. C 2007, 111, 5286-5299
Orientational Order Properties in Fluorinated Liquid Crystals from an Optical, Dielectric, and 13C NMR Combined Approach D. Catalano,† M. Geppi,*,† A. Marini,‡ C. A. Veracini,*,† S. Urban,§ J. Czub,§ W. Kuczyn´ ski,| and R. Dabrowski⊥ Dipartimento di Chimica e Chimica Industriale, UniVersita` di Pisa, Via Risorgimento 35, 56126 Pisa, Italy, Scuola Normale Superiore, Piazza dei CaValieri 15, 56126, Pisa, Italy, Institute of Physics, Jagiellonian UniVersity, Reymonta 4, 30-059, Krako´ w, Poland, Institute of Molecular Physics, Polish Academy of Sciences, Smoluchowskiego 17, 60179, Poznan´ , Poland, and Institute of Chemistry, Military UniVersity of Technology, 00-908 Warszaw, Poland ReceiVed: October 12, 2006; In Final Form: December 22, 2006
Orientational order properties of two fluorinated nematogens, exhibiting a wide nematic range, have been investigated by means of optical methods, dielectric spectroscopy, and 13C NMR. 13C NMR spectra have been recorded by 1H-SPINAL decoupling CP techniques under both static and magic angle spinning conditions. The order parameters of the fluorinated aromatic fragments have been calculated by analyzing the 13C-19F dipolar couplings at different levels of approximations by means of a least-squares fitting procedure using geometrical parameters determined by DFT methods, eventually including empirical corrections for vibrations and anisotropic scalar couplings. The nematic order parameters determined from optical birefringence data, dielectric anisotropy, and NMR have been compared: their trends with temperature, analyzed by the Haller model and by more sophisticated ones, are very similar, even if the order parameters from optical birefringence are shifted to slightly higher values. The differences among the results obtained by the three methods can be related to the different anisotropic properties monitored, described by tensors whose principal or “long” axes can be located at slightly different places on the molecule. The assumptions and approximations used in each case are discussed in detail.
1. Introduction Fluorinated liquid crystals (FLCs) represent an important class of materials with possible applications in active matrix liquid crystal displays, especially thanks to their wide nematic ranges, low rotational viscosity, and high dielectric anisotropy ∆.1 An important requirement of a usable liquid crystal is also “reliability”, which includes chemical and photochemical stability and specific resistivity and voltage holding ratio: liquid crystals that derive their molecular dipole moment from one or more carbon-fluorine bonds (the so-called “superfluorinated” materials) are usually reliable. On the other hand, the anisotropy of physical macroscopic properties arises from long-range orientational ordering of rodlike molecules originating the mesophase. At a first approximation (for instance neglecting molecular biaxiality and flexibility), a quantitative description of the ordering can be done using the order parameter
1 Sl ) 〈P2(cos2 θl,n)〉 ) (3〈cos2 θl,n〉 - 1) 2
(1)
where θl,n is the angle between the phase director n and the l axis fixed on the molecule, desirably the “long’’ molecular axis, and the averaging is on the molecular reorientational motions. * To whom correspondence may be addressed. † Dipartimento di Chimica e Chimica Industriale, Universita ` di Pisa. ‡ Scuola Normale Superiore. § Institute of Physics, Jagiellonian University. | Institute of Molecular Physics, Polish Academy of Sciences. ⊥ Institute of Chemistry, Military University of Technology.
In principle, each experimental method measuring an anisotropic property of the liquid crystalline system can be used for determining order parameters. However, different techniques will measure parameters relative to peculiar molecular axes (we could say that, in some sense, any anisotropic property defines its “long’’ molecular axis) and consequently it happens to find significant disagreement among the order parameters, and among their temperature trends, obtained for the same compound by different experiments.2,3 In order to tackle this problem, we have undertaken comparative investigations of two FLCs throughout the broad temperature ranges of their nematic phase by employing optical and dielectric anisotropic measurements and 13C NMR spectroscopy. From the dielectric spectroscopy (DS) point of view, the number and positions of the dipole groups in the molecule are the key properties determining the dielectric anisotropy of the nematic phase.4 In addition, the rodlike shape of the molecule and the axial symmetry of the nematic phase make possible a simple application of the birefringence measurements for determining the order parameter.5,6 NMR experiments contain information about the local order parameters, depending on the type of nuclei under investigation.7,8 Despite the requirement of suitably isotopically enriched samples, the most investigated nucleus is deuterium, since the extraction of order parameters from simple NMR spectra is quite straightforward. On the contrary, 13C NMR can be performed on naturally abundant samples, but obtaining order parameters is often more complex. This can be due to bad spectral resolution and/or complicated signal assignment, as well as to the
10.1021/jp066710u CCC: $37.00 © 2007 American Chemical Society Published on Web 03/16/2007
Properties of Fluorinated Liquid Crystals assumptions usually performed in linking experimental observables (either anisotropic chemical shifts or C-H dipolar couplings) to order parameters.10 The presence of 19F nuclei in the molecule gives rise to 13C-19F couplings, which can be more directly related to order parameters, and which can be easily extracted from 13C spectra, provided that a sufficiently good spectral resolution is achieved. To this aim variable-angle sample spinning techniques have been employed in the past11,12 and efficient 13C-{1H} decoupling schemes are nowadays available, which allow good spectra to be recorded directly under static conditions.13 Orientational order of fluorinated liquid crystals has been already studied by NMR exploiting different nuclei and/or techniques.11,14-16 However, some complications arise in the 13C-19F coupling analysis, mainly due to the fact that non-negligible contributions of the anisotropic scalar interaction can affect the dipolar couplings. In the present work, the good resolution obtained in static 13C spectra allowed accurate 13C-19F splittings and anisotropic chemical shifts to be measured for all the carbons of the rigid aromatic moiety. The 13C-19F splittings, containing combined contributions of dipolar, isotropic, and anisotropic scalar couplings, have been analyzed for investigating orientational order properties at different levels of complexity in the treatment of experimental data, using molecular structural parameters computed by DFT methods. Moreover, a determination of the 13C chemical shielding tensors elements was attempted from chemical shift anisotropy data, exploiting the order parameters previously obtained. 2. Experimental Section 2.1. Samples. The chemical structures of the two fluorinated liquid crystals 1-fluoro-4-(4-(trans-4-propylcyclohexyl)cyclohex-1-enyl)benzene (3CyHeBF) and 1,2-difluoro-trans,trans4-(4-(4-propylcyclohexyl)cyclohexyl)benzene (3CyCyBF2) are shown in Figures 4 and 5, respectively. The phase transition temperatures of 3CyHeBF are 423 K from the isotropic to the nematic phase and 332 K from the nematic to the crystalline phase. The phase transition temperatures of 3CyCyBF2 are 397 K from the isotropic to the nematic phase and 321 K from the nematic to the crystalline phase. Both samples were synthesized following the synthetic route described in ref 17. 2.2. Dielectric and Optical measurements. The optical birefringence ∆n ) ne - n0 in the nematic phase of 3CyHeBF and 3CyCyBF2 was measured by the method described in ref 18. The birefringence was measured using a sample cell of variable thickness composed of a glass plate and a convex lens. The sample was placed between crossed polarizers on a microscope stage. In this arrangement a system of circular interference fringes was observed. From the diameters of fringes the optical birefringence ∆n can be calculated. For both samples, 3CyHeBF and 3CyCyBF2, the optical measurements were performed by decreasing the temperature from isotropic to nematic phase, but in the case of 3CyHeBF the sample was not chemically stable at high temperatures and several runs with new fillings of the cell had to be performed in order to obtain good experimental data. (Perhaps, due to the particular experimental conditions used in this technique, where the sample is in contact with metallic components, a reaction of the double bond of the cyclohexene ring with oxygen can take place, with consequent formation of some impurities and disalignment of the sample.) The static dielectric permittivity components in the nematic phase, || and ⊥, were measured by means of an impedance analyzer, HP 4192A, using a gold-covered parallel plate
J. Phys. Chem. C, Vol. 111, No. 14, 2007 5287 capacitor (C ∼ 50 pF). The samples were oriented by a magnetic field of 0.8 T. The thickness of the sample was 0.7 mm. The temperature was stabilized within (0.2 K. In the case of 3CyCyBF2 the dielectric measurements were performed by decreasing the temperature from the isotropic phase down to the crystallization point of the nematic phase, whereas in the case of 3CyHeBF the opposite procedure was applied in order to avoid the decomposition effects observed in the optical measurements. 2.3. 13C NMR Measurements. Solution-state spectra were recorded, at room temperature, on a Varian Unity 300 spectrometer, operating at 75.42 MHz for 13C and at 299.93 MHz for 1H, dissolving the samples in CDCl3. 13C NMR experiments on neat liquid crystals were carried out on a double-channel Varian Infinity Plus 400 spectrometer, working at 100.56 MHz for 13C, equipped with either a 5 mm goniometric probe or a 7.5 mm cross polarization magic angle spinning (CP-MAS) probe. In the case of the static experiments performed using the goniometric probe, the NMR glass tube was directly filled with the sample, while in MAS experiments the sample was put within a glass ampule fitting the ZrO2 rotor and sealed by an epoxydic glue. MAS experiments were recorded by spinning the sample at the magic angle (54.74°) with respect to the external magnetic field with a spinning frequency of 6 kHz. Both static and MAS experiments were acquired under highpower 1H-decoupling conditions, realized by means of the SPINAL-64 pulse sequence,19 with a decoupling field of about 40 kHz, and using the proton-carbon cross-polarization (CP) technique with a linear ramp on the carbon channel.20 The sample was macroscopically aligned within the superconducting magnet by slowly cooling from the isotropic phase. A stabilization time of 20 min was used at every temperature before acquiring the spectrum. The 1H 90° pulse length was 4.3-4.8 µs. CP spectra were recorded with a contact time of 4 and 10 ms for static and MAS experiments, respectively, accumulating 64 scans and using a relaxation delay of 15 s in order to minimize rf heating effects due to 1H decoupling. Temperature was always controlled within 0.2 K. The temperature calibration was performed for a given air flow using the known phase transition temperatures of some liquid crystals. 2.4. Calculations of Molecular Geometry, Dipole Moments, and Chemical Shifts. The molecular models of the mesogens 3CyHeBF and 3CyCyBF2 were built by GaussView 3.0 (Gaussian, Inc., Pittsburgh, PA) relative to the molecular fragments 1-fluoro-4-(cyclohex-1-enyl)benzene and 1,2-difluoro4-(cyclohexyl)benzene, respectively. The geometry of these fragments was optimized by Gaussian ’0321 using DFT method at the B3LYP/6-31G(d) level, in vacuo. After complete optimization of the systems, relaxed scans were executed, relative to the dihedral angle (C3-C4-C7-C8) with steps of 15° in both cases, so that the relative energy minima were optimized without constraints.22 The location and the components of the dipole moment, µ, have been calculated by CS Mopac Pro23 using a semiempirical AM1 method (a quantum mechanical molecular orbital method with classical empirical parametrization) and DFT method, after an optimization of the molecular geometry. The results obtained are summarized in Table 1. The isotropic chemical shift values for each carbon nucleus have been obtained by means of quantum-mechanical calculations, using Gaussian’03,21 on the two full molecules. All the calculations have been determined at the DFT level of theory using the B3LYP/6-31G(d)24 and MPW1PW91/6-311+G(d,p)25
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TABLE 1: Dipole Moments µ and Its Components Obtained by Different Methods: Group Dipole Moment Method (Empirical, GDMM),39 MOPAC Calculations (Semiempirical, SE),23 DFT Method (Quantum Mechanics Calculations, QM)21 3CyHeBF method
µ (D)
µz (D)
µx (D)
µy (D)
GDMM SE QM
1.8 2.116 2.612
-1.7 -2.105 -2.6041
-0.3 -0.032 -0.075
-0.153 -0.234
3CyCyBF2 β (deg)
β′ (deg)
µ (D)
µz (D)
µx (D)
µy (D)
4.38
3.1 3.251 3.596
-2.7 -2.712 -3.405
-1.6 -1.777 -1.157
-0.230 -0.1394
∼10 10.12
combination of hybrid functional and basis set, respectively. The 13C isotropic chemical shift have been calculated by the method of gauge-including atomic orbitals, GIAO.26 3. Theory 3.1. Optical and Dielectric Properties in Nematic Liquid Crystals. The optical methods for order parameter determination are considered the most popular and simple. This is connected to the fact that most applications of LCs rely on their optical properties. The order parameter obtained by optical methods is relative directly to the principal axis of the polarizability tensor, which individuates the most natural molecular frame of reference, since just the optical anisotropy determines the liquid crystalline appearance and most liquid crystal applications. However, because the electric field experienced by a molecule in a condensed phase differs from that applied across the macroscopic sample, the problem of evaluating the internal field has to be solved. Generally, the Vuks’ or Neugebauer’s model of the local field is accepted. Comprehensive reviews of the theories and a discussion about the influence of particular model assumptions on the order parameter values can be found in refs 5, 17, 18, and 27. In the dielectric spectroscopy method the probing electric field interacts with the dipole moment of a molecule that is embedded in a continuum of the same molecules. The interactions among molecules are taken into account by introducing the local field, which is larger than the external one. For the nematic phase the form of the local field has to reflect the principal features of the system (anisotropy of molecular interactions, shape of molecules, value and position of the dipole moment in the molecule, anisotropy of the molecular polarizability, density, etc.). Due to a weak knowledge of molecular interactions and to the complexity of the problem, several simplifications and approximations were introduced in the theoretical approaches describing the dielectric properties of the nematic state. For the discussion of the experimental results, the most useful is the Maier and Meier approach,28 which combines the Onsager model of the local field (valid for isotropic liquids) with the Maier and Saupe29 theory of the nematic state, in which the orientation-dependent potential energy of a rodlike molecule in the field of their neighbors is taken to be proportional to the order parameter S. Due to the axial symmetry of the nematic phase, with the macroscopic z-axis parallel to the director n, the dielectric tensor consists of two different principal elements: | ) zz, ⊥ ) xx ) yy. Depending on whether the measuring field is adjusted parallel or perpendicular to the director n, we obtain | or ⊥, respectively. The dielectric anisotropy, ∆ ) | - ⊥, will certainly depend on the extent to which adjacent molecules are parallel aligned, that is, the dependence on the order parameter S will be particularly relevant. Maier and Meier considered a molecule with a permanent dipole moment µ that makes an angle β with the long molecular axis assumed to be coincident with the minimum inertia moment axis. The anisotropy of the polarizability is taken into account by two principal elements Rl and Rt, along and transverse to the long axis, that give the
β (deg)
β′ (deg)
∼ 30 30.02 18.77
anisotropy of the molecular polarizability ∆R ) Rl - Rt. According to Maier and Meier the dielectric anisotropy is given by
[
∆ ) | - ⊥ ) 0-1N0hF ∆R - F
]
µ2 (1 - 3 cos2 β) S 2kBT (2)
where 0 is the permittivity of free space and N0 is the number density (which is equal to NAF/M, where M is the molar mass, F is the density, and NA is the Avogadro number). The local field factors h and F are dependent upon the mean dielectric permittivity 〈〉 ) (| + 2⊥)/3, while the anisotropy of the permittivity is ignored. Despite the various simplifications implied, eq 2 is commonly used for discussing the experimental results.4,30-32 3.2. 13C NMR Spectroscopy in Oriented Phases. In the high-field condition (i.e., when the Zeeman interaction is much larger than the other nuclear spin interactions) a spectral observable is given by the time average of the components of the corresponding NMR tensor T along the direction of the external magnetic field, 〈TZZ〉, where T indicates the type of interaction.33 The transformation of the components of tensor T from a Cartesian coordinate system (,τ,ν) to another one (a,b,c) follows the equation
Tab )
cos θa cos θτb Tτ ∑ τ
(3)
where θa is the angle between the and a axes. Now we fix the {,τ,ν} system on the molecule or on a molecular fragment, and the {a,b,c} system in the laboratory, with one axis, Z, coinciding with the magnetic field direction. The diagonal element TZZ is given by
TZZ )
1
cos θZ cos θτZTτ ) ∑ T + ∑ 3 τ 2
1
∑ (3 cos θZ cos θτZ - δτ)Tτ 3 *τ 2
(4)
Taking the time average of the previous equation, we have
〈TZZ〉 ) Tiso + Taniso ZZ
(5)
aniso where Tiso and TZZ , which represent the isotropic and anisotropic parts of the tensor, respectively, are given by
1 1 Tiso ) Tr{T} ) 3 3
∑ 〈T〉
(6)
and
Taniso ZZ )
2
∑ Sτ〈Tτ〉
3 *τ
(7)
with Sτ ) 〈1/2(3 cos θZ cos θτZ - δτ)〉. Equation 7 implies
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that the averaging processes due to molecular internal motions and to reorientations independently affect the tensorial components Tτ and the angle-dependent coefficients, respectively. Therefore, the possible correlation between rotation and conformational and vibrational motion is neglected. The order parameters Sτ, which are themselves elements of a Cartesian second rank tensor, or Saupe matrix, contain information on the probability distribution of molecular orientations with respect to the external magnetic field. Under 13C-{1H} decoupling, the 13C spectra of fluorinated organic samples are determined by chemical shift and by 13C-19F scalar and dipolar interactions. In anisotropic phases like the liquid crystalline ones, both isotropic and anisotropic contributions of each of these interactions must be taken into account. The analysis of the anisotropic contributions allows orientational order parameters to be determined by means of (7). In the spectra under study, the signal of each inequivalent 13C nucleus i is split into a doublet by each 19F nucleus j to which it is coupled and the separation between the two lines of the doublet is given by iso ∆νij ) 2Dexp ij + Jij
(8)
For simplicity, in eq 8 and in the following, the indices ZZ aniso pertaining to Dexp and to other anisotropic experimental ij , Jij quantities are omitted. The scalar coupling Jiso ij can be determined from isotropic spectra. The experimental Dexp ij includes the dipolar coupling, in turn given by a sum of contributions, and the anisotropic part of the scalar coupling
1 aniso eq h ah d Dexp ij ) Dij + Dij + Dij + Dij + Jij 2
Sij r3ij
(10)
where rij is the equilibrium distance between the two nuclei i and j and Kij is the dipolar constant defined as
Kij )
µ0pγiγj 8π2
Janiso ) ij
2 1 ∆J S + (J - Jij,yy)(Sxx - Syy) + 3 ij zz 2 ij,xx
[
]
2Jij,xySxy + 2Jij,xzSxz + 2Jij,yzSyz (13) The quantity
1 ∆Jij ) Jij,zz - (Jij,xx + Jij,yy) 2
(9)
Here Deq ij is the dipole-dipole coupling corresponding to the equilibrium structure of the molecule, Dhij is the contribution from the harmonic vibrations, Dah ij arises from the anharmonicity of the vibrational potential, and Ddij is the deformation contribution of the molecular structure due to anisotropic forces d of the solvent molecules.33 The terms Dah ij and Dij are usually estimated to be smaller than the experimental error on the experimental splittings, and therefore they can be safely neglected.34 The “equilibrium’’ dipole-dipole coupling, Deq ij , is related to the order parameter Sij of the internuclear ij direction (S(ij)(ij) in a more complete notation) through the equation
Deq ij ) -Kij
where θij, is the angle between the ij direction and the axis. As shown in eq 9, Dexp ij is also affected by the contribution from the harmonic vibrations, Dhij. This term depends on the equilibrium geometry of the molecule, on the order parameters, and on vibrational frequencies, normal modes, and temperature. Dhij is considered a correction of Deq ij , nonnegligible only for couples of nuclei rather close to one another, because it shows a 1/r5ij dependence.35 It is possible to calculate this contribution, if all the necessary constant quantities are known, and then to optimize, for instance, the order parameters, using the h 36 h expression of Deq ij + Dij. Another possibility is to evaluate Dij as the difference between the experimental data and the computed values, if the other contributions to Dexp ij are negligible. Finally, the Dhij values can be roughly estimated in analogy with those determined for molecules of similar structure and orientation.33 The contribution of 1/2Janiso to Dexp ij ij is usually very small for 1 X- H couplings, while in the case of 13C-19F couplings it may be nonnegligible34 and must be taken into account. From eq 7, is the following expression can be derived, where Janiso ij expressed in terms of the order parameters and of the tensorial components Jij,τ relative to the molecule-fixed coordinate system (x,y,z)
(11)
The local order parameter Sij can be expressed in terms of the components of the Saupe matrix relative to the (x,y,z) molecular frame
1 1 Sij ) Szz(3 cos2 θij,z - 1) + (Sxx - Syy)(cos2 θij,x 2 2 cos2 θij,y) + 2Sxz cos θij,x cos θij,z + 2Sxy cos θij,x cos θij,y + 2Syz cos θij,y cos θij,z (12)
(14)
defines the anisotropy of J with respect to the molecular z-axis for the ij couple of nuclei. Altogether, the components of the Saupe matrix can be determined by fitting a set of experimental Dexp ij couplings to a combination of eq 9 with eqs 10, 11, 12, and 13. As far as the chemical shift tensors are concerned, the relevant experimental quantities are, for the ith carbon nucleus, the ) δexp - δiso differences δaniso i i i , between the chemical shifts determined in the anisotropic and isotropic phases, respectively. (Also in this case the ZZ indices are here omitted.) As done for Janiso , an expression of δaniso can be derived from eq 7, where ij i this experimental quantity is related to the tensorial components σi,τ of the ith chemical shielding tensor in the molecule-fixed coordinate system.
) δaniso i
2 1 ∆σiSzz + (σi,xx - σi,yy)(Sxx - Syy) + 2σi,xySxy + 3 2
[
]
2σi,xzSxz + 2σi,yzSyz (15) The quantity
1 ∆σi ) σi,zz - (σi,xx + σi,yy) 2
(16)
defines the anisotropy of σ with respect to the molecular z-axis. The order parameters can be determined from a set of δaniso i values by using eq 15, on condition that all the necessary components of the shielding tensor are known. Alternatively, if the order parameters are known from the analysis of the dipolar splittings at various temperatures, the chemical shielding
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Figure 1. Optical birefringence vs temperature collected for 3CyHeBF and 3CyCyBF2 in the nematic phase. The lines are the fits to eq 17 giving the parameters shown in the inset.
Figure 3. Dielectric anisotropy ∆ ) | - ⊥ vs shifted temperature in the nematic phase of 3CyHeBF and 3CyCyBF2.
simplified relation between ∆ and S can be applied
S(T) ∼
Figure 2. Static dielectric permittivity components vs shifted temperature in the nematic phase of 3CyHeBF and 3CyCyBF2.
elements ∆σi (σi,xx - σi,yy), σi,xz, σi,yz, and σi,xy can be determined, at least in principle, for each 13C nucleus. 4. Results 4.1. Optical Results. In this study we have applied a simplified procedure, described in refs 18 and 37, where it was demonstrated that this method, despite its simplicity, provides very reliable results. The method demands the measurement of one physical quantity, the optical birefringence ∆n ) ne - n0, that is the difference between the extraordinary and ordinary refractive indices. The temperature dependence of ∆n was fitted by the following equation
(
∆n ) δn 1 -
T λ T*
)
(17)
where T is the absolute temperature and T*, δn, and λ are fitting parameters. No assumption on the local field model is needed. This procedure is equivalent to the extrapolation of ∆n to the temperature of absolute zero. Assuming that at this temperature the order parameter S has its maximum value, 1, we can calculate S(T) as ∆n(T)/δn. The optical birefringence ∆n ) neno in the nematic phase of 3CyHeBF and of 3CyCyBF2 is presented in Figure 1. The order parameters determined in the described way for both substances are shown in Figure 14. 4.2. Dielectric Results. The measured static permittivity components, |, ⊥, and the mean value 〈〉 ) (| + 2⊥)/3, are shown in Figure 2, whereas the dielectric anisotropy ∆ ) | - ⊥ is presented in Figure 3. For strongly polar compounds, the dipolar polarizability µ2/kBT dominates in square brackets of eq 2 and ∆R can be safely ignored. So, the following
T∆(T) hF2
(18)
The density of the substances studied is not known, but the expansion coefficient in the nematic phase is ∼10-4 K-1 and the temperature dependence of N0 can be safely ignored in relation to the change of ∆(T). For both compounds the polarizability anisotropy ∆R was estimated to be ∼13 Å3.38 The location and components of the dipole moments µ have been calculated by the group dipole moments method (GDMM),39 semiempirical (SE),23 and DFT methods,21 and the results obtained are summarized in Table 1. In the cases of GDMM and SE, β is the angle between the long molecular axis (coincident with the principal axis of the polarizability tensor) and µ, estimated with the aid of HyperChem software (Release 7.51),40 while in the case of DFT, β′ is the angle between the para-axis of the phenyl ring and the dipole moment. Looking at the chemical structures of the molecules, it seems that β and β′ could differ due to a flexibility of the cyclohexyl and cyclohexene rings. However, in the light of the results shown in Table 1, the value of µ ∼ 2.6 D obtained by DFT for 3CyHeBF seems to be overestimated. In the following, the β and µ values obtained by the GDMM method are used. Anyway, the choice among the various computed values is not critical for the final results. The values of the local field parameters are h ∼ 1.31 and 1.38 and F ∼ 1.33 and 1.43 for 3CyHeBF and 3CyCyBF2, respectively, and they slightly increase with decreasing temperature. Taking into account the above data, the following relations are valid: ∆R ∼ Fµ2/2kBT for 3CyHeBF, and ∆R , Fµ2/2kBT for 3CyCyBF2. In that situation, relation 18 is justified for the 3CyCyBF2 only. Because the absolute value of the order parameter cannot be obtained directly using eqs 2 or 18, the Haller relation41 was assumed
S(T) ) S0(∆T)γ
(19)
where ∆T ) TNI - T is the relative (shifted) temperature and S0 is a fitting parameter supposed to be related to the clearing temperature by the equation S0 ) 1/TγNI. Altogether, the experimental ∆(T) data trends are fitted to eqs 2 or 18 combined with eq 19, with a scaling factor (containing N0) and γ as fitting parameters. The γ parameters values are reported in Table 5. The order parameters S(T) are finally computed by eq 19 and shown in Figure 14 together with other results. The Haller relation is inadequate very close to TNI, since it predicts
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Figure 4. 13C NMR CP-MAS spectrum of 3CyHeBF, recorded with SPINAL-6419 decoupling techinique at 343 K. Molecular structure, numbering of carbon nuclei, and spectral assignment.
Figure 5. 13C NMR CP-MAS spectrum of 3CyCyBF2, recorded with SPINAL-6419 decoupling techinique at 343 K. Molecular structure, numbering of carbon nuclei, and spectral assignment.
S(T) ) 0 at T ) TNI, while the isotropic-nematic transition is experimentally and theoretically known to be first order.42 Therefore, the points for which ∆T < 2 K were discarded in the analysis. 4.3. 13C NMR Results. 4.3.1. Spectral Assignment and Spectral Parameters Determination. The assignment of the
solution state 13C spectra (not shown) for both 3CyHeBF and 3CyCyBF2 has been carried out on the basis of 13C DEPT, 1H-13C 2D-HETCOR, and 1H spectra, as well as of isotropic chemical shift values calculated by means of the DFT-GIAO method (see Figures 4 and 5 and Table 2). From the solution state spectra, the 13C-19F absolute values of the isotropic scalar
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TABLE 2: Isotropic, MAS, and Theoretical Chemical Shifts for Both Fluorinated Nematogens Studied in This Worka 3CyHeBF
3CyCyBF2
Cn
δGIAO (ppm)
δisotropic (ppm)
δMAS (ppm)
δGIAO (ppm)
δisotropic (ppm)
δMAS (ppm)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
163.27 115.07 126.30 137.13 126.30 115.07 139.27 122.57 35.56 42.86 34.14 29.45 41.37 29.04 33.38 36.53 32.18 27.45 38.42 19.75 14.56
161.32 115.08 126.57 135.57 126.57 115.08 138.67 120.75 34.13 43.82 33.72 31.16 39.08 29.52 32.35 33.72 31.94 28.47 40.72 20.28 14.65
161.8 115.1 127.2 136.2 127.2 115.1 138.9 121.3 34.8 44.4 34.8 31.4 40.2 29.5 31.4 34.8 31.4 28.5 40.3 20.3 14.4
149.54 154.49 116.32 143.77 122.94 115.28 43.99 33.18 33.84 41.42 32.87 33.22 42.30 29.49 29.49 35.71 31.51 30.05 38.76 19.91 13.72
149.39 151.83 116.89 144.88 122.97 115.67 43.90 33.62 34.62 42.84 34.62 33.62 43.38 30.21 30.21 34.62 30.21 30.12 40.10 19.43 14.65
149.3 151.6 117.7 145.7 123.2 116.2 44.7 35.5 34.8 41.2 34.8 35.5 43.9 31.4 31.4 35.5 31.4 31.4 39.2 19.2 14.4
a The isotropic chemical shifts were detected from solution state spectra recorded in CDCl3. MAS chemical shift values were obtained as average over the different temperatures in the whole nematic range. The theoretical chemical shifts were computed by DFT calculations using the GIAO method26 in Gaussian ’03.21
coupling constants (Jiso ij ), substantially independent of temperature, have been determined for the aromatic carbons (see Tables 3 and 4). Their signs have been assigned following the literature.43 From the 13C CP-MAS spectra (see Figures 4 and 5) recorded on both samples throughout their nematic ranges, it has been found that the values of the chemical shifts for each carbon signal experience only small fluctuations with temperature (up to a maximum of 30 Hz, much less than the experimental line width) and therefore can be safely considered constant in the following analysis. The average values of the 13C MAS chemical shifts, also reported in Table 2, are in very good agreement with both calculated and solution-state chemical shifts: most differences are less than 1 ppm and none exceeds 3 ppm. 13C CP spectra of both 3CyHeBF and 3CyCyBF2 under static conditions have been recorded at different temperatures in their whole nematic ranges. In Figures 6a and 7a expansions of the aromatic regions of these spectra for each sample are reported, together with the signal assignment. The difference between static and MAS spectra is due to the effects of the anisotropic interactions, and, in particular, of the 13C-19F dipolar coupling and the anisotropic component of chemical shift (δaniso). The dipolar coupling and the anisotropic scalar interaction split each 13C aromatic signal in one doublet for each 19F nucleus present in the ring (see eq 8), with splittings, ∆ν, ranging from tens to thousands of hertz, which are also determined by the anisotropic scalar interaction (see eq 9). The chemical shift anisotropy results in a high-frequency shift of the center of the multiplets (δobs) by up to 70 ppm. The strong dependence of splittings and chemical shifts on the order parameters, expressed by eqs 10, 13, and 15, causes the regular changes experienced by the spectra with temperature (see Figures 6b and 7b). The assignment of the static spectra has been performed on the basis of the magnitude of the observed splittings and of the trends of both the individual signals and δexp with temperature.
These last trends are reported in Figures 8 and 9. In the case of 3CyCyBF2, our assignment is in complete agreement with that previously reported by Fung et al.16 for a 13C Off-MAS spectrum. This assignment has been validated a posteriori by the following global analysis of the splittings ∆ν performed for determining the order parameters on the basis of eqs 8-12. Indeed, the relative values of the splittings ∆ν are strictly constrained by the molecular geometry, and therefore an incorrect assignment of the signals would give rise to a noticeable difference between calculated and experimental splittings for the mistakenly assigned carbon nuclei. Moreover, being δexp ) δaniso + δiso i i i and, referring to eq 15, exp the δi values of all aromatic 13C nuclei end up to coincide with the corresponding δiso i values if all the order parameters of the aromatic ring vanish. This condition occurs at the nematic-isotropic transition. However, because at the TNI temperature the order parameters have a discontinuity and the values abruptly collapse to zero, the correspondence δaniso i and δiso between δaniso i i values may not be straightforward in a crowded spectrum. On the other hand, if the δexp i (T) trends are extrapolated to temperatures higher than TNI, the δiso i values of all 13C nuclei of the same rigid fragment should be intercepted at the same temperature, namely, the virtual temperature at which the order parameters would vanish in the overheated nematic phase. The results of extrapolation procedure here outlined are shown in Figures 8 and 9 and confirm the coherence of the 13C spectra assignments in the isotropic and nematic phases. The complete list of assigned splittings at all temperatures is available as Supporting Information. From each splitting a value of Dexp was computed using eq 8 and the ij values of Jij are reported in Tables 3 and 4. 4.3.2. Determination of Order Parameters. To obtain the order parameters relative to the aromatic fragments of the two fluorinated mesogens, we have performed a global analysis of the Dexp ij values for the six carbons of the aromatic ring at all temperatures, using eq 9 and the subsequent ones. The internuclear distances and the angles required to use eqs 10 and 12 were determined by DFT calculations. The energetic barriers for the rotation of the aromatic fragments about their para axes for both fluorinated mesogens are relatively small: 2.8 kcal/ mol for 3CyHeBF and 2.2 kcal/mol for 3CyCyBF2, indicating the occurrence of an almost free rotation. The bond lengths and angles calculated for minimum energy conformations of 3CyHeBF and 3CyCyBF2 are reported in Tables 3 and 4, respectively. The geometrical parameters calculated for the various conformers are substantially equal to those calculated for the minimum energy conformer, bonds and angles differing by less than 0.01 Å and 0.01°, respectively. Fixing the axes frames as indicated in Figures 6a and 7a, and taking into account the different symmetry of the two aromatic fragments, the order parameters that can be determined are Szz and (Sxx - Syy) in the case of 3CyHeBF and Szz and (Sxx - Syy) and Sxz in the case of 3CyCyBF2. In fact, as always happens dealing with sets of couplings between nuclei of an aromatic ring, Sxyand Syz cannot be determined since in eq 12 they multiply vanishing geometrical factors. Moreover, the fast rotation around the para axis and the C2V symmetry of the aromatic ring of 3CyHeBF produce an averaging of symmetric couplings, so that the resulting experimental data are independent of Sxz. To estimate the contributions of the terms Dah, Dh, Dd, and aniso J to Dexp (see eq 9), we exploited the results reported for p-difluorobenzene in refs 33 and 34, where the authors performed very accurate determinations of all the terms by
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Figure 6. (a) Aromatic region of the 13C NMR CP static spectrum of 3CyHeBF, recorded with SPINAL-6419 decoupling techinique at 343 K. Structure of the aromatic fragment, numbering of carbon nuclei, and spectral assignment. (b) Evolution of this spectral region in the whole nematic range, from 423 to 332 K.
means of a combined theoretical and experimental approach. In particular, the terms Dah and Dd are very small and therefore can be safely neglected in the analysis, since they amount at most to 0.05 and 0.13% of Deq, respectively. The term Dh has been considered a possible correction to be value before performing the global applied to each Dexp ij analysis. The contribution percentage of Dh to Dexp has been estimated for each 13C-19F dipolar coupling from the ratio Dh/Deq 34 and is reported in Tables 3 and 4. By so doing, we are confident that the geometrical and vibrational features of the model molecule p-difluorobenzene at least roughly resemble those of the aromatic rings of 3CyHeBF and 3CyCyBF2, a severe requirement certainly better fulfilled for the former than for the latter compound. Moreover, in order to justify our procedure, the orientational behavior of p-difluorobenzene in nematic solvents should be similar to that of the relevant molecular fragments of 3CyHeBF and 3CyCyBF2, with the exception of a scaling factor for all the order parameters. This certainly does not happen, as it can be seen a posteriori by the proper comparison of order parameters. Nevertheless, as we are
going to see, this empirical procedure proves able to extensively improve the agreement between experimental and computed Dij values in the fittings. The term Janiso could be included in the global analysis of the Dexp ij values by means of eq 13, deriving an estimate of ∆J and Jxx - Jyy from ref 33. The values used in the cases of 3CyHeBF and 3CyCyBF2 are shown in Tables 3 and 4, respectively. Of course, the data transfer from p-difluorobenzene was much more straightforward for 3CyHeBF than for 3CyCyBF2. In the last case, only the most important Janiso contributions have been taken into account, relative to the two couples of directly bonded 13C-19F nuclei. The data reported in Table 4 for the C2-Fb couple have been obtained after applying the appropriate rotation to the Janiso tensor, given in ref 33, from its principal axes system to the ring-fixed (x,y,z) one. Both for 3CyHeBF and for 3CyCyBF2, the fitting of the Dexp ij values to determine the order parameters has been performed at various levels of approximation, taking or not taking into account the
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Figure 7. (a) Aromatic region of the 13C NMR CP static spectrum of 3CyCyBF2, recorded with SPINAL-6419 decoupling techinique at 343 K. Structure of the aromatic fragment, numbering of carbon nuclei, and spectral assignment. (b) Evolution of this spectral region in the whole nematic range, from 397 to 321 K.
contributions of Dh and Janiso as just described. The following four cases have been so obtained: Case 1: The simplest analysis of the Dexp ij values is carried out completely neglecting both Dh and Janiso contributions and eq thus roughly considering Dexp ij ≈ Dij . h Case 2: The estimated D contributions are taken into eq h account, thus considering Dexp ij - D ≈ Dij . Case 3: The estimated Janiso contributions are taken into eq 1 aniso. account, thus considering Dexp ij ≈ Dij + /2J h aniso Case 4: Both D and J contributions are considered, so h ≈ Deq + 1/ Janiso. D that Dexp 2 ij ij A compact presentation of the fitting quality obtained in the various cases is given in Figures 10 and 11 for 3CyHeBF and 3CyCyBF2, respectively. As far as 3CyHeBF is concerned, it is evident that the most refined data treatment (case 4) leads to an excellent reproduction of all the Dexp ij values at all temperatures. Also for 3CyCyBF2 the global best fitting is obtained in case 4, but significant residuals, of opposite sign, systemati-
cally concern the couplings C2Fa and C1Fb. This fact can be easily drawn back to the lack of correction for the Janiso contribution and/or to a wrong evaluation of the Dh contribution, crucial for these two couplings. In Figures 12 and 13 the trends of Szz obtained with the various data treatments are shown for 3CyHeBF and 3CyCyBF2, respectively. The fitting quality improvement corresponds to a moderate but systematic increase of Szz. Anyway, the “roughly” computed order parameters (case 1) always differ less than 5% from the most refined ones (case 4), where the uncertainty on each Szz value is estimated about 2 × 10-4 and 5 × 10-4 for 3CyHeBF and 3CyCyBF2, respectively. The biaxiality (Sxx - Syy) varies with increasing temperature from -0.030 to 0.005 ((8 × 10-3) for 3CyHeBF, while it is about constant (-0.068 ( 4 × 10-3) for 3CyCyBF2. The Sxz order parameter, determined only for the latter compound, is quite small but significant, ranging from -0.012 to -0.009 with an uncertainty of about 1 × 10-3. The
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Figure 8. Trends of δobs(T) for each chemically distinguished carbon of the aromatic and the alchenylic units of 3CyHeBF are reported throughout the nematic range. The extrapolation of δobs(T) to δiso MAS, at a virtual temperature T* ) 452.3 K is also shown.
Figure 9. Trends of δobs(T) for each chemically distinguished carbon of the aromatic unit of 3CyCyBF2 are reported throughout the nematic range. The extrapolation of δobs(T) to δiso MAS, at the virtual temperature T* ) 412.3 K is also shown.
nondiagonal order matrix obtained for 3CyCyBF2 can be diagonalized, at each temperature, with a rotation in the x,z plane of less than 1° and a nonsignificant increase of Szz of about 10-4. Therefore, in the following, we will consider the “para” or z-axis of the aromatic ring as the “long molecular axis” from
the NMR point of view. The Szz values of Figures 12 and 13, cases 4, are the corresponding principal order parameters. 4.3.3. Determination of 13C Chemical Shielding Tensors. As described at the end of the theoretical section, the components of the Saupe matrix could be determined from the
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TABLE 3: Geometrical Parameters: Fa-Cn Distances, Tξn Angles between the Cartesian Axis ξ and the Vector Connecting Fluorine(a) with Carbon n, and Molecular Parameters (Jiso, ∆J, Jxx - Jyy, and Dh) Relative to the Aromatic Fragment of 3CyHeBF Fi
Cn
rij (Å)
ϑzn (deg)
ϑxn (deg)
ϑyn (deg)
Jiso (Hz)
∆J (Hz)
Jxx - Jyy (Hz)
Dh (%)
a a a a
1 2,6 5,3 4
1.351 2.363 3.628 4.152
0.00 (30.86 (19.36 0.00
90.00 (120.86 (109.36 90.00
90.00 90.00 90.00 90.00
-244.6 21.0 7.8 0.0
400.0 -39.0 -17.6 0.0
13.0 -20.5 13.7 0.0
-2.57 -0.99 -0.35 -0.14
TABLE 4: Geometrical Parameters: Fa/b-Cn Distances, Tξn Angles between the Cartesian Axis ξ and the Vector Connecting Fluorine(a/b) with Carbon n, and Molecular Parameters (Jiso, ∆J, Jxx - Jyy, Jxz, and Dh) Relative to the Aromatic Fragment of 3CyCyBF2 Fi
Cn
rij (Å)
ϑzn (deg)
ϑxn (deg)
ϑyn (deg)
Jiso (Hz)
∆J (Hz)
Jxx - Jyy (Hz)
a a a a a a b b b b b b
1 2 3 4 5 6 1 2 3 4 5 6
1.346 2.364 3.635 4.155 3.642 2.377 2.360 1.346 2.370 3.652 4.112 3.626
1.26 -29.73 -18.92 0.41 19.72 31.28 90.53 59.41 29.09 40.26 58.74 79.45
-88.74 -119.73 -108.92 -89.59 -70.28 -58.72 0.53 -30.59 -60.91 -49.74 -31.26 -10.55
90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00 90.00
-245.3 12.5
400.0
13.0
-45.12
458.12
Jxz (Hz)
3.8 16.7 12.7 -247.9 16.7 4.8
257.0
Dh (%) -2.57 -0.99 -0.35 -0.14 -0.35 -0.99 -0.99 -2.57 -0.99 -0.35 -0.14 -0.35
TABLE 5: Best Fitting Parameter Values Obtained by Applying Equations by Haller41 and Chirtoc et al.44 to Optical, Dielectric, and NMR Experimental Results Haller systems
method
S0 (K - γ)
γ
TNI (K)
S**
A
T** (K)
η
3CyHeBF
∆n ∆a NMR ∆n De NMR
0.441 0.395 0.390 0.429 0.294 0.311
0.135 0.146 0.156 0.138 0.192 0.182
423.2 423.2 423.2 397.2 397.2 397.2
0.296 0.177 0.233 0.215 0.119 0.093
0.726 0.840 0.818 0.853 0.841 0.853
422.1 423.4 424.4 397.4 397.2 397.4
0.221 0.220 0.250 0.220 0.249 0.220
3CyCyBF2
a
Chirtoc et al.
In this case the fittings were done in the temperature range 421-360 K.
calc Figure 10. Mean values of the differences (Dexp ij - Dij ), computed on the whole temperature range investigated, for each 13C-19F couple of 3CyHeBF. The different cases refer to the different levels of refinement in the data analysis, as explained in the text.
anisotropy of the chemical shift by using eq 15, if all the necessary components of the shielding tensor were known. In the present cases, the order parameters of the aromatic fragments had been determined and the experimental trends of δaniso (T) i could be used to estimate the values of the parameters related to the shielding tensor components (as ∆σi, etc.) for the aromatic 13C nuclei. It is useful to recall that not only Sxy and Syz vanish for the planar aromatic rings of both compounds but also the corresponding multiplying parameters σxy,i and σyz,i are expected to vanish for all carbons (that is, two principal axes of all chemical shielding tensors can be reasonably located in the ring plane).
On the other hand, Sxz vanishes in the case of 3CyHeBF, while the σxz,i values are certainly different from zero at least for C2, C3, C5, and C6 in both compounds. In fact, in general, one of the principal axes of the chemical shielding tensor is probably more or less aligned to the CH or CF bond direction, so that the x, z axes are, to a good approximation, the principal axes for C1 and C4 chemical shieldings but not for the other 13C nuclei. Altogether, we could have aimed to determine ∆σi and (σxx,i - σyy,i) for all the 13C nuclei of both compounds, and also σxz,i for 3CyCyBF2. In practice, however, the widely dominant term in eq 15 is always the first one, owing to the very small values assumed by (Sxx - Syy) and Sxz, so that the only parameters which could be determined with reasonably small uncertainties were ∆σi. The results obtained are reported in Table 6. 5. Discussion The three experimental methods used to determine the orientational order parameters of the two fluorinated nematogens (optical, dielectric, and NMR experiments, respectively) measure different anisotropic physical quantities and, consequently, refer to different axis frames in which the order parameters are defined. Dielectric and optical methods characterize the ordering of the whole molecule, whereas NMR carries information about the order of molecular fragments, namely, in the present case, about the rigid fluorinated phenyl rings. For a detailed comparison of the three sets of results, it must also be kept in mind that, while from NMR measurements it was possible to derive order parameters independently at each temperature, this was
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calc Figure 11. Mean values of the differences (Dexp ij - Dij ), computed on the whole temperature range investigated, for each 3CyCyBF2. The different cases refer to the different levels of refinement in the data analysis, as explained in the text.
Figure 12. Order parameter Szz of 3CyHeBF, determined from 13C NMR spectral data. Different symbols are relative to the different levels of refinement in the data analysis, as explained in the text.
not possible from optical birefringence and dielectric measurements, for which the assumption of a suitable model giving the trend of the principal order parameter with temperature was necessary. Therefore, in order to compare the three sets of data, we needed a model to describe both the trend of the order parameters in the whole nematic range and a suitable normalization procedure in the attempt to refer the three sets of order parameters to the same axis frame. As far as the model for the trend of order parameters is concerned, many authors accept the Haller equation (19), despite the fact that it is incompatible with the weakly first order character of the nematic-isotropic transition, so that a good reproduction of the experimental trends in a range of about 2 K above the TNI transition is prevented. This problem can be empirically overcome by introducing a third parameter into the model (as, for instance, T* in eq 17), thus removing the strong assumption that the order parameter must continuously decrease to zero approaching TNI. Recently, Chirtoc et al.44 have proposed a refined four-parameter expression, consistent with the meanfield theory for a weakly first order phase transition
S(T) ) S** + Aτη
(20)
with η the critical exponent and τ ) (1 - T/T**) the reduced
13
C-19F couple of
Figure 13. Order parameter Szz of 3CyCyBF2, determined from 13C NMR spectral data. Different symbols are relative to the different levels of refinement in the data analysis, as explained in the text.
TABLE 6: Values of ∆σ ) [σzz - 1/2(σxx + σyy)] for 3CyHeBF and 3CyCyBF2, Determined by Eq 15a 3CyHeBF 3CyCyBF2
C1
C2
C3
C4
C5
C6
126.2 81.3
56.3 8.4
52.5 31.2
140.1 109.8
52.5 46.7
56.3 45.2
a The reference systems and numbering of atoms are indicated in Figures 6 and 7. Typical values of ∆σ are about 133 ppm for aromatic nonprotonated carbons on para axis, and about 47 ppm for aromatic protonated carbons in ortho and meta positions.45,46
temperature. T** is the effective second-order (quasi-critical or quasi tricritical) phase transition point seen from below TNI and is slightly higher than TNI. With the condition S(0) ) 1 at T ) 0, we have S** + A ) 1. In the same work, the authors have also revisited the order parameters determined by optical methods in the well-known nCB homologous series, finding η ≈ 0.25 for all members of the series, in agreement with the mean-field theory. The fits of the experimental data to the Chirtoc et al. equation, determined by the three experimental methods for both the nematogens investigated, give S** + A close to 1 and η very close to the suggested value of 0.25 (see Table 5). We can also
5298 J. Phys. Chem. C, Vol. 111, No. 14, 2007 notice that the γ parameter of eq 19, which plays a role analogous to η in eq 20, in all cases resulted much lower than 0.25. The determination of order parameters from optical and dielectric methods required several simplifying assumptions. In the case of dielectric anisotropy data it was assumed that the Maier-Meier formula (see eq 2) may be reduced to a simple relation (see eq 18), thus neglecting the temperature dependence of the density, as well as the polarizability anisotropy of the molecules: while the first assumption is well fulfilled, the second one is reliably justified only in the case of strongly polar compounds. In the case of optical studies, the local field problem was overcome by applying, for the normalization of the optical birefringence, an empirical formula proposed by Haller for polarizabilities, leading to eq 17. In the case of NMR, the large set of 13C-19F couplings was treated in a quite refined way, taking into account the contributions of anisotropic scalar interaction and possible deformations of the geometry due to harmonic vibrations; the contributions of additional terms to the measured dipolar couplings were neglected on the basis of either theoretical or experimental data present in the literature for analogous systems. In effect, the Dhij values depend on the order parameters of the molecule and the use of a “contribution percentage” taken from other cases is somewhat arbitrary. Similarly, the transfer of Janiso values from p-difluorobenzene to the fluorinated rings of our nematogens is partial and, strictly speaking, not rigorous. However the combined application of these two corrective procedures, besides improving the agreement between the experimental and computed couplings, allowed us to estimate the weight of such corrections for a reliable determination of the order parameters. It is evident and comforting that the increase of the Szz values consequent to the described refinements is quite smaller than the difference among the Szz values determined by different techniques. In the NMR data analysis, the aromatic ring order biaxiality (Sxx - Syy) was not neglected a priori and was very small (less than 5% of the corresponding Szz value) for both compounds at each temperatures, as usual for nematic compounds.6 The most refined NMR results, for which the location of the principal axis of order is along the ring para axis, have been chosen as reference data, which normalize both optical and dielectric results. The simplest normalizing procedure consists of applying a scaling factor independent of temperature to the values from optical or dielectric methods, in order to obtain the best superposition on the NMR trends for both compounds. A multiplying parameter, besides compensating possible systematic effects due to the different approximations underlying the three data sets, is also required in order to refer the order parameters of different sets to the same principal axis. The normalization of the optical and dielectric data to the NMR ones was performed privileging the superposition of the trends far from the nematic-isotropic transition. From Figure 14 it is apparent that NMR and dielectric results are about coincident for both 3CyHeBF and 3CyCyBF2, suggesting that the principal order axis monitored by the dielectric measurements is substantially parallel to the phenyl ring para axis. On the other hand, the optical results must be reduced by factors from which it is possible to estimate the angles between the principal axis of the optical anisotropy tensor and the para axis of the aromatic ring. Such angles result in about 10° and 15° for 3CyHeBF and 3CyCyBF2, respectively. The three sets of data so obtained (see Figure 15) almost coincide for both liquid crystals throughout their nematic ranges,
Catalano et al.
Figure 14. Order parameter in the nematic phase of 3CyHeBF and 3CyCyBF2 determined from optical, dielectric, and NMR data as explained in the text. The lines refer to the fittings of the experimental data using Chirtoc et al. equation,44 whose best fitting parameters are reported in Table 5.
Figure 15. Order parameter presented in Figure 14, where the optical and the dielectric data were normalized to the NMR data at 370 K for 3CyHeBF and at 330 K for 3CyCyBF2.
in agreement with previous findings,2,3 with the sole exception of the low-temperature dielectric data in 3CyHeBF, which below 360 K are hardly increasing; such peculiar behavior, probably ascribable to the particular experimental conditions, was not further investigated. 6. Conclusions In this paper a detailed analysis of orientational order parameters obtained throughout the wide nematic ranges of two fluorinated liquid crystals by means of optical, dielectric and 13C NMR techniques has been reported. In particular, the analysis of 13C-19F experimental couplings obtained by NMR is improved by taking into account the empirically estimated contributions arising from both anisotropic scalar interaction and possible deformations of the geometry due to harmonic vibrations. However, the order parameters determined in this way always differ by less than 5% from those roughly calculated by considering the contributions from dipolar and isotropic scalar couplings only. This indicates that the last, simpler method of analysis can be safely applied whenever a very accurate determination of the order parameter values is not strictly necessary. The order parameters obtained by optical, dielectric, and 13C NMR techniques were in very good agreement, also considering the intrinsic differences present in the three methods, and the difference is typically within 5% of the parameter values. In
Properties of Fluorinated Liquid Crystals effect, the order parameter trends from the three methods can be superimposed by means of a simple, physically sensible procedure aimed to refer the order parameters obtained by different techniques to the same molecular frame. While for NMR and dielectric relaxation the principal axes of order are substantially coincident for both compounds, they form with the principal axis of the optical anisotropy tensor a maximum angle of 10° and 15° for 3CyHeBF and 3CyCyBF2, respectively. All the experimental order parameters trends well fit the Chirtoc et al. equation throughout the wide nematic stability ranges, and the relevant parameters describing these trends are physically meaningful. However, it must be noticed that even the simpler Haller equation gives a similarly good agreement with the obvious exception of the temperatures close to the nematic-isotropic transition. Altogether no deviation from predictable nematic behavior is observed even far from the isotropic-nematic transition for the two fluorinated liquid crystals studied. This work should now allow one to approach more confidently similar studies on other interesting liquid crystals, for instance exhibiting more complex ferroelectric and anti-ferroelectric phases. Acknowledgment. This work was partially supported by the executive programme of scientific and technological cooperation between the Italian Republic and the Republic of Poland 20042006 (project no. 10) and by Italian PRIN 2005 035119. The authors are grateful to Professor Benedetta Mennucci for her support and helpful discussions concerning the DFT calculations. Supporting Information Available: Tables of 13C-19F experimental splittings, ∆νi, and of differences between experimental and calculated Dij values for both 3CyHeBF and 3CyCyBF2. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Virchow, R. Angew. Chem., Int. Ed. 2000, 39, 4216. (2) Urban, S.; Gestblom, B.; Kuczyn´ski, B. W.; Pawlus, S.; Wu¨rflinger, A. Phys. Chem. Chem. Phys. 1999, 1, 2787. (3) Urban, S.; Wu¨rflinger, A.; Gestblom, B. Phys. Chem. Chem. Phys. 2003, 5, 924. (4) Kresse, H. AdV. Liq. Cryst. 1983, 6, 109. (5) de Jeu, W. H. Physical Properties of Liquid Crystalline Materials; Gordon & Breach: New York, 1980; Chapter 4. (6) Dunmur, D. A.; Toriyama, K. in Handbook of Liquid Crystals. Fundamentals; Demus, D., Goodby, J., Gray, G. W., Spiess, H. W., Vill, V., Eds.; Wiley-VCH: Weinheim, 1998; Vol. 1, Chapter 3. (7) Veracini C. A. In NMR of Liquid Crystals; Emsley, J. W., Ed.; Reidel Publishing Co.: Dordrecht, 1985; pp 99-121. (8) Emsley, J. W. Nuclear Magnetic Resonance of Liquid Crystals; Emsley, J. W., Ed.; Reidel Publishing Co.: Dordrecht, 1985; pp 379-412. (9) Dong, R. Y. Nuclear Magnetic Resonance of Liquid Crystals; Springer-Verlag, Inc.: New York, 1994. (10) Fung, B. M. Prog. Nucl. Mag. Res. Sp. 2002, 41, 171. (11) Magnuson, M. L.; Tanner, L. F.; Fung, B. M. Liq. Cryst. 1994, 16, 857. (12) Edgar, M.; Emsley, J. W.; Furby, M. I. C. J. Magn. Reson. 1997, 128, 105. (13) Hodgkinson, P. Prog. Nucl. Magn. Reson. Spectrosc. 2005, 46, 197. (14) Catalano, D.; Gandolfo, C.; Shilstone, G. N.; Veracini, C. A. Liq. Cryst. 1992, 11, 151.
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