Conformational Changes at Mesophase Transitions in a Ferroelectric

Jul 26, 2010 - properties of a ferroelectric liquid crystal mesogen, namely, M10/**, through the combination of high resolution solid state 13C NMR an...
0 downloads 0 Views 4MB Size
Download PDF
J. Phys. Chem. B 2010, 114, 10391–10400

10391

Conformational Changes at Mesophase Transitions in a Ferroelectric Liquid Crystal by Comparative DFT Computational and 13C NMR Study Alberto Marini* and Valentina Domenici Dipartimento di Chimica e Chimica Industriale, UniVersita` degli studi di Pisa, Via Risorgimento 35, 56126, Pisa, Italy ReceiVed: June 3, 2010; ReVised Manuscript ReceiVed: July 1, 2010

In this work, we report a detailed investigation on both the conformational and the orientational ordering properties of a ferroelectric liquid crystal mesogen, namely, M10/**, through the combination of high resolution solid state 13C NMR and density functional theory (DFT) computational methods. The trends of the observed 13 C chemical shift in the blue, cholesteric, and ferroelectric SmC* phases of M10/** were analyzed in terms of conformational changes occurring in the flexible parts of the molecule. In particular, we focused on the aliphatic alpha methylenoxy carbons because of their high sensitivity to mesophase environment, as evidenced by experimental 13C chemical shift anisotropy (CSA). DFT computation of the chemical shift tensors as a function of geometrical parameters, such as dihedral angles, put in evidence significant changes in the average conformation at the mesophase transitions. The conformations predicted by DFT have been validated by comparing the calculated 13C chemical shifts with those experimentally observed for the alkoxylic carbons, whose relative orientation plays a key role in establishing the overall conformation of the molecule in each liquid crystalline phase. Furthermore, the orientational order parameters of the relevant flexible fragments were calculated and found to be in good agreement with those characterizing similar systems, thus validating our approach. 1. Introduction The conformational properties of liquid crystalline (LC) molecules are of fundamental importance in determining the liquid crystalline behavior: mesophase appearance at different temperatures, nature and thermodynamic stability of the mesophases themselves.1 Owing to the relatively dense molecular packing in the LC phases, the shape of the molecules determines the anisotropy of their local coordination environment. It is wellknown, for instance, that molecules consisting of rigid flat cores with symmetrically distributed six or eight lateral flexible chains most likely form discotic LC phases2 and that, depending on the most stable conformation of the rigid aromatic core, columnar mesophases of different symmetries may be formed.3-5 The difference in the local anisotropy of the calamitic and discotic molecules in the LC phases, along with their structuralchemical features, accounts for the fact that the conformational states of side chains of discotic molecules, for instance, in the discotic nematic phase, have a more profound effect on the order parameter S and on the temperature dependence S(T) as compared to that in the calamitic nematic phase.6 In general, the thermal conformational mobility of the chains7 results in a decrease in their contribution to the energy of the anisotropic intermolecular interaction and has a strong disordering effect on the molecular cores.8 The above factors are responsible for the inter-relationship between the orientational order of molecules and the conformational state of their chains in the LC phases. In turn, this relation should manifest itself in the dependence of the magnitude and the temperature behavior of the order parameter S on the chain length, especially when the mesophase is stable at high temperature, due to high thermal mobility of the molecular lateral chains.9 * Corresponding author. E-mail: [email protected]. Fax: +39 050 2219 260. Phone: +39 050 2219 204.

The conformational properties of bent-core liquid crystals was also the object of intense interest in the recent years because of the molecular chirality of “banana-shaped” molecules,10-13 due not to the presence of chiral carbons but to the stability of propeller-like (thus chiral) conformers stable in packed organized structures.14-16 In the case of banana-shaped liquid crystals, much attention was indeed devoted to the study of the molecular cores, usually consisting of 5-7 aromatic rings having different substituents and linking groups, and not much on the aliphatic lateral chains, since the sequence of peculiar bent liquid crystalline phases (Bi) seems to be more related to the bent aromatic cores.17 In the case of low molecular weight rod-like mesogens, it is generally assumed that the averaged molecular shape is likely to be cylindrical, especially in the nematic and smectic A phases, where intermolecular motions are extremely fast.18 This statement was confirmed by several studies on thermotropic LCs based on nuclear magnetic resonance (NMR):19 here, the molecular biaxiality is neglected or estimated to be very low (less than 0.05).20,21 However, particularly for chiral molecules forming the SmC* phase, the conformational properties are predicted22 to be crucial in determining the occurrence of the ferroelectric phase, and its subphases, as well as its typical properties: spontaneous polarization, helical pitch length, and molecular tilt. According to several theoretical works,22-24 the transition to the SmC* phase is related to a conformational change. Several theoretical25 and experimental26 works suggest that, due to the particular packing typical of the SmC* phase, the most stable conformer in the ferroelectric phase is bentlike, which is more stable than the more elongated uniaxial ones. Moreover, recent FT-IR studies27,28 have succeeded in showing a significant conformational change at the mesophase transitions of ferroelectric LCs.

10.1021/jp105095m  2010 American Chemical Society Published on Web 07/26/2010

10392

J. Phys. Chem. B, Vol. 114, No. 32, 2010

SCHEME 1: Schematic Representation of the Mesophases Formed by the M10/** Sample: (A) Blue Phase (BPII), (B) Cholesteric Phase (N*), and (C) Ferroelectric Smectic (SmC*) Phase

A powerful technique in studying the conformational properties is NMR spectroscopy, widely applied to investigate the average conformation of small molecules29 dissolved in LC environments30-33 as well as the specific solute-solute or solute-solvent interactions.34 Recently, the combination between computational and NMR methods12,35,36 allowed a more suitable and complete view of this topic, thanks to the development of more sophisticated computational tools,37 mostly applied to the study of molecules diluted in LC solvents. Moreover, few studies have been done on perdeuterated LC systems where 2H NMR data were analyzed in terms of conformational properties with the help of phenomenological and theoretical approaches, such as AP and Chord models.38-40 In this work, we are reporting a detailed conformational study based on the analysis of experimental 13C NMR data in combination with the DFT approach mostly focused on the two lateral chains, chiral and achiral ones of a ferroelectric mesogen,41 namely M10/**, showing blue (BPII), cholesteric (N*), and ferroelectric (SmC*) phases (see Scheme 1). This work fully supports the theoretical models25,42 which predict a significant conformational change at the origin of the ferroelectric SmC*

Marini and Domenici phase. The molecular orientational order,43 and in particular the molecular biaxiality in the SmC* phase, is also discussed in the frame of recent experimental and theoretical findings.20,21,42,44 2. Experimental and Computational Details 2.1. NMR Measurements. The compound 4′-(2-(-methylbutoxy)-propanoyloxy-biphenyl-4-yl-3-methyl-4-nonyloxy-benzoate, denoted here as M10/**, has been synthesized as reported in ref 45 and the mesomorphic behavior as detected by differential scanning calorimetry (DSC), optical polarizing microscopy, spontaneous quantities measurements and smallangle X-ray scattering (SAXS) is discussed in ref 41. Experimental details of the NMR data analyzed in the present work were first reported in ref 41. In the following paragraph, the relevant details of the solid state 13C NMR measurements of M10/** in the bulk are summarized. 13C NMR spectra on the bulk liquid crystal M10/** were recorded on a Varian Infinity Plus 400 spectrometer, operating at 100.56 MHz for carbon13, by using a 5 mm goniometric probe. In the whole mesomorphic temperature range, 13C NMR spectra were collected by using the proton-carbon cross-polarization (CP) technique with a linear ramp on the carbon channel.46 Proton decoupling during the 13C signal acquisition was done by the SPINAL-64 pulse sequence.47 To avoid sample heating, the recycle delay between each free induction decay (FID) acquisition was 8 s. The number of scans used is 400. The temperature calibration was made using the known phase transition temperatures of this liquid crystal. The 1H 90° pulse width was 4.2 µs, and the temperature gradient across the sample was estimated to be within 1 °C. 2.2. Computational Methods. In the last decades, DFT (with a suitable choice of both functional and basis sets) has succeeded in predicting various molecular properties for systems in the ground state at the equilibrium geometry. This approach, which has a computational cost of the same order as the HF method (considerably less than traditional correlation techniques), often gives a quality of calculations comparable to or even better than those of MP2.48 To shed further light on the experimental 13C NMR work of M10/** mesogen, in vacuum DFT calculations have been performed to obtain (i) optimized geometries and conformational distributions, (ii) the orientation and the principal components of the relevant chemical shielding tensors, and (iii) the dependence of CSTs on both structural parameters and conformational states. The molecular structure of M10/** (see Figure 1) was built up by GaussView 4.1, and all the calculations were done with the Gaussian 03 computational package.49 The geometry of M10/** was optimized in vacuo with DFT methods by exploiting the B3LYP/6-311G(d) combination of hybrid functional and basis set. In order to obtain the most populated conformational states of M10/**, the main relevant potential energy surfaces (PES) of the system were obtained by scanning the dihedral angles φ1, φ2, and φ3. In particular, φ1, φ2, and φ3 were scanned every 30, 45, and 30°, respectively, in the range 0-180°. Symmetry relationships were exploited to perform a complete conformational analysis. For our convenience, the following conventions have been chosen: (i) φ1 ) 0 represents the conformation where the OsCH2 (Ca) bond is in the phenyl plane, on the side opposite to the methyl group; (ii) φ2 ) 0 means that the CsH bond of Cb is on the same plane of the CzdO; and (iii) φ3 ) 0 is obtained when the OsCH2 (Cc) bond is on the same plane of the CsH bond of Cb. For each conformational state obtained for M10/** in the PES analysis, the 13C nuclear shielding tensors were calculated

Conformational Changes at Mesophase Transitions

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10393

Figure 1. (top) Molecular structure with labeling of the relevant carbons and of the dihedral angles investigated is also reported. (bottom) 13C NMR spectra of M10/** in its whole mesomorphic temperature range (BPII-N*-SmC*); the dashed red box shows the experimental peculiar trends of the alkoxylic 13C resonances (relative to carbons Ca, Cb, and Cc).

at the DFT level of theory using the GIAO approach50 with the Perdew-Wang exchange-correlation functional MPW1PW9151 and the 6-311+G(d,p) basis set, which revealed to be the best compromise between accuracy and CPU time resources.52 Finally, a suitable scale for referencing is required to relate the carbon chemical shielding values (σ scale) and NMR chemical shifts (δ shift scale), which are referenced to some standard. This can be built by computing the chemical shielding σref of the reference. In particular, both the 1H and 13C isotropic values for M10/** conformers can be obtained by referencing the absolute shielding tensors obtained by DFT to the absolute shielding of TMS (32.08 for 1H and 185.97 ppm for 13C), which is calculated at the same level of theory as for the molecular models. 2.3. Data Analysis. NMR data were acquired on the Varian instruments and processed using the software from Varian Inc. (Vnmrj and Spin-Sight 4.3.2 software for Sun microsystem workstation and Varian). Both the calculated NMR properties and the spectral parameters were mostly analyzed using homemade programs written in Mathematica 5.0 software for PC (copyright 1988-2003, Wolfram Research, Inc.). 3. Results and Discussion The molecular orientational order parameters and the conformational properties of M10/** are reported in the sections 3.1 and 3.2, respectively. The first section concerns the determination of molecular order parameters in the SmC* phase of M10/**, while the second section concerns the establishing of the most populated conformational states in the various LC phases by comparing the theoretical predictions with the experimental observed chemical shifts. 3.1. Orientational Order Properties of M10/**. The molecular orientational order parameters can be determined by analyzing the trend of measured 13C chemical shift anisotropies (CSA), reported in Figure 2. For each carbon nucleus in the M10/** sample, the observed chemical shift (δobs) measured

from static {1H}-13C spectra in the uniaxial LC phases (it is known that the phase biaxiality is negligible in the chiral tilted smectic phases35) can be related to orientational order parameters Sij and chemical shift tensor elements (δab, with ab ) xx, yy, zz, xy, xz, yz) by the following equation:53

δobs ) δiso + δaniso ) δiso +

2 ∆δ · Szz + 3

[

1 (δ - δyy)(Sxx - Syy) + 2δxySxy + 2δxzSxz + 2δyzSyz 2 xx (1)

]

where

1 ∆δ ) δzz - (δxx + δyy) 2

(2)

is the anisotropy of the chemical shift tensor, δ, with respect to the molecular z-axis. Both the Saupe ordering matrix S and the tensor δ are written in the molecular (MOL) frame (x, y, z). The observed chemical shift, δobs, has two main components, δaniso and δiso, which is defined as one-third of the trace of the chemical shift tensor δ. For symmetry reasons,30 eq 1 can be further simplified to

δobs ) δiso +

2 1 ∆δ · Szz + (δxx - δyy) · ∆biax 3 2

[

]

(3)

where ∆biax ) Sxx - Syy is the molecular biaxiality. In general, it is helpful to know the relationship between the molecular (MOL) and principal (PAS) frame. The tensor δ written in the molecular frame (see Figure 3, top) can be indeed related to that defined in its principal axes (PAS) system by means of the following equation:

10394

J. Phys. Chem. B, Vol. 114, No. 32, 2010

δMOL ) ab

∑ cos ϑεa cos ϑεbδPAS εε

Marini and Domenici

(4)

ε

where ϑεa is the angle between the ε principal axis and the a molecular axis. The local order parameters can, in turn, be expressed in terms of the elements of the Saupe order matrix relative to a frame fixed on a rigid molecular fragment using the following relationship:

SRβ )

∑ lRiSijljβ

(5)

i,j

where lRi is the direction cosine between the R and i axes. By using the combination of eqs 1, 2, 4, and 5, it is possible to calculate the orientational order parameters relative to both the two aromatic cores and the flexible aliphatic fragments. In the first part of our work, we focused our attention on the aromatic core of the M10/** mesogen, since it is the most rigid part of the molecule and the values of the order parameters found by performing a global fitting procedure on the aromatic carbons (labeled from C1 to C13 in Figure 1) and quaternary carbons (Cx and Cz in Figure 1) can be safely assumed to be identical to those of the whole molecule.20,21,43 In this analysis, the problem of knowing the shielding tensor elements in the molecular coordinate system, where the orientational order Saupe matrix is defined, has been overcome by employing DFT calculations, able to give the complete 3 × 3 shielding matrix for each carbon (principal components and relative orientation). In fact, the DFT calculations can reliably give the relative orientation of the PAS frame of the shielding tensors with respect to the molecular frame where the Saupe matrix is defined, thus overcoming the assumption of regular angles often used in the literature.43 13 C NMR Spectra in the Mesophases. The 13C NMR spectra relative to both the BPII and N* phases are characterized by broad and not well-defined peaks (see, for instance, the aromatic region in the range 100-150 ppm in the bottom part of Figure 1). This is due to the fact that, on one hand, the BPII phase has a whole isotropic structure and the N* phase is characterized by a cylindrical distribution of orientations. On the other hand, the CP-SPINAL technique is not effective in the presence of high internal mobility (characterizing low viscosity phases). Nevertheless, from the change in the line-shape, both in the aromatic (from 100 to 150 ppm) and the aliphatic (from 10 to 80 ppm) regions, it is possible to distinguish between these two phases. At the phase transition between the N* and SmC* phases, the observed 13C chemical shifts, δobs, of the aromatic carbons (from 125 to 250 ppm) increase markedly and those of the aliphatic carbons (from 0 to 50 ppm) decrease slightly. This fact is typical of ordered phases, such as the SmA* phase (paraelectric orthogonal smectic A*), but it is not expected in the SmC* one, in which the helical structure usually orients with the helical axis, h (and the local phase director, n), parallel (tilted) with respect to the magnetic field, H.54 The increasing of aromatic δobs with the decreasing of temperature is due to the total unwinding of the helical structure in the SmC* phase of M10/**. This means that the operating NMR magnetic field of 9.4 T is higher than the critical field, Hc, thus able to unwind the helical structure. This phenomenon has been observed in other chiral smectogens20,21,43 with a similar chemical structure, in which the critical field Hc was found to be in the range 2-20 T. As a consequence of the total unwinding of the SmC* helical

TABLE 1: Experimental Isotropic Chemical Shifts (Measured in the Melt at 100 °C), GIAO-DFT, Calculated on the Minimum Energy Conformation of M10/**, Chemical Shift Tensor Principal Components, and Isotropic Part (ppm)a carbon

δiso Exp

δiso DFT

δXX

δYY

δZZ

ϑ

C1 C2 C3 C4 C3p C2p Cx C6 C7 C8 C9 C10 C11 C12 C13 Cz

161.8 127.0 132.2 122.2 130.1 110.1 172.1 150.7 120.8 128.2 138.4 137.8 128.1 121.7 149.9 165.2

162.5 125.8 130.7 120.5 131.4 107.3 175.8 152.0 120.8 126.8 138.9 139.4 126.7 119.8 150.9 171.8

173.3 156.4 143.4 132.0 150.7 120.4 143.8 139.5 171.3 181.8 172.2 175.3 181.8 169.9 136.2 118.6

70.2 15.8 21.3 24.0 3.6 7.2 148.6 71.5 13.3 15.1 16.3 15.0 15.4 13.3 73.4 116.3

244.1 205.1 227.2 205.7 239.9 194.1 234.9 245.1 177.9 183.5 228.3 228.0 183.0 176.3 243.1 280.3

0.1 60.5 129.7 178.5 –125.3 –52.9 137.8 0.3 64.7 119.2 0.1 0.2 60.7 112.3 4.3 128.3

a ϑ (deg) is the angle between the z-axis of the chemical shift principal axes frame and the para-axis of the relevant aromatic fragment (values are derived from DFT calculations).

structure, the tilt angle of the phase cannot be determined from the analysis of the temperature variation of chemical shifts. Coming back to the spectral feature analysis, in the middle region of the spectra (from 50 to 100 ppm), the signals of the alkoxylic carbons Ca, Cb, and Cc (see Figure 1 for the assignment) exhibit quite peculiar trends with the decreasing of the temperature. In fact, δobs for all three signals changes abruptly at each phase transition, while it is very stable (maintaining a constant frequency) within each LC phase. This experimental evidence can be ascribable to the occurrence of conformational changes at the mesophase transition, rather than to a continuous increase of the orientational order of the fragments with the decreasing of the temperature. Chemical Shift Tensor Calculations. The agreement between DFT and experimental isotropic chemical shifts is very good (see Table 1, RMSE ) 1.4 ppm), and the values calculated for the principal components are in agreement with those reported for similar compounds.12-14,43 In particular, the CSTs used in the analysis of the aromatic δobs correspond to those evaluated for the minimum energy conformer found in the PES of M10/ **, which turned out to be that mostly populated in the SmC* one, as will be demonstrated in section 3.2. However, it is worth mentioning that the DFT calculated chemical shielding tensors of the aromatic carbon, used for obtaining the molecular order parameters, were found to be substantially independent from the conformations of the flexible aliphatic chains. In particular, this is true for the aromatic carbons C1-C12, not affected by the rotations of the aliphatic parts, while is less obvious for the Cz, where a small dependence of its CST components (max. 1.5 ppm) from the chiral branched chain rotation has been found. Moreover, several tests performed with different subsets of CSTs and the corresponding δobs (e.g., by excluding carbon Cz from the analysis, or by evaluating the order parameters for the biphenyl and phenyl moieties independently) were used to support the reliability of the derived order parameters. All this considered, the calculations of molecular order parameters can be safely considered to be independent from the conformations assumed by the aliphatic moieties. Molecular Order Parameters. The use of computational methods has allowed us to correctly reassign the 13C NMR

Conformational Changes at Mesophase Transitions

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10395

Figure 2. Temperature trends for the 13C NMR chemical shifts (ppm) for the aromatic and carbonyl carbons of M10/** observed in its mesophases (SmC*, N*, BPII) and isotropic melt (Iso).

spectra in both the isotropic melt and in the mesophases, which is now shown in Figure 2. All of the anisotropic chemical shifts measured from 13C-1H static spectra for the aromatic and carbonyl carbons were simultaneously analyzed using eqs 1, 2, 3, and 4 in purposely written software and exploiting nonlinear least-squares methods to give the molecular orientational order parameters, Szz and ∆biax, reported as a function of temperature in Figure 3. According to eq 3, the Saupe matrix has been assumed to be diagonal in the MOL frame and related, via eq 5, to the fragmental frames (FRAG) of each aromatic core by two angles R and β defined as the angles between the ZMOL axis and the para-axes of the phenyl and biphenyl, respectively (see Figure 3, top). These angles can be obtained from the simultaneous fitting of the trend of CSA. The main molecular order parameter, Szz, for M10/** was found to be in the interval 0.88-0.92 by decreasing the temperature. The molecular biaxiality, ∆biax, is almost constant (∼ -0.265) in the whole SmC* temperature range (see Figure 3, bottom). The quality of the present fitting (see Figure 2) was extremely good, with an estimated variance [defined as the mean value of the square of the deviation of the variable (in our case the order parameters) from its expected value or mean] of 0.976 and a mean absolute deviation in the recalculated chemical shift anisotropies of 0.742 ppm (see Figure 4). The obtained values of Szz are in agreement with those previously determined41 by exploiting CST values taken from the literature. Moreover, the order parameters as well as the chemical shifts have a slight temperature dependence within the SmC* phase, in agreement with the other physical properties measured for M10/** (i.e., small-angle X-ray scattering, spontaneous polarization, tilt angle, and dielectric spectroscopy data reported in ref 41). The values of R and β, constant within the SmC* phase, were found to be 10.6 and 0.4°, respectively, leading ZMOL to be almost coincident with the Zbiphe axis. The angle γ between the aromatic fragments, defined as

Figure 3. Molecular orientational order parameters, Szz, and biaxiality (∆biax ) Sxx - Syy) of M10/** in its SmC* phase. The principal axis system of the molecular order is reported on the top, with the molecular core structure and the relevant structural angles R and β, which define the orientations of the phenyl and the biphenyl units, respectively.

Figure 4. Plot of the residuals (ppm) for the aromatic and carbonyl 13 C of M10/**, used for the determination of the orientational order parameters in its SmC* phase.

γ ) R - β, is found to be 10.2° from this analysis, in good agreement with that predicted by DFT calculations (11.4°). As a final remark of this first part of the work, the biphenyl unit is the most uniaxial part of the molecular core even though it is attached to the chiral (branched) chain,20 while the phenyl moiety is the more biaxial part. This could be justified by the presence of a CH3 substitute on the phenyl moiety, thus giving it a biaxial character. However, a recent review20 over several ferroelectric LCs studied by 2H and 13C NMR techniques

10396

J. Phys. Chem. B, Vol. 114, No. 32, 2010

Marini and Domenici

Figure 5. (a) Conformational energy, ∆E (kcal/mol), as a function of the dihedral angle φ1 (deg) variation in the 0-180° torsional range (an expansion of the graph, showing the range 0-90°, is reported in the inset). (b) Trend of the 13C δiso for Ca carbon (achiral chain) as a function of φ1 angle. The experimental values in the three LC phases are also reported as continuous lines within the dihedral angle variation 0-180°. The gray area represents the region of phase space with energy greater than 6 kcal/mol and with 0% population according to Boltzman distribution analyses performed in the 25-125 °C temperature range.

suggests that a limitation in the internal degrees of freedom (or symmetry breaking) is likely to be present in FLCs and that this reduction of mobility reflects in the high value of the biaxiality of both the aromatic core and overall molecule. Indeed, the molecular biaxiality found in this analysis (∆biax ∼ -0.265) is rather large, in agreement with both experimental and theoretical studies, where a large molecular biaxiality was experimentally observed in several LCs in their SmC* phase.42,44 3.2. Conformational Properties of M10/** in the Different Mesophases. In this second part of the work, we focused our attention on the analysis of the 13C NMR spectral region from ∼50 to ∼100 ppm, put in evidence in Figure 1 (bottom), which is related to the alkoxylic carbons, Ca, Cb, and Cc, of M10/** smectogen, defined in Figure 1 (top). In order to shed light on the peculiar trends of the 13C NMR chemical shift observed in this spectral region, detailed DFT calculations of the potential energy surfaces and of the 13C isotropic chemical shifts have been performed. The aim is to understand if the conformational properties of this molecule in the different mesophases can justify the observed changes in the chemical shift trends at the phase transitions. To do that, we followed the steps here itemized: (1) DFT calculations of the δ tensors of Ca, Cb, and Cc carbons as a function of different conformations of the M10/** smectogen; (2) identification of the most populated conformers of M10/** in the three mesophases by comparing the observed chemical shift and the computed δiso (in the hypothesis of substantial neglecting of the anisotropic contribution δaniso ≈ 0); (3) validation and discussion of the previous hypothesis and calculation of the fragmental order parameters S relative to Ca, Cb, and Cc local frames. (1) In Figure 5a, the conformational energy, ∆E (kcal/mol), as a function of the dihedral angle φ1 (deg) is reported. The graphic shows that (i) the most stable conformation for Ca is obtained for φ1 ) 0° and that (ii) the energy increases with the increasing of the dihedral angle variation in the range 0-180°. Therefore, the conformations with φ1 > 90° are largely disadvantaged in terms of energy and, consequently, the

Boltzmann populations at 25 °C (125 °C) for φ1 ) 0°, 30°, 60°, and 90° < φ1 < 180° were found to be 95.6 (90.8), 4.3 (8.8), 0.1 (0.4), and 0, respectively. Of course, we know that the computed in Vacuo conformational populations may be drastically altered in the condensed phases due to intermolcular interactions, but all this cannot change the fact that the torsional energy barrier at φ1 ) 180° is extremely high, around 120 kcal/ mol, due to the steric repulsion of the Ca with respect to the ortho methyl substituent in the phenyl ring. A similar situation was found in a bent-core LC mesogen, A131, recently studied by combined 13C NMR and DFT calculation approach.12 Preliminary tests showed that the chemical shift tensors of Ca carbon, very sensible to the variation of φ1 dihedral angle, are completely not affected by the rotation of the other two scanned angles, φ2 and φ3, which instead have a direct influence on Cb and Cc carbons. This allowed us to separate the complete phase space F[φ1,φ2,φ3] in the subphase spaces P[φ1] and Q[φ2,φ3], which consequently lead to the following reparametrization of the problem: δF[φ1,φ2,φ3] = δP[φ1] x δQ[φ2,φ3] (with δ and x indicating the isotropic part of the chemical shift tensor of the carbons relevant for the analysis and the summation between the two chemical shift parametric phase spaces). This separation of variables, guaranteed by the fact that the chemical shift is a local property (Ca ∈ P, Cb ∈ Q, and Cc ∈ Q), leads to the generation of one 1D profile (see Figure 5b) and two 2D surfaces (see Figure 6) of the calculated isotropic chemical shifts, δiso, for Ca, Cb, and Cc carbons as a function of the interested angles. The 1D profile and the 2D surfaces, which represent the predicted variations of the isotropic chemical shifts as a function of the investigated geometrical parameters, will then be used for establishing the most populated conformational states of M10/** in its whole mesomorphic range. (2) In a first approximation, we have compared the δobs, measured in the static 1H decoupled 13C spectra, with the theoretical ones by assuming their chemical shift anisotropies to be negligible, namely, δobs ≈ δiso. By searching for the unique sets of [φ1,φ2,φ3] coordinates (defined here as “unique points”

Conformational Changes at Mesophase Transitions

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10397

Figure 6. 13C δiso hypersurfaces relative to the alkoxylic carbons of the chiral chain (Cb and Cc) as a function of the dihedral angles φ2 and φ3 (deg). The experimental δiso (ppm) values for carbons Cb and Cc, in correspondence of the proper φ2 and φ3 pair of values found in the three LC phases, are also reported as filled circles with different colors: BPII (red), N* (blue), SmC* (green).

TABLE 2: Experimental Observed Chemical Shifts (Data Averaged from the Data Measured within Each LC Phase), GIAO-DFT Calculated δiso (ppm) for the Aliphatic Ca, Cb, and Cc Carbons of M10/**, and Dihedral O1, O2, and O3 Angle Values (deg) Determined by the Analysis of the Experimental and Computed Data, as Explained in the Texta BPII N* SmC*

a

Ca Cb Cc Ca Cb Cc Ca Cb Cc

EXP

DFT

67.1 72.3 72.3 65.0 71.5 72.8 64.1 69.2 82.4

66.5 (65.0-69.0) 72.5 72.4 64.8 (64.5-65.5) 71.8 72.6 64.0 71.1 79.3

EXP and DFT φ1 φ2 φ3 φ1 φ2 φ3 φ1 φ2 φ3

30-60 60 45 0-30 0 90 0 120 135

The labels of carbon atoms and dihedral angles refer to Figure 1.

for our convenience) for each distinct LC phase of the phase space F which gives the lowest root mean square error (RMSE) between the experimental, δobs, and the theoretical isotropic shifts, δiso, for Ca, Cb, and Cc, it is possible to determine the average conformation of the molecule in the three LC phases (BPII, N*, and SmC*). The numerical results of our analysis are reported in Table 2, where the experimental δiso for Ca, Cb, and Cc are compared with those obtained by DFT on the investigated conformations. Moreover, the unique phase space points are shown in (i) Figure 5b by the intersections of the calculated profile (blue line) with the three experimental straight lines (black, red, blue) and in (ii) Figure 6 by filled circles of different colors, which represent the experimental δiso values. The sets of dihedral angles φ1, φ2, and φ3 (see Table 2) necessary for the definition of the orientation of the chiral chain with respect to the principal molecular axis system are found directly from the phase space points shown in Figures 5b and 6. In particular, the dihedral angles φ1, φ2, and φ3 reported in Table 2 have been selected also on the basis of their Boltzmann weights, evaluated from their relative energies (see previous section). Concerning φ1, the range of variation 90-180° (marked in gray color in Figure 5b) has been excluded from the analysis because it corresponds to high energy (6 kcal/mol < E < 120

kcal/mol, which corresponds to a 0% population in the 25-125 °C temperature range) and very distorted molecular geometries. The dihedrals φ2 and φ3 exhibit quite the same behavior with respect to their angle variations, thus showing high-energy regions in the intervals 120-180 and 150-180°, respectively. The main populated conformers of M10/** in the three investigated LC phases are displayed in Figure 7, which put in evidence that there is a progressive loss of the motional freedom relative to Ca of the achiral (linear) chain, when decreasing the temperature, passing from the BPII to the N* and finally reaching the SmC* phase. This decrease of conformational freedom is supported by the analysis of both the computed and the experimental chemical shifts of the alpha methylenoxy Ca carbon (see Figure 5b), as well as from the torsional energy profile relative to φ1 (see Figure 5a). It is worth noticing that our analysis is focused on the first carbon (Ca) of the achiral chain, since the other carbons in the chain clearly do not show any temperature dependence trend in their 13C chemical shift. For this reason, what happens in the rest of the chain cannot be inferred directly from 13C NMR. It is possible, however, to speculate that in the low temperature LC phases the lateral chains are stable in a single conformation, while in the higher temperature ones the rotational freedom is supposed to be active so that the other carbons of the tails pass from one conformation to another giving rise to an “averaged” chemical shift in the NMR time scale. As observed in discotic systems,55 the conformational change interesting first carbon linking the aromatic core to the lateral chain, the Ca in this case, undoubtedly affects the orientational order properties and the motional freedom of the rest of the chain, which should remain in a sufficiently elongated shape to not completely lose its overall uniaxiality. Furthermore, it is worth noticing that, assuming the linear chain to be in the full extended all trans configuration, the calculated molecular lengths for M10/** in its conformational states populated in BPII, N*, and SmC* phases are 36.3, 35.8, and 35.1 Å, respectively. The decreasing of the maximum length of the M10/** molecule by decreasing the temperature is also supported by SAXS measurements.41 (3) In order to verify the hypothesis of δobs ≈ δ iso, we have focused our considerations in the SmC* phase, where the

10398

J. Phys. Chem. B, Vol. 114, No. 32, 2010

Marini and Domenici

Figure 7. Main populated conformers in the different LC phases.

presence of a single average conformer for the M10/** molecule is easy to be accepted on the basis of the literature and where the molecular order parameters are known (see section 3.1). The first assumption is that the molecular order of the M10/** is not influenced by the lateral chains. This is confirmed in the literature for many other LC systems, since the rigid part of the molecule, the aromatic core, is commonly used to investigate the whole molecular orientational order.21,43 As a consequence, the values of Szz and ∆biax reported in section 3.1 could be used to evaluate the anisotropic component of the chemical shift, δaniso ) δobs - δiso, for the three carbons Ca, Cb, and Cc, by recurring to eqs 1-4. More specifically, for each alkoxylic carbon, the computed values of the chemical shift tensor components, δii, and the relative orientations of the CasO, Cbs(CdO), and CcsO bonds with respect to the molecular frame, were used. The relevant geometrical parameters used in the above-mentioned analysis are reported in Table 3, where the angles ΘZ (FRAG-MOL) and ΘZ (PAS-MOL) define the orientations of the principal 1-axis with respect to the fragments (CasO, Cbs(CdO), and CcsO bonds) and the molecular frames, respectively. The calculation of δaniso components has been done by considering the simplified eq 4 in the case of (i) molecular uniaxiality (∆biax ) 0) and (ii) molecular biaxiality not negligible (∆biax * 0), by using the value of ∆biax ≈ -0.265, obtained from the analysis of the aromatic chemical shift (section 3.1). The values of δaniso found for Ca, Cb, and Cc are 0.29 (0.37), 0.43 (0.60), and -0.36 (-0.47), respectively, with (without) considering the molecular biaxiality. By considering the values of δiso reported in Table 3 and the corresponding δaniso, one can quite straightforwardly conclude that δobs ) δaniso + δiso ≈ δiso, with δaniso being of the order of the experimental error; thus, δaniso ≈ 0 for the three carbons. If this is true for the SmC* phase, we can easily extend this conclusion also to the less ordered phases (blue and cholesteric ones). It is important to notice that, in our analysis, the assumption of δaniso ≈ 0 is even more true if the molecular biaxiality is included.

TABLE 3: GIAO-DFT Calculated Chemical Shift Tensor Components (δxx, δyy, δzz) and Parameters (∆δ, δbiax) (ppm) for the Aliphatic Carbons Ca, Cb, and Cc of M10/**a Ca

Cb

Cc

δxx δyy δzz ∆δb δbiaxb Θz PAS-FRAG Θz FRAG-MOL Θz PAS-MOL δxx δyy δzz ∆δb δbiaxb Θz PAS-FRAG Θz FRAG-MOL Θz PAS-MOL δxx δyy δzz ∆δb δbiaxb Θz PAS-FRAG Θz FRAG-MOL Θz PAS-MOL

BPII

N*

SmC*

75.2 36.7 87.5 31.5 50.8 10.2 43.1 53.3 85.1 41.4 90.4 27.1 49.0 7.7 42.1 49.8 83.1 27.4 106.3 51.0 78.9 –1.9 72.3 70.4

71.5 32.8 90.3 38.1 57.5 8.9 44.5 53.4 90.0 32.5 91.8 30.6 59.3 13.8 38.9 52.7 87.8 23.9 106.5 50.7 82.6 –4.8 67.8 63.0

69.2 34.1 88.8 37.1 54.7 7.3 46.8 54.1 80.0 46.2 81.4 18.3 35.2 16.2 36.4 52.6 93.1 39.1 115.1 49.0 76.0 –6.2 61.6 55.4

a The orientations (deg) of the principal 1-axis of the CS tensors are also reported w.r.t. the relevant frames (FRAG and MOL) used in the calculations of molecular order parameters. The labels of the carbon atoms refer to Figure 1. b In this paper, we denote the principal elements of the symmetric part of the shift tensor by δzzPAS > δxxPAS > δyyPAS. The isotropic part, δiso, is equal to (δzzPAS + δxxPAS + δyyPAS)/3, and the anisotropy, ∆δ, and the biaxiality, δbiax, of the tensor are defined as [δzzPAS - (δxxPAS + δyyPAS)/2] and (δzzPAS δyyPAS), respectively.

This result justifies our previous hypothesis, and as a consequence, we can exclude that the temperature variation (in

Conformational Changes at Mesophase Transitions particular, at the mesophase transitions) of the chemical shift observed in Figure 1 (bottom) is due to changes of the anisotropic component and to the orientational order. Our previous treatment of the problem, confirmed in its main hypothesis, allows us to say that this abrupt change of the observed chemical shift at the mesophase transitions is related to conformation changes, which largely affect the isotropic chemical shift component, δiso. The very low values of δaniso arise from the particular orientation of the fragments interesting Ca, Cb, and Cc carbons, as can be achieved from the values of the angle between the PAS z-axis and the molecular (MOL) long axis for the three carbons, as reported in Table 3. As a further test, we have used the calculated values of the δaniso to evaluate the local order parameters of the three carbons, Ca, Cb, and Cc, in the SmC* phase, and we found values of ∼0.2, 0.4, and -0.2, respectively, in agreement with what is usually found in the literature for fragments close to the aromatic core.56,57 4. Conclusions In this paper, we have presented a reliable strategy to search for the most populated conformational states in different liquid crystalline mesophases by directly comparing the observed 13C NMR chemical shift of selected carbons, highly sensitive to conformational changes, with the isotropic 13C chemical shift calculated at the DFT level. The proposed strategy bases on the hypothesis of negligible δaniso contribution to the δobs: this condition has been verified through the calculation of order parameters relative to the alkoxylic fragments of the mesogen and it is further supported by the estimation of δaniso for the involved alkoxylic carbons. This approach could be in principle applied to molecular systems where the temperature dependence of the observed chemical shift presents a peculiar trend not simply ascribable to the temperature behavior of the orientational order, but, eventually, to conformational changes occurring at the mesophase transition. In the particular case of M10/**, the occurrence of significant conformational changes at the blue-cholesteric and cholestericSmC* phase transitions has been demonstrated through a detailed analysis of the flexible parts of the mesogen, which resulted in playing a significant role in its mesomorphic behavior. At the two phase transitions of M10/**, the conformational changes concern the lateral aliphatic moieties: (i) the achiral chain undergoes a reduction of degrees of freedom by decreasing the temperature, while (ii) the chiral chain assumes different stable conformational states (molecular shapes) in the three different mesophases. In particular, in the SmC* phase, the stable molecular conformation, which has an overall bent shape, gives rise to a molecular biaxiality rather large in agreement with recent studies on several ferroelectric LCs.20,21 As a main result, our study supports the idea of a significant conformational change of the mesogens at the origin22 of the ferroelectric SmC* phase. Acknowledgment. Authors are grateful to Dr. V. Hamplova for providing the starting material. Prof. B. Mennucci and Prof. C. A. Veracini are also acknowledged for their support. References and Notes (1) Neubert, M. E. In Liquid Crystals; Kumar, S., Ed.; Cambridge University Press: Cambridge, U.K., 2001; Chapter 10. (2) Maliniak, A.; Luz, Z.; Poupko, R.; Krieger, C.; Zimmerman, H. J. Am. Chem. Soc. 1990, 112, 4277. (3) Kannan, R.; Sen, T.; Poupko, R.; Luz, Z.; Zimmermann, H. J. Phys. Chem. B 2003, 107, 13033.

J. Phys. Chem. B, Vol. 114, No. 32, 2010 10399 (4) Dvinskikh, S. V.; Sandstrom, D.; Zimmermann, H.; Maliniak, A. Prog. Nucl. Magn. Reson. Spectrosc. 2006, 48, 85. (5) Marini, A.; Dvinskikh, S. V.; Stevensson, B.; Zimmermann, H.; Maliniak, A. Manuscript in preparation. (6) Collings, P. J. Liquid Crystals: Nature’s Delicate Phase Of Matter; Princeton University Press: Princeton, NJ, 2001. (7) Collard, D. M.; Lillyia, C. P. J. Am. Chem. Soc. 1991, 113, 8577. (8) de Gennes, P. G.; Prost, J. The Physics Of Liquid Crystals; Oxford University Press: Oxford, U.K., 1995. (9) Aver’yanov, E. M. Phys. Solid State 2004, 46, 1554. (10) Domenici, V. Pure Appl. Chem. 2007, 79, 21. (11) Domenici, V.; Madsen, L. A.; Choi, E. J.; Samulski, E. T.; Veracini, C. A. Chem. Phys. Lett. 2005, 402, 318. (12) Dong, R. Y.; Marini, A. J. Phys. Chem. B 2009, 113, 14062. (13) Marini, A.; Prasad, V.; Dong, R. Y. In Nuclear Magnetic Resonance Spectroscopy of Liquid Crystals; Dong, R. Y., Ed.; World Scientific Publishing Co.: Singapore, 2009; Chapter 13. (14) Xu, J. D.; Dong, R. Y.; Domenici, V.; Fodor-Csorba, K.; Veracini, C. A. J. Phys. Chem. B 2006, 110, 9434. (15) Zennyoji, M.; Takanishi, Y.; Ishikawa, K.; Thisayukta, J.; Watanabe, J.; Takezoe, H. Mol. Cryst. Liq. Cryst. 2001, 366, 2545. (16) Barbera, J.; Puig, L.; Romero, P.; Serrano, J. L.; Sierra, T. J. Am. Chem. Soc. 2006, 128, 4487. (17) Takezoe, H.; Takanishi, Y. Jpn. J. Appl. Phys. 2006, 45, 597. (18) Domenici, V.; Veracini, C. A. In Nuclear Magnetic Resonance Spectroscopy of Liquid Crystals; Dong, R. Y., Ed.; World Scientific Publishing Co.: Singapore, 2009; Chapter 8. (19) Musˇevicˇ, I.; Blinc, R.; Zˇeksˇ, B. The Physics of Ferroelectric and Antiferroelectric Liquid Crystals; World Scientific Publisher: Singapore, 2000; Chapter 7. (20) Cifelli, M.; Domenici, V.; Marini, A.; Veracini, C. A. Liq. Cryst. (Alfred Saupe’s Memory Issues), 2010, 37, 935. (21) Domenici, V.; Marini, A. Ferroelectrics 2010, 395, 46. (22) Photinos, D. J.; Samulski, E. T. Science 2005, 270, 783. (23) Kutnjak-Urbanc, B.; Zˇeksˇ, B. Liq. Cryst. 1995, 18, 483. (24) Walba, D. M.; Richards, R. M.; Hermsmeier, M.; Haltiwanger, R. C. J. Am. Chem. Soc. 1987, 109, 7081. (25) Osipov, M. A.; Gorkunov, M. V. Liq. Cryst. 2009, 36, 1281. (26) Yoshizawa, A.; Kikuzaki, H.; Fukumasa, M. Liq. Cryst. 1995, 18, 351. (27) Cheng, Y.; Wang, X.; Cheng, J.; Sun, L.; Xu, W.; Zhao, B. Spectrochim. Acta, Part A 2005, 61, 905. (28) Korlacki, R.; Steiner, M.; Meixner, A. J.; Vij, J. K.; Hird, M.; Goodby, J. W. J. Chem. Phys. 2007, 126, 224904. (29) Emsley, J. W. Liq. Cryst. 2005, 32, 1515. (30) Dong, R. Y. Nuclear Magnetic Resonance of Liquid Crystals; Sprinter-Verlag: Berlin, 1997. (31) Luckhurst, G. R., Veracini, C. A., Eds. The Molecular Dynamics of Liquid Crystals; Kluwer: Dordrecht, The Netherlands, 2003. (32) Burnell, E. E.; de Lange, C. A. Chem. ReV. 1998, 98, 2359. (33) Jokisaari, J.; Hiltunen, Y. Mol. Phys. 1983, 50, 1013. (34) Barili, P. L.; Veracini, C. A.; Longeri, M. Inorg. Chim. Acta 1980, 40, X92. (35) Marini, A. Understanding Complex Liquid Crystalline Materials: A multinuclear NMR spectroscopy and ab initio calculations approach; VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG: Saarbru¨cken, Germany, 2010 (ISBN-13: 978-3639254228). (36) Benzi, C.; Cossi, M.; Barone, V.; Tarroni, R.; Zannoni, C. A. J. Chem. Phys. B 2005, 109, 2584. (37) Mennucci, B.; Cances, E.; Tomasi, J. J. Phys. Chem. B 1997, 101, 10506. (38) Photinos, D. J.; Samulski, E. T.; Toriumi, H. J. Chem. Phys. 1991, 94, 2758. (39) Photinos, D. J.; Luz, Z.; Zimmermann, H.; Samulski, E. T. J. Am. Chem. Soc. 1993, 115, 10895. (40) Emsley, J. W.; Wallington, I. D.; Catalano, D.; Veracini, C. A.; Celebre, G.; Longeri, M. J. Phys. Chem. 1993, 97, 6518. (41) Bubnov, A.; Domenici, V.; Hamplova, V.; Kaspar, M.; Veracini, C. A.; Glogarova, M. J. Phys.: Condens. Matter 2009, 21, 035102. (42) Gorkunov, M. V.; Osipov, M. A. J. Phys. A: Math. Theor. 2008, 41, 295001. (43) Domenici, V.; Geppi, M.; Veracini, C. A. Prog. Nucl. Magn. Reson. Spectrosc. 2007, 50, 1. (44) Ossowska-Chruœciel, M. D.; Korlacki, R.; Kocot, A.; Wrzalik, R.; Chruœciel, J.; Zalewski, S. Phys. ReV. E 2004, 70, 041705. (45) Kasˇpar, M.; Hamplova´, V.; Pakhomov, S. A.; Stibor, I.; Sverenya´k, H.; Bubnov, A. M.; Glogarova´, M.; Vaneˇk, P. Liq. Cryst. 1997, 22, 557. (46) Metz, G.; Wu, X.; Smith, S. O. J. Magn. Reson. 1994, A110, 219. (47) Fung, B. M.; Khitrin, A. K.; Ermolaev, K. J. Magn. Reson. 2000, 142, 97. (48) Cramer, C. J. Essentials of Computational Chemistry, Theories and Models, 2nd ed.; Wiley: Chichester, U.K., 2004.

10400

J. Phys. Chem. B, Vol. 114, No. 32, 2010

(49) Frisch, M. J.; et al. Gaussian 03, revision E.05; Gaussian, Inc.: Wallingford, CT, 2003. (50) Ditchfield, R. J. Chem. Phys. 1972, 56, 5688. (51) (a) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664. (b) Lynch, B. J.; Zhao, Y. Y.; Truhlar, D. G. J. Phys. Chem. 2003, 107, 1384. (c) Benzi, C.; Crescenzi, O.; Pavone, M.; Barone, V. Magn. Reson. Chem. 2004, 42, S57. (52) Cheeseman, J. R.; Trucks, G. W.; Keith, T. A.; Frisch, M. J. J. Chem. Phys. 1996, 104, 5497.

Marini and Domenici (53) Xu, J.; Veracini, C. A.; Dong, R. Y. Phys. ReV. E 2005, 72, 51703. (54) Domenici, V.; Marini, A.; Veracini, C. A.; Zhang, J.; Dong, R. Y. ChemPhysChem 2007, 8, 2575. (55) Rutar, V.; Blinc, R.; Vilfan, M.; Zann, A.; Dubois, J. C. J. Phys. (Paris) 1982, 43, 761. (56) Poon, C. D.; Fung, B. M. J. Chem. Phys. 1989, 91, 7392. (57) Poon, C. D.; Fung, B. M. Liq. Cryst. 1989, 5, 1159.

JP105095M