JOURNAL
OF MAGNETIC
63, 3 l40 (1985)
RESONANCE
NMR Studies of Molecular Dynamics of Isotropic and Anisotropic Liquids J. CZAPLICKI Institute
of Molecular
Physics,
AND N. F’ISLEWSKI
Polish Academy of Sciences, Poznari 60I 79. Poland
ul. Smoluchowskiego
17/19,
Received May 8, 1984; revised November 16, 1984 Microscopic parameters describing dynamics of molecules which do and do not undergo fast anisotropic reorientations have been extracted from measurements of temperature and frequency dependence of relaxation times T, for pnheptylaniline (PHA; isotropic liquid) and pnpentylpcyanobiphenyl (PCCB;nematic liquid crystal). One and twodimensional NMR spectra allowed for direct measurements of activation energies of different groups of nuclei in isotropic phases of PHA and PCB. The order parameter as well as some conformational data of PCB have been obtained from dipolar spectra and their temperature dependence. The mobility of alkyl chain segments decreases gradually from almost freely rotating terminal CHJ groups toward CH, groups connected with the aromatic rings. The chain flexibility does not vary much in PHA as opposed to PCB where the difference between the two ends of chain is much more distinct. 0 1985 Academic press, Inc.
Numerous data concerning liquid crystals that have been collected until now provide a basis for formulating necessary conditions for the occurrence of a liquidcrystalline phase. However, there exist molecules which resemble those exhibiting mesomorphic states but which remain isotropic in all temperatures. Thus, the sufficient conditions are not yet known. The work presently reported has been undertaken to provide information concerning the dynamics of particular groups of nuclei in molecules which belong to the groups of compounds which do and do not exhibit the occurrence of liquidcrystalline phases despite their structural and shape similarities. MATERIALS
AND METHODS
The two classes of compounds investigated were represented by isotropic pheptylaniline (PHA) and nematic pnpentylcyanobiphenyl (PCB). Small quantities (ca 0.1 ml) of these compounds were placed inside tubes 4 = 5 mm and sealed after having been subjected to five consecutive freezethaw cycles in order to avoid the influence of paramagnetic impurities on resultant signals. All measurements were performed on a Bruker SXP 4 100 pulsed NMR spectrometer interfaced to a Nicolet BNC 12 computer. The temperature dependence of relaxation times 7’r was studied over the range 1 lo340 K at 90 MHz. The frequency dependence of r, for PCB was investigated in the range 30 100 MHz for temperatures characteristic for the mesomorphic phase (295308 K). Measurements 31
00222364185 $3.00 Copyright 0 1985 by Academic FWs% Inc. All rights of reproduction in any form rscwed.
32
CZAPLICKI
AND PI~LE’iVSKI
of Ti vs temperature were made by the inversionrecovery method, whereas the frequency dependence of T, was studied by the saturationrecovery method. To facilitate the performance of numerous measurements a few programs in the assembly language of the BNC12 computer were written. They enable totally automatic measurements of relaxation times r, and T2, as well as TI for chemically nonequivalent groups of nuclei by the inversionrecoveryFourier transform (IRPT) method. Another program allows for obtaining 2D NMR spectra. Because of the limited core memory it utilizes a 56 X 64 complex data matrix. Conventional NMR spectra resulted from accumulated, digitally processed, and Fourier transformed free induction decay signals (4 K data points). In the case of liquid phases of samples the acquisition time was equal to 0.82 s, whereas for the solid samples it was about 4 ms. RESULTS
The temperature dependences of the spinlattice relaxation time for PCB and PHA are shown in Figs. 1 and 2, respectively. In the solid phase for PCB there occurs a minimum at 180 K. The phase transition to the nematic state is accompanied by a stepwise change of Tl at 295 K. Another jump of Tl values at 308 K occurs at the nematic isotropic liquid phase transition. The temperatures of phase transitions are within 0.5 K of literature values (1). For PHA the temperature dependence of T, in the solid phase is similar to PCB: there is a distinct minimum at 165 K. However the phase transition to the isotropic phase is diffuse, occurring over the range 230265 K. Two components appear in the FID signals. The relaxation time Tl of the fast decaying component is long and allows for reconstruction of the hightemperature slope of the curve. The slowly decaying component corresponds to decreasing TI on increasing the temperature. A typical spectrum representing this intermediate phase is shown in Fig. 3. Above 265 K the FID signal is single exponential and its relaxation time increases with temperature.
t
0
 308K r \I/
0
295K I I00 I I so 1; 00
3
4
0 0
5
6
7
y3
[Kl]
FIG. 1. Plot of log T, vs l/T for PCB measured at 90 MHz. The isotropic (I), nematic (N), and solid (S) phases have been obsexved.
MOLECULAR
DYNAMICS
33
OF L:IQUIDS
0
0
0 0 0 0
FIG. 2. Plot of log T, vs l/T for PHA at 90 MHz. The observable phases are isotropic (I), intermediate (IM), and solid (S). The two components appear in the resultant FID signals.
For each temperature at which T, was measured in the nematic phase of PCB (Fig. 1) the frequency dependence of T, was also studied. The measurements were performed for the frequencies 30, 40, 60, 65, and 70 MHz, and every 2 MHz from 70 to 98 MHz for temperatures every 2 K from 296306 K. The results are presented in Fig. 4. For each of these temperatures the dipolar spectra were obtained. They are shown in Fig. 5. In the isotropic phases of both compounds 2D homonuclear spincoupling and chemicalshift correlation spectra have been obtained, which served as an aid in line assignments in 1D spectra. Magnetization recoveries of all spectral lines allowed for determination of T, times for all groups of resonating nuclei which were represented in the spectra by sufficiently resolved lines. DISCUSSION
Solid phases. Low temperature inhibits molecular mobility; hence one may expect the methyl group rotations to be responsible for the observed relaxation. Assuming the fast spin diffusion limit one may calculate the maximal relaxation rate and the interproton distance within CH3 groups. For PCB the calculations, based upon the O’ReillyTsang formula
PHA T= 250K
FIG. 3. A PHA spectrum at 250 K illustrating the coexistence of two components, representing two different phases.
34
CZAPLICIU
AND PISLEWSKI
0.45  T=iaK
o oow 00
0.65

o 0
0.45
298K
_
,J OOOO 0
OF O
0 I
I
I
I
300K
off

I
I
302
K
’
&.gcPo 0: 0
0 D
1

00 oooe 0.65
I
0
0
304
306
K
K
o”o
0.45 CO0
0,008
6p”8
0
0
00” %
8”
0
0.65 Lillll 1.55
1.75
1.95 kl(5i
1.55
1.75
1.95
10j
FIG. 4. The frequency dependence of the spinlattice relaxation time T’, of PCB for temperature within the mesomorphic state.
_1 = 9 Y4h2 7.2 + _ 47, T, 20 r6 1 + W2T2 c 1 + 4w22c
VI
yield r = 1.80 A and for PHA r = 1.76 A which are consistent with data from other sources (average r = 1.78 A). To calculate activation energies and correlation time, computer rnultiparameter fitting has been employed, which gave the values E, = 3.48 kcal/mol for PCB and E, = 1.65 kcal/mol for PHA, as well as preexponential factors from the Arrhenius formula of T: = 7.5 X lol4 s for PCB and T: = 8.8 X loi2 s for PHA. A typical fit is presented in Fig. 6. In the case of PHA in the first approximation we neglect the NH2 group relaxation due to their small fraction. Nematic phasein PCB. Following Noack et al. (2) we assume that the resultant relaxation rate in PCB is a sum of a few components, resulting from different kinds of motion: order fluctuations (OF), selfdiffision (SD), and reorientations (R) associated with mobility of CH2 and CHs groups., as well as rotations about long and short molecular axes. Following Sung (3) we write
MOLECULAR
DYNAMICS
OF IJQUIDS
35
FIG. 5. The temperature dependence of spectra for PCB in the nematic phase. The numbers on the left side of the figure are order parameters calculated from dipolar splittings.
1 5,
0
“,,2 = 9 y4h2 A+B ( 8
1
PI
where A and I3 are functions of the order parameter S, temperature T, Armor frequency w, viscosity 1, internuclear distance r, short range correlation time I’, and angle fI between the long molecular axis and the director. They are given by the following expressions:
FIG. 6. The result of numerical fitting to the experimental data in the solid phase of PCB. The circles are experimental points, whereas the solid line represents the fitted curve with the following parameters: E. = 3.48 kcal/mol, 7: = 7.5 X lol4 s.
36
CZAPLICIU
AND
PISLEWSKI
A _ 2’12 S2kTq’12 n ,6~312
t31
B = 2r (sin’B;SoPtr) where y is the magnetogyric ratio, k is the Boltzmann constant divided by 27r, and K is the elasticity constant. According to Torrey (4)
141
constant, h is the Planck
[51 Z(w) =
s0
* B:,2(X) ~ 37SDlX2 1 + (3w&X2)2
dx X
K51
where N is the spin density, d is the minimal distance between two molecules, and 7sn is the translational correlation time. B3,2 denotes a Bessel function of the order 3. The description of the rotational reorientations follows that given by Noack et al. in (2) who modified Woessner’s theory (5). Molecules rotate rapidly about their long axes. The CH3 and CH2 groups undergo very rapid reorientations about their symmetry axes. Hence it appears that only the slowest motions are expected to affect the resultant relaxation rate. Thus, we assume that only the rotations of molecules about their short axes, which are strongly inhibited by anisotropic orientations of molecules in the nematic phase, contribute significantly to the observed relaxation rate. In this case we may put 1 (
T,. >
= 2 r4h2[J(w) + 4J(2w)] 8
J(w) = gi
1 +T;2T2
s
[71
181
where I is the distance of o&o protons in aromatic rings, T, is the correlation time for rotations about the short molecular axes, and t is the anisotropy factor (2). Since the experimental data prove the validity of the assumption about the occurrence of fast spin exchange in the cases investigated (68), the three contributions given by Eqs. [2], [5], and [7] are combined to get $=
y+,
1,
j=OF,SD,R
191
where pj are corresponding spin fractions. From the numerical analysis of the experimental data it follows that the reorientational term (R) is negligible within the frequency range studied. Hence, the rates of motions contributing to the relaxation are far from the Larmor frequencies, at least by one order of magnitude. The two other contributions are approximately equal. All three are given in Fig. 7, showing an exemplary fit at 304 K. Table 1 gives values of parameters A and 7sn. Parameter B does not vary much and is
MOLECULAR
DYNAMICS
37
OF LIQUIDS
(OF, SO)
0.25
0.65
FIG. 7. Contributions to the frequency dependence of the resultant relaxation rate from order fluctuations (OF), selfdiffusion (SD), and rotational reorientations (R) at 304 K for PCB in the nematic phase. Solid line shows the sum of the three contributions (Eq. [9]); circles are experimental points.
approximately equal to 0.1 s‘, which corresponds to the angle (I = 35“. As for A, following Karat and Madhusudana (I), we assume that the elasticity constant 6K is proportional to S2.5 from which we get A  S‘.75 which does not vary significantly within the mesomorphic range of temperatures. Thus AThe slope in the plot ln(A/T) vs l/T yields the activation energy E, for reorientations of molecular long axes which in this case equals 12.9 kcal/mol. The translational motion is described by the activation energy E, = 15.0 kcal/mol, which can be obtained in a similar way from temperature dependence of Tsn. Rough estimates of the diffusion coefficient DT for translations of ellipsoidal molecules (9) lead to values TABLE 1 Numerically Fitted Parameters A and Tso for PCB in the Mesomorphic State Temperatures T(K) A (s~‘~) +sD(ns)
296 41,356
298 35,589 2.0
300 34,738 1.7
304 30,983
302 34,818 1.4
1.2
1.0
306 28,522 0.9
38
CZAPLICIU
AND PISLEWSIU
DT  lo’ cm2/s which are in good agreement with Dr obtained from the relation, D, = (d2)/6rSD, where d = 5 A is the intermolecular distance in nematic PCB. The order parameters given in Fig. 5 were calculated from dipolar splittings of side lines (the central line is believed to originate from aliphatic protons). Since the side bands are split, too, it has been assumed that this is caused by dipolar interactions between “internal” protons of the biphenyl core (see Fig. 8). In this case the dipolar splitting will be reduced by s, = 4(3 cos.~  1)
[Ill
coscP = [I  3(~~sin2~J”2
WI
with
where (Yis the twist angle between the planes of the phenyl rings involved and other symbols are explained in the caption of Fig. 8. From the analysis of spectra it follows that the twist angle cy = 52”. From the available data it appears that in the nematic phase, with regard to longrange interactions which induce molecular ordering, both translational diffusion and hindered rotations about the short molecular axes become efficient sources of relaxation. In our case none of these mechanisms is predominant. On the other hand, rotations about molecular long axes are so rapid that their contribution to the total relaxation is negligible; hence they are responsible for averaging out the horizontal components of local physical properties of molecules. Intermediate phase in PHA. For PHA there is evidence for coexistence of two phases: solid and liquid. The fraction of the liquid phase increases with temperature. The decrease of relaxation time can be explained by assuming a gradual activation of relaxation mechanisms characteristic for liqukls, translational and rotational diffusion. Liquid phases. Above 265 K for PHA and 308 K for PCB both compounds are isotropic liquids. The relaxation time T, changes monotonically with temperature. Its value results from the contributions of various parts of molecules which relax in many ways. In the first approximation let us assume that only the slowest motions
axis .
RG. 8. The “core” of a PCB molecule. The symbol r denotes the distance. between orrho protons, a denotes the twist angle between planes of the phenyl ring, ,p is the distance between the “internal” protons (‘5”) of biphenyl, po is the distance p for the angle OL= O”, and (P is the angle determining the reduction factor in dipolar splittings, defined by Eqs. [I I] and 1,121.
MOLECULAR
DYNAMICS
39
OF LIQUIDS
FIG. 9. Plot of log Tr vs l/T for PCB in the isotropic liquid phase. Circles represent experimental points. The solid line is the curve fitted from two contributions: selfdi&ion (SD) and rotations (R) of whole molecules.
contribute significantly to the observed T, . The motions involved will be rotational (R) and translational (SD) diffusion of whole molecules. Fitting yields: E,(R) = 7.38 kcal/mol for PCB and 6.26 kcal/mol for PHA, E,(SD) = 5.11 kcal/mol for PCB and 4.10 kcal/mol for PHA. The preexponential factors in the Arrhenius formula in the case of rotational motions are 0.6 X lor4 s for PCB and 1.5 X lol4 s for PHA, which gives T,  low9 s for the studied range of temperatures. The translational correlation time could not be determined precisely because of rather poor number convergence. Even large changes of this parameter did not influence the final fitting quality. Hence, rotations dominate in the nuclear relaxation process in these temperatures, which has been depicted in Fig. 9, showing the fitting to our experimental data. To obtain such results the difhtsion coefficient & must be equal to or greater than 10m7cm’/s. The assignment of line:; in 1D and 2D spectra allowed the determination of activation energies for all groups of chemically nonequivalent nuclei. They have been tabulated in Table 2. Since for aliphatic protons we may consider these values to be describing hindered rotations about the CC bond axes, TABLE 2 Activation Energies (EJ in kcal/mol for Groups of Protons in PHA and PCB”
CH3
PHA PCB
4.9 4.2
Wb),
CHz
NH2
Aromatic protons
5.6 4.5
5.9 6.1
6.0 
6.5 7.4
0 n = 5 for PCB, n = 7 for PHA, CH2 denotes the methylene group directly attached to the aromatic
40
CZAPLICKI
AND PISLEWSKI
it can be seen that the nuclear mobility for PCB which can be identified with the flexibility of the alkyl chain increases on moving along the chain away from the aromatic core. Similar conclusions resulting from studies of the order parameter S and the second moment of NMR lines have been reported heretofore (1013). In the case of aromatic protons the motion they undergo is described by 180” flips about the ring symmetry axis. For PHA the differences of flexibility of the alkyl chain are much less pronounced on account of the fact that the molecule is much less rigid and no distinct partition between “core” and “tail” can be made. ACKNOWLEDGMENT The authors express their thanks to Professor J. Stankowski for continuous interest in this work. The help of H. Zimmermann from the Department of Molecular Physics of the Max Planck Institute for Medical Research in Heidelberg who provided us with the samples used in our experiments is greatly appreciated. REFERENCES 1. P. P. KARAT AND N. V. MADHUSUDANA, Mol. Cryst. Liq. Cryst. 36, 51 (1976). 2. V. GRAF, F. NOACK, AND M. STOHRER, Z. Nafurforsch. A 32, 61 (1977). 3. C. SUNG, Chem. Phys. Lett. 10, 35 (1971). 4. H. TORREY, Phys. Rev. 92,962 (1953). 5. D. E. WOESSNER, J. Chem. Phys. 36, I (1962). 6. J. R. ZIMMERMANN AND W. E. Bnrrrr~, J. Chem. Phys. 61, 1328 (1957). 7. K. R. BROWNSTEIN AND C. E. TARR, J. Magn. Reson. 26, 17 ( 1977). 8. D. E. WOESSNER,J. Chem. Phys. 35,41 (1961). 9. H. MORAWETZ, “Macromolecules in Solution,” Wiley, New York, 1965. 10. S. MAR&LJA, Solid State Commun. 13, 759 (1973). 11. S. MAR~LJA, J. Chem. Phys. 60, 3599 (1974). 12. 0. EDHOLM AND C. BLOMBERG, Chem. Phys. 42,449 (1979). 13. N. B~DEN, Y. K. LEVINE, D. LIGHTOWLERS, AND R. T. SQUIRES, Chem. Phys. Letf. 31, 511 (1975).