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Molecular self-diffusion in the isotropic liquid phase of the homologous series of 4-n-alkyloxybenzylidene-4′-n-butylanilines
CHEMICALPHYSICSLElTERS
Volume101, number4,s
MOLECULAR SELF-DIFFUSION
28 October 1983
IN THE ISOTROPIC LIQUID PHASE
OF THE HOMOLOGOUS SERIES OF 4-n-ALKnOXYBENZ~‘-~-B~~~ SK. GHOSH, E. TETTAMANTI and A. RICCHIUTO * Istiruro di Fisica and Unita’de1 Gh’SM de1 CNR. University dell’Aquila, 67100 L ‘Aquila. Italy Received
12 May 1983;in
final form 16 August
1983
We report the molecular self-diffusion D in the isotropic liquid phase of the homologous series of 4+&kyloxybenzylidene4’-n-butylanilines measured over a temperature range of ==25 K above the transition temperature Tc_ In all cases reported here, we find that D can be fitted to the Arrhenius relation D = Doexp (-W/T)_ The quantities DC, Do, W, and W/Tc show the “odd-even” effect similarto that of Tc, where DC = D at Tc_
A few years ago, two of us reported in this journal [l] the molecular self-diffusion coefficient D in the isotropic liquid phase of the homologous series of 4,4’-di-n-alkoxyazoxybenzenes (the first member of this series is PAA and henceforth will be referred to as the PAA series)_ We showed that D for all the members of the series could be represented by the Arrhenius relation D = Doexp(-W/T) for the temperature range studied. We further observed that DC,0 at the
a differ-
Such
be-
* Deceased.
0 009-2614/83/0000-0000/$03.00
0 I983 North-Holland
havior has even been observed for mesogenic molecules in non-liquidcrystalline media [8], suggesting this alternating behavior to be an intrinsic molecular property. This observation is in conformity with ours that show an alternating behavior of the intermolecular potential in the PAA series [I] J although with a slightly different periodicity than that of Tc or DC. Such a slight change of the periodicity can be understood by a small change in the number of nearest-neighbor molecules [9] _With these considerations, we have undertaken measurements of D in the isotropic liquid phase of the commercially available MBBA series over a temperature range of x25 K above Tc_ The choice of this series for such studies has been dictated mainly by two considerations: (i) this has been widely studied from the “odd-even” aspect, and (ii) the molecular structure is asymmetric, unlike the PAA series. The molecular formula of this homologous series is given below:
The first member of this series with n = 1 is MBBA which is a widely studied room-temperature nematic. The first seven members show nematic-isotropic liquid transitions [ 10,l l] _ The seventh was not available for our studies, and the eight shows a smecticisotropic liquid transition [ 10.1 l] _ All these materials were obtained from the American Liquid Crystal 499
Volume 101, number 4,5
Chemical Corporation of Kent, Ohio, and were used without further purification. The samples were degassed using a freeze-thaw technique and were sealed under vacuum (=1W5 Torr) in flat-bottom glass tubes (6.45 xmn i-d.) obtained from Wilmad Glass Company, Inc. The sample lengths were 5-7 mm. We employed the variable field gradient spin echo technique as in our earlier study [I]: no appreciable effect on our measuremcnts of D waspresent for the rf power (x2.4 ~.ls for the 90” pulse) and the maximum field gradient (~15 G/cm) used. The field gradients G were obtained from echo shape modulation and the same sets of G were used for all D measurements. The echo positions were so chosen that their amplitudes could be varied by factors of 4 to 5 for the range of G used. We used an online personal computer (Commodore CBM model 2001) for data processing immediately after data acquisition by a digital signal averager (Datalab model DLI 02s). The introduction of the online compurer was helpful in two important ways apart from reducing experimental time: (i) the signal averager could be triggered by a pulse generated from the same source of the two pulses used for the echo signal, and (ii) the signal hold device could be dispensed with. The signals in each measurement were averaged at least S times and the amplitudes were obtained by subtracting the base line (average of the last 10 of the 200 sampling points) from the maxima. The constant D at any temperature was then obtained by least-squares fits to the standard relation [ 12]_ At least three such measurements were carried out at any temperature. The transition temperatures Tc to the isotropic liquid phase were measured with an error of 33.5 K as earlier. A slightly different procedure was followed for the eighth member which showed the SmA-to-isotropic liquid transition_ This simple did not show any modulation structure on the free induction signal in the smectic phase as usually observed in the nematic phase under normal experimental conditions with an operating frequency of 25 MHz (~5.95 kG magnetic field)_ But an echo signal of very small amplitude could be observed with two pulses. The amplitude of this echo signal could be enhanced by reducing the pulse separation and applying a small field gradient. The transition to the isotropic liquid phase and vice versa could be monitored with the accuracy noted above by the observation of this echo signal. This Tc was confirmed by monitoring the modulation structure on FID for which the sample 500
28 October 1983
CHEMICAL PHYSICS LETTERS
Q(lO-‘Cm?5’) .
D (rd’cm2o
.
i’)
l
W(lo’
K)
. %
1%. 1. Plots of Tc, DC. DO. W, and W/Tc for different mernbcrs (n) of the homologous series. See the text for details.
needed to be prealigned in the smectic phase but close to Tc under a higher magnetic field of ~20 kG. The measured average D and the corresponding temperature T for the different members II of the series were fitted to the Arrhenius relation D = Doexp(-W/T), using the least-squares method. The best-fit results together with one standard deviation are given in table l_ The correlation coefficient in each fit was better than 0.99. We show in fig. 1 the plots of Tc, DC, Do, W, and LU/Tcwith n, the number of carbon atoms in the alkoxy chain of the homologous series. It can be noticed that all the quantities
Table 1 Pauametersobtained by the least squ-aresfits to the relation
D = Doexp(-IV/n n
DO (IO” i + + + +
IV (103 K)
JV/TC
cm*/s) 1.0 0.15 0.8 0.3 0.6
3.77 3.35 3.78 3.52 3.74
f 0.09 I 0.09 f 0.10 -r 0.11 t 0.11
12.04 9.49 11.34 10.16 10.93
3.56 + 0.17 3.78 * 0.12
10.13 10.63
1 2 3 4 S
9.0 2.27 7.0 3.1 5.4
6 8
2.75 * 0.3s 4.62 + 0.48
CHEhlICAL PHYSICS LE-ITERS
Volume 101, number 4,5
show the “odd-even” effect very similar to that observed for T,_ It is interesting to note that the members with 11odd have lower Tc but higher Wand W/Tc than the members with n even, and there is a tendency for their convergence with increasing n. A further point of interest is almost identical variations in T, and W observed in this series, the former is -4.3% around the mean value of 342.2 K while the latter is ~4.6% around 3643 K. The corresponding values for the PAA series are ~3.6% and 7-9% around the mean values of 406.8 and 2780 K. On the other hand, the variations in IV/T,for both the series are almost identical, =-8%. ft is to be noted that the variation of the order parameter at the nematic-isotropic liquid transition with increasing chain length has been qualitatively explained with different order parameters for the rigid and flexible molecular parts [ 13]_ This behavior can be explained without the concept of multiple order parameters by the simple introduction of an alternating intermolecular potential [ 141 as suggested by our observed W for the series. The relation between W observed in the isotropic liquid phase and the anisotropic intermolecular potential in the ordered phase becomes apparent from the following simple considerations: the anisotropic two-body intermolecular potential can be expressed from very general considerations as &(‘12Q12)
= &(‘I21
+ U2(r,2)cos4e12
-28 October 1983
observed either in the isotropic or ordered phase it becomes necessary to consider more than one nearest neighbor. Similar suggestions about more th& one nearest neighbor come from other sources [9,16,17]. In this context, the observed variations in the PM series [I] can be understood when we consider the expected variations in the number of nearest neighbors in the ordered phase [9] _A similar suggestion is also contained in the observation of intrinsic molecular optical anisotropy in cyanobiphenyls by Ldanne et al. [9] who could qualitatively reproduce the alternating behavior by considering molecular conformations. Finally. we should like to comment on our observed values for MBBA. These values are slightly at variance with our earlier measurements [ lS]_ This discrepancy seems to arise from impurities as suggested from measurements with some old samples in our laboratory. The nature of impurities could not be ascertained, although all the samples have almost identical T,. Our
observations suggest that impurities present do not have significant influence on T, but can have on other properties. Similar insensitivity of T, of MBBA to impurities has been observed in our nuclear relaxation studies [ 191. It is to be noted that the present values of D and W for MBBA are in good agreement with those observed by Hakemi and Labes [20] by a different technique.
+ U&12)cos2~12 + -._ )
where the notation is obvious. The first term represents the isotropic interaction and the subsequent terms anisotropic interaction of increasing order. Tile well known Maier-Saupe potential [ 151 is a special form of the first anisotropic term and can be obtained by subtracting its value in the isotropic phase. None of the angle-dependent terms becomes zero in the isotropic phase. Hence a relation between the observed Wand the anisotropic intermolecular potential is not unexpected, although a quantitative relation is difficult to establish at this stage. But a qualitative understanding can be obtained when we consider that the orientational order persists to higher temperatures than the positional order, suggesting it to be stronger. Hence it is expected that a major contribution to W comes from the angle-dependent part of the above potential. Furthermore, considering the magnitude of IV
References 1I] SK. Ghosh and E. Tettamanti, Chem. Phys. titters 69 (1980) 403. [ 21 H. Arnold. 2. Physik. Chem. (Leipzig) 226 (1964) 146. [3] A. Pines, DJ. Ruben and S. ABison, Phys. Rev_ Letters 33 (1974) 1002. [4] E.G. Hanson and Y-R. Shen, Mol. Cryst. Liquid Cryst. 36 (1976) 193. [5] R. Chang, F-B. Jones and J-J. Ratto, hiol. Cryst. Liquid Cryst. 33 (1976) 13. [6] R. Yamamoto, S. Ishihara, S. Hayakawa and K. Morimoto, Phys. Letters 69A (1978) 276. [7] S-K. Ghosh. E. Tettamanti and S. Amadesi, in: Advances in liquid crystal research and applications, Vol. 1. ed. L. Bata (Pergamon Press. Oxford. 1981) p_ 309. [8] J-R. LaIanne, B. Lemaire, J. Rouch, C. Vaucamps and A. Proutike. J. Chem. Phys. 73 (1980) 1927. [9] H. Arnold, 2. Chem. 4 (1964) 211. IlO] B. Flannery and Iv- Haas, J. Phys. Chem. 74 (1970) 3611. [ll] G-W- Smith and 2-G. Gardlund. J. Chem. Phys. 60 (1974)
3214.
501
Volume 101, number 4,s
CHEMICAL
PHYSICS
[ 121 A. Abragam. The principles of nuclear magnetism (Clarendon Press, Oxford, 1961) p. 61. [ 131 S. hiarcelja, J. Chem. Phys. 60 (1974) 3599. [ 141 CD. Mukherjee. T. Bose. D. Ghosh, Xl. Saha and ht. Roy, to be published. [ I.51 W_ hiaier and A. Saupe. Z. Naturforsch. 13a (1958) 564; 14a (1959) 882; 15a (1960) 287. [ 161 SK Ghosh, Mol. Cryst. Liquid Cryst. 37 (1976) 9_
502
LETTERS
28 October
1983
[ 171 SK. Ghosh and S. Amadesi. Phys. Letters 59A (1976) 282. [ 181 SK Ghosh and E. Tettamanti, Phys. Letters 37A (1973) 361. [ 191 SK. Ghosh, E. Tettamanti and A. Panatta, Phys. Rev. BZl(1980) 1194. [ 201 H. Hakemi and h1.M. Labes, J. Chem. Phys. 61 (1974)
4020.
Volume101, number4,s
MOLECULAR SELF-DIFFUSION
28 October 1983
IN THE ISOTROPIC LIQUID PHASE
OF THE HOMOLOGOUS SERIES OF 4-n-ALKnOXYBENZ~‘-~-B~~~ SK. GHOSH, E. TETTAMANTI and A. RICCHIUTO * Istiruro di Fisica and Unita’de1 Gh’SM de1 CNR. University dell’Aquila, 67100 L ‘Aquila. Italy Received
12 May 1983;in
final form 16 August
1983
We report the molecular self-diffusion D in the isotropic liquid phase of the homologous series of 4+&kyloxybenzylidene4’-n-butylanilines measured over a temperature range of ==25 K above the transition temperature Tc_ In all cases reported here, we find that D can be fitted to the Arrhenius relation D = Doexp (-W/T)_ The quantities DC, Do, W, and W/Tc show the “odd-even” effect similarto that of Tc, where DC = D at Tc_
A few years ago, two of us reported in this journal [l] the molecular self-diffusion coefficient D in the isotropic liquid phase of the homologous series of 4,4’-di-n-alkoxyazoxybenzenes (the first member of this series is PAA and henceforth will be referred to as the PAA series)_ We showed that D for all the members of the series could be represented by the Arrhenius relation D = Doexp(-W/T) for the temperature range studied. We further observed that DC,0 at the
a differ-
Such
be-
* Deceased.
0 009-2614/83/0000-0000/$03.00
0 I983 North-Holland
havior has even been observed for mesogenic molecules in non-liquidcrystalline media [8], suggesting this alternating behavior to be an intrinsic molecular property. This observation is in conformity with ours that show an alternating behavior of the intermolecular potential in the PAA series [I] J although with a slightly different periodicity than that of Tc or DC. Such a slight change of the periodicity can be understood by a small change in the number of nearest-neighbor molecules [9] _With these considerations, we have undertaken measurements of D in the isotropic liquid phase of the commercially available MBBA series over a temperature range of x25 K above Tc_ The choice of this series for such studies has been dictated mainly by two considerations: (i) this has been widely studied from the “odd-even” aspect, and (ii) the molecular structure is asymmetric, unlike the PAA series. The molecular formula of this homologous series is given below:
The first member of this series with n = 1 is MBBA which is a widely studied room-temperature nematic. The first seven members show nematic-isotropic liquid transitions [ 10,l l] _ The seventh was not available for our studies, and the eight shows a smecticisotropic liquid transition [ 10.1 l] _ All these materials were obtained from the American Liquid Crystal 499
Volume 101, number 4,5
Chemical Corporation of Kent, Ohio, and were used without further purification. The samples were degassed using a freeze-thaw technique and were sealed under vacuum (=1W5 Torr) in flat-bottom glass tubes (6.45 xmn i-d.) obtained from Wilmad Glass Company, Inc. The sample lengths were 5-7 mm. We employed the variable field gradient spin echo technique as in our earlier study [I]: no appreciable effect on our measuremcnts of D waspresent for the rf power (x2.4 ~.ls for the 90” pulse) and the maximum field gradient (~15 G/cm) used. The field gradients G were obtained from echo shape modulation and the same sets of G were used for all D measurements. The echo positions were so chosen that their amplitudes could be varied by factors of 4 to 5 for the range of G used. We used an online personal computer (Commodore CBM model 2001) for data processing immediately after data acquisition by a digital signal averager (Datalab model DLI 02s). The introduction of the online compurer was helpful in two important ways apart from reducing experimental time: (i) the signal averager could be triggered by a pulse generated from the same source of the two pulses used for the echo signal, and (ii) the signal hold device could be dispensed with. The signals in each measurement were averaged at least S times and the amplitudes were obtained by subtracting the base line (average of the last 10 of the 200 sampling points) from the maxima. The constant D at any temperature was then obtained by least-squares fits to the standard relation [ 12]_ At least three such measurements were carried out at any temperature. The transition temperatures Tc to the isotropic liquid phase were measured with an error of 33.5 K as earlier. A slightly different procedure was followed for the eighth member which showed the SmA-to-isotropic liquid transition_ This simple did not show any modulation structure on the free induction signal in the smectic phase as usually observed in the nematic phase under normal experimental conditions with an operating frequency of 25 MHz (~5.95 kG magnetic field)_ But an echo signal of very small amplitude could be observed with two pulses. The amplitude of this echo signal could be enhanced by reducing the pulse separation and applying a small field gradient. The transition to the isotropic liquid phase and vice versa could be monitored with the accuracy noted above by the observation of this echo signal. This Tc was confirmed by monitoring the modulation structure on FID for which the sample 500
28 October 1983
CHEMICAL PHYSICS LETTERS
Q(lO-‘Cm?5’) .
D (rd’cm2o
.
i’)
l
W(lo’
K)
. %
1%. 1. Plots of Tc, DC. DO. W, and W/Tc for different mernbcrs (n) of the homologous series. See the text for details.
needed to be prealigned in the smectic phase but close to Tc under a higher magnetic field of ~20 kG. The measured average D and the corresponding temperature T for the different members II of the series were fitted to the Arrhenius relation D = Doexp(-W/T), using the least-squares method. The best-fit results together with one standard deviation are given in table l_ The correlation coefficient in each fit was better than 0.99. We show in fig. 1 the plots of Tc, DC, Do, W, and LU/Tcwith n, the number of carbon atoms in the alkoxy chain of the homologous series. It can be noticed that all the quantities
Table 1 Pauametersobtained by the least squ-aresfits to the relation
D = Doexp(-IV/n n
DO (IO” i + + + +
IV (103 K)
JV/TC
cm*/s) 1.0 0.15 0.8 0.3 0.6
3.77 3.35 3.78 3.52 3.74
f 0.09 I 0.09 f 0.10 -r 0.11 t 0.11
12.04 9.49 11.34 10.16 10.93
3.56 + 0.17 3.78 * 0.12
10.13 10.63
1 2 3 4 S
9.0 2.27 7.0 3.1 5.4
6 8
2.75 * 0.3s 4.62 + 0.48
CHEhlICAL PHYSICS LE-ITERS
Volume 101, number 4,5
show the “odd-even” effect very similar to that observed for T,_ It is interesting to note that the members with 11odd have lower Tc but higher Wand W/Tc than the members with n even, and there is a tendency for their convergence with increasing n. A further point of interest is almost identical variations in T, and W observed in this series, the former is -4.3% around the mean value of 342.2 K while the latter is ~4.6% around 3643 K. The corresponding values for the PAA series are ~3.6% and 7-9% around the mean values of 406.8 and 2780 K. On the other hand, the variations in IV/T,for both the series are almost identical, =-8%. ft is to be noted that the variation of the order parameter at the nematic-isotropic liquid transition with increasing chain length has been qualitatively explained with different order parameters for the rigid and flexible molecular parts [ 13]_ This behavior can be explained without the concept of multiple order parameters by the simple introduction of an alternating intermolecular potential [ 141 as suggested by our observed W for the series. The relation between W observed in the isotropic liquid phase and the anisotropic intermolecular potential in the ordered phase becomes apparent from the following simple considerations: the anisotropic two-body intermolecular potential can be expressed from very general considerations as &(‘12Q12)
= &(‘I21
+ U2(r,2)cos4e12
-28 October 1983
observed either in the isotropic or ordered phase it becomes necessary to consider more than one nearest neighbor. Similar suggestions about more th& one nearest neighbor come from other sources [9,16,17]. In this context, the observed variations in the PM series [I] can be understood when we consider the expected variations in the number of nearest neighbors in the ordered phase [9] _A similar suggestion is also contained in the observation of intrinsic molecular optical anisotropy in cyanobiphenyls by Ldanne et al. [9] who could qualitatively reproduce the alternating behavior by considering molecular conformations. Finally. we should like to comment on our observed values for MBBA. These values are slightly at variance with our earlier measurements [ lS]_ This discrepancy seems to arise from impurities as suggested from measurements with some old samples in our laboratory. The nature of impurities could not be ascertained, although all the samples have almost identical T,. Our
observations suggest that impurities present do not have significant influence on T, but can have on other properties. Similar insensitivity of T, of MBBA to impurities has been observed in our nuclear relaxation studies [ 191. It is to be noted that the present values of D and W for MBBA are in good agreement with those observed by Hakemi and Labes [20] by a different technique.
+ U&12)cos2~12 + -._ )
where the notation is obvious. The first term represents the isotropic interaction and the subsequent terms anisotropic interaction of increasing order. Tile well known Maier-Saupe potential [ 151 is a special form of the first anisotropic term and can be obtained by subtracting its value in the isotropic phase. None of the angle-dependent terms becomes zero in the isotropic phase. Hence a relation between the observed Wand the anisotropic intermolecular potential is not unexpected, although a quantitative relation is difficult to establish at this stage. But a qualitative understanding can be obtained when we consider that the orientational order persists to higher temperatures than the positional order, suggesting it to be stronger. Hence it is expected that a major contribution to W comes from the angle-dependent part of the above potential. Furthermore, considering the magnitude of IV
References 1I] SK. Ghosh and E. Tettamanti, Chem. Phys. titters 69 (1980) 403. [ 21 H. Arnold. 2. Physik. Chem. (Leipzig) 226 (1964) 146. [3] A. Pines, DJ. Ruben and S. ABison, Phys. Rev_ Letters 33 (1974) 1002. [4] E.G. Hanson and Y-R. Shen, Mol. Cryst. Liquid Cryst. 36 (1976) 193. [5] R. Chang, F-B. Jones and J-J. Ratto, hiol. Cryst. Liquid Cryst. 33 (1976) 13. [6] R. Yamamoto, S. Ishihara, S. Hayakawa and K. Morimoto, Phys. Letters 69A (1978) 276. [7] S-K. Ghosh. E. Tettamanti and S. Amadesi, in: Advances in liquid crystal research and applications, Vol. 1. ed. L. Bata (Pergamon Press. Oxford. 1981) p_ 309. [8] J-R. LaIanne, B. Lemaire, J. Rouch, C. Vaucamps and A. Proutike. J. Chem. Phys. 73 (1980) 1927. [9] H. Arnold, 2. Chem. 4 (1964) 211. IlO] B. Flannery and Iv- Haas, J. Phys. Chem. 74 (1970) 3611. [ll] G-W- Smith and 2-G. Gardlund. J. Chem. Phys. 60 (1974)
3214.
501
Volume 101, number 4,s
CHEMICAL
PHYSICS
[ 121 A. Abragam. The principles of nuclear magnetism (Clarendon Press, Oxford, 1961) p. 61. [ 131 S. hiarcelja, J. Chem. Phys. 60 (1974) 3599. [ 141 CD. Mukherjee. T. Bose. D. Ghosh, Xl. Saha and ht. Roy, to be published. [ I.51 W_ hiaier and A. Saupe. Z. Naturforsch. 13a (1958) 564; 14a (1959) 882; 15a (1960) 287. [ 161 SK Ghosh, Mol. Cryst. Liquid Cryst. 37 (1976) 9_
502
LETTERS
28 October
1983
[ 171 SK. Ghosh and S. Amadesi. Phys. Letters 59A (1976) 282. [ 181 SK Ghosh and E. Tettamanti, Phys. Letters 37A (1973) 361. [ 191 SK. Ghosh, E. Tettamanti and A. Panatta, Phys. Rev. BZl(1980) 1194. [ 201 H. Hakemi and h1.M. Labes, J. Chem. Phys. 61 (1974)
4020.