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J. Phys. Chem. B 2008, 112, 9050–9052
Temperature Behavior of the Electric Field-Induced Entropy Increment within a Homologous Series of Nematogenic Compounds Jan Jadz˙yn,*,† Urszula Sokołowska,† and Jean-Louis Déjardin‡ Institute of Molecular Physics, Polish Academy of Sciences, M. Smoluchowskiego 17, 60-179 Poznan´, Poland, and Groupe de Physique Statistique et Mole´culaire, LAMPS, UniVersite´ de Perpignan Via Domitia, 52 AVenue Paul Alduy, 66860 Perpignan Cedex, France ReceiVed: April 4, 2008
Based on the temperature behavior of the entropy increment induced by the probing electric field in the isotropic phase of mesogenic compounds belonging to the homologous series CnH2n+1PhCOOPhCN (n ) 4-10), it is found that an ability to the dipolar aggregation of the molecules depends on the alkyl tail length, and, in particular, the ability is strongly reinforced when the number n changes from 7 to 8. The role of the molecular structure in the self-assembling process is discussed. Introduction Molecular self-assembling processes occurring in the prenematic region of isotropic mesogenic liquids manifest themselves in numerous pretransitional phenomena.1–12 These assembling processes reflect the molecular preferences for aggregation, which usually are realized in the liquid state, but in the pretransitional circumstances the effects are only markedly enhanced. So, the studies of the prenematic molecular aggregation allow one to recognize more clearly than in the studies of “normal” liquids which elements of the molecular structure are essential in determination of a given physical property of the liquid, as its effective polarity, for example. As new nematic liquid crystals of high dielectric anisotropy are constantly in request, the studies of the relation between the molecular structure and the efficiency of the molecular aggregation, which, in general, results in a reduction of the static permittivity, are important also from a technical point of view. In the present Article, we show that the two fundamental elements of the molecular structure, the length of the alkyl tail of the mesogenic molecule and the polar lateral substituent of the molecule, have a very efficient influence on the molecular self-assembling process. As the main problem in such a type of investigations is a formulation of the quantitative description of that “efficiency”, we shall take into account the temperature behavior of the electric field-induced entropy increment related to the liquid under consideration.
plateau of the real part of the complex dielectric permittivity is recorded. The measuring capacitor consisted of three plane electrodes, one central and two grounded on each side, with a distance between them of about 0.5 mm. The probing electric field intensity E was equal to ∼1 V/mm. The electrical heating of high performance was realized by using a “Scientific Instruments” temperature controller, model 9700, assuring a good temperature stabilization (at the milikelvin level) with the possibility of varying the temperature by steps of 10-2 K. Such equipment allows one to determine the permittivity with a relative accuracy better than 0.5%.
Experimental Section
Results and Discussion
The subject of our studies is the homologous series of nematogenic 4-cyanophenyl 4′-alkylbenzoates (CnH2n+1 PhCOOPhCN, nCPAB, n ) 4-10). The compounds were synthesized and purified at the Institute of Chemistry, Military Technical University, Warsaw, Poland. The temperatures of the isotropic (I) to nematic (N) phase transition (TNI) of nCPABs are shown in Figure 1. The static dielectric characteristics of the compounds were measured with a HP 4194A impedance/gain phase analyzer at the frequency of ∼100 kHz, where in the dielectric spectrum a
As results from the Fro¨hlich theory,13 the thermodynamic outcomes of an application of the probing electric field to a polar liquid, the Helmholtz free energy (∆F) and the entropy (∆S) increments, are related to the static dielectric permittivity (εs) and its derivative (∂εs/∂T), respectively, as follows:
* Corresponding author. E-mail:
[email protected]. † Polish Academy of Sciences. ‡ Universite ´ de Perpignan Via Domitia.
Figure 1. Temperatures of the isotropic to nematic phase transition (TNI) for the compounds from the homologous series of nCPABs.
∆F(T) F(T, E) - F0(T) ε0 ≡ ) εs 2 E2 E2 ∆S(T) S(T, E) - S0(T) ε0 ∂εs ≡ ) 2 ∂T E2 E2
(1) (2)
where E denotes the strength of the probing electric field, U0, S0, and F0 are the values of the thermodynamic quantities (per
10.1021/jp802923b CCC: $40.75 2008 American Chemical Society Published on Web 07/09/2008
Entropy Increment within a Homologous Series
J. Phys. Chem. B, Vol. 112, No. 30, 2008 9051
Figure 3. ∆TS, a postulated measure of the self-assembling ability of the mesogenic nCPAB molecules, as a function of the number n of carbon atoms in the alkyl tail of the molecules. Figure 2. Temperature dependence of (a) the static dielectric permittivity (εs) and the Helmholtz free energy increment (∆F) and (b) the static permittivity derivative (dεs/dT) and the entropy increment (∆S), measured for the homologous series of nCPABs.
unit volume) in the absence of the electric field, T is the absolute temperature, and ε0 ) 8.85 pF/m is the permittivity of free space. Figure 2 presents the experimental results on the temperature dependence of the static permittivity, its derivative, and the corresponding ∆F and ∆S increments, obtained for nCPAB homologous series. Similarly as observed for other nematogenic liquids,14–17 in the vicinity of the phase transition from the isotropic liquid to the nematic liquid crystalline phase of nCPABs, the entropy increment shows a critical-like temperature dependence, and, a few degrees before the phase transition, the increment changes its sign from a negative value to a positive one. The negative value of the electric field-induced entropy increment corresponds to the normal field-ordering effects in polar liquids, and in the case of nonmesogenic polar liquids or in mesogenic liquids far from the I-N phase transition, ∆S shows only a slow increase when the temperature decreases, reflecting a change of the number of molecules per unit volume.12 From about 15 °C before the phase transition, one observes an anomalously strong increase of ∆S, and several degrees before the transition, the entropy increment attains the zero value. The characteristic temperature, T∆S ) 0, at which one observes an equilibrium between the electric field ordering action (∆S < 0) and the disordering one (∆S > 0), in relation to the temperature of the phase transition, TNI, can be considered as a measure of the efficiency of the self-assembling process of the dipolar mesogenic molecules. In the prenematic region, this process leads to the formation of pseudonematic domains, precursors of the approaching nematic phase. The positive value of the entropy increment (∆S > 0) in the vicinity of the transition to the nematic phase means undoubtedly that in the spontaneously formed pseudonematic domains, the molecules are arranged predominantly in the antiparallel way, so that the electric field, forcing the parallel orientation of the dipoles, breaks down the molecular structures of domains, thus giving an increase of
Figure 4. Static dielectric permittivity of the compounds from the homologous series of nCPAB as a function of n, measured at 80 °C.
the entropy of the system. Hence, it seems to be reasonable to assume that the temperature distance between the point where the entropy increment changes its sign and the point where the I-N phase transition occurs, ∆TS ) T∆S ) 0 - TNI, can represent the ability for dipolar molecules aggregation in the liquid studied. Figure 3 presents the dependence of ∆TS on n, that is, on the length of the molecules from the homologous series of nCPAB. It seem to be interesting to mention that within the series of the compounds having the same polarity, one observes a significant increase of ∆TS when the number of carbon atoms in the alkyl tail of molecule changes from 7 to 8. It is quite possible that these n values are random only, but if one takes into account that in some well-known homologous series of mesogenic compounds just beginning from n ) 8, the high selforganized smectic phases are appearing, it is quite possible that the ∆TS can reflect, in some extent, the molecular ability to the self-aggregation. If so, one should expect some anomalous behavior in the static permittivity dependence on n, because the enhanced dipolar (mostly antiparallel) molecular aggregation must lead to the anomalous decrease of the permittivity for nCPAB compounds with n g 8. Figure 4 illustrates the n dependence of the values of the static permittivity of nCPABs, measured at 80 °C, that is, far from the transition to the nematic phase of these compounds
9052 J. Phys. Chem. B, Vol. 112, No. 30, 2008
Jadz˙yn et al. presents a comparison of the temperature dependences of the static permittivity and its derivative, measured for two mesogenic compounds composed of the following molecules: C6H13PhPhCN (6CB)14 and C6H13PhCOOPhCN (6CPAB). The -COO- group introduces in 6CPAB molecule an additional (in comparison to 6CB, molecular dipole moment µ ≈ 5D10) dipole moment of ∼1 D along the long molecular axis and ∼1 D in the perpendicular direction. So, the 6CPAB molecule is more polar than the 6CB one. As can be seen in Figure 5, the dielectric behavior of the two compounds is quite different, but unexpectedly for the usual reasoning, the more polar compound presents only a part of the aggregation ability of the less polar compound. Thus, the presence of the lateral polar CdO group effectively limits the molecular aggregation process of 6CPAB molecules, and, as a consequence, the noticeable difference in the static permittivity of these two compounds results not only from the different values of their molecular dipole moments but also from the different degrees of the dipolar aggregation. References and Notes
Figure 5. Comparison of the temperature dependence of the static permittivity (a) and its derivative (b) for two compounds of different structures: 6CB and 6CPAB, ∆T ) T - TNI.
and where the prenematic effects can be neglected. Indeed, the static permittivity of these isotropic liquids, composed of the molecules with the same polarity, exhibits some anomaly: for n g 8, one observes a distinct change in the character of εs(n) dependence, indicating, as expected, an anomalous decrease of the permittivity of the compounds. The compatibility of the results presented in Figures 3 and 4 suggests that the quantity ∆TS can be a measure of the aggregation ability of strongly polar mesogenic molecules. Of course, the alkyl tail length of the molecules is only one from the numerous structural elements, which are important for an efficiency of the aggregation process discussed here. Among these other elements, the existence of the lateral substituent in the mesogenic molecule seems to be one of the most crucial in the self-assembling process. To show that aspect, Figure 5
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