Smectic A: cholesteric phase transition investigated by small angle X-ray diffraction and viscosity measurements

Abstract

We have studied the in influence of the mean molecular length on the nature of the cholesteric (N*) – smectic A (A) liquid crystal phase transition for thermotropic compounds of cholesteryl myristate (C14), cholesteryl nonanoate (C9), and binary mixtures of C14 – C9 and cholesteryl caproate (C6) phase (dA), the mean molecular length (<img src="http:/img/fbpe/bjp/v32n2b/07eq01.gif">) in the N* domain, and the correlation length (epsilon), as well as changes along the N* – A phase transition, were determined from the X-ray diffraction data. The results show a decrease in A phase domain and an expansion of the N* – domain as the mean molecular length is diminished. Such effect induces a second order A – N* phase transition for a particular mixture of 63.1 mol% of C9 and 36.9 mol% of C6, evidenced by viscosity measurements in good agreement with previous density data.

Smectic A - Cholesteric Phase Transition Investigated By Small Angle X-Ray Diffraction and Viscosity Measurements

E. L. Duarte¹, R. Itri¹, A. R. Sampaio², M. Simões³, and A. J. Palangana²

¹ Instituto de Física, Universidade de São Paulo,

Caixa Postal 66318, 05315-970 - São Paulo, SãoPaulo, Brazil

² Departamento de Física,Universidade Estadual de Maringá,

87020-900 - Maringá, Paraná, Brazil

³ Departamento de Física, Universidade Estadual de Londrina, 86051-970, Londrina, Paraná, Brazil

Received on 30 November, 2001

We have studied the in influence of the mean molecular length on the nature of the cholesteric (N*) – smectic A (A) liquid crystal phase transition for thermotropic compounds of cholesteryl myristate (C₁₄), cholesteryl nonanoate (C₉), and binary mixtures of C₁₄ – C₉ and cholesteryl caproate (C₆) phase (dA), the mean molecular length () in the N* domain, and the correlation length (e), as well as changes along the N* – A phase transition, were determined from the X-ray diffraction data. The results show a decrease in A phase domain and an expansion of the N* – domain as the mean molecular length is diminished. Such effect induces a second order A – N* phase transition for a particular mixture of 63.1 mol% of C₉ and 36.9 mol% of C₆, evidenced by viscosity measurements in good agreement with previous density data.

I Introduction

The first (discontinuous) and second (continuous) order nature of the liquid crystal phase transitions have been the subject of many works along the last 30 years. In particular, the Smectic A (A) - Nematic (N) or cholesteric (N^*) phase transition was demostrated to be of either first order or second order, depending on the smectic layer thickness and the reduced temperature, according to McMillan's molecular model [1, 2]. The reduced temperature is defined as [1]: r = T_AN/T_NI, where T_AN and T_NI represent, respectively, the A-N and N-Isotropic (I) phase transition temperatures, also known as McMillan ratio. In a extension of the McMillan's model proposed by Lee et al. [3], the theoretical results point out that the energy associated to the smectic ordering increases with molecular length and r, occurring a second order phase transition for r 0.88. Several calorimetric measurements were performed on binary mixtures (where the molar ratio was varied between two different homologous liquid crystal molecules of distinct lengths) and showed that the reduced temperature can vary from 0.89 to 0.99 [4, 5]. In fact, calorimetric measurements performed by two of us on binary mixtures composed of cholesteryl palmitate (C₁₆) , cholesteryl myristate (C₁₄) , cholesteryl nonanoate (C₉) and cholesteryl caproate (C₆) [6] and C₉, cholesteryl heptanoate (C₇) and C₆ [7], that present a A-N^* phase transition, gave evidence of a tricritical point around r 0.90 - 0.92. Recently, we have investigated the possible existence of a second order phase transition at r 0.92 for a particular mixture of C₆-C₉ (63.1 mol% of C₉) through density measurements [8].

It is well known that the average correlation length (e) in a second order phase transition diverges continuously in the vicinities of the transition. With a view of investigating the correlation length behavior in our systems, we extended the previous work [8] making use of the X-ray scattering technique to explore the values of e within the N^* and A phases domain as well as along the A-N^* phase transition. In this context, we have studied the same samples previously investigated [8] composed of pure C₉ and C₁₄, and binary mixtures of C₁₄ - C₉ and C₉ - C₆. The mean molecular lengths (l_M) are displayed in Table 1, calculated from the molecular structure taking into account the molar ratio of the compounds employed in the mixtures. The molecular length of each compound was estimated as a sum of the cholesterol length (18Å) [9] plus a radical length given by Tanford's formula [10].

The variation in concentration implies a change in the mean molecular length and plays an important role as a thermodynamical variable in the study of these systems. The X-ray data furnishes the distance between the smectic layers (d_A) in A phases and the experimental mean molecular length () in N^* phases from the diffraction peak position, and e from the diffraction line width, as shown below. In the literature, few investigations have been reported on the viscosity (h) values associated to the A-N^* phase transition. In particular, Porter et al.[11] have carried out viscosity measurements as a function of temperature for cholesteryl myristate (C₁₄) in the A, N^* and I phases. The authors showed that the viscosities for both the cholesteric and smectic A phases present a non-Newtonian behavior with a sharp transition between the two mesophases.

II Experimental

II.1 Samples

Cholesteryl n-alkanoate homologous series C₁₄, C₉ and C₆ were obtained from Sigma and used without further purification. Calorimetric and X-ray scattering measurements were performed on C₁₄ and C₉ and on three binary mixtures in the following concentrations: 81.5 mol% and 63.5 mol% C₁₄ in the binary mixture of C₁₄-C₉ and 63.1 mol% of C₉ in the mixture of C₉-C₆.

It should be remarked that only the C₁₄ compound presents the crystalline, A, N^* and I phases at heating and cooling cycles. The other samples present monotropy in the A phase [6, 7]. Then, the samples were first heated up to the I phase in a fast way followed by a slower cooling procedure up to the A phase. When the latter was reached (without the appearance of a crystalline phase) the process was reverted, rising again the temperature. Such procedure permitted to acquire the A-N^* phase transition data at both cooling and heating cycles.

II.2 Methods

The X-ray scattering measurements were performed by using a focusing camera in a 18 kW rotating anode X-ray generator (Rigaku-Denki) with CuKa (Ni filter, l = 1.5418Å) radiation at 50kV × 200mA and an image plate detection system. Samples were acconditioned in sealed 1 mm-thick flat mylar windows, perpendicular to the incident X-ray beam, placed in a copper sample holder in which a temperature control was attached (Euro Control model PC-850A). Further, the sample holder was rotated during the X-ray data acquisition to avoid textures effects (preferential orientation) in the diffraction lines. Data acquisition of three hours was taken for each studied temperature and the temperature step was 2^°C at both cycles. The spectra registered in the image plate were digitized using a Scanner model STORM 820 with a help of a PC-microcomputer.

The 2-D spectra were converted in 1-D (area integration) by using the "X-Ray" program [12], that showed to be an excellent software to analyse this type of image, furnishing the X-ray intensity (I_obs(q)) as a function of the scattering vector (q = 4p·sinq/l, where 2q is the X-ray scattering angle). The total intensity was normalized by the exposition time and corrected by subtracting a parasitic scattering considered as the low scattering of the I phase. The position and width of the diffraction peak were obtained through fitting a Lorentzian function [13] to the experimental data as:

where

q

_c is the peak position, and e is the correlation length. From

q

_c, we obtain the distance between the smectic layers in the

A phase:

d

_A=2p/

q

_c; and the mean molecular length in the

N

^* phase [14]:

= s2p(1.229) /

q

_c. The values of

d

_A and

presented in the current work, correspond to the mean values obtained at cooling and heating cycles due to their similarity.

Viscosity measurements as a function of the temperature near the A-N^* phase transition were determined by means of a Brookfield Cone/Plate Rheometer model LVDV-III. The rheometer was calibrated with a standard oil of known viscosity. The sample temperature was controlled by a HetoCB8-30E/DT-1 circulating temperature bath, ensuring that the temperature readings were stable at 0.01 K. A cooling rate of 6 mKs^-1 was used during the measurements. Additional measurements were also made as a function of shear rate. The phase transition temperatures were checked by using a polarized light microscope.

III Results and discussion

III.1 X-Ray Scattering

The X-ray scattering spectra of thermotropic mesophases A and N^* present two rings [14]. The first ring appears in a small angle range and is associated to the layer repetition distance in the A phase, and the mean molecular length in the N^* phase. The second ring, presented in larger angles, is characteristic of an average distance between the molecules perpendicular to the long axis of the same, with small variation along of the phases.

In this work, we are interested in investigating the variation of the correlation length (e) in the two mesophases, as well as along the A-N^* phase transition. Therefore, we focus our attention on the first diffraction ring (2q 2.5^°). The features of the X-ray spectra (Fig. 1) of each phase can be summarized as follows:

1. I phase: the X-ray scattering is diffuse (

   Fig.1-a), characteristic of a disordered distribution of the molecules.

2. N

   ^* phase: the X-ray scattering presents a well defined ring (

   Fig. 1-b), related to the correlation between molecules nearly oriented along a director axis.

3. A phase: the X-ray scattering presents a thinner and stronger ring than that observed in the

   N

   ^* phase (

   Fig. 1-c), due to a more ordered structural arrangement.

III.1.1 Distance between smectic planes and the mean molecular length

Figure 2 (part I) presents the distance between the smectic A planes (d_A), and the experimental mean molecular length () in the N^* phase [14] as a function of the temperature ratio: t = (T - T_N^*A)/T_N^*A [8]. Accordingly, d_A is practically constant in the A phase domain, whereas decreases as temperature increases in N^* phases. Table 1 shows the observed d_A values in comparison with those calculated from the mean molecular structure (l_M). Thus, one can note that the distance between the layers in the A phase is circa 10% smaller than the corresponding mean molecular length calculated by assuming a total extended chain conformation. Moreover, d_A decreases with l_M, as expected.

On the other hand, the observed mean molecular length in the N^* phase near the A-N^* phase transition (_AN^*) is greater than l_M (Table 1). This behavior can be due to the fact that the expression to calculate , suggested by de Vries [14], is valid in I and N phases, when the molecules do not have a strong orientational order effect. Therefore, we believe that _IN^* ( in the N^* phase near the N^*-I phase transition) is, indeed, the mean molecular length, and _AN^* has no meaning. Anyway, d_A is always smaller than _IN^* due to the contraction of the molecules as the temperature is reduced.

As previously mentioned, one can note from the Fig. 2 (part I) that the A phase domain decreases and the N^* phase increases as l_M decreases.

III.2 Correlation length

Figure 2 (part II) shows the correlation length (e) in the A and N^* phases for all studied samples. As one can observe, e increases in N^* phase as temperature decreases. This is due to an increase in the orientational order when the temperature moves away from the I-N^* phase transition and approachs to the N^*-A phase transition.

In contrast, the correlation length is practically constant in the A phases with a small decrease in the N^*-A phase transition vicinity, still in the A phase domain. Regarding to 63.1 mol% C₉ in the C₉-C₆ binary mixture, just one temperature in the A phase (Fig. 2.I-e) was experimentally obtained, because its domain is very narrow before the appearance of the crystal phase. Moreover, there is a clear discontinuity in the values of e along the N^*-A phase transition (Fig. 2.II). However, the decrease in the mean molecular length is accompanied by a decrease in the correlation length discontinuity (De) at the N^*-A phase transition. This because the correlation length in the N^* phase near the N^*-A phase transition is greater for samples with shorter mean molecular length bringing about a decrease in De in the referred phase transition.

III.3 Viscosity

The viscosity, h, results versus temperature ratio and shear rate, g, near the A-N^* phase transition, from the pure compounds C₁₄ and C₉ are shown in the figure 3. Note the presence of a peak [15, 16] at the A-N^* phase transition for the C₁₄ pure compound (Fig. 3-a). Indeed viscosity data have provided a sensitive measurement for phase transitions[15] and, in this case, a clear distinction between the smectic A and the cholesteric phases viscosity values. The magnitude of the peak as well as the viscosity values at A phase decrease markedly with increasing shear rate. This might be correlated to the fact that it is easier to breakup the smectic structure as the shear rate is increased. Similar results for the same compound was obtained by Porter et al. [11].

The viscosity values increase at the A-N^* phase transition for the C₉ while r diminishes from 0.986 (C₁₄) to 0.956 (C₉) shown in figure 3-b. On the other hand, the changes in the h values are not sharp in C₉ as in C₁₄ compound from N^* to A phases (Dt » 0.2 for C₉). This A-N^* phase transition has been considered as being weakly of first order by McMillan[1]. His X-ray experiments point up to the growth of smectic-like short-range order in the cholesteric phase near the A-N^* phase transition. Our experimental results seem to be consistent with this fact. Such pretransition effect can be related to the increase in the viscosity values and reduced temperature interval observed in this phase transition.

Figure 4 shows the viscosity values at shear rate of g = 0.4s^-1 for 63.1 mol% C₉ at r = 0.918 in the C₉-C₆ system, where the existence of a possible second order A-N^* phase transition was recently investigated[8]. Such low value of shear rate was used due to the strong increase in the viscosity values near the phase transition. Note that the viscosity for this mixture at g = 0.4s^-1 is on the same order of magnitude observed for C₁₄ compound at g = 3s^-1. Such increase in viscosity for the C₉-C₆ compound in the N^*-A phase transition can be related to the small domain of the A phase in this mixture, as shown in the x-ray experiments, followed by a very near crystal phase. Moreover, the interval of temperature associated to the changes in the h values from N^* to A is larger than for C₉ (Dt » 0.4 for this mixture).

To sum up, the results obtained through X-ray and viscosity measurements used in this work, investigating the same liquid crystalline compounds of the homologous series of the cholesteryl n-alkanoates [8], present several interesting features in the nature of the A-N^*phase transition, depending on the mean molecular length. As far as the X-ray scattering data are concerned, a decrease in A phase domain and an expansion of the N^* phase domain with the reduction of the l_M were observed. This behavior is the same obtained theoretically by Lee et al. [3]. The distance between layers in the A phase is compatible, although a little smaller, to the calculated l_M and the experimental _IN^* mean molecular length. Moreover, d_A decreases with l_M as expected. The correlation length in the N^* phase is greater for the samples with smaller mean molecular lengths. The viscosity values increases at the A-N^* phase transition while r diminishes. For 63.1 mol% C₉ in the C₉-C₆ a big increase in the viscosity of the system was observed as N^*-A phase transition is approached, where the existence of a possible second order phase transition was pointed out[8].

Acknowledgments

This work was supported by research grants from Pronex/MCT and FAPESP to R. Itri, Fundação Araucária and CNPq to A. J. Palangana and M. Simões. E. L. Duarte and A. R. Sampaio had a master fellowship from FAPESP and CAPES, Brazil, respectively. Research fellowship to R. Itri from CNPq is also appreciated.

[12] http://www.umh.ac.be/~poly/XRay/X-Ray.htm.

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Publication Dates

• Publication in this collection
  20 Nov 2002
• Date of issue
  June 2002

History

• Received
  30 Nov 2001