Elsevier

Magnetic Resonance Imaging

Volume 19, Issues 3–4, April–May 2001, Pages 433-438
Magnetic Resonance Imaging

Surface-induced order and diffusion in 5CB liquid crystal confined to porous glass

https://doi.org/10.1016/S0730-725X(01)00262-4Get rights and content

Abstract

Liquid crystals confined into small cavities are known to have a weak orientational order even above the nematic-isotropic transition temperature. The surface-induced order and molecular dynamics in this temperature range are studied with the aid of deuteron NMR spectra, spin relaxation times T1 and T2, proton dipolar-correlation effect, and direct measurements of the effective diffusion coefficient for the liquid crystal 5CB confined to controlled-pore glasses. Our results show that an arrangement of molecules parallel to the wall is induced by local molecular interactions between the liquid crystal and solid, resulting in a weak and temperature independent surface order parameter, S0 ∼ 0.02 ± 0.01. There is no indication of a significant slowing-down of molecular diffusion at the wall, neither rotational nor translational. In cavities of nanometer size, where the nematic order evolves gradually upon cooling, a broadening of the NMR linewidths due to dynamic effects should be taken into account.

Introduction

Nuclear magnetic resonance (NMR) is a well established technique to study orientational order and dynamics of liquid crystals in porous matrices [1], [2], [3], [4]. A common feature of confined liquid crystals is a large surface-to-volume ratio which makes the effect of liquid crystal-surface interactions and geometrical constraints accessible to NMR observation. An interesting point of such systems is that the liquid crystal in contact with a solid surface usually becomes partially ordered even above the nematic-isotropic transition temperature TC. The orientational order parameter S is largest at the interface (S = S0) and decreases then exponentially with the increasing distance from the wall [5]. The characteristic decay length is the nematic correlation length ξ which shows a strong pretransitional increase on approaching TC from above. The thickness of the ordered layer at the wall is a few nanometers at the temperature 10 K above TC and increases then up to 10 nm - 15 nm just above the transition into the nematic phase. In sufficiently small enclosures, however, the surface-induced order extends over a large part of the enclosure and the discontinuous transition from the isotropic into the nematic phase disappears altogether [5], [6], [7]. It is replaced by a continuous growth of nematic order with decreasing temperature. Porous glasses with different, but well controlled pore sizes (Fig. 1) form appropriate matrices to get an insight into discontinuous and continuous liquid crystal transitions from the disordered into the ordered phase.

In this paper we present a study of liquid crystal properties in constrained geometry by measuring, for a few selected pore sizes, the deuterium NMR spectra, spin-lattice relaxation time T1, transverse spin relaxation time T2, the proton dipolar-correlation effect, and the effective diffusion coefficient. Liquid crystal under study is the common 4′-pentyl-4-cyanobiphenyl (5CB), selectively deuterated in the first position of the hydrocarbon chain. Its nematic phase extends from 24°C to 35°C in bulk. Porous glasses used as the constraining matrices have average pore sizes ranging from 7.5 nm to 140 nm and the corresponding porosities from 0.50 to 0.75 (CPG Inc., New Jersey). The NMR spectra and transverse relaxation time of deuterons were measured by the quadrupolar echo pulse sequence at Larmor frequency 58 MHz. Test measurements were performed by the Carr-Purcell-Meiboom-Gill sequence at 42 MHz for the bulk and one pore size. No difference in the values of T2 was observed. The deuteron spin-lattice relaxation time T1 was obtained by the standard inversion-recovery technique with an alternation of phases in subsequent cycles.

To get a direct notion of the diffusion coefficient, the stimulated echo pulse sequence (π2 − τ − π2 − tmπ2 − τ – echo) in a static magnetic field gradient of magnet with an ‘anti-Helmholtz’ arrangement of superconducting coils was used [8]. Stimulated echo attenuation in a static field gradient g is a product of attenuation factors due to spin-lattice (Ar1) and transverse (Ar2) relaxation, translational diffusion (Adiff), and dipolar-correlation effect (Adc) [9]: A(τ,tm,g)=Ar1(tm)Ar2(τ)·Adiff(τ,tm,g)Adc(τ,tm) The measurement of stimulated echo of protons at Larmor frequency 90 MHz in two different magnetic field gradients (g1 = 171 T/m and g2 = 45 T/m) enabled us to simultaneously determine the attenuation caused by self-diffusion and the attenuation caused by the dipolar-correlation effect. The analysis of Adiff = exp(−Dγ2g2τ2tm) yielded an effective diffusion coefficient Deff, since in the time of the experiment (100 μs ≤ tm ≤ 50 ms) the 5CB molecules diffuse through many pores. Since the complete analysis of Adc(τ, tm) was not possible due to the limitations imposed by the extremely high gradient, we used Adc(τ = 60 μs, tm = 10 ms) as an indication of the averaging of proton dipolar interactions in the system. Here Adc = 1 (no attenuation) in the isotropic phase and Adc<1 in any phase where the orientational order does not average out [9].

In the following, deuteron NMR spectra, relaxometry and the proton dipolar-correlation effect are used to investigate the orientational order of confined 5CB and the extent of its averaging by molecular translational diffusion. In Fig. 2 a few selected NMR spectra and temperature dependence of linewidths/splittings are shown. In the isotropic phase of bulk 5CB, fast and isotropic local molecular reorientations take place. They average out completely the quadrupolar interaction of deuterium nuclei giving rise to a single, narrow line in the NMR spectrum (Δν < 100 Hz). Only one line is observed also for 5CB in porous glasses. Its width, however, is larger than in the bulk, though well below 1 kHz for all cavity sizes and all temperatures above TC. At the transition into the nematic phase, the bulk spectrum splits abruptly into a well separated doublet (inset to Fig. 2). Its splitting Δν is proportional to the order parameter S of the nematic phase and depends on the liquid crystal orientation, i.e., Δν ∝ 12(cos2ΘB−1)S, where ΘB denotes the angle between the liquid crystal director and magnetic field [1]. In porous glass, 5CB orients, in spite of the magnetic field, parallel to the glassy surface and along the elongated, cylindrically shaped enclosures which are randomly oriented in space. As a consequence, the spectrum is powder-like for cavities of diameter ∼120 nm (inset to Fig. 2). The separation between the two peaks, Δν, is slightly smaller than one half of the bulk value due to the partial averaging effect of translational diffusion; a molecule travelling along bends and joints of enclosures namely changes its orientation with respect to the magnetic field. In cavities with smaller diameter (∼12 nm) no abrupt change in the spectrum is observed on cooling. The linewidth continuously increases as the temperature is lowered. At about 7 K below the bulk TC a splitting of the line starts to appear, as observed before [2], [3], [4], [9].

In the analysis of NMR linewidths in small enclosures it is important to take into account the correct origin of broadening. Besides the effect of the non-homogeneous magnetic susceptibility of the sample, this might be either the dynamic homogeneous broadening related to the transverse spin relaxation rate, Δν ≈ 1/(πT2), or the residual static quadrupolar broadening. The inhomogeneity of the magnetic field might be important high above TC but it would not show any pretransitional increase. On the other hand, the spectra clearly show an increase in the linewidths as TC is approached from above. Moreover, a comparison of measured Δν and Δν calculated from T2 data shows that the whole broadening up to 5 kHz and more is due entirely to the dynamic modulation of quadrupolar interaction and not to a residual static broadening. Therefore the linewidth of the 5CB in porous glass has not a linear dependence on the surface order parameter, which must be alternatively determined from the relaxometric data. The above statement is further confirmed by the fact that the attenuation of the proton stimulated echo due to the dipolar-correlation effect (Fig. 3) was not observed for 5CB in 7.5 nm CPG in the whole temperature range studied (Adc = 1). This indicates that the orientational order, though present in individual cavities, is averaged out on a larger scale. On the other hand, in the nematic phase of the 100 nm and 140 nm CPG samples the attenuation due to nonzero average dipolar coupling is clearly seen (Fig. 3), albeit at temperatures few degrees below the bulk transition temperature TC.

In view of the important role of molecular translational diffusion in averaging-out of the orientational order, we decided to measure the effective diffusion coefficient directly (Fig. 4). The bulk 5CB self-diffusion coefficient Dbulk demonstrates an Arrhenius-like temperature dependence with activation energy Ea = 33 kJ/mol which is about the same in the isotropic and in the nematic phase. The discontinuous jump of Dbulk at TC is a consequence of the onset of anisotropy in the nematic phase where only the component of the anisotropic self-diffusion tensor along the nematic director was measured. In the CPG confined samples no jump at TC is observed due to the fact that here an effective diffusion coefficient over many pores is measured. Since the distribution of cavities directions is isotropic, Deff is isotropic even in the nematic phase. Within the experimental error the activation energy is the same for the bulk sample and for the confined samples irrespectively of the pore sizes, both in the isotropic and in the nematic phase. The direct impact of the surface on the effective diffusion seems therefore to be negligible. Deff is completely determined by Dbulk and CPG structural properties and strongly decreases with decreasing pore size. In pores of diameter 7.5 nm, Deff is almost 10-times smaller than in the bulk. Comparing the relative values of Deff (inset to Fig. 4) we find that the empiric Archie’s law D ∝ ϵm with m ≈ 3 ± 0.3 is valid for all CPGs studied. ϵ denotes here the porosity of the glass.

Finally, a relaxometric study of confined and bulk 5CB was performed by measuring the deuteron spin-lattice relaxation time T1 at 58 MHz and the transverse relaxation time T2 which is sensitive to slower motions. In Fig. 5 the spin-lattice relaxation rate T1−1 is presented for 5CB in cavities of two different sizes and for the bulk. No effect of confinement which would exceed the experimental error is observed above TC. This means that fast local molecular reorientations, which are the dominating relaxation mechanism in the MHz range, do not undergo a significant slowing-down in cavities, though they become slightly anisotropic at the wall. We can conclude that the slowing-down, if any, does not affect the correlation times by more than one order of magnitude, what is in agreement with earlier dielectric measurements [4].

In contrast to T1−1, the transverse spin relaxation rate of deuterons T2−1 shows a considerable increase upon confinement. The smaller the pores, the larger increase in T2−1 is observed. In Fig. 6 the temperature dependence of T2−1 for 5CB confined into 72 nm pores is presented as well as the bulk relaxation rate. The increase upon confinement is ascribed to a slow, kHz frequency modulation of the residual quadrupolar interaction, which is superimposed on fast molecular reorientations. Order fluctuations cannot be responsible for this increase in T2−1 as the decay time of nematic clusters is shorter in confined isotropic phase than in the bulk [10]. Similarly, fluctuations in the thickness of the surface layer differ from the bulk fluctuations only in the temperature interval of about 1 K above TC [11], [12], whereas the increase in T2−1 is observed as far as 30 K above the transition.

The slow modulation originates therefore either in the exchange of molecules between the ordered region at the wall and disordered interior, or in the reorientations mediated by translational displacements of molecules (RMTD mechanism). These two relaxation mechanisms predict a different temperature dependence of T2−1. Within a two-site model, where a fraction of ordered liquid crystal at the wall (layer of thickness ξ and S = S0) and the remaining liquid crystal with S = 0 are assumed, the transverse spin relaxation rate induced by reorientations mediated by translational displacements with a typical correlation time τRD is [13] T2−12 220 e2qQh2S02τRD. Here (e2qQ/h) is the quadrupole coupling constant averaged by molecular conformational changes and by rotation around the long axis, and η denotes the fraction of molecules in the ordered site. To obtain T2−1 related to the exchange of the molecules between the ordered and disordered sites with a correlation time τexch, the factor η2 in Eq. (2) should be replaced by η(1-η) and τRD by τexch. In cavities with radius R much larger than ξ, η≈R=0R T∗T−T∗ with ξ0 ≈ 0.65 nm for 5CB and T∗ denoting the bulk supercooling limit (T∗ ∼ TC - 1 K). The solid line in Fig. 6 represents a fit of expression T2−1(CPG)=T2−1(bulk)+Cη2 to the experimental data. It provides obviously a good fit and shows that reorientations mediated by translational displacements (RMTD) are responsible for the increase of T2−1 in small enclosures. Within this simple model the only fitted constant C = 2500 s−1 yields an estimate of the surface order parameter S0. Assuming that the length of an enclosure is roughly 4-times its diameter [2] and that the local diffusion constant is similar to the bulk one, we obtain S0 = 0.02 ± 0.01. This value is much smaller than the bulk nematic order parameter just below TC (S ≈ 0.3). In a more elaborate analysis, a distribution of correlation times related to the RMTD process should be taken into account [14].

It is important to point out that the relaxation data are explained by a temperature independent surface order parameter S0, which is therefore entirely determined by the local interactions between the liquid crystal molecules and the solid at the interface. A similar conclusion was drawn for 5CB confined into inorganic Anopore cavities (S0 ≈ 0.02) [12] and in the polymer dispersion (PDLC), where 5CB is surrounded by epoxy material (S0 ≈ 0.08) [15]. In all three cases liquid crystal molecules tend to orient parallel to the solid substrate. On the other hand, we find-in contrast to PDLC results [15] - that the sticking of molecules to the wall, i.e., a retardation of translational motion, is negligible in CPG. The model which explains the experimental T2−1 data assumes namely a uniform translational diffusion of molecules throughout the cavity.

This work was partially supported by Slovene-German INCO Grant No. SLO-040-95.

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