Magnetic Resonance in Colloid and Interface Science

8 Self-Diffusion in Lyotropic Liquid Crystals Measured by NMR

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GORDON J. T. TIDDY and ETHNA EVERISS Unilever Research Port Sunlight Laboratory, Port Sunlight, Wirral, Merseyside, United Kingdom L62 4XN

ABSTRACT The pulsed field gradient NMR technique has been used to measure the self diffusion coefficients of all the components in an aligned lamellar phase sample of lithium perfluoro-octanoate. Water diffusion coefficients were ~8 x 10-10 m2s-1 and ~6 x 10-10 m2s-1 for diffusion parallel and perpendicular to the lipid bilayers at 320K. In the same temperature region the comparable lithium diffusion coefficients were 3 x 10-11 m2s-1 and 1.4 x 10-11 m 2 s -1 . Perfluoro-octanoate ion diffusion within the bilayer was estimated to be 6 x 10-12 m 2 s -1 , assuming zero diffusion perpendicular to the bilayer. 1.

INTRODUCTION

Surfactants with perfluoroalkyl chains are similar to hydrocarbon surfactants i n that they form micelles (1) and lyotropic liquid crystals (2^_3). The liquid crystals are good materials for NMR studies since there i s no p o s s i b i l i t y of overlap between the water and alkyl chain signals. The lamellar liquid crystalline (I.e.) phase i s often used as a model of biological membranes In previous studies, a combination of neutron scattering and NMR measurements have been used to measure water translational d i f f u sion across fluorinated l i p i d bilayers (4). The diffusion was less than one order of magnitude lower than that observed for normal water, and the anisotropy of diffusion was small. In this paper measurements of a l l the constituents (water, counterion and surfactant) of a lamellar phase are reported. At 298K the system Lithium Perfluoro-octanoate (LiPFO) + water forms a uni-axial viscous I.e. phase containing 69% - 76% LiPFO (by wt) and this material melts i n the range 303-13K to fora a lamellar phase (3).

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Resing and Wade; Magnetic Resonance in Colloid and Interface Science ACS Symposium Series; American Chemical Society: Washington, DC, 1976.

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Self-Diffusion in Liquid

Crystals

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The viscous phase, originally thought to have the reversed hexagonal structure (3), can be aligned with uni-axis perpendicu lar to the surface of microscope cover-slips by heat cycling through the phase transition. In this way, samples with domains aligned in the same direction can be prepared. The alignment i s unaltered by raising the temperature above the phase transition to the lamellar phase. Thus large, single alignment, lamellar phase samples can be prepared which give strong NMR signals for the measurement of self diffusion coefficients ( D ) . In order to use the pulsed f i e l d gradient NMR technique for measurements of D i t i s necessary to observe an echo with a π/2-t-ïï pulse interval of ^ 10ms. The residual dipole or quadrupole couplings that occur i n liquid crystals (5) make this impossible for powder samples, with the exception of the water signal of 1^0 where the residual dipole coupling i s usually averaged by proton exchange. However, with counter-ions having a quadrupole moment and non-integer spin quantum numbers an echo i s often observed due to the non shifted +1/2/-1/2 transition. In addition, i n single alignment samples, echos modulated by the appropriate s p l i t t i n g frequency can be observed (e.g. for D2O, L i , Na ). So, for water and counter-ions, the pulsed f i e l d gradient technique can be used to measure diffusion p a r a l l e l (DJJ ) and perpendicular (D^) to the bilayer surfaces i n the lamellar phase. For the surfactant the situation i s more complex. If a single alignment sample i s placed i n the magnetic f i e l d at the magic angle then the non-averaged dipolar couplings vanish, and the resulting signal can be used for D measurements (6). Unless a quadrature f i e l d gradient c o i l i s available, the measurements are restricted to one specific angle (J). These techniques have been used for the measurements of self-diffusion coefficients reported here. A single alignment lamellar phase sample of the LiPFO/water system has been prepared, and, for the f i r s t time measurements of self diffusion of a l l the components are reported. In addition, this i s the f i r s t report of the anisotropy of counterion diffusion i n a lamellar phase. 2.

EXPERIMENTAL

Sample homogenization and materials were the same as those described previously (2,3). The single alignment sample was made from a mixture of 72% LiPFO (0.099 mol. fraction) and 28% water (H 0:D 0 9:1 by wt., see below). The mixture (^l/2g) was placed in a 7mm o.d. NMR tube and nine glass rectangles cut from microscope cover-slips were added to form a series of p a r a l l e l layers. The tube was cycled through the phase transition ca. 100 times over a period of 6 months. The degree of alignment was monitored using the free induction decays after a π/2 pulses of the L i and H resonances. The i n i t i a l powder pattern was gradually replaced by the modulated signal of the single alignment sample, 2

7

2

2


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u n t i l > 95% of the sample gave the modulated signal. No further change was observed, and the 'non-aligned' material was thought to be that adjacent to the wall of the NMR tube. MIR measurements were made using a Bruker-Physik variable frequency milsed NMR spectrometer (B Kr 322s) operating at 60.0 Mhz Γ Η , F , π/2 pulse - 2 ys), 35.0 Mhz ( L i , π/2 6 ys and 14.0 Mhz ( H, π/2 « 10 ys). The Bruker f i e l d gradient unit (BKr - 300 - 218) and variable temperature unit were used as reported previously (4), with the exception that the amplitude of the f i e l d gradient pulses was monitored using the Bruker pulsed gated integrator and a d i g i t a l volt meter. The instrument was calibrated with d i s t i l l e d water for i^O measurements and 2.0M lithium chloride and bromide solutions (for L i measurements). Because of the lack of a suitable standard for F measurements both the above standards were used, and this gives rise to the larger error for the fluorocarbon self diffusion coefficient. Also, the maximum T value observed for the F resonance was VL0 ms. This i s much less than T^ and i s probably due to the presence of a small distribution of alignment directions (^0.5°) in the ordered material. 1 9

7

2

7

1 9

1 9

2

3.

RESULTS AND DISCUSSION

The pulsed f i e l d gradient method for measuring self-diffusion coefficient consists of : (i) The measurement of the echo height (h ) following a π/2-ί-π r . f . pulse sequence. Q

( i i ) The application of equal f i e l d gradient (f.g.) pulses between the π/2 and π pulses and between the π-pulse and the resulting echo, followed by measurement of the echo height (h ). The self-diffusion coefficient i s given by Equation (1) (10). fc

In

~

2

- -D

γ δ

2

(Δ - ·| 6)G^

»

-DL

(1)

ο where γ - gyromagnetic ratio δ * duration of the f.g. pulses Δ » time interval between f.g. pulses G * amplitude of f.g. pulses t

D can be obtained from a graph of ln(h /h ) against L, with variation of δ ,Δ or G « In practice the absolute determination of G i s tedious. Because of this, G was determined i n the present study by using standards with known D values, and measure ments were made relative to these. 2

t

t

fc


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Crystals

In d i s p e r s e systems, the phenomenon of " r e s t r i c t e d d i f f u s i o n " o f t e n occurs (11). For s m a l l homogeneous regions s e l f - d i f f u s i o n can be f a s t , but the presence of impermeable b a r r i e r s between d i f f e r e n t regions can r e s u l t i n slow d i f f u s i o n over l a r g e d i s tances. This causes a n o n - l i n e a r dependence of I n ( h / h ) on δ , G and Δ. In the present system measurements were made over the ranges h /h = 0.02 - 1.0, Δ = 10-40ms f o r water, h /h = 0.05 - 1.0, Δ = 10-90ms f o r l i t h i u m i o n s , and h / h » 0.1-1.0, Δ = 10ms f o r p e r f l u o r o - o c t a n o a t e i o n s . In every case the curves In h /h against L were l i n e a r , t o t

2

o

2

t

Q

Water D i f f u s i o n Measured d i f f u s i o n c o e f f i c i e n t s are l i s t e d i n Table The values f o r water are c o n s i d e r a b l y higher than those of L i ions or p e r f l u o r o - o c t a n o a t e i o n s , and are of the same order of magni tude as values reported f o r l a m e l l a r phase samples c o n t a i n i n g cesium and ammonium counter-ions ( 4 ) . The a n i s o t r o p y of water d i f f u s i o n i s lower than that reported p r e v i o u s l y , when values of D /D = 2 were obtained. However, the most s u r p r i s i n g f e a t u r e of these r e s u l t s i s the very high d i f f u s i o n c o e f f i c i e n t f o r water t r a n s l a t i o n p e r p e n d i c u l a r to the l i p i d b i l a y e r s . Two explanations can be proposed f o r t h i s : (i)

The water t r a v e l s through d e f e c t s i n the b i l a y e r s u r f a c e ,

or (ii)

the b i l a y e r i s h i g h l y porous to water.

While n e i t h e r e x p l a n a t i o n can be proven, a l i m i t a t i o n on the type of defect can be suggested. Since the a n i s o t r o p y of water d i f f u s i o n i s lower than t h a t of l i t h i u m i o n d i f f u s i o n then a l a r g e p r o p o r t i o n (>50%) of the water t r a n s p o r t must occur i n regions s m a l l enough to prevent d i f f u s i o n of hydrated l i t h i u m i o n s , i . e . l e s s than M).5nm. Assuming a D value equal to that of pure water f o r d i f f u s i o n w i t h i n d e f e c t s , the surface area of the d e f e c t s i s c a l c u l a t e d to be ^20% of the t o t a l b i l a y e r area. Thus the d i s t a n c e between adjacent d e f e c t s must be ^3nm. In a powder l a m e l l a r phase sample the s i z e of i n d i v i d u a l c r y s t a l l i t e s i s > 2 ym. ( I f the c r y s t a l l i t e s were s m a l l e r than t h i s then deuteron quadrupole s p l i t t i n g s would be averaged to zero.) Thus the d e f e c t s r e f e r r e d to above cannot be those between i n d i v i d u a l crystallites. I t i s p o s s i b l e that the f a s t d i f f u s i o n i s due to the occurrence of 'pores* w i t h i n the b i l a y e r s u r f a c e through which water (and l i t h i u m i o n s ) can move. By comparison w i t h s i m i l a r l a m e l l a r phase samples the water and f l u o r o c a r b o n l a y e r s would be expected to have thicknesses of ^1.5 nm and 1.2 nm r e s p e c t i v e l y . I f water penetrates one or two CF£ groups along the chain from the head groups, then the t h i c k n e s s of the b i l a y e r zone i s reduced


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Table I 3

S e l f - D i f f u s i o n C o e f f i c i e n t s of Water, L i t h i u m Ions and Perfluoro-Octanoate Ions i n LiPFO L a m e l l a r Phase

4

Temp

Water

- -1 ΧΙΟ"" ; m s

(K)

A(ms)

τ (ms)

314.3 314.8

30.5 25.3

20.0 20.0

7.1

315.0 320.5 326.5

12.4 12.4 12.4

10.0 10.0 10.0

8.1 8.5 9.9

10

+

316 322 328

11.2 11.2 11.2

10.8 10.8 10.8

a) b)

10.4 10.4 10.4

10.0 10.0 10.0

:Ί

1

2.6 2.6 3.0

1.35 1.42 1.48

xlQ^mV

1

1.34 1.43 1.51

5.2 6.0 6.8

1.94 1.82 1.99 C

Di. ( c a l c ) ' -13^2-1 xlQ m s 7.8 9.0 10.2

+

Values a c c u r a t e to + 10% (water, L i ) and + 25% (PF0). -9 C a l c u l a t e d from r e f e r e n c e v a l u e s of water (D = 2.3 χ 10 . nus"? a t 296K) (8) and L i i n 2.0M L i C l . (D « 8.4 χ 10 m s at 296K) ( 9 ) . S u b s c r i p t s r e f e r t o d i f f u s i o n p a r a l l e l (DII ) or perpendicu l a r (ϋχ) t o l i p i d b i l a y e r . ' Q

1

c)

1.30

6.0 6.0 6.7

D(54.74°) - 1 2 2 -1 xlO m s P e r f l u o r o - 314.5 Octanoate 320 326

D /D

1Λ

5

xlO^mV Li

-10 2-1 xlO m s

C a l c u l a t e d assuming Dj_ = 0 a f t e r r e f . _7.


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t o ^l.Onm. Because o f the absence of hydrogen bonding t o neighboring molecules, water d i f f u s i o n w i t h i n the b i l a y e r might be expected to be more r a p i d than i n pure water r e s u l t i n g i n the observed r a p i d d i f f u s i o n . L i t h i u m Ion and P e r f l u o r o - o c t a n o a t e Ion D i f f u s i o n The slow l i t h i u m i o n d i f f u s i o n along the water l a y e r s compared to t h a t o f aqueous l i t h i u m c h l o r i d e i s probably due to the h i g h degree of counter-ion b i n d i n g t h a t i s thought to occur i n t h i s system (3). The hydrated l i t h i u m ions spend most o f the time a s s o c i a t e d w i t h s u r f a c t a n t head groups, perhaps occupying the spaces between head groups. T h e i r t r a n s l a t i o n a l d i f f u s i o n along the water l a y e r s i s then determined by t h a t o f the s u r f a c tant i o n s . D i f f u s i o n p e r p e n d i c u l a r to the l a y e r s i s due e i t h e r to the presence of pores o r cracks on the b i l a y e r s as d e s c r i b e d above. The low a n i s o t r o p y of l i t h i u m i o n d i f f u s i o n may be due to the s t r o n g a s s o c i a t i o n between head groups and counter-ions g i v i n g r i s e to u n u s u a l l y low values of D \\ together w i t h a l a r g e r than expected value o f D^ because o f the low v a l u e of the b i - l a y e r thickness. The values of DJJ l i s t e d i n the t a b l e f o r PFO d i f f u s i o n should be regarded as upper l i m i t s s i n c e they were c a l c u l a t e d assuming that D ^ was zero. In view of the low a n i s o t r o p y o f the water and L i d i f f u s i o n t h i s may not be v a l i d . The values l i s t e d are two orders of magnitude l e s s than values reported f o r potassium o l e a t e (7) and potassium l a u r a t e (12) i n l a m e l l a r phase under s i m i l a r c o n d i t i o n s . Since the molecular weight dependence of d i f f u s i o n w i t h i n the b i l a y e r i s expected to be r a t h e r s m a l l (7) the d i f f e r e n c e between the two s e t s of values may be due t o d i f f e r e n c e s i n counter-ion b i n d i n g between l i t h i u m and potassium i o n s . The stronger counter-ion b i n d i n g of l i t h i u m i o n s could reduce the t r a n s l a t i o n a l motion of the l i p i d . The D values f o r PFO i o n s are s i m i l a r to those reported f o r the z w i t t e r i o n i c l i p i d l e c i t h i n from probe experiments (13). F u r t h e r s p e c u l a t i o n on the o r i g i n of the d i f f e r e n c e s r e q u i r e s i n f o r m a t i o n on the dependence of D on s u r f a c e area and c o u n t e r - i o n . +

REFERENCES 1. K. Shinoda, M. Hato and T. Hayashi, J. Phys. Chem. 76, 909 (1972); N. Muller and H. Simsohn, Ibid, 75, 942 (1971); I. K. Lin, Ibid, 76, 2019 (1972); P. Mukerjee and K. J. Mysels, ACS Symposium "Colloidal Dispersions and Micellar Behavior", 239 (1975). 2. G. J. T. Tiddy, J.C.S. Faraday 1, 68, 608 (1972); G.J.T. Tiddy and B. A. Wheeler, J. Colloid Interface Sci. 47, 59 (1974).


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3. E. Everiss, G.J.T. Tiddy, and B.A. Wheeler, J.C.S. Faraday Trans. 1, 72, 1747 (1976). 4. G.J.T. Tiddy, J.B. Hayter, A.M. Hecht and J.W. White, Ber. Bunsenges. Phys. Chem., 78, 961 (1974); J.B. Hayter, A.M. Hecht, J.W. White and G.J.T.Tiddy, Faraday Disc. Chem. Soc., 57, 130 (1974). 5. A. Johansson and B. Lindman, Ch. 8 in "Liquid Crystals and Plastic Crystals", Vol. 2, G.W. Gray and P. A. Winsor, eds., Ellis Horwood Ltd., Chichester, England, 1974. 6. E.T. Samulski, B.A. Smith and C.G. Wade, Chem. Phys. Lett., 1973, 20, 167. 7. S.B.W. Roeder, E.E. Burnell, An-Li Kuo and C.G. Wade, J. Chem. Phys. 64, 1848 (1976). 8. (1970).

J.S. Murday and R.M. Cotts, J. Chem. Phys. 53, 4724

9. E.A. Bakulin and G.E. Zavodnaya, Zh.Fiz.Khim. 36, 2261 (1962). 10. (1965).

E.O. Stejskal and J.E. Tanner, J. Chem. Phys. 42, 288

11. J.E. Tanner and E.O. Stejskal, J. Chem. Phys. 49, 1768 (1968). 12.

R.T. Roberts, Nature 242, 348 (1972).

13. P. Devaux and H.M. McConnell, J. Amer. Chem. Soc. 94, 4475 (1972); E. Sackmann and H. Träuble, Ibid., 94, 4482, 4492, 4499 (1972).


Magnetic Resonance in Colloid and Interface Science

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