12 M a g n e t i c Reorientation a n d C o u n t e r r o t a t i o n in Poly(γ-Benzyl Glutamate)
Liquid
Crystals
ROBERT W. FILAS
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Department of Chemistry, Princeton University, Princeton, NJ 08540
Poly(γ-benzyl glutamate) (PBG) is a synthetic polypeptide which adopts the α-helical conformation in various organic sol vents. Its essentially rod-like shape is responsible for the formation of a liquid crystalline phase above a critical concen tration of polymer (1,2). The nature of this mesophase is usually cholesteric (2,3) due to the chirality of the PBG molecules, but particular solvent mixtures (4) or a racemic mixture of the D and L enantiomorphs (3,5) form a nematic phase. NMR studies have shown that in a magnetic field the PBG molecules tend to align parallel to the field in a nematic-like structure (6-9). If such a magnetically oriented sample is rotated by some angle, θ , the reorientation process can be described very accurately (10), but above a critical angle the reorientation mechanism becomes more complicated. The purpose of this paper is to report the detec tion of this critical angle by NMR, optical, and viscometric techniques in solutions of PBG in dichloromethane. o
Experimental Liquid crystalline solutions of PBDG were prepared using reagent grade dichloromethane and sealed in NMR tubes. Their concentrations were determined gravimetrically and are expressed in w/w percent. Each sample contained a 0.38 mm diameter stain less steel sphere used for viscosity measurements. The racemic mixture, abbreviated as (D+L)PBG, is the same sample used in a previous study (10), and is composed of equal masses of PBLG and PBDG having molecular weights 270 000 and 217 000, respectively. NMR spectra were recorded on a Varian HA-100 spectrometer in an "unlocked mode using an external oscillator and frequency counter to calibrate its sweep parameters. Samples were equili brated in the magnetic field without spinning at ambient tempera ture (ca. 32°C ) for nearly a day before each reorientation. The temperature was controlled with a precision of ±0.2° with a Varian temperature-control unit. The samples were rotated by accurately known amounts with the aid of small aluminum sleeves 11
0-8412-0419-5/78/47-074-157$05.00/0 © 1978 American Chemical Society
Blumstein; Mesomorphic Order in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
158
M E S O M O R P H I C
ORDER
I N
P O L Y M E R S
attached to the tube h o l d e r . Apparent v i s c o s i t i e s were determined using a f a l l i n g sphere method on samples that had been matured for more than a year. As i n the NMR experiments, the samples were m a g n e t i c a l l y o r i e n t e d with the f i e l d d i r e c t i o n p e r p e n d i c u l a r to the NMR tube a x i s . Crossed p o l a r i z e r s were mounted on the magnet f o r c o r r e l a t i o n of o p t i c a l and v i s c o m e t r i c d a t a . A f t e r a r o t a t i o n experiment was performed, the sample was removed from the magnetic f i e l d and placed i n a 25-0 ± 0.02°C constant temperature b a t h . The v e l o c i t y of the sphere f a l l i n g along the a x i s of the NMR tube, meas ured using a cathetometer and timer, was used to c a l c u l a t e the S t o k e s law apparent v i s c o s i t y . A Faxen c o r r e c t i o n ( l l ) of about 5fo was a p p l i e d to a l l d a t a .
Downloaded by CORNELL UNIV on October 13, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0074.ch012
1
Results and D i s c u s s i o n The equations of motion f o r a memory-dependent nematic l i q u i d undergoing r e o r i e n t a t i o n i n a magnetic f i e l d have r e c e n t l y been presented ( l u ) . The equations were d e r i v e d using the theory of micropolar continuum mechanics as introduced by E r i n g e n (12, 15)In the s p e c i a l case when the memory can be n e g l e c t e d , the result is 0(t)
= tan" (tane 1
e" ) A t
Q
(l)
where θ ( t ) i s the instantaneous o r i e n t a t i o n of the microelement, and θο i s the value of θ at t = 0. The parameter A i s d e f i n e d by A = X H / C , where X i s the anisotropy of the diamagnetic sus c e p t i b i l i t y , Η i s the magnetic f i e l d s t r e n g t h , and C i s the ap parent r o t a t i o n a l v i s c o s i t y c o e f f i c i e n t . A convenient method f o r o b t a i n i n g θ ( t ) data i n the present case i s to monitor the time dependence of the NMR s i g n a l of the s o l v e n t . The d i p o l a r coup l i n g of the proton p a i r on each C H C 1 molecule produces a doub l e t whose s e p a r a t i o n (ΔΗ) v a r i e s with the o r i e n t a t i o n of the surrounding PBG h e l i c e s . In terms of the e q u i l i b r i u m s e p a r a t i o n , ΔΗ .> the r e l è v e n t expression i s a
2
a
2
2
0
AH(t)
=
(
3
c o s 6 ( t ) - 1). 2
(2)
The v a l i d i t y of Equation 2 r e l i e s upon the assumption that the i n f l u e n c e of the a n i s o t r o p i c environment of the polymer molecules on the solvent remains constant during a r e o r i e n t a t i o n . It is t h e r e f o r e implied that the PBG h e l i c i e s r e t a i n t h e i r o r i g i n a l degree of p a r a l l e l i s m on a s c a l e which i s large compared to the d i s t a n c e a solvent molecule d i f f u s e s during i t s s p i n l i f e t i m e . Using the technique o u t l i n e d above, Equation 1 has been tested under a v a r i e t y of c o n d i t i o n s . The r e s u l t s i n d i c a t e that Equation 1 i s only capable of d e s c r i b i n g the r e o r i e n t a t i o n when θο i s l e s s than some c r i t i c a l a n g l e , 9 , which v a r i e s with the C
Blumstein; Mesomorphic Order in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
12.
FILAS
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Magnetic Reorientation and Counter rotation
sample and the c o n d i t i o n s of the experiment. For example, F i g u r e 1 d i s p l a y s θ ( t ) data for a racemic PBG sample and the corresponding t h e o r e t i c a l curves generated by Equation 1 using A = 0.0203 m i n " . The agreement between theory and experiment i s e x c e l l e n t f o r small values of θο ( s o l i d d o t s ) , but when θο = ^ 4 . 4 ° (open squares), the r e o r i e n t a t i o n appears to proceed more r a p i d l y than p r e d i c t e d by the theory. Even by i n c r e a s i n g A to 0.0237 m i n " , agreement with Equation 1 can only be obtained f o r about the f i r s t Ik- minutes. For s l i g h t l y l a r g e r values of θο (open t r i a n g l e s ) , the d e v i a t i o n i s much more pronounced and the data can only be approximated by Equation 1 f o r about k- minutes i f A i s chosen to be 0.0321 m i n " . In a d d i t i o n , i f s e v e r a l consecu t i v e r e o r i e n t a t i o n s are performed with θο j u s t above θ , the r a t e of r e o r i e n t a t i o n appears to increase i n each successive e x p e r i ment. T h i s apparent change i n the p h y s i c a l p r o p e r t i e s of the system, or " y i e l d " behavior, i s small very c l o s e to θ , but r a p i d l y becomes more s i g n i f i c a n t as θο i n c r e a s e s . When θο i s a few degrees above Q , the " y i e l d i n g " i s o f t e n q u i t e abrupt i n racemic PBG samples, as shown i n F i g u r e 1. For values of θο > 5 1 ° ; no part of the r e o r i e n t a t i o n curve could be f i t by Equation 1. The d e v i a t i o n from the p r e d i c t e d r e o r i e n t a t i o n curves de s c r i b e d above suggests that some fundamental change i n the r e o r i e n t a t i o n mechanism might be o c c u r r i n g . T h i s conjecture i s supported by the changes i n the appearance of the NMR spectra during " y i e l d i n g " . The p a i r of peaks begin to shorten and broad en, with shoulders or small a d d i t i o n a l peaks appearing between them, i n d i c a t i n g a d i s r u p t i o n of the o r i g i n a l degree of order of the PBG molecules. None of these changes i n the NMR l i n e shape occurs when Qq < Q . Even a f t e r s e v e r a l consecutive r e o r i e n t a t i o n s below θ , the same " A " value i s found to apply f o r each r e o r i e n t a t i o n and the only v a r i a t i o n i n peak height as the peak sep a r a t i o n changes i s due to magnetic s u s c e p t i b i l i t y e f f e c t s (l5 ) » The d i s r u p t i o n of the b a s i c s t r u c t u r e of the l i q u i d c r y s t a l , f o r any reason, can have serious i m p l i c a t i o n s concerning the use of Equations 1 and 2. For example, i f the "microelement" of the continuum theory i s composed of a c o l l e c t i o n of PBG molecules a c t i n g i n a cooperative f a s h i o n , then any change i n the PBG degree of order c o n t r a d i c t s the assumption of a constant m i c r o element, upon which the d e r i v a t i o n of Equation 1 i s based. The c o n d i t i o n s r e q u i s i t e f o r the use of Equation 2 are a l s o v i o l a t e d once d i s r u p t i o n begins to occur. The values of θ p l o t t e d i n F i g u r e 1 with • and Δ a r e , t h e r e f o r e , not to be taken l i t e r a l l y as a n g l e s , but r a t h e r as "apparent" a n g l e s . The reason f o r the existence of a c r i t i c a l angle and the d i s r u p t i o n that occurs when θο > θ can be explained by the f a c t that even at e q u i l i b r i u m with the f i e l d not a l l the PBG molecules are p e r f e c t l y a l i g n e d . Orwoll and Void (ik) have shown, f o r ex ample, that only about Qjfo of the polypeptide h e l i c i e s i n t h e i r sample (17-5% P B L G / C H o C l ; molecular weight 310 000; l h . l kG f i e l d ) were w i t h i n 20 of the f i e l d d i r e c t i o n . I f θο i s large 1
1
1
Downloaded by CORNELL UNIV on October 13, 2016 | http://pubs.acs.org Publication Date: June 1, 1978 | doi: 10.1021/bk-1978-0074.ch012
0
0
C
C
0
0
2
Blumstein; Mesomorphic Order in Polymers ACS Symposium Series; American Chemical Society: Washington, DC, 1978.
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M E S O M O R P H I C ORDER IN P O L Y M E R S
enough so that some PBG molecules are rotated beyond 90 to the f i e l d , then some f r a c t i o n of them w i l l r e o r i e n t i n the opposite d i r e c t i o n from the remainder. This process has been c a l l e d " c o u n t e r r o t a t i o n " and i s r e s p o n s i b l e f o r at l e a s t a p a r t i a l randomization of the PBG axes (lA ) . Figure 2 shows a sequence of spectra of a 27-2$ PBDG sample at various times a f t e r a 75° r o t a t i o n of the sample. In less than h a l f a minute the o r i g i n a l doublet (A) has s p l i t i n t o a quartet (B), the inner peaks ap proaching each other while the outer two are separating. In (c), the two inner peaks have merged into one, and i n (D) they have separated again, now moving a p a r t . As the r e o r i e n t a t i o n c o n t i n ues ( Ε - ! ) the peaks f i r s t broaden, then sharpen again, e v e n t u a l l y r e t u r n i n g to t h e i r o r i g i n a l shape and separation as i n ( A ) . These r e s u l t s are very s i m i l a r to those presented by Orwoll and Void and are good evidence for the existence of c o u n t e r r o t a t i n g regions. It i s a l s o p o s s i b l e to detect the onset of changes i n the p h y s i c a l p r o p e r t i e s of the system by other procedures. For exam p l e , the apparent v i s c o s i t y (T] ) of the l i q u i d c r y s t a l , as meas ured by the f a l l i n g sphere method, i s very s e n s i t i v e to any d i s r u p t i o n of the o r i e n t a t i o n of the PBG molecules. When θο < θ , ΤΙ i s found to remain constant at a l l times during the r e o r i e n t a t i o n . Above Q , however, T] f i r s t decreases, goes through a minimum, then increases back to i t s o r i g i n a l v a l u e . The maximum amount of c o u n t e r r o t a t i o n (and d i s r u p t i o n ) occurs when θο = 90°, and the change i n 7| as a f u n c t i o n of time a f t e r such a r e o r i e n t a t i o n i s shown i n Figure 3. Of course, the v i s c o s i t y of the l i q u i d c r y s t a l can only be sampled once during any given experiment, so each data point represents a separate sequence of o r i e n t a t i o n , r o t a t i o n , and measurement. In order to a c c u r a t e l y determine Q from v i s c o s i t y measure ments, i t i s d e s i r a b l e to amplify the small d i s r u p t i v e e f f e c t s that occur when θο
