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MACROSCOPIC FEATURES. b)
CholestericsPOLYPEPTIDE LIQUID CRYSTALS : DIAMAGNETIC ANISOTROPY, TWIST ELASTIC
CONSTANT AND ROTATIONAL VISCOSITYCOEFFICIENT
C. Guha Sridhar, W. Hines, E. Samulski
To cite this version:
C. Guha Sridhar, W. Hines, E. Samulski. MACROSCOPIC FEATURES. b) CholestericsPOLYPEP- TIDE LIQUID CRYSTALS : DIAMAGNETIC ANISOTROPY, TWIST ELASTIC CONSTANT AND ROTATIONAL VISCOSITYCOEFFICIENT. Journal de Physique Colloques, 1975, 36 (C1), pp.C1- 269-C1-272. �10.1051/jphyscol:1975145�. �jpa-00216224�
MACROSCOPIC FEA TURES. b ) Cholesterics
Classification Physics Abstracts
7.130
POLYPEPTIDE LIQUID CRYSTALS : DIAMAGNETIC ANISOTROPY, TWIST ELASTIC CONSTANT AND ROTATIONAL VISCOSITY COEFFICIENT(")
C. GUHA SRIDHAR (**), W. A. HINES and E. T. SAMULSKI (***) Departments of Physics and Chemistry and Institute of Materials Science
University of Connecticut, Storrs, Connecticut 06268, U. S. A.
Rksumk. - On observe, pour des cristaux liquides ntmatiques orient& de poly-y-benzyl-L- glutamate (PBLG) dans du dichloromethane, une anisotropie de la susceptibilite diamagnitique, Ax, Bgale A 6,8 i 0,7 x 10-9 emu/cm3. Pour un PBLG de rapport axial 150, on calcule une valeur de la constante de torsion 6lastique K22 = 582 x 10-8 dynes en mesurant le champ magnktique critique pour eliminer la torsion de la structure supramolCculaire cholesterique dans des cristaux liquides de PBLG. Le taux de reorientation de l'axe nkmatique de la structure d'un PBLG nkmatique aligne fournit une valeur de y 1 = 4,4 x 104 poise pour le coefficient de viscosite rotationnelle. On observe que K22 et y I dkpendent du rapport axial du polypeptide et de la composition du solvant.
Abstract. - The observed anisotropy of the diamagnetic susceptibility, AX, for oriented nematic liquid crystals of poly-y-benzyl-L-glutamate (PBLG) in dichloromethane is 6.8 &0.7 x 10-9 emu/cm3.
For a PBLG axial ratio of 150, a value of the twist elastic constant K22 = 582 x 10-8 dynes is calculated by measuring the critical magnetic field for untwisting the cholesteric supramolecular structure in the PBLG liquid crystal. The rate of reorientation of the nematic director of an aligned nematic PBLG structure yields a value for the rotational viscosity coefficient, y 1=4.4 x 104 poise.
K22 and y l appear to be sensitive to the polypeptide axial ratio and solvent composition.
1 . Introduction. - Synthetic polypeptides form cho- lesteric lyotropic liquid crystals in various helicogenic solvents. Specific solvent-polymer interactions are not responsible for this behavior. Liquid crystal formation is spontaneous when the rodlike, a-helical polypep- tides exceed a critical concentration in solution [I].
Experimental observations in reasonable agreement with theory [2], show that the critical polypeptide concentration depends primarily on the polymer axial ratio (i. e. polypeptide molecular weight). The asymmetry of the intermolecular forces between helices causes a small angular displacement of one rod relative to another. This generates a macroscopic helicoidal supramolecular structure analogous to the cholesteric structure exhibited by thermotropic liquid crystals consisting of asymmetric molecules.
A sufficiently strong magnetic [3a-c] (electric [ 3 d ] ) fields exerts a torque on the anisotropic diamagnetic (dielectric) rods, and untwists the cholesteric structure
(*) This investigation was supported in part by a NIH research grant (PHs Grant AM, 17497-01) from the National Institute of Arthritis, Metabolism, and Digestive Diseases and The University of Connecticut Research Foundation.
(**) Present Address : Guest Worker, NASA Ames Research Center, Moffet Field, California.
(***) Address correspondence to : E. T. Samulski, Institute of Materials Science, U-136, University of Connecticut, Storrs, Conn. 06268.
to form an aligned nematic structure. In this arran- gement, the rodlike molecules are more or less parallel to the nematic director which in turn, is parallel to the applied field. Herein we show that the magnetic field-induced cholesteric-nematic transition can be described satisfactorily by de Gennes' theory [4]. The twist elastic constant of the liquid crystal, Kz2, can be determined using measurements of the critical field strength, H,, for untwisting the cholesteric structure and the diamagnetic anisotropy, AX, of the aligned nematic. The twist or rotational viscosity coefficient, y,, can be calculated from the rate of reorientation of the nematic director after changing the direction of the applied field.
2. Experimental. - All of the magnetic measure- ments were made at room temperature in magnetic fields up to 20 kOe with a P. A. R. model 155 Vibrating Sample Magnetometer. (See ref. [ 5 ] for experimental details.) The spacing between the retardation lines was on the order of tens of microns. Therefore, for various magnetic field strengths, the pitch of the cholesteric structure (twice the retardation line spacing) could be measured by direct optical observation [5].
The synthetic polypeptides were supplied by Pilot Chemical Company (New England Nuclear). Poly- peptide solutions were matured for one or more weeks to insure complete solubilization of the polymer and
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1975145
C1-270 C. GUHA SRIDHAR, W. A. HINES AND E. T. SAMULSKI
homogeneity of the liquid crystal. In most cases, the have shown that de Gennes' theory applies equally development of the pattern of retardation lines charac- well to the lyotropic cholesteric polypeptide liquid teristicof the cholestericstructure occurred afterseveral crystal [7]. In figure 1, we have plotted PIPo versus
days. HIH, for the PBLG-dichloromethane liquid crystal,
3. Results and discussion. - 3.1 DIAMAGNETIC
ANISOTROPY. - Unless otherwise indicated, all of the experimental magnetic and optical results described in the remaining sections were obtained from a sample of liquid crystalline polypeptide solution consisting of poly-y-benzyl-L-glutamate (PBLG) and dichlorome- thane, 25.5 % (wt./vol. ; PBLG M. W. = 550,000).
After allowing the sample to mature for two weeks to insure homogeneity, the retardation lines develop and the liquid crystal supramolecular structure is cholesteric with the twist axis randomly oriented throughout the macroscopic sample. In a magnetic field, the cholesteric structure is untwisted and a macroscopically aligned nematic supramolecular structure is formed. During the field-induced cholesteric-nematic transition, a time dependent anisotropy in the observed magnetic moment, Ap(t), develops in the liquid crystal (see ref. [5]). By observing Ap(t) as a function of time, we can obtain a value for the diamagnetic anisotropy per mole of the aligned nematic polypeptide liquid crystal using Ap = Ap(@)/nH, where Ap(co) is the asymptotic value of Ap(t) for large t, H is the applied magnetic field and n is the number of moles of polypeptide residues. For the sample described above, we determi- ned a value of AX = 6.8 & 0.7 x emu/cm3. Similar measurements were made on a PBLG-dioxane (+ 2 %
trifluoroacetic acid) liquid crystal sample, 21.4 %
(wt./vol. ; PBLG M. W. = 310,000). For this liquid crystal AX = 6.5 f 0.7 x emu/cm3.
3.2 TWIST ELASTIC CONSTANT. - In 1968, de Gennes [4] derived a theoretical relationship between the pitch of a cholesteric structure, P, and the applied magnetic field, H. He predicts an increase in the pitch as. the applied field is increased with a logarithmic divergence of P when the field strength approaches a critical value, H,. This behavior has been verified for thermotropic liquid crystals [6]. Duke and DuPr6
H / ~ c
FIG. 1. - The observed pitch of the PBLG-dichloromethane cholestericstructure, P, after equilibrating the liquid crystal in a magnetic field H for 24 hours plotted in reduced units, PIP0 and H m . The solid curve is the theory of de Gennes [4] (PO =72f 2 p,
Hc = 20 kOe).
- .
where Po is the initial pitch in the absence-of a magne- tic field. The solid curve is the theoretical relationship for Po = 72 p and H, = 20 kOe. The observed values for H,, Po and AX yield the twist elastic constant, K,,, with the following relationship 141
H, = Z ~ ( K ~ ~ I A X ) ~ ' ~ / ~ Po . (1) For the PBLG-dichloromethane liquid crystal (PBLG M. W. = 550,000) eq. (1) gives
K,, = 582 x dynes [8].
Using our value for AX in eq. (I), Duke and DuPrC [7a]
calculate Kzz = 6.2 x dynes for the PBLG- dioxane crystal (PBLG M. W. = 310,000) [8].
Recent solvent studies have shown that, for the same PBLG molecular weight (310,000), K,,/Ax increases by six fold in changing solvents from dioxane to dichloromethane [7b]. Since AX has been shown to be essentially independent of these solvents, it is now clear that the values of K2, may show a pronounced solvent dependence. The observed differences in K,, for the two liquid crystals can also be explained in part by the difference in molecular weight of the PBLG. Recent calculations yield the elastic constants as a function of axial ratio for the hard-rod liquid crystal with a value for K,z/p2L4DkT z 0.02 191.
For the PBLG-dichloromethane and PBLG-dioxane liquid crystals, the PBLG axial ratio LID is 150 and 85 respectively ; the helix length is L = n x 1.5 A and helix diameter is D x 25 A. Hence, the differences in helix lengths for the two liquid crystals alone, according to the theory [9], account for an order magnitude change in K,,. These two factors alone (axial ratio and solvent) reconcile the differences in K,, for these systems.
3.3 ROTATIONAL VISCOSITY COEFFICIENT. - Obser- vation of the rate of reorientation of the nematic direc- tor in a magnetic field allows a determination of the rotational viscosity coefficient, y
,,
for the liquid crystal.After equilibrating the sample in a magnetic field the sample (orientation of the nematic director) was quickly rotated by 900 and the magnetic anisotropy, Ax(t), was observed as a function of time during which the nematic director realigned parallel to the field.
A,u(t) goes from an initial value of Ap(co) to an asymp- totic value of - Ap(co). The time dependence of the reorientation process can be described by
tan cp = (tan 9,) e-*I7 , (2) where cp is the angle between the nematic director and the magnetic field [lo]. cp varies from some initial value of cp, to a final value of 00 (nematic director parallel to the field). The characteristic relaxation time for this reorientation process, 2, can be directly related to yl by z = yl/(Ax) Hz. Hence, a plot of In (tan cp) versus t should provide a straight line with a slope of
POLYPEPTIDE LIQUID CRYSTAL VISCOELASTIC PROPERTIES C1-271
- 117. The time dependence of the reorientation of the nematic director (i. e. cp) can be determined from the measured values of Ap(t) using
Figure 2 shows a plot of In (tan cp) versus t for the reorientation of the nematic director of the PBLG- dichloromethane liquid crystal at four fields. In each case, the aligned nematic was equilibrated in a 20 kOe field before beginning the rotation experiment.
Although the rotation experiments were carried out at fields H c H,, the time scale for reforming the choles- teric structure as evident by the appearance of the retardation lines is quite long (several days) and contributions to Ap(t) from the twisting process could be ignored.
T l t i E (HOURS)
FIG. 2. - A plot of In (tan 9) versus t describing the reorienta- tion of the PBLG-dichloromethane nematic director after rotating the aligned nematic axis (z-axis) 90° to the applied magnetic field at t = 0. The characteristic reorientation times, z, were determined for four field strengths
.=
15kOe, =12kOe and.
=9kOe. ; 0 = 18 kOe,The linear sections of the data in figure 2 yield values of z = 4.6 f 1.0, 8.5
+
1.9, 15.8+
3.6 and20.0 If: 4.5 hours for field strengths H = 18, 15, 12 and 9 kOe, respectively. These values of z vary directly as H-2 with a constant of proportionality, y,/Ax = 1.78 x lo9 hours x Oe2. Using our value of AX (section 3.1) we obtain a value for the rotational viscosity coefficient y, = 4.4 x lo4 poise [8, 1 11. The rather high value of y, seems consistent with relative viscosity measurements in similar polypeptide liquid crystals (q -- lo4 poise) [12].
y, was markedly reduced upon addition of small amounts of trifluoroacetic (TFA) acid to the solution ; z decreased from hours to minutes. Similar changes in these liquid crystals upon addition of trifluoroacetic acid were reported in NMR studies of the solvent order parameter [13]. At low acid concentration (1-2 %) in the liquid crystal, the acid more than likely behaves in the same manner as suggested in dilute polypeptide solutions. That is, the acid breaks up end-to-end and lateral aggregation of helices [14].
This type of aggregation among the close-packed rods in the liquid crystal would lead to a 3-dimen-
sional network. Disruption of this network by acid would in turn markedly increase the fluidity of the liquid crystal and be reflected as a substantial decrease in y,. The rather large value of y , in these systems compared to thermotropic liquid crystals also appears reasonable. The response times of the latter in magne- tic fields of this magnitude is of the order of milli- seconds [15] in contrast with times ranging to several hours for the polypeptide liquid crystal. Magnetic resonance techniques provide a method for observing such reorientation processes in therrnotropic liquid crystals [16, 171.
The apparent intercept in figure 2 leads to a value of cp, w 590. Although the nematic director is rotated to make an angle of 90° with H at t = 0, this value of cp, seems to indicate that the average starting angle of the rods is less than 900, or, that the rods on the average make an angle 4 2 - cpo with the nematic director. This average angle, 310, leads to an order parameter S 2 0.6. Earlier reports focusing attention on the solvent order parameter, indicated that about 15 % of the PBLG helices align with their long axis at angles greater than
+
200 to the nematic director [18].4. Concluding remarks. - Lyotropic polypeptide liquid crystals exhibit static and dynamic properties which are comparable to those characteristic of ther- motropic cholesteric liquid crystals. The diamagnetic anisotropy, the twist elastic constant and the rota- tional viscosity coefficient are amenable to straight forward determination by exploiting the unusually long times required for these liquid crystals to establish equilibrium structures in external fields. The extreme differences in the hydrodynamic shape of the consti- tuent molecules in the polypeptide liquid crystal (LID z 100) as compared to that of thermotropic systems (LID ZY 2-3) must be responsible for the striking differences in the response times for these two classes of liquid crystals. This shape factor over- rides the disparity in the intrinsic anisotropy of the constituent molecules ; e. g. A ~ = n ( 7 x emu/mole (n x 1,000) for PBLG, whereas AX = 57 x emu1 mole for PAA [19].
Our preliminary findings suggest that K2, and y, are strongly dependent on the polypeptide axial ratio and the solvent composition. A systematic study of the dependence of these parameters on molecular weight (axial ratio), solvent composition, amount of TFA added and polypeptide concentration is currently in progress and should provide a method for evaluating theoretical models of the liquid crystalline state [20].
Moreover, a thorough understanding of the response of this ideal system of rods and balls to external stimuli may suggest new phenomenological models for dynamics in thermotropic liquid crystals.
5. Acknowledgments. - We gratefully acknow- ledge stimulating discussions on the twist elastic constant with Dr. D. B. DuPrC and rotational viscosity coefficients with Dr. J. W. Doane.
C1-272 C. GUHA SRIDHAR. W. A. HINES AND E. T. SAMULSKI
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