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Kerr effect in solutions of cellulose carbanilate in polar solvents
Eur. Po(rm. J. Vol. 26. No. 10, pp. 1103-1107. 1990 Printed in Great Britain
0014-3057/90 $3.00 + 0.00 Pergamon Press plc
KERR EFFECT IN SOLUTIONS OF CELLULOSE CARBANILATE IN POLAR SOLVENTS V. N. TSVETKOV, A. V. LEZOV, N. V. TSVETKOV and L. N. ANDREEVA Institute of Macromolecular Compounds of the Academy of Sciences of the U.S.S.R., Bolshoi Prospekt 3I, Leningrad 199004, U.S.S.R.
(Received 23 January 1990) Abstract--Electric birefringence has been investigated by using rectangular-pulse and sinusoidal-pulse fields in four low molecular weight liquids with different molecular polarities and also in solutions of cellulose carbanilate (CC) in these liquids. The parameters of equilibrium and kinetic flexibility of molecules of this polymer in various solvents were determined from the data on the dispersion of the Kerr effect in sinusoidal-pulse fields in solutions of CC. The data on equilibrium electro-optical and dynamo-optical properties of solutions of CC led to the conclusion that orientational correlation exists between the dipolar molecules of the solvent and the polar units of the polymer chain.
INTRODUCTION
1 shows the dependence of FBAn on shear stress Az - g ( r / - r/0) in flow (where g is the shear rate and ~/and r/0 are the viscosities of the solution and the solvent, respectively). The values of the shear optical coefficient An/Az obtained from the slopes of straight lines in Fig. 1 are given in Table I. The viscometric data for the same solution are shown in Fig. 2 and Table 1 (intrinsic viscosities [r/I).
It is known that an effective method for studying the kinetic, conformational and electro-optical properties of rigid-chain polymer molecules in solution is electric birefringence (EB, the Kerr effect) [1]. This method has been applied to various esters and ethers, in particular to samples of cellulose carbanilate (CC) by using a non-polar solvent, dioxane, in which CC is well soluble and forms molecularly disperse solutions [2]. However, most rigid-chain polymers (including cellulose esters and ethers) are soluble only in strongly polar solvents. In these solvents, EB investigations became possible only recently after special instrumentation had been developed [3, 4]. Therefore, it seems important to carry out comparative investigation of EB in solutions of the same polymer in non-polar and polar solvents in order to study the effect of strong intermolecular interactions in a polar medium on the conformational, dynamic and electrooptical properties of dissolved polymer molecules.
RESULTS AND DISCUSSION
SAMPLES AND EXPERIMENTAL PROCEDURES The present investigations were carried out with a CC sample having molecular weight 4 x l05 (determined from sedimentation and diffusion [5]), with that of the monomer unit being 480 (degree of substitution 2.7). Apart from the non-polar dioxane, three polar liquids were used as solvents. They differ in dipole moment /~ [6] of the molecule and dielectric permittivity E [7] which (as well as density p, viscosity r/0 and refractive index n) are given in Table 1. In all these solvents, the polymer forms molecular solutions and does not undergo noticeable degradation. The investigations of EB were carried out by a procedure described previously [3, 4] in a cell with electrode length of 8cm and the gap between them of 0.8 mm at 20~C in rectangular-pulse and sinusoidal-pulse fields in the range of radio-frequencies from 5 x 102 to 1 x 1 0 6 Hz. m helium neon laser (2 = 632.8 nm) served as a light source. For characterization of the optical anisotropy of the polymer, flow birefringence (FB) in solutions was measured by using a standard photoelectric procedure, laser radiation and modulation of ellipticity of the polarized light [1]. A dynamo-optimeter with a gap of 0.25 mm was used. Figure
EB of CC solutions in all solvents (as for all solvents) is proportional to the square of the field strength E 2 (Kerr law). This point is illustrated in Fig. 3 which shows as an example the dependence of An on E 2 (in a pulse field of constant direction) for CC solutions of various concentrations c in ethyl acetate and for pure ethyl acetate, Since the EB of the solvent is positive and that introduced by the dissolved polymer is negative, with increasing concentration the EB of the solution changes sign. The slope of the straight line corresponding to a pure solvent determines its Kerr constant K0 = Ano/E 2. The slope of the straight line obtained for CC solution of concentration c with the subtraction of K0 makes it possible to determine the specific Kerr constant K~ = (An - Ano)/cE 2 of the polymer at a concentration c. The values of specific constants Kc (on the logarithmic scale) as functions of the concentration of CC solutions in four solvents are shown in Fig. 4. The Kerr constants of CC were determined from the data in Fig. 4: K - - l i m c ~ 0 K¢ in the solvents used. The values of K and those of K0 (for the solvents) are listed in Table 1. Figure 5 illustrates the results of EB measurements in CC solutions in sinusoidal-pulse fields. This figure shows the dependence of FB An,. on the square of effective strength E 2 of the applied field in CC solution (at a concentration c = 0.13 x 10 -2 g. cm-3) in dimethylacetamide (DMA). Each of the straight lines (Kerr law) was obtained at a certain frequency v of the sinusoidal field. With increasing frequency, the slopes of the straight lines increase, showing a decrease in the negative contribution of the dissolved
1103
1104
V.N.
TSVE'rKOV et al.
Table I. Electro-optical characteristics of the solvents---dioxane (DO), ethyl acetate (EA), cyclohexanone (CH) and D M A - - a n d of CC solutions in these solvents Solvents p ( g ' cm -3)
rt0 x 102 (g. c m - i . sec-')
('~2-- ~I)L
('~2 -- "~I)LS
E
#(D)*
K0 X 1012 [cm2(200 v) -~]
('~2 --'~l)On
rt
(1025¢m 3)
(102s cm 3)
(1025em 3)
1.03 0.90 0.94 0.94
1.26 0.44 2.2 0.96
1.42 1.37 1.45 1.44
2.3 6.4 16 40
0 1.8 2.8 3.8
0.4 10 81 330
15 11.6 30 50
15 4.2 3.2 1.0
12.6 + 3 27~" 27.6 _ 0.4 34 + 12
S
Aa x 1025 (cm 3)
F
~ . (D)*
Z cos #
50 38 33 32
-40 -32 - 38 -40
0.67 0.73 1.17 1.06
0.95 1.4 2.8 5.6
0 0.25 0.66 1.22
DO EA CH DMA CC solutions
An - - x 10 m
[q] x 10 2 (g- i . cm 3)
Solvent
Ar (g- i . c m . sec 2)
K x 109 ~" x 106 [g--n. cm 5 . (300 v)-2] (sec)
DO 4.0 -154 EA 3.1 -90 CH 2.7 - 96 DMA 2.6 - 100 *lD(Debye) = 10-is gn,2. cm5:2, sec- i. t E r r o r unknown.
-7 -10 - 45 -200
polymer to the observed positive EB of the solution. At a frequency l0 5 Hz (straight line 6), the observed An,. of the solution virtually coincides with An0 of pure DMA. It is possible to calculate the specific Kerr constant K~ of the dissolved polymer for each frequency from the difference in the slopes of two straight lines (Fig. 5) one of which was obtained for the solution (at a concentration c) at a frequency v and the other line corresponds to pure solvent: K,. = (An,. - Ano)/cE 2. The results thus obtained for CC in all the solvents used are shown in Fig. 6 in the form of dispersion curves of the dependence K~/Kv~ o on log v. The experimental points obtained at different concentrations (I-V) do not exhibit a monotonic concentration dependence of dispersion, so justify discussion of experimental data in terms of the theory of extremely dilute solutions. All the curves in Fig. 6 decrease virtually to zero with increasing v, showing that the only mechanism for the observed EB is the dipolar orientation of CC molecules related mainly to their large-scale motion, i.e. the rotation as a whole in a solvent medium. The
lo[
,/
Z
60 15 40 18
dispersion curves obtained here are slightly wider than the corresponding Debye curves (broken line for curve I), which shows that distribution of relaxation time exists in the investigated EB. Each curve may be characterized by the "average" relaxation time z calculated from its half-height according to the equation z = l/2nv m where vm is the frequency at which K~ = Kwo/2. The values of T are given in Table 1. Relaxation times obtained in polar solvents are much lower than for CC solution in dioxane. This fact indicates that the size of the molecular coil in a polar solvent is smaller (and hence the equilibrium chain flexibility is higher) than in a non-polar solvent. A similar conclusion may be drawn from viscometric and dynamo-optical data listed in Table 1. The quantitative parameter of equilibrium chain rigidity (the number S of the monomer units in the Kuhn segment) for CC in dioxane is 50 [2, 5]. The values of S in other solvents may be estimated from the values of [r/l, comparing them with the value of [q] in dioxane, and proceeding from the fact that for a polymer chain with a weak hydrodynamic interaction [q] ~ S/ln S [see Ref. [1] equation (2.124)]. The values of S thus estimated are given in Table 1. They decrease with increase of solvent polarity. Comparing the S and An/A~ values [see Ref. [1] equation (5.60)], it is possible to estimate the values of optical anisotropy Aa of the monomer unit of the CC chain in the solvents (see Table 1). The values of 6~
v~ 5 I
¢
~
T
o..~/ 270 @
&-I 0-2
o
O-3 4''4
04 N
IL
Fig. 1. Value of An vs shear rate A~ in flow for CC solutions in various solvents. I, in dioxan:, range of concentration c = ( 0 . 0 9 ~ . 1 9 ) x 10-2g,cm-3; 2, in ethyl acetate, c = (0.08-0.19) x 10-2g.cm-3; 3, in c y c l o h e x a n o n e , c = ( 0 . 0 5 - 0 . 1 2 ) x 1 0 - - ' g . c m ~; 4, in D M A , c = ( 0 . 0 4 - 0 . 1 3 ) x 10 - z g . c m - 3 .
~ o'"
:
°
/
-'-----J~ Q_........_..-- o
T_. 4 o
2
.+_
----
o
c" 10 a g. cm "s Fig. 2. D e p e n d e n c e o f % / c = - ( q - qo)/qoc o n c o n c e n t r a t i o n c for C C s o l u t i o n s . Solvents: 1, d i o x a n e ; 2, ethyl acetate; 3, c y c l o h e x a n o n e ; 4, D M A .
Kerr effect in CC solutions in polar solvents
o/O/°/°'2.~.a
1o ~] | I "S
1105
o/ o/I- . /
o L~='-- ° ~
,/ _---
5
".~
-s i
47
o-g
°
['~,
~
6
10
E2 10"z(3c-~m)2 °~,
\.
O
.
.
2,5
-I0
"~'~*
Fig. 3. Dependence of EB An on E 2 of rectangular-pulse field for CC solutions in ethyl acetate, c. 102g . cm -3= 0.199 (l); 0.084 (2); 0.05 (3); pure solvent (4). Aa in all solvents except ethyl acetate are in practice the same, meaning that the optical properties of the monomer unit CC remain invariable when the polarity of solvent is changed. The value of Aa in ethyl acetate is somewhat less than could be explained by smaller value of n and so it is more influenced by optical microform effect [1] in this solvent. Comparing the values of [q] and An~AT with those of T, one should bear in mind that the former two values may characterize only the equilibrium chain rigidity, whereas z in principle also depends on its kinetic flexibility. The quantitative relationship between z and [~/] is known to be given by the equation (!)
z = M[q]rlo/2FRT
where F is the numerical coefficient the value of which depends on the hydrodynamic model used in the theory for describing the dynamic properties of the macromolecule in solution. Thus, for kinetically rigid macromolecules, the theoretical value of F ranges from 0.13 (rigid rod) to 0.42 (compact globule) [1]. The values of F calculated from equation (1) using experimental data on T, [q] and r/0 for the investigated polymer are given in Table !. For the polymer in all solvents, the values of F exceed the maximum theoretical value for kinetically rigid particles. This result may be interpreted as manifestation of some kinetic flexibility of the polymer chain the motion of which in a sinusoidal electric field is not just its rotation as a whole but also includes local re-orientations of its
.
.'.5,0
300V 2 E 2 (.-;-~---)
Fig. 5. The dependence of EB An,.on the square of effective strength E 2 of sinusoidal-pulse fields for CC solution in DMA (c = 0.13 x 10-2 g. cm-3). Different lines correspond to different field frequencies: v kHz = 0 (1); 3,2 (2); 10 (3); 30 (4); 50 (5); I00 (6). polar elements according to the higher modes in the Zimm model [2, 8]. The same process may also explain (at least partially) the width of dispersion curves in Fig. 6. The data in Table l show that the coefficient F is particularly high for strongly polar solvents. This fact implies that not only the equilibrium but also the kinetic flexibility of the CC polymer chain increases when a non-polar solvent is replaced by a polar solvent. A decrease in rigidity (both equilibrium and kinetic) of CC molecules in polar solvents shows that an important role in the mechanism responsible for this rigidity is played by the interaction between side groups, i.e. the substituents in neighbouring glucose rings. This interaction ensures a high degree of hindrance to intramolecular rotations in the chains of cellulose esters and ethers [9]. In fact it is the bonds (Van der Waals and hydrogen bonds) formed as a result of interactions between the side groups should be weakened and subjected to rupture by the influence of the molecules of a strong solvent, capable of forming intermolecular hydrogen bonds. This process is similar to the wellknown phenomenon of despiralization of polypeptide molecules in strong solvents.
-b 4
+
÷
\\ \o
1000 o 0
0
3 o - - o
eo i
100
~
•~
.....
/%
2
• &
A
• 1
3
4
5
6
Log v c • I 0 a g"
cm
-a
Fig. 4. Specific Kerr constant Kc vs concentration c for CC solutions, l, dioxane; 2, ethyl acetate; 3, cyclohexanone; 4, DMA.
Fig. 6. Dependence of relative Kerr constants K , / K ~ o on frequency v of sinusoidal-pulse field in CC solutions. 1, dioxane; 2, ethyl acetate; 3, cyclohexanone; 4, DMA. Concentrations c. 102g.cm-3=0.19 (1); 0.13 (II) 0.10 (liD; 0.08 (IV); 0.05 (V).
1106
V.N. TSVETKOVet al.
Hence, the study of the kientics of the Kerr effect in CC solution shows that the electro-dynamic properties of its molecules in solvents of various strengths and polarities, reasonably correlating with the data of other methods, leads to information on equilibrium and kinetic chain rigidity in these solvents. It should be noted in discussing the equilibrium values of K0 and K listed in Table 1 that at present there is no universal quantitative theory of EB in polar liquids, not only for polymer solutions but also for pure solvents. The main difficulty of this theory is related to the necessity of taking into account intramolecular orientational interaction in the liquid, which formally may sometimes be reduced to finding suitable "internal field" factors. If one tries (as in Ref. [11]) to introduce the internal field model developed by Onsager for the description of dielectric properties of polar liquids into the EB theory of Langevin-Born [12], then for a low molecular weight liquid (solvent), with axial symmetry of optical polarizability of molecules, the Kerr constant K0 is given by:
r0=
(PQ)22nNAp(n2 + 2)2(71 - 72) 135nkTM [ /tz 3C°S20--1] x 71--3'2-t kT" 2
K = (pQ)2 2ttNg(n2 + 2)2S/t211(~l - ~2) ! 35n (kT)2Mo (2)
where 71 and 72 are the optical (and dielectric) polarizabilities of the molecule in the direction of its axis and normal to it, respectively, 0 is the angle formed by the dipole of the molecule /t and the axis 7~; NA, k, T have their usual meanings and PQ is the factor of the internal field according to Onzager equal to PQ = E(n 2 + 2)/(2E + n2).
scattering dipolarization. Although the averaged data of the light-scattering method have been obtained with considerable error, it can be seen that they are in incomparably better agreement with the values of (72-71)on than with those of (72--71)L. The latter values are absurdly low especially the higher is the solvent polarity. Reasonable agreement between (72 - 71)o, and (72 - 71)LSjustifies the use of equation (3) in the EB theory in polar liquids, whereas the comparison of (72- 71)L and (72- 7J)Ls shows that the application of Lorentz factor is impossible in this case. It seems evident that this conclusion is valid as much for dilute polymer solutions in low molecular weight polar solvents. These results on the kinetics of the Kerr effect in CC solutions show that the main mechanism responsible for the observed EB is the large-scale orientation of polar CC molecules in the electric field. In accordance with this, for the solution of a high molecular weight polymer (Gaussian range) according to the EB theory of rigid worm-like chains [1], the Kerr constant is given by
(3)
For a non-polar medium (E =n2), equation (3) becomes (E +2)/3, the Lorentz factor [12] usually applied to dilute solutions of polar molecules in non-polar solvents. For the molecules of all four solvents investigated here, the structure with an axial symmetry of polarizability (71) normal to the "plane" of the molecule may be assumed (for dioxane and cyclohexanone this is the "plane" of the cyclohexane ring whereas for ethyl acetate and DMA they are the planes of the ester and the amide groups, respectively). In this case for three polar solvents, the molecular dipole/t lies in the plane of the molecule in a direction close to that of the C~------Obond (axis 2) and, correspondingly, in equation (2) we have 0 = n/2. The positive sign of K for these solvents implies that for them (just as for dioxane) 72 > 7J. Noting these considerations, equation (2) was used for calculation of the anisotropy (72-71) of molecules of the investigated solvents from the experimental values of K0 and the known values of n, p, E, /t and M. These values of (72 - 7~) are given in Table I with the symbols (~2- 71)on and (72--TI)L, which mean that they are calculated by application of Onsager's and Lorentz' factors, respectively. The last column of Table l gives the values of (75 - 71)Ls, the anisotropy of the same molecules according to the literature data [13] obtained by the method of light-
(4)
where (~1- ct2) is optical anisotropy of the Kuhn segment and #011is the longitudinal (along the chain) component of the dipole moment of the monomer unit of the polymer. Comparing equation (4) with a known Kuhn expression for the shear optical coefficient An/Az for the Gaussian chains [see in Ref. [1] equation (5.60)], one obtains the equation S/t2ji/Mo = 6kTK/(pQ)2NA(An/Az)
(5)
making it possible to determine the value of S/t021r/Mo from the experimental values of K and An/Az. For CC in dioxane, the value of S/t ~i~/Mo calculated by using equations (5) and (3) is 9.4 × 10-38cm4 (300 v)~, in good agreement with its value 9 x l0 -38 cm4(300 v)2, obtained from direct measurements of dielectric properties (dipole moments) of CC solutions in dioxane in the Gaussian range [14]. Using the values S = 50 [2, 5], M 0 =480 and SP~lt/M = 9.4x 10-38 cm4(300 v)2 for the investigated CC sample in dioxane, we find/t0Ji = 0.95D, which is close to the values of/t001 for some other cellulose ethers and esters in a non-polar solvent and is in reasonable agreement with the molecular structure of the polyglucoside chain [15]. The values of S given in Table 1 are used for the calculation of/t011 from equations (5) and (3) and the experimental values of K and An/At for CC in polar solvents. The values of/t01; obtained for CC in polar solvents (Table 1) greatly exceed that in dioxane, and this difference increases with the polarity of the solvent. These high values of P0rl cannot be explained by the dipolar structure of the chain alone and must be considered as "effective" values indicating the existence of orientational correlation (association) between the polar molecules of the solvent and the dipolar bonds of the chain. The manifestation of this association has already been detected in the investigation of EB for aromatic polyamides in polar solvents [16]. In order to obtain an idea of the scale of this
Kerr effect in CC solutions in polar solvents correlation, one can use, for instance, an equation of the type #0!l = (/~01)D + Z~, COS fl (6) where (/~0~)o and hi! are the values of the longitudinal component of the m o n o m e r dipole obtained for CC in dioxane and a polar solvent, respectively, # is the dipole moment of the solvent molecule, Z is the number of the solvent molecules associated with a m o n o m e r unit of the polymer and fl is the angle formed by the longitudinal component of the m o n o m e r dipole of the polymer and the dipole of the solvent molecule in the associate. The values of the parameter Z cos/3, characterizing the degree of orientational correlation in solution calculated from equation (6), are listed in Table 1. They increase with the polarity of the solvent. However, it can be seen that the degree of orientational order in the associate is not high. Thus, if it is assumed that Z = 6, then even for the most polar D M A , it is found that cos fl = 0.2, whereas for other solvents it is even lower. However, this degree of order in the associate is sufficient for the generation of a large effective macromolecular dipole and is related to high EB in the polymer solution. REFERENCES
1, V. N. Tsvetkov. Rigid-Chain Polymers, Consultants Bureau. Plenum, New York (1989).
1107
2. N. V. Pogodina, K. S. Pojivilko, H. Dautzenberg, K. J. Linow, B. Philipp, E. I. Rjumtsev and V. N. Tsvetkov. Vpsokomolek. Soedin B, 19, 851 (1976). 3. V. N. Tsvetkov, I. P. Kolomiets, A. V. Lesov and A. S. Stepchenkov. V gsokomolek. Soedin A, 25, 1327 (1983). 4. A. V. Lesov and N. V. Tsvetkov. Vpsokomolek. Soedin A, 32, 200 (1990). 5. L. N. Andreeva, E. U. Urinov, P. N. Lavrenko, K. J. Linov, H. Dautzenberg and B. Philipp. Faserforsch. Text Tech. 28, 117 (1977). 6. O. A. Osipov, V. I. Minkin and A. D. Garnovski. Reference Book on Dipole Moments. High School, Moscow (1971). 7. Ya. Yu. Ahadov. Dielectrical Property of Liquids'. Standarts, Moscow (t972). 8. B. Zimm. J. chem. Phys. 24, 269 (1956). 9. V. N. Tsvetkov. Advances in Chemistry (Russ) 38, 1674 (1969). 10. J. Onsager. d. Am. chem. Soc. 5g, 1486 (1936). 11. V. N. Tsvetkov. Kolloid. J. (Russ) 33, 154 (1971). 12. H. A. Stuart. Die Physik d. Hochpolymeren. Springer, Berlin (1950). 13. A. N Vereschagin. Characteristics of Anisotropy qf Molecular Polarisability. Nauka, Moscow (1982). 14. E. I. Rjumtsev, L. N. Andreeva, F. M. Aliev, L. H. Kutsenko and V. N. Tsvetkov. V~sokomolek. Soedin A, 17, 1368 (1975). 15. V. N. Tsvetkov, E. I. Rjumtsev, I. N. Shtennikova, T. V. Peker and N. V. Tsvetkova. Dokl. (Proc.) Acad. Sci. U.S.S.R. 207, 1173 (1972). 16. V. N. Tsvetkov, A. V. Lesov, N. V. Tsvetkov and L. N. Andreeva. Fur. Polym. J. 26, 575 (1990).
0014-3057/90 $3.00 + 0.00 Pergamon Press plc
KERR EFFECT IN SOLUTIONS OF CELLULOSE CARBANILATE IN POLAR SOLVENTS V. N. TSVETKOV, A. V. LEZOV, N. V. TSVETKOV and L. N. ANDREEVA Institute of Macromolecular Compounds of the Academy of Sciences of the U.S.S.R., Bolshoi Prospekt 3I, Leningrad 199004, U.S.S.R.
(Received 23 January 1990) Abstract--Electric birefringence has been investigated by using rectangular-pulse and sinusoidal-pulse fields in four low molecular weight liquids with different molecular polarities and also in solutions of cellulose carbanilate (CC) in these liquids. The parameters of equilibrium and kinetic flexibility of molecules of this polymer in various solvents were determined from the data on the dispersion of the Kerr effect in sinusoidal-pulse fields in solutions of CC. The data on equilibrium electro-optical and dynamo-optical properties of solutions of CC led to the conclusion that orientational correlation exists between the dipolar molecules of the solvent and the polar units of the polymer chain.
INTRODUCTION
1 shows the dependence of FBAn on shear stress Az - g ( r / - r/0) in flow (where g is the shear rate and ~/and r/0 are the viscosities of the solution and the solvent, respectively). The values of the shear optical coefficient An/Az obtained from the slopes of straight lines in Fig. 1 are given in Table I. The viscometric data for the same solution are shown in Fig. 2 and Table 1 (intrinsic viscosities [r/I).
It is known that an effective method for studying the kinetic, conformational and electro-optical properties of rigid-chain polymer molecules in solution is electric birefringence (EB, the Kerr effect) [1]. This method has been applied to various esters and ethers, in particular to samples of cellulose carbanilate (CC) by using a non-polar solvent, dioxane, in which CC is well soluble and forms molecularly disperse solutions [2]. However, most rigid-chain polymers (including cellulose esters and ethers) are soluble only in strongly polar solvents. In these solvents, EB investigations became possible only recently after special instrumentation had been developed [3, 4]. Therefore, it seems important to carry out comparative investigation of EB in solutions of the same polymer in non-polar and polar solvents in order to study the effect of strong intermolecular interactions in a polar medium on the conformational, dynamic and electrooptical properties of dissolved polymer molecules.
RESULTS AND DISCUSSION
SAMPLES AND EXPERIMENTAL PROCEDURES The present investigations were carried out with a CC sample having molecular weight 4 x l05 (determined from sedimentation and diffusion [5]), with that of the monomer unit being 480 (degree of substitution 2.7). Apart from the non-polar dioxane, three polar liquids were used as solvents. They differ in dipole moment /~ [6] of the molecule and dielectric permittivity E [7] which (as well as density p, viscosity r/0 and refractive index n) are given in Table 1. In all these solvents, the polymer forms molecular solutions and does not undergo noticeable degradation. The investigations of EB were carried out by a procedure described previously [3, 4] in a cell with electrode length of 8cm and the gap between them of 0.8 mm at 20~C in rectangular-pulse and sinusoidal-pulse fields in the range of radio-frequencies from 5 x 102 to 1 x 1 0 6 Hz. m helium neon laser (2 = 632.8 nm) served as a light source. For characterization of the optical anisotropy of the polymer, flow birefringence (FB) in solutions was measured by using a standard photoelectric procedure, laser radiation and modulation of ellipticity of the polarized light [1]. A dynamo-optimeter with a gap of 0.25 mm was used. Figure
EB of CC solutions in all solvents (as for all solvents) is proportional to the square of the field strength E 2 (Kerr law). This point is illustrated in Fig. 3 which shows as an example the dependence of An on E 2 (in a pulse field of constant direction) for CC solutions of various concentrations c in ethyl acetate and for pure ethyl acetate, Since the EB of the solvent is positive and that introduced by the dissolved polymer is negative, with increasing concentration the EB of the solution changes sign. The slope of the straight line corresponding to a pure solvent determines its Kerr constant K0 = Ano/E 2. The slope of the straight line obtained for CC solution of concentration c with the subtraction of K0 makes it possible to determine the specific Kerr constant K~ = (An - Ano)/cE 2 of the polymer at a concentration c. The values of specific constants Kc (on the logarithmic scale) as functions of the concentration of CC solutions in four solvents are shown in Fig. 4. The Kerr constants of CC were determined from the data in Fig. 4: K - - l i m c ~ 0 K¢ in the solvents used. The values of K and those of K0 (for the solvents) are listed in Table 1. Figure 5 illustrates the results of EB measurements in CC solutions in sinusoidal-pulse fields. This figure shows the dependence of FB An,. on the square of effective strength E 2 of the applied field in CC solution (at a concentration c = 0.13 x 10 -2 g. cm-3) in dimethylacetamide (DMA). Each of the straight lines (Kerr law) was obtained at a certain frequency v of the sinusoidal field. With increasing frequency, the slopes of the straight lines increase, showing a decrease in the negative contribution of the dissolved
1103
1104
V.N.
TSVE'rKOV et al.
Table I. Electro-optical characteristics of the solvents---dioxane (DO), ethyl acetate (EA), cyclohexanone (CH) and D M A - - a n d of CC solutions in these solvents Solvents p ( g ' cm -3)
rt0 x 102 (g. c m - i . sec-')
('~2-- ~I)L
('~2 -- "~I)LS
E
#(D)*
K0 X 1012 [cm2(200 v) -~]
('~2 --'~l)On
rt
(1025¢m 3)
(102s cm 3)
(1025em 3)
1.03 0.90 0.94 0.94
1.26 0.44 2.2 0.96
1.42 1.37 1.45 1.44
2.3 6.4 16 40
0 1.8 2.8 3.8
0.4 10 81 330
15 11.6 30 50
15 4.2 3.2 1.0
12.6 + 3 27~" 27.6 _ 0.4 34 + 12
S
Aa x 1025 (cm 3)
F
~ . (D)*
Z cos #
50 38 33 32
-40 -32 - 38 -40
0.67 0.73 1.17 1.06
0.95 1.4 2.8 5.6
0 0.25 0.66 1.22
DO EA CH DMA CC solutions
An - - x 10 m
[q] x 10 2 (g- i . cm 3)
Solvent
Ar (g- i . c m . sec 2)
K x 109 ~" x 106 [g--n. cm 5 . (300 v)-2] (sec)
DO 4.0 -154 EA 3.1 -90 CH 2.7 - 96 DMA 2.6 - 100 *lD(Debye) = 10-is gn,2. cm5:2, sec- i. t E r r o r unknown.
-7 -10 - 45 -200
polymer to the observed positive EB of the solution. At a frequency l0 5 Hz (straight line 6), the observed An,. of the solution virtually coincides with An0 of pure DMA. It is possible to calculate the specific Kerr constant K~ of the dissolved polymer for each frequency from the difference in the slopes of two straight lines (Fig. 5) one of which was obtained for the solution (at a concentration c) at a frequency v and the other line corresponds to pure solvent: K,. = (An,. - Ano)/cE 2. The results thus obtained for CC in all the solvents used are shown in Fig. 6 in the form of dispersion curves of the dependence K~/Kv~ o on log v. The experimental points obtained at different concentrations (I-V) do not exhibit a monotonic concentration dependence of dispersion, so justify discussion of experimental data in terms of the theory of extremely dilute solutions. All the curves in Fig. 6 decrease virtually to zero with increasing v, showing that the only mechanism for the observed EB is the dipolar orientation of CC molecules related mainly to their large-scale motion, i.e. the rotation as a whole in a solvent medium. The
lo[
,/
Z
60 15 40 18
dispersion curves obtained here are slightly wider than the corresponding Debye curves (broken line for curve I), which shows that distribution of relaxation time exists in the investigated EB. Each curve may be characterized by the "average" relaxation time z calculated from its half-height according to the equation z = l/2nv m where vm is the frequency at which K~ = Kwo/2. The values of T are given in Table 1. Relaxation times obtained in polar solvents are much lower than for CC solution in dioxane. This fact indicates that the size of the molecular coil in a polar solvent is smaller (and hence the equilibrium chain flexibility is higher) than in a non-polar solvent. A similar conclusion may be drawn from viscometric and dynamo-optical data listed in Table 1. The quantitative parameter of equilibrium chain rigidity (the number S of the monomer units in the Kuhn segment) for CC in dioxane is 50 [2, 5]. The values of S in other solvents may be estimated from the values of [r/l, comparing them with the value of [q] in dioxane, and proceeding from the fact that for a polymer chain with a weak hydrodynamic interaction [q] ~ S/ln S [see Ref. [1] equation (2.124)]. The values of S thus estimated are given in Table 1. They decrease with increase of solvent polarity. Comparing the S and An/A~ values [see Ref. [1] equation (5.60)], it is possible to estimate the values of optical anisotropy Aa of the monomer unit of the CC chain in the solvents (see Table 1). The values of 6~
v~ 5 I
¢
~
T
o..~/ 270 @
&-I 0-2
o
O-3 4''4
04 N
IL
Fig. 1. Value of An vs shear rate A~ in flow for CC solutions in various solvents. I, in dioxan:, range of concentration c = ( 0 . 0 9 ~ . 1 9 ) x 10-2g,cm-3; 2, in ethyl acetate, c = (0.08-0.19) x 10-2g.cm-3; 3, in c y c l o h e x a n o n e , c = ( 0 . 0 5 - 0 . 1 2 ) x 1 0 - - ' g . c m ~; 4, in D M A , c = ( 0 . 0 4 - 0 . 1 3 ) x 10 - z g . c m - 3 .
~ o'"
:
°
/
-'-----J~ Q_........_..-- o
T_. 4 o
2
.+_
----
o
c" 10 a g. cm "s Fig. 2. D e p e n d e n c e o f % / c = - ( q - qo)/qoc o n c o n c e n t r a t i o n c for C C s o l u t i o n s . Solvents: 1, d i o x a n e ; 2, ethyl acetate; 3, c y c l o h e x a n o n e ; 4, D M A .
Kerr effect in CC solutions in polar solvents
o/O/°/°'2.~.a
1o ~] | I "S
1105
o/ o/I- . /
o L~='-- ° ~
,/ _---
5
".~
-s i
47
o-g
°
['~,
~
6
10
E2 10"z(3c-~m)2 °~,
\.
O
.
.
2,5
-I0
"~'~*
Fig. 3. Dependence of EB An on E 2 of rectangular-pulse field for CC solutions in ethyl acetate, c. 102g . cm -3= 0.199 (l); 0.084 (2); 0.05 (3); pure solvent (4). Aa in all solvents except ethyl acetate are in practice the same, meaning that the optical properties of the monomer unit CC remain invariable when the polarity of solvent is changed. The value of Aa in ethyl acetate is somewhat less than could be explained by smaller value of n and so it is more influenced by optical microform effect [1] in this solvent. Comparing the values of [q] and An~AT with those of T, one should bear in mind that the former two values may characterize only the equilibrium chain rigidity, whereas z in principle also depends on its kinetic flexibility. The quantitative relationship between z and [~/] is known to be given by the equation (!)
z = M[q]rlo/2FRT
where F is the numerical coefficient the value of which depends on the hydrodynamic model used in the theory for describing the dynamic properties of the macromolecule in solution. Thus, for kinetically rigid macromolecules, the theoretical value of F ranges from 0.13 (rigid rod) to 0.42 (compact globule) [1]. The values of F calculated from equation (1) using experimental data on T, [q] and r/0 for the investigated polymer are given in Table !. For the polymer in all solvents, the values of F exceed the maximum theoretical value for kinetically rigid particles. This result may be interpreted as manifestation of some kinetic flexibility of the polymer chain the motion of which in a sinusoidal electric field is not just its rotation as a whole but also includes local re-orientations of its
.
.'.5,0
300V 2 E 2 (.-;-~---)
Fig. 5. The dependence of EB An,.on the square of effective strength E 2 of sinusoidal-pulse fields for CC solution in DMA (c = 0.13 x 10-2 g. cm-3). Different lines correspond to different field frequencies: v kHz = 0 (1); 3,2 (2); 10 (3); 30 (4); 50 (5); I00 (6). polar elements according to the higher modes in the Zimm model [2, 8]. The same process may also explain (at least partially) the width of dispersion curves in Fig. 6. The data in Table l show that the coefficient F is particularly high for strongly polar solvents. This fact implies that not only the equilibrium but also the kinetic flexibility of the CC polymer chain increases when a non-polar solvent is replaced by a polar solvent. A decrease in rigidity (both equilibrium and kinetic) of CC molecules in polar solvents shows that an important role in the mechanism responsible for this rigidity is played by the interaction between side groups, i.e. the substituents in neighbouring glucose rings. This interaction ensures a high degree of hindrance to intramolecular rotations in the chains of cellulose esters and ethers [9]. In fact it is the bonds (Van der Waals and hydrogen bonds) formed as a result of interactions between the side groups should be weakened and subjected to rupture by the influence of the molecules of a strong solvent, capable of forming intermolecular hydrogen bonds. This process is similar to the wellknown phenomenon of despiralization of polypeptide molecules in strong solvents.
-b 4
+
÷
\\ \o
1000 o 0
0
3 o - - o
eo i
100
~
•~
.....
/%
2
• &
A
• 1
3
4
5
6
Log v c • I 0 a g"
cm
-a
Fig. 4. Specific Kerr constant Kc vs concentration c for CC solutions, l, dioxane; 2, ethyl acetate; 3, cyclohexanone; 4, DMA.
Fig. 6. Dependence of relative Kerr constants K , / K ~ o on frequency v of sinusoidal-pulse field in CC solutions. 1, dioxane; 2, ethyl acetate; 3, cyclohexanone; 4, DMA. Concentrations c. 102g.cm-3=0.19 (1); 0.13 (II) 0.10 (liD; 0.08 (IV); 0.05 (V).
1106
V.N. TSVETKOVet al.
Hence, the study of the kientics of the Kerr effect in CC solution shows that the electro-dynamic properties of its molecules in solvents of various strengths and polarities, reasonably correlating with the data of other methods, leads to information on equilibrium and kinetic chain rigidity in these solvents. It should be noted in discussing the equilibrium values of K0 and K listed in Table 1 that at present there is no universal quantitative theory of EB in polar liquids, not only for polymer solutions but also for pure solvents. The main difficulty of this theory is related to the necessity of taking into account intramolecular orientational interaction in the liquid, which formally may sometimes be reduced to finding suitable "internal field" factors. If one tries (as in Ref. [11]) to introduce the internal field model developed by Onsager for the description of dielectric properties of polar liquids into the EB theory of Langevin-Born [12], then for a low molecular weight liquid (solvent), with axial symmetry of optical polarizability of molecules, the Kerr constant K0 is given by:
r0=
(PQ)22nNAp(n2 + 2)2(71 - 72) 135nkTM [ /tz 3C°S20--1] x 71--3'2-t kT" 2
K = (pQ)2 2ttNg(n2 + 2)2S/t211(~l - ~2) ! 35n (kT)2Mo (2)
where 71 and 72 are the optical (and dielectric) polarizabilities of the molecule in the direction of its axis and normal to it, respectively, 0 is the angle formed by the dipole of the molecule /t and the axis 7~; NA, k, T have their usual meanings and PQ is the factor of the internal field according to Onzager equal to PQ = E(n 2 + 2)/(2E + n2).
scattering dipolarization. Although the averaged data of the light-scattering method have been obtained with considerable error, it can be seen that they are in incomparably better agreement with the values of (72-71)on than with those of (72--71)L. The latter values are absurdly low especially the higher is the solvent polarity. Reasonable agreement between (72 - 71)o, and (72 - 71)LSjustifies the use of equation (3) in the EB theory in polar liquids, whereas the comparison of (72- 71)L and (72- 7J)Ls shows that the application of Lorentz factor is impossible in this case. It seems evident that this conclusion is valid as much for dilute polymer solutions in low molecular weight polar solvents. These results on the kinetics of the Kerr effect in CC solutions show that the main mechanism responsible for the observed EB is the large-scale orientation of polar CC molecules in the electric field. In accordance with this, for the solution of a high molecular weight polymer (Gaussian range) according to the EB theory of rigid worm-like chains [1], the Kerr constant is given by
(3)
For a non-polar medium (E =n2), equation (3) becomes (E +2)/3, the Lorentz factor [12] usually applied to dilute solutions of polar molecules in non-polar solvents. For the molecules of all four solvents investigated here, the structure with an axial symmetry of polarizability (71) normal to the "plane" of the molecule may be assumed (for dioxane and cyclohexanone this is the "plane" of the cyclohexane ring whereas for ethyl acetate and DMA they are the planes of the ester and the amide groups, respectively). In this case for three polar solvents, the molecular dipole/t lies in the plane of the molecule in a direction close to that of the C~------Obond (axis 2) and, correspondingly, in equation (2) we have 0 = n/2. The positive sign of K for these solvents implies that for them (just as for dioxane) 72 > 7J. Noting these considerations, equation (2) was used for calculation of the anisotropy (72-71) of molecules of the investigated solvents from the experimental values of K0 and the known values of n, p, E, /t and M. These values of (72 - 7~) are given in Table I with the symbols (~2- 71)on and (72--TI)L, which mean that they are calculated by application of Onsager's and Lorentz' factors, respectively. The last column of Table l gives the values of (75 - 71)Ls, the anisotropy of the same molecules according to the literature data [13] obtained by the method of light-
(4)
where (~1- ct2) is optical anisotropy of the Kuhn segment and #011is the longitudinal (along the chain) component of the dipole moment of the monomer unit of the polymer. Comparing equation (4) with a known Kuhn expression for the shear optical coefficient An/Az for the Gaussian chains [see in Ref. [1] equation (5.60)], one obtains the equation S/t2ji/Mo = 6kTK/(pQ)2NA(An/Az)
(5)
making it possible to determine the value of S/t021r/Mo from the experimental values of K and An/Az. For CC in dioxane, the value of S/t ~i~/Mo calculated by using equations (5) and (3) is 9.4 × 10-38cm4 (300 v)~, in good agreement with its value 9 x l0 -38 cm4(300 v)2, obtained from direct measurements of dielectric properties (dipole moments) of CC solutions in dioxane in the Gaussian range [14]. Using the values S = 50 [2, 5], M 0 =480 and SP~lt/M = 9.4x 10-38 cm4(300 v)2 for the investigated CC sample in dioxane, we find/t0Ji = 0.95D, which is close to the values of/t001 for some other cellulose ethers and esters in a non-polar solvent and is in reasonable agreement with the molecular structure of the polyglucoside chain [15]. The values of S given in Table 1 are used for the calculation of/t011 from equations (5) and (3) and the experimental values of K and An/At for CC in polar solvents. The values of/t01; obtained for CC in polar solvents (Table 1) greatly exceed that in dioxane, and this difference increases with the polarity of the solvent. These high values of P0rl cannot be explained by the dipolar structure of the chain alone and must be considered as "effective" values indicating the existence of orientational correlation (association) between the polar molecules of the solvent and the dipolar bonds of the chain. The manifestation of this association has already been detected in the investigation of EB for aromatic polyamides in polar solvents [16]. In order to obtain an idea of the scale of this
Kerr effect in CC solutions in polar solvents correlation, one can use, for instance, an equation of the type #0!l = (/~01)D + Z~, COS fl (6) where (/~0~)o and hi! are the values of the longitudinal component of the m o n o m e r dipole obtained for CC in dioxane and a polar solvent, respectively, # is the dipole moment of the solvent molecule, Z is the number of the solvent molecules associated with a m o n o m e r unit of the polymer and fl is the angle formed by the longitudinal component of the m o n o m e r dipole of the polymer and the dipole of the solvent molecule in the associate. The values of the parameter Z cos/3, characterizing the degree of orientational correlation in solution calculated from equation (6), are listed in Table 1. They increase with the polarity of the solvent. However, it can be seen that the degree of orientational order in the associate is not high. Thus, if it is assumed that Z = 6, then even for the most polar D M A , it is found that cos fl = 0.2, whereas for other solvents it is even lower. However, this degree of order in the associate is sufficient for the generation of a large effective macromolecular dipole and is related to high EB in the polymer solution. REFERENCES
1, V. N. Tsvetkov. Rigid-Chain Polymers, Consultants Bureau. Plenum, New York (1989).
1107
2. N. V. Pogodina, K. S. Pojivilko, H. Dautzenberg, K. J. Linow, B. Philipp, E. I. Rjumtsev and V. N. Tsvetkov. Vpsokomolek. Soedin B, 19, 851 (1976). 3. V. N. Tsvetkov, I. P. Kolomiets, A. V. Lesov and A. S. Stepchenkov. V gsokomolek. Soedin A, 25, 1327 (1983). 4. A. V. Lesov and N. V. Tsvetkov. Vpsokomolek. Soedin A, 32, 200 (1990). 5. L. N. Andreeva, E. U. Urinov, P. N. Lavrenko, K. J. Linov, H. Dautzenberg and B. Philipp. Faserforsch. Text Tech. 28, 117 (1977). 6. O. A. Osipov, V. I. Minkin and A. D. Garnovski. Reference Book on Dipole Moments. High School, Moscow (1971). 7. Ya. Yu. Ahadov. Dielectrical Property of Liquids'. Standarts, Moscow (t972). 8. B. Zimm. J. chem. Phys. 24, 269 (1956). 9. V. N. Tsvetkov. Advances in Chemistry (Russ) 38, 1674 (1969). 10. J. Onsager. d. Am. chem. Soc. 5g, 1486 (1936). 11. V. N. Tsvetkov. Kolloid. J. (Russ) 33, 154 (1971). 12. H. A. Stuart. Die Physik d. Hochpolymeren. Springer, Berlin (1950). 13. A. N Vereschagin. Characteristics of Anisotropy qf Molecular Polarisability. Nauka, Moscow (1982). 14. E. I. Rjumtsev, L. N. Andreeva, F. M. Aliev, L. H. Kutsenko and V. N. Tsvetkov. V~sokomolek. Soedin A, 17, 1368 (1975). 15. V. N. Tsvetkov, E. I. Rjumtsev, I. N. Shtennikova, T. V. Peker and N. V. Tsvetkova. Dokl. (Proc.) Acad. Sci. U.S.S.R. 207, 1173 (1972). 16. V. N. Tsvetkov, A. V. Lesov, N. V. Tsvetkov and L. N. Andreeva. Fur. Polym. J. 26, 575 (1990).