Anisotropy of the tensor characteristics of copolymer molecules and its dependence on the copolymer composition

Anisotropy of tensor characteristics of eopolymer molecules

3047

REFERENCES 1. S.eI. ZHDANOV, Uspokhi khimii 38: 1390, 1959 2. T. E. LIPATOVA, G. S. SHAPOVAL, N. P. BAZILEVSKAYA and Ye. S. SH:EVCHUK, Vysokomol. soyed. 11: 2280, 1969 (Translated in Polymer Sci. U.S.S.R. 11: 10, 2594, 1969) 3. F. SOMMER and J. W. BREITENBACH, Internat. Symposium on Macromolecular Chemistry, Budapest, v. 2, p. 257, 1969 4. J. W. BREITENBACH and Ch, SRNA,' Pure and Appl. Chem. 4: 245, 1962 5; FUNT, BADANY and RICHARDSON, Polymer Chem. and Tcctmol., No, 1, 33, 1967 6. W. STROBEL a n d R. SCHULZ, Makromolek. Chem. 133: 303, 1970 7. T. E. LIPATOVA, G. 8. SHAPOVAL, Ye. S. SHEVCHUK and N. P. BAZILEVSKAYA, I n t e r n a t . Symposium on Macromolocular Chemistry, Budapest, v. 2, p. 131, 1969 8. G. J. HOIJTINK, Rccueil trav. Chem. 76: 885, 1957 9. T. E. LIPATOVA and V. M. 8IDERKO, Vysokomol. soyed. 7: 1476, 1965 (Translated in Polymer Sci. U.S.S.R. 7: 8, 1636, 1965) 10. T. E. LIPATOVA and V. M. SIDERKO, Dokl. AN SSSR 178: 856, 1968 l l . T. E. LIPATOVA, G. S. SIIAPOVAL and Ye. S. SHEVCHUK, Zavodsk. lab. 35: 1175, 1969 12. A. I. BRODSKII, L. Ya. GORDIENKO and L. S. DEGTYAREV, Zh. Vses. khim. obshch. im. Mendeloyeva 11: 196, 1966 13. L. I. ZEil~YANOVA, Sovremennaya electronnaya mikroskopiya (Modern Electronmicroscopy), p.90, 1965 14. O. N. GRIGOROV, I. F. KARPOVA, Z. P. KOZ'MINA, K. P. TIKHOMOLOVA, D. A. FRIDRIKHSBERG and Yu. M. CHERNOBERZHSKII, Rukovodstvo k praktichoskim r a b o t a m pc kolloidnoi khimii (Handbook on Practical Experiments in Colloid Chemistry). p. 301, Izd. " K h i m i y a " , 1964 15. H. KAWASURA, Makromolek. Chem 59: 201, 1963 16. Kh. S. BAGDASAR'YAN and A. N. NEPOMNYASHCHII, Kinotika i kataliz 4: 60, 1963 17. A. V. IL'YASOV, Yu. M. KARGIN, A. A. LEVIN, I. D. MOROZOVA and N. N. SOTNIKOVA, Izv. A N SSSR, Chem. series, 1030, 1968

ANISOTROPY OF THE TENSOR CHARACTERISTICS OF COPOLYMER MOLECULES AND ITS DEPENDENCE ON THE COPOLYMER COMPOSITION* T. M. BIRSHTEIRT High-molecular Compounds Institute, U.S.S.R. Academy of Sciences

(Received 26 March 1971) SHnVDO a n d S t e i n [1] a n d B i r s h t e i n a n d c o w o r k e r s [2] r e c e n t l y c a r r i e d o u t a theoretical analysis of the conformational properties of linear macromolecules containing segments with different physical characteristics (polymorphic macro* Vysokomol soyed. A14: No. 12, 2616-2620, 1972.

3048

T.M.

BIRSHTEIN

molecules [2]). These m a y be chemically or stereochemically differing segments in copolymers or non-stereoregular macromolecules, or segments differing in s~ortrange order, such as the helix and coil regions in partially helicalized polypeptides, helices having different signs in optically active isotactic polymers, etc. [1, 2]. When analysing the conformational properties of the macromolecules authors have mainly used a zigzag chain model consisting of segments of different types; the authors of [1] assume free coupling of the segments, while the investigation reported in [2],relates to cases of free coupling and free rotation of the segments with a fixed valency angle between the segment axes. The analysis of the anisotropies of the tensor characteristics of the macromo|ecules (in [1] the authors dealt with the optical anisotropy and the dichroism of the absorption bands, while in [2] a study is made of the optical anisotropy and the anisotropy of optical activity) showed that it is possible, by means of experimental investigation of the relationship between these quantities and the composition of polymorphic (copolymer) molecules, to obtain quantitative information about the structure and flexibility of the macromo|ecules. The aim of the present investigation was to proceed to a more detailed analysis of the relationship that m a y exist between the anisotropy of the tensor characteristics and the composition of polymorphic macromolecules. The case analysed is a common one where the lengths of homogeneous segments (blocks) are comparable in size, or smaller, than those of statistical segments of the corresponding monomorphic macromolecules. An extreme case, where the lengths of the blocks greatly exceed those of the statistical segments, was analysed in [1]. The anisotropy of the tensor characteristics of macromolecules depends on the degree of orientation of segments relative to the vector of the length of a macromolecule. Starting with the theory of K u h n and Griin [3], or using a general expression for analysis of the tensor characteristics of any macromolecular structure, the authors of papers [1, 2] show that the degree of orientation of a segment depends on its length. The longer the segment is the more marked will be the degree of orientation of the segment w h e n the latter is stretched, and the greater will be the contribution of the segment to the anisotropy of the macromolecule. The anisotropies of the different tensor characteristics of the molecule are described by equivalent expressions; in particular, for the average anisotropy of polarizability of, a macromolecule consisting of freely linked segments of two types we have --

AA . . . .

3 N

5 h2

2

2

[XA (AaAl A ) Jr-XB (,daBl B)],

( 1)

where N : N A + N B is the total number of segments in the molecule, X A = N A / N and X B are the number of segments of two types, and la and lB are the lengths and anisotropies of the segments, respectively, and h* is the mean square of the length of the macromolecule

h~=N (XA+X,),

(2)

Anisotropy of tensor characteristics of copolymer molecules

3049

where ( ) denotes averaging in respect to the possible distribution of segment lengths for a given type oi segment; it is suggested in [1] t h a t no such distribution exists, and the averaging sign is therefore omitted by the authors.

N

I

~r e

xe F~G. 1. Size of the copolymer molecule (l~ and ls are independent of XB) (a) and average optical anisotropy of the copolymer molecule (1A, 1B, zla~ and AaB are independent of XB;

h~B/N>]~/N): A~A A~B (2) (b). First, let us consider a polymorphic macromolecule with a high degree of "blocking", so t h a t the lengths of the individual blocks greatly exceed the lengths of statistical segments for the corresponding monomorphie macromolecules. I n this case neither Is nor Aas ( S = A , B) will depend on composition, and accordingly the relationship of h 2 and AA to composition will be determined solely by Xs. I t follows from equations (1) and (2) t h a t h2/N will in this case be a linear function of XB, while AA will be a curvilinear function of XB (see Fig. 1). The curved nature of the relation of AA to the composition of a copolymer with a high degree of "blocking" is directly related to the fact t h a t the longer segment make a greater contribution to AA. There is therefore a tendency for the anisotropy to remain such as corresponds to the more rigid component of the copolymer when segments of the flexible component are introduced, and, contrariwise, there is a tendency for a more rapid change to occur in the value corresponding to the more flexible component when segments of the rigid component are introduced (Fig. 1). The magnitude of 1A/1B 2 2 may t)e found from the deviation of the curve in Fig. lb from linearity. The result obtained is in complete agreement with t h a t reported in [1] where it was assumed by the authors t h a t the sizes of segments did not depend on composition, but the limits of the validity of this assumption were not discussed in [1]. In the polymorphic macromclecules generally investigated by authors the sizes of the homogeneous blocks are quite small, so it is no longer possible to assume t h a t the sizes of segments will be constant. This is reflected in the curvature of the h 2 vs. composition plot, and must alter the shape of the AA vs. composition curve.

3050

T . M . BIRSHTEIN " ._

.

"' '

A: curved relation of h~- to composition was obtained in a large number of theoretical investigations by authors analysing concrete macromolecules Which had structural elements of two types. Figure 2 shows the general character of the relationship, with the proportion ~B of monomers of type B showing the changes in composition. It will be seen that the introduction of the flexible component greatly alters the value of h 2. In some cases the curve in Fig. 2 passes through a minimum [5-7].

N

I

e8

~

_

FIG. 2

FIG. 3

FIG. 2. Size o f t h e e o p o l y m e r molecule w h e n va a n d VB are f u n c t i o n s o f ~B. FIG. 3. A v e r a g e optical a n i s o t r o p y o f t h e e o p o l y m e r molecule

(h~/N > h ~ / N ) : AA.a
AAa >AAB (2).

Relationships of this type have been obtained (and in some cases confirmed by experimental work) particularly for polypeptides in the region of helix-coil transition [5-8] (the helix being the rigid component, and the coil the flexible one) for optically active isotactic macromolecules that have helical segments of two directions of spiraling [9, 10] (the rigid component being the energetically favourable long segments, and the flexible component the energetically unfavourable short segments) for stereoregular vinyl polymers [8] (the rigid component) and for a coil-shaped copolymer of L-alanine (rigid component) and glycerin (flexible component) [8, 11]. I t should be noted that these examples include both a case where structurally different segments are not too mixed, so that rigid segments of two types, with lengths dependent on composition, may be isolated [5-7, 9], and also a ease involving statistical eopolymers, when the rigid segments contain different monomers [8, 11]. In the former case we m a y use a zigzag model consisting o f segments of two types, and the shape of the curve (Fig. 2) follows directly from formula (2), which may be written as h 2 = N ([Oa (1 +g~)) la~A-OB (1 A-g(~)) lifo],

(3)

where , and lao 1s0 are the average number and length of monomers in a given type of segment, and g(s~)= 2>/ 2 is a numerical coefficient taking account of the distribution of segments of a given type according to length. On passing from the rigid polymer B to a eopolymer with a small amount of the flexible component A (@B is close to 1)the lengths of the rigid segments will

Anisotropy of tensor characteristics of copolymer molecules

3051

be reduced on account of the appearance of further defectiveness. For instance, in the ease of polypeptides [2, 6] (VB)~" (1--~B) -+. This reduction is the main factor influencing h 2, which in the region of ~B--~1 is approximately proportional to

(vs). Similarly a relationship of the type shown in Fig. 2 is obtained for simple models of statistical copolymers. For instance, assuming that the rotations in the chain are independent, and are described by a symmetrical potential, and that in the individual components of the copolymer only the mean cosine of the rotation angle ~8=cos (0s differs, we obtain

1 --

~AI~A -- ~BI~B'

where h02 is the size of the chain in the case of free rotation. It will readily be seen that in accordance with Fig. 2 h 2 ( ~ A = , g B : ½ ) < [ h 2 ( , g A = I ) + h 2 ( ~ B : I ) ] / 2 . As has already been pointed out, the same result is obtained by strict calculation of ~2 for concrete statistical copolymers [8, 11]. Obviously, under conditions giving rise to a loss of linearity of the ~2 vs. composition plot, (Fig. la), the curve of A A vs. composition will differ from that shown in Fig. lb. It should be noted that whereas in Fig. lb the properties of the rigid component of the copolymer tend to be preserved, in Fig. 2, on the other hand, the introduction of the flexible component brings a rapid change in the properties of the rigid component. This means that in the copolymers normally investigated the composition dependence of the size of the rigid segments will result in an effect having the opposit_eesign to that of greater orientation of rigid segments. The shape of the resulting A A vs. ~B curve [2] AA =

3

5

~qA(VA) 2 (1 ~-g~)) ZfaAOIAO--~gB(VB) 9 (1 +g~)),daBol~o

aa(va) ( l + g ~ ) ) ~ o + a B ( v . )

(1 +g(~))l~o

'

(5)

(g(,a)= ( v , - - ( v s ) ) 3 / ( v , ) a, Aaao and AaBoare the anisotropies of the polarizabilities of the monomers) will be determined by the influence of both effects. It can be shown by analysis, that in most cases the curvature of the zfA vs. ~B plot will be directly opposite to that shown in Fig. lb corresponding to a rapid change in the properties of a rigid homopolymer (Fig. 3). So for polypeptides in the region of helix-coil transition when OB~ 1 z/A-~h~~ (1--~B) -+ [2]. A curve of the type shown in Fig. 3 is similarly obtained for primitive models of a statistical copolymer. For instance for a copolymer modelled by units with free rotation with different valence angles of u--Ya, x--YB in different components of the copolymer, and with the same anisotropy of polarizability zfao for the monomers of both types [12] 2

AA =--

5

Aao

F__2_2 Lsin2y

-4

3cos7

3]

1-- (cos 7)2

2

. ,

(6)

3052

T.M. BIItSI~EIN

w h e r e cos 7=~A COS7A+$S COS7S, sin= 7=~A sin2

7A+OB Sin2 7B. I t will r__eeadilybe seen t h a t AA (~A=0s=½)<[AA (OA= 1)+ztA (~= 1)]/2. As in this case zIAs>,~AA and hB>hA -2 -2 we obtain a curve similar to curve I in Fig. 3. Curves of the type of curves 1 and 2 in Fig. 3 were also obtained in [13] for a model of a statistical copolymer with independent oscillations of the units in a rectangular depression close to the trans-position, the width of the depression differing for the copolymer components. Obviously, an experimental investigation of the anisotropy of the tensor characteristics of a polymorphic macromolecule in relation to its composition m a y provide valuable information about the structure of this molecule, as well as the parameters determining the length of the different types of segments, in the same way t h a t an analysis of E2 of polypeptides [6] and desoxyribonucleic acid [14] in the region of helix-coil transition makes it possible to determine the size of helical segments. We would also point out t h a t the linearity of the relation of ~A and the other tensor characteristics of a molecule to composition is possible only in cases where ~2 is composition-independent. CONCLUSIONS (1) I t has been shown t h a t in molecules of copolymers and polymers containing segments with different physical characteristics, the anisotropy of the tensor characteristics of the macromolecules (optical anisotropy, dichroism of the absorption bands, etc) will be a nonlinear function of composition. The deviation from linearity is determined both by the difference in the rigidity of the copolymer composition, and by the relationship between the length of the rigid segment of each component, and the sizes of their blocks in the copolymer. (2) In the case of macromolecules in which the sizes of homogeneous blocks do not greatly exceed the lengths of the rigid segments of each of the components, and anisotropy and the dimensions of the rigid polymer change rapidly with the introduction of the more flexible component, while on the other hand the anisotropy and dimensions of the flexible polymer are only slightly sensitive to the introduction of the rigid component.

Translated by R. J. A. HEND~Y REFERENCES

1. Y. SHINDO and R. S. STEIN, J. Polymer Sei. 7, A-2: 2115, 1969 2. T. M. BIRSHTEIN, V. A. ZUBKOV and M. V. VOL'KENSHTEIN,J. Polymer Sci. 8,A-2: 177, 1970 3. W. KUHN and F. GRt~N, Kolloid-Z. 101: 248, 1942 4. Yu. Ya. GOTLIB, Zh. tekh. fiziki 27: 707, 1957 5. K. NAGAI, J. Chem. Phys. 34: 887, 1961 6. O. B. PTITSYN, Conformations of Biopolymers, vol. 1, p. 381, 1967 7. W. G. MILLER and P. J. FLORY, J. Molee. Biol. 15: 298, 1966 8. P. J. FLORY, Statistical Mechanics of Chain Molecules. Interscience, 1969

Polymerization of aorylonitrile

3053

9. T. M. BIRSHTEIN and P. LUISI, Vysokomol. soyed. 6: 1238, 1964 (Translated in Polymer Sci. U.S.S.R. 6: 7, 365, 1964) 10. T. M. BIRSHTEIN and O. B. PTITSYN, Conformations of maeromolecules, Izd. "Nauka", 1964 11. W. G. MILLER, D. A. BRANT and P. J. FLORY, J. Molec. Biol. 23: 67, 1967 12. T. M. BIRSHTEIN and O. B. PTrrSYN, J. Polymer Sci. C16: 4617, 1969 13. T. M. BIRSHTEIN, V. P. BUDTOV, E. V. FRISMAN and N. K. YANOVSKAYA, Vysokomol. soyed. 4: 455, 1962 (Not translated in Polymer Sci. U.S.S.R.) 14. A. V. SHUG/tLH, M. D. FRANK-KAMENETSKII and Yu. S. LAZURKIN, Mol. biol. 3: 133, 1969; 4: 275, 1970

P O L Y M E R I Z A T I O N OF ACRYLONITRILE IN T H E P R E S E N C E OF L I T H I U M DIPROPYLBUTIrI, C A R B I N O L A T E * A. V. NOVOSELOVA,S. 1~. VOL'F-MAGDEBURGSKAYAand B. L. YERUSALIMSKII High-molecular Compounds Institute, U.S.S.R. Academy of Sciences

(Received 26 March 1971) THE initiating activity of alkali metal alkoxides is usually lower than t h a t of the alkyls, as is evident in the polymerization of unsaturated hydrocarbons or acrylic esters. However, no data have been published in this connection such as would allow definite conclusions to be drawn in regard to characteristic features of the behaviour of alkoxides during acrylonitrile (AN) polymerization processes. Some data are given in papers [1-4] regarding A ~ - R O L i systems, b u t it would scarcely be possible, with the information so far available, to determine the special features of these initiators as opposed to those of butyllithium (BuLl). I t was found [1] that ROLi compounds may be used for the synthesis of high-molecular monodisperse polyacrylonitrile. I n the present investigation our aim was to discover whether the use of ROLi initiators would obviate side reactions t h a t are so characteristic feature of AN polymerization initiated by metal alkyls [5, 6]. Moreover, systems of the type studied are usually more suitable for investigation of the effect of dimethylformamide (DMFA) upon acrylonitrile polymerization processes; BuLi reacts with DMFA to form an alkoxide even at low temperatures, [7], and this greatly increases the difficulty of interpreting the results of investigations of AN polymerization processes in the presence of these initiators. At the same time the collection of data characterizing the effect of DMFA (varying from catalytic amounts to quite high DMFA contents) on the general course of AN polymerization processes is of major importance, seeing that the homogeneous low-temperature anionic polymerization of AN is possible only in DMFA medium.

This paper relates to an investigation of polymerization in the system AN-ROLi, as exemplified by lithium dipropylbutylcarbinolate (DPBL) in DMFA, in toluene, and in the presence of small amounts of DMFA. In toluene the initiating efficiency is as low as in a system in which BuLi participates (of the order of 1%). How ever, the reasons for this low initiating efficiency are not the same in both eases; a * Vysokomol. soyed..4.14: No. 12, 2621-2626, 1972.