Dynamic birefringence of poly-(4,4′-hydroxydiphenylene) pyromellitic amic acid solutions

Science U.S.S.R. Vol. 28, 1~o. 8, ppo 650-656, 1 9 8 1

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0082---8950/81/080660-07507.50/0

O 198ZPergamonPrm Ltd.

.... DYNAMIC BIREFRINGENCE OF POLY- (4,4'-HYD~)XYDIPffRNYLENE) PYROMELLITIC ACID SOLUTIONS*

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S. YA. M~O~La~K,G. E. TmOF~.Y~VA and M. I. B~ssoNov High Polymer Institute, U.S.S.R. Academy of Sciences (Reee/ved 27 December 1979) The dynamic bireffingenee of poly-(4,4'-hydroxydiphenylene) pyromellitie amic acid solutions has been investigated in the molecular weight interval from 4 × 10' (monomer unit) to 4.7 × 10'. The statistical segmental length estimated on the basis of the reduced birefringence limiting value was found to be A=38× 10-a cm. The experimental dependence of birefringence on macromolecular length cannot be ac. counted for q,lantitatively in terms of existing monoparametrie theories based on a persistent thread 9model. The structure of fragments formed during degradation of this polymer is practically identical to that of the initial macromolecules. I ~ the light of investigations of solutions of poly-(4,4'-hydroxydiphenylene) pyromellitic amic acid (P~APM), which is .widely used as a prepolymer in t h e production of ~olyimide materials, the authors of [1-4] felt t h a t the flexibility of the PAAPM chains must be considerable. This conclusion based on the length of the macromolecules actually rests solely on measurement of the intrinsic viscosity [q]. I t therefore appeared highly desirable t h a t the unperturbed dimensions, i.e. the flexibility of the macromolecules, Should be determined by independent means, using another experimental method. Our approach in this instance was accordingly based on the dynamic birefringence method. Moreover PAAPM lends itself quite readily to an investigation of dynamic birefringence relative to the length of the m~cromolecule L, since a homologous series of the macromolecules was readily obtainable by natural degradation of the'polymer with time. I n addition this provides an opportunity for verifying t h a t degradation fragments have a structure identical to t h a t of the initial macromolecules. Two nonreprecipitated PAAPM specimens were investigated, one prepared in the laboratory, and the other of commercial grade. Both polymers were prepared by heterogeneous polycondensation of diaminodiphenyl ether and dianhydride of pyromellitic acid in DMF, the initial concentration being c=0.1 g/ml. l~or further investigations the solution was diluted with DMF to c=0.02 g/ml. * Vysokomol. soyed. A2S: No. 3, 581-586, 1981. 650

Dymunie b'n~rinsenoe of PAAPM aohitions

68i''

Storage of the solution at room temperature is accompanied by degrsdati0n

of the polyamic acid [5] which w ~ Utilized for the preparation of P ~ A P M fractions. The last fraction was obtained 510 days after preparation of the initial solution. I t was found by inRa~ed t h a t the degree of imidization in the fraction did not exceed 20~/o. The specimen of lowest molecular weight--.the individual substance Io-diphenylamide of pyromellitic acid--differs from the PAAPM monomer unit only by the absence of a single oxygen atom and its molecular weight is M ~ 4 0 4 . Relative viscosities of the solutions were measured in an Ostwald capillary viseosimeter (outflow time for DMF 66.6 see). A device fitted with an internal rotor was used in line with the method outlined in [6] for birefringence measurements. Parameters of the dynamooptimeter were as follows: slit width 0.033 cm, rotor length (width of birefringent layer), 4 cm. The elliptical compensator path difference was 22.4 × 10 -~ cm. All measurements were carried out at 22% Viscosity of the DMF yo~0.805 × 10 -2 poise, refractive index n~1.427. Molecular weight determination involved use of the relation

[ ~ ] = K M a,

(1)

where values of K----1.1 × 10-' and a~-0.91 were based on measurement of the light scattering and viscosity of solutions of unreprecipitated polymer synthesized in DMF [4]. The results reported in [7] were used to determine molecular weights of polymers below 14× 10' (the validity boundary for formula (1)). According to [7] that the onset of longrange action appears only after attainment of a macromolecular length equal to ~0 Kuhn segments. Molecular weight values of shorter macromolccules may then be calculated by the formula [~]=KoM °'~, (2) where Ko ~ (KN~ -°'5 ~(x-za)/a(M/L) sa-1)sl(4-.la), (3) while ~=2.86 × 10as. It was shown in [7] that N0=9 is admissible for flexible chain polymers. The molecular weight of the monomer unit M0=418, and its length 2==15.9× 10-s cm [8], and so the molecular weight of the unit length M/L----Mo/2-~26.46 × l0 s. Hence, according to formula (3), Ks:0.45. Plots of the M values obtained from formulae (1) and (2) are seen in Fig. 1. I n all cases relations between the dynamic birefringence An and the shear stress g (qw~o) (g being the flow velocity and ~ the solution viscosity) are expressed by a straight line which goes through the origin. This enabled us to find values of the reduced dynamic birefringence [n]/[~?]~-n[ff(~-'-~o) plotted on the Y-axis in Fig. 1. The value of zin was obtained by subtracting the DMF birefringence (An)o, allowing for the fact t h a t the value of (zJn/g)0~0-1--~0.51 × 10 -l°. I t is clear from Fig. 1 t h a t the reduced blrefringence attains saturation for the highest molecular weigh~ ' fractions. This means t h a t the macroshape effect m a y be neglected, despit~ the magnitude of the refractive index increment (dn/&) ----0.198. . Certainly in view of the low molecular weights the m a c r o s ~ p e

effee~ [6] [~1I

o'28~'~(n=+ ~)= (d~/&)z.~ "

is 0nly slight (0.7x 10-z=) for the highest molecular weight specimen) and accounts for only an insignificant fraction of the reduced birefringence Jimiting value ([n]/[F/])~.., = = 4 1 x 10 -x°. ([n_J/DlJ),/O m

20

I

r

20

1

I

40 PI,IO -a

FIG. 1. Reduced birefringence ([n]/[t/]) vs. molecular weight of PAAPM. Here and in Fig. 2 the blaok point relates to p-diphenylamide of pyromellitie sold.

The limiting value of [n]/[~] is therefore made up of the intrinsic anisotropy and the microshape effect [6], and may be expressed as

The notation in formulae (4) and (5) is as follows: p I p o l y m e r density, H the gas constant, Arm the Avogadro number, T absolute temperature, (L=--Lz) the segmental shape function, A the length of a statistical Kuhn segment, (~a) the optical anisotropy of the-monomer unit at the axes of the fully extended chain conformation. The following diagram representing the repeating portion of the chain in fully extended planar conformation was used by us when calculating the value of ( z i a ) ~ . (Lia)~, where (Aa)~ is the contribution of t h e / t h bond or group

{1 is th~ main valency C h i i n ~ e e t i o n ; & is the ~ l e ~ t w e e n the bond direction and 1; ~, is the a ~ l e l ~ t ~ e e n the axis of the monomer ~mit and 1; ¢~ and ¢, are a ~ l e s atmut which the chain r o t ~ . Values given in [9, 10] based on X-ray analyais were taken for angles ~, between the polymer chain axis and axes of the monomer unit as well as the ~izes of angles Wbetween bonds. The valency angle P h - O - P h (angle W1 about which chain rotation takes place) is 120°. This differs only insignificantly (for our calculations) from !24 °, the value obtained for the angle of P h - O - P h in [11]. Considering that angle W2 of the second joint (meta-addition in the dianhydride ring) is likewise 120°, it was assumed that axes of the monomer unit will make angle ~ = 3 0 ° with the X - X direction of the polymer chain. On this basis we determined sizes of angles 8~ between the ith bond direction and that of the main valency chain in extended planar conformation. Benzene rings make the main contribution to the optical anisotropy of the monomer unit. Although the polarizability tensor for the rings has three major axes [12] it was accepted for simplicity that the polarizability is identical in all directions in the ring plane, and is equal to ~1=0.5 (114.9-{-117-3)× 10 -25 cm8=116.1×10 -~6 cm s. I n the perpendicular direction the polarizability is • 2-~59.7 × 10 -s~ and (J~)~--56.4 × 10-26 cmS..In anisotropy calculations allowance was also made for a possible rotation of benzene rings linked via oxygen about an axis situated in the plane of the above scheme (as shown by the pointers). A theoretical analysis reported in [8, i3] shows that ~he latter approximates to free rotation. The equilibrium conformation for the P h - O - P h group is a "propeller" conformation with the ring plate turning through an angle of J=30--40 ° from the plane of the scheme. It may readily be demonstrated that under these conditions (Aa)Ph----0"5(A~)~(3(cos~ph+ cos~ - cos~9~cos2~)--2) (6) For the remaining bonds the polarizability tensor has axial symmetry. Calculation ot the contribution of these bonds to the optical anisotropy was accordingly based on "the formula (A~)l= (~t~)¢(3 c o s ~ - - 1)/2,

(7)

where (J~)~ is the polarizability difference for the ith bond along the bond and in the perpendicular direction. Data on bond polarizabilities were taken from the monograph by Vuks [12]. The optical anisotropy of the monomer unit proved to be (A~)~160× 10 -~8 cm ~. Substituting the latter value into equation (~), as well as the values p----1.3 g/cm~ and (L~--L1)~2~ [6], we obtain A----38 × 10 -s cm. The length of a statistical segment A was also found from the above value of K0~0.48. Using the equation

is) we "obtain A = 36 x 10 -~ cm.

654

8. YA. MAoAmx ~ a/.

Thus the statistical segmental length o f the PAAPM m~eromole~ule was found by two experiment&l methods to have ~imi|ar values of A. Values of .4 were determined to within 10~/o, this being the total error for the methods used.

LI

0

2~

75

x'"

FIG. 2. Relative birefr/ngence J---([nl/M)/([n]/M),.,® vs. relative length of the macromolecule x=2Z/A: 1,2--theoretlcal Curves taken from [14] (1) and [15, 16] (2); 3-5--experimental curves for PS [17] (3)~[18, 19] (5) and'for PAAPM (4). A value of A=(30:E5)X 10 -8 cm was obtained by Koton and coworkers, using t h e Stoekmayer-FJxman method. It was .pointed out by those authors t h a t prior reprecipitation of the polymer m a y to some extent alter unperturbed dimensions of the macromoleeu]es. Let us now t u r n to the reduced birefringence [n]/[t/] in relation to the macromoleculas length L. This relationship is normally expressed in "normal" coordinates: the relative birefringence A=([n]/[t/])/([n]/[~])®~® is investigated as a function of relative macromolecular length x=2L/A=2M/~4(M/L). This was clone in the case of Fig. 2, curve 4. We would emphasize t h a t this is t h e first time t h a t experimental values have been obtained for flexible chain polymers over so wide an interval of variation in A: 0.07 ~
Dynamic b i r e f ~ e e

of PAAPM solutions

66~

of macromolecular dimensions ( h y ~ a m i c s , hght scattering). Good agreement was found in such comparisons for rigid chain polymers (the~ Knhn'segmental lengths being several hundred AngstrSms [14-16]. On the other hand, application of the theory of [15] to flexible chain polymers leads to A v~lues considerably exceeding those obtained through experimental measuring of macromolecular dimensions [15, 211. This is also evident from Fig. 2, where parameter ~ is determlned from independent measurements, and not by selecting a scale. It is seen t h a t experimental curves for PS and PAAPM are situated significantly lower than theoretical curves 1 and 2. The formula of V. N. Tsvetkov [23] which was used in [17, 22] "to find values of A for flexible macromolecules is based on the theory of photoelasticity o f Langevin networks. However, the formula is valid only where x ~>15 [23], when deviations of reduced birefringence from a maximum exceed experimenta~ error .to no significant extent. It should be noted that the [n]/[~] ratio in the formula is a function not solely of x, but also of the intrinsic viscosity [~]. This, on the one hand, is at variance with experimental evidence that swelling does not influence [n]/[V], and, on the other hand, means that one must introduce another parameter to determine the rigidity of the naacromolecules. Despite the lack of a theory adequately covering flexible chain macromolecules over the entire range of variation in x, one may still conclude on the basis of the data in Fig. 2 that there is an unambiguous relationship between A and x for flexible (with a Kuhn segment some tens of Angstr5ms in length) maeromolecules with a variety of structures. This conclusion is favoured b y the position on a general curve of a point relating to an analogue of the repeating unit. In addition, while it is true that there is quite a considerable scatter of points around curve 4, there is no tendency of any sort involving a molecular weight reduction in the course of the curve. In our view two considerations emerge from the situation as described above. Firstly, a second parameter must be introduced if one is to describe the behaviour of chains of varying rigidity in terms of a single theory. Secondly, the optical densities of macromolecules of whatever length may be expressed in terms of an optical density per unit chain length, which points to w h a t amount to practically identical structure being possessed by initial polymer and by fragments appearing during degradation of the polymer, so we have what could be regarded as a homologous series of macromolecules of poly-(4,4'-hydroxydiphenylene) l~rromellitie amic acid. Differences in the homologues could stem only from anhydride (or acid) endgroups and from cyclization of some internal amic acid groups at the expense of hydrolysis and slow imidization accompanying a main process o f spontaneous c~egradation of PAAPM [5, 24, 25]. However it readily appears that the latter effects will. have no significant influence on optical anisetropy values, the main contribution being made by stable phenyl rings . . . . . . , • Tranala~d by R. J. A. ~ a Y

656

S. YA. MaGamx e~ a/~

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