Effect of branching on the dependence of the hydrodynamic parameters of macromolecules upon their molecular weights

74

I. YA. PODDUBNYIand V. A. GR~C~NOVSKll

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A. A. BERLIN, Khim. i tekh. polimerov, ~o. 7-8, 139, 1960 A. A. BERLIN and Yo. F. RAZV0DOVSKII, Dokl. Akad. Nauk SSSR 140: 598, 1961 W. ]~ERN and E. BRENNEISEN, J. prakt. Chem. 159: 193, 1941 L P. WIBAU and F. W. BROEKMAN, Rec. tray. chim. 78: 593, 1959 C. F. GIBBS and C. S. MARVEL, J. Amer. Chem. Soc. 56: 725, 1934 D. JERCHEL, H. FISCHER and K. THOMAS, Chem. Ber. 89: 2921, 1956 V. A. I~T.1MOVAand M. D. VITALEqA, Zh. analit, khim. 15: 339, 1950 G. V. KOROLEV, B. P. PAVLOV and A. A. BERIJN, Vysokomol. soyod. 1: 1396, 1959 W. BRAUDE, J. Chem. Sot., 379, 1950 A. A. BERLIN, L. A. BLYUMENFEL'D, M. I. CHER~kSHIN, A. E. KALMANSON and O. G. 8EL'SKAYA, Vysokomol. soyed. 1: 1361, 1959

EFFECT OF BRANCI~ING ON THE DEPENDENCE OF HYDRODYNAMIC PARAMETERS OF MACROMOLF,CULES UPON THEIR MOLF,CULAR WEIGHTS* I. YA. PODDUBNYI and V. A. GRECHANOVSgTT S. V. Lebedev All-Union Scientific Research Institute for Synthetic Rubber (2e~e/~d 6 Aufu~ 1962)

THE hydrodynamic behaviour of macromolecules in dilute solutions is determined by their geometrical parameters--in the first place by the mean square radius of inertia ~ l .

The connection between the dimensions and experimentally determiuA.ble magnitudes, on the one hand, and the intrinsic viscosity [7] and the sedimentation constant ao on the other hand, in Flory's theory [1] are expressed by the equations:

(~)8/2(z+,). [7]=~"

M

'

(~)

~v(1--~p0) ~'~ ~ " P'(~o~) a+')/~" 70"

(~)

]:[ere, M is the molecular weight, qo the viscosity of the solvent, Pc its density, v - - t h e specific partial v o l u m e o f t h e polymer, N - - A v o g a d r o ' s n u m b e r , a n d e a p a r a m e t e r charac terizing t h e t h e r m o d y n a m i c i n t e r a c t i o n in t h e p o l y m e r - s o l v e n t system. Allowance for t h e n o n - G a u s s i a n n a t u r e o f t h e molecular b u n d l e in " g o o d " solvents leads to t h e c i r c u m s t a n c e t h a t ~ a n d P are functions o f e (i.e. the * Vysokomol. ~oyed. 6: No. 1, 64-68, 1964.

Effect of branching of macromoiecules

75

magnitude of the volume effects). The analytical form of the relations • (e) and P (e) in this case is unknown [2]. Equations (1) and (2) are valid for fairly dilute solutions of long monodisperse polymers. Tabing into consideration the dependence of ~ on the molecular weight, Equations (1) and (2) may be rewritten in the following forms: ; (3) so= KsM b ,

(4)

where K ~ , K s, a a n d b a r e parameters which are constant for a given series of poly~aer homologues in a given solvent. (Here and subsequently, it will be a question of sedimentation and diffusion constants extrapolated to infinite dilution). As follows from equations (1) and (2), the m l n l m n m value of a, corresponding 1 to the m a ~ m u m value of b, is achieved in a 0 solvent (8----0), where a ~ b ~ • moreover, the following relation always holds 2 ' a

2 +b= y.

The presence of branching in the macromolecular chains leads to the situation that equatiozm (1) and (2) cease to be obeyed. This is connected with the fact t h a t branching a~octs geometrical dimensions and hydrodynamic prolaertiee di~orently--that is, the geometrical dimensions fall more rapidly than, for example, the ooet~cient of progressive friotion [3] and, consequently, the sedimentation ( ~ o n ) constant, which is connected with it. An ~n~logous situation apparently occurs with respect to the intrinsic viscosity. Under these conditions, equations (3) and (4) formally retain their form, but for branched polymers the exponents have unusual values; for example, in a number of investigations [4, 5] values of a<0-5 were found, although values of b~0-5 have not been recorded in the literature. The influence of the branching of the molecular chain on the nature of the progressive and rotational friction has been st-adied theoretically in a number of papers. The question of the influence of branching on the nature of the viscosity has been studied by Stockmayer and FiTman [6] and by Zimm and Kilh [7] from different angles, and the applicability of equation (2) to branched polymers has been anal ,yzed by Ptitsyn [3]. Thus, a comparative study of the complex of hydrodynamic properties of macromolecules determined by the coet~cients of progressive and rotational friction for linear and branched polymers, particularly in a 0-solvent, may be extremely useful to decide between one point of view and another, and also to check the quantitative conclusions of theory. Nevertheless, the experimental material devoted to this question in the literature is extremely limited. Investigations of this type have been carried out with dextrans [5, 8] but their general

?8

I. YA. PODDUBNYI and V. A. GRICK~OVSKII

disadvantage is a considerable degree of polydispersity of the fractions, and also the lack of clarity in determining the boundary between linear and branched polymers.

to#l'o) to#,;o

o

~ 47

5~

5'5

-

$0109 M

0

8o/og/~ 4

~

Graphs of the sedimentation oonsts~t (a) and the intrinsio viscosity (b) as functions of the • molecular weight: I - - s a m p l e D - l , 9 - - s a m p l e D.2.

These factors greatly hinder the interpretation of the experimental results, The present investigation is devoted to a study of the hydrodynamic parameters of samples of linear and branched c/~-l,4-polybutadiene and a comparison of the experimental results with theoretical conclusions. EXPERIMENTAL

Two samples of c/~.l,4-polybutadiene were used as the subjeet of investigation: a linear sample D . I and a branched sample D-2 obtained b y polymerization on eomplex eatalysts [9, I0]. The polymers were fractionated b y the usual m e t h o d [U]. The q - , d ; t y of the fraotionation was eetimated from an An,dysis of sedimentation d i a g ~ m , . All t h e frac. tions investigated h a d a Gaussiau distribution of molecular weights, i.e. their range, charaoterlzed b y the ratio of t h e weight-average a n d number-average weights .Mw/M,~ did not exceed I . I . The m o l e c u ~ weights of the fractions were ealeulated from Svedberg's formula: M=

ao

RT

D O I--VPo '

where D O is the diffusion coefficient, R is the universal gas constant, and T is the absolute temperature. The m e t h o d of deterrnlnin~ the sedimentation and diffusion constants and extrapolating t h e m to inAnlte dilution has been described previously [12]. The solvent used was a rniTture of hexane a n d beptane (in a 1 : 1 ratio); as has been shown previously [12], for the polymers investigated this rniTture is almost an "ideal" solvent (#.temperature + 5°). The intrinsic viscosities were measured in an Ubbelohde viseometer with a "suspended" level (displacement effects were small a n d were neglected). All the measurements were carried out a t -t-20°. The results which we obtained on t h e sedimentation constants, intrinsic viscosities, a n d molecular weights of the fractions investigated are given in Figures a a n d b. A graphical analysis of the results led to the following equations: sample D - h s0= 3.02 × 1 0 - S M ~ ;

[~7]= 1 . 3 8 x

10~M~";

so----l'80X 10-SM~";

[q]=8-72 X 10-SMHs.

sample I)-2: Here,

so

is expressed in svedbergs, and [q] in I00 emS/g.

Effect of branching of macromolecules

77

DISCUSSION

We may note first of all that the values of the exponents in the equations [~]=fz(M) and 8o=fs(.M ) obtained satisfy the equation (5) of the general theory of solutions of polymers, for both samples D-1 and D-2. However, the value of ~l/sp-z for sample I)-I found from equations (1), (2), (6), and (7)--2.69 × 10e--is far closer to the theoretical value of 2.73 × 106 than that for sample D-2 (2-95 × × 106). The fact mentioned confirms the hypothesis [3, 13] of the non-Gaussian nature of the chain of branched macromolecules even in a 0-solvent. We may consider the question of the absolute values of the power indices in equations (3) and (4) when they are used for branched polymers. Using the data given in Ptitsyn's paper [3], it is easy to show that if a model of a macromolecule with trifunctional branching nodes and fixed values for the length of the units is used, in the case of an "ideal" solvent the magnitude of b in equation (4) must be taken as 0.56. When the functionality of the branching increases, the value of b will rise (for example, for tetrafunctional branches b~0.60, and for a 64-functional model b=0-74). Further, adopting the point of view substantiated by Zimm and Kilb [7] that the ratio between the intrinsic viscosity of a linear polymer [t/]~ and that of a branched polymer [t/]br has the form (for practically any model of branching): where

and once more making use of the data of Ptitsyn's Table 1 [3], we find that for the above-mentioned model of a branched macromolecule the magnitude of a in equation (3) assumes the value of 0-41 (in a 0-solvent). Neglecting the small effects, we find that for the polymer-solvent system investigated (sample D-2) the corresponding values of the exponents in the proposed trifunctional model of branching with fixed values for the lengths of the units will be:

a=0.53--0.09---~0.44,

b=0.48~-0.06~0.54.

This calculation, as we shall see, leads to somewhat high figures for the parameters a and b as compared with those found experimentally. The explanation of this is apparently connected with the possibility of a random distribution of the lengths of the units and also with the presdnce of a certain amount of tetrafunctional branching nodes. On the other hand, a calculation based on the relation [6]: leads to the value a-~--0.23, which is in marked contrast to the experimental value.

78

I. YA. PODDUBNYIand V. A. GRECHANOVSEII

Thus, the branching of macromolecular chains leads to a fairly considerable decrease in the exponent a in equation (3) and correspondingly to an increase in b in equation (4). In other words, when a 0-solvent is used, the separating capacity of the ultracentrifuge rises on passing from linear polymers to branched polymers in approximately the same way as on passing from a "good" solvent to a "poor" solvent, which is extremely important in an investigation of the molecular weight distributions of polymers. At the same time, with a considerable degree of branching the dependence of the characteristic viscosity on the molecular weight is expressed far more feebly. We may mention one more important fact. Since branching, like the v effects, influences the hydrodynamic properties and the dimensions differently, it is possible in principle to obtain information on the degree of branching of macromolecules by measuring any pair of hydrodynamic parameters connected with the coefficients of progressive and rotational friction without comparison with corresponding model linear polymers, which are by no me~-~ always obtainable (such a situation arises in calculating the molecular weight from any pair of hydrodynamic parameters). A slmilar conclusion on the possibility of determining the dimensions of macromolecules, and consequently their degree of branching, has previously been arrived at by Tsvetkov [14]. The authors thank S. A. Fedosova and A. V. Podalinskii for help in the investigation.

CONCLUSIONS (1) Equations for the dependence of the intrinsic viscosity and sedimentation constant on the molecular weight for linear and branched samples of c/a-l,4-polybutadiene in a solvent approTimating to an "ideal" solvent have been established. (2) I t has been shown that an increase in the degree of branching of the macromolecules leads to a weakening of the dependence of the intrinsic viscosity on the molecular weight and to an enhancement of the dependence of the sedimentation constant upon it. With the latter fact is associated an increase in the separating power of the ultracentrifuge. (3) The experimental data obtained satisfactorily agree with theoretical ideas on the connection between the intrinsic viscosity and the mean square radius of inertia of linear and branched macromolecules. (4) The molecular chains of branched polymers have a non-Gaussian nature even in a 0-solvent. Tra~d~ed by B. J. H~z~au REFERENCES

1. P. J. FLORY, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, N.Y., 1953 2. O. B. FITrSYN and Yu. Ye. EIZNER, Zh. tekh. flz. 29: 1117, 1959 3. O. B. PTITSYN, Zh. tekh. fiz. 29: 75, 1959

Sedimentation and diffusion in polymer solutions by polarization interferometry 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

?9

F. P. PRICE, S. G. MARTIN and J. P. BIANCJ~I_,J. Polymer Sci. 22: 41, 1956 K. A. GRANATH, Colloid. Sci. 1B: 308, 1958 H~ 8TOCKMAYER and M. FIXMAN, Ann. N.Y. Acad. Sci. 5?: 334, 1953 B. H. ZIMM and R. N. ~rT.R, J. Polymer Sci. B?: 19, 1959 F. P. 8ENTY and N. N. ~ . L M ~ N e~aJ., J. Polymer SoL 17: 527, 1955 B. D. BAB1TSKII, L. S. BRESL~R and B. A. DOLGOPI~SK, Khlm. nauka i prom. '~: 391, 1957 B. A. DOLGOPLOKK, Ye. N. KROPACHEVA e~ a~., I)okl. Akad. Nauk SSSR 155: 847, 1960 S. Ye. RRESLER, I. Ya. PODDUBNYI and S. Ya. FREN~EL', Zh. tekh. fiz. 28: 1521, 1953 I. Ya. PODDUBNYI, V. A. GRECHANOVS~i~ and M. I. MOSEVITSKII, Vysokomol. soyed. 5: 1049, 1963 A. M. BUECHE, J. Polymer Sci. 41: 549, 1959 V. N. TSVETKOV, Dokl. Akad. Nauk SSSR ?8: 465, 1951

INVESTIGATION OF SEDIMENTATION .AND DIFFUSION IN POLYMER SOLUTIONS BY POLARIZATION I N T E R F F ~ 0 M E T R Y * V. N. TSVETKOV, V. S. SKAZKA, N. A. N u r r r I N and I. B. SI~PANENKO Physical Institute, J.~ai~orad State Univermty

(Reeek,~ 6 A ~

1962)

THE use of polarization interferometry [!] in investigations of the diffusion of polymers in solutions [2] has permitted the concentration of the solutions studied to be lowered to a considerable extent. This fact has played a decisive part in establishing new laws in the phenomena of the ~ o n of flexible chain molecules [3-5]. I n the previous paper [6], it was shown that the same optical method.may be used in principle for studying sedimentation processes in the ultracentrifuge. The present work was devoted to the practical performance of such a type of investigations, which were carried out with fractions of poly-(phenyl methscrylate) (PPMA)+. In order to obtain more complete information on the hydrodynamic properties of the mscromolecules of PPMA, measurements of the viscosity and diffusion of the same samples was carried out in parallel with the serl;mentation investigations. * Vysokomol. soyed. 6: No. I, 69--75, 1964. The sample of poly-(phenyl mothacrylate) was synthesized in the laboratory of M. M. Koton (Institutn of High-molec~lar-weight Compounds, U.S.S.R. Academy of Scieuoe~), to whom the authors exprea their deep gratitud~