Acta Polymcria 36 (1965) Xr. 12

652 BERGER and STRAUBE: Ultrasonic attenuation of polymer solutions. I

removing of amorphous material in the second process (28% increase of crystallinity degree for t h e isotropic sample and 32% for t h e oriented one).

cracks in direction of orientation a n d formation of sepa- ra te microfibres. The morphology of isotactic polypropylene effects its thermal stability.

4. Conclusions

The oxidation of isotactic polypropylene films occurs in the amorphous regions. These regions are situated, however, in different way in an oriented sample before and after annealing than in an isotropic one. This causes different ra te of t h e oxidation connected with t h e diffu- sion of oxygen a n d nitric acid into t h e films. The reorgani- zation of crystalline and amorphous regions in oriented samples during annealing leads t o t h e creation of per- pendicular continuous regions of amorphous material and t o t h e formation of cracks perpendicular t o t h e orien- tation direction in t h e thermo-oxidation process. The rate of polymer chain scission is higher for t h e oriented sample with fixed ends (no relaxation) than for t h e oriented sample with free ends. Etching leads t o the creation of

References

[I] MUCHA, M., and KRYSZEWSKI, M.: Colloid & Polymer Sci.

[2] MUCHA, M., and KRYSZEWSKI, M.: IUPAC International

[3] MUCHA, M.: J. Polymer Sci., Polymer Symposia 69 (1981)

141 MUCHA, M.: Colloid & Polymer Sci. 269 (1981) 984. [5] BONART, R., and HOSEMANN, R.: Kol1oid.-Z. 186 (1962) 16. [6] FISCHER, E. W., and GODDAR, H.: J. Polymer Sci., Part C

[7] PETEELIN, A.: J. Polymer Sci., Part C 9 (1965) 61. 181 FISCHER, E. W., GODDAR, H., and PIESCHEK, W.: J.

Polymer Sci., Polymer Symposia 82 (1971) 149. [9] BALT~ CALLEJA, F. J., and PETERLIN, A.: Makromol.

Chemie 141 (1971) 91. [I03 KRYSZEWSKI, M., and PAKULA, T.: Makromol. Chemie,

Suppl. 4 (1981) 207. Received October 3, 1984

268 (1980) 743.

Symposium on Macromolecules, 1980, Vol. 3, p. 329.

79.

16 (1969) 4405.

Ultrasonic attenuation of polymer solutions 1. Dilute solutions

H.-R. BERGER~) and E. STRAUBE

Technische Hochschule ,,Carl Schorlemmer“, Sektion Physik, DDR-4200 Merseburg

The ultrasonic attenuation in dilute polymer solutions is treated in the framework of the KIRKWOOD diffusion equa- tion. A ROUSE-ZIMM type relaxation behaviour of the ultrasonic attenuation results from the calculations, and a rela- tionship between the intrinsic shear and bulk viscosity is derived.

Ultraschalldam.pfung in Polymerlosungen. I . Verdiinnte Liisungen Die Ultraschalldampfung in einer verdunnten Polymerlosung Vird im Rahmen der KIRKWOODschen Diffusionsglei- chung untersucht. Eine Frequenzabhangigkeit vom ROUSE-ZIMM-TY~ und eine Relation zwischen Scher- und Volu- menviskositat werden erhalten.

3amyxanue ynampaaeyxa e n o n w p n m pacmeopax. I . Pa36aenennw pacmeopu B a ~ y x a ~ ~ e y n b ~ p a a ~ y ~ a B paa6aBneHHbl.X n0naslepHbl.x pacmopax AaysaeTcR B p a m a x A H @ @ Y ~ A O H H O ~ O ypanae- HAR KAPHBYRA. 06beMHOa BRIKOCTRMU.

ITOJIYqeHH 9aCTOTH;LII IaBHCIIMOCTb TAna P A Y B A - q H M M A U COOTHOIUeHHe MeHcAy CABUrOBOa II

1. Zntroduction

During the last years, increasing interest has been given to the investigation of dynamic properties of polymer solutions. Among other experimental methods ultrasonic attenuation measurements are used to obtain information about the mole- cular mobility of such polymer systems [I-31. For some poly- mersolvent systems a ROUSE-ZIMM type behaviour of the ultrasonic excess attenuation a divided by the square of thc frequency ws2 is observed [2, 41 (excess attenuation means that. the attenuation by the solvent is substracted). The simplest explanation of this bebaviour is obtained by substituting the ROUSE-ZIMM results for the frequency dependent viscosity 153 into the attenuation formula of the classical fluid continuum theory (e.g. [S]). However, additional assumptions are necessary to treat the problem of the “bulk viscosity”, which appears in this ormula and which is often used as an adjustable parameter [2].

l) Present address: Akademie der Wissenschaften der DDR, Institut fur Mechanik, DDR-9010 Karl-Marx-Stadt, PSF 408

In a microscopic approach, GOTLIB and SALICHOY [7] explained the ROUSE-ZIMM type attenuation behaviour in concentrated solutions on the basis of a temporary polymer network. But the assumption of (temporary) fixed network knots cannot be maintained for solutions of lower concentra- tions. Another crucial point in this theory is the introduction of the “local viscosity”, whose molecular nature is not yet clear.

An essential progress from a theoretical point of view is made by the theory of METIU and FREED [8], who obtained the intrinsic bulk viscosity as minus 1/3 of the intrinsic shear vis- cosity. But a disadvantage of this paper is the rather complex formalism. The aim of the present work is t o calculate the ultrasonic attenuation in the context of the well-established semimicroscopic picture of the bead-spring model. Using the standard KIRKWOOD diffusion equation and the normal mode concept, we explain the ROUSE-ZIMM type attenuation be- haviour. The result for the intrinsic hulk viscosity of METIU and FREED is confirmed. In a subsequelit paper concentrated poly- mer solutions will be considered.

BERGER and STRAUBE: Ultrasonic attenuation of polymer solutions. I

Acta Polymerica 36 (1985) Nr. 12

653

2. Theoretical basis 3. Calculation of the ultrasonic attenuation

We consider a polymer molecule containing N segments zi = (xi, yi, z i ) of the mean statistical length b in a viscous medium of the viscosity vo. The neighbouring segments are coupled by harmonic springs of the constant x = 3kBT/b2 (kBT - Boltzmann factor) and each segment acts as a point source of friction (described by the coefficient 5) in the unperturbed external velocity field 5;. We describe the time 5volution of the segment distribution function P(&, . . ., R N , t ) by the generalized diffusion equation [9] :

The ultrasonic attenuation is given by [6]

(7)

where e is the density of the solvent, c, the sound velocity and the mean dissipated energy per time. The averages are taken over the ensemble of polymer segments, the phase angles and one period of the sound wave. In our model, the mean dissipated energy per time is determined by the viscous forces between the polymer segments and the solvent ( n - number of chains per volume):

where V j is the gradient vector and H i k denotes the pre- averaged hydrodynamic interaction matrix 1

(9) = -n (Bjijo> (8)

Substituting eqs. ( 3 ) and (5) into eq. (8) and transforming (2) into normal coordinates yields 1 5

( i / f t i k ) (1 - 6jk) * 1

The force 3;Sk exerted on the fluid by the segments is the sum of the harmonic nearest-neighbour spring forces and a thermodynamic force caused by the heat bath formed by the solvent:

A is the commonly used nearest-neighbour interaction matrix. In eq. (3) all contributions from external potential fields and excluded-volume interactions are neglected.

Assuming a propagation of a planar sound wave in the 2-direction with the frequency w, and the wavelength 1, the unperturbed velocity dio a t the location of the j th segment is described by

1 2n 1 (9) = n - cos w,t cos y e x [z p i ( X t ) - kBT . ( 9 )

i

The mean square displacement (X i z ) is obtained from eq. (6) by multiplying i t with X i and integrating by parts over the whole configuration space of the polymer segments. A straightforward calculation leads to the following equation for (Xi”, if the contribution from ( X i ) is assumed to be zero :

a 4n - at (q) = - 1 uo cos w,t . cos p(Xt)

z? = uo cos w,t. sin (r xi + y ) , 0, 0) . ( 4 )

In eq. ( 4 ) the random location of the chains is taken into

sion of the polymer is small compared with the wavelength R we get the expansion

This equation is easily solved with the approximation that the amplitude of the ultrasonic waves so is small compared with the wavelength 1:

(X i2 ) = - - 4n - cos p - sln wd

( account by a random phase angle y [7]. Since the dimen- kBT SO kBT .

Pix 1 %Pi

Following the usual procedure [S] we transform the coordinates Bi into normal coordinates $j = ( X i , Yj, Z i ) by an orthogonal transformation. Suppose tha t the unper- turbed velocity Tj? is given by eq. (5), then eq. (1) reduces t o (substituting eq. ( 3 ) )

where pivi = li and vo = sow,. In the stationary state the last term on the right-hand side goes to zero. We substitute eq. (11) into eq. (9) and carry out the averages over the

2n ap . ap phase angles and one period of the sound wave. Together with eq. (7) this leads t o the final result

2n aP = 7 [ - vo cos w,t * cos y . P

80 cos * x. - cos w,t - vo cos wd * sln ’?’ - -- il 3 ax, ax,

k T 5 1 x l . + f Vi(ZiP) + JL VjVi2P

where Vj is now the differential operator with respect to $ and pi, vj, li are the eigenvalues of the matrices A, H , H A , respectively. Eq. (6) together with the transformed

where the relaxation times t i are the same as those known from the ROUSE-ZIMM theory

5 eq. ( 3 ) are the basis for the further calculations of ultrasonic attenuation. - 2%1;

t. - -

Acta Polymeric8 36 (1985) Nr. 12

654 B~~CHTEMANN, SCHULZ und TAUER: Oberflachenstruktur von PVC( E)-Latexteilchen

A formula analogous to eq. (12) was derived by GOTLIB and SALICHOV [7] in the framework of a network model for concentrated solutions.

4. Discussion

Evidently, the frequency behaviour of the ultrasonic attenuation from eq. (12) is of ROUSE-ZIMY type. Hence, we can substitute the result for the frequency dependent intrinsic viscosity [r](w8)] into eq. (12) and get

t ha t this behaviour may be closely connected with local conformational rearrangements of the segments of the polymers. With our present work we want to clarify by the help of a transparent approach within the framework of well settled polymer solution dynamics what contributions to the ultrasonic attenuation are to be expected from viscous losses, since a complete and consistent picture of the ul- trasonic attenuation of polymer solution is still lacking. We hope tha t a more complete theory can be built on the basis presented in this paper.

_-- a C ' r l O (14) Acknowledgement - [rl(w8)i W8Z 2C83@

We are grateful t o Professor G. HELMIS for helpful (c - concentration of the polymer solution). Since we have used the condition tha t the sound wavelength is much greater than the dimension of the macromolecule (5. eq. ( 5 ) ) , we can compare our relation with the result of the classical fluid continuum theory [6]

discussions and stimulating interest.

Referenres [ I ] BELL, W., NORTH, A. M., PETHRICK, R. A., und POH, R. T.:

J. Cliem. Soc.. Farad. Trans. I1 76 (1979) 1115; BELL, W., DALY, J., NORTH, A. M., and PETHRICK, R. A.: ibid. 76 (1979) 1452; DUNBAR, H., NORTH, A. M., PETHRICK, R. A., and STEINHAUER, D. B.: ibid. 71 (1975) 1478.

121 HAUPTMANN, P.: Dissertation B. TH Merseburiz', 1979. (I5)

q,, denotes the bulk viscosity of the solution. It is seen from the comparison with eq. (14) t ha t the intrinsic bulk viscosity is minus 1/3 of the shear viscosity. This confirms the earlier results by METIU and FREED [8 ] .

There are still some remarks to be made. We consider in our work only viscous contributions to the ultrasonic attenuation. However, additional phenomena, caused by the direct coupling of the temperature and pressure fields of the sound wave with the degrees of freedom of the chain, have to be taken into consideration. These may substantially influence the attenuation and change the type of the relaxation from the "normal mode" t o the often observed single or double DEBYE-type mode [I, 3, lo ] . Attempts by FROLICH e t al. [3] and ALIG [ lo] have shown

[3j FROELICH, B., JASSE, B., NOEL, .C., and M O N N E ~ E , L.:

[4] ALIG, I., FELLER, K.-H., and SAUBERLICH, R.: Acta J. Chem. SOC., Farad. Trans. I1 74 (1978) 445.

Polvmerica 31 (1980) 316. [5] RO~TSE, P. E.: J. Chem. Phys. 21 (1953) 1272; ZIMM, B. H.:

ibid. 24 (19561 269. [6] LANDAU,' L. D., and LIFSCHITZ, E. M. : Hydrodynamik.

[7] GOTLIB, J. J., and SALICHOV, K. M.: AkustiE. 2. 9 (1963)

[8] METIU, H., and FREED, K. P.: J. Cheni. Phys. 67 (1977)

[9] YAMAKAWA, H.: Modern Theory of Polymer Solutions.

Berlin: Akademie-Verlag 1966.

301.

3303.

New York: Harper & Row 1971. [ l o ] ALIG, I.: Dissertation A, TH Merseburg, 1983.

Received September 10, 1984

Elektronenmikroskopische Untersuchungen zur Oberflachenstruktur von PVC(E)-Latexteilchen mittels Etzung in einer Glimmentladung A. BUCHTEMANN, E. SCWLZ und K. TAUER

Akademie der Wissenschaften der DDR, Institut fur Polymerenchemie ,,Erich Correns", DDR-1530 Teltow-Seehof

PVC(E)-Latexproben aus der Normal- und der Saatpolymerisation wurden in einer Glimmentladung unter milden Bedingungen bei zwei verschiedenen Temperaturen geatzt. Die geatzten Teilchen weisen in Abhangigkeit von den experimentellen Bedingungen verschieden deutlich ausgepragte Struktureinheiten von weniger als 10 nm bis ca. 20 nm GroBe auf. Diese Untereinheiten werden als Bereiche hoherer Ordnung innerhalb der PVC(E)-Teilchen diskutiert.

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Electron microscopic investigation of the surface structure of PVC latex particles by glow discharge etching PVC(E) latex samples of polymers obtained by standard and seed polymerization were subjected to glow discharge etching under mild conditions a t two different temperatures. Depending on the experimental conditions the etched particles reveal more or less distinctly differentiate dstructural units extending from less than 10 nm to about 20 nm in size. These subunits are considered as regions of higher order within the particles observed.

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