Multiphase Polymers - American Chemical Society

27 Brillouin Scattering from Polymer Blends G. D . PATTERSON

Downloaded by HARVARD UNIV on October 21, 2015 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0176.ch027

Bell Laboratories, Murray Hill, NJ 07974

Brillouin scattering measures the velocity and attenuation of hypersonic thermal acoustic phonons. A theory of Brillouin scattering from polymer blends is presented and illustrated qualitatively by several examples. The study of blend com patibility is illustrated for the system PMMA-PVF . The detection of inhomogeneous additives is shown for commer cial PVC film and cellulose acetate, and simultaneous mea surements on separated phases are presented for Mylar film. The main purpose of the paper is to stimulate further work in a potentially promising field. 2

I D r i l l o u i n scattering measures the spectrum attributable to the inter action of light with thermal acoustic phonons ( J ) . The scattered light is shifted i n frequency with a splitting given b y Δ ω —gV(ç)

(1)

where q = (4πη/λ) sin 0/2 is the magnitude of the scattering vector for light of incident vacuum wavelength λ traveling i n a medium of refractive index η and scattered through an angle θ i n the scattering plane, a n d V(q) is the velocity of the phonons with wavevector magnitude q. The shifted peaks have a linewidth given by Γ _ V/2w a

(2)

where a is the phonon attenuation coefficient and Γ is the halfwidth at halfheight measured i n Hertz. Brillouin scattering has now been studied i n a large number of bulk amorphous polymers (2-13) and the behavior of Δ ω and Γ have been determined as a function of temperature. If the incident light is polarized 0-8412-0457-8/79/33-176-529$05.00/0 © 1979American Chemical Society

In Multiphase Polymers; Cooper, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

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MULTIPHASE

POLYMERS

vertically with respect to the scattering plane and the scattered light is observed through an analyzer set vertical, then the Brillouin peaks attributable to the longitudinal phonons are observed. If the analyzer is set horizontal with respect to the scattering plane then the I v spectrum displays the Brillouin peaks attributable to transverse phonons. A spec trum of bisphenol A polycarbonate showing both longitudinal and trans verse Brillouin peaks is presented i n Figure 1. There is also a strong central peak which w i l l not be discussed in this chapter. A t high temperatures, the longitudinal phonon velocity is given by Equation 3 (13): Downloaded by HARVARD UNIV on October 21, 2015 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0176.ch027

H

νι=~(Ύ/ βτ)

(3)

υ2

Ρ

where y = C / C is the ratio of specific heats, /> is the density, and β is the isothermal compressibility. The linewidth is (13) : p

v

τ

Zp

' v . + J V s +

K

i

y

c

Cp

X

;

J I

(4)

where η is the volume viscosity, η is the shear viscosity, and κ is the thermal conductivity. As the fluid is cooled, the relaxation times of the system become comparable with ( Δ ω ι ) " , and the viscoelastic nature of polymer liquids must be taken into account. The longitudinal velocity becomes (13): ν

8

1

where M(q) = K(q) - f 4/SG(q) is the longitudinal modulus, K(q) is the modulus of compression, G(q) is the shear modulus, and M'(q) is the real part of the complex modulus. I n the viscoelastic region, trans verse phonons can propagate with a velocity given by (13):

ν

-(τ-ώ·Γ

(6)

where G is the limiting shear modulus and T is the average shear relaxa tion time. F o r small values of qr, the transverse phonons w i l l be overdamped and only a central peak w i l l be observed. T h e longitudinal linewidth Γι can still be represented as in Equation 4, but all the quanti ties in the brackets must be evaluated at finite q since qr w i l l be signifi cant. The value of Y w i l l go through a maximum when V\qr equals one. The transverse linewidth is given by (13): s

m

x

r

t

— l/2r.


(7)


27.

PATTERSON

531

Brillouin Scattering

!

i

Figure I. Rayleigh-Brillouin spectrum of bisphenol A polycarbonate showing both longitudinal (L) and trans verse (T) Brillouin peaks

As the fluid is cooled further towards the glass transition the phonon velocities reach their limiting frequency values (13) :

ΟΛ

ι/2


(8)

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MULTIPHASE

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where Μ and G are the infinite frequency values of the longitudinal and shear modulus. The longitudinal and transverse linewidths are pre dicted to be negligible since the relaxation times that determine them become very long. However, the observed longitudinal linewidths are much larger than predicted and i n fact are i n the range 100-400 M H z near T . The reason for the excess linewidths is inhomogeneous phonon attenuation attributable to regions of different average density. This effect is usually ignored i n the simple linear theories of Brillouin scattering. In the present chapter we consider the effect of a mixture of species on the Brillouin spectrum. T h e theory w i l l be described and examples w i l l be presented which illustrate the theory. χ

a


g

Theory The linear theory of Brillouin scattering from a viscoelastic medium has been presented by Rytov (14). A summary and discussion of this theory are given i n Ref. 13. In a real experiment, light scattering is observed from a finite scattering volume and at a finite value of q. As a result, the predicted spectrum must be averaged over the scattering vol ume w i t h a characteristic length given by 2m/q. Ii(q,a>) a f

Ρ( ,Μ)Ι^ ω ,Μ) Ρ

}

)Ρ

d dM P

(9)

Jy where P(P,M) is the probability that a volume of radius 2w/q has a density ρ and modulus M , l (q,w p,M) is the spectrum predicted for such a material, and the integration is carried out over the scattering volume. F o r a homogeneous, low-viscosity fluid the probability P(p,M) is essentially a delta function centered at < p > and < M > and the linear result is recovered. However, when V\qr is much greater than one, there should be a thermodynamic distribution of density and modulus for a region of size 2w/q. x

y

• - (- i ^ P ) Thus, for Vflr

« - ( - -) «·

> > 1, the observed spectrum should be of the form:

(„*- .Y 9

v«(^)>-), In Multiphase Polymers; Cooper, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

27.

PATTERSON

533


since I,(q^ MJ Pf

-

δ (ω

2

-

g

(12)

2

near T . The above result seems to adequately describe the observed Brillouin scattering of a homogeneous single-component-polymer fluid near its glass transition (13). If a binary mixture is truly homogeneous, then Equation 11 also should be valid for this case. However, if the two com ponents phase separate, then the distribution function given b y Equation 10 is invalid and further analysis is required. If the microphase regions are small relative to 2π/q, then some addi tional broadening w i l l be observed attributable to greater fluctuations i n in Moc/p. If the moduli of the two phases differ significantly, then as the size of the regions grows, the Brillouin peaks w i l l broaden considerably and w i l l have non-Gaussian shapes. Eventually two sets of Brillouin peaks w i l l be observed, reflecting phase-separated regions with size large relative to 2w/q but still smaller than the scattering volume. F o r large phase-separated regions, the observed spectrum w i l l depend strongly on the part of the sample that is probed. If the two polymers are compatible at high temperatures, Brillouin studies of the quenched glassy materials can reveal how homogeneous the mixtures remain on cooling. Examples of this type of study w i l l be presented. If there are well-defined, phase-separated regions, then the behavior of both phases can be studied simultaneously. This case also w i l l be presented.


g

Experimental Typical Brillouin splittings are i n the range 10 -10 H z . Brillouin linewidths are i n the range 16 -10 H z . Thus, a very high resolution instrument is required. Brillouin scattering is a weak effect so that an intense source of light is needed and a sensitive means of detection. A l l of these criteria have been met, and Brillouin scattering is now a routine tool of experimental physics (13). The light source is an argon ion laser operated i n a single-frequency mode. More than one watt of power can typically be obtained with a laser linewidth of approximately 10 M H z . The incident-beam polariza tion can be continually adjusted with respect to the scattering plane. The frequency distribution of the scattered light is analyzed with a Fabry-Perot interferometer. A detailed discussion of this instrument is given in Ref. 12,13, and 15. F o r the present chapter, it is most important 8

6

10

9


534

MULTIPHASE

POLYMERS

to note the high contrast that can be obtained by operating the interferometer i n the multiple pass mode. The Brillouin peaks i n a polymerblend sample or i n a semicrystalline polymer sample can be more than six orders of magnitude smaller than the strong central peak. Contrasts of greater than 10 are routinely available now for a three-pass system. Thus Brillouin scattering from polymer blends is quite feasible. The scattered light is detected with a photomultiplier tube and photon-counting electronics. The digital spectrum is then recorded with a multichannel analyzer and analyzed with a computer. A typical experimental arrangement is shown i n Figure 2. Translucent bulk samples are not suitable for study, but polymer films are quite acceptable (16). W i t h films care must be taken to properly define the true scattering angle. The use of index-matching fluids is not recommended because they are likely to alter the polymer sample.


7

•

POLARIZATION LASER

SAMPLE

RAYLEIGH HORN

ROTATOR

POLARIZER

FABRY-PEROT INTERFEROMETER

SCAN GENERATOR

COMPUTER

-

MULTICHANNEL ANALYZER

VISUAL DISPLAY

;

PINHOLE

•

FILTER

PHOTON COUNTER

Figure 2.

PHOTO MULTIPLIER TUBE

Light-scattering spectrometer


27.

PATTERSON


535

PMMA


100°C

Figure 3. Brillouin spectrum of a film of pure PMMA at 100°C showing two Fabry-Perot orders

Examples and Discussion Polymer blends of poly (methyl methacrylate) ( P M M A ) and poly( vinylidene fluoride ) ( P V F ) have been shown to be compatible above the melting point of P V F (17). Clear films can be prepared b y rapid quenching from the melt. The Brillouin spectrum of a film of pure P M M A near its glass transition is shown i n Figure 3. The longitudinal peaks are sharp and well resolved. The corresponding spectrum of a blend of 7 5 % by weight P V F w i t h P M M A is shown i n Figure 4. The 2

2

2

Figure 4. Brillouin spectrum of a quenched film of 75% PVF 25% PMMA by weight at 20°C 2


MULTIPHASE

POLYMERS


536


27.

PATTERSON

537


quenched film appears to be homogeneous based on the sharp peaks. Measurements of the Brillouin splitting as a function of temperature have been carried out for several P V F - P M M A blends (18). The quenched films appear amorphous and a single glass transition is observed. Above T , the P V F crystallizes from the mixture and the Brillouin splitting is greater than would be predicted for the amorphous blend. Finally the P V F melts and the spectrum is again characteristic of a homogeneous amorphous phase. The spectra of P M M A , a 4 0 % P V F blend, and pure P V F at 180°C are shown i n Figure 5. The linewidths at 180°C are determined mostly by the dynamic viscosity contributions given i n Equation 4. Many commercial polymer films are blends of different polymers and other additives. The Brillouin spectrum (16) of Vynalloy P V C film is shown in Figure 6. The small peaks at higher Brillouin splitting are attributed to the presence of styrene-acrylonitrile copolymer that is blended into the film. These peaks are absent i n the spectrum of pure P V C . The spectrum (16) of a commercial cellulose acetate film is pre sented i n Figure 7. The lower frequency shoulder is probably caused by the inhomogeneous addition of a plasticizer. Again, pure celluloseacetate films do not display the above feature. The existence of mechani cal inhomogeneities is easily detected using Brillouin scattering. A Brillouin spectrum of commercial Mylar film is shown i n Figure 8. The longitudinal ( L ) and transverse ( Τ ) Brillouin peaks are easily seen. 2

g

2

2

2


2

ir PVC!|

Figure 6.

Brillouin spectrum of Vyn alloy PVC film


538

MULTIPHASE

POLYMERS


CA

Figure 7. Brillouin spectrum of a commercial cellulose-acetate film These are the only peaks seen i n quenched amorphous poly (ethylene terephthalate) ( P E T ) films (19). The third set of peaks was a mystery until the Brillouin spectrum was examined using a larger free-spectral range. The result is shown i n Figure 9. T h e transverse peaks are now hidden i n the wings of the central peak. The third set of peaks has a Brillouin splitting almost twice that of the normal longitudinal peaks. This feature is attributable to the presence of crystals of the cyclic trimer of P E T on the surface of the Mylar film. T h e Brillouin splitting of the crystals is plotted as a function of temperature i n Figure 10.

MYLAR

Figure 8. Brillouin spectrum of commercial Myhr film showing longitudinal (L), transverse (T), and unknown (?) Brillouin

peaks



27.

539


PATTERSON

Figure 9. Brillouin spectrum of commercial Myhr film at hrger free-spectral range than in Figure 8 Commercial M y l a r film is partially crystalline and mechanically anisotropic. The longitudinal Brillouin splitting is observed to be greater than that for quenched amorphous P E T and to be different for films oriented parallel and perpendicular to the film-roll edge. Longitudinal Brillouin splittings for Mylar and for amorphous P E T are plotted vs. temperature in Figure 11. The apparent value of T also is elevated for the Mylar film from 70° to 80°C. Measurement of the Brillouin spectrum of polymer films is now straightforward using multiple-pass Fabry—Perot interferometry. The use of Brillouin scattering to study polymer blends as films should be a very fruitful area for further study. g

20

40

60

80

Ï0Ô

Ï2Ô

140

160

Ï8Ô

200

T°C

Figure 10. Brillouin splitting Αω vs. temperature for cyclic trimer PET cry stab on the surface of Myhr film ι


540

MULTIPHASE

POLYMERS

PET - At received II -At received I » Amorphous


200-

»

«

20

1

40

«

1

60

80

1

100

I

I

t

120

140

160

T°C

Figure 11. Brillouin splittings Δω vs. temperature for amorphous PET, Mylar film oriented parallel to the film-roll edge and perpendicular to the film edge ι

Literature Cited

RECEIVED

1. Brillouin, L., Ann. Phys. (Paris) (1922) 17, 88. 2. Peticolas, W. L., Stegeman, G. I. Α., Stoidreff, B. P., Phys. Rev. Lett. (1967) 18, 1130. 3. Friedman, Ε. Α., Ritger, A . J., Andrews, R. D., J. Appl. Phys. (1969) 40, 4243. 4. Romberger, A . B., Eastman, D. P., Hunt, J. L., J. Chem. Phys. (1969) 51, 3723. 5. Wang, C . H., Huang, Y. Y., J. Chem. Phys. (1976) 64, 4847. 6. Coakley, R. W., Mitchell, R. S., Stevens, J. R., Hunt, J. L., J. Appl. Phys. (1976) 47, 4271. 7. Brody, E. M., Lubell, C. J., Beatty, C. L., J. Polym. Sci., Polym. Phys. Ed. (1975) 13, 295. 8. Jackson, D. A., Pentecost, Η. Τ. Α., Powles, J. G., Mol. Phys. (1972) 23, 425. 9. Lindsay, S. M., Hartley, A . J., Shepherd, I. W., Polymer (1976) 17, 501. 10. Mitchell, R. S., Guillet, J. E., J. Polym. Sci., Polym. Phys. Ed. (1974) 12, 713. 11. Patterson, G. D., J. Polym. Sci., Polym. Phys. Ed. (1976) 14, 741. 12. Patterson, G. D., J. Macromol. Sci., Phys. (1977) B13, 647. 13. Patterson, G. D., "Methods of Experimental Physics: Polymer Physics," R. Fava, Ed., Academic, New York, 1979. 14. Rytov, S. M., Sov. Phys. JETP, Engl. Transl. (1970) 31, 1163. 15. Patterson, G. D., ADV. IN CHEM. SER. (1974) 174. 16. Patterson, G. D., J. Polym. Sci., Polym. Phys. Ed. (1976) 14, 143. 17. Nishi, T., Wang, T. T., Macromolecules (1975) 8, 909. 18. Patterson, G. D., Nishi, T., Wang, T. T., Macromolecules (1976) 9, 603. 19. Patterson, G. D., J. Polym. Sci., Polym. Phys. Ed. (1976) 14, 1909. April 14, 1978.


Multiphase Polymers - American Chemical Society

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