Quantitative Evaluation of the Dynamic Mechanical Properties of

6 Quantitative Evaluation of the Dynamic Mechanical Properties of Multiphase Polymer Systems

Downloaded by UNIV LAVAL on October 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0142.ch006

LOTHAR BOHN Hoechst AG, Frankfurt/Main-Höchst, West Germany

This work demonstrates that it is possible to obtain quantitative information about phase volumes and phase structure of multiphase polymer systems from the findings from dynamic mechanical tests using existing theories of the elastic moduli of composites. Furthermore, some special features of the loss spectra of two-phase systems are discussed. Variation in the volume of the dispersed rubbery phase affects not only the magnitude of the loss peak but also its temperature position. A crosslinked and well grafted rubber phase within a rigid matrix undergoes appreciable dilatation on cooling; this causes a shift in the rubber glass transition to lower temperatures.

D

ynamic mechanical characteristics, mostly i n the form of the temperature response of shear or Young's modulus and mechanical loss, have been used w i t h considerable success for the analysis of multiphase polymer systems. In many cases, however, the results were evaluated rather qualitatively. One purpose of this report is to demonstrate that it is possible to get quantitative information on phase volumes a n d phase structure b y using existing theories of elastic moduli of composite materials. Furthermore, some special anomalies of the dynamic mechanical behavior of two-phase systems having a rubbery phase dispersed w i t h i n a rigid matrix are discussed; these anomalies arise from the energy distribution a n d from mechanical interactions between the phases. Analysis Using Young's or Shear Moduli Only

1

Theory. Basic theories for the prediction of the modulus of a composite from those of the components were derived b y , for example, Hashin i n 1955 ( I ) , Kerner i n 1956 ( 2 ) , a n d v a n der Poel i n 1958 ( 3 ) . Takayanagi (4, 5 ) , and Fujino et al. (6) developed a very promising a n d instructive model theory w h i c h includes calculation of the loss spectra of composites, and it may easily be extended to anisotropic morphologies. Furthermore, Nielsen a n d coworkers may be cited for fundamental theoretical and experimental contributions (7, 8, 9 , 1 0 ) . 66

In Copolymers, Polyblends, and Composites; Platzer, N.; Advances in Chemistry; American Chemical Society: Washington, DC, 1975.

6.

Dynamic

BOHN

Mechanical

67

Properties


vol.-Vo soft phase

0

20 —*

40

60

vol.-Vo hard

60

100

phase

Figure 1. Modulus Ε of two-phase systems as a function of the volume fraction of the dispersed phase and the ratio of the hard phase modulus (Ei,) to the soft phase modulus (E ) s

According to the theories of K: Kerner (2), P: van der Poel (3), and T: Takayanagi (4. 5)

Figure 1 represents the predictions of the composite modulus from the components according to the different theories. T h e lower part of the figure depicts the reinforcement of a rubbery matrix by incorporation of isotropic rigid particles. T h e increase i n the composite modulus Ε is given i n relation to the soft matrix phase modulus E (at the right side) as a function of the volume content of rigid filler with hard phase modulus E . T h e parameter is the ratio of the moduli of the rigid and rubbery components, E /E . Takayanagi's approximation ( T ) as well as the unmodified Kerner equation give values that are much too low for this phase morphology, especially at high 8

h

h

8


68

COPOLYMERS,

POLYBLENDS,

A N D COMPOSITES

E /E ratios. O n the other hand, calculations based on van der P o d ' s work ( P ) agree very w e l l with experimental findings (11). Unfortunately, the v a n der Poel theory requires the evaluation of a set of eight linear equations, and it can be applied only i n tabulated form. The upper part of Figure 1 depicts the reduction of the modulus of the rigid phase E/E by incorporation of a soft rubbery phase, again w i t h E /E as the parameter. T h e three theories agree well i n this reverse phase position (see the curve for E /E = 1 0 0 ) . T h e composite moduli can therefore be calculated easily by one of the well known equations from Takayanagi's ap proximative model theory ( E q u a t i o n 1 ) or from Kerner's theory ( Equation 2 ). h

s

h

h

h

s

EH


Ε

When E » h

-

+

1

E:

n

(i -

VT,

(D ft)

a

h

Ε

Eh ~ Gh _ Ë~ ~ G~ ~ h

/

V

ι E

When E »

8

E or G » 8

h

-,

= 1

+

1 -

VTs

15(1 - v ) φ fc

,

(7 -

5ν ) φ φ±^ Λ

Λ

(la)

^ T =

8

\^ »

-

l)

/

l ) ^+ 15(1 -

/o\ VA)

G: s

W

7

-100

0

100 °C

Figure 2. Dynamic Young's modulus E ' of polystyrene (PS), high impact polystyrene (HIPS), separated gel, and crosslinked polybutadiene rubber. Data from Ref. 17.


^ '

6.

Ε ξ,

0,8

Theory

0,6

OA0 Downloaded by UNIV LAVAL on October 2, 2015 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1975-0142.ch006

69

Dynamic Mechanical Properties

BOHN

20

10

Gel

^

G

7.

30

Figure 3. Correlation between modulus reduction and experimen tally determined gel content

Volume

=

1

+

15(1

-

v„) φ s

^ (7 - 5ν ) φ Λ

Λ

^

1

+1.9

(ι -

φ )

(2a)

In these equations, the subscripts h and s refer to the hard continuous phase and the soft rubbery phase, respectively, Ε = Young's modulus, G = shear modulus, v = Poisson's ratio ( = 0.35 for polystyrene and most rigid poly mers), and φ and /, = volume fractions of the components. If the modulus of a dispersed rubbery component is only 1/1000 that of the surrounding rigid matrix, an air-filled structure is approximated. The two experimental points for foamed polypropylene i n Figure 1 fit fairly well into the theoretical curves. It is apparent from Figure 1 that the modulus of a composite of known volume composition reflects clearly the phase distribution, i.e., it indicates w h i c h component forms the continuous phase. The moduli may differ up to two decades after reversal of the continuous and the dispersed phases when the ratio of the component moduli is about 1000:1. It should be pointed out that the relations plotted i n Figure 1 apply only for ideal isotropic morphologies. Deviations are an indication of anisotropy, of anomalous structures like interlocking networks, or of an intermediate state of phase reversion. Thus, the statement by some authors (12, 13) that the theory d i d not correlate with their experiments is no argument against the theory, but rather against its application to composites of unknown structure. The morphologies should have been determined by, for example, microscopic or electron microscopic methods. The situation with block copolymers is highly complex. A change in composition, usually by variation of the block length ratio of the two different species, may induce not only a phase reversal but also a fundamental change i n the basic morphology to some rodlike or layer structures of high anisotropy. It is not surprising that Kerner's theory was not applicable to such a system (14). Experimental Examples. A n example may be given of the applicability of the forementioned theories to a complex but well defined morphology. It is well known that in commercial high impact polystyrene ( H I P S ) the dispersed rubber phase, the gel, is filled with up to 7 5 % occluded polystyrene (PS) (15, 16). In principle, we have a three-phase system! Keskkula and Turley (17) succeeded i n isolating the gel and determining its dynamic mechanical h

s



70

COPOLYMERS,

Figure 4.

POLYBLENDS,

A N D COMPOSITES

High impact PVC

a. Dynamic Young's modulus E ' and mechanical loss factor d of an impact modifier containing 47 wt % styrene-butadiene rubber ( ) and of the pure rigid graft phase ( ) b. Dynamic characteristics of PVC ( ) and of impact PVC containing 15 wt % modifier ( )

properties i n addition to those of the original H I P S and the crosslinked rubber (Figure 2 ) . They reported that the gel constituted 19-20 v o l % of the H I P S , and that there was about 66 v o l % occluded PS within the gel. W i t h E /E — 1000 (modulus A/modulus D ) , the experimentally determined reinforcement E/E = 32 (modulus C/modulus D ) is i n good agreement w i t h Figure 1. T h e same is true for another investigation of a H I P S gel by Wagner and Robeson (18). T h e experimentally obtained value for the reduction of the modulus of pure PS (at A ) to the value of H I P S (at B ) by the incorporation of 19-20 vol % gel phase is E/E — 0.75. This result fits well into the curve with E /E = 30 (moduli at A and C i n Figure 2) i n Figure 1. A fairly good correlation between modulus reduction and gel volume is demonstrated i n Figure 3 for a number of different H I P S and acrylonitrilebutadiene-styrene ( A B S ) materials. T h e gel volume was determined b y the usual high speed centrifugation of the methyl ethyl ketone-acetone solution. U s i n g the modulus drop through the rubber phase transition as an indi cation of phase volume means approximating the real modulus of the rigid phase at A (Figure 2) b y the modulus at A ' of the composite i n its glassy state (19, 20, 21). T h e greater the temperature dependence of the rigid phase modulus and thus the larger the difference between the moduli at A and A ' , the greater the deviation from the exact calculation (see Figure 4 for an ex ample). Figure 4a is characteristic of the curve for an impact modifier for h

s

s

h


h

s

6.

Dynamic

BOHN

Mechanical

71

Properties

poly (vinyl chloride) ( P V C ) containing about 5 0 % styrene-butadiene rubber. Here the use of the modulus at A ' instead of that at A has no appreciable effect. Figure 4b depicts the mechanical properties of a high impact P V C that con tains 15 w t % modifier. T h e modulus of pure, unmodified P V C has a strong temperature dependence just through the transition of the rubber component at — 40°C. Whereas the use of the exact modulus of the rigid phase at A i n comparison with the composite modulus at Β gives, w i t h a reduction E/E = 0.88, the right rubber concentration of 9-10 vol % (Figure 1 ) , the application of the modulus drop method (i.e., the use of the m u c h higher modulus at A ' for the rigid phase) results i n a completely wrong rubber volume w h i c h is about three times too high! h


Special Effects in the Dynamic Mechanical Characteristics of Systems Having a Rubbery Phase Dispersed within a Rigid Matrix Effect of the Rubber Content. O n deforming a composite that has a dispersed rubbery phase i n a rigid matrix, the magnitude of strain i n the rubber w i l l be bound to that i n the surrounding rigid matrix. F o r this reason, the distribution of stored energy between the rubbery and rigid phases depends to a first approximation on the ratio of the moduli of the soft and hard com ponents, E /E , and of course on the composition by volume. In going through the glass transition range of the rubber, which covers some 2 0 - 3 0 ° C , this s

h

Rubber

0

>

10 JO

Matrix

Temperature

Figure 5. Schematic: effect of the volume fraction of the dispersed rubbery phase on Ε', E", and tan δ of a twophase system


72

COPOLYMERS,


IbC

-100

-SO

0

POLYBLENDS,

50

A N D COMPOSITES

100

Figure 6. Dynamic characteristics of three ABS samples with different volume fractions of rubbery phase Arrows indicate the rubber transition in the modulus curves

modulus ratio E /E ranges from 1 to about 0.001 which indicates that less and less energy is taken u p b y the softening phase compared w i t h the rigid matrix. A t some temperature within the softening range of the rubber, the energy stored becomes negligible, i.e., a rubber particle acts like an empty hole. The composite modulus then remains constant at some level determined by the rubber phase volume (cf. Figure 1 ) ; the further characteristic of the dispersed phase as well as its absorption capacity are no longer reflected in the composite properties. The schematic representatition i n Figure 5 indicates the consequences for the dynamic mechanical method of analysis. T h e well known increase i n the modulus drop a n d i n the magnitude of tan δ or E" with increasing rubber content should be accompanied by a shift i n the position of tan δ to higher temperatures. T h e E" peak temperature at first increases like that of tan δ, then it may remain constant or even decrease again at higher rubber contents. The E" of rubber has a lower peak temperature than the dispersed rubber in the composite i n contrast to the behavior of tan δ. In the matrix transition range, tan δ—something like a reduced absorption of the composite—should remain unaffected both i n magnitude and position, whereas the E" peak should decrease i n magnitude and shift slightly toward higher temperatures with increasing rubber content. In Figure 6, the sharp cutting of the rubber transition in the modulus curves is accompanied by the shift i n the tgδ or E " peak to higher tempera tures. Quite similar behavior was reported for block copolymers with u p to 4 0 % polybutadiene (22, 23). I n Figure 7, the shift i n the matrix E" peak to s

h



6.

73

Dynamic Mechanical Properties

BOHN

higher temperatures w i t h increasing soft phase volume is apparent. F o r addi tional examples, see Figures 8 and 10 of Ref. 4. D y n a m i c mechanical measurements may be represented by modulus and loss modulus (E' and E" or G ' and G " ) curves or b y modulus and tg8 = E" E' or G " / G ' curves. B y incor porating a dispersed component which exhibits no transition i n the temperature range under study, the tg8 curve of the matrix remains practically unaffected. This was observed not only i n systems diluted b y holes (foamed material) (24) and i n those reinforced b y fillers ( I I , 1 2 ) , but also i n composites with a dis persed rubbery component i n the temperature range far enough above the softening of the rubber. F o r this reason, the tg8 characteristic should be preferred to the loss modulus curves i n analyzing a multicomponent system. Effect of Mechanical Interaction. It was shown both theoretically (25, 26, 27) and experimentally (28) that, on cooling a composite having a dis persed rubbery phase to temperatures well below the matrix glass transition, the rubber undergoes appreciable dilatation attributable to the expansion mis match. I n compounds with sufficient adhesion between the phases and crosslinked rubber, this dilatation is clearly reflected by a shift i n the rubber glass transition to lower temperatures (29, 30). Figure 8 exemplifies the A B S system (29). W e l l dispersed but ungrafted rubber particles, w h i c h are expected to give insufficient adhesion between the phases, cause a rubber transition 12°C higher than i n a well grafted latex rubber exhibiting the dilatation shift to lower temperatures. Additional examples are found i n the literature (31, 32).

ST A N NBR

CO Lu

ζ

>

a

9 io

160

1 4 0 -120 -100

80

-60

-40

-20

0

TEMPERATURE

20

40

60

80

100

120

140

( C) e

Figure 7. Shear modulus G ' and loss modulus G " of [nitrile-butadiene rubber (NBR)~\-[styrene-acrylonitrile (SAN)] copolymer blends. Data from Ref. 4. NBR (vol %), 36 and 51 respectively


74

COPOLYMERS,

ΙΟ 71

-150


•

I

-50 •

•

•

•

I

A N D COMPOSITES

°C •

•

ι

•

E-

I F

^

-100

1—ι

POLYBLENDS,

—

-150

-100

-50

°C

Angewandte Makromolekulare Chemie

Figure 8. Dynamic Young's modulus E ' and loss factor d of two ABS materials containing grafted and ungrafted latex rubber respectively (29) Conclusions The modulus functions can be quantitatively evaluated to obtain informa tion on the phase structure of composites. Consequently, the complex but well defined three-phase, double-emulsion morphology of high impact poly styrene can be described as agreeing w e l l w i t h theory i n a l l essential features. Evaluation of the modulus drop disregards the temperature dependence of the rigid phase of composite modulus through the transition range. Therefore caution is recommended i n drawing quantitative conclusions by this method. The mechanism of energy distribution between the phases has some con sequences for two-phase systems w i t h dispersed rubber within a rigid matrix. Not only the magnitudes but also the positions of the peaks of tan 8 and E " are dependent on the rubber phase volume (Figure 5 ) . A shift to higher temperature with increasing rubber content need not be caused b y an increase of Τ resulting from crosslinking (18, 33). T h e higher F" peak temperature of the matrix transition of an A B S polymer, compared w i t h the peak position i n the unmodified matrix material, does not necessarily indicate a higher matrix Τ i n the A B S polymer caused b y stresses (33). The nature (e.g., the softening range) of a hard occlusion i n the interior of a rubber particle can never be determined b y dynamic mechanical methods. A n y dispersed phase can only be characterized i n the region of higher modulus. Its l o w modulus or higher temperature properties are completely lost. Thus, the relaxation spectrum of a composite is generally not a superposition of the component spectra. g

g


6.

BOHN

Dynamic

Mechanical

75

Properties

Semi-empirical rules, w h i c h correlate the static glass transition tempera ture T from differential thermal analysis or dilatometry with the dynamic T taken from the tan 8 or E" peak, may be used with caution in analyzing twophase systems with a dispersed rubbery phase. T h e dynamic T depends on the rubber phase volume, and it may be shifted further toward lower tempera ture for effectively crosslinked and grafted rubber particles because of dilatation. g

y

g


Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.

Hashin, Z., Bull Res. Counc. Israel (1955) 5C, 46. Kerner, Ε. H., Proc. Phys. Soc. London (1956) Β 69, 808. van der Poel, C., Rheol. Acta (1958) 1, 198. Takayanagi, M., Mem. Fac. Eng. Kyushu Univ. (1963) 23, 57. Takayanagi, M . , J. Appl. Polym. Sci. (1966) 10, 113. Fujino, K., Ogawa, Y., Kawai, H . , J. Appl. Polym. Sci. (1964) 8, 2147. Nielsen, L . E . , J. Appl. Phys. (1970) 41, 4626. Nielsen, L . E . , Biing-Lin, Lee, J. Compos. Mater. (1972) 8, 136. Nielsen, L . E . , Lewis, T. B., J. Polym. Sci. Part A-2 (1969) 7, 1705. Lewis, T. B., Nielsen, L . E . , J. Appl. Polym. Sci. (1970) 14, 1449. Schwarzl, F. R., Bree, H . W., Nederveen, C. J., Schwippert, G. Α., Struik, L . C. E., van der Waal, C. W . , Rheol. Acta (1966) 5, 270. Kraus, G . , Rollmann, K. W . , Gruver, J. T., Macromolecules (1970) 3, 92. Zitek, P., Zehlinger, J., J. Polym. Sci. Part A-l (1968) 6, 467. Angelo, R. J., Ikeda, R. M . , Wallach, M . L . , Polymer (1965) 6, 141. Molau, G . E . , Keskkula, H., J. Polym. Sci. Part A-l (1966) 4, 1595. Bender, B. W . , J. Appl. Polym. Sci. (1965) 9, 2887. Keskkula, H., Turley, S. G., J. Polym. Sci. Part Β (1969) 7, 697. Wagner, E . R., Robeson, L . M . , Rubber Chem. Technol. (1970) 43, 1129. McCrum, N . G., J. Polym. Sci. (1958) 27, 555. Wada, Y., Kasahara, T., J. Appl. Polym. Sci. (1967) 11, 1661. Keskkula, H . , Turley, S. G . , Boyer, R. F., J. Appl. Polym. Sci. (1971) 15, 351. Matsuo, M . , Ueno, T., Horino, H., Chujyo, S., Asai, H . , Polymer (1968) 9, 425. Robinson, R. Α., White, E . F. T., Amer. Chem. Soc., Div. Polym. Chem., Prepr. 10, 662 (New York, September, 1969). Bohn, L., unpublished data. Matsuo, M . , Wang, Tsuey T., Kwei, T. K., J. Polym. Sci. Part A-2 (1972) 10, 1085. Beck, Jr., R. H., J. Polym. Sci. Part Β (1968) 6, 707. Wang, Tsuey T., Matsuo, M . , Kwei, T. K., J. Appl. Phys. (1971) 42, 4188. Schmitt, J. Α., I U P A C Symp., Toronto (1968) 2, A9. Bohn, L . , Angew. Makromol. Chem. (1971) 20, 129. Turley, S. G., J. Polym. Sci. Part C (1973) 1, 101. Morbitzer, L . , Ott, Κ. H., Schuster, H . , Kranz, D . , Angew. Makromol. Chem. (1972) 27, 57. Sternstein, S. S., I U P A C Symp., Leiden (1970) 2, 973. Matsuo, M . , Ueda, Α., Kondo, Y., Polym. Eng. Sci. (1970) 80, 253.

R E C E I V E D April 1, 1974.


Quantitative Evaluation of the Dynamic Mechanical Properties of

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