blends of linear and branched polyethylenes

Blends of Linear and Branched Polyethylenes

HEON SANG LEE" and MORTON M. D E N "

Materials Sciences Division Lawrence Berkeley National Laboratory

and

Department of Chemical Engineering University of California, Berkeley Berkeley, California 94720- 1462

We employ rheological measurements of polyethylene blends in the melt and solid state, together with thermal analysis, to infer phase behavior. Partial-miscibility in the melt is characterized by use of the double-reptation model to define the complex modulus of the continuous phase for input into the emulsion model for the blend; this approach introduces a new fitting parameter, the fraction of the minor component contained in the continuous phase. The results on binary systems suggest the use of HDPE as a compatibilizer for LLDPE/LDPE blends, appar- ently creating a fully miscible ternary system.

WTRODUCTION

lends of high-density polyethylene (HDPE), linear B low-density polyethylene (LLDPE), and low- density polyethylene (LDPE) have been of growing in- terest (e.g., 1-7), motivated by issues associated with the recycling of plastic waste as well as the design of blends with desired properties: the polyethylenes also provide well-studied components for testing theories of blends.

Polyolefin blends can be miscible, partially-miscible, or immiscible; see Crist and Hill (6) for a recent re- view. Phase separation is often reported for blends of linear and branched polyethylenes (8-10). with molecular weights, co-monomers, and degrees of branching serving as important factors in determining miscibility (7, 1 1). Blends of high-density and linear low-density polyethylenes have been reported to be homogeneous and co-crystallized (12). Blends of linear low-density and low-density polyethylenes exhibit both lower- and upper-critical solution temperatures; hence, phase separation has been reported in both the solid and melt states (13). Blends of high-density and low-density polyethylenes exhibit phase separation in the solid state (8, 9). Two melting peaks have been reported with differential scanning calorimetry in an acetone-quenched HDPE/LDPE sample, indicating

'Present address M c h Institute, Citj' college ofthe City Unhrersity of New Y a k . 1-M Steinman Hall, Convent Avenue at 140th Street, NewYork. NY 10031.

Taqon 305 343. Korea. 'Present address: LG Chemical Ltd.. Tech. CUI~RX. JW-Dang 84. Y~sUng-gU.

phase separation (8), while a single phase for HDPE/ LDPE was reported using small-angle neutron scatter-

We report here on a study of blends of high-density, linear low-density, and low-density polyethylenes hav- ing number-average molecular weights from 13,000 (HDPE) to 39,000 (LDPE), polydispersity from 3 (HDPE) to 10 (LDPE), and fewer than four short-chain (< octene) branches per 100 backbone carbon atoms; the phase behavior of binary polyethylene blends appears to be insensitive to these three factors within the range studied (7-13). Our primary focus has been on the behavior of partially-miscible blends and the possible role of a third polyethylene component as a compatibilinng agent for an immiscible binary pair.

ing (7, 9).

RBEOLOGICAL MODELS

Double Reptation

The double-reptation model of Tsenoglou (14, 15) and des Cloizeaux (16) is often used to represent dynamic viscoelastic data of miscible linear polymer melts (17). The starting point is a mixing rule for the relaxation modulus,

G(t) = [ Xh GY2 (q (1)

where +i is the volume fraction of component i The storage and loss moduli of the blends are then given in terms of the pure-component properties, as follows:

1132 POLYMER ENGINEERING AND SCIENCE, MAY 2000, Vol. 40, No. 5


where

G& - G: (0) G& - G;(w) + - (2C) = 2G': (0) 2 GY( 0)

G i denotes the plateau modulus. The zero-shear viscosity is obtained from the limit of G"/w as w goes to zero and is given by

Our pure-component measuremeiits do not extend to sufficiently high frequencies to obtain the plateau modulus with confidence, and we have used the value 1.4 X lo7 dyne/cm2, which has been reported for both HDPE and LLDPE (18, 19).. The measured dynamic moduli in the terminal region are much smaller than this value in all cases: for the case where the plateau modulus is the same for both members of the binary pair and Gg >> G and G", Eqs 2% b and 3 re- duce approximately to the following equations, which are independent of the plateau modulus:

1 1 - ' G"(o) = 2 x Z + L +,( ~- + -) (4b)

I J G,"(o) G,"(w)

Calculations using Eqs 4 and 5 give essentially the same results for our data as calculations using Eqs 2

and 3, so the uncertainty in the value of the plateau modulus has only a neghgible effect on the calculated blend properties.

Groves and coworkers (1) have shown that the double-reptation theory needs to be modified empirically to fit their melt rheology data on a series of polyethylene blends in which one component is linear and one is branched that they believe to be miscible or "miscible dominated." They have introduced an empirical index in the double reptation combining rule for a mid-volume-fi-action range of HDPE/LDPE blends, as follows:

where

C = 2 corresponds to the double reptation model. C is about 4.4 for the HDPE/LDPE pair studied here: for C = 4 the equation for the zero-shear viscosity analo- gous to Eq 5 becomes

A closed-form equation cannot be obtained for non- integer values of C.

The double-reptation combining rule assumes that the two components are monodisperse. A combining rule for G for highly-polydisperse components can be developed following ideas of h4ilner (20) and Tuminello (21). as discussed in the Appendix.

Emulsion Model

The emulsion model of Palierne (22, 23) has been very successful in characterizing the linear viscoelastic behavior of immiscible blends of flexible polymer melts (24-27). One characteristic of such systems is an elevated value of the storage modulus at low frequencies relative to the matrix because of an elastic response associated with the interfacial tension. For a monodisperse droplet size distribution, the model gives the following result for the complex modulus of the blend:

1 + 3+H (0) 1 - 2bH (w)

G* = G ( w ) + i G ( w ) = (84

Table 1. Properties of Polyethylenes.

TY # branched M, (9) rl0 ("C) 100 backbone at 160°C,

carbons Poise

T,("C) AH (519)

HDPE 135.6 167.5 - -1 22 - 40,000 4.48 x 103 LLDPEl 130.5 107.4 -25 -1 29 1 68,320 3.33 x 104 LLDPE2 130.6 105.5 -25 -1 24 1.6 134,400 3.78 x 105 LDPE 1 14.0 94.3 -20 -1 32 3.2 388,400 3.26 x 105

POLYMER ENGINEERING AND SCIENCE, MAY 2000, Vol. 40, No. 5 1133

H e o n Sang Lee and Morton M. Denn

where (4a/R)[2GL(w) +5Gb(0)] + [Gb(w) - Gxw)][ 16G20) + 19Gb(0)]

(40a/R)[Gaw) + Gb(w)] + [2Gb(0) + 3G&w)][ 16G20) + 19Gb(w)] H ' =

6, and 6, are the complex moduli of the matrix and dispersed phases, respectively; a is the interfacial tension, + the volume fraction of the dispersed phase, and R the radius of the dispersed phase. When the polydispersity of the droplet size distribution is less than 2.3, the effect of polydispersity is negligible and Eq 8 can be used with R set equal to the volume-average droplet radius (28). For dilute immiscible blends, the zero-shear viscosity is given to first order in + by (29, 30)

where k is the ratio of the zero-shear viscosity of the dispersed phase to the zero-shear viscosity of the matrix.

EXPERIMENTAL

Materiala and Blend Preparrrtion

Polyethylene samples were obtained from commer- cial sources, as follows: high-density polyethylene (HDPE), Union Carbide DMDA 8940 (M, = 40,000, M J M , = 3.1); linear low-density polyethylene (LLDPE), Union Carbide HS 7027 (LLDPEl, M, = 68,300, M J M , = 3.2) and Union Carbide HS7037 (LLDPE2, M , = 134,000, M J M , = 3.81, both ethene/hexene copolymers; and low-density polyethylene (LDPE), DuPont Alathon 20 ( M , = 388,440, M J M , = 10.0). The properties of the polyethylenes are presented in Table 1. Blends were prepared using a PRISM 16-mm co-rotating twin-screw extruder, with a 25:l length-to-diameter ratio. The temperature of the extruder was set at 160°C in the barrel zones and the temperature of the die was set at 155°C; the screw speed was set at 50 rpm.

Melt Rheology

Storage (G') and loss (G'j modulus measurements in the melt were carried out on a Rheometrics Mechani- cal Spectrometer RMS 800 with parallel plates under a nitrogen atmosphere at 160"C, with 25-mm disk samples fabricated by vacuum molding at 160°C. Rheological measurements were made at 15Oh strain, which was within the linear range for all samples. Two-hundred-gram and 2000-gram transducers were used in the low- and high-frequency ranges, respectively. G' and G" were found in all cases to be the same at the start and conclusion of the measurements. The loss modulus was linear at low frequencies for all polyethylene samples used in this work, so zero-shear viscosities were computed from the low- frequency values of G / w .

S3dd-S- Rheolom

Solid state relaxations of the polyethylene blends were measured with a heating rate of 2"C/min from -150 to 120°C using a Rheometrics Solids Analyzer RSAII in the bending mode at a frequency of 1 Hz. Rectangular samples 7.9 mm wide, 48 mm long, and 2.8 mm thick were prepared by molding at 160°C.

T h e r m a l A m a l p i B

Thermal analysis was carried out with a Perkin- Elmer differential scanning calorimeter DSC-7. Tem- perature calibration was performed using Indium (T, = 156.6"C, AHr= 28.5 J/@. Blend samples of 10 to 15 mg were initially heated in a nitrogen atmosphere from 25°C to 200°C at a heating rate of 2O"C/min. The samples were then cooled from 200°C to 25°C at a cooling rate of 320"C/min, corresponding to natural cooling at room temperature. Finally, the samples were reheated from 25°C to 200°C at a heating rate of 20"C/min. The melting point reported here is the temperature of the maximum in the melting peak.

RESULTS AND DISCUSSION

Brpnchine The solid-state storage (E3 and loss (ET moduli and

loss factors (tan 6 = E"/E') at 1 Hz are shown as functions of temperature in Fig. 1 for the four resins. We focus on the y- and p-transitions, both of which are associated with molecular motion in the amorphous region (3 1, 32). The p-transition is associated with the onset of motion at branch points, and the magnitude of the transition is an indication of the degree of branching; following Lee and coworkers (33) and Ward and Hadley (34), we estimate the number of branches per 100 backbone carbons from the p-transition data to be 1, 1.6, and 3.2 for LLDPE1, LLDPE2, and LDPE, respectively. There is no obvious p-transition for the linear HDPE. The y-transition is associated with seg- mental motion and is often considered to be the glass transition temperature.

HDPElLLDPE Blends

We see in Rg. 2 that HDPE/LLDPEl blends exhibit a single melting peak at all compositions, which is consistent with the report that HDPE/LLDPE blends co-crystallize to form a single phase (12). m e 5°C difference in melting temperatures between the two resins might mask the superposition of two peaks, but there is no indication of a shoulder and the 5°C difference is well-outside experimental uncertainty.) The loss factor in the y-transition region is shown in



4

3 n m e 2 (3

1 L I

W 0

0.16 0.14 0.12 n a 0.10 0.08

w 0.06 (3 0.04 I

I

LLI 0.02 0.00

-200 -150 -100 -50 0 50 100 150

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.00

v LLDPE2

-200 -150 -100 -50 0 50 100 150 a'

I -200 -150 -100 -50 0 50 100 150

TEMPERATURE ("C)

m. 1. Solid state storage mDdulus E), loss modulus (E), and loss factor (tan 8) of HDPE, LLDPEl, LLDpE2, and LDPE.


Heon Sang Lee and Morton M . Denn

1 I I I I I I I

I I I I I I I I

40 60 80 100 120 140 160 180200

Fig. 3a, where there is a single y-relaxation peak; the location of the peak follows the empirical Fox equation for miscible amorphous polymers with negligible ther- modynamic interaction (35, 36).

The dynarmc data for the HDPE/LLDPEl blends at 160°C are shown in Fig. 4, together with the curves computed from the double-reptation theory. The agreement is very good and is consistent with the no- tion that these polymers are miscible in the melt at all compositions. Zero-shear viscosities as functions of composition are shown in Fig. 5 for the two HDPE/ LLDPE blends, together with the double-reptation cal- culation. The fit is very good in both cases: the ten- dency for the data for the LLDPEP blend to lie slightly below the line may be a consequence of the higher degree of branching for this polymer relative to LLDPE 1.

HDPELDPE Blend.

The HDPE/LDPE blend shows two melting peaks for LDPE-rich compositions, but a single peak for HDPE-rich compositions (Fig. s). Similarly, there appear to be two y-transitions (or a very broad shoulder) for LDPE-rich compositions, but a sinde r-peak at - . - HDPE-rich composkions (Fig. 3b). These results are consistent with reports that the HDPE/LDPE system is biphasic in the solid state (8, 9), but they indicate crystalline and amorphous solid-phase miscibility for

TEMPERATURE ("c) Fig. 2 . Effect of composition o n melting temperatures of H D P E - D P E I blends.

LLDPE 1

20 %

40 %

60 %

80 %

HDPE 100 %

(b)

LDPE

20 %

40 %

60 %

80 %

HDPE 100 %

LDPE

20 %

40 %

60 %

80 %

LLDPE2 100 %

-200 -150 -100 -50 -200 -150 -100 -50 -200 -150 -100 -50

TEMPERATURE ("C) Q. 3. Effect of composition on the y-relawations of blends. (a) HDPE-LLDPEI (b) HDPE-LDPE (el LLDPE2-LDPE.



1 o6

105 n cv E 104 0

- l o 2 i9

10'

1 oo I

Double-Reptation Model 1.. HDPE

0 HDPE10%

1 0-1

1 o8

107 cv-

E lo6 3

105 - i2

104

0

c )r 'LI

m

103

1 o2 lo-' 1 oo 1 o1 1 o2

Frequency (rad/s) Fig. 4. Comparison of dynamic moduli at 160°C with doublereptation model for HDPE-LLQPEl blends.

HDPE-rich compositions. Zero-shear viscosities as functions of composition are s h a m in Q. 7, together with the Palieme emulsion model (Eq 9) and the double-reptation model with C = 2 (Eq 5) and C = 4 (Q 7). The emulsion model for immiscible blends is qualita- tively incorrect, the more so at the LDPE-rich compositions, where we might expect phase separation based on the solid-phase results. The modification to double-reptation by Groves and coworkers (1) using C = 4 provides a reasonable fit to the data, especially in the mid-composition range for. which the equation was designed, indicating a miscible or 'miscible dominated" melt. (We have computed the relaxation modulus G(t) for the individual components and for the blend by Fourier transforming the measured storage and loss moduli. The curve computed with C = 4 does not differ significantly from the curve computed with C = 4.4. Both are close to the Fourier-tansformed blend data, with the former slightly closer to the data than the latter.)

1 06 n Q, UJ 0 LL .I

Y

.I E 105

UJ 5

= 104 9

L 0 0)

0 HDPElLLDPEl 0 HDPEILLDPE2

Double-Reptation Model

0.0 0.2 0.4 0.6 0.8 1.0

Weight Fraction HDPE Fig. 5. Comparison of zero shear viscosity (q0) at 160°C with doublereptation model for HDPE-LLDPE blends.


Heon Sang Lee and Morton M. Denn

I

4 ' 103,

1 I I I I I I I

c=2 c=4

_ _ ......

I I I I

40 60 80 100 120 140 160 180200

TEMPERATURE W) Fig. 6. Effect of composition on melting temperatures of HDPE-WPE blends.

LLDPEnDPE Blends Blends of LLDPEP and LDPE show two melting peaks

at all compositions (Rg. 8), indicating crystalline phase separation. The melting peaks of both components are depressed slightly relative to the pure components; the depression of the higher melting peak (LLDPE2) may be due to co-crystallization of LLDPE2 with the more linear molecules of LDPE, while the depression of the lower melting peak (LDPE) may be due to deple- tion of the more linear (higher-melting) molecules of LDPE (8). The y-transition for the blend compositions is broad (Rg. 3c), and while it is suggestive of amorphous phase separation the result is ambiguous.

The scaled storage modulus (G'(blend)/G'(matrix)) for LLDPEP/LDPE blends is shown in Flg. 9. The storage modulus at low frequencies exceeds that of either pure component, which is a definitive demonstration of a non-homogeneous melt. The data cannot be described, however, by the Palierne emulsion model, suggesting partial miscibility.

n

0 HDPWLDPE - Emulsion Model Q) u)

.I E

5 '..,O \

u)

0 u)

.. .. \ 'Q, '

' .o \

L '.. . , o \

Double-Reptation Model c

0.0 0.2 0.4 0.6 0.8 1.0

Weight Fraction HDPE FXg. 7. Effect of blend composition on zero-shear viscosity (qo) of HDPE-WPE blends at 160°C.

It seems reasonable to extend the emulsion model to a partially miscible system by assuming that a fraction X of the minor component is miscible with the major component, and the matrix is comprised of this miscible blend. Matrix properties are then determined from the double-reptation model (the viscosities of the linear and branched polymers in this case are

I I I I I I I

LLDPE2 100 '%

80 %

40 60 80 100 120 140 160 180 200 TEMPERATURE Cc)

Fig. 8. Effect of composition on melting temperatures of LLDPE2-WPE blends.



Q. 9. G ' ~ l e n d ) / G & L D P E 2 ] as a function offrequency and composition f o r LLDPEZ-LDPE blends at 160°C.

1 0 7

1 o6 n

N

E o 1 0 5 - 1 0 4

i!l 1 0 3

\ Q) S >r w

1 o2

LLDPE2/LDPE 0 0

D

(90/10), a/R=105dyne/cm2, X = 0.45 (80/20), a/R=105, X = 0.45 (20/80), a/R=106, X = 0.15 (10/90), a/R=106, X = 0.15

Hybrid Approach

1 o8

1 0 7

1 o6

105

1 0 4

103 1 o-2 1 0-1 1 oo 1 o1 1 o2

Frequency (radls) Ffg. 10. Dynamic moduli for LLLlPE2-LDPE blends. ?he lines represent the hybrid calculatro ' n combining the doubkrepta t ion model for the matrix and emulsion model for the blend



0 LLDPWLDPE - Hybrid Approach

0.0 0.2 0.4 0.6 0.8 1.0

Weight Fraction LLDPE Fig. 11. Comparison of zero-shear viscosity (qo) at 160°C with the hybrid approach for LLDPE2-LDPE blends.

sufficiently close that C from Eq 6b is close to 21, and the properties of the blend are defined by the emulsion model with a dispersed phase consisting of 1 -X of the minor component. (Miscibility of the major component in the dispersed phase is ignored.) There are now two parameters, X and a / R . Dynamic data for both LLDPEP-rich and LDPE-rich compositions are shown in Fig. 10. a / R was fixed at ascending powers of ten and a suitable value of X was found by a one-parameter search; a detailed two-parameter search did not seem warranted. The data in the LLDPE-rich regime are fit with a / R = lo5 dyne/cm2 and X = 0.45, while the data in the LDPE-rich regime are fit with a / R = lo6 dyne/cm2 and X = 0.15. We cannot image the dispersed phase because of the lack of contrast between the two polyethylenes, but it seems reasonable to assume the size of the inclusions is no smaller than 0.1 pm, in which case the interfacial tension would be no larger than 1 mN/m. This value is larger than might be expected for species that are chemically nearly identical, but it is comparable to that reported for other immiscible polymer blends (37). Hence, the measurements are consistent with the hypothesis that the polymers are partially miscible in the melt, but it is unlikely that the parameters have hdamen- tal meaning.

The zero-shear viscosity is shown as a function of composition in Fig. 1 1. There is a large positive devia- tion from linearity. The lines represent Eq 9 for the two limiting cases, with the matrix properties determined using the double-reptation theory and the Same parameters as in Fig. 10.

Ternary Blend@

We have found that HDPE is miscible with LLDPE and LDPE in the melt, while LLDPEP is partially miscible with LDPE. This observation suggests that HDPE

I I I I I I I

LLDPWLDPE (80MO) + HDPE

HDPE 0 %

A

HDPE 20 %

HDPE 40 %

HDPE 50 %

40 60 80 100120140160180200 TEMPERATURE (“C)

FXg. 12. Eflect of HDPE weightfraction on melting temperatures of LlDPE2-LDpE (80/20) blends.

might act as a compatibilizing agent in ternary blends of HDPE, LLDPEP. and LDPE. The effect of HDPE on the melting peaks of an LLDPE2/LDPE (80/20) blend is shown in Flg. 12. As the composition of HDPE is in- creased for a fixed ratio of the other two components, the second melting peak disappears and the ternary system shows a single melting peak between those for pure LLDPE2 and HDPE, indicating that the ternary system forms a single crystalline phase. The storage modulus of ternary blends of LLDPEP/LDPE (80/20) and HDPE at 160°C is shown in Fig. 13, together with emulsion model calculations based on the assump- tion that the matrix consists of the LLDPEO/HDPE and a fraction of the LDPE, with the matrix properties calculated from the double-reptation model. At 1Wh HDPE the model fit suggests that a small fraction of the LDPE remains in a separate phase with a very small interfacial tension, but at higher HDPE frac- tions the best fit assumes nearly complete miscibility and no interfacial tension. The fit becomes succes- sively poorer with increasing HDPE fraction, with the theory overestimating the data at all but the highest frequencies: this is consistent with the behavior of blends of LDPE with HDPE, and probably reflects the inapplicability of the double-reptation model with C = 2 to systems with branching.

CONCLUSIONS

The rheological and thermal measurements permit us to infer phase behavior of the polyethylene blends.


Fig. 13. Effect of HDPE weight fraction on storage modulus

blends at 160°C. (G'(w)) of LLDPE2-LDPE [80/20)


1 0 7

LLDPE2/LDPE (80/20) + HDPE

1 o6

1 0 5

1 0 4

1 0 3

1 o2 b " 0 501 0

x 0.45 0.90 0.99 0.99 0.99 0.99

I

10' ' I I I

lo-*

LLDPE/LDPE blends appear to be partially miscible in the melt, and their behavior can be described by a hybrid that employs the double-reptation model to describe the matrix phase and the Palierne emulsion model to describe the blend. This approach appears promising as a way of correlating blend data for partially miscible polymers, although the physical signs- cance of the two parameters X arid a / R is not clear. Perhaps the most si@cant result of this study is the demonstration that HDPE, which is miscible in at least some composition ranges with both UDPE and LDPE, can be used as a compatibilizing agent for LLDPE/LDPE blends to create a ternary system that appears to be fully miscible.

APPENDIX Following Milner (20) and Turninello (21). we may

write the storage modulus for a highly-polydisperse melt as

G ( w ) G t W M ) I 2 (All

where IJJ (M) is a normalized molecular-weight distribution and the criterion w(M) = 1 m the lower-limit of the integral defines the "active" entanglements as those that cannot relax over a time scale w-l. For a binary blends of polydisperse components, the function + (M) is the weighted sum of the two distributions. If we now further assume that the two components have

m

[ I,. 1

POLYMER ENGINEERING AND SCIENCE, MAY 2000, Vol. 40, No. 5

1 0-1 1 oo 1 o1 I o2 Frequency (radkec)

the Same plateau modulus and the same lower limit of integration (the obvious weak point in the analysis) we then immediately obtain

G' (0) G;(w)"' + +z G ~ ( W ) " ~ ] ~

Equation A 2 differs from Eq 4a by a term 2+1+2 (G;Ga1/2{4[(G;/G;)1/4 + (G; /G;)lI4T2 -11. The quan- tity (4[(G;/G;)1/4 + (G; /G;)'l4f2 -1) varies between zero (G; = G;) and -1 (G; >> G& or G& >> G;). The difference between Eq A 2 and Eq 4a was always less than 15% for the HDPE/LLDPE blend studied here.

ACKNOWLEDGMENT

This work was supported in part by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Science Division of the U.S. De- partment of Energy under Contract No. DE-AC073- 76SF00098, and in part by DuPont. HSL received fellowship support from the Korea Research Founda- tion.

REFERENCES 1. D. J. Groves, T. C. B. McLeish. R. K. Chohan, and P. D.

2. A. R. Nesarikar, S. H. Carr, K. Khit, and F. M. Mirabella.

3. J. Schellenberg, A&. Polyrn Tech, 16, 135 (1997). 4. D. Abraham, K. E. George, and D. J. Francis, J. AppL

5. D. Abraham, K. E. George, and D. J. Francis, Polymer,

Coates, RheoL Acta, 35,481 (1996).

J. Polyrn Sci.. Polgrn Phy., 83, 1179 (1997).

Polyrn Sci, 67. 789 (1998).

39, 117 (1998).

1141


6. B. Crist and M. J. Hill, J. Blym Sci. Pdym Phys., 35. 2329 (1997).

7. R. G. Alamo, W. W. Graessley, R Krishnamoorti, D. J. Lohse. J. D. Londono. L. Mandelkem, F. C. S teh lg . and G. D. Wignall, Macromole&s, SO, 561 (1997).

8. M. J. W, A. Keller, and C. C. A. Rosney, Polymer, 32. 1384 (1991).

9. R. G. Alamo, J. D. Londono, L. Mandelkern, F. C. Stehling, and G. D. Wignall, Macromok&s, 27, 41 1 (1994).

10. T. Kyu, S.-R Hu, and R S. Stein, J. Polym Sci, Polym Phgs., 25.89 (1987).

11. M. J. Hill, P. J. Barham, and A. Keller, Polymer, 33, 2530 (1992).

12. S.-R Hu. T. Kyu, and R. S. Stein, J. Polym Sci Polym Phys., 25. 71 (1987).

13. A. J. Muller and V. Balsamo, in Advances in Polymer Blends and Alloys Technology. Chap. 1, 1-2 1, K. Finday- son, ed.. Technomic Publishing Company, Lancaster, Pa. (1994).

14. C. Tsenoglou, J. Polym Sci, Polym Phys., 26, 2329 (1988).

15. C. Tsenoglou, Mmmolecules, 24, 1762 (1991). 16. J. des Cloizeaux, Macromolecules, 23. 3992 (1990). 17. C. B. Gell, R. Krishnamoorti. E. Kim, W. W. Graessley,

and L. J. Fetters, R h L Acta, 36.217 (1997). 18. J. D. Ferry, Viscoelastic hoperties of Polymers, 3rd Ed.,

Wiley, New York (1980). 19. C. Carrot and J. Guillet, J. RheoL, 41, 1203 (1997). 20. S. T. Milner, J. R h e o L , 40, 303 (1996).

21. W. H. Tuminello, Polym Eng. Sci, 26, 1339 (1986). 22. J. F. Palieme, RheoL A d q 2s. 204 (1990). 23. J. F. Palieme. RheoL A d q SO, 497 (1991). 24. I. Vinckier, P. Moldenaers, and J. Mewis, J. RheoL, 40,

613 (1996). 25. S. Kitake, A. Ichikawa, N. Imura, Y. Takahashi, and I.

Noda. J. RkoL, 41, 1039 (1997). 26. C. Lacroix, M. Grmela, and P. J. Carreau, J. RheoL, 42.

41 (1998). 27. H. M. Yamane, M. Takahashi, R Hayashi. K. Okamoto,

H. Kishihara, and T. Masuda, J. RheoL, 42, 567 (1998). 28. D. Graebling. R. Muller, and J. F. Palieme, Macromole-

&s. 26. 320 (1993). 29. D. Graebling and R. Muller, J. RheoL, 34, 193 (1990). 30. D. Graebling and R. Muller, J. RheoL. 34, 333 (1990). 31. R. H. Boyd, Polymer. 86, 1123 (1985). 32. R. H. Boyd, Polymer, 26, 323 (1985). 33. H. Lee, K. Cho, T.-K. Ahn, S. Choe, 1.4. Kim, I. Park,

and B. H. Lee, J. Polym Sci, Polym Phys., 36, 1633 ( 1997).

34. I. M. Ward and D. W. Hadley, An lntrodtlrtion to the Me- chanical Properties of Solid Polymers, John Wiley and Sons Inc., Chichester, U.K. (1993).

35. 0. Olabisi, L. M. Robeson, and M. T. Shaw, Polymer- Polymer Miscibility, Chap. 1, Academic Press, New York ( 1979).

36. T. G. Fox, BulL A m Phys. Soc., 1, 123 (1956). 37. B. Brahimi, A. Ait-Kadi, A. Ajji. R. Jerome, and R. Fayt,

J. RheoL, 35, 1069 (1991).


blends of linear and branched polyethylenes

Documents