Polymer Degradation and Stability 92 (2007) 1632e1639www.elsevier.com/locate/polydegstab

Static ultrasonic oscillations induced degradation and its effect on thelinear rheological behavior of novel propylene based plastomer melts*

Bo Peng a, Hong Wu a, Shaoyun Guo a,*, Shih-Yaw Lai b, Jinder Jow c

a The State Key Laboratory of Polymer Materials Engineering, Polymer Research Institute of Sichuan University, Chengdu 610065, Chinab Dow Chemical (China) Investment Company, Shanghai 200120, China

c Dow Chemical Pacific (Singapore) Pte Ltd, Asia-Pacific Technical Center, Singapore 638025, Singapore

Received 7 February 2007; received in revised form 17 March 2007; accepted 22 March 2007

Available online 14 April 2007

Abstract

The ultrasonic degradation of novel propylene based plastomer (DP) melts with different melt viscosities was conducted in a ‘‘static’’ ultra-sonic device where the samples were taken from various distances from the tip of an ultrasonic probe. The effects of ultrasonic time, oscillationtemperature, ultrasonic intensity and the distance from the ultrasonic probe tip on the degradation behavior of DP melts as well as the ultrasonicdegradation effect on the linear rheological behavior of DP melts were studied. The results show that the increase of initial melt viscosity of DP(higher molecular weight) has greater impact on the ultrasonic degradation of DP melt. The molecular weight and intrinsic viscosity of DPdecrease with the increase of ultrasonic oscillation time and they approach to a limiting value. The molecular weight distribution of DP increasesafter ultrasonic degradation. Decreasing oscillation temperature and distance from probe tip and increasing ultrasonic intensity lead to anincrease in the degradation of DP melt. The linear rheological behavior measurements of the samples obtained near the ultrasonic probe tipshow that ultrasonic oscillations decrease the complex viscosity, zero shear viscosity, viscoelastic moduli, cross modulus, relaxation timeand the slope of log G0 � log G00 for DP melts.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Propylene based plastomer; Ultrasonic oscillations; Degradation; Linear rheological behavior

1. Introduction

High-intensity ultrasound has been used to speed up andcontrol chemical reactions as a novel technique since the20th century [1]. When ultrasound is initially introduced intopolymer solutions, the homolytic cleavage of the polymerchain is observed. In addition to the occurrence of chainscission and faster degradation [2e8], the recombination ofdifferent macroradicals formed through the sonochemical

* Contract grant sponsors: The Dow Chemical Company (USA); Dow

Agreement Number: 215930, Special Funds for Major State Basic Research

Projects of China; contract grant number: 2005CB623800, National Natural

Science Foundation of China; contract grant number: 20374037, Funds for

Doctoral Disciplines of The Ministry of Education of China; contract grant

number: 20050610028.

* Corresponding author. Fax: þ86 28 85405135.

E-mail address: nic7702@scu.edu.cn (S. Guo).

0141-3910/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.polymdegradstab.2007.03.025

rupture of chemical bond of polymer in solution could producenovel block and graft copolymers [9e12]. It is also expectedthat polymerization of monomer at room temperature andmodification of solid polymer in the liquid can occur by theaid of high-intensity ultrasound [13e16]. The ultrasonic cavi-tation in liquids is responsible for these phenomena [17].

Recently, ultrasonic oscillations were introduced to poly-mer processing to improve the processability of polymermelts. It is found that the superposition of ultrasonic wavesin extrusion can greatly decrease the die pressure, die swelland apparent viscosity of polymer melts [18e22]. It is alsofound that ultrasonic oscillations can cause the degradationof polymer melts and the ultrasonic degradation rate of poly-mer melts is much faster than that of polymer solutionsinduced by heat and vibration and the degradation is stronglydependent on the structure of polymers [23e28]. Apparently,ultrasonic cavitation could not explain this phenomenon. In

1633B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

our previous work [26e28], a plausible mechanism based onmolecular relaxation related resistance force model was pro-posed to explain the ultrasonic degradation of polymer melts.

The average energy flux put in unit area of medium verticalto the direction of ultrasound movement, is named energy fluxdensity I, representing acoustic energy intensity. The equationis as follows:

I ¼ 2p2rcf 2x2 ¼ Af 2x2 ð1Þ

where r is density of medium, c is movement velocity of ultra-sound in medium, f is frequency of ultrasound, x is amplitudeof ultrasound (for the ultrasonic equipment in our lab, x isidentical with ultrasonic intensity), and A is constant. If parti-cles of the medium can move without any resistance, energyflux density I can be totally transformed into their vibrationalenergy Ek:

Ek ¼ I ¼ Af 2x2 ð2Þ

However, the entanglement between polymer chains alwaysinhibits macromolecular movement. Therefore, energy fluxdensity I is partly transformed into vibrational energy Ek

0 ofpolymer chains and another part of energy flux density I isconsumed by the resistance force attributed to macromolecularentanglements with each other:

I ¼ Af 2x2 ¼ E0kþZ

F dx ð3Þ

where F is resistance force. It is evident that the rupture ofpolymer chain occurs if the resistance force F is large enough.The resistance force F can be expressed as a function of meltviscosity h (internal cause) and energy flux density I (externalcause).

F¼ FðI;hÞ ¼ Fðf ; x;hÞ ð4Þ

The higher the melt viscosity h of polymer and energy fluxdensity I of ultrasound, the greater the resistance force Fwhich makes ultrasonic degradation easier.

Developmental Plastomers (abbreviation: DP) are a novelseries of specialty copolymers of propylene containing smallamounts of ethylene, produced with a revolutionary catalystin combination with Dow’s proprietary INSITE technologyand solution process [29]. The unique molecular architectureof these new polymers differs from ZieglereNatta catalyst-based and metallocene catalyst-based copolymers of propyl-ene, including the narrow molecular weight distribution, broadmelting distribution and slower crystallization, providingfilms, fibers and molded parts with an outstanding combina-tion of excellent optics, sealing and hot tack performance,plus elasticity, flexibility, softness and compatibility in blends[30]. However, an improvement in the processability of DP isfurther explored for their wide applications. Our work showedthat introduction of ultrasonic oscillations could visiblydecrease the apparent viscosity during extrusion. In orderto confirm the ultrasonic degradation of DP copolymers, theDP copolymers having different melt viscosities were

subjected to ultrasonic oscillations through a ‘‘static’’ ultra-sonic device in our lab where the polymer melts were confinedin the device (no flow) during ultrasonic oscillations. The ef-fects of ultrasonic conditions (ultrasonic time, oscillation tem-perature, ultrasonic intensity and distance from ultrasonicprobe tip) on the degradation behavior of DP melt as well asultrasonic degradation mechanism, were investigated. The ob-jectives of the article are to explain the ultrasonic degradationof the DP melt through the above-mentioned model and tooffer a theoretical base for the grafting modification of DPthrough the initiation reaction of macroradicals formed duringultrasonic extrusion processing in the peroxide free conditions.

2. Experimental

2.1. Materials and equipment

Novel propylene based plastomers used were provided by DowChemical Co. (USA). Their properties are listed in Table 1.For convenience, the code name of each specimen is listed inTable 1. A specially designed ‘‘static’’ device described in Refs.[26e28], was used for the ultrasonic degradation of DP melts.The maximum power output and fixed frequency of ultrasonicprobe were 300 W and 20 kHz, respectively. The pellets of DPwere filled into the ultrasonic device and heated rapidly to thepre-determined experimental temperature. Then the ultrasonicoscillations were introduced to DP melts for a certain time. Afterthat, the DP melts were cooled down to room temperature. Solid-ified polymer was sliced into 1 mm thick layers from the top (tip ofthe ultrasonic probe). Four samples were taken (up to 4 mm fromthe ultrasonic probe tip) for the measurements of intrinsic viscos-ity, molecular weight and distribution, as well as the linear rheo-logical behavior. For comparison, the samples heated in thedevice in the absence of ultrasonic oscillations were taken throughthe same measurements.

2.2. Measurements and characterization

The intrinsic viscosity [h] could be used to evaluate the ultr-asonic degradation of DP melts by semi-quantitative analysis.The intrinsic viscosity [h] was measured at 135 �C by capillaryviscometer whose diameter was 0.54 mm, according toISO1628/1-1984(E). All the results were the average of fivemeasurements. The solvent used was decahydronaphthalene.

The molecular weight and molecular weight distributionwere measured by GPC-150C instrument (Waters AssociatesCompany). The solvent used was o-dichlorobenzene; the stan-dard sample was polystyrene; chromatographic column was

Table 1

DP material properties

Code

name

MI,

g/10 min

Density,

g/cm3Hardness,

shore A

Comonomer,

wt.%

DP-1 2 0.876 70 8

DP-2 5 0.888 75 5

DP-3 8 0.888 75 5

1634 B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

ultrastyragel linear column; temperature of column was135 �C; flow rate was 1.0 ml/min; the detector was a refractom-eter whose temperature was also kept at 135 �C. The standarddeviations of GPC measurements were less than �5% to en-sure the statistical reliability of the observed changes.

FTIR analysis of ultrasonic degraded and undegraded DPfilms was conducted with a Nicolet 170X FTIR spectrometerat a resolution of 4 cm�1 and with 32 scans.

Dynamic rheological measurements were carried out ona Gemini 200 (Malvern Co.) dynamic stress rheometer. Thesamples were pressed at 160 �C into 1 mm thick disks. Themeasurements were then run with 25 mm parallel plate geom-etry and a 1 mm sample gap. The dynamic viscoelastic proper-ties were determined with frequencies from 0.01 to 100 Hz,using strain values determined with a stress sweep to keepwithin the linear viscoelastic region. Measurements werecarried out at 160 �C under air atmosphere.

3. Results and discussion

3.1. Intrinsic viscosity

The samples were taken from the ultrasonic degraded DP ata temperature and intensity of ultrasonic oscillations of 160 �Cand 200 W, respectively, and DP heated at a temperature of160 �C. The intrinsic viscosity ratio [h]u/[h]0 was used to char-acterize the extent of ultrasonic degradation, where, [h]u and[h]0 are the intrinsic viscosities of degraded and undegradedDP, respectively. Fig. 1 shows the dependence of [h]u/[h]0 ratioon ultrasonic time (0e600 s) for DP taken from the cross sec-tion at 1 mm from ultrasonic probe tip. It can be clearly seenthat [h]u/[h]0 ratio of DP-1 and DP-2 depends strongly on ultra-sonic time. At the initial 200 s of ultrasonic oscillations, thedegradation of DP is fast, leading to a significant decrease ofthe [h]u/[h]0 ratio. After that, the decrease of [h]u/[h]0 ratio con-tinues, but the extent becomes weaker. During the entire processof ultrasonic oscillations, the velocity and extent of [h]u/[h]0

reduction in DP-1 is greater than those in DP-2. On the other

0 100 200 300 400 500 6000.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

Ultrasonic time, s

[η] u

/[η]

0

DP-1DP-2DP-3

Fig. 1. Dependence of [h]u/[h]0 on ultrasonic time for DP (oscillation temper-

ature: 160 �C, ultrasonic intensity: 200 W, distance from probe tip: 1 mm).

hand, the [h]u/[h]0 ratio of DP-3 appears to be constant with in-creasing ultrasonic time, suggesting that the extent of degrada-tion is lower for the given ultrasonic condition. In other words,the extent of ultrasonic degradation is so slight that the viscom-eter barely measures the variation of [h]u/[h]0 ratio of DP-3.These phenomena can be interpreted by Eq. (4). When ultra-sonic intensity and frequency are constant, higher initial meltviscosity (higher molecular weight) could produce greater resis-tance force F, which facilitates severe degradation of DP melt.Once the melt viscosity of DP decreases to a critical value, theresistance force F is so small as not to break up polymer chainsfurther. Ultrasonic degradation would be terminated.

Since melt viscosity is temperature dependent, it is impor-tant to study the effect of oscillation temperature on ultrasonicdegradation of DP melt. Time and intensity of ultrasonic oscil-lations are fixed at 90 s and 200 W, respectively. Intrinsicviscosity of DP-1 and DP-2 taken from the cross section at1 mm from ultrasonic probe tip is measured. The results areshown in Fig. 2. It is clearly seen that the negative ‘tempera-ture coefficient’ is evident during ultrasonic degradation ofDP-1 and DP-2 melts. Namely, [h]u/[h]0 ratio rises with in-creasing oscillation temperature, indicating the lower extentof degradation in higher temperature. With the increase of os-cillation temperature, the melt viscosity decreases and macro-molecular movement becomes easy. Consequently, DP meltendures lower resistance force F on the basis of our modelof ultrasonic degradation, resulting in weaker degradation ul-timately. This phenomenon also occurs in ultrasonic degrada-tion process of polymer solutions [4,31,32] but mechanism isdifferent. In polymer solution, higher vapour pressures athigher temperatures cause a cushioning effect on the cavitationbubbles thereby lessening the shock waves generated, leadingto weaker degradation ultimately.

When time and temperature of ultrasonic oscillations arefixed at 90 s and 160 �C, we studied the effect of ultrasonic in-tensity on [h]u/[h]0 ratio of DP-1 and DP-2 taken from thecross section at 1 mm from ultrasonic probe tip. As shownin Fig. 3, the [h]u/[h]0 ratio decreases with increasing

150 160 170 180 190 200 210 220 2300.90

0.91

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

Oscillation temperature,°C

DP-1DP-2

[η] u

/[η]

0

Fig. 2. Effect of oscillation temperature on [h]u/[h]0 of DP (ultrasonic time:

90 s, ultrasonic intensity: 200 W, distance from probe tip: 1 mm).

1635B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

ultrasonic intensity. According to Eq. (4), ultrasonic intensity,as an external cause to degradation of DP melt, decides thevalue of energy flux density I of ultrasound. When melt viscos-ity is constant, the higher ultrasonic intensity gives higher re-sistance force F, which leads to higher ultrasonic degradationat the tip of the probe, resulting in lower [h]u/[h]0 ratio (higherreduction in viscosity).

In general, energy flux density I of ultrasound is graduallyattenuated with ultrasound advancing in polymer melt withvery high viscosity, because parts of energy flux density Iare consumed by resistance force F. It certainly causes a greatdecrease of degradation extent with the distance from probetip. To study this effect, intrinsic viscosity of degraded DP-1and DP-2 taken from the cross section at 1, 2, 3 and 4 mmfrom ultrasonic probe tip was measured, when ultrasonictime, oscillation temperature and ultrasonic intensity werefixed at 300 s, 160 �C and 200 W, respectively. As shown inFig. 4, [h]u/[h]0 ratio increases and approaches 1 with increas-ing distance from probe tip, due to the attenuation of energyflux density I. This indicates that the effective distance ofultrasonic oscillations in DP melt is ca. 4 mm under theultrasonic condition.

3.2. GPC

Variation of [h]u/[h]0 ratio of DP versus ultrasonic condi-tions, including ultrasonic time, oscillation temperature, ultra-sonic intensity and distance from probe tip, discloses somebasic rules of ultrasonic degradation. In order to study furtherthe ultrasonic degradation of DP melt, we investigated theeffect of ultrasonic time on GPC curves of DP-1 as an example,taken from the cross section at 1 mm from ultrasonic probe tip,when temperature and intensity of ultrasonic oscillations arefixed at 160 �C and 200 W. It can be found from Fig. 5 that,with increasing ultrasonic time, the peak value of GPC curvedecreases and slightly moves to the direction of low molecularweight, along with the decrease in high molecular weight por-tions and the enhancement of the low molecular weight

0 50 100 150 200 250 3000.80

0.82

0.84

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

Ultrasonic intensity,W

DP-1DP-2

[η] u

/[η]

0

Fig. 3. Dependence of [h]u/[h]0 on ultrasonic intensity for DP (ultrasonic time:

90 s, oscillation temperature: 160 �C, distance from probe tip: 1 mm).

components. All GPC curves show an intersection point atabout log M¼ 4.87, indicating that the chain scission of DP-1melt may be mainly concentrated on higher molecular weightportions (>104.87). The molecular weight and molecularweight distribution of degraded and undegraded DP-1 areshown in Figs. 6 and 7, respectively. As shown in Fig. 6, thenumber-average molecular weight (Mn) and weight-averagemolecular weight (Mw) together decrease with increasing ultra-sonic time, similar to the variation of [h]u/[h]0 ratio versus ul-trasonic time. Fig. 7 shows that molecular weight distribution(Mw/Mn) of DP-1 increases with increasing ultrasonic timeand gradually levels off. This should be attributed to the in-crease of low molecular weight portions and the appearanceof ultra-low molecular weight portions, as shown in Fig. 5.As expected, appearance of limiting molecular weight indi-cates that molecular weight distribution (Mw/Mn) changes nolonger with time.

According to the preliminary [h]u/[h]0 ratio, we know thatDP-3 barely undergoes ultrasonic degradation due to its lowermelt viscosity, when temperature and intensity of ultrasonic

1.0 1.5 2.0 2.5 3.0 3.5 4.0

0.86

0.88

0.90

0.92

0.94

0.96

0.98

1.00

DP-1DP-2

Distance from probe tip, mm

[η] u

/[η]

0

Fig. 4. Effect of distance from probe tip on [h]u/[h]0 for DP (ultrasonic time:

300 s, oscillation temperature: 160 �C, ultrasonic intensity: 200 W).

3.0 3.5 4.0 4.5 5.0 5.5 6.00.0

0.2

0.4

0.6

0.8

1.0

logM

Are

a pe

rcen

t,

600s

300s

90s

30s

0s

Fig. 5. Effect of ultrasonic time on GPC curves of DP-1 (ultrasonic conditions

as in Fig. 1).

1636 B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

oscillations were fixed at 160 �C and 200 W. In order to con-firm the ultrasonic oscillation effect on the degradation of DP-3,two GPC curves of degraded (ultrasonic time: 300 s) andundegraded DP-3 taken from the cross section at 1 mm fromultrasonic probe tip were investigated (Fig. 8). With theintroduction of ultrasonic oscillations, we discover that thedecrease in high molecular weight portions accompaniesthe increase in low molecular weight components and theappearance of ultra-low molecular weight components. Italso indicates the prior scission of the longest polymer chainsin DP-3. The molecular weight and molecular weight distribu-tion of DP-3 are listed in Table 2. It is clearly seen from Table 2that Mn and Mw decrease but Mw/Mn increases with the intro-duction of ultrasonic oscillations, similar to variation of themolecular weight and its distribution of DP-1. There is one in-teresting observation that Mw of degraded DP-1 and DP-3tends to approach about 200,000, suggesting that under a givenultrasonic oscillation condition, it may be the critical molecu-lar weight for ultrasonic degradation.

0 100 200 300 400 500 6003

4

5

6

7

8

9

10

Mw , x 10

4

Ultrasonic time, s

Mn,

x 1

04

19

20

21

22

23

24

25

26

27

28

Fig. 6. Effect of ultrasonic time on Mn and Mw for DP-1 (ultrasonic conditions

as in Fig. 1).

0 100 200 300 400 500 6003.00

3.25

3.50

3.75

4.00

4.25

4.50

4.75

5.00

5.25

5.50

5.75

Ultrasonic time, s

Mw

/Mn

Fig. 7. Effect of ultrasonic time on Mw/Mn for DP-1 (ultrasonic conditions as

in Fig. 1).

3.3. Ultrasonic degradation mechanism

On the basis of above results, we draw a conclusion thatchain scission of DP is a localized effect that occurs mainlynear the tip of ultrasonic probe and is concentrated on theportion of high molecular weight which mainly contributesto melt viscosity. With introduction of ultrasonic oscillations,the occurrence of ultra-low molecular weight portions meansthat chain scission is random and not concentrated on the mid-point of polymer chain. It is obviously different from the non-random rupture of polymer chain in polymer solution underultrasonic oscillations. This characteristic of ultrasonic degra-dation in polymer solution is possibly due to less molecularentanglement in solution and ensures the decrease of molecu-lar weight distribution in the presence of ultrasonic oscilla-tions [28]. In our experiment, the elevation of molecularweight distribution in the presence of ultrasonic oscillationscould be attributed to higher extent of molecular entanglementand the molecular weight during the entire ultrasonic degrada-tion process is too high to ensure non-random rupture. In orderto further study the degradation mechanism of DP melt in thepresence of ultrasonic oscillations, FTIR analysis of degradedand undegraded DP was carried out. As shown in Fig. 9, com-pared with undegraded DP (ultrasonic time: 0 s), in the FTIRspectra of degraded DP (ultrasonic time: 90, 200 and 300 s)taken from the cross section at 1 mm from ultrasonic probetip when temperature and intensity of ultrasonic oscillationsare fixed at 160 �C and 200 W, there are no new absorptionbands, but the intensity of the absorption band of nC]O

(1724 cm�1) increases clearly. It is postulated that oxygen inair participates in the termination of macroradicals produced

3.0 3.5 4.0 4.5 5.0 5.5 6.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

logM

Are

a pe

rcen

t,

0s300s

Fig. 8. Effect of ultrasonic time on GPC curves of DP-3 (ultrasonic conditions

as in Fig. 1).

Table 2

The GPC results of DP-3 (ultrasonic conditions as in Fig. 1)

Ultrasonic time, s Mn, �104 Mw, �104 Mw/Mn

0 6.90 21.12 3.06

300 6.41 19.97 3.12

1637B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

by ultrasonic oscillations. The bands at 1380 cm�1 and720 cm�1 are associated with the dCH of eCH3 and e(CH2)ne, n� 2, respectively [33]. Fig. 10 shows the depen-dence of their area ratio A1380/A720 on ultrasonic time forDP. A1380/A720 ratio tends to decrease with increasing ultrasonictime, indicating that eCH2e content increases compared witheCH3 content with the introduction of ultrasonic oscillations.Accordingly, ultrasonic degradation of DP melts is proposedto be represented by the following schemes:

polymer [35]. The data listed in Table 3 show that ultrasonicoscillations can reduce Gx value of DP but enhance its ux

value. It also indicates that ultrasonic oscillations could causethe rise of polydispersity and decrease relaxation time for DPdue to ultrasonic degradation. Again, the effect of ultrasonicoscillations on Gx and ux for DP-3 is rather slight as comparedwith that of DP-1 primarily due to molecular effects where theultrasonic oscillation is repeatedly seen to be less effective todegrade low molecular weight polymers.

CH-CH2-CH-CH2 -CH2

CH3 CH3

expansion and compression induced by ultrasonic irradiation

CH3-CH-CH2-CH2˙CH-CH2˙

CH3

+

+O2

..................... .....................

..................... .....................

C=CH2

CH3

............... CH3-CH2-CH2-CH2......... CH-C=O

CH3

............CH3-C-CH2-CH2

..........

O

principal chain scission

principal termination

3.4. Dynamic rheological analysis

3.4.1. Viscoelastic moduliUltrasonic degradation should necessarily induce the devel-

opment of the viscoelastic nature of DP. Hence, dynamic rhe-ological results are used to confirm further their degradationbehaviors under ultrasonic oscillations. Fig. 11 shows the lin-ear viscoelastic moduli of degraded (ultrasonic time: 300 s)and undegraded DP taken from the cross section at 1 mmfrom ultrasonic probe tip, when temperature and intensity ofultrasonic oscillations are fixed at 160 �C and 200 W. Visco-elastic moduli of DP-1, including storage modulus (G0) andloss modulus (G00), markedly decrease with introduction of ul-trasonic oscillations, whereas those of DP-3 only show a slightdecrease. This represents a fact that different extents of ultra-sonic degradation occur between DP-1 and DP-3 where thehigher molecular weight sample (DP-1) is more prone to bedegraded by ultrasonic oscillations. Also, it is clearly seenfrom Fig. 11 that viscoelastic moduli of DP-1 and DP-3 allshow cross point in our studied frequency range, where G0

and G00 are equal. The polymer behaves more viscous belowthis cross point but more elastic above it. The values of crossmodulus Gx and cross frequency ux of DP are listed in Table 3.Recent experimental data [34] exhibited that Gx value is wellcorrelated with polydispersity and decreases with the increasein the polydispersity of polymer. Moreover, the inverse of ux

may also represent a characteristic relaxation time of the

According to the molecular theory [36], in the terminal fre-quency region (u / 0), the relationship of log G0 � log G00 forhomogeneous polydispersed polymer is as follows:

log G0 ¼�2� b

�log G00 þ

�b� 1

�log�8G0

Np�2�;�0< b< 1

�ð5Þ

where GN0 is the plateau modulus. It relates to the entangle-

ment molecular weight of the polymer. Thus, the slope oflog G0 versus log G00 plots should be between 1 and 2, whichdecreases with the rise of polydispersity of the polymer. Therelationship between log G0 and log G00 of DP is shown inFig. 12. The slopes decrease with the introduction of ultrasonicoscillations, indicating the rise of polydispersity. All the re-sults of viscoelastic moduli agree well with those of intrinsicviscosity and GPC.

3.4.2. Complex viscosity and zero shear viscosityIn our studies, the complex viscosity of DP at 160 �C is de-

fined as h� ¼ ½ðG0=uÞ2 þ ðG00=uÞ2�1=2. Fig. 13 shows for DP-1and DP-3 the variation of complex viscosity h* versus fre-quency u. Ultrasonic oscillations also lead to a severe decreaseof h* in DP-1, but slight decrease of h* in DP-3, similar to theeffect of ultrasonic oscillations on G0 and G00. In addition, it is

1638 B. Peng et al. / Polymer Degradation and Stability 92 (2007) 1632e1639

found that all experimental values of h* can be reasonably fit-ted by cross model [37]:

h¼ h0�1þ ðt0� gÞ1�n� ð6Þ

0 50 100 150 200 250 3000

1

2

3

4

5

6

7

8

9

10

11

12

Ultrasonic time, s

A13

80/A

720

DP-1DP-2

Fig. 10. Plot of A1380/A720 versus ultrasonic time (ultrasonic conditions as in

Fig. 1).

4000 3500 3000 2500 2000 1500 1000 500

A

720

1380

1724

300s

200s

90s

Wavenumbers,cm-1

0s

4000 3500 3000 2500 2000 1500 1000 500

720

1380

1724

B

300s

200s

90s

0s

Wavenumbers,cm-1

Fig. 9. FTIR spectra of degraded and undegraded DP (A: DP-1; B: DP-2;

ultrasonic conditions as in Fig. 1).

where h0 is the zero shear viscosity, t0 is the relaxation timerelated to the longest relaxation time, and n is an exponent.The fitted h0 values for DP-1 and DP-3 are given in Table 3and show a variation similar to h* values with introductionof ultrasonic oscillations. The t0 value of DP-1 decreasesbut that of DP-3 remains nearly constant with the introductionof ultrasonic oscillations, which can also be attributed to thedifference in the extent of ultrasonic degradation.

4. Conclusions

In our experimental range, the ultrasonic degradation is a lo-cal phenomenon. DP-1 and DP-2 melts near the ultrasonicprobe tip readily degrade due to higher molecular weight(or melt viscosity) whereas the extent of degradation of DP-3melt is slight due to lower molecular weight (or lower melt

10-2 10-1 100 101 102

102

103

104

105

A

G'

G"

G' a

nd G

", P

a

ω, rad/s

10-2 10-1 100 101 102

101

102

103

104

105B

0s300s

0s300s

G"

G'G

' and

G",

Pa

ω, rad/s

Fig. 11. Dependence of G0 and G00 on u for DP (A: DP-1; B: DP-3; ultrasonic

conditions as in Fig. 1).

Table 3

Some rheological parameters for DP (ultrasonic conditions as in Fig. 1)

Code name Ultrasonic time, s Gx, Pa ux, Hz h0, Pa s t0, s

DP-1 0 50,557 2.15 19,790 1.92

300 41,393 3.59 11,045 1.49

DP-3 0 46,931 12.48 3422 0.34

300 46,163 12.55 3079 0.33

B. Peng et al. / Polymer Degradatio

viscosity). The number-average molecular weight (Mn), weight-average molecular weight (Mw) and [h]u/[h]0 value of DP melttogether decrease with increasing ultrasonic time and theytend to reach to a critical value, along with the increase ofmolecular weight distribution (Mw/Mn). The random rupture

103 104 105101

102

103

104

105A

0s,slope=1.664300s,slope=1.604

G',

Pa

G", Pa

102 103 104 105100

101

102

103

104

105B

G',

Pa

G", Pa

0s,slope=1.800300s,slope=1.750

Fig. 12. Dependence of G0 on G00 for DP (A: DP-1; B: DP-3; ultrasonic con-

ditions as in Fig. 1).

10-2 10-1 100 101 102102

103

104

η∗,

Pas

ω, rad/s

0s300s

DP-3

DP-1

Fig. 13. Dependence of h* on u for DP (ultrasonic conditions as in Fig. 1).

of macro-chain of DP melt is mainly concentrated on the por-tion of high molecular weight due to long relaxation time.

In addition, other ultrasonic conditions also affect the deg-radation behavior of DP-1 and DP-2 melts. The decrease of os-cillation temperature and increase of ultrasonic intensity canaccelerate the degradation. It is interesting to note that the ef-fective distance of ultrasonic degradation is ca. 4 mm from theprobe tip. The degradation mechanism of DP can be explainedby our model of ultrasonic degradation.

Dynamic rheological results also confirm the ultrasonic deg-radation behavior of DP melts for the samples obtained fromstatic ultrasonic oscillations. The complex viscosity, zero shearviscosity, viscoelastic moduli, cross modulus, relaxation timeand the slope of log G0 � log G00 for DP melt decrease withthe introduction of ultrasonic oscillations, whereas its crossfrequency gets increased due to ultrasonic degradation.

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