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レオロジー特性の制御とプラスチック成形加工
山形大学理工学研究科杉本昌隆
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• 研究室紹介• レオロジー特性の改良• レオロジーと成形加工性‒ブロー成形‒フィルム成形
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本日の内容
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今からの米沢
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１９１０年（明治４３年） ・山形大学工学部の前身である米沢高等工業学校開校 ・秦逸造教授が日本で初めて人造絹糸の紡績に成功大正５年 秦逸造教授が帝国人造絹糸（帝人）の前身であるベンチャー企業「東レザー分工場米沢人造絹糸製造所」で人造絹糸を工業化
２０１０年 開学１００周年を迎える。
旧米沢高等工業学校（国の重要文化財）
山形大学工学部の生い立ち
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MELT TENSION TESTER
Extruder’s die
Polymer melt strand
Tension sensor6
自由表面下でのレオロジー
ひずみ速度が変化非等温
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LDPE
LDPE
HDPE
PS
ひずみ硬化性
粘度の急激な上昇
伸長流動が支配的な成形方法に最適
ひずみ速度を変えて測定したPS, HDPE, LDPEの一軸伸長粘度挙動
eg. Extrusion Foaming
超臨界流体Pellets
Cell Wall
Foamed Sheet
Foaming Agent
Elongational FlowShear Flow
Melting Phase Foaming and Cooling Phase 8
Air
blow upAir
伸長流動（ひずみ硬化性）
��!�"�#���
9
せん断流動
OR
O
O O
O
O
OO
O
O
O
O
O
O n
OR
O
O O
OH
OH
OO
O
O
O
O n
OR
O
O OH
OH
OH
OHO
O
O
n
O
O
trans-esterification sulfamic acid
O
OO
Fig
.1S
ugim
oto
et al.
Sugimoto et al. J Polym Sci Part B
10
Hyperbranched PS
time period needed to perform the frequencysweep tests at various temperatures. The isother-mal dynamic viscoelastic measurements were car-ried out at 160–240 !C. The resulting storagemodulus G0 and loss modulus G0 were horizontallyshifted to the curve at reference temperature of160 !C. The principle of time–temperature super-position was valid for all samples. The thermo-rheological simplicity was confirmed by themethod proposed by van Gurp and Palmen23: theplots of the phase angle as a function of the com-plex modulus d(|G*|) at different temperatures.The temperature dependence of the horizontalshift factors aT followed the WLF-type equation24:
logaT " # C1$T # T0%C2 & $T # T0%
(1)
where C1 and C2 are WLF coefficients and T0 isreference temperature. A significant change ofthe sift factors as a function of temperature is notdetected for hyperbranched-PS comparing withlinear PS. It can be concluded that the sift factor
is independent of the macromonomer concentra-tion and resulting molecular architecture of thehyperbranched-PS. This is consistent with theresults of the graft PS studied by Hepperle et al.17
and Kapnistos et al.25
Figure 3 shows G0 and G00 as a function of angu-lar frequency for PS-A, B, and C. The master-curves reveal that G0 decreases with increase ofmultimethacryloyl macromonomer dose at inter-mediate frequency region. In the high-frequencyregion, which corresponds to the onset of segmen-tal relaxation, the dynamic moduli tends to con-verge on a single curve. In the low-frequencyregion below 10#3 rads#1 G0 indicates signs of aslight increase with macromonomer content,though PS-A shows terminal flow transitionwhere slopes of log G0 and log G00 against log xare 2 and 1, respectively. This suggests marginalchange of relaxation time distribution before theterminal region. Thus, the difference between lin-ear PS and hyperbranched-PS is not significant
Table 1. Molecular Characterization of PS-A, B, and C
MacromonomerContent (ppm) Mw (kg/mol) Mn (kg/mol) Mw/Mn g0
a ('106 Pa s) mb
PS-A 0 263 143 1.8 1.58 –PS-B 500 306 118 2.6 1.44 15PS-C 900 445 132 3.4 1.16 80
aZero-shear viscosity at 160 !CbNumber of branches at shoulder of the molecular weight distrubution
Figure 2. Molecular weight distribution of PS-A, B,and C.
Figure 3. Mastercurves of the dynamic moduli G0
and G0 as a function of angular frequency for PS-A,B, and C. The reference temperature T0 is 160 !C.
MELT RHEOLOGY OF HYPERBRANCHED-POLYSTYRENE 2229
Journal of Polymer Science: Part B: Polymer PhysicsDOI 10.1002/polb
11
GPC-MALS
0
50
100
150
103 104 105 106 107
dW /
dlog
Mm
M / gmol-1
PS-A
PS-B
PS-CPS-B
PS-C
12
101
102
103
104
105
106
100
101
102
103
104
105
10-4 10-3 10-2 10-1 100 101 102
PS-APS-BPS-C
G' /
Pa G
" / Pa
ωaT
-1 / rads-1
2
1
Tr:160 oC, T: 160 ~ 240 oC13
103
104
105
106
10-4 10-3 10-2 10-1 100 101 102
PS-APS-BPS-C
|η*|
a T-1 /
Pa s
ω aT / rad s-1
than expected from the polydispersity of molecu-lar weight and the presence of high-molecularweight tail.
Figure 4 shows the angular frequency depend-ence of the dynamic complex viscosity |g*(x)| ofPS-A, B, and C. The value of |g*(x)| at low-frequency region decreases as increasing concen-tration of macromonomer added in the polymer-ization process, whereas |g*(x)| fall into a sameviscosity curve at higher frequencies. To representthe angular frequency dependence of |g*(x)|, thegeneralized Cross-Carreau-Yasuda model26,27 wasemployed and the zero-shear viscosity g0 wasobtained according to the following equation:
g!j j " g0 1# $kx%af g$n&1%=a (2)
where k, a, and n are model constants. Stadlerand Munstedt28 proposed an extended Carreau-Yasuda model to describe the shear viscosity func-tion with two curvatures for highly entangledpolymer:
g!j j " g0 1# $k1x%a1f g$n&1%=a1 1# $k2x%a2f g$n&1%=a2
(3)
Equation 3 provided best fit for long-chainbranched metallocene-catalyzed polyethylenes,whereas eq 2 failed to fit the viscosity data withsufficient accuracy. The successful expression ofmetallocene polyethylene with long-chainbranches using eq 3 would result from the long
relaxation modes of long-chain branching in addi-tion to those of substantially linear chains. Themodified-model is, however, unable to describe theviscosity function of hyperbranched-PS-B and Cwith realistic values of k1 and k2. The derivativesof viscosity functions of PS-B and C in double-log-arithmic plots are characterized by monotonicallydecreasing curves until reaching power-lawregion, though long-chain branching polyethyleneexhibited a plateau or a shoulder in double-loga-rithmic slope. It should be considered that thisdisparity results from the polymer compositionand the relaxation time mode distribution.
The obtained results of g0 are shown in Table 1.Figure 5 shows the zero-shear viscosity as a func-tion of weight-average molecular weight deter-mined by light scattering method for PS-A, B, andC. The solid line represents the following scalinglaw for linear PS:
g0 ' Mw3:4 (4)
It is well known that this relationship is inde-pendent of the polydispersity. Hepperle et al.17
reported that the power-law relation held even forlinear bimodal blends of PS. For PS-B and C, it isfound that g0 are lower than that of linear PSwith same molecular weight. This deviation fromthe above scaling law can be seen in comb-likegrafted-PS17 and star-branched-PS,29,30 which isshown in Figure 5. The rheological parameter isdirectly related to the molecular structure such aslong-chain branching. The viscosity reduction and
Figure 5. Zero-shear viscosity as a function ofweight-average molecular weight for PS-A, B, and C.The reference temperature T0 is 160 (C. The solidline represents the scaling law for linear PS.
Figure 4. Mastercurves of the dynamic complex vis-cosities as a function of angular frequency for PS-A,B, and C. The reference temperature T0 is 160 (C.
2230 SUGIMOTO ET AL.
Journal of Polymer Science: Part B: Polymer PhysicsDOI 10.1002/polb
Carreau-Yasuda model
14
105
106
107
105 106
PS-APS-BPS-CMasuda et al. 6 arm-starYamamoto et al. Multi-arm star
η0 /
Pa s
Mw / gmol-1
than expected from the polydispersity of molecu-lar weight and the presence of high-molecularweight tail.
Figure 4 shows the angular frequency depend-ence of the dynamic complex viscosity |g*(x)| ofPS-A, B, and C. The value of |g*(x)| at low-frequency region decreases as increasing concen-tration of macromonomer added in the polymer-ization process, whereas |g*(x)| fall into a sameviscosity curve at higher frequencies. To representthe angular frequency dependence of |g*(x)|, thegeneralized Cross-Carreau-Yasuda model26,27 wasemployed and the zero-shear viscosity g0 wasobtained according to the following equation:
g!j j " g0 1# $kx%af g$n&1%=a (2)
where k, a, and n are model constants. Stadlerand Munstedt28 proposed an extended Carreau-Yasuda model to describe the shear viscosity func-tion with two curvatures for highly entangledpolymer:
g!j j " g0 1# $k1x%a1f g$n&1%=a1 1# $k2x%a2f g$n&1%=a2
(3)
Equation 3 provided best fit for long-chainbranched metallocene-catalyzed polyethylenes,whereas eq 2 failed to fit the viscosity data withsufficient accuracy. The successful expression ofmetallocene polyethylene with long-chainbranches using eq 3 would result from the long
relaxation modes of long-chain branching in addi-tion to those of substantially linear chains. Themodified-model is, however, unable to describe theviscosity function of hyperbranched-PS-B and Cwith realistic values of k1 and k2. The derivativesof viscosity functions of PS-B and C in double-log-arithmic plots are characterized by monotonicallydecreasing curves until reaching power-lawregion, though long-chain branching polyethyleneexhibited a plateau or a shoulder in double-loga-rithmic slope. It should be considered that thisdisparity results from the polymer compositionand the relaxation time mode distribution.
The obtained results of g0 are shown in Table 1.Figure 5 shows the zero-shear viscosity as a func-tion of weight-average molecular weight deter-mined by light scattering method for PS-A, B, andC. The solid line represents the following scalinglaw for linear PS:
g0 ' Mw3:4 (4)
It is well known that this relationship is inde-pendent of the polydispersity. Hepperle et al.17
reported that the power-law relation held even forlinear bimodal blends of PS. For PS-B and C, it isfound that g0 are lower than that of linear PSwith same molecular weight. This deviation fromthe above scaling law can be seen in comb-likegrafted-PS17 and star-branched-PS,29,30 which isshown in Figure 5. The rheological parameter isdirectly related to the molecular structure such aslong-chain branching. The viscosity reduction and
Figure 5. Zero-shear viscosity as a function ofweight-average molecular weight for PS-A, B, and C.The reference temperature T0 is 160 (C. The solidline represents the scaling law for linear PS.
Figure 4. Mastercurves of the dynamic complex vis-cosities as a function of angular frequency for PS-A,B, and C. The reference temperature T0 is 160 (C.
2230 SUGIMOTO ET AL.
Journal of Polymer Science: Part B: Polymer PhysicsDOI 10.1002/polb
PS-BPS-C
6-arm Star
Multi-arm Star
15
10-1
100
101
102
103
104
100 101 102
G(t,
γ) /
Pa
t / s
10-1
100
101
102
103
104
100 101 102
G(t,
γ) /
Pa
t / s
τk
16
-0.8
-0.6
-0.4
-0.2
0
0.2
-1 -0.5 0 0.5 1
PS-APS-BPS-CD. E.
log
h(γ)
log γ
PS-B is not shown here), it is clear that thesmaller slope of G(t, c) resulting from the longrelaxation time is observed for PS-C [Fig. 7(b)]. Atlarge strains, the curve may be characterized bythe inflection point at sk !10 s. The curves at vari-ous strains are parallel each other at longer timethan t " sk. We will discuss it below.
We can evaluate the damping function fromdependence of the nonlinear relaxation moduluson the strain. The nonlinear feature of G(t, c) forentangled flexible polymers can be often factora-ble in time- and strain- dependent at long time(t[ sk);
G#t; c$ " G#t$h#c$ #t > sk$ (5)
where G(t) is time-dependent shear modulus atsmall strain and is independent of strain and a
unique function for a given polymer. h(c) is strain-dependent damping function34–38 and representshow the stress is lower than the linear viscoelas-ticity limit. It has been known that h(c) is a uni-versal function of c for entangled flexible polymerliquids with narrow molecular weight distributionand is independent of molecular weight and con-centration. Although G(t, c) of PS-Awas factorableaccording to eq 5 within the experimental time,the curves of PS-B and C can be superimposedonly at times longer than sk 1.5 and 10 s, respec-tively. According to Doi-Edwards theory,41 thedecrease of the relaxation modulus results fromchain retraction along the tube contour andremaining orientation of a strand after the retrac-tion. When the step-strain is applied to polymermelts, retraction of the chain quickly occurs alongthe tube contour compared with reptation motion.The retraction of molecule yields the contourlength of the primitive path back to its equilib-rium length. The retraction is complete in a timeof sk, which is roughly equal to the Rouse time sR.Therefore, it can be expected that increased valueof sk of PS polymerized with multimethacryloylmacromonomer possesses the longer Rouse time,leading to tendency of chain stretching under aflow in which the elongational flow is particularlydominant.
Step-shear damping function h(c) of PS-A, B,and C are provided in Figure 8. The experimentalresults were compared with theoretically pre-dicted values by Doi-Edwards for monodispersedpolymer. At small strains, for PS-A, the strainsoftening is small and deviation of h(c) fromDoi-Edwards theory is also small. As strain
Figure 8. Comparison of step-shear damping func-tion h(c) of PS-A, B, and C. The solid line representsthe prediction of Doi-Edwards theory.
Figure 7. Time-dependent nonlinear shear relaxa-tion modulus G(t, c) for (a) PS-A and (b) PS-C at vari-ous strains, 0.3, 0.5, 0.7, 1, 2, 3, 4, and 6 from top tobottom.
2232 SUGIMOTO ET AL.
Journal of Polymer Science: Part B: Polymer PhysicsDOI 10.1002/polb
17
104
105
106
10-1 100 101 102 103
0.010.030.050.10.30.51.0
3η+(t)
ηE+ (t,
ε) /
Pa
s
t / s
.
.ε / s-1
3η0
104
105
106
10-1 100 101 102 103
0.0030.0050.010.030.050.10.30.51.03η+(t)
ηE+ (t,
ε) /
Pa
s
t / s
.
.ε / s-1
3η0
18
19
Chain extender
:
COOH
RRR
回収PETのレオロジー改質
20
Modified PETCollected PETNon Strain hardening
回収PETのレオロジー改質
103
104
105
106
10-2 10-1 100 101 102
0.05 (1/s)0.1 (1/s)0.5 (1/s)1.0 (1/s)
η+ e /P
a s
t / s
103
104
105
106
10-2 10-1 100 101 102
0.05 (s-1)0.10.51.0
η+ e /P
a s
t / s
21
エアーノズル
ブローアップ過程
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������
Key point
45mm
80mm
55mm
22
23
PET collected for recycling Modified recycled PET
Direct Blow Molding at 270 oC
24
フィルム成形性の少量評価と可視化技術
• 少量で押出性を評価できる装置の開発‒ 混練性
‒ 粘度測定
‒ 多層フィルム成形性
• 口金（ダイ）内可視化技術
25
研究背景
26
g�
kg(
ton(
��&�
'�Step�
ラボ
パイロット
本プラント
基本物性の評価
研究開発期間コスト
エネルギー
小型・中型試作物性、成形性
実成形成形性、製品物性顧客評価
27
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GP
Return flow path
P1�
P2�
P;�P3�T-die�
Sample�
Screw barrel�
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GP
Return flow path
P1�
P2�
P;�P3�T-die�
Sample�
Screw barrel�
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GP
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Introduction What is multilayer film ?Polymer A
Polymer A
Polymer B
Polymer B
Polymer C
Flow direction
Multilayer film
[Wave type] [Zig-zag type]Interfacial roughness Encapsulation
AB
31
Interfacial Roughness in Multi-layer FlowPP-A/PP-B
PP-A/PS-A
QL/QU=2.3 QL/QU=5 QL/QU=14
32
QL/QU=2.3 QL/QU=5 QL/QU=14
33
100µm
Polymer A
100µm
Polymer B+蛍光剤
変位と時間から流速分布
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相構造の動的観察
�#�
34
ドメイン構造の変化 スタートアップ流れ
35
ドメイン構造の変化 流動→停止
Polymer/Polymer interfacial slip
WallWall
Slip ?
Polymer A
Polymer A
Polymer B
Motivation
Polymer/Polymer Interfacial Slip in Multi-layer Flow
Interfacial Roughness
36
PS
PP
Wash(THF)
�
�
�
Results Polymer/polymer interfacial slip velocity and roughness
37
38
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