Macromolecules 1986,19, 2520-2524
2520
Effect of Diluent on Viscoelastic Properties of Binary Blends of Narrow Molecular Weight Distribution Polystyrenes Hiroshi Watanabe and Tadao Kotaka* Department of Macromolecular Science, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan. Received February 12, 1986
ABSTRACT: The effect of diluent on the viscoelastic properties of binary blends of narrow molecular weight distribution polystyrenes (PS)having molecular weights Mwland Mwz (>>Mwl)was investigated. The content of the long-chain component (2-chain) was kept small so that entanglement among 2-chains did not occur. At the iso-free-volume state, the relaxation time 712 of the 2-chain was proportional to w:Mwlo for blends with Mwl> M*. Here the critical value, M*, was approximately wp-lMeo,with wp and Meo being the total polymer content in the blends and the molecular weight between entanglement points of the bulk PS, respectively. These and previous results were interpreted as follows. In blends with Mwl > M*, the 2-chain relaxes also by a Rouse-like mode only after the constraint on the 2-chain has become ineffective due to the diffusion of the entangling l-chains. However, wP-lMeo.In the the effective segment size for these Rouse-like modes appears to be proportional to M* framework of a generalized tube model, the latter process is identical with the tube renewal process.
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Introduction Binary blends of polymers having narrow molecular weight distributions (MWD) and different molecular weights are a simple but interesting model system for examining effects of entanglement on viscoelastic properties of polymers because these blends often exhibit relaxation modes not observable in monodisperse systems. We examined binary blends of narrow MWD polystyrenes (PS) in the molten state and found the following feat u r e ~ . ~The - ~ relaxation modes of the short-chain component (designated as the l-chain) were essentially unaffected by blending, while those of the long-chain component (the 2-chain) were strongly affected by the l-chain through two mechanisms: one due directly to 1-2 entanglement and the other to 2-2 entanglement diluted by the l-chain.2 When the weight-average molecular weight Mw2 of the 2-chain was sufficiently larger than Mwl of the 1chain, these relaxation mechanisms were clearly separable in the long-time region.’l3 For such blends with content w2 of the %-chainlarger than a critical value w, corresponding to the onset of 2-2 entanglement, the 2-chain relaxed from 2-2 entanglement just as in a concentrated solution, where l-chains simply acted as a low molecular weight solvent. On the other hand, in blends with w2 well below w, where 2-2 entanglement was nonexistant, the 2-chain relaxed under the influence of 1-1 and 1-2 entanglement. As reported p r e v i ~ u s l ythe , ~ ~relaxation ~ time T~~ of the 2-chain in blends with w2 C w, is given by 712
= C{owu,0MwloMw22 (Mw2>> M*
>> Mwl)
712
= C ’ { ~ W Z ~ M ~ ~ (Mw2 ~ M >> , ~Mwl ~ >> M*)
(la) (lb)
depending, respectively, on whether Mwl is above or below a critical molecular weight M*. Here M* ( r 2 0 X lo3 for PS) is close to the molecular weight Meo between entanglement points in the bulk polymer (=18 X lo3 for PS),4 and lo, the monomeric friction coefficient, and the constants C and C’ are independent of Mwl and Mw2. We interpreted eq l a and l b as follow^:^,^ In blends with Mwl > M*, the 2-chain relaxed only after the constraint (or entanglement) due to l-chains became ineffective (eq lb). However, the Mw22dependence of r12 suggested that the relaxation behavior was still Rouse-like for with an effective friction factor proportional to MWl3 an effective segment of an unknown size (presumably comparable with Meo). The above molecular picture was found to be useful in clarifying the nature of the entanglement effect not only in binary blends but also in monodisperse system^.^ However, our previous studies were limited only to PS/PS blends in the molten state where M* (=Meo)was the same for all systems. Therefore, the picture was not sufficiently complete to elucidate the exact nature of the Rouse-like relaxation in blends of the latter type. Also there remained uncertainty in the interpretation of C and C’ in eq 1. To refine our molecular picture, we extended our study to blends consisting of a diluent and binary blends of narrow MWD PS’s. By adding a diluent to the binary blends, we should be able to change the molecular weight Me between entanglement points. Thus, we attempted to examine the effect of diluent on the relaxation behavior of the 2-chain in the blends, particularly by observing the effect of changing Me on the relaxation time r12by dilution. In this paper we present the results and discuss the meaning of the front factors C and C’. Experimental Section Anionically polymerized narrow MWD polystyrene (PS) samples were used. For convenience, hereafter, we call such samples monodisperse. The characterization of these samples was carried out by gel permeation chromatography. The details were described previously.’V2 Table I summarizes the codes and characteristics of the samples used in this study. The systems examined were binary blends (bB) of PS samples diluted with dibutyl phthalate (DBP; Wako Pure Chemical Industries, Ltd., guaranteed grade). The L2810 sample was chosen as the 2-chain (the long-chain component), with others serving as the l-chains (the short-chain component). The content w pof the 2-chain was always 1wt % of the whole system, and the total polymer content wp (=wl + wz)examined was 36.4 and 60 wt %. For comparison, DBP solutions of the l-chain alone with concentration wl,m = 36.4 and 60 w t % were also examined. In the following, such solutions are designated as parent-monodisperse (p-m) systems for the corresponding blends.
0024-929~/86/22~9-2520$o1.5o/o 0 1986 American Chemical Society
Viscoelastic Properties of Blends of Polystyrenes 2521
Macromolecules, Vol. 19, No. 10, 1986 Table I Characteristics of PS Samples
6
5
11 -5
1
-3
-4
-2
0
-1
lag (we,
15-1
1
3
2
4
)
Figure 2. Master curves of loss moduli G”for the PS/PS/DBP systems examined in Figure 1. 41
I
I
PSI PS/DBP f, = 0 . 0 6 4 4 Mw2= 281 X lo4
w2 = 1 w t %
2
-5
1
I
-4
-3
-2
I
I
-1
0
log (
I 1
2
3
4
w q 15-1 I
Figure 1. Master curves of storage moduli G’for PS/PS/DBP systems with wp = 60 wt % at TIand values of Mwl,Mw2,and w2 as shown. Broken curves indicate master curves for the corresponding parent-monodisperse systems. Since the densities of DBP (=LO465 g/cm3 at 25 0C)5and bulk ~ ) ~close to each other, we neglected PS (=1.04-1.065 g / ~ m were the volume change due to mixing PS and DBP and assumed the weight fraction of the PS sample to be equal to its volume fraction. To prepare a PS/PS/DBP blend, we dissolved prescribed amounts of L2810 (the 2-chain) and other low molecular weight PS samples (the 1-chain) and DBP in excess methylene chloride (Nakarai Chemicals, Ltd., guaranteed grade). The methylene chloride was subsequently evaporated a t room temperature to obtain a homogeneous PS/PS/DBP blend of the desired composition. Dynamic measurements were carried out on the PS/PS/DBP systems at several temperatures between 10 and 120 OC with a conventional cone-and-plate rheometer (Autoviscometer L-111, Iwamoto Seisakusho, Kyoto). The details were described prev i o ~ s l y . ~The - ~ time-temperature superposition principle4 was applicable to the storage (G? and loss (G”) moduli. All data, including the previous data for PS/PS melt blends, were compared a t an iso-free-volume state with the free-volume fraction f, = 0.0644.3 At such a state, the monomeric friction coefficient lo should be the same for all the systems.
Results Figures 1 a n d 2 respectively show master curves of G’ a n d G” for PS/PS/DBP systems with wp = 60 wt % at f, = 0.0644. Broken curves i n t h e figures represent t h e behavior of t h e p-m systems with w,,,,= 60 wt %. In these figures, we see t h a t t h e G’and G ” curves of the blends coincide with those of t h e p-m systems at high frequencies b u t exhibit a prominent shoulder at low frequencies. For t h e three blends with M,, I23.4 X lo3 t h e position of t h e shoulder is independent of M,,, while for all other blends with M,, 1 41.5 X lo3t h e shoulder rapidly
- 50
0
50
100
T - T,/T
Figure 3. Temperature dependence of the shift factor aT reduced at Tf with f, = 0.0644 for PS/PS/DBP systems. The solid curve represents the WLF equation log UT = -6.74(T - T1)/(133.6 + T
- TI).
Table I1 Reference Temperature T,Where f, = 0.0644 for the PS/PS/DBP Systems w,/(wt 900) 10-3~,, TJ0C 100” 5.2 146 10.5 155 167 223.4 44 60 5.2 10.5 49 223.4 54 -1 5.2 36.4 2 10.5 6 223.4
’Reference 3. shifts with increasing M,, t o t h e lower frequency side. Although t h e figures are n o t shown here, t h e features of PS/PS/DBP systems with wp = 36.4 wt % were essentially t h e same. All these features were also observed for PS/PS m e l t blend^.^ Figure 3 shows t h e temperature dependence of t h e shift factor aT reduced at t h e reference temperature TI with f, = 0.0644 for the PS/PS/DBP systems examined here and for t h e PS/PS melt blends in our previous s t ~ d y We . ~ see t h a t t h e t e m p e r a t u r e dependence is nearly t h e same for all t h e systems. Table I1 summarizes the values of TIused
Macromolecules, Vol. 19, No. 10, 1986
2522 Watanabe and Kotaka 0
I
monodisperse PSI DBP 7
-
1, = 0.0644
-
0 100lmrlil
w
1.m
6
4l
-* 3
-
IWi%
0
0
60
m
36 4
I
I
PSI PSIDBP
100 ( m e l t )
:I w'
h
--
I
I
3
5
4 109 Mw,
6 3
4 '09 wp M*,
5
6
.
Figure 5. Dependence of the weight-average relaxation time of the 2-chain in the blends at T,on Mwl(left panel) and wJdw1 (right panel).
Jz,bBvz,bs
3
4
5
6
l o g W1,mMwl
Figure 4. Dependence of the viscosity vl,m of parent-monodisperse systems on their reduced molecular weight wl,,Mwl a t T,
contribution of the 2-chain to the viscosity q2,bB, the elastic coefficient A2,bB, and the compliance J2,bB can be evaluated as
with f, = 0.0644.
in this and previous3 studies. As is ~ e l l - k n o w nTI , ~ becomes lower with decreasing wp. We also notice in Table I1 that the change in T, with decreasing Mwl becomes smaller at lower wp. The excess free volume due to the polymer chain ends becomes less significant with decreasing wp because DBP molecules provide most of the excess free volumes. Figure 4 shows the dependence of the zero-shear viscosity qlF of the p-m systems at T,with fI = 0.0644 on their reduced molecular weight wl,mMwl.When the viscosity data at different T,are compared, a small correction for the magnitude of the rubber elasticity (a7') and the density of the system is nece~sary.~ In Figure 4, the data were corrected for these effects at 167 O C . In Figure 4 we see a universal relation between ql,m and wl,mMwl,which is well established for concentrated polymer system^:^ For systems with w,,,MWl less than the characteristic molecular weight Mco ( r 3 1 X lo3 for melt PS)? qlF is proportional to wlJVwl, while for systems with wl,,MWl> Mco,q1,, a ( W ~ , , M , ~ ) ~ . ~From . this result and the temperature dependence of aT shown in Figure 3, we may conclude that the correction for f , (and hence for is well achieved. From the master curves of G'and G"for the blends, we evaluated the characteristic relaxation time of the 2-chain in the blend. For this purpose, we used the following blending law, proposed previ~usly:~
r0)
HbB(7)
= WlHl,bB(7) +
W2H2,bB(7)
(2)
where H b B is the relaxation spectrum of the binary blend and H1,m and H2,mare the spectra (per unit chain content) of the 1- and 2-chains in the blend, respectively. Generally, H1,bB and H2,bB depend on Mwl,Mw2,wl, and w2, because the entanglement state in the blend depends on these quantities. However, as seen in Figures 1 and 2, the behavior of the blend with w1 >> w2 at high frequencies is the same as that of the p-m system. The results suggest that the relaxation modes of the 1-chain are the same in such a blend and in the p-m system. This allows us to replace H l , b B ( T ) by the spectrum f f l , m ( ~(per ) unit chain content) of the 1-chain in the p-m system. Then the
Here the subscripts bB and l,m stand for the quantities of the blend and the corresponding p-m system, respectively. (In our previous paper, the quantities q2,bB and A 2 b B were designated by Aq,, and AAG, re~pectively.~) For blends containing the L2810 sample as the 2-chain, 7/2,bB and A2,bB were proportional to w2 in the range w2 I 1 wt %, as reported previously.' This indicates that H2,bB(~) does not depend on w2, and hence, 2-2 entanglement does not exist in the blend with w2 I 1 wt %. The product J 2 , b ~ q ~ (defined ,b~ as 712 in the Introduction) is the weight-average relaxation time of the 2-chain in the blend. The arrows in Figure 1indicate the characteristic frequencies I/ (Jz,bBO2,bB). Figure 5 shows the dependence of J2,bBq2,bB at T,on Mwl (left) and w,,Mwl (right). We recognize that there is a critical molecular weight M* for Mwl,where the dependence of the J z , b e t z , b ~on Mwlchanges. For blends with Mwl sufficiently larger than M* (but still sufficiently smaller than Mwz),we see that J2,bBP2,bB is almost proportional to MWl3 and depends on wp as well. On the other hand, for blends with sufficiently small Mwl ( 2Mb. The molecular weight dependence of T~ for randomly branched polymers is much lower than that of linear ones. With decreasing Mb, qo of randomly branched samples a t the same molecular weight decreases. Data on randomly branched polymers having M,/Mb of about 3.5 fall well on the line for 3-4-armed-star polystyrene solutions. The steady-state compliance J," is proportional to M , a t M , < Mb, is independent of M , in the range M b < M , < 2Mb, is again proportional to M , in the range 2Mb < M , < (5-6)Mb, and increases rapidly with molecular weight a t M , > (5-6)Mb. Moreover, the effect of Mb on the relaxation spectra for randomly branched samples with different M b are compared.
Introduction The effect of branching on viscoelastic properties is one of the most important problems to be solved in polymer 0024-9297/86/2219-2524$01.50/0
industry as well as in polymer science. Recently, preparation of model branched polymers with a narrow distribution of molecular weights has become possible, and 0 1986 American Chemical Society
