Znd. Eng. Chem. Res. 1995,34, 3496-3507
3496
Nonlinear Viscoelasticity of ABA Block Copolymer Melts: Stress Relaxation and Recovery Robert D. Spaanst and Michael C . Williams* Department of Chemical Engineering, University of Alberta, Edmonton, Alberta T6G 2G6, Canada
The nonlinear rheological character of microphase-separated ABA-type block copolymer melts was investigated in the context of stress relaxation experiments. Five grades of triblock copolymers were studied in step strain programs. End blocks were polystyrene and middle blocks either polybutadiene or polyisoprene. Molecular weights ranged from 61 300 to 140 000 and styrene fractions from 0.14 to 0.44. Test temperatures (90-110 “C)were above Tgof the styrenic microphases and below the separation temperatures of these polymers, so all were multiphase systems with each phase in the liquid state. Strain amplitudes ( y o )ranged from 0.05%to 3.86%. At the highest y o , relaxation moduli dropped steadily in liquidlike fashion; at lowest y o , the stress relaxation was overtaken by a competing microstructural recovery process which caused the modulus to pass through a minimum and then increase. Results are discussed in terms of the interfacial diffuse phase (interphase), morphology, and molecular weight.
Introduction
J
The structure existing in the microphase-separated state of block copolymers (AB, ABA, etc.) gives these materials a unique (nonlinear) rheological character. It was revealed in the classical work of Holden et al. (1969) that in ABA copolymers a three-dimensional structure of effective cross-links can exist without vulcanization, even when all phases are above their glass transition temperatures (T,)and are therefore in the liquid state
(T >
>
TS
k
‘B
AT
e).
Meier (1969) developed a thermodynamic model defining conditions for phase separation in terms of an interfacial surface tension and a critical molecular weight (MW). This was later refined by the model of Leary and Williams (1974),which featured a substantial mixed region of continuously varying composition (with no surface tension explicit), which they termed the “interphase”. They also defined a critical “separation” temperature (T,).This T, was conceived to be the temperature below which, for a given MW and volume fraction of minor component (C~A), a phase-separated structure is thermodynamically most stable (lowest free energy state). Evidence of profound rheological differences in the material above and below T,,both conditions representing melt behavior, was later advanced (Pic0 and Williams, 1976; Chung and Gale, 1976; Gouinlock and Porter, 1977). The phase-separated structure is now widely acknowledged to consist of two homogeneous nearly-pure major phases (either co-continuous or dispersed and matrix phases), and a third diffuse interphase ($hen and Kaelble, 1970; Spontak et al., 1988). These three regimes for a styrene-butadiene-styrene copolymer are shown schematically for cylindrical or spherical morphology and lamellar morphology in Figure 1. At the bottom of Figure 1,the styrenic fraction (4s) distribution in these systems is displayed. The interphase always has an average Cjs close to 0.50, although usually slightly richer (generally so, for the component of highest Tg). This smoothly varying interphase composition profile has been measured directly (Spontak et al.,1988) by
* To whom correspondence should be addressed. Present address: ZCL Composites, Nisku, Alberta T9E 723, Canada.
S
+ B
Figure 1. Schematic representation of ABA (here, SBS) block copolymer molecule embedded in a phase-separated microstructure consisting of matrix B, core S, and broad interphase of mixed S and B.
image enhancement of a transmission electron micrograph of a polystyrene cylindrical microphase viewed end-on, and indirectly (Diamant et al.,1984) by fitting a composite rheological model to data on G ( T )and G ( T ) for poly[b-styrene-b-butadiene-b-styrene] (SBS)solids. Henderson and Williams (1979) proposed that the
0888-5885/95/2634-3496$09.00/0 0 1995 American Chemical Society
Ind. Eng. Chem. Res., Vol. 34, No. 10,1995 3497 Table 1. Polymer Identification and Properties
M n
4s (%)
morph. 7pC) butadiene 69 400 30.4 cylindrical 60-70 butadiene 61 300 44 lamellar 60-70 butadiene 101 000 31.3 cylindrical 96 29.8 cylindrical ethylenehutylene random copolymer 67 000 SIS isoprene 140 000 14 spherical 65-75 a [TIrepresents a T,which was not measured, but predicted on the basis of Leary-Williams theory,
descriptor SBSl SBS2 SBS3 SEBS
center block
qcoo
T,("C)
-92 -92 -92 da -60
243 255 [482Ia [a391 260
composition gradient through the interphase from uniform A-rich t o B-rich regions gives rise t o a chemical potential @A) gradient and a resultant interphase barrier force
-vPA
(1) resisting the extraction of A segments from their compatible A-phase into the incompatible adjacent B-phase. As flow requires the disruption of the threedimensional network, the degree of chemical incompatibility between blocks was predicted t o have a great influence on melt rheology; the existence of a yield stress (t,>was proposed, associated with the force FA = (FA)I. The degree of chemical incompatibility was characterized by the square of the difference in solubility param~. and Meinecke (19771, in a eters, ( B A - 6 ~ ) Futamura study with ABA copolymers having differing center blocks but the same end blocks (styrene), demonstrated that the relaxation times associated with long-range motions of chains increased with increasing IBA - &I. The focus of the present study is on the role of structure-forming (thermodynamic) forces in determining the relaxational and structural-recovery processes in triblock copolymers, all having styrenic end blocks and rubbery center blocks. Rheological characterization is achieved by tracking stress transients (z(t))following the imposition of a step strain. This simple strain program seems to be little employed in block copolymer melt rheological studies, preference being given to dynamic oscillatory and steady shear testing; however, a wealth of information can be gleaned from the step strain test. Kamykowski and Ferry (1982) studied stress relaxation following a step strain in mixtures of triblock SBS with diblock SB and unattached linear polybutadiene, at temperatures ranging from -20 to +20 "C. These temperatures were clearly below From their study it was found that there was no contribution t o relaxation from the dangling butadiene segments. Hsiue and Wu (1980) examined stress transients in an SBS copolymer following a 30% elongation a t temperatures ranging from +86 to +95 "C. All of these temperatures may well have been above (see Figure 2 and arguments below). They found that under certain heating conditions the stress did not decay to zero, but leveled to a plateau which was attributed to the network structure. (FA11 =
e.
e
Experimental Section Materials. Copolymers SBS1, SBS2, and SBS3 were supplied by Dow Chemical Co. U.S.A., while SEBS was supplied by Shell Chemical Co. U.S.A. Copolymer SIS was an older sample of Shell Kraton-D 1107, which was found to dissolve completely in tetrahydrofuran, indicating that it was not cross-linked and probably close to being preserved. These materials are characterized in Table 1. Molecular weight and composition data were provided by the manufacturers. Our laboratory performed thermal analysis (Figure 2) to obtain glass
"
I -100
0
100
200
300
Temperature ("C) Figure 2. DSC traces for SBS1, SBS2, SBS3, and SIS.
transition temperatures of the styrenic (in these cases, dispersed) phase ( p )and T,(where measured), using a TA Instruments fA2200 differential scanning calorimeter. The Tis measured for the polystyrene phase were significantly lower than that normally quoted for highMW polystyrene (PS),namely 100 "C. Some of this can be attributed to depression of Tgdue to low MW of the PS end blocks, and correspondingly higher free volume in the PS microphase; for example, the use of Tg= Tg.. - K/Mn for PS (Rodriguez, 1989) gives, with K = 21 x lo4 "C g/mol, a value T6 =z 80 "C for SBSl which possesses Ms = 10 400. fn addition t o this, Tgof the "rigid" phase in thermoplastic elastomer block copolytends to be lower than that of a pure mers (here, homopolymer of the same chemical structure and MW as that of the end blocks (Krause et al., 1982). This is due to entrapment of some center-block rubbery segments (Krause et al., 1982), a kinetic effect which is not thermodynamically favored. This is observed in the Tg values listed in Table 1 for SBS1, SBS2, and SIS, but not for SBS3. Also in Table 1,the T,values too high t o be measured were calculated by using the theory of Leary and Williams (1974). Rheological Testing. Test specimens were sheared torsionally in the parallel plate geometry with 50 mm diameter plates (platens) on a Rheometrics RMS 800 equipped with a 2000 gcm force rebalance transducer. Stress transients were measured following the sudden imposition of varying strain amplitudes (yo), where the strain field is characterized by that at the platen rim:
c)
y=o
t < O
(2)
y = y o = BRIH t20 (3) Here, 8 = angular step displacement in radians, R = radius of platens, and H = platen separation (gap). Samples were supplied as granules. Molded specimens for rheological testing were prepared by loading a consistent weight of granules into a heated and
3498 Ind. Eng. Chem. Res., Vol. 34,No. 10,1995
evacuated compression mould a t 225 "C, forming 50 mm disks. Before these disks were placed in the RMS, platens were preheated to 190 "C to promote polymer adhesion a t their surfaces. A disk specimen (at room temperature) was then rolled onto the lower platen using a glass rod, so as to expel1any air bubbles between the platen and specimen. The upper platen was then lowered t o place a compressive force on the specimen. While the specimen was maintained under this force, it was heated and then kept at a constant thermal soak temperature while the upper platen was lowered further t o close any gaps between the specimen and platen surfaces. This resulted in some extrusion of the specimen outward from the edges of the platens. The thermal soak temperature was 190 "C for SBSl and 170 "C for SBS2 and SIS. A fresh specimen was used for each test. Temperature control for all tests was achieved with a convection oven under N2. Specimen temperature was characterized by the "tool" thermocouple extending through the center shaft of the bottom platen holder to contact the underside of the lower platen. The tool temperature so measured was within 1 "C of the specimen temperature with a stability of f0.2 "C over the course of a test. The RMS 800 control and analysis computer permits electronic sampling of torque and strain during stress transients in four sequential time zones, with 512 samples taken in each zone. For example, zone 1 may extend from 0 to 1 s, zone 2 from 1 to 10 s, zone 3 from 10 to 100 s, and zone 4 from 100 s t o the terminal time of the test. As an equal number of samples are taken in each zone, the sampling rate would be highest in the first (shortest) zone. However, problems were encountered when the lower platen did not maintain a steady position a t the transition times between zones. At the end of the first zone (1s) the platen skipped to a higher strain amplitude, and at the end of the second and third zones (10and 100 s) it made a brief excursion to its pre1-s position. This resulted in stress spikes in the data. For this reason, multiple sampling zones were only used for SBSl at 90 "C-the slight corruption of the data is evident in Figures 3 and 4-and for all subsequent testing a single sampling zone was used extending from t = 0 to the terminal time of the test. However, because only 512 equally spaced stress values could be sampled in that one zone, it was not possible to obtain shorttime data (within the first few seconds). Both y ( t ) and z(t) were recorded throughout the 4-h tests by high speed digital sampling. Strain magnitudes quoted are actual measured strains (y"), as opposed to commanded strains. Additional experimental details are available elsewhere (Spaans, 1993).
Results SBS1. Figures 3 and 4 display the relaxation modulus G,(t) = t(t)/y" for SBSl at T = 90 "C, following the imposition of six yo. At this temperature, all miFigure 3 crophases were liquid, i.e., T,=- T =- @! > displays the relaxations at y o = 0.9b5% and 3.86%, which resemble those of an entangled but un-crosslinked homopolymer ( M W =- M,, the critical MW for entanglement onset). However, moduli a t differing strain amplitudes do not superimpose and therefore, by definition, the response is nonlinear. In Figure 4, Gr(t) for 0.050 s y o s 0.292%display exponential relaxation followed by a recovery which becomes evident between lo2 and lo4 s. Here again, moduli do not superimpose.
c.
-mn v
1
n c,
5 SBSl -9OOC
."1 0
in4
lop
101
10'
1C
10
Time (s) Figure 3. Relaxation modulus G,(t) for SBSl at 90 "C, yo = 0.955%and 3.86%.
rp rp rp
1
0.050% 0.093% 0.192% ----rp=O.292% - - -
n
_ .
-mn v
I
0.06%
n 10 c,
3 Time (s) Figure 4. Relaxation modulus G,(t) for SBSl at 90 "C, y o = 0.050.292%.
t
n
h
0.18%
U
n c,
5 f ~0.377% ----f=0.955% --rp=3.84% - - lop 10'
I
102
1
,
-
SBSl 100°C
,,,,,,I
I
I
lop
I , , , , ,
I
,
1C
I , , , , ,
10
Time (s) Figure 5. Relaxation modulus G,(t) for SBSl at 100 "C.
The moduli at termination of the test for y o = 0.955% and 3.86% are also indicated in the lower right corner of Figure 4. The trend in terminal modulus is consistent, with lower terminal values of Gr a t higher yo. At T = 100 "C and 0.085% Iy o I3.84%(Figure 51, GAt) for SBSl follows a trend similar to that a t 90 "C. At low y o (0.085% and 0.183%) there is a relaxation
rp'0.197% rp=o.382% -----
+\
l n
rp
f
0.954% f
8ooc
-
10o°C -
i 1Q
h
v,
n
n
c,
c,
... ....., -7
t 10'
102
1 6
v,
-. 104
a
104
106
Time (s) Figure 6. Relaxation modulus G&) for SBSl at 110 "C.
followed by recovery, perhaps leveling out to a plateau near the terminal time in the case of y o = 0.183%. For y o = 0.955% stress relaxes monotonically to what appears t o be a plateau-similar to the behaviour of a cross-linked rubber-while a t a higher amplitude ( y o = 3.84%) Gr(t) relaxes in liquidlike fashion, dropping rapidly near the terminal time. The trend of lower terminal Gr(t) with increasing y o is again followed, the single exception being that at y o = 0.377%. There G,(t) relaxes rapidly in liquidlike fashion, even dropping below the terminal Gr of yo = 3.84%. In trying to understand the latter behavior, we note that the only difference in testing this specimen was that H = 1.637 mm whereas H = 1.713 and 1.770 mm at y o = 0.183% and 0.085%, respectively. The lower H at yo = 0.377% indicates that the sample experienced greater compression and radial deformation associated with the resulting extrusion from the platen edges, during loading prior to the test. Sample and test preparation were otherwise identical for every sample. At T = 110 "C (Figure 6), Gr(t) follows a relaxation and subsequent recovery for 0.197% 5 y o 5 0.954%, while at y o = 3.84% Gr(t) relaxes rapidly in liquidlike fashion. Terminal modulus is again generally lower for higher y o , except in the case of y o = 0.382%, for which G&) is higher than a t any other y o within the entire window of time observed. Temperature Dependence for SBS1. In Figure 7, GJt) curves a t two different temperatures are compared for SBSl at a constant commanded (nominal) strain, YN, of 0.1% ( y o = 0.093% at 90 "C and 0.085% at 100 "C). With only a 10 "C temperature variation there is a profound change in the relaxation behavior. First it is noted that no amount of shifting along the time axis or the Gr axis will cause these two curves to superimpose, so that time-temperature superposition will not yield a single master curve. Both curves pass through a minimum, but the test at 90 "C results in a minimum modulus roughly 3 times that at 100 "0. While the 100 "C curve does indicate more rapid initial relaxations, dropping to a lower modulus than that at 90 "C, it also recovers more rapidly, the two curves becoming coincident at roughly 3500 s until the end of the test at 14 500 s. Only for these smallest y o was major recovery clearly and generally observed, and coincident moduli displayed (at long times) for all temperatures. For step strains of YN = 0.2% the resulting G,(t) curves are compared a t temperatures of 90, 100, and 110 "C in Figure 8 ( y o = 0.192%, 0.183%, and 0.197%, respec-
Time (s) Figure 7. Temperature dependence of G,(t) for SBSl at YN = 0.1%. lb
I
' """'I
'
'
"""'I
woc 10o°C
-
" " /
1
1ff
n c,
104
YNo
= 0.2%
tively). Again it is noted that no shifting along the time axis will yield a master curve, although the three shapes are quite similar. The drastic change in modulus magnitude over this narrow temperature range is again noted as the Gr values (at any fixed time) vary by a factor of about 7. A distinct recovery trend is again noted, though it is less striking than for y h = 0.1%. Figure 9 shows the comparison of curves at the same three test temperatures but for YN = 1%.At the end of the test the 90 "C ( y o = 0.955%) curve is still relaxing in liquidlike fashion, but the 100 "C ( y o = 0.955%)curve appears to have leveled out, and the 110 "C ( y o = 0.954%) curve has begun to recover. At 110 "C there should be greater molecular mobility resulting in more rapid relaxations, as well as recoveries. When YN = 4%, liquidlike relaxation is observed everywhere in this temperature bracket, as seen in Figure 10, which compares the Gr(t) curves again at 90, 100, and 110 "C ( y o = 3.86%, 3.84%, and 3.84%, respectively). Here we see for the first time curves which would come close to superimposing if shifted along the time axis. For example, the portion of the curve a t 90 "C between 1200 and 12 000 s is parallel to the section between 100 and 1000 s on the curve a t 100 "C, which in turn is parallel to the section of the curve at 110 "C between 40 and 400 s. In each'case, the curves a t short times are close to parallel.
3500 Ind. Eng. Chem. Res., Vol. 34, No. 10, 1995
T-----I Li--
,
I
,
/,,,,I
, ,
I
, , , ,,,,,/
,,,,,,
, , ,
y
/ / , ,
I
SBSI -
90% 1w0c 110%
lo8
10
10i
SBS2 - - n
8
v n
n
Y
IC,
104
1
yNo= 1% 10'
102
16
Time (s)
10
104
Time (s)
Figure 9. Temperature dependence of G,W for SBSl at YN = 1%.
Figure 12. Relaxation modulus G,(t)comparison for SBSl and
SBSB a t 110 "C, YN = 1%. 19t
I
I
I
( I , , , ,
,
,,,,,,,I
, ,,,,,,,
up=o.oso% up =0.183%
90°C 1W0C -
, ,,,,,
1
-
104 :
n
8
n
8
v n
v n 103
c,
z IC,
..._ .-
102 7
10'
I
,
1
,,,,,,I
I
1
I , , , , ,
I
I
I
/ , , / /
Time (s) Figure 10. Temperature dependence of G,(t) for SBSl at YN =
4%.
-
SBSP 11O°C 104 n
8
103 F
v n IC,
102 F
up=O.060% up 1 0185 %""..""'.' .
IO' F
up = 0.388% ----up 0.955% 1
l@ 10'
1
102
,
I
/ 1 1 1 1 1 1
I
/,,11111
103
I
I , , , , ,
104
19
Time (s) Figure 11. Relaxation modulus G,(t) for SBS2 at 110 "C.
SBSB. For SBSB at 110 "C (Figure 111, Gr(t)drops rapidly in an almost straight-line fashion, typical of a short-chain ( M W Mc)homopolymer. Gr(t) at y o = 0.955% and y o = 0.388% superimpose closely, while a t y o = 0.080% and 1.85% the amplitude of the noise makes it difficult to assess how well the data superimpose. Figure 12 displays a comparison of the "relaxationn behaviour of SBSl and SBSB a t 110 "C and y o = 0.955%. These two materials behave drastically differ-
ent under these same conditions. Gr(t)for SBSB begins higher than that of SBS1, but rapidly drops below. SBSl displays a recovery of modulus which is not witnessed under any conditions tested for SBS2. SIS. For SIS at 110 "C (Figure 13), Gr(t) at all y o superimpose closely for 15 s It I200 s. At roughly 200 s, a classification is seen with higher-strain specimens relaxing t o lower G,. At y o = 0.090%, Gr(t)levels out and then recovers slightly before the terminal time of 8 x lo3 s. At y o = 0.183% and 0.378% the curves level out t o a plateau, while a t y o = 0.950% and 3.83% the curves are relaxing rapidly in liquidlike fashion at the terminal time. Again, terminal Gr are lower for higher yo. At 90 "C (Figure 14) Gr(t) almost superimposes at all y o , to the point that it is difficult to distinguish these curves. SBSS and SEBS. An attempt was made to load both SBS3 and SEBS into the rheometer. Problems were encountered in trying to achieve good contact over the entire surface of the upper platen. This was because the relaxation times for these polymers were so long that they would not relax in a reasonable time, even at a thermal soak temperature of 300 "C. Therefore, the normal procedure of closing the gap by lowering the upper platen, and thus extruding some sample out around the platen edges, could not be employed.
Ind. Eng. Chem. Res., Vol. 34,No. 10, 1995 3501
I 10'
I '1 I
f=S.Ss%
101
102
104
10
Time (s) Figure 14. Relaxation modulus G,(t) for SIS at 90 "C.
t
T
Figure 15. Eyring rate model for (a) homopolymer segment with no imposed stress,(b) homopolymer segment with imposed stress, and (c) block copolymer segment junction with imposed stress. 5 is an imposed stress and t~ss d n A , where n A is the molar density of A units. &A is a chemical potential difference.
Discussion
Theory. The rheology of block copolymers is dominated by the interplay of thermodynamic and mechanical forces. Consider an Eyring-type flow model, first for a segment of a homopolymer molecule positioned in a potential well as shown in Figure 15a, with equal probability of making a segmental jump in any direction, unless a stress is imposed as in Figure 15b. This stress has the effect of lowering the potential in the direction of the imposed stress and raising it in the opposite direction, thus biasing the probability of a segmental jump in the direction of the stress. Note that any imposed stress, no matter how small, will bias the potential, and probability argues that eventually flow will occur. Consider next such arguments applied to a junction between blocks (or segments) in a block copolymer residing in the interphase. It, too, is positioned in a potential well as in Figure 15a. When a stress is imposed, the potential is biased in the direction of the stress as in Figure 15b. However, as soon as the junction moves away from its rest point, the free energy of the junction increases. Henderson and Williams proposed that the free energy gradient would cause a
force (FA)Ion the chain (eq 1). Therefore, the increase in the free energy of the junction biases the forces in the opposite direction, as depicted in Figure 15c. As long as these two biases are balanced, flow cannot be initiated; Le., the yield stress is not exceeded. A large enough stress, of course, will bias the potential in the direction of the stress t o a greater extent than the free energy gradient can counter, being limited by the thermochemistry of the system. SBS1. We begin our discussion with SBSl a t 90 "C. At y o = 0.955% and 3.86% (Figure 3) the relaxation behavior is that which is typical of entangled molten polymers, for which "structure" exists (the transient entanglement network) but no long-term stress can be supported. Whether Gr(t)would eventually settle to a nonzero plateau cannot be determined within the window of time observed. At lower strain amplitudes ( y o = 0.05-0.292%) the initial relaxation is not followed by an entanglement plateau, but by a recovery of the modulus (Figure 4) which has not been reported before, t o our knowledge. This recovery can be explained by a microstructuralthermodynamic model. The stress resulting from a step strain tends to deform the local microstructure. The stress can only be relieved if flow occurs, which necessitates a disruption of the network structure. However, the network structure can only be disrupted if end blocks are pulled from their domains. Thermodynamic forces, and in particular those related to interphase composition gradients, oppose the extraction of blocks from their domains. Upon sudden imposition of a step strain, the microstructure is perturbed from its initial state. This may cause migration of segment junctions partially through the interphase, or it may involve complete block extraction. If a block is not entirely pulled out, but rather the position of the segment junction is merely perturbed within the interphase, then the free energy gradients will tend to force it back in the direction from which it moved. This provides a mechanism for stress recovery. We next attempt t o develop a simple model for recovery data. In Figure 16 it is shown that the Gr(t) curve for yo = 0.085% step strain a t 100 "C is well fit by a curve of the form G,(t) = xG,e-t''n n
+ cGpe-v@ P
(4)
The first sum represents a series of relaxing Maxwell elements with moduli G, and relaxation times A,. The second sum, consisting of inverse time exponentials, characterizes the microstructural recovery and ap00. This is proaches a stable final state (ZpGp)as t typical of rate processes. The prefactor Gpis a modulus is a characteristic time while the exponential factor analogous to the relaxation time, but more appropriately termed "recovery time". The second term therefore represents the re-formation process, the rate of which is determined by the thermodynamic force balance of the system. We propose that the Gr(t) curve could be modeled as the result of two such competing processes: The first process is an exponential decay of stress associated with the free chain ends pulled out of their original host domains, and the second is an inverse exponential growth of stress as the partially-dislodged chains diffuse back into those domains, thus repairing the strain-induced damages and establishing a firmer microstructure than prevailed immediately after the damage event. An attempt at modeling this overall
-
vp
3502 Ind. Eng. Chem. Res., Vol. 34,No. 10,1995 10
I
' """'I
'
"
1
"
"
~
'
"
"
"
~
n
v n CI
v,
(3
1 t
Digitized Data -
SBSl - 1 O O ' k
CurvrFit - - -
4=o*085%
i
Time (s) Figure 16. G,(t) for SBSl at 100 "C and y o = 0.085% fit with a curve of the form G,(t) = C,G,e-t'An &G,e-@.
+
process should require more than one relaxing element and one recovering element, as there are known to be several relaxation modes even for homopolymers and structural recovery modes are sure to be complex. In Figure 16, G,(t) is fit by a curve of the form of eq 4 having four relaxing and four recovering elements. Some structural recovery can involve the strain-freed end blocks. If an end block were pulled completely out of its domain and interphase, then it would encounter a locally homogeneous environment of center-block molecules. It would then not experience any compositional gradients which would tend to force it back toward its original position or toward any other position in particular. However, such an end block could still migrate randomly and thus by Brownian motion seek out another domain. Furthermore, because of the considerable stress built up in the center block, it may recoil, like an elastic band, toward the domain in which its opposite end is anchored. Except for the stressdirected recoil, the diffusional process would have a significant probability of leading to a different, closer domain. Whichever occurs, stress relaxation would be much more rapid after block pull-out, and stress recovery would not follow. Furthermore, the trend would be toward a decrease in the number of interconnections between domains. With sufficientlynumerous pull-outs and losses of interdomain ties would come the appearance of disconnected small "chunks" consisting of a smaller number of interconnected domains which could move relative to other chunks. Such "chunk flow" would result in a lowering of modulus, and more liquidlike behavior. Considering the above arguments, it becomes clear that the trend toward lower final modulus at higher step strains observed in these tests is due to greater microstructural damage. At strains of 0.292% and lower, end blocks are not fully extracted from their domains and so a microstructural recovery drives the structure back toward its initial state. At higher strains, end blocks are pulled from their domains resulting in more chunk flow (liquidlike behavior) and a relaxation which is not followed by a recovery. The drastic drop in G,(t) for SBSl for 0.05% to 0.093% strain at 90 "C (Figure 4),as compared to the variation in G,(t) from y o = 0.093% to 0.292%, may be explained by some critical degree of microstructural damage. Perhaps segment junctions are dragged over some locally steep portion of the composition gradient.
It is not known whether the moduli would recover to the same final value at each yo for which stress recovery is observed. If the y o = 0.05% and 0.093% curves at 90 "C continue to recover a t the same rate as a t 14 500 s, then they would reach the same value at approximately 2 x lo6 s, or 23 h. While it does not seem likely that the curves will continue with the same slope until they intersect-this would be atypical for rate processes-the point is clear that it may require an exceptionally long test to determine what the final state will be. If modulus would recover in these tests to the initial value, irrespective of strain amplitude, it would mean that segment junctions would be fully restored to their initial positions without having lost contact with their original domains (or else some permanent stress relaxation would have to occur). In general, we suspect that this will not occur. So far, we have discussed these effects as if each segment junction in a specimen behaves the same in any given test. However, as Morrison and Winter (1989)have pointed out, domains oriented in different directions will behave differently in shear. Just because stress recovery is observed in a test does not mean that no end blocks are extracted, but rather that fewer end blocks are extracted than at higher strains. The average microstructural damage over all domains in the sample is lower at lower strains. Therefore, we again would argue that G,(t) curves at different strain amplitudes would probably not recover to the same levels. Some stress would be permanently relieved by block pull-out and the curve would level out to a modulus, or stress, which represents the new balance of thermodynamic and mechanical forces. This reasoning suggests that the yield stress is unique to sample history. At 100 "C (Figure 5 ) , the curve at y o = 0.377% is anomalous by relaxing rapidly in liquidlike fashion &r small y o . As mentioned earlier, H for this test was anomalously low, indicating greater deformation during loading. This loading trauma severely damaged the microstructure before the test had even begun. It was this same effect which motivated Hugenberger and Williams (1988)to explore "hot loading", or loading the sample above T,(in the homogeneous state) and forming an isotropic and undeformed microstructure in-situ upon cooling. However, they worked with solutions having depressed T,so that high-temperature degradation was not a concern. In our case, T,was always so high (see Table 1) that we elected not to try exceeding it. At y o = 0.183% and 0.955%, with T = 100 "C, G,(t) levels to a plateau, analogous to the behavior of a crosslinked rubber. The level of this plateau represents a different balance of thermodynamic and mechanical forces for each yo. Both block pull-out, resulting in permanent stress relaxation, and segment junction displacement with subsequent recovery, occur to different extents and in differing ratios. The analogy to cross-linking suggests that an intact load-bearing network exists for both plateaus, with the lower-level one ( y o = 0.955%) having the lower density of original "networking" styrenic domains because of more extensive block pull-out upon strain imposition. The fact that a plateau is manifested a t all indicates that few intact interdomain connections from the original network remain, or else the restorative forces of reentry of end blocks into their original domains would cause a stress increase as for y o = 0.085%. The case of complete disruption of the three-dimensional character
Ind. Eng. Chem. Res., Vol. 34, No. 10, 1995 3603
of the original network leads t o the ultimate stress decay seen at y o = 3.84%, where Gr(t) at long times rapidly relaxes in liquidlike fashion. Much greater microstructural damage resulted from this "large" yo, causing a solid-to-liquid transition and some kind of chunk structure without three-dimensional connectivity. These results demonstrate that there exists a strain magnitude (and corresponding material-dependent magnitude of shear stress) below which the solidlike structure of the material does not fail, but in fact recovers from damage suffered during its initial deformation. This stress level is history dependent, but we propose that it is a true liquid phase yield stress. When this stress level is precisely achieved during a stress relaxation test, the structural damage is such that the longterm balance of forces results in a leveling out of the modulus to a plateau with no subsequent increase. This has been demonstrated by the tests at 100 "C with strains of 0.183% and 0.955%. This concept of yield stress is perhaps the most controversial feature in block copolymer rheology. In recent years, the debate over whether any material exhibits a true yield stress has resurfaced. The most current literature in this debate was reviewed by De Kee and Fong (1993). Many researchers have "measured" yield stresses, or else inferred their existence from experimental data, in block copolymers (Bauer and Meerlender, 1986; De Kee and Mohan, 1986; Diamant et al., 1984; Han et al., 1991, 1992; Hansen and Williams, 1987; Kotaka and White, 1973;Masuda et al., 1980; Watanabe et al., 1982). However, the methods in general are open to criticism from skeptics. The procedure for measuring a yield stress normally involves loading the sample with some finite stress and watching to see whether the material flows. This opens wide the questions of instrument sensitivity and experimenters' patience. Alternatively, one could argue from noninfinite viscosity values at extremely low steady strain rates that no yield stress exists. However, steady shear, no matter how slow, will eventually disrupt the network, resulting in a solid-to-liquid transition, so this is not a fair criterion for discounting the existence of a yield stress. By comparison, the stress relaxation test offers attractive features for assessing the existence of zr. This has been presented elsewhere by Spaans and Williams (1995)in conjunction with these block copolymer experiments. Temperature Dependence. Plots showing Gr(t)for SBSl a t constant YN but varying temperatures between 90 and 110 "C (Figures 7-10) reveal the strong temperature dependence of the properties of these materials. Curves differ significantly over what is only a 20 "C range, a fact requiring some explanation. The most important temperature for interpreting this behavior is p, found in the vicinity of 65-75 "C (Table 1). Just above Tg, in the range to Tg+ 100 "C associated with the Williams-Landel-Ferry free volume theory (Ferry, 1970), the relaxation times (and, by extension, the viscosity) for the styrenic phase drop extremely quickly, more than exponentially. Therefore, a 10 or 20 "C temperature variation in this case (from roughly Tg+ 20 "C to Tg+ 40 "C) should have a significant effect on the mobility of styrene blocks in their domains. This would allow more rapid relaxations, but also more rapid recovery. In addition, elastomeric forces become stronger at higher temperatures, but this relationship is only linear with temperature; an increase from 90 to 110 "C would result in only a 5%increase in elastomeric forces.
A second characteristic temperature of importance is
T,.Thermodynamic forces favoring microphase separation (Le., structural formation) would resist structural degradation-a form of remixing-upon the imposition of strain and would therefore promote the Gr(t)recovery process; these forces would become stronger as temperature is dropped further below Ts.This factor also contributes to the temperature dependence seen in Figures 7-10, but is difficult to evaluate quantitatively. However, its role is believed to be minimal here; the test temperatures from 90 to 110 "C were much further from T,(243 "C) than from Tg,and so it is suspected that temperature variation effects associated with Tg would be stronger. In reference to Figure 7, comparing relaxations at YN = 0.1% for 90 and 100 "C, a t 100 "C G,(t)initially drops as much as 4 times lower than at 90 "C, but by 3500 s the two curves become coincident until the end of the test. This indicates more rapid relaxations and recoveries at the higher temperature, due to lower viscosities and higher elastomeric forces. The fact that the curves are coincident from 3500 s seems to suggest that a t Y N = 0.1% the same magnitude of structural damage is incurred a t the two temperatures, so that temperature variations (over this narrow range) affect only the early rates of stress changes but not the recovered structure itself. At YN = 0.2% (Figure 8), modulus varies by a factor of about 7 over a temperature range from 90 to 110 "C. For an ideal rubber, modulus would scale proportionally with temperature, but as noted above this would result in only a 5% variation. This suggests a temperature dependence more dominated by Tgeffects. When YN = 1%we see in Figure 9 the full range of behavior by the end of the test. At 90 "C the curve is still dropping, while at 100 "C the curve has leveled out, and at 110 "C it is recovering. The data of Figure 7 (at YN = 0.1%) suggested that the same magnitude of structural damage is incurred at the two test temperatures, provided that YN is constant, resulting in recovery to the same final state, though the rates are different. Following the same reasoning, we could interpret Figure 9 in the same way: For YN = 1%,the recovery observed at 110 "C would also occur at 100 and 90 "C, but would be delayed to longer times. At YN = 4% (Figure 10) we despair of the curves ever recovering, as by the end of the test the 100 and 110 "C curves have passed the "entanglement" plateau and are curving downward indicating liquidlike, rather than solidlike, character. By the above arguments (for YN = 0.1% and 1%)it seems likely that the curve a t 90 "C will also drop off at longer times. As mentioned earlier, these curves come close t o being superimposable by a shift along the time axis. Time-temperature superposition is generally considered invalid for "structured fluids" such as phase-separated ABA block copolymers (Arnold and Meier, 1970; Chung and Lin, 1978; Futamura and Meinecke, 1977; Gouinlock and Porter, 1977). Therefore, the potential for superposition after large deformations is additional evidence that the long-range microstructural network has been fatally altered, as superposition by time shifting should only be possible for "rheologically simple" materials. SBS2. It was demonstrated in Figure 11 that Gr(t) for SBS2 showed no evidence of recovery but dropped rapidly a t about the same rate for all y o ; as shown in Figure 12, this drop is approximated by Gr = t-l. The behavior is similar t o that of an unentangled short-chain
3504 Ind. Eng. Chem. Res., Vol. 34, No. 10, 1995
polymer. In Figure 12 the relaxation of SBSB is compared t o the behavior of SBSl at the same temperature and strain. G,(t) for SBSB is initially higher, as is consistent with the higher styrene content. At 4s = 44% the structure of SBS2 would be lamellar, while that of SBSl at 4s = 30.4% would be cylindrical (Shen and Kawai, 1978). The lamellae, being continuous in two spatial dimensions, should have a greater reinforcing effect in the solid state than cylinders which are continuous in only one dimension (speaking in terms of flexural stiffness and shear modulus, not tensile strength), so it is not surprising t o see a higher peak modulus in SBS2. What is surprising is how rapidly it drops below the curve for SBS1. The styrene end blocks in SBSB each have a molecular weight of 13 480, compared t o only 10 550 in SBS1. The higher molecular weight of the styrenic blocks should result in a slower relaxation for SBSB than SBS1. However, the reverse is observed. Therefore, the end block molecular weight cannot be the cause of the differences observed. The molecular weight of the butadiene center block in SBSB is 34 320, and that in SBSl is 48 320. The critical (entanglement-onset) molecular weight of bulk polybutadiene is M,= 6380 (Colby et al., 1991) so that the center blocks in both samples have M w > M,. Therefore, viscosity and hence relaxation times would vary according to (Mw)3.4.The relaxation times associated with the polybutadiene entanglements would therefore be 3.2 times greater in SBSl and SBS2 [from (48300/34200)3.41. However, it will be demonstrated later that the relaxations associated with center block entanglements are not the longest, or controlling, relaxation times of the material. In addition to the greater speed of stress relaxation in SBS2, another qualitative difference relative to SBSl is the apparent absence of microstructural repair. No recovery of modulus is seen in SBSP, while the recovery in SBSl at the same temperature and strain amplitude is clearly evident. T,is an average overall measure of the thermodynamic balance, and Table 1shows that T, of SBSB is more than 10 "C higher than that of SBSl (255 "C us 243 "C). This should lead t o stronger thermodynamic driving forces toward the phase-separated state in SBSB than SBSl a t the same temperature, provided it was below T,. This point also seems t o be violated here. The key t o understanding this profound difference in the behavior of these two polymers, which initially seem so similar, appears t o be the differences in interphase character. Henderson and Williams (1985) predicted that in this range of 4s interphase thickness increases with increasing styrene content. The interphase thickness in SBSB with 44% PS could be anywhere from 30% to 80% greater than that in SBSl with 30.4% PS [see Henderson and Williams (1985), Figure 81. With a broader interphase, the average composition gradient and hence force barriers in SBSB would be lower. This would result in easier block extraction and smaller ty. This reasoning argues that all strain amplitudes in our range of SBSB testing caused greater microstructural damage through a greater number of block extractions than the same tests performed on SBS1. This results in more rapid relaxations and little or no microstructural recovery. One another explanation for the rapid stress decay in SBSB can be advanced. This is based on the geometrical character of lamellar microstructures, which
contribute to a high solid-state modulus because of twodimensional (platelet) reinforcement which is generally more effective than one dimensional (cylindrical) elements. For the liquid state, however, a mechanism for relaxation exists which we have not heretofore discussed: molecular migration laterally, with the A-B junction remaining in the interphase rather than being extracted. While such a local lateral "flow" would have little effect when domains are totally isolated as spheres, the effect would be somewhat greater with cylinders (especially if the cylinders could be aligned uniformly) and would be much greater in the lamellar case. [See the discussion of Hugenberger and Williams (19881, in the context of spherical and cylindrical morphologies.] For lamella, an A-B junction in a phase-separated melt could be dragged laterally for considerable distances with no pull-out being necessary, so resistance would be low and z, might not appear at all. Thus, despite having major microstructural resistance to block mixing, the lamellar morphologies (eg., SBS2) might actually provide lateral-flow mechanisms for rapid stress relaxations governed by the styrenic-phase (short block) viscosity and largely independent of interphase barriers. This picture fits all the features observed for the SBSB Gr(t)behavior, but no direct confirmation is available. SIS. For SIS at 110 "C Figure 13 shows again that greater strain amplitudes do more microstructural damage resulting in lower final moduli. In the case of y o = 0.183%and 0.378%, Gr(t)reaches a plateau a t long times. At y o = 0.090% there appears to be a slight recovery, although the test was terminated early. Furthermore, comparing Gr(t)for both SBSl and SIS at the same temperature and YN reveals that SIS relaxes faster than SBSI. At 110 "C and Y N = 0.2% (Figures 6 and 13), at t = 100 s SIS has relaxed t o a modulus of 4700 Pa while that of SBSl is 11000 Pa, or more than twice as high. Therefore, relaxations are faster and recovery is weaker in SIS than in SBS1. In order to explain this we compare the two polymers. The thermodynamic driving forces are characterized by both T,and interphase characteristics. T,of SIS (255 "C)is higher than that of SBSl (243 "C). This would argue for stronger driving forces toward the phaseseparated state, resulting in longer relaxations and stronger recovery for SIS over SBS1, which is opposite t o the trend observed. SIS, having an even lower styrene content than SBSl (14% us 30.4%) should also have narrower interphases than SBS1, and thus higher average gradients in the interphase. This also would argue for longer relaxation times and stronger recovery in SIS than in SBS1. The styrene block molecular weights are around 10 000 for both SIS and SBS, so this cannot explain the difference. Morphologicaldifferences are likewise not responsible, since SIS consists of linked spherical domains that would not present even the limited lateral A-B junction flow possessed by cylindrical morphologies. The explanation appears t o lie with the molecular weight of the center blocks. In SIS the isoprene center block has a molecular weight of 120 000, while in SBSl the butadiene block has a molecular weight of 48 000. This results in roughly 2.5 times the density of entanglements in the SIS center block over that in the SBSl center block. This greater entanglement density results in a more effective transmission of stress through the viscous medium at the same strain amplitude. At short times, as the glassy-response limit is approached (not shown in Figure 131, the stress resulting from the
--
Ind. Eng. Chem. Res., Vol. 34, No. 10, 1995 3506
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Figure 17. Graphical fit of relaxation times for SBSl at 90 "C and y o = 0.955%.
Figure 18. Graphical fit of short time relaxation for SBSl at 90 "C and yo = 0.955%.
high strain rate during the initial strain transient would be more effectively transmitted through the material, resulting in more microstructural damage and hence chunk formation. Therefore, the microstructure of SIS was more highly damaged than that of SBSl (at the same strain amplitude) before the first data point was logged. Because the microstructure in post-strained SIS a t 110 "C is presumed to be damaged, largely ''chunky" and fluidlike, we can infer the same for SIS at 90 "C. Figure 14 is consistent with this hypothesis: Even though the initial modulus is much higher than at 110 "C (due to the temperature being 20 "C closer to p),the decay shows rather good superposition a t alf yo-as one expects of unstructured liquidlike relaxation behavior, and similar to the yo-superposition at 110 "C (down to Gr = 2000 Pa; see Figure 13). Furthermore, temperature superposition is also possible with SIS; Figures 13 and 14 form a single curve if the time scales are shifted laterally by a factor of about 15 (with the 110 "C curve displaying the long-time relaxations most sensitive to residual microstructural connectivity). Therefore, it is likely that the terminal G, at 90 "C would show the same classification according to strain amplitude, in the same pattern as those a t 110 "C, if the test were continued for a longer time. Relaxation Times. From attempts to fit the Gr(t) data with a series of relaxing Maxwell elements, it can be argued that (1)there are relaxational mechanisms that cannot be fit by a series of Maxwell elements, (2) the longer relaxation times observed are extremely long, and (3) the mechanisms associated with the longest relaxation times are not those related to chain entanglements. Rather, the longest relaxation times are associated with motion of the segment junctions through the interphase, a conclusionthat will now be argued in more detail. Curves of Gr(t) for SBSl and SIS under conditions where they exhibited liquidlike stress relaxation were fit with equations of the form
fitting similarly. Figure 17 shows the i = 1-4 fit of
+
+
G, = Gle-t/A1 G2e-t'Az ... (5) where 1s: are relaxation times corresponding to a fluid model having several Maxwell elements. Values of Gi and Ai were obtained by the classical method of fitting the long-time portion of the curve first, to secure GI and 11, and then subtracting that Maxwell element's contribution from the total stress to get the next curve for
Gr = 15800e-t~600000 + 5500e-t/5800+
+
31000e-t/436 50000e-t/70 (6) t o the curve of Gr(t)for SBSl a t 90 "C and y o = 0.955%. However, eq 6 is not an ideal fit as can be seen by the deviation between roughly 200 and 3000 s. Because both relaxation and recovery are occurring, it is not surprising that a simple series of relaxing Maxwell elements will not fit the curve perfectly. The i = 1-3 curve
+
+
Gr = 25000e-t'12500 35000e-t/305 50000e-t/47 (7) shown in Figure 18 fits the early relaxations better. In this time range the recovery is not dominant, and so a series of relaxing Maxwell elements fits the curve well until t = 4000 s. For t > 4000 s the severe discrepancy between the model's predictions and the data can be taken as an indication of the thermodynamic restorative forces at work, even though they fail to reestablish solidlike structures. In general, the short- and long time portions of the data cannot both be perfectly fit by a single curve representing relaxing Maxwell elements. However, despite the minor deficiency of the fit by eq 6, that equation still demonstrates that the longest relaxation time observed over the duration of the test was very large, being 6 x lo5 s. For SIS a t 90 "C and y o = 0.955%, with weaker recovery forces than in SBS1, Gr(t) can be fitted quite well with only three Maxwell elements, as shown in Figure 19. We can derive from eq 8 that the largest 1 is 1.85 x lo4 s, much smaller than for SBSl (AI= 6 x lo5) a t the same test conditions. In trying to explain this difference, we first examine the two middleblock relaxations. The rubbery (polyisoprene) center block in SIS has a molecular weight of 120 000, much higher than that of the SBSl center block which is 34 320. Polyisoprene, with an extra pendant methyl group, would have a higher viscosity and longer relaxation times than a polybutadiene having the same number of repeat units. However, for the purposes of this comparison we can ignore these differences and apply the ikP4 scaling rule to estimate the relative relaxation times of the two rubbery center blocks. This calculation shows that the rubbery relaxations in SIS
3606 Ind. Eng. Chem. Res., Vol. 34,No. 10, 1995
Conclusions Digitized Data Maxwell Fit - - -
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The interplay of thermodynamic and mechanical forces dominates the rheological character of ABA block copolymers. Following the imposition of a step strain, at low yo, G,(t)relaxes and then recovers, indicating that the solidlike network has not been fully disrupted. This recovery is interpreted in terms of the thermodynamic forces associated with the interphase free energy gradient. Therefore, even when all phases are liquid (Ts> T> > there exists a yo, and material-dependent z, below which the material is an elastic solid, and as such a true ty exists. Temperature variations in the range tested affect only the early rates of stress changes, but not the recovered structure itself. Larger yo result in greater microstructural damage, forming “chunks” which lead to liquidlike behaviour. Thus a solid-to-liquid transition can be effected by straining the material. The damaged microstructures display more rapid relaxations and lower terminal moduli. Long relaxation times are associated with the motion of segment junctions through the composition gradient of the interphase, i.e., with structural repair whose kinetics is dominated by the interphase force barriers. Broader interphases, having lower overall gradients, result in more rapid relaxations.
e)
Time (s) Figure 19. Graphical fit of relaxation times for SIS at 90 “C and y o = 0.967%.
should be roughly 70 times as long as those in SBS1. Instead, 11 in SBSl at 0.955% strain and 90 “C is roughly 32 times 11 in SIS under the same conditionsopposite t o the computed order of rubbery relaxations, which mismatches the data by a factor of about 2200! This demonstrates that the relaxation times associated with the entanglements in the rubbery center block are not the controlling, or longest, relaxation times in these Acknowledgments materials. Earlier it was demonstrated that the relaxations This work was supported by the Natural Sciences and associated with the viscosity of the styrenic phase are Engineering Research Council (NSERC) of Canada also not controlling, provided the sample is at a temOperating Grant Number OGP0089809, as well as an Therefore, the long “relaxation” perature above NSERC Post Graduate Scholarship to R.D.S.Dr. Kevin times must be associated with the motion of segment Mackay a t Dow Chemical U.S.A. is thanked for providjunctions through the composition gradient of the ining SBS samples. terphase, Le., with structural repair whose kinetics is dominated by the interphase force barriers. Literature Cited The “anomalous” cases of SBS3 and SEBS can be characterized as having relaxation times that are Arnold, K.; Meier, D. J. A Rheological Characterization of SBS extremely long, so long that they cannot be effectively Block Copolymers. J . Appl. Polym. Sci. 1970, 14, 427. loaded into the rheometer. However, the overall moBauer, H.; Meerlander, G. Polymer Solutions with Threshold lecular weight of SBS3 is 101 225,less than that of SIS, Values of Shear Stress and Shear Rate in the Flow Curve. Prog. Colloid Polym. Sci. 1986, 72, 106. and its 4s is only 31%,or roughly the same as that in Chung, C. I.; Gale, J. C. Newtonian Behavior of a StyreneSBS1. For SEBS the molecular weight is even lower, Butadiene-Styrene Block Copolymer. J. Polym. Sci., Polym. at 67 000, and 4s is also similar t o that in SBS1. Phys. Ed. 1976, 14, 1149. Therefore, neither the molecular weights nor the styrene Chung, C. I.; Ming, I. L. Nature of Melt Rheological Transition in contents could be individually responsible for the long a Styrene-Butadiene-StyreneBlock Copolymer. J . Polym. Sci., relaxation times. Polym. Phys. Ed. 1978, 16, 545. However, the predicted T, listed in Table 1 are 482 Colby, R. H.; Fetters, L. J.;Funk, W. G.; Graessley, W. W. Effects and 839 “C for SBS3 and SEBS, respectively. These are of Concentration and Thermodynamic Interaction on the Viscoelastic Properties of Polymer Solutions. Macromolecules higher than for any other polymer tested. Such high 1991,24,3873. T, reflect the very high thermodynamic driving forces De Kee, D.; Mohan, P. Yield Stress Determination of Styrenetoward the phase-separated state encountered a t our Butadiene-Styrene Triblock Copolymer Solutions. J . Macromol. loading temperatures, which were increased as high as Sci., Phys. 1986,25, 153. 300 “C in an attempt to load the samples. This results De Kee, D.; Fong, C. F. A True Yield Stress? J . Rheol. 1993, 37, in very long relaxation times, as the driving forces 775. retard the displacement of S blocks from the miDiamant, J.; Soong, D. S.; Williams, M. C. Modeling the Viscoelascrophases into the matrix. The thermodynamic driving tic Behavior of SBS Copolymer Solids. In Contemporary Topics forces, and hence the T,, are particularly high for SEBS in Polymer Science; Bailey, W. J., Tsuruta, T., Eds.; Plenum Publishing: New York, 1984; Vol. 4, p 559. because of the higher Ad between the center and end Ferry, J. D. ViscoelasticProperties ofPolymers, 2nd ed.; John Wiley ~ Leary-Williams model. blocks; T,= (BA - 6 ~ in) the 1 and 16s - B B ~= 0.5 ( c a l / ~ m ~ ) ~ ’ ~ & Sons: New York, 1970; Chapter 11. Using 16s - 8 ~ =~0.8 Futamura, S.; Meinecke, E.A. Effect of Center Block Structure as reported by Futamura and Meineke (19771, we see on the Physical and Rheological Properties of ABA Block the chemical enhancement of T, to be about (0.8/0.5)2 Copolymers. Part 11. Rheolo&cal Propekies. Polym. Eng. Sci. = 2.5 in comparisons of those two systems. Hugen1977, 17, 563. ] 1.2 berger and Williams (1988) reported 16s - ~ E B = Gouinlock, E. V.; Porter, R. S. Linear Dynamic Mechanical ( c a l l ~ m ~ )which ~ ’ ~ , would lead t o predictions of even Properties of an SBS Block Copolymer. Polym. Eng. Sci. 1977, greater T,for SEBS. 17, 535.
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Received for review January 9,1995 Revised manuscript received July 7, 1995 Accepted July 25, 1995@
IE950035L
@
Abstract published in Advance ACS Abstracts, September
1, 1995.
