16
Rheokinetic Measurements of Step- and Chain-Addition Polymerizations Downloaded by UNIV OF AUCKLAND on May 3, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch016
D. Rosendale and J. A. Biesenberger Department of Chemistry and Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ 07030
The dependence of viscosity on the extent of reaction, or conversion, is information necessary for accurate modeling and control of reactive extrusion and reaction injection molding. This chapter presents rheokinetic data and describes a new instrument, called the rheocalorimeter, which simultaneously measures the heat released and viscosity of a polymerizing solution and makes it possible to obtain viscosity-vs.-conversion data directly. Experimental results and a simple model show that this viscosity growth behavior is different for different polymerization mechanisms. Methyl methacrylate polymerization, styrene-acrylonitrile copolymerization, and polyurethane polymerization data are presented and compared to the predictions of the model.
T H E
E F F E C T O F C O N C E N T R A T I O N A N D M O L E C U L A R W E I G H T on the vis-
cosity of linear (non-network) polymers during their formation has long been ignored, and only recently have crude attempts been made to produce realistic models of this dependence. The effect is enormous, spanning seven or more decades of viscosity, diminishing by comparison the effects of shear rate ("shear-thinning") and even reaction temperature, which are not i n considerable. Most polymerizations can be viewed as falling into one of three broad categories based upon fundamentally distinguishable chain-growth mechanisms (I): random: m + m —» m x
y
t + y
0065-2393/90/0227-0267$06.00/0 © 1990 American Chemical Society
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
(1)
268
POLYMER
step addition: m
x
+ m—>
m
CHARACTERIZATION
t + 1
chain addition: m * + m - » m, x
(2) (3)
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where the subscript denotes the number of monomer units in a particular molecule, and the asterisk refers to a highly reactive free radical site. Random polymerization is characterized by chain growth occurring throughout the reaction randomly among molecules of all sizes. Examples are polycondensations and catalyzed linear urethane polymerizations. At the onset of a random reaction, monomer molecules are most likely to encounter another monomer molecule and form a dimer. The dimer may react with either a monomer or another dimer, depending on which is present in higher concentration, to form a longer molecule. Thus, in the beginning, the polymer molecules form very slowly, but as the average length of molecules in the reacting mixture increases, the chains begin growing very rapidly through each individual reaction step as long chains link with other long chains. The random polymerization mechanism is in contrast to the addition mechanisms whereby chains grow by addition of one monomer molecule at a time. Chain addition differs from step addition because termination reactions occur only in chain addition: in,* —> m
x
(4)
that make it impossible for the same molecules to continue growing throughout the reaction. Each chain lives only a very short time compared to the overall time of polymerization, and termination of fully grown chains is followed by initiation of succeeding generations of new ones: m —» mx*
(5)
Free-radical polymerizations are obvious examples of the scheme illustrated by equations 3-5. By contrast, in both step-addition and random polymerization, the same molecules grow (in principle) throughout the entire course of the reaction. These distinct features are reflected in the molecular-weight growth of the resulting polymers, giving rise to three very different degrees of polymerization (DP) versus conversion curves (J). They are illustrated in Figure 1 for number-average DP. Thus, the steep rise in D P at the very end of the random reaction stands in sharp contrast to the very large initial D P of chainaddition polymers. In fact, D P in chain-addition polymers actually declines when the kinetic parameter a* < 1 (I). This result can be explained only by the existence of chain termination, for if the same chains grew throughout the entire reaction it would be impossible for the D P to decline. The pa-
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
Downloaded by UNIV OF AUCKLAND on May 3, 2015 | http://pubs.acs.org Publication Date: May 5, 1990 | doi: 10.1021/ba-1990-0227.ch016
16.
ROSENDALE &
i
BIESENBERGER
Step- ir Chain-Addition Polymerizations 269
i i i I i i i i i i i i i I i i » i i i i i i I i i i i i i i i i I t i i i i i » i i
0.0
0.2
0.4
0.6
0.8
1.0
Conversion Figure 1. Number-average degree of polymerization (x ) vs. conversion for various polymerization mechanisms. N
rameter a* is denned as the ratio of the time constant for monomer conversion to that for initiator decomposition, and for a conventional chainaddition polymerization without branching or chain transfer: (kk
d
(6)
k (2C )y* p
0
The k , k , and k are the rate constants for the termination, dissociation of t
d
p
initiator, and propagation steps, respectively, and C is the initial initiator concentration. When a* > 1, initiator is depleted before monomer and the reaction "dead ends" (DE). 0
In an attempt to predict the effect of polymer molecular weight and concentration on reaction viscosity, Malkin (2) evidently classified polymerizations in precisely the same way. Thus, our term "random" corresponds
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
270
POLYMER
CHARACTERIZATION
to his "condensation", and our "step-addition" to his "ionic" polymerization. It can be argued that random is a more general label, because not all reactions of the form of equation 1 are condensations, for example, linear polyurethane formation from diisocyanates and diols. Similarly, step addition is a more general term because it includes at once such extremes as very rapid ionic polymerizations and relatively slow, uncatalyzed ring-opening polymerizations. The absence of termination is the criterion for step addition, not the speed of the propagation step.
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Theory Following the approach of Malkin with some modification, we shall attempt to predict the general behavior of viscosity growth with polymer formation for the aforementioned reaction types. Anticipated viscosity growth versus time curves based upon Figure 1 have been sketched elsewhere (la). They show chain-addition viscosity rising most rapidly, random most slowly, and step addition between them. The random curve is concave upward, whereas the addition curves exhibit downward concavity. The treatment reported here, which is more quantitative, will examine this expected behavior more closely. We postulate that the dependence of viscosity (TJ) upon shear rate (7), temperature (T), weight fraction of polymer in solution (w ), p
and weight-
average D P (x J : r\(y,T w ,xJ
TJ =
9
(7)
p
can be separated into the product (lb): n =
i(y)MT,w ,x ) p
(8)
w
and that the Newtonian or "zero shear" viscosity T | can be separated further 0
as follows (lc): n
0
=
Kp)w«xf
(9)
where exponents a and P depend upon the "entanglement" D P in solution (* )es> and K(T) is a temperature-dependent empirical constant. Thus, tt
a = 1, p = 1 a = 4.7, p = 3.4 The locus of values 0c ) w
es
when
x
< (x )
(10)
when
5^ > (xj
(11)
w
w
es
es
corresponding to concentrations w
p
is computed
from the expression: Wp(Xw)es = y
0Uep
7
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
(12)
16.
ROSENDALE
where ( x j
e p
&
Step- ir Chain-Addition Polymerizations 271
BIESENBERGER
is the entanglement D P for polymer melt (w
p
= 1). Whereas
values of 0.63 and 0.68 have been suggested for the empirical constant 7 (3), we used 1.0 (Id). The following expressions, when substituted into equation 9, subject to equations 10-12, predict growth of T J with conversion
where x is the number-average D P . These equations follow directly from those tabulated elsewhere (le, If). Equation 13 reflects the fact that monomer is also counted as polymer with length of one unit in random-type polymerizations. n
For step addition, (16) x
N
(17)
= 1 + x $ 0
x
N
~ 1
(18)
X
N
where x is the ratio of monomer to initiator in the feed. These equations 0
also follow directly from those listed elsewhere (le, lg). Equation 16 reflects the fact that molar conversion of monomer is proportional to weight of polymer formed in addition polymerizations. The dispersion index
x /x w
N
approaches 2.0 at high conversions. For chain addition with the gel effect, u>, = *
(19)
1 x
w
[1 + i/ a,G(ln(l 2
))]
2
= 2x
N
K
J
(21)
where parameter a * indicates whether the reaction will dead end (a* > 1) or not (a* < 1), as well as whether the D P will drift upward or downward, respectively. One may incorporate the gel effect into the model by substituting for G an appropriate gel-effect model for comparison with data, for example, G = exp [~(B/2.0)4>], where B is an empirical constant. If no gel effect is present, then G is set equal to 1.0. Other gel-effect models may be In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
272
POLYMER
CHARACTERIZATION
found in ref. Ih. Equation 20 applies to all values of monomer conversion below the conversion where dead-ending occurs (4> ), given elsewhere (Ij) as: DE
*
D E
= 1 -
exp —
(22)
The dispersion index in equation 21 has been arbitrarily taken to be 2. This analysis differs in several ways from that of Malkin (2). H e used number-average D P (x ) instead of weight-average (xj in equation 9, and he did not incorporate an entanglement DP, but instead used exponents in excess of 1 (5 and 3.4) throughout the polymerization. Malkin also assumed that D P remains constant throughout chain-addition polymerization, whereas we have allowed it to drift with reaction, and even to dead end.
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N
The curves in Figure 1 are graphs of equations 14, 17, and 20. Corresponding graphs of T | versus conversion have been plotted in Figure 2. A n 0
0.0
0.2
0.4
0.6
0.8
Conversion Figure 2. Viscosity vs. conversion for various polymerization types.
In Polymer Characterization; Craver, C., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1990.
1.0
16.
ROSENDALE
&
BIESENBERGER
Step- 6" Chain-Addition Polymerizations 273
average value of K(T) from equation 9 was computed from experimental n versus-
