Conversion

During the course of conversion, all effects of concentration as discussed in subchapter 2.4.2 apply as the concentration of monomer declines with conversion and in case of partially ionized or protonized monomer the degree of ionization of monomer may change with conversion, which has consequences on the kinetics as discussed in subchapter 2.4.3. Apart from that, viscosity increases during the course of polymerization, which is dealt with in this subchapter. As all chemical reactions with molecularity other than unity are preceded by mutual approach of the reactants by diffusion and diffusion rate is decreased towards higher viscosity of medium, diffusion controlled reactions become slower and non-diffusion-controlled reactions may run under diffusion control. This can be understood by combining the Smulochwski (eq. (2.20)), and the Stokes-Einstein equation (eq. (2.21)) as discussed previously in this work (introduction 2.4).

It is important to understand that macroscopic viscosity and the effective viscosity which applies for the growing radicals are not necessarily the same. k_t^1,1 at negligible conversion scales with dynamic viscosity, , i.e. if the value in one solution

is known, the value in a different solvent can be predicted easily by scaling of k_t^1,1 with the ratio of reciprocal solution viscosities:^[102]

But k_t^1,1 does not decrease by addition of polymer to the same degree as fluidity. This is demonstrated in Figure 2-8 (purple triangles). The same is true for k_t(red diamonds, black squares, and magenta triangles).

0.0 0.1 0.2 0.3 0.4 experimental data for MAA/pMAA is plotted. Values are given as ratio to the value at zero polymer content. Green spheres: relative fluidity^[120], red diamonds: <kt> SP-PLP–

NIR technique, wMAA0 = 0.6;^[121] black squares: <kt> SP–PLP–NIR technique, wMAA0 = 0.6;^[121] purple triangles: kt1,1 SP–PLP–EPR technique, wMAA = 0.1 polymer-premix;^[120]

magenta triangles: <kt> SP–PLP–EPR technique, wMAA = 0.1, polymer-premix.^[120] It should be noted that the polymer produced during laser experiments is of smaller size than the polymer used for premix and viscosity measurements.

 

In the following section, viscosity and its influence on termination are discussed. It turns out that k_t and



^1 are influenced by the presence of polymer to different extent (Figure 2-8). The growing chains are not influenced by polymer coils around them in the same way as with the solvent, with which they stand in direct contact.

The exact relationship is not known.

In order to characterize the change in viscosity over conversion, relative viscosity,

r,

 is defined as the ratio of viscosity at a certain conversion X,



^X, to viscosity at zero conversion



⁰:

The termination reaction of two macroradicals proceeds in a three-stage mechanism according to Benson and North.^[122,123] First, both macroradicals have to come into contact by translational (center-of-mass) diffusion (TD). Subsequently, the radical functionalities have to come into immidiate proximity (a few Å) by segmental diffusion (SD). The third and final step is the chemical reaction (CR) proceeding either by combination or disproportionation. Hence the rate coefficient of diffusion-controlled termination,

k

_t,D, is given by:

Another mechanism, by which two radical centers of growing chains can approach each other is reaction diffusion (RD), where radical sites advance towards each other not by movement of the polymer chain, but by growing in the direction of the other radical center. This term has to be added:

r 0

X

 ^  ^(2.37)

t,D t,SD t,TD t,CR

1 1 1 1

k ^k ^k ^k ^(2.38)

At low degree of monomer conversion, segmental diffusion mostly dominates. The associated rate coefficient

k

_t,SD is controlled by the type of polymer and the viscosity of the monomer-solvent mixture. As the former is conversion-independent and the latter does not change much,

k

_t,SD remains more or less constant, which results in a plateau value of

k

_tup to moderate degree of monomer conversion.

At higher conversion,

k

_tstarts to decrease notably, when TD becomes slower than SD and constitutes the bottle neck thus controlling the mechanism. The corresponding rate coefficient,

k

_t,TD, scales with the inverse viscosity of the polymerizing medium.

k

_t,TD can be expressed relative to

k

_TD⁰ , the theoretical termination rate coefficient under translational diffusion control at conversion zero, and relative viscosity. The stark decrease of

k

_t with k_p staying constant leads to an augment of both rate of polymerization and molar mass of polymer produced. This is called the Norrish–Trommsdorff or gel effect.^[124,125]

Towards even higher conversion, center-of-mass diffusion of macroradicals essentially ceases and termination runs under RD control. Termination under RD conditions scales with k_pvia the reaction-diffusion constant,

C

_RD, which is enhanced by chain flexibility. Studies into the termination kinetics of ethene indicated that the reaction-diffusion constant may be estimated with the help of the volume-swept-out model which considers the diameter of the macroradical and the jump distance.

[126-128] Typically, CRD is independent of temperature, but decreases towards higher pressure.^[129,130] It should be noted that, in this work,

C

_RD is defined differently from some other publications, where bulk polymerizations have been analyzed and RD was correlated with conversion, X, via a constant C_RD^ (see eq. (2.40)). The k_t,TD expression of the present work into solution polymerization uses monomer concentration (eq. (2.41)).

At very high conversion and thus high viscosity even propagation may run under diffusion control. This is especially the case for bulk polymerizations. As termination by reaction diffusion is proportional to propagation, from this point on both

k

_t and kp begin to decline rapidly and radicals remain “frozen” in the polymer matrix. This is called the glass effect.

Diffusion controlled k_p,D may be scaled to viscosity applying a diffusion controlled rate coefficient of propagation at zero conversion, k_p,D⁰ , and relative viscosity, _r, which changes with conversion. This leads to modification of eq. (2.20) into eq. (2.42).

Including diffusion-controlled propagation and assuming translation-diffusion controlled and reaction-diffusion-controlled termination to occur in parallel, yields Equation (8) for the overall termination rate coefficient of bulk polymerization.^[123,130]

Information about the effective reduced viscosity in polymer solution is hardly available (v.s.). The variation of relative viscosity has been approximated by an exponential relation containing one single parameter C_:^[90]

Combining eq. (2.42) with eq. (2.44) yields:

r

Combining eq. (2.43)(2.42) with eq. (2.44) yields:

These two equations are plotted in Figure 2-9.

0.0 0.2 0.4 0.6 0.8 1.0

respectively. Rate coefficients are taken from literature.^[130,136]

 

If initiator decay is a truly unimolecular reaction, it should not be influenced by viscosity. An initiator system with higher molecularity, e.g., a redox initiator can become diffusion controlled. Initiator efficiency decreases as the viscosity increases.

The two newly formed radicals remain near one another, i.e. in the solvent cage, for a longer period, so they have more time to terminate or undergo side reactions. The time span between addition of two monomer molecules also increases with

The physical properties of a polymer derive from the functionalities of its monomer units, but also from its molecular mass distribution (MMD) and microstructure.

Thus, with the same monomer (composition) the production of quite different polymers is possible. This is one of the reasons why even though lots of new monomers have been developed over the last decades, predominantly the same monomers as in the beginning of large-scale industrial application of polymerization are used. New requirements on products were rather met by modification of production processes of existing monomers than by application of new monomers.

This may demonstrate the importance of meticulous optimization of industrial polymerization processes.

Modeling can be used to simulate polymerization, e.g., conversion and thereby heat production, but also all properties of the resulting polymer as they are determined by the process. It is a more sophisticated approach than just doing experiments to see how modification of one parameter, e.g., temperature, affects others, e.g., M_w. As far as possible, all relevant reactions with all their individual dependencies are regarded separately. Hence, special experiments should be carried out to yield individual rate coefficients.

Modeling can be used to test hypothesis about mechanisms, i.e. checking if they lead to correct predictions, or to plan experiments. In addition, a model may be used for evaluation and interpretation of a complex experiment. Thus, modeling may lead to a better understanding of the underlying kinetics.

Im Dokument Kinetics and Modeling of the Radical Polymerization of Acrylic Acid and of Methacrylic Acid in Aqueous Solution (Seite 53-59)