Rheokinetic polymerization

Figure 1.12 Dual stream injection system for in situ rheokinetic study of anionic ring opening polymerization of caprolactam...

This chapter reviewed the chemistry of ring opening polymerization of cyclic monomers that yield thermoplastic polymers of interest in composite processing. In addition, this chapter focuses on the chemistry, kinetics, and rheology of the ring opening polymerization of caprolactam to nylon 6. Finally, these rheokinetics models are applied to the reactive injection pultrusion (RIP) process. 

The rheokinetics of polycaprolactam polymerizing in the monomer shows that below 50 percent conversion, the relative complex viscosity versus conversion of the nylon 6 homopolymerization is defined by the phenomenological equation ri / t]Q = exp(19.6 X), where // is the complex viscosity of nylon 6 anionically polymerizing in its monomer, 0 is the viscosity of caprolactam monomer, and X is fractional conversion. 

It should be emphasized that in all these cases, combined or superimposed phenomena must be dealt with, viz. for stage IV, fluiddynamics, kinetics of polymerization, and rheokinetic changes caused by chemical reactions for stage V, polymerization kinetics, crystallization kinetics and heat transfer effects a thermomechanical problem in combination with crystallization kinetics. Construction of a mathematical model requires simultaneous solution of a set of equations in order to describe these related phenomena. 

Real examples illustrating different types of time dependences of viscosity, can be found elsewhere.52 It is worth mentioning that the rheokinetics of polymerization, even for a specific type of polymer (for example, polyurethane) depends on the composition, which determines both the kinetics of the process and the structure of the newly formed polymer. Clearly, the important factor is whether a linear or three-dimensional polymer is formed. In the first case, the viscosity increases... 

These equations must be supplemented by a kinetic equation for the time dependence of the degree of conversion P(t), and the dependence of the viscosity of a reactive mass on (3, temperature, and (perhaps) shear rate, if the reactive mass is a non-Newtonian liquid. The last two terms in the right-hand side of Eq. (2.89) are specific to a rheokinetic liquid. The first reflects the input of the enthalpy of polymerization into the energy balance, and the second represents heat dissipation due to shear deformation of a highly viscous liquid (reactive mass). 

The manufacture of products by reactive molding results in the superposition of interrelated chemical and physical phenomena. These include polymerization, crystallization, vitrification, heat transfer, rheokinetic effects, changes in the physical properties and volume of a material injected into a mold. It is quite natural that special experimental methods are required to study and control the complex processes which take place in molds. 

A complete analysis of the role of the radial distributions of all the parameters that determine the flow through a tubular reactor during polymerization is a very complicated, and it is doubtful whether general solutions can be found. However, solutions can be obtained for various situations for a system with known kinetic and rheological properties, because we will be searching for specific details rather than for a general physical picture of the process. It is also possible to carry out a general analysis at certain simplified models, which nevertheless include the principal rheokinetic effects. 

The investigation by Lynn and Huff201 was the first one in which the true velocity profiles during polymerization in a tubular reactor were determined. The idea of the dependence of the hydrodynamic field on the varying rheokinetics during a chemical reaction is quite fruitful and has... 

The degree of conversion inside this volume is constant, but the MWD function qw(n, r), where n is the degree of polymerization, depends on r. This is a reflection of different reaction time in the various layers of the polymer. The residence time distribution function f(r) for the reactive mass in a reactor is determined from rheokinetic considerations, while the MWD for each microvolume qw(n,t) is found for various times t from purely kinetic arguments. The values t and r in the expressions for qw are related to each other via the radial distribution of axial velocity. 

In this review, the rte<4dnetic ai )toach is presented, complete mathematical and physical statements of the preplan are given, and the operation of a tubular polymerization reactor is analyzed as an example. The fundamental necessity of using the rheokinetic approach, whenever there is a sharp growth in the viscosity, is demonstrated. The trends of further investigation are presented. 

Rheokinetic processes for polymerizing media have clearly defined specific properties. These are as follows a complex kinetic scheme, variation of molecular-mass distribution (MMD) of products with time, and viscosity growth during reaction. The first two peculiarities were investigated in detail in numerous works both in general form and in connection with different types of polymerization and polycondensation... 

It should be noted that all investigations of flow stability of polymerizing liquids are few in number and have been carried out up till now only for unidimensional problems. The problem of stability of steady rheokinetic two-dimensional flows to local hydrodynamic perturbations has not been discussed in the literature yet. Obviously the problem can be solved (the solution is difficult from the technical point of view), for example, by numerical methods solving the problem on unsteady development of the flow of polymerizing mass directly after a forced local change of the profile of the flow velocity. 

A complete analytical examination of the role of distribution of the flow velocity over the radius of a tube is obviously impossible. A formulated problem for a complete description of the flow of rheokinetic liquid seems to be quite difficult and it is clear that the first steps in investigating a two-dimensional flow were based on very simple assumptions. In a number of works [43,44], the authors took a fixed parabolic profile which is incorrect in principle for the flow of polymerizing media and leads to important mistakes. This is demonstrated very well in Ref. [45] where the possibility for styrene polymerization in a tubular reactor has been estimated it hse been shown that, if a real distribution of flow velocities and residence times over the radius is taken into account, the answer must be negative, in Ref. [44] however, a positive answer is obtained for an a priori parabolic profile. 

The fact that the results obtained earlier and described above were experimentally confirmed was of great importance. The literature does not contain e iq)erimental investigations of rheokinetic problems in which the distribution of flow velocities or residence times (conversion) at the output of the tubular reactor would be studied. Therefore, the results of the experimental investigation of hydrolytic polymerization of dodecalactam in a pilot tubular reactor and the comparison of these results with computation [58] deserve a more detailed presentation. 

R tly, theoretical investigatimis were carried out of the effect of hydrocfynamics of polymerizing liquids [Pg.132]

However, rheokinetic effects cause the develproducts accumulate on the walls and in the axial zone the flow is accelerated, i.e. the feed rate of the reactants increases. As a result, the Vf = U,. equilibrium is violated, the front line is distmted and its central part is displaced towards the ouq ut. Consequently, the temperatiure becomes lower, the rate of combustion dr<, and the feed—combustion equilibrium is violated still more. Also, the frcmt region is cooled down and is transferred out of the tube. Therefore, for a rheokinetic liquid (polymerizing medium with a sharp viscosity growth), a low-temperature condition for the process is the only steady-state solution. The polymerization front normal to the flow can exist only as an unsteady state and this solution is unstable. 

The conclusion of a review is a review of the review , i.e. an abstraction of the third order, if a theoretical analysis of a specific problem is conridered as an abstraction of the first order and the review of such analysis, i.e. the present work on the whole, as an abstraction of the second order. Such an approach reminds one of a view of an artist working in the field of nonrepresentational art , who escapes from the sxirrounding practical world. It is hardly probable that this would be fruitful in the present case. Therefore, concluding the discussion of the results of analyzing the flow of polymerizing liquids ( rheokinetic liquids), we would like to make only a few general remarks. 

The important problems include the control of polymerization reactors containing rheokinetic liquids. These problems have not been solved in many respects even for more simple situations. Both mathematical modelling and physical understanding of the process are the key problems [112]. 

Malkin (8) derived rheokinetic equations for different polymerization mechanisms by substituting the kinetic relations for concentration and molecular weight into Eq. (4.12). 

Table 4.1 Values of the Constant fi as Obtained from Rheokinetic Data for Different Polymerization Reactions [after Malkin (8)]...

To optimize the pre-reaction a detailed understanding of the polymerization kinetics and resulting changes of material properties is necessary. As it is mentioned before, the chain growing will increase the viscosity of the polymer. A novel approach to combine the rheology with kinetics is called rheokinetics and is the subject of discussion in the following second chapter. 

The influence of viscosity on atomization of polymer solutions is extensively discussed in the previous chapter. But the atomization of reactive solutions means changing molecular weights, polymer concentrations, and changes in the viscosity as well. To investigate the kinetics of viscosity during polymerization, the rheokinetics is applied. 

In contrast to the later used specific viscosity, rjs is the viscosity of the diluted polymer solution and i/o is the viscosity of the pure solvent. With consideration of (20.24) Malkin developed a method to connect a measured viscosity diuing a polymerization with the kinetics of the reaction and called this method, rheokinetics [41]. The initial equation from 1980 is shown in (20.25). 

Fig. 20.14 Working with rheokinetics of polymerization of sodium acrylate (NaAA) and acrylic acid (AA) with different concentration and initiator ratio is 0.8 mmol/mol—raw data by rheometer left), viscosity as a function of time—analysis of the viscosity gradient right) by the use of a reduced time and specific viscosity, see (20.29), dots mark the intersection point of the different fits, see (20.28) mass fraction of acrylates ( ) is equivalent mass fraction related to acrylic acid, where the molar concentration of acrylate and acrylic acid in solution is the same...

---