Rates polymerization

The concentration of active centres ([C ]) and polymerization rate (Rp) are given by 

As no completely satisfactory representation of the formation and nature of active species in heterogeneous catalysts has yet been devised this may be an over-simplification. Clearly the first order dependence of rate on monomer concentration is indicative of comparable solvent and monomer adsorption, even with what might be considered more strongly adsorbed monomers, such as butadiene, in comparison with mono-olefins or aliphatic hydrocarbons. The role of the more strongly adsorbed metal alkyl is more difficult to assess. The proportion of active alkylated transition metal atom sites will obviously increase with increase in [A] up to a limiting value. 

If alkylation of the surface were irreversible and catalysts were preformed (i.e. no concurrent initiation and propagation) the polymerization rate should rise to a sharp maximum and then decline as occupancy of the surface by monomer and solvent is reduced. However, in view of the relatively low activity of most heterogeneous catalysts the maximum rate would be expected at much lower levels of metal alkyl (i.e. 

Al/Ti 1) than are observed. Broad maxima at Al/Ti 1 are more consistent with reversible site formation or occupation, but with the qualification that only a fraction of the available sites (0 a ) cataly tically active. The reaction rate can then be written 

The influence of increasing [A]/[T] is represented in a simplified form in Fig. 3a(a) for values of if a and K (the dissociation constant of dimeric metal alkyl) reasonably close to those reported in the literature. At all values of [A] reactions will be first order in [M], and rates at a particular monomer concentration will increase with increase in alkyl concentration to a maximum defined by the ratio of 0 a/ A then decline. The height of the maximum and the value of [A] at which it occurs will obviously fall as 0a/ A decreases. Fig. 3a(b) shows the dependence of polymerization rate on metal alkyl concentration for J p Q and Rp 6a- The curves are clearly of a similar shape although since 6 a a the absolute rates would be different. 

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Figure 6.2 Acceleration of the polymerization rate for methyl methacrylate at the concentrations shown in benzene at 50 C. [Reprinted from G. V. Schulz and G. Haborth, Makromol. Chem. 1 106 (1948).]...

Initiators of suspension polymerization are organic peroxides or azo compounds that are soluble in the monomer phase but insoluble in the water phase. The amount of initiator influences both the polymerization rate and the molecular weight of the product (95). 

Solvent Polarity and Temperature. The dielectric constant and polarizabihty are of Htde predictive value for the selection of solvents relative to polymerization rates and behavior. In spite of the similarity of the dielectric constants of CH2CI2, CH Cl, and C2H C1 these solvents yield quite different isobutylene polymerization rates that decrease in the same order. 

Itaconic acid, anhydride, and mono- and diesters undergo vinyl polymerization. Rates of polymerization and intrinsic viscosities of the resulting homopolymers ate lower than those of the related acrylates (see Acrylic ester polymers) (8,9). 

Bulk Polymerization. This is the method of choice for the manufacture of poly(methyl methacrylate) sheets, rods, and tubes, and molding and extmsion compounds. In methyl methacrylate bulk polymerization, an auto acceleration is observed beginning at 20—50% conversion. At this point, there is also a corresponding increase in the molecular weight of the polymer formed. This acceleration, which continues up to high conversion, is known as the Trommsdorff effect, and is attributed to the increase in viscosity of the mixture to such an extent that the diffusion rate, and therefore the termination reaction of the growing radicals, is reduced. This reduced termination rate ultimately results in a polymerization rate that is limited only by the diffusion rate of the monomer. Detailed kinetic data on the bulk polymerization of methyl methacrylate can be found in Reference 42. 

Kinetic models describing the overall polymerization rate, E, have generally used equations of the following form ... 

Heterogeneous Catalytic Polymerization. The preparation of polymers of ethylene oxide with molecular weights greater than 100,000 was first reported in 1933. The polymer was produced by placing ethylene oxide in contact with an alkaline-earth oxide for extended periods (61). In the 1950s, the low yield and low polymerization rates of the eady work were improved upon by the use of alkaline-earth carbonates as the catalysts (62). 

The above mechanism, together with the assumptions that initiator decomposition is rate controlling and that a steady state in chain radicals exists, results in the classical expressions (eqs. 8 and 9) for polymerization rate, and number-average degree of polymerization, in a homogeneous,... 

Fig. 15. Polymerization rate vs molecular weight relationship for spontaneous bulk styrene polymerization under neutral and acidic conditions.

Another economically driven objective is to utilize initiators that increase the rate of styrene polymerization to form PS having the desired molecular weight. The commercial weight average molecular weight M range for general-purpose PS is 200,000—400,000. For spontaneous polymerization, the is inversely proportional to polymerization rate (Fig. 16). 

Anionic polymerization offers fast polymerization rates on account of the long life-time of polystyryl carbanions. Early studies have focused on this attribute, most of which were conducted at short reactor residence times (< 1 h), at relatively low temperatures (10—50°C), and in low chain-transfer solvents (typically benzene) to ensure that premature termination did not take place. Also, relatively low degrees of polymerization (DP) were typically studied. Continuous commercial free-radical solution polymerization processes to make PS, on the other hand, operate at relatively high temperatures (>100° C), at long residence times (>1.5 h), utilize a chain-transfer solvent (ethylbenzene), and produce polymer in the range of 1000—1500 DP. 

Most of the LFRP research ia the 1990s is focused on the use of nitroxides as the stable free radical. The main problems associated with nitroxide-mediated styrene polymerizations are slow polymerization rate and the iaability to make high molecular weight narrow-polydispersity PS. This iaability is likely to be the result of side reactions of the living end lea ding to termination rather than propagation (183). The polymerization rate can be accelerated by the addition of acids to the process (184). The mechanism of the accelerative effect of the acid is not certain. 

Polymerization Solvent. Sulfolane can be used alone or in combination with a cosolvent as a polymerization solvent for polyureas, polysulfones, polysUoxanes, polyether polyols, polybenzimidazoles, polyphenylene ethers, poly(l,4-benzamide) (poly(imino-l,4-phenylenecarbonyl)), sUylated poly(amides), poly(arylene ether ketones), polythioamides, and poly(vinylnaphthalene/fumaronitrile) initiated by laser (134—144). Advantages of using sulfolane as a polymerization solvent include increased polymerization rate, ease of polymer purification, better solubilizing characteristics, and improved thermal stabUity. The increased polymerization rate has been attributed not only to an increase in the reaction temperature because of the higher boiling point of sulfolane, but also to a decrease in the activation energy of polymerization as a result of the contribution from the sulfonic group of the solvent. 

Studies of the copolymerization of VDC with methyl acrylate (MA) over a composition range of 0—16 wt % showed that near the intermediate composition (8 wt %), the polymerization rates nearly followed normal solution polymerization kinetics (49). However, at the two extremes (0 and 16 wt % MA), copolymerization showed significant auto acceleration. The observations are important because they show the significant complexities in these copolymerizations. The auto acceleration for the homopolymerization, ie, 0 wt % MA, is probably the result of a surface polymerization phenomenon. On the other hand, the auto acceleration for the 16 wt % MA copolymerization could be the result of Trommsdorff and Norrish-Smith effects. 

Polymerization Kinetics of Mass and Suspension PVC. The polymerization kinetics of mass and suspension PVC are considered together because a droplet of monomer in suspension polymerization can be considered to be a mass polymerization in a very tiny reactor. During polymerization, the polymer precipitates from the monomer when the chain size reaches 10—20 monomer units. The precipitated polymer remains swollen with monomer, but has a reduced radical termination rate. This leads to a higher concentration of radicals in the polymer gel and an increased polymerization rate at higher polymerization conversion. 

Polymerization in two phases, the Hquid monomer phase and the swollen polymer gel phase, forms the basis for kinetic descriptions of PVC polymerization (79—81). The polymerization rate is slower in the Hquid monomer phase than in the swoUen polymer gel phase on account of the greater mobiHty in Hquid monomer, which allows for greater termination efficiency. The lack of mobiHty in the polymer gel phase reduces termination and creates a higher concentration of radicals, thus creating a higher polymerization rate. Thus the polymerization rate increases with conversion to polymer. 

Solution Polymerization. In solution polymerization, a solvent for the monomer is often used to obtain very uniform copolymers. Polymerization rates ate normally slower than those for suspension or emulsion PVC. Eor example, vinyl chloride, vinyl acetate, and sometimes maleic acid are polymerized in a solvent where the resulting polymer is insoluble in the solvent. This makes a uniform copolymer, free of suspending agents, that is used in solution coatings (99). 

Thus the thiol 0 2 25511 is capable of terminating a growiug chain and also initiating a new chain. If the initiation-rate constant, k is not much slower than the propagation-rate constant, the net result is the growth of a new chain without any effect on the overall polymerization rate (retardation). That represents a tme chain transfer, ie, no effect on the rate but a substantial decrease iu molecular weight (12). 

To maintain a high polymerization rate at high conversions, reduce the residual amount of the monomer, and eliminate the adverse process of polyacrylamide structurization, polymerization is carried out in the adiabatic mode. An increase in temperature in the reaction mixture due to the heat evolved in the process of polymerization is conductive to a reduction of the system viscosity even though the polymer concentration in it rises. In this case, the increase in flexibility and mobility of macromolecules shifts the start of the oncoming gel effect into the range of deep transformation or eliminates it completely. 

The reported values for the exponent of the dose-rate for the polymerization rate in gamma radiation-induced copolymerization of acrylamide with methyl chloride salt of A, A -dimethylaminoethyl methacrylate (DMAEM-MC) in aqueous solution was found to be 0.8 [16]. However, the dose-rate exponent of the polymerization rate at a lower dose-rate was found to be slightly higher than 0.5 for gamma radiation-induced polymerization of acrylamide in aqueous solution [45,62]. 

It will be known that for the radical polymerization the increase on the rate of initiation would increase the polymerization rate Eq. (I) and decrease the degree of polymerization Eq. (2). In the present systems, the monomer concentration was relatively high so that initiating radicals are formed to some extent from the monomer and solvent, i.e., / , in Eq. (1) may be represented as follows [51] ... 

In general, the overall activation energy for the polymerization rate is given by ... 

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