Kinetics of Addition Polymerization to Polydimethylsiloxane

Many polymers are produced in stirred tank reactors, either batch or continuous. As an example, the polymerization of poly(dimethylsiloxane) (PDMS) is shown in Figure 1. In this reaction, "Me" represents methyl groups and potassium hydroxide is the catalyst. The [Me₂SiO]₅ is a 5-membered ring which is opened to form the basic building block (the "link") of the polymer. The second product represents finished polymer (it reacts with something called an "endblocker" to stop growth), the first one is a still-growing ("living") polymer. All growth takes place while the chain is attached to the catalyst.

Figure 1: Ring opening polymerization of PDMS.

This is a type of addition polymerization, which is discussed in many kinetics³ and all basic polymer-science textbooks.⁴ The reaction is mostly thermoneutral and is usually run between 110 - 140 °C and atmospheric pressure. A small amount of molecular weight modifier ("endblocker") is used to stop chain growth, but the catalyst then starts a new chain. Common endblockers are dimethylsiloxanes with trimethylsiloxy end-groups. A "living" chain reacts with the endblocker, forming an end-capped "dead" polysiloxane product with a trimethyl end group.

The Me₃SiOK reacts with another polysiloxane to create another trimethylsiloxy end-group. The overall effect is not only the endcapping of the polymer, but also control of the chain length. Average chain lengths (m+n) between 43 - 205 are typical for industrial PDMS in which several different grades of product are synthesized. Because the monomer addition rate >> reaction rate with endblocker (otherwise you would never get to a high molecular weight), the endblocker doesn't influence the reaction kinetics, only the molecular weight distribution.

In analyzing polymerization kinetics, the most difficult step is determining the molecular weight from a physical property, such as kinematic viscosity, and calculating the fraction conversion. The viscosity-average molecular weight, which is measured in this demonstration, is an intermediate measurement with a value in between the number-average and weight-average molecular weight of the polymer. The number average molecular weight is the statistical average molecular weight and indicates that 50 % of the polymer chains are below the number average molecular weight, and 50 % are above. The weight average molecular weight is calculated from the weight fractions in which 50 % of the sample weight consists of chains of lower molecular weight and 50 % consists of chains of higher molecular weight.

Dividing the number average MW by the monomer weight gives the number average degree of polymerization, which is related to fraction conversion. The fraction conversions vs. time are used to determine the order of the reaction as learned in Physical Chemistry and Reactor Design classes.

The molecular weight can be determined by empirical relationships, such as Barry's relationship for polydimethylsiloxanes with molecular weights above ~2,500.⁵

This gives the viscosity-average molecular weight. For molecular weight predictions < 2,500, interpolate the experimental data found in Kuo,⁶ using the kinematic viscosity of the DC-245 monomer for chain length 1. Divide the viscosity (cP) by the polymer density (g/cm³) to obtain the kinematic viscosity in cSt. Divide the viscosity average MWs by 1.6 (empirical factor for PDMS) to get the number average molecular weight, and divide this value by the monomer molecular weight to get the average chain length, (P_N)_avg, which includes the unreacted monomer.

To get the fraction conversion (f_m), start with the mass balance for the average of P_N (polymer only):

  (1)

The left-hand side is the average of P_N (polymer only) up to time t, where f = f_m. But the average P_N that you measure includes the monomer. To account for monomer in (P_N)_avg, recall that by definition:^3-4

and therefore:

(2)

The average polymer and (P_N)_avg for the entire batch are almost equal at the last batch, where f_m approaches 1. Compute f_m for the last point using a mass balance and the amount of low boilers that was collected. Solve for . For many addition polymerizations, is constant for the entire batch, which allows f_m to be computed at all other times from Equation 2. Also, compute the equilibrium constant K (first-order reversible kinetics model) for the reaction by mass balance.

Once f_m has been determined as a function of time, assume irreversible kinetics and determine the reaction order with respect to monomer. Use statistical analysis to determine the quality of the fits and the confidence limit on the rate constant k_p. Determine the fit for first-order kinetics (expected from theory),^3-4 and test if the two fits actually differ.

At similar conditions, others have reported a first-order rate constant of 10^-3 s^-1 for the DC-245 monomer, and a K > 60.

Figure 2. Typical polymerization results."DOP" = degree of polymerization. The MW's were computed from available data (see ref. 6) or Barry's equation (>2500).⁵

The workup of representative raw data is shown in Figure 2. These data are for the polymerization of Dow Corning DC-245 monomer. The reaction conditions were: 0.04 wt% catalyst solution, 12 wt% endblocker (modifier), 130 °C and 1 atm pressure. With a relatively large amount of endblocker used, the final degree of polymerization (DOP) was quite low.

In this experiment, 11.36 L of monomer were reacted, and only 15 mL low boilers were recovered, indicating that the data should follow irreversible kinetics. The fit to first-order (in monomer) kinetics is shown in Figure 3 below. The fraction conversions (f) were determined using Equations 1 and 2 with the assumption that the polymer produced is at constant chain length (P_N). The resulting fit is reasonable, but not perfect. Slight deviations from the theoretically expected first-order kinetics can arise for several reasons such as diffusional effects, which is when the viscosity increases and the diffusivities decrease significantly. Two other reasons for deviations are suggested by the raw reaction temperature data (temperature oscillations affect the rate constant) and by small leaks that may be present in the pumps, reactor, and heat exchangers. If there are leaks, some O₂ could get into the system and gradually inhibit the reaction.

Figure 3. Kinetics analysis. "F" is the 1^st order function, the solution of the batch reactor mass balance for a 1^st order irreversible reaction.

Polymer science provides many examples of the basic principles of chemical kinetics and reactor design. Simple rate expressions can describe fairly complex chemical processes, as in this experiment. Reactor system design must find the optimal reactor type (batch, stirred tank, plug flow, or hybrid) considering kinetics, capital costs, and molecular weight distribution. In particular, the last factor is usually the most important, because it largely defines the product. Depending on this factor alone the product can often range from a hard brittle solid to a rubber to a liquid. A bulk (no solvent) polymerization, such as the one performed in this experiment, has the advantage that subsequent processing to obtain a pure polymer is simple - just strip out the low boilers and filter out the neutralized catalyst. However, the disadvantage of bulk polymerization is that if one loses control of temperature (too high), even in a thermoneutral polymerization, other reactions will dominate and lead to "runaway", which is an uncontrolled exothermic reaction that may result in explosion. Polymerizations with higher heats of reaction are reacted either in solution, suspension (a continuous water phase is present, and the monomer is in droplet form), or in the gas phase.

The major takeaways from the experiment are how one can process raw data of an easily measurable physical property (viscosity) to ultimately determine the monomer fraction conversions and the kinetics of the reaction. Many other physical properties, e.g., density and particle light scattering, are used for this purpose in other polymerizations.

Polymers made by ring-opening polymerizations include Nylon-6 from caprolactam, acetal copolymers with ethylene oxide and dioxolane, which are used in everything from fuel tanks to sprinklers, poly(ethyleneimines), which are used in detergents and cosmetics, and many other silicon-backbone polymers.With the exception of Nylon-6, most of these polymers are commercially produced by anionic or cationic polymerizations. Other polymers that are made similarly include copolymers of styrene (especially with isoprene), isobutene-isoprene (butyl) rubber and its halogenated variants, and poly(alkyl vinyl ethers), which are typically used in paints and adhesives. For some such polymerizations, the chain terminations are so controlled that an almost homogeneous molecular-weight distribution is possible. Except for certain specialty grades, it has been found that such narrow distributions present other problems, such as extrusion difficulties.

Many polymers are vacuum-stripped as the first part of their purification to a commercial product. Among these are the poly(vinylidene chloride) copolymers, poly(chloroprene), and many grades of poly(styrene) and its copolymers such as SAN (styrene-acrylonitrile).

Silicone polymers are used in many products, including lubricants, personal care products, medical devices, antifoams, sealants, waterproof coatings, and as components of detergents, electrical insulation, and paints.⁸ Medical devices composed of very high molecular weight crosslinked silicone may be approved by the FDA for implantation. More common medical uses are consumables such as catheters, tubing, gastric bags, and surgical incision drains. Commercial PDMS is non-hazardous with a flash point higher than 300 °C, minimal toxicological effects, and good resistance to moderately concentrated aqueous alkali and acids.^8,9 It does not corrode most common materials. But like many polymers it can oxidatively decompose, in this case above ~150 °C.

Materials List

Name	Company	Catalog Number	Comments
Equipment
Rotational (cup and bob) viscometer	Brookfield		Use to measure the viscosity of polymer samples
Stirred tank reactor	custom		20 L
Reactor Agitator	McMaster-Carr		46-460 RPM; 6-blade, flat turbine (Rushton) type, ~4” diameter.
Reagents
Dimethlysiloxane monomer	Dow Corning	DC-245	specific gravity = 0.956 at 25 °C; viscosity = 4.2 cSt; m = average number of dimethylsiloxanes = 5
Endblock A	Dow Corning	10082-147	specific gravity = 0.88 at 25°C; m = 4.5 (not counting the two end groups)
KOH catalyst	VWR	470302-140	45 wt% solution in water
Nitrogen	Airgas	UHP grade	Used to blanket the system
Carbon dioxide	Airgas	Tech. grade	Used to neutralize the catalyst

Viscosity and Density Data at Low Molecular Weight

Data originally from: Dow Corning.¹⁰

MW, g/mol	162	410	1250	28000
Viscosity, cs, 25 °C	0.65	2.0	10	1000
Specific gravity, 25 °C	0.760	0.872	0.935	0.970