Rate constants depolymerization

Polymer Depolymerization rate constant (fl) Activation energy (kcal/mol deg)... 

Depolymerization was in chloroform solution with a polymer concentration of 10 mg/ml. The depolymerization rate constant was determined by viscosity measurements over 24 hours. Details as described in the text. 

The depolymerization rate constant ki, expressed in moles cm sec , is the product of Csat (or Keq) and 2 1> 2, 22, 27). The chemical meaning of such a constant is that for a given temperature, pH, and ionic strength, ki represents the maximum solution flux per unit area which can be expected from a given silica sample. At equilibrium this flux must be equal and opposite to the product of 2 and Cboi when Csoi = Csat i-e., dC/dt = 0. 

Using the enthalpy and entropy of polymerization data for methyl methacrylate from Table 6.13, calculate the depolymerization rate constant of poly(methyl... 

If the polymer assembly is unobstructed, its elongation rate is simply Vp = 8 (konM — feotr) where 8 [nm] is the size of the monomer ( 5.4 nm for actin), M [/rM] the monomer concentration, and on(l/[/rMsec]),A off [1/sec] are the polymerization and depolymerization rate constants, respectively. In the case of a helical actin polymerization, as shown in Figure 1, the step size is half the monomer diameter 55.4 = 2.7 nm. 

The dinuclear complex [(H3N)5Ru(/i-N2)Ru(NH3)5] has an aquation rate constant >10 s at room temperature, much faster than that for [Ru(NH3)5(N2)]. The tetranuclear cation [Ru4(OH)4] undergoes depolymerization, presumably giving initially [Ru2(OH)2], much more slowly. At 298 K the depolymerization rate constant is 2.5xl0 s = 63kJmorO. Linkage isomerization of complexes [Ru(NCS) -(SCN)6 ] n = 1-4), produced by reacting ruthenium trichloride with potassium thiocyanate in aqueous solution, under various conditions has been discussed in qualitative terms. ... 

Condensation occurs most readily at a pH value equal to the piC of the participating silanol group. This representation becomes less vaUd at pH values above 10, where the rate constant of the depolymerization reaction k 2 ) becomes significant and at very low pH values where acids exert a catalytic influence on polymerization. The piC of monosilicic acid is 9.91 0.04 (51). The piC value of Si—OH decreases to 6.5 in higher order sihcate polymers (52), which is consistent with piC values of 6.8 0.2 reported for the surface silanol groups of sihca gel (53). Thus, the acidity of silanol functionahties increases as the degree of polymerization of the anion increases. However, the exact relationship between the connectivity of the silanol sihcon and SiOH acidity is not known. 

Zavitsas et al. account for the effects of water in their calculations. Water promotes depolymerization of the paraformaldehyde as well as the hemiformals. Their modifications correct for the apparent reduction in methylolation rate as the extent of reaction proceeds, in that the hemiformals remove formaldehyde reactivity from the reaction mixture. Their rate constants look large because they are written for phenate concentrations rather than phenol and because of the formaldehyde equilibrium adjustments. They note that unsalted phenol is a by-... 

Example 4. Depolymerization under Pressure.62 PET resin was depolymerized at pressures which varied from 101 to 620 kPa and temperatures of 190—240° C in a stirred laboratory reactor having a bomb cylinder of2000 mL (Parr Instrument) for reaction times of 0.5, 1, 2, and 3 h and at various ratios of EG to PET. The rate of depolymerization was found to be directly proportional to the pressure, temperature, and EG—PET ratio. The depolymerization rate was proportional to the square of the EG concentration at constant temperature, which indicates that EG acts as both a catalyst and reactant in the chain scission process. 

Since the depolymerization process is the opposite of the polymerization process, the kinetic treatment of the degradation process is, in general, the opposite of that for polymerization. Additional considerations result from the way in which radicals interact with a polymer chain. In addition to the previously described initiation, propagation, branching and termination steps, and their associated rate constants, the kinetic treatment requires that chain transfer processes be included. To do this, a term is added to the mathematical rate function. This term describes the probability of a transfer event as a function of how likely initiation is. Also, since a polymer s chain length will affect the kinetics of its degradation, a kinetic chain length is also included in the model. 

Protocol Increase in tubule number concentration Increase in depolymerization rate OfF-rate constant (sec- ) On-rate constant (M- sec" ) Reference... 

P n is a reactive molecule of the polymer with n monomer units in the chain, and it is unimportant whether the polymerization mechanism is radical or ionic. The rate constant of the propagation step is kp. Under certain conditions, monomer units can be split off the reactive polymer molecule. Then it is necessary to consider also the depolymerization reaction (with the rate constant kd). 

Equation 3 shows that for a given monomer concentration [M]eq at temperatures above a critical value Tc the rate of the depolymerization step becomes greater than the rate of the polymerization step and dominates the reaction. The critical temperature Tc is called ceiling temperature (22, 23). (AH is the enthalpy of polymerization, and AS° is the entropy of polymerization at the monomer concentration [M] = 1 mole/liter.) The concentration of the monomer at equilibrium [M]eq is identical to the equilibrium constant K, which is defined by the rate constants kp and kd. 

The reactive position in the chains is written as a dot. The constants kn, kw, k22, and k21 are the rate constants of the propagation steps ke, 22, and k2i are the rate constants of the depolymerization steps. It is assumed that the constants are independent of the last member of the chain. 

The behavior of the reaction rate as a function of temperature dispels any notion that the reaction is simple. Figure 3 shows that there is a maximum in the first-order rate constant-temperature curve at approximately 80 °C. At such a low temperature, the rate-temperature maximum cannot be explained by depolymerization, nor can it be explained by deactivation of the catalyst as a result of more rapid polymer accumulation on the catalyst at higher temperatures since the maximum is obtained for initial rates measured as a function of temperature. Theoretical considerations predict that a maximum in the rate-temperature curve may be expected from the Langmuir-Hinshelwood model for polymerization on solid surfaces but not from the Rideal model (5). The rate of reaction for the Langmuir-Hinshelwood model is given by ... 

The isothermal pyrolysis in the presence of air proceeds at a much faster rate and higher weight losses are obtained as compared to vacuum pyrolysis at the same temperature. The first order rate constant obtained is linearly related to the expression [%LOR + o-(% crystallinity)]//o with a degree of correlation r = 0.923, where a is the accessible surface fraction of the crystalline regions according to Tyler and Wooding [501], and / is the orientation factor. No correlation could be found with DP due to very rapid depolymerization. The fact that the rate is inversely proportional to the orientation and that it decreases with the increase in the thickness of the fibers indicates that the rate of the diffusion of the oxygen into the fibers controls the kinetics and that oxidation is the predominant process in air pyrolysis. 

Methyl methacrylate (MMA) has the formula CH2 = ClCHa) (COOCH3). The vapor pressure of MMA due to its vaporization is estimated by [3] In P(Atm) = 11.79 — 4410/T(K), assuming a constant heat of vaporization. For the depolymerization reaction, the temperature which gives 1 atm of MMA (the product) is 164 C [26]. This temperature establishes the pressure equilibrium constant and therefore the Gibbs fiiee energy for the depolymerization reaction. Answer The depolymerization of PMMA rate constant given by [26] rate constant = 3.87 x 10 exp(—175 kJ/mole/RgT) gm/cm sec. 

Table I. Rate Constants for the Depolymerization of Cellulose in Air and Nitrogen...

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