Predicting Rates of Decomposition of Free-Radical Initiators

Chapter 32

Predicting Rates of Decomposition of Free-Radical Initiators

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on June 15, 2016 | http://pubs.acs.org Publication Date: August 29, 1989 | doi: 10.1021/bk-1989-0404.ch032

Azo Compounds, Peresters, and Hydrocarbons Richard A. Wolf Department of Applied Organics and Functional Polymers Research, Michigan Applied Science and Technology Laboratories, 1710 Building, The Dow Chemical Company, Midland, M I 48674

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trans-symmetric bisalkyl diazenes, trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon -carbon bond homolysis). Transition state effects are calculated by the HMO p i - derealization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. Although there are many theoretical calculations of properties of free radicals in the literature, there have been few attempts to predict the rates of radical forming decompositions of free radical initiators, using structure activity relationships. For many of the applications of diazenes and peresters, such as initiating the free radical polymerization of vinyl monomers, a quantitative structure activity relationship for the rates of initiator decomposition would be very helpful in terms of predicting the u t i l i t y of potential new initiators before they are prepared. The ability to predict the rates of carbon-carbon homolysis of hydrocarbons would be extremely useful in assessing the ability of alkyl group-terminated vinyl polymers to dissociate, to continue "living radical" polymerization reactions (1,2). An excellent correlation between heats of formation of reactants and products versus activation energies has been made for the homolysis of trans-symmetric diazenes (3). 0097-6156/89/0404-0416$06.00/0 ο 1989 American Chemical Society

Provder; Computer Applications in Applied Polymer Science II ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

32.

417

Rates of Decomposition of Free-Radical Initiators

WOLF


CALCULATIONS Predictive equations for the rates of decomposition of four families of free radical initiators are established in this research. The four initiator families, each treated separately, are irans-symmetric bisalkyl diazenes (reaction 1), irans-phenyl, alkyl diazenes (reaction 2), tert-butyl peresters (reaction 3) and hydrocarbons (reaction 4). The probable rate determining steps of these reactions are given below. For the decomposition of peresters, R is chosen so that the concerted mechanism of decomposition operates for a l l the members of the family (see below) (4): R-N^N-R C H -N^

R-C( 0-0-*Bu

> R» +

+ -R

0

(1)

Z

>

C 6

V

N

+

^

» R» + C0

N

R-R

N

o

# R

2

()

+ •Offiu

(3)

z

> R* + »R

(4) e

Each reaction is assumed to be forming an alkyl radical (R ) in the transition state of its rate determining step. If this is true, the rates of these reactions ought to be affected by the stabilités of the R radicals being formed (transition state effect), as well as by the stabilties of the reactant initiators (reactant state effects). In the present research transition state effects are measured by the p i - derealization energies (ΔΕ(τ)) of the R radicals, as calculated by Hùckel Molecular Orbital (HMO) pi calculations. Reactant state effects are assumed to be estimated by the destablization energies of the reactant due to back strain steric crowding of groups attached to the potential radical center carbon atom of the reactants. HMO calculations of the pi electronic energies of the radicals were done using the values of coulomb and bond integrals suggested by Streitwieser (5). The only exception to these integral values was for the case of a heteroatom (with lone electron pair) bonded to the radical center carbon. The bond integrals for this case were chosen to be one-half the values suggested by Streitwieser: #

#

-C-O-R' • »•

r

β c-o

= 0.4 β o r

The rationale behind this choice of bond integrals is that the radical stabilizing alpha effect of such radicals are explained not by the usual "resonance form" arguments, but by invoking frontier orbital interactions between the singly occupied molecular orbital of the localized carbon radical and the highest occupied molecular orbital (the non-bonding electrons' atomic orbital) of the heteroatom (6). For free radicals the result of the S0M0-H0M0 interaction Ts a net "one-half" pi bond (a pi bond plus a one-half



418

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II

pi antibond). The hyperconjugative model of methyl group contributions to the pi systems was chosen (5.7), as well as the auxiliary inductive parameter (a multiplier of 0.1) for modifying the coulomb integrals of atoms adj acent to heteroatoms (7). The HMO calculations were run in BASIC on a microcomputer, using the Jacobi method to diagonalize the secular determinant. P i delocalization energies of the radicals were calculated from the pi energies minus the sum of the localized pi energies of the groups bonded to the radical center carbon. The ΔΕ(τ) values are calculated in units of the standard bond integral for the HMO method (/?) . By multiplying these values by the typical value for β ^, -20 kcal/mole (5), the ΔΕ(τ) values are expressed in the same energy units as are the ΣΑ* values (see below). o

STERIC PARAMETERS The steric parameters for the estimation of reactant state effects were chosen to be the conformational free energy differences for cyclohexane axial-equatorial equilibria (A-values) (8). In order to establish the methyl group as the standard size group, modified Avalues (Α') for the various groups were used, by simply subtracting the A value for the methyl group (1.70) from the A values of the various substituents:

-Ç-X

A'(X) = A(X) - 1.70

The contributions of a l l the groups bonded to the radical center carbon were presented as a sum of the contributing groups (ΣΑ*). The empirical isokinetic relationship for a series of compounds, undergoing reaction by the same mechanism, suggests that there could be an empirical linear relationship between the temperature (T) at which a series of reactants decompose at a constant rate and the enthalpies of activation for that series of reactions (9,10): Τ

= -Μ' χ ΔΗ* + Β (5) y y If equation 5 is valid, i f a linear relationship exists between ΔΗ* and the calculated ΔΕ(τ) parameters, and i f a linear free energy relationship exists between ΔΗ·" and ΣΑ', we might expect that the following linear relationship might hold for the decomposition of reactant Y to produce free radicals R(Y) : ν J

#

Τ

=

Μ

χ

ΔΕ(ΐΓ)

+

Ν

χ

ΣΑ*

+

Τ

(6)

y y y ° Equation 6 would hold for a family of free radical initiators of similiar structure (for example, the irans-symmetric bisalkyl diazenes) reacting at the same rate (at a half-life of one hour, for example) at different temperatures Τ . Slope M would measure the sensitivity for that particular famiïy of reactants to changes in the pi-delocalization energies of the radicals being formed (transition state effect) at the particular constant rate of decomposition. Slope Ν would measure the sensitivity of that family to changes in the steric environment around the central carbon atom (reactant state effect) at the same constant rate of decomposition. The i n i t i a l four families of reactions were chosen to test the above linear relationship for several reasons. A l l four decompose



32. WOLF

419

Rates ofDecomposition of Free-Radical Initiators

by first-order kinetics with relatively well defined mechanisms. Collections and reviews of decomposition rate data for diazenes (4,11), peresters (4) and hydrocarbons (12) are accessible and allow one to test the validity of equation 6 by using the decomposition rate data for at least six members of each family. The syntheses of members of each of these families of initiators are relatively straightforward. New members of each family could be readily prepared and used for particular applications, i f equation 6 predicts the reactivity of these compounds to be correct for the application. Published activation parameters, for the radical forming decompositions of the families of initiators, were used to calculate the temperatures at which members of the four reactions react at one- hour and at ten-hour half lives. For a given family of initiators, at a given decomposition rate, the experimental temperatures were plotted by linear regression against the calculated ΔΕ(Α*) values for the R products of the rate determining step: e

Τ

=

y

χ

Μ

ΔΕv (τ) y

+

y

οΤ'

v

'(7)

Temperature error differences (ΔΤ), equal to the experimental temperature minus the linear regression temperatures, were then plotted by another linear regression analysis against the ΣΑ* values to obtain the reactant state effect slope: ΔΤ

=

y

Ν

χ

ΣΑ'

y

+

ΔΤ

v

ο

(8)

'

Equations 7 and 8 were added together, to obtain equation 6, for each family of radical initiators. It should be emphasized that the above equations, which relate reaction temperatures to calculated reactant or product energies, are equivalent to the more conventional linear free energy relationships, which relate logarithms of rate constants to calculated energies. It was felt that reactant temperatures would be more convenient to potential users of the present approach those seeking possible new free radical initiators for polymerizations. RESULTS #

In Table I are listed the radical products (R )(column 2), ΔΕ(τ) values (column 3), ΣΑ' values (column 4) and the experimental temperatures for the one- and ten hour half l i f e rates for the decomposition of irans-symmetric bisalkyl diazenes (columns 5 and 6), irans-phenyl,alkyl diazenes (columns 7 and 8), peresters (columns 9 and 10) and hydrocarbons (columns 11 and 12). The following entries from Table I were used for the i n i t i a l linear regression analyses of Τ(experimental) versus ΔΕ(τ): Reaction 1 - Entries 3-6, 9-12, 14-17 and 20

(13 entries)

Reaction 2

- Entries 5, 16, 17, 20, 21 and 23

(6 entries)

Reaction 3

- Entries 3, 5, 9, 10, 17-19 and 23

(8 entries)

Reaction 4

-

Entries 3, 5, 9, 10, 13, 16 and 22

(7 entries)


420

COMPUTER APPLICATIONS IN APPLIED POLYMER SCIENCE II

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I I I

ΙΟ 1 CO CO I ο CO 1 CN

Iο 1 -tf I Η 1 CN

1 CO 1 CO 1 CO

\> 1 CN I ΗΗ

ΙΟ 1 CO CO 1 CO CO 1 CN

Iο 1 00 1 CO 1 CN

1 1 CO 1 CO

\> 1 t> 1 CN I Η


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V 05

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1 I

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1 1 1

u 3 CN Η 1 00 CO 1

1 1 1 I

CN

!'

g aa © » «

* CO CO

ν a> ν a> CN LO

νονό

Π3 ι t LO CO CN 1 LO CN CO ι 1 W H O1 00 LO 1 1 Η i-l

α ο LO CO h- ^ 1 LO H CO CO 1 CO ^

ι 1 I 1

α CO Η 1

ΙΩ G no . ο Μ no ··-».* ι .]

Predicting Rates of Decomposition of Free-Radical Initiators

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