Thermal degradation of polyisobutylene: effect of rotational motion around CC· bond on the β scission leading to monomer formation

Po/wer

Dqradurion

Prmted ELSEVIER

PII:

SO141.3910(96)00104-8

and Srahi/ir,v 54 ( I YY6) 23-32

0 1996 Elsevier Science Limited in Northern Ireland. All nghts reserved 0111-3910/96/$1.5.(K)

Thermal degradation of polyisobutylene: effect of rotational motion around C-C* bond on the p scission leading to monomer formation T. Sawaguchi & M. Seno Department o,f Industrial Chemistry, College of Science and Technology, Tokyo 101, Japan

(Received 25 January

Nihon University, Kandasurugadai,

Chiyoda-ku,

1996; accepted 9 March 1996)

The formation of isobutylene monomer and volatile oligomers by the thermal degradation of polyisobutylene at 300°C is simulated by using assigned values of the rate constants (ktd and kpd) of the depolymerization of primary and tertiary terminal macroradicals (R; and R;), based on a radical chain reaction model including diffusion-controlled termination reactions. With increasing reaction time, the composition of isobutylene monomer in the volatiles increases and that of the volatile oligomers decreases. This change in composition is well matched by the simulation using the value of k,, larger than k,,. This result is caused by a marked decrease in [R;] and a gradual decrease in [R;] with reaction time. The difference in the rate constants of the radicals R; and R; is estimated to be k,,/k,, = 50-100 and the ratio of rate constants corresponds to the values 18.8-21.7 kJ/mol of the difference of activation energy AE,. This difference is reasonably explained by assuming that the /3 scission depends on the energy barrier of rotation of the C-C. bond of R; and R;, whose value is estimated from an extended Htickel molecular orbital calculation on the molecular model of R; and R;. 0 1996 Elsevier Science Limited

1 INTRODUCTION

was observed in a kinetic analysis of the corresponding composition ratios of respective components,4,h which are formed via different elementary reactions. These results lead to the construction of a total reaction model. By computer simulation of the products based on the reaction model including diffusion-controlled termination, it was revealed that a decrease in molecular weight of the matrix leads to decreases in concentrations of respective radicals (R;, R; and S.) owing to an increase in the rate of self-diffusion-controlled termination.7 The decrease of rate is in the order; S. > R; >> R,.; this order results from an increase in the rate of termination with decreasing molecular weight of the matrix. Furthermore, the relative occurrence of the respective reactions was evaluated from the values of a set of rate constants which are

The molecular weight of the reaction medium strongly affects the behavior of thermal degradation of polymers,’ but this effect is not yet adequately understood. In a series of papers,2-7 we attempted to elucidate the effect of molecular weight on the thermal degradation of polyisobutylene based on the structural and kinetic analyses of the products. It was observed that composition ratios between some components of interest in the volatile and nonvolatile oligomers decrease clearly with increasing time,3,6 and this decrease results from a decrease in molecular weight of the matrix during the degradation.“.’ Moreover, a similar molecular weight dependence of the ratio [R;]/[R,.] (see Fig. 1 for meanings of the symbols) during the degradation 23

24

T. Sawaguchi, CH3

CH3

R;

:

I

’ Ch

;H

t5Hz

R,&’

:

-CH2

R;

CH3

I

CH3

CH3

I

-Cc-

CHy+-C-CH&-C

’

I CH,

I

CH3

R,,, I ’ :

CH3

I -C,,+!“;

-CH2-C

W

H$=C

I

tH?

I

CH3

R,,2’

:

CH,

CH3

Ro$ -

U’VD),

:

3

I I -C-_-H&C-CH&-C-CCHj’ I

CH.s

CH3

CH3

I -C-CH+Y-CH2~C-CH~’ ’ CHs

M. &no

-CH+,6i

I

CHT

CH3

:

VW, I kH3

‘53

VW,

U-W,

H3C

-C=CH+C-CH2+H ’ CH3

bH3

eH3

CH3

Ch

’ CH3

LH 3

I

I

n : number of monomer unit, n 30

Fig. 1. Abbreviations

of respective radicals and mono-olefins.

to satisfy these results. The rate determined constant (ktd) of direct p scission of R,* is about 50 times larger than k,, of R;.’ It was also observed from a preliminary experiment that the proportion of isobutylene monomer in the volatiles increases with reaction time.’ The increment of isobutylene monomer would result from a marked decrease in [R;] and a gradual decrease in [R,.] with reaction time.’ This suggests that the reactivity for /3 scission is related to the segmental rotational motion of the reacting radical. In this paper, the compositions of isobutylene monomer and volatile oligomers are traced by a simulation using the reaction model including self-diffusion-controlled termination, and the mechanism of rotation-dependent p scission is examined in terms of the energy barrier of rotation around the C-C. bond.

2 EXPERIMENTAL 2.1 Sample The polyisobutylene sample and the purification procedure were described in detail elsewhere.* Molecular weight characteristics of the purified polyisobutylene are as follows: M, = 2.5 X 10’ and M,,,/ M, = 2.50. 2.2 Apparatus The apparatus used for degradation is shown in Fig. 2. The experimental procedure was described in detail elsewhere.* One gram of the sample was used for each degradation experiment at 4 mmHg and 300°C. During the reaction the volatiles including monomer and volatiles oligomers were collected in a fraction trap chilled with liquid N,. After the reaction, the monomeric

Effect of rotational motion of C-C.

25

bond on p scission

8

Fig. 2. Apparatus used for thermal degradation: (1) reaction flask, (2) metal bath, (3) electric furnace, (4) Nz bomb, (5) thermocouple, (6) fraction trap, (7) liquid NZ, (8) mercurial manometer, (10) fractionation column, (11) gas storage tank, (12) gas syringe.

component in the fraction trap was collected into the gas storage tank (11 in Fig. 2), which was previously evacuated to 4 mmHg, by holding the trap at room temperature, and then the apparatus was kept at ca. 760 mmHg in a stream of N, gas. The remaining volatile oligomers, which are liquid at room temperature, were dissolved in acetone for analysis. The gaseous component was collected with a gas syringe from the gas storage tank for analysis. The polymer residue in the reaction flask was dissolved in 10cm” of chloroform. The solution was reprecipitated by dropping into 50cm3 of acetone to remove a small amount of the semi-volatile oligomers. The reprecipitates were termed the nonvolatile oligomers and analyzed after vacuum drying under heating. As reported previously,* the nonvolatile oligomers thus obtained were almost completely separated from the semivolatile oligomers. The yields and compositions of gaseous components (gas) and volatile oligomers (liquid) were defined as follows: Yeild of volatiles (C) = (Weight of sample) - (Weight of polymer residue) (Weight of sample) Yield of liquid (L) = (Weight of volatile oligomers) (Weight of sample)

Yield of gas (G) = (Yield of volatiles) - (Yield of liquid) Volatilization Composition

(wt%) = 100 X (Yield of volatiles) of liquid (wt %) 100 X (Yield of liquid) =

Composition

of gas (wt%) =

(Yield of volatiles) 100 X (Yield of gas) (Yield of volatiles)

2.3 Analysis

The analytical GC of the gaseous products was measured on a Shimadzu GC-8A gas chromatograph equipped with a flame-ionization detector and a 13 m X 3 mm i.d. stainless steel column packed with Sebaconitrile (25%) on Uniport C (60-80 mesh). The instrumental conditions were as follows: injector and detector temperature, 100°C; column temperature, 60°C; N, gas flow rate 30 cm3/min. GC of the volatile oligomers was recorded on a Shimadzu GC-8A gas chromatograph equipped with a flame-ionization detector and a fused silica capillary column (50 m X 0.35 mm i.d.) containing OV-1. The instrumental conditions were de-

26

T. Sawaguchi,

M. Sent

scribed elsewhere.3 Number-average molecular weight of polyisobutylene A4, was determined by the following equation’ using the limiting viscosity number measured at 30°C in toluene: [v] = 3.71 X 1o-4 P75, where P is the number average degree of polymerization determined by the osmotic pressure method.

3 RESULTS

6 G ui

AND DISCUSSION

3.1 Characterization

of volatile products

The results of thermal degradation at 300°C are given in Table 1, where A4, and M,,,/M, of the nonvolatile oligomers, and the yield and composition of gas and liquid in the volatiles are listed as a function of reaction time. The M, value of the nonvolatile oligomers decreases but the MJM, value keeps a nearly constant value of 2. The sum of yields of the products in this table gives the volatilization (yield of volatiles). The yield of the volatiles including gas and liquid increases and the yield of the polymer residue decreases with increasing time. Moreover, it is clearly shown that the proportion of gas increases with time in contrast to that of liquid. An example of a gas chromatogram of the gaseous products is given in Fig. 3. The peaks in this figure are assigned by comparing their retention times with those of known compounds. The chemical formula, retention time in minutes,

0

5

10

Retention

Fig. 3. Gas chromatogram

15

of the gaseous product.

and relative intensity of respective peaks are given in parentheses. The gaseous products contain over 95% of isobutylene monomer and a small amount of other lower hydrocarbons such

Table 1. Changes in volatilization and the composition of gas and liquid in the volatiles by the thermal degradation of polyisobutylene (M. = 2.50 x 10’) at 300°C

Time (min)

Nonvolatile Mnh x lo-’

20 25 45 90 90 120 150 240 240 300

27.6 18.6 14.3 9.69 9.09 7.44 8.97 5.25 5.21 4.74

Volatiles

oligomers”

2.06 2.20 2.23 2.11 2.05 2.15 2.01 1.97 2.00 1.88

Composition

Yield (wt%)

MJM,

(wt%)

Gas

Liquid

Sum”

Gas

Liquid

0.21 0.34 0.63 1.88 2.09 2.39 3.23 5.60 5.66 7.38

2.10 2.76 4.09 5.60 6.48 7.27 10.0 12.9 14.0 19.7

2.31 3.10 4.72 7.48 8.57 9.66 13.2 18.5 19.7 24.1

9.3 11.0 13.3 25.1 24.4 24.7 24.4 28.7 30.2 30.6

90.7 89.0 86.7 74.9 75.6 75.3 75.6 71.3 69.8 69.4

LIPrepared from the polymer residue. ’ By limiting viscosity number measurements. ’ By GPC measurements. “ Volatilization: gas + liquid.

20

time (min)

Effect of rotational motion of C-C. Dimcrs (n=O)

Trimers

Tctramers

Pentamers

Hexamers

(n.2)

(n=3)

(n=4)

(n=l)

27

bond on p scission Heptamers (n=5)

Acetone

I 0

I

I

I

10

20

30

I

I

40

50

E;;T4);y;;~~DJF(ES A A

Retention

,

I

1

60

70

80

time,

Fig. 4. Gas chromatogram

k

(direct p

pd

RP* R,*

k td

Intramolecular

hydrogen

and successive

p scission

(3)

(TTD)p

(TVD)t

I

I

90

100

(TVD)p -

110

product.

3.2 Reaction scheme and rate for formation

of

volatile products

The formation processes of respective components of the volatile products are shown in Scheme 1. Isobutylene monomer in the gaseous products is formed by the depolymerization (direct j3 scission) of R; and R,., as given by eqns (1) and (2),’ and the volatile oligomers consisting of mainly four types of mono-olefins are formed by the intramolecular hydrogen abstraction (back-biting) of R; and R,. and the subsequent p scission at the inner position of the

scission)

*

monomer

w

monomer

abstraction

t

+

RP’

(1)

t

+

I$*

(2)

(back-biting)

k\phl

kph,

/*

(TTD)t

min

of the liquid

propane, butane, propylene, as isobutane, ethylene (and ethane) and methane. This result is roughly consistent with that reported by Tsuchiya et ~1.~ The relative intensities of these component peaks remain nearly constant during the degradation. Figure 4 shows an example of a gas chromatogram of the liquid products obtained by together with assignment to the degradation, respective oligomers. As reported in previous papers,2.3 most of the peaks consist of four types of terminal mono-olefins, (J-.TD),, (TVD),, (TTD), and (TVD),, ranging from dimers to dodecamers. Depropagation

ES)

%!A,*

b

(TWP

t

+

U-WI,

t

+

(TVD),

t

+

(TTD),

t

+

RP*----I

RP-

(3)

RP*

(4)

(CH,) k,,,

Scheme

1. Formation

RP*

RPe

of isobutylene monomer and four types of terminal mono-olefins in the volatiles (depolymerization) and back-biting followed by /3 scission.

(5)

(6)

by direct

p scission

28

T. Sawaguchi, M. Seno

main chain.2*3,9Depending on the position of the hydrogen abstraction, two types of in-chain macroradicals, Ropb,. and Roph2., are formed from R;, and the subsequent p scissions lead to two types of monoolefins, (‘ITD), and (TVD),, respectively, (eqns (3) and (4)). On the other hand, two types of on-chain macroradicals, Roth,. and Rotb2*, are formed from R,. and the p scission leads to two types of monoolefins, (TTD), and (TVD),, respectively, (eqns (5) and (6)). It was verified in the previous papers,4’6 that the hydrogen abstraction followed by p scission occurs under steady-state conditions, where the concentrations of respective in-chain macroradicals are kept low and constant and, therefore, the rates of reactions (3)-(6) could be represented by only the rates of the back-biting. The rate of decrease in the volume (V) of polymer matrix corresponds to the rate of increase in the yield (C = 1 - V/VJ of the volatiles. This rate is given by a sum of the rates of depolymerization (eqns (1) and (2)) and the rates of back-biting (eqns (3)-(6)) as follows: --=dV dt

{(

k,, + k,,

;)[&.I

+ (ktd + k,, ;)[RJ} dC -dt =

i(

&

(7)

b + &)[R;] +

(k,,+k, ;)PGl}$$)

(8)

where m and o are the molecular weights of monomer and volatile oligomers, respectively, and [N] is the concentration of monomer units of the polymer and is expressed by p/m,“,” where p is the density of polymer. From this, [N] could be set to be nearly constant during the degradation,’ owing to a nearly constant value of the specific volume of polyisobutylene (M, from 3540 to 115000).‘2 Accordingly, the rates of formation of isobutylene monomer and the volatile oligomers, which correspond to those of the gaseous products (G) and the volatile oligomers (L), respectively, are given as follows:

$ =(&,,[R,-I + k,[R-I) $

= (k,,;

y

[R;] + k,, ; [Rt.]) $$)

where dC/dt = dG/dt + dL/dt.

(9)

3.3 Total model of degradation computation

and

procedure

The reaction model proposed for the whole process of degradation has been described in detail in a preceding paper.’ The model includes the elementary reactions of R;, R,. and volatile small radicals (S.) and consists of the following three steps: (1) end- and random-initiation reactions; (2) depropagation, consisting of depolymerization and intramolecular and intermolecular hydrogen abstraction followed by /? scission; and (3) diffusion-controlled termination, consisting of bimolecular reaction between the respective macroradicals and vaporization of volatile radicals. By assuming that the degradation reaction proceeds under steady-state conditions in [R,.], [R;] and [Se], these concentrations could be approximately estimated. Therefore, these concentrations are expressed as a function of number-average degree of polymerization DP. When mono-dispersity holds for the molecular weight distribution of the polymer residue, DP is given by DP = p/(m[P]). It is noticed in Table 1 that the molecular weight distribution keeps a constant value of about 2 during the degradation. The molecular weight on computation is determined by M = mDP. The changes in volume of matrix, volatilization and yields of respective products at a given reaction time are obtained by integration of eqns (7)-(10). The simultaneous differential equations are solved by the method of Runge-Kutta-Gil. For given initial values, the radical concentrations are calculated using the initial DP value. The changes in volume and yields of respective products for time interval (At) are obtained by the Runge-Kutta-Gil subroutine using the calculated radical concentration. These calculations are repeated in the subroutine until a given time. Thus, the integrated radical concentrations are estimated as follows:

[R;l = j- [R;]dt + c [R;]At

(11)

[R,.] = j- [R,.]dt + c

[R,.]At

(12)

[S]At

(13)

(10) [S-l = j- [S]dt +

c

29

Effect of rotational motion of C-C. bond on /3 scission

Here, At is set to be 0.05 min. Thus, the gas (G) and liquid (L) for a given calculated from eqns (9) and (10) compositions of respective products are from the values of yields.

yields of time are and the obtained

3.4 Results of simulation A set of reasonable values of rate constants of respective reactions could be determined by fitting of many variables. Although a set of kinetic constants giving a best fit was shown in a preceding paper,7 the compositions of respective products are re-simulated by setting several values for the ratio between the rates of the depolymerization of R; and R,. in the present study. The results of calculation of the composition of gaseous and liquid products in the volatiles are shown in Fig. 5, where the calculated values are drawn in solid, dotted or chain lines, and the observed values are plotted with marks against IV, (logarithmic scale) of the nonvolatile oligomers. The figure shows clearly that the observed values are consistently fitted by the line calculated using the value of the rate ratio (kld/kpd) from 50 to 100 rather than 0.4. The latter value of &/&, corresponds to setting 2.5 for the ratio k,,/k,, between the rates of the back-biting (eqns (3)-(6)).7 However, simulation using values of k,,/k,, lower than unity could not fit the fact that the fraction of gaseous products increases with a decreasing M, as shown in Fig. 5. It was shown in a preceding paper,7 that the decrease in molecular weight of the matrix during

the degradation leads to decreases in concentrations of R;, R,. and Se, owing to an increase in the rate of self-diffusion-controlled termination. The order of the decrement was observed as follows: SW> R; > > R,.. Moreover, [R;] and [S] were lower than [R,.] in a range of M, lower than ca. 10,000. Under these conditions, the value of k,, larger than k,, could reasonably explain that the increment of isobutylene monomer results from a marked decrease in [R;] and a gradual decrease in [R;] with reaction time. 3.5 Difference in reactivities of R,- and R,- for P scission

If the value of frequency factor of the p scission of R; (eqn (1)) is assumed to be the same as that of R,. (eqn (2)) the difference between activation energy E, of the p scission could be estimated from the equation: RTln (k,d/k,,d). The value of the ratio k,,/k,, in the range 50-100 corresponds to a value of AE from 18.8 to 21.7 kJ/mol. The E, value could be also estimated from the bond dissociation energy (BDE) of respective terminal macroradicals.‘-1.‘4 However, the calculated value of BDE is about 88.07 kJ/mol for the p scission of both R; and R,* and this could not explain the AE value of R; and R;. Although little is known about the kinetic parameters of the p scission, if the p scission of R; and R,. proceeds with a nearly equal E, value, the estimated value (18.821.7 kJ/mol) of AE, should be interpreted in another way. Thus, we notice a difference in the rotational mobility of the interesting C-C. bond of respective macroradicals and its effect on the p scission is examined later in this paper. 3.6 Rotation-dependent

0

: Liquid

o : Gas

4

Log Mn Fig. 5. Plots of the proportions of gaseous products and liquid products, together with the calculated curves: --; k,,/k,, 0.4, - - -; 50, --;

100.

p scission

It is well-known in organic chemistry that many experimental and theoretical results indicate that the reactivity of most types of organic molecules depends on the stereochemistry of reaction intermediates, and the concept of a stereoelectronic effect has been proposed.” In particular, it should be noted that the formation of a double bond by elimination of a P-proton occurs when the C-H bond is properly aligned with the P-orbital of th e carbenium ion and that the migration of hydride ion and anionic alkyl group to carbenium ion occurs, to form a new

30

T. Sawaguchi,

rearranged carbenium ion. This mechanism could apply to the /3 scissions of terminal macroradicals described above. According to this concept, the p scission takes place just when the C-C bond of interest is properly aligned with the p-orbital of the radical carbon and depends on the rotation around the C-C. bond. The Newman projection diagram of the rotational isomeric state of the C-C. bond of R; or R,. favorable for the p scission is shown in Fig. 6. A marked difference in size between the substituents of respective carbon radicals is found between R; and R;. Specifically, the R; radical has dimethyl groups bonded to the radical carbon and an extremely bulky main chain bonded to the P-carbon. This structure generates a high conformational energy barrier around the C-C. bond owing to the high interaction energy between these substituents. It is expected that the conformer favorable for the p scission shown in Fig. 6 would occur predominantly. On the other hand, the radical R; has two hydrogen atoms bonded to C. and a bulky main chain and dimethyl groups bonded to the P-carbon. Thus, the C-C. bond of R; would freely rotate owing to a lower conformational energy barrier and all the rotational isomeric states at any rotation angle would occur with nearly equal probability.‘h We attempt to estimate the E, value of the p scission and the energy barrier of R; and R,. by molecular orbital Hiickel an extended calculation.” The computation program coded by KikuchilX was revised to apply to a relatively were larger alkyl radical.” Some parameters determined according to Mulliken’s population analysis.” The stability and bond strength of the C-C bond of interest in each quasi-conformer were evaluated by the values of the total energy (ET) and the atomic bond population (EABP),

CH2

H3C CtCH3

M. &no

respectively. Two types of radicals, 2,2,4-trimethylpentyl-l-radical and 2,2,4_trimethylpentyl2-radical, are used as models of R; and R;, respectively. The geometry of these compounds was not optimized but treated as trunk conformation. The bond lengths and bond angles used in the calculations are listed in Table 2. The results of the calculation for the models of R; and R; are shown in Figs 7 and 8 as a function of torsional angle of the C-C+ bond. For R; (Fig. 7), the difference between minimum and maximum values of E,, which would correspond to the energy barrier of rotation around the C-C. bond, is lower than about 4 kJ/mol, and this suggests that the C-C. bond rotates freely at higher temperatures; that is, the stable conformer of R; is not present. The difference between minimum and maximum values of EABP, which would correspond to the AE value of the p scission, is estimated to be about 4 kJ/mol. This result suggests that the p scission predominantly occurs when the p-orbital of the radical carbon is properly aligned with the C-C bonds linked to methyl groups and to the main chain, depending on the rotation around the C-C. bond. In contrast, the torsional angle dependence of AE,,, obtained for the radical R,. is shown in Fig. 8. A maximum value of AE, is obtained at the angles around 80 and 250” and a minimum value is found near 0 and 180”, respectively. The energy barrier is estimated to be about 320 kJ/mol, which is much larger than the thermal energy of RT. This is probably caused by a highly strained structure of the model which is Nevertheless, the R; radical not optimized. would have two most stable conformers, both of which correspond to the eclipsed conformation where C. is properly aligned with the P-bond. The p scission of R; occurs more frequently because of the high probability of occurrence of Table 2. Parameters

Bond c-c C(spZ)-c C-H C(sp’)-H

(Rd Fig.

6. Newman

rotational

(W

projection diagram of the possible isomeric states around C-C. bond of R; and R; for the fi scission.

Valence angle C(sp’) C(spZ)

used in calculation

Bond length (A) 1.%I 1.44 1.09 1.06 Deg. 109.47 120 -_.-

Effect of rotational motion of C-C* bond on p scission

Main

deduction dependent

chain

is supported also by the mechanism mentioned here,

31

rotation-

4 CONCLUSION

60

120

Torsional

180 angle,

240

300

360

degree

Fig. 7. Torsional

angle dependencies of total energy (A&) and atomic bond population (AEABP) for R;.

the conformer having the eclipsed conformation, in contrast to R;. Consequently, the difference between the rate constants of depolymerization (direct /3 scission) of R; and R; results from a large difference in the energy barrier described above. Recently, it was shown in the thermal degradation of poly(cu_methylstyrene),2’ polystyrene:’ and polymethylmethacrylate2’ that the rate of /3 scission leading to monomer formation depends on the type of terminal macroradicals such as primary, secondary and tertiary radicals. These results are deduced from the simulation for changes in molecular weight, molecular weight distribution and volatilization during the degradation. We have formerly suggested that the p scission of the on-chain macroradical near the center of the main chain depends on the rotational motion of the C-C. bond.‘,” This

_

2,

1

The rates of formation of isobutylene monomer by the depolymerization of R; and R; were examined experimentally and theoretically in the kinetics of thermal degradation of polyisobutylene. At 3OO”C, the proportion of isobutylene monomer increases and that of the volatile oligomers decreases with increasing time. This experimental result is simulated based on a radical chain reaction model including diffusioncontrolled termination reactions with assigned values of the rate constants (ktd and kpd) of depolymerization of R; and R;.’ The changes in the composition are successfully modelled by the simulation using a value of k,, larger than k,,. This is suggested by a marked decrease in the concentration [R;] and a gradually decrease in [R,.] during the degradation.’ The value of 50-100 assigned for the ratio k,,/k,, means the difference in activation energy AE, of 18.821.7 kJ/mol. This difference is reasonably explained by an extended Htickel molecular orbital calculation on the model molecules of R; and R,* under the assumption that the activation energy of @ scission depends on the energy barriers of rotation around the C-C. bond of R,; and R;.

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3. Sawaguchi, T., Ikemura, T. & Seno, M., Macromof. Chem. Phy., 197 (1996) 215. 4. Sawaguchi, T. & Seno, M., Polym. J., 28 (1996) 392. 5. Sawaguchi, T. & Seno, M., Polymer, in press. 6. Sawaguchi, T., Ikemura, T. & Seno, M., Polymer, in press. Sawaguchi, T. & Seno, M., Polymer, in press. :: Sakaguchi, Y. & Sakurada, I., Koubunsi Kagaku, 5 (1948) 242.

9. Tsuchiya,

Y. & Sumi, K., J. Polym. Sci., Part A-l. 7

(1969) 813. 0

60

120

Torsional

Fig. 8. Torsional

180 angle,

240

300

360

degree

angle dependencies of total energy (A&) and atomic bond population (AEABP) for R;.

10. Cameron, G. G., Makromol. Chem., 100 (1978) 255. 11. Cameron, G. G., Meyer, J. M. & McWalter, I. T., Macromolecules,

11 (1978) 696.

12. Fox, T. G. & Flory, P. J., J. Phys. Colloid Chem., 55 (1951) 221. 13. O’Neal, H. E. & Benson, S. W., Free Radical. Vol. II,

32

14.

15. 16. 17. 18.

T. Sawaguchi, ed. J.K. Kochi. John Wiley & Sons, New York, 1973, p. 275. Benson, S. W., Cruickshank, F. R., Golden, D. M., Hangen, G. R., O’Neal, H. E., Rodgers, A. S., Shaw, R. & Walsh, R., Chem. Rev., 69 (1969) 279. Deslongchamps, P., Stereoelectronic Effects in Organic Chemistry. Pergamon Press, Oxford, 1983. Imam, M. R. & Allinger, J., J. Mol. Struct., 126 (1985) 345. Hoffman, R., J. Chem. Phys., 39 (1963) 1397. Kikuchi, O., Bunshikidoho. Kodansha, Tokyo, 1971.

M. Seno

19. Sawaguchi, T., Takesue, T. & Ikemura, T., Proc. 35th Research Convention, College of Science and Technology, Nihon University, 1991, p. 871. 20. Mulliken, R. S., J. Chem. Phys. 23 (1955) 1833, 1841, 2338, 2343. 21. Guaita, M. & Chiantone, O., Polym. Degrad. Stab., 11 (1985) 167. 22. Guaita, M., Chiantone, 0. & Costa, L., Polym. Degrad. Stab., 12 (1985) 315. 23. Inaba, A., Kashiwagi, T. & Brown, Degrad. Stab., 21 (1988) 1.

J. E., Polym.