Free Radical Polymerization Kinetics of Immobilized Chains

2 Free Radical Polymerization Kinetics of Immobilized Chains Bulk Polymerization of Acrylonitrile

Downloaded by UNIV LAVAL on July 14, 2016 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0091.ch002

O. G. L E W I S and R. M . K I N G , JR. Central Research Division, American Cyanamid Co., Stamford, Conn. 06904

A kinetic study was made of the polymerization at 50°C. of acrylonitrile and acrylonitrile-benzene mixtures catalyzed by azodiisobutyronitrile, using a mercury dilatometer specially designed to maintain isothermal conditions even at high rates of polymerization. A plot of rate vs. catalyst concentration, I, on logarithmic scales is a curve, the rate varying as I at I = 10-4M—but as I . at I = 10-2M. These results were accounted for by generalizing the usual steady-state kinetic scheme for radical chain reactions, taking into account geminate termination and termination by primary radicals. Certain functions of the rate constants for the component reactions were estimated and found to be consistent with published values. 0.89

0

33

T t is well known that the presence of precipitated polymer can influence the course of polymerization. In bulk acrylonitrile polymerization the effects are most dramatic and have been the subject of many studies. The literature on this subject has been reviewed by Bamford et al. (4) by Thomas (29), and by Peebles (23). Under conditions where the system becomes heterogeneous owing to precipitation of small particles of polym e r i a protracted acceleration period is observed at the start of polymerization, and the final rate is found to depend on the 0.8 power of the concentration of free radical initiator. Unusual post-polymerization effects are observed i n photoinitiated polymerization of acrylonitrile, owing to the presence of trapped radicals which can be detected b y electron spin resonance. None of the detailed mechanisms proposed to 25

Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

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ADDITION

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account for these observations have found general acceptance, and sev eral different expressions have been derived to account for the kinetic results. The work described here was undertaken on the premise that mea surements of the number of particles, total particle surface, and concen tration of trapped radicals are needed in conjunction with rate measure ments over a wide range of initiation rate and monomer concentration to understand more thoroughly the important factors i n this type of hetero geneous polymerization. However, as w i l l become apparent from the results reported here, variations in particle number and total surface are small and have little effect on the polymerization rate. Under our condi tions trapped radicals were present in too low a concentration to be detected and cannot account for the peculiar features of the reaction kinetics. The mechanism can be best understood within the framework of the conventional theory of radical chain kinetics, provided that certain of the usual simplifying assumptions are omitted. A solution is given to the problem of steady-state polymerization rate as a function of monomer and initiator concentration, taking into account termination reactions of primary radicals and recombination of geminate chains arising from the same initiation event. This model is shown to account for the kinetic data reported herein. W i t h appropriate rate constants it should be gen erally applicable to radical polymerizations.

Microscopic

Observations

The polymer precipitates initially in the form of roughly spherical aggregates of small particles. A typical example is shown in the electron micrograph i n Figure 1. The aggregates are fairly uniform in size. The diameters of the aggregates sampled at different degrees of conversion were taken from electron micrographs, and it was found that the calcu lated number of particles per milliliter of polymerizing solution was constant, indicating that polymerization takes place entirely on or within the existing aggregates, and no new aggregates are formed beyond about 0.4% conversion. A study of the aggregates formed i n bulk polymeriza tion at 50 ° C . revealed that the number increased roughly as the square root of the concentration of azodiisobutyronitrile ( A I B N ) initiator con centration, from about 7 Χ 10 1 0 m l . ' 1 at 10" 4 M of A I B N to 7 Χ 10 1 1 m l . " 1 at 10~ 2 M. The rate of polymerization increased as the initiator concen tration to an exponent significantly higher than 0.5, as we shall see later, so that the rate per aggregate must also increase with initiation rate.



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Chains

Figure 1. Particles from bulk polymerization of acrylonitrile at 50°C. AIBN concentration, 3 X 103M Surface

Area

The aggregates of precipitated polyacrylonitrile particles are highly porous, as can be seen in the electron micrograph. The total surface is very large and can be measured by the B.E.T. nitrogen adsorption method, after removal of the unreacted monomer. Table I gives the results of a series of bulk polymerizations carried to different conversions at 5 0 ° C . The specific surface decreases gradually, presumably because the interstitial volume becomes filled by polymerization within the aggregates. However, the total surface is still an increasing function of time. The suspension becomes very difficult to handle above about 2 5 % conversion, and no results were obtained in this region. It is quite possible that the total surface levels off above 2 5 % conversion, where the polymerization rate becomes constant. The specific surface was measured over a very wide range of A I B N concentration (Table I I ) . A l l the measurements were made at 10—15% Table I. Specific Surface of Particles Formed in Bulk Polymerization of Acrylonitrile at 5 0 ° C . [AIBN] = 1.3 X 10" 3 M Time, min.

20 30 45 75 90 180

Conversion,

0.79 2.2 4.1 10.0 10.3 26.1

%

B.E.T. Area, sq. meters/gram

155 150 134 116 109 84


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ADDITION A N D C O N D E N S A T I O N P O L Y M E R I Z A T I O N

PROCESSES

Table II. Specific Surface of Particles Formed in Bulk Polymerization of Acrylonitrile at 5 0 ° C . Conversion =10-15%


[AIBN],

7.4 2.0 6.6 7.6 1.3 4.0 1.0 2.0

Χ Χ Χ Χ Χ Χ Χ Χ

M

Rp,

1.2 5.8 2.2 2.9 3.9 9.4 1.8 2.2

ΙΟ" 5 ΙΟ"4 ΙΟ"4 ΙΟ"4 ΙΟ"3 ΙΟ"3 ΙΟ"2 ΙΟ"2


mole/liter/sec. Χ Χ Χ Χ Χ Χ Χ Χ

89 85 121 107 109 123 98 94

ΙΟ"5 ΙΟ" 5 ΙΟ"4 ΙΟ"4 ΙΟ"4 ΙΟ"4 ΙΟ"3 ΙΟ"3

conversion. The range of areas is admittedly rather large, and no ex planation for this is offered, but the differences do not seem to be corre lated with initiator concentration or rate of polymerization. As a first approximation, it will be assumed that the surface area is independent of the rate of initiation. Benzene—Acrylonitrile

Mixtures

Polyacrylonitrile is also quite insoluble in benzene, so that dilution of the monomer with benzene does not change the heterogeneous poly merization in any essential way. The effect of dilution on the specific surface is shown in Table III. There is a discernible trend toward lower surface areas at low acrylonitrile concentration. This is also evident in electron micrographs (Figure 2), where the particles from a benzeneacrylonitrile mixture are more compact and dense in appearance than those in Figure 1. Nevertheless, the surface is still extensive, and this has profound effects on the rate of polymerization. Table III.

Specific Surface of Particles Formed in Polymerization of Acrylonitrile—Benzene Mixtures at 5 0 ° C . [AIBN] = 2 X 10" 2 M Acrylonitrile-Benzene

100/0 98/2 60/40 40/60 20/80 15/85 10/90


117 94.4 71.7 45.7 25.5 89.0 43.7



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Figure 2. Particles from polymerization of 80/20 benzene acrylonitrile mixture at 50°C. AIBN concentration, 3 X 10~3M Kinetic

Results

The rate of polymerization was measured dilatometrically, using mercury as the confining liquid. Dilatometers of conventional design and 5-10-ml. capacity were found to give erratic results at high rates of polymerization, owing presumably to inadequate rate of removal of the heat of reaction from the almost solid suspension of particles. Hence, a "J" t v P e dilatometer was built with a flattened reaction cell so that the monomer solution was confined within a uniformly thin space between mercury and a thin glass wall. A schematic is shown in Figure 3. The volume of monomer solution was 1 ml. delivered by micropipet, except at high polymerization rates where it was necessary to reduce the volume to 0.1 ml. No measurements of temperature within the cell were attempted, but the achievement of substantially isothermal conditions could be deduced indirectly from the fact that the measured rate was independent of volume, below a critical volume which decreased as the initiator concentration increased. Acrylonitrile was washed with phosphoric acid, then with sodium carbonate, then dried over calcium hydride and distilled (b.p., 77.6— 7 7 . 9 ° C . / 7 6 0 mm. H g ) . A I B N was recrystallized from cold methanol. Solutions were made by volume at 2 5 ° C , and the required amount was pipetted into the dilatometer cell. The cell was connected to the capillary by a lightly greased ground glass joint. The cell contents were frozen with liquid nitrogen, then evacuated on a high vacuum line. After several cycles of thawing, freezing, and pumping, the stopcock was closed, and the dilatometer removed from the vacuum line. The mercury i n the bulb was first warmed in the 5 0 ° C . bath, then poured through the capillary into the cell. The cell was immediately mounted i n the bath, and measurements of the column height were taken at intervals with a cathetometer.


30

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-

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PRECISION BORE CAPILLARY

I0N0MER AND AIBN Hg

Figure 3.

Schematic of dilatometer

A typical rate curve is shown i n Figure 4. The measured contraction has been converted to percent conversion by means of a calibration constant derived from a number of direct measurements of polymer formed in the dilatometer cell. The measurements were timed from the instant the dilatometer was placed i n the bath. A t the highest rates of initiation, the constant rate stage was achieved in less than 10 min., indicating that thermal equilibration of this assembly is rapid compared with whatever process is responsible for the gradual acceleration observed i n Figure 4 up to 15% conversion (120 min.). The protracted acceleration period is not caused by the presence of a retarder since it is only observed when polymer precipitates during the reaction (4). Above 15% conversion the rate is constant. A t about 45% conversion the agglomerates become too closely packed to contract further, and the rate can no longer be measured by dilatometry. It should be noted that because of the insolubility of the polymer, there is no change in monomer concentration at the particle interface i n


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bulk polymerization. Hence, the constant rate is not a fortuitous com pensation of increasing radical concentration and decreasing monomer concentration, but indeed represents a steady-state rate. The effect of using too large a volume of solution in the dilatometer is to extend the acceleration period, resulting in too high a rate. This is symptomatic of nonisothermal conditions.


I

ι

ι

TIME (MIN.) Figure

4.

Bulk AIBN

polymerization concentration,

of acrylonitrile 2.07 X 10~3M

at

50°C.

The rate of polymerization i n the constant rate period is shown i n Figure 5 as a function of A I B N concentration, both on logarithmic scales. A t low concentrations of initiator (I) the rate varies as I 0 · 8 9 , but the slope drops as low as 0.33 at high rates of initiation. Similar results have been reported by Chapiro and Sebban-Danon (12) for polymerizations initiated by ionizing radiation at 1 9 ° C . Initiator exponents significantly higher than the "normal" value of 0.5 have been reported by many work ers (6, 10, 17, 25, 30, 31) for the polymerization of acrylonitrile under heterogeneous conditions. Polymerization of acrylonitrile-benzene mixtures at 50 ° C . resulted in a monomer exponent of about 1.7 in the rate expression. This is also in agreement with previous work (17, 20, 28, 31 ) on heterogeneous poly merization of acrylonitrile but not with homogeneous systems where a monomer exponent of unity is expected (4).



32

ADDITION

-5 I -5

Figure

Trapped

AND CONDENSATION

I -4

I -3 LOdoEAIBOMOLES

POLYMERIZATION

I -2

PROCESSES

1

-I

I ) -1

5. Rate of bulk polymerization of acrylonitrile 50°C. as a function of AIBN concentration

at

Radicals

Bamford and Jenkins (8) discovered high concentrations of stable free radicals i n polyacrylonitrile produced by heterogeneous bulk poly merization. The initial estimate of 5 Χ 10 1 6 per m l . was derived from measurement of the decoloration of diphenylpicrylhydrazyl. It was postu lated that the growing polymer radical can be trapped mechanically i n the precipitated polymer and hence shielded from reaction with other radicals. Termination by radical trapping was advanced by Thomas and Pellon (30), and later by Imoto and Takatsugi (17), as an explanation for the high initiator exponent in the rate expression. Radical trapping is a first-order process, and the simultaneous occurrence of first- and second-order termination reactions would give rise to initiator exponents between 0.5 and 1.0. Bamford and Jenkins (7) objected to such mecha nistic schemes on the grounds that a very small fraction of the radicals generated actually become trapped, so that the kinetics should be affected to a negligible extent. Measurements of the lifetime of the kinetic chain in heterogeneous acrylonitrile polymerization tend to support this view. Using a thermocouple method for taking non-steady-state measurements under essentially adiabatic conditions, Bengough (10) found that even in the presence of precipitated polymer a steady state is established within minutes of the commencement of irradiation of a photosensitized solution. This means that long lived radicals must contribute little toward the over-all rate of polymerization.



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Recently, even higher concentrations of trapped radicals have been observed by electron spin resonance. Bamford et al. (5) found up to 1.3 χ 10 1 7 radicals per ml., and Ingram et al. (18) found 3.5 Χ 10 1 7 per ml. i n the photopolymerization of acrylonitrile at 20 ° C . A t the same time, it was found that the concentration was greatly reduced when polymeri zation was carried out at higher temperatures, and Bamford et al. were unable to detect any radicals at 60 ° C . Repeated attempts i n this laboratory to demonstrate the presence of unpaired electrons i n polyacrylonitrile initiated by A I B N at 5 0 ° C , using a Varian spectrometer, have failed to detect any signal at all. Measure ments have been made both at room temperature and at —196 ° C , and we believe that we could have detected concentrations as low as 10 1 4 radicals per ml. Hence, it is not possible under the conditions reported here to account for the kinetic results by the mechanism of first-order termination of growing chains by entrapment in precipitated polymer. This is not to say, however, that under other conditions, such as photoinitiated polymerization at low temperature, the trapped radicals are unimportant to the kinetics of polymerization. Mechanism

Peebles ( 23 ) has proposed that three separate loci of polymerization exist during the heterogeneous polymerization of acrylonitrile. These are: ( 1 ) The solution phase. Radicals are generated in the monomer-rich liquid phase, and hence polymer chains must be initiated i n this phase. (2) The surface phase. While this may not be a separate phase i n the thermodynamic sense, adsorption of a growing radical on the particle surface would confine the reaction to this locus throughout much of the life of the chain. (3) The interior phase. Precipitated polymer chains are expected to be tightly coiled. A coiled radical would have reduced reactivity since there is a high probability that the radical end w i l l be occluded within the coil. Trapped radicals are presumed to be deeply buried i n the interior phase. Occlusion of growing radicals within the precipitated polymer has been emphasized by Bamford and co-workers (4) as the paramount factor i n the kinetics of heterogeneous polymerization. The following argument endeavors to show that at least under the conditions discussed here the kinetic results can be accounted for by considering surface polymerization only. It is well known that the acceleration in rate at high conversion (Trommsdorff effect) in the bulk homogeneous polymerization of vinyl monomers is caused by a marked increase in the concentration of growing radicals (21). Despite this, at still higher conversion the reaction virtually



34

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stops, even though unreacted monomer is still present in amounts up to 5% (9, 16, 21). This can only be caused by a reduction i n propagation rate constant by many orders of magnitude, caused by vitrification of the system. If the temperature is raised above the glass temperature of the polymer, polymerization resumes and proceeds to completion (21). Polymerization of acrylonitrile in the interior phase of the precipitated particles can therefore make a significant contribution to the over-all rate only if the polymerization temperature is above the glass temperature of the interior phase. The composition and properties of the particles may be inferred from the properties of homogeneous castings of polyacrylonitrile. These can be made by an ingenious technique devised by Shavit, Konigsbuch, and Oplatka (26), in which fresh monomer is continuously supplied to the casting so that the interstices between particles ultimately fill with polymer, resulting i n optically clear, consolidated material. Pellon et al. (24) found that the monomer content of such castings was about 5 % , even after 5 days at 4 0 ° C . The monomer content could be reduced to less than 0.3% by heating to 8 0 ° C . or above (24). W e conclude, therefore, that the precipitated phase contains about 5% monomer, has a glass temperature of about 8 0 ° C , and does not polymerize appreciably below 8 0 ° C . The amount of polymer formed in the solution phase must also be greatly restricted. Even assuming that all of the radicals are generated in the solution phase, they become insoluble after adding only perhaps five or 10 monomer units (23). Precipitation should occur rapidly on existing nuclei such as the surface of already precipitated polymer. Hence, the large surface of the particle constitutes an efficient radical trap which maintains the concentration of radicals in the solution phase at a very low level. The situation is comparable with that in emulsion polymerization. A n analysis similar to that of Smith (27) for the emulsion polymerization of styrene shows that the average lifetime of a radical i n the solution phase is sufficient to add only one to 10 acrylonitrile units before the radical collides with a polymer particle. The preceding discussion has led us to the conclusion that the surface is the only locus of polymerization which needs to be considered i n the heterogeneous polymerization of acrylonitrile. Radicals arrive at the surface at a rate determined by the decomposition of the initiator and efficiency of initiation. Propagation occurs on the surface at a rate determined by the activity of monomer at the surface. By analogy with emulsion polymerization, where monomer diffuses into the particles rapidly enough to maintain near equilibrium activity (14), we assume that the activity of the monomer adsorbed on the particle surface is approximately equal to the mole fraction in solution. The propagation rate constant is presumably influenced somewhat by the presence of the solid surface.



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The principal difference from homogeneous polymerization is that the rate constant for bimolecular termination should be greatly reduced since the growing chains are an integral part of a solid particle. Termination of growing chains by initiator radicals can become an important reaction, as has already been proposed (13). It has also been shown that under conditions where chain mobility is very low, there is a high probability of termination between chains arising from the same initiator molecule ( I , 3). This arises from the fact that in the early stages of growth the chain lies closer to its "twin," on the average, than to other radicals. The probability of "geminate chain termination," as it has been called ( J ) , increases as the radical concentration decreases or as conditions favor less chain mobility. The kinetic scheme developed below for these conditions is perfectly general for homogeneous or heterogeneous polymerization. Geminate chain termination and termination by initiator radicals are ordinarily neglected i n simple kinetic schemes, but they must be included in any case where the growing chain is immobilized, as by adsorption in a heterogeneous polymerization, or as a result of high viscosity i n homogeneous polymerization. The use of the steady-state approximation is justified on the basis of two separate, independent observations. Firstly, after sufficient polymer has accumulated, the rate remains constant over an extended range of conversion (Figure 4). Secondly, Bengough's measurements (10) of the non-steady-state kinetics of acrylonitrile polymerization show that a steady state is established within minutes, whereas the polymerization continues for hours. Kinetic

Scheme

The subject of the kinetics of vinyl polymerization by radical mechanisms is treated exhaustively in a book by Bamford, et al. (4) and more briefly in many textbooks of polymer chemistry. The polymerization of vinyl monomers is a chain reaction in which the primary reactions are: ( 1 ) Initiation. The initiator ( I ) decomposes to form free radicals ( R - ) , which initiate the growth of polymer by sequential addition of monomer molecules. The fraction (/) which successfully initiate chains is called the efficiency of initiation. (2) Propagation. Each radical adds monomer to form longer and longer molecules ( P - ), each having one unpaired electron. Except for the initiator radical, all the radicals are assumed to add monomer with equal reactivity and at a rate which is first order in monomer concentration. (3) Chain transfer. The radical undergoes a displacement reaction to form a new free radical species. Unless the new radical is very inefficient in initiating new chains, there is no effect on the over-all kinetics.


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(4) Termination. T w o radicals react to form one or two molecules having no unpaired spins. If the radicals are assumed randomly dis tributed i n space, the termination rate is second order i n radical concen tration. Under conditions where diffusion is restricted, however, the twin chains initiated by radicals from the same initiator molecule may remain close together for a time, so that termination has a higher probability than i n the case of random distribution of radicals. This case has been discussed by Allen and Patrick (J, 3). It results i n a rate expression formally equivalent to a reaction first order in radical concentration, with half-life τ. Termination by initiator radicals is also taken into account here. The following reactions summarize the scheme: Downloaded by UNIV LAVAL on July 14, 2016 | http://pubs.acs.org Publication Date: June 1, 1969 | doi: 10.1021/ba-1969-0091.ch002

I - * 2 R - dR-/dt

= 2fkdl

R- + M —» P x - — dR/dt

(1) = dR/dt

Ρ η · + Μ - > Ρ Λ + 1 · -dM/dt

= kiMR-

(2)

= Rp = kpMP-

Ρ η · + P w . - » P M + m - dF/dt

(3)

= 2M>- + 2 P / r

Ρ η · + R- - * P n - d?/dt=-dR/dt

=

(4)

fc/P-R-

(5)

2R · -> products - dR · /dt = 2kt" R · 2

(6)

The concentrations of reactants are represented by I = initiator radicals, M =

monomer, Ρ η · =

initiator, R- —

macroradicals

of degree of

polymerization n, and P „ + m = polymer formed by combination of radicals of length η and m. Assuming steady-state conditions in all radical species we can write dR/dt

and

= 0 = 2fkdl

dP/dt

- J^MR- - V P R - " 2fc/'R' 2

= 0 = kiRM

- 2kfP'

2

- 2P/T -

(?)

fc/P-R-

(8)

Hence, P- = - j ^ r

[ 2 / M - k.RM - 2 t t " R - 2 ]

(9)

and 2 ^ Ρ · 2 + — Ρ· R

w-w-

=

m

Using Equation 3 we can combine the above expressions for Ρ · and Rto obtain an expression only in Rp which is, after some rearranging,

- [( ψ) τ 4

~ Γ(τρ") ' Μ

+

2

(fc)

+

M

(£)

(T^)"'*»' M M ]

(Ψ) R

»+

< w

&]

v

*' Μ 2 / β ι > roots w i l l be unacceptable since F 2 ( R P ) is strictly negative in this region, and while R p is positive, R · is implied to be negative. Therefore, one and only one root of the quartic equation has physical meaning. If it is desired to estimate β s for other polymerization systems, a better way of writing the function is in its most elementary form. That is, merely equating Equations 9a and 10a [eliminating the negative square root i n Equation 9a since it gives negative R · ' s ] .

= 2J8lj33Rp

M M

j34 2

R


(23)

44

ADDITION

AND CONDENSATION

POLYMERIZATION

PROCESSES

This form w i l l assure that i n using Newtons Method to solve for R , the extraneous positive root (giving negative R- ) w i l l never be found since it does not satisfy the equation i n this form. p

Acknowledgments


W e are indebted to A . M . Thomas for the electron microscope mea surements, R. A . Herrmann and G . F . Yates for the surface area deter minations, and W . G . Hodgson for performing the E S R spectroscopy.

Literature

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19)

Cited

Allen, P. Ε. M., Patrick, C. R., Nature 191, 1194 (1961). Allen, P. Ε.M.,Patrick, C. R., Makromol. Chem. 47, 154 (1961). Allen, P. Ε.M.,Patrick, C. R., Trans. Faraday Soc. 59, 1819 (1963). Bamford, C. H . , Barb, W . G., Jenkins, A. D., Onyon, P. F., "The Kinetics of Vinyl Polymerization by Radical Mechanisms," Academic Press, New York, 1958. Bamford, C. H . , Ingram, D. J. E., Jenkins, A . D., Symons, M . C. R., Nature 175, 894 (1955). Bamford, C. H . , Jenkins, A . D., Proc. Roy. Soc. (London) A216, 515 (1953). Bamford, C. H., Jenkins, A. D., J. Polymer Sci. 14, 511 (1954). Ibid., 20, 405 (1956). Bengough, W . I., Melville, H . W . , Proc. Roy. Soc. (London) A230, 429 (1955). Bengough, W. I., Proc. Roy. Soc. (London) A260, 205 (1961). Chandrasekhar, S., Rev. Mod. Phys. 15, 1 (1943). Chapiro, Α., Sebban-Danon, J., J. Chim. Phys. 54, 776 (1957). Durup, J., Magat, M . , J. Polymer Sci. 18, 586 (1955). Flory, P. J., "Principles of Polymer Chemistry," p. 210, Cornell University Press, Ithaca, Ν. Y., 1953. Grassie, N . , Vance, E., Trans. Faraday Soc. 52, 727 (1956). Hayden, P., Melville, H . W., J. Polymer Sci. 43, 201 (1960). Imoto, M . , Takatsugi, H . , Makromol. Chem. 23, 119 (1957). Ingram, D. J. E., Symons, M . C. R., Townsend, M . G., Trans. Faraday Soc. 54, 409 (1958). Mark, H . , Immergut, B., Immergut, Ε. H . , Young, L . J., Beynon, Κ. I., "Copolymerization," G. W . Ham, Ed., Appendix A , Interscience, New York, 1964.

(20) Nakatsuka, K., Chem. High Polymers Japan 15, 43 (1958).

(21) Nishimura, N., J. Macromol. Chem. 1, 257 (1966). (22) Noyes, R. M . , J. Am. Chem. Soc. 77, 2042 (1955). (23) Peebles, L . H . , Jr., "Copolymerization," Chap. IX, Interscience, New York, 1964. (24) Pellon, J. J., Smyth, N . M., Kugel, R. L., Valan, K. J., Thomas, W . M . , J. Appl. Polymer Sci. 10, 429 (1966)

(25) Prevot-Bernas, Α., Sebban-Danon, J., J. Chim. Phys. 53, 418 (1956). (26) Shavit, N . , Konigsbuch, M., Oplatka, Α., British Patent 964,533 (1964); French Patent 1,398,711 (1965); German Patent 1,225,390 (1966); Israeli Patent 14410 (1962); Italian Patent 685,058 (1963). Platzer; Addition and Condensation Polymerization Processes Advances in Chemistry; American Chemical Society: Washington, DC, 1969.

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(27) (28) (29) (30) (31) (32)

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45

Smith, W . V., J. Am. Chem. Soc. 70, 3695 (1948). Srinivasan, N . T., Santappa, M., Makromol. Chem. 26, 80 (1958). Thomas, W . M . , Advan. Polymer Sci. 2, 401 (1961). Thomas, W . M., Pellon, J. J., J. Polymer Sci. 13, 329 (1954). Tokura, N . , Matsuda, M., Yazaki, F., Makromol. Chem. 42, 108 (1960). White, E. F. T., Zissell, M . J., J. Polymer Sci. A 1, 2189 (1963). April 1, 1968.


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Free Radical Polymerization Kinetics of Immobilized Chains

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