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Kinetic model for the 60Co-γ ray initiated inverse emulsion polymerization of sodium acrylate solutions
Radiat. Phys. Chem. Vol.45, No. 5, pp. 825-827, 1995
~
Pergamon
0969-806X(94)00126-X
Copyright .4' 1995ElsevierScienceLtd Printed in Great Britain.All rights reserved 0969-806X/95 $9.50+ 0.00
KINETIC M O D E L FOR THE 6°Co-'~ RAY INITIATED INVERSE E M U L S I O N P O L Y M E R I Z A T I O N OF S O D I U M A C R Y L A T E SOLUTIONS PEI-YUN JIANG,? ZHI-CHENG ZHANG and MAN-WEI ZHANG Applied Chemistry Department, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China (Received 18 October 1993; accepted 13 September 1994)
Abstract--The conversion-time curves have been measured and treated quantitatively for the 6°Co-7 ray initiated inverse emulsion polymerization of aqueous sodium acrylate solutions on the basis of a monomer-droplet-nucleation mechanism. A method has been proposed to estimate the average number of polymerizing radicals in a droplet, ti, that characterizes the polymerization kinetics. For the system studied under the experimental conditions, the value of ri was derived as several hundreds, which is much larger than that for conventional emulsion polymerization.
I.
INTRODUCTION
Following the pioneering work of Vanderhoff et al. (1962), numerical studies have been carried out on the inverse emulsion polymerization of water-soluble monomers in nonaqueous media containing waterin-oil emulsifiers, more recently due to its main advantages of high polymerization rate and easy dissolution of the obtained polymers in water by phase inversion. The inverse emulsion polymerization of acrylamide solutions has been studied frequently, mainly on the nucleation mechanisms and the polymerization kinetics (Kurenkov et al., 1978, 1982; Trubitsyna et al., 1978; Dimonie et al., 1982; DiStefano et al., 1983; Reichert and Baade, 1984; Baade and Reichert, 1984, 1986; Vanderhoff et al., 1984; Pichot et al., 1985; Graillat et al., 1986; Glukhikh et al., 1987; Zhang et al., 1990). Recently we have studied the kinetics of the inverse emulsion polymerization of sodium acrylate solutions in kerosene containing Span 80 as the emulsifier with 6°Co-7 ray and potassium persulfate initiation (Jiang, 1988; Zhang et al., 1989; Jiang et al., 1990, 1995). Contrary to conventional emulsion polymerization, there seems no quantitative treatment for inverse emulsion polymerization. In our previous studies of the 6°Co-7 initiated emulsion polymerization of sodium acrylate solutions (Jiang, 1988; Zhang et al., 1989). we have proposed a monomer-dropletnucleation mechanism for this system under the experiment conditions investigated, which means that the polymerization proceeds in compartmentalized tAuthor to whom all correspondence should be addressed at: Radiation Laboratory. University of Notre Dame, Notre Dame, IN 46556, U.S.A. ~P~-455 ~
independent (by hypothesis) small systems, viz. monomer droplets. Based on this concept, the kinetics of the 6°Co-y initiated inverse emulsion polymerization of sodium acrylate solutions is treated quantitatively in this work.
2. EXPERIMENTAL Acrylic acid was distilled under reduced pressure just before use. Kerosene and Span 80 (reagent grade) and other chemicals (analytical grade) were used as supplied. Sodium acrylate solutions were prepared by neutralizing acrylic acid with sodium hydroxide (the pH was adjusted to 7.0 ___0.1) and were emulsified in kerosene containing Span 80 by stirring under nitrogen purging. The monomer emulsions were then vaccum-degassed. Polymerization was carried out at controlled temperatures with a 6 kCi ~Co-7 source, which provided dose rates in the range of 0.08-0.3 Gy s ~as determined by the Fricke dosimeter with G(Fe ~+ ) = 1.62/Jmol J ~, and was continuously followed with an automatic dilatometer remotely as described elsewhere (Jiang, 1988; Jiang et al., 1990). The monomer emulsions and the polymer latex were observed and their particle sizes estimated with an Olympus BX-2 optical microscope. 3. EXPERIMENTALRESULTS The volumetric contraction constant upon polymerization for sodium acrylate has been estimated as 1.59 × 10-2dm 3 mol ~ sodium acrylate at 303 K and as 1.59× 10--'-4.44x 10 5 ( T - 3 0 3 ) d m 3 m o l t a t a given temperature T (K) (Jiang, 1988; Jiang et al., 1995). The conversion of monomer was calculated by assuming that the volumetric contraction constant
825
Pei-Yun Jiang et al.
826
was unchanged with the emulsion ingredient under out experimental conditions. The conversion-time curves are generally S-shaped as shown in Fig. 1 and could be reproduced well. The rate of polymerization increases to maximum at around 20% conversion, showing no constant-rate-region that is typical for conventional emulsion polymerization (Smith and Ewart, 1948). Induction period was normally observed, typically 3-30 min depending mainly on the dose rate, presumably due to the existence of oxygen in the monomer emulsions, which was found to have no apparent effects on the rate of polymerization at conversions higher than about 10%. The monomer emulsions and the polymer latex were diluted with kerosene and observed by optical microscope. No apparent change in particle size was observed after polymerization. The particle diameters of the monomer emulsions and the polymer latex were roughly estimated as around 1/~m, without significant change with the emulsion ingredient and the polymerization conditions as observed by optical microscope. The distribution was rather narrow though no quantitative estimation was made. It is to be expected that the polymerization is initiated in the monomer droplets since the radiolysis of water in the droplets generates e~q, OH and H with G ( e ~ q + O H + H ) = 0 . 6 / ~ m o l J -~ in pure water (Buxton, 1987) (presumably significantly higher for the present system due to the scavenging effect of sodium acrylate), which react very rapidly with sodium acrylate, and the radiolysis of the continuous oil phase (kerosene, mixed alkanes) generates alkyl radicals with G ~ 0 . 5 # m o l J t typical for pure alkanes (Swallow, 1987; Tabata et al., 1991), which are water insoluble and thus of little importance in initiating polymerization since the monomer sodium
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acrylate is insoluble in the oil phase. The polymerization thus proceeds by a monomer-dropletnucleation mechanism, viz. in the compartmentalized monomer droplets independently, which is supported by the results that the particle size is almost unchanged after polymerization. In this sense the inverse emulsion polymerization of the present system resembles suspension polymerization except the smaller size of the droplets for the inverse emulsion system. 4. KINETIC T R E A T M E N T
Assuming that (1) the droplets do not coalesce or split during polymerization, (2) the droplets are of the same size, (3) the conversion is the same in all droplets, and (4) the average number of polymerizing radicals in a droplet reaches a constant steady-state value after the conversion reaches a certain value, the polymerization rate can be expressed by equation (1) by analogy with seeded conventional emulsion polymerization (Soh, 1980), where [M] is the monomer concentration (mol dm 3) in the droplets at time t, Vp the volume of a droplet (dm 3) at time t, t the polymerization time (s), r~ the average number of polymerizing radicals in a droplet, k r the propagation rate constant (din 3 mol ] s L), and No the Avogadro number.
-d([M]Vp)/dt = (ff/No)kp[M ].
(1)
Equation (1) is expressed in terms of conversion, x, to give equation (2) with [M] = ( 1 - x)[M]0/(l - ( x ) and Vp=(1--Ex)Vp~/(1--E), where V0~ is the volume (dm 3) of a droplet of 100% conversion, x the conversion of monomer to polymer, and the volume contraction coefficient given by E = (Vp0 - Vp~ )/1/'00 = K [M]0 with Vp0 being the volume (dm 3) of a droplet before polymerization, K the volumetric contraction constant (dm3mol ~) as indicated above, and [M]0 the monomer concentration ( m o l d m -3) in the droplets before polymerization. [Vp~_/(1 - ~)]dx/dt = (ff/No)kp(l - x ) / ( 1 - ~x).
(2)
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8 E o a. 0
i
0.0
10
20
30
i
i
J
Assuming the ri and k v are constant in the steadystate, equation (2) is integrated to give equation (3) with the initial condition of x = x 0 at t = to, where to is the beginning time of the steady-state.
0
40
I / mln
Fig. I. Conversion of sodium acrylate (x) and rate of polymerization (Ax/At) as a function of polymerization time (t). Ingredient: aqueous phase (75wt%), 2.93 mol dm 3 sodium acrylate, pH = 6.94, d = 1.1 kg dm 3; oil phase (25wi%), 6.8 wt% Span 80 in kerosene, d = 0.78 kgdm 3; volume ratio w/o = 2.1 (all parameters are given for room temperature of around 296 K). Polymerization temperature T = 296 K. Dose rate = 0.188 Gy s for the dosimeter solution. Induction time = 3 rain.
~x/(l -- ~)-- In(I -- x) = A +[ffkp/(Vp~No)]t
(t >to)
(3)
A = o:0/( 1 - E) - In( 1 - .% ) - [vikp/( Vp, No )]t0.
(4)
Thus a plot of [~x/(1 - ~ ) - ln(I - x ) ] vs t should be linear with slope ~kp/(Vp, No) if fi reaches a constant steady-state value. The experimental results are shown in Fig. 2. When the conversion is over about 20%, [~x/(I - ~) - In(l - x ) ] is linear with the
Inverse emulsion polymerization model
~"
1.0
1.0
0.50
0.5
x
827
present model and analysis to the inverse emulsion polymerization of sodium acrylate solutions initiated by 6°Co-~, ray and potassium persulfate will be discussed elsewhere. Although the present ad hoc model is somewhat limited by the assumptions, it is of considerable interests to extend its application to other systems.
us
REFERENCES ~
0.(~
0.0
I
10
20
30
[
I
0
40
t / rain
Fig. 2. Plots of [~x/(l - ~) - ln(l - x)] and x vs t. See Fig. 1 for ingredient and polymerization conditions.
polymerization time t to give ~ k p / ( V p ~ N o ) = 7.7 × 10 4s ~, confirming our steady-state assumption for ft. Principally k o and Vo:~" can be obtained separately and thus fi can be estimated experimentally according to the above treatment. F r o m the optical microscope observation, the diameter d (dm) of the droplets is about 1/zm (I0 -5 dm), thus Vp_~= red3~6. The value ofkp has been reported as 650 dm 3 m o l - ~s- ' (Karaputadse et al., 1972; cited by Brandrup and Immergut, 1989) under the more or less similar experimental condition to that of the present study. Thus ti was estimated as around 370, which is 2 orders higher than that considered for conventional emulsion polymerization, e.g. ideally 0.5 for water-insoluble monomers (Smith and Ewart, 1948). The large ti value also suggests that there should be no basic difference between inverse emulsion polymerization and solution polymerization for sodium acrylate solutions (at least in the concentration range studied in the present work) when the conversion is higher than about 20%. The difference is at the initial stage of the polymerization where the termination of the polymerizing radicals is retarded by compartmentalization in inverse emulsion polymerization, leading to higher polymerization rate than in solution polymerization. Since ri is very sensitive to the droplet size d and rather sensitive to kp, the present estimation of fi is only qualitative and tentative due to the uncertainties in d and kp. Nevertheless, the above analysis provides a feasible way to estimate experimentally the value of ri that characterizes the polymerization process. Detailed examination and application of the
Baade W. and Reichert K. H. (1984) Eur. Polym. J. 20, 505. Baade W. and Reichert K. H. (1986) Macromol. (Twin. Rapid Commun. 7, 235. Brandrup J. and Immergut E. H. (1989) PoO,mer Handbook. Wiley, New York. Buxton G. V. (1987) Radiation Chemisto,: Principles and Applications (Edited by Farhataziz and Rodgers M. A. J.), Chap. 10. VCH. Dimonie M. V., Boghina C. M., Marinescu N. N., Marinescu M. M., Cincu C. 1. and Oprescu C. G. (1982) Eur. Polym. J. 18, 639. DiStefano F. V., Schaffer O. M., E1-Aasser M. S. and Vanderhoff J. W. (1983) J. Colloid Interl'ace Sci. 92, 269. Gtukhikh V., Graillat C. and Pichot C. (1987) J. Polvm. Sci. Polym. Chem. Ed. 25, 1127. Graillat C., Pichot C., Guyot A. and EI-Aasser M. S. (1986) J. Polym. Sci. Polym. Chem. Ed. 24, 427. Jiang P. Y. (1988) M.Sc. thesis, the University of Science and Technology of China. Jiang P. Y., Zhang Z. C. and Zhang M. W. (1995) Submitted to J. Polvm. Sci. Polym. Chem. Ed. Jiang P. Y., Zhang Z. C., Wu X. Y. and Zhang M. W. (1990) J. Radiat. Res. Radiat. Process. 8, 100. Karaputadse T. M., Kurilova A. I., Topchiev, P. A. and Kabanov V. A. (1972) I/vsokomol. Soedin. BI4, 323. Kurenkov V. F., Osipova T. M., Kuznetsov E. V. and Myagchenkov V. A. (1978) Vysokomol. Soedin. B20, 647. Kurenkov V. F., Verzhnikova A. S., Kuznetsov E. V. and Myagchenkov V. A. (1982) hit. J. Polvm. Sci. Technol. 9, 65. Pichot C., Graillat C. and Glukhikh V. (1985) Makromol. Chem. Suppl. 10/11, 199. Reichert K. H. and Baade W. (1984) Angew. Makromol. Chem. 123]124, 361. Smith W. V. and Ewart R. H. (1948) J. Chem. Phys. 16, 952. Soh S. K. (1980) J. Appl. Polym. Sci. 25, 2993. Swallow A. J. (1987) Radiation Chemisto,: Principles and Applications (Edited by Farhataziz and Rodgers M. A. J.), Chap. 11. VCH. Tabata Y., lto Y. and Tagawa S. (1991) CRC Handbook Of Radiation Chemistry, Chap. XII. CRC Press, Boca Raton, Fla. Trubitsyna S. N., lsmailov K. and Askarov M. A. (1978) Vysokomol. Soedin. A20, 2608. VanderhoffJ. W., Bradford E. B., Tarkowski H. L., Schaffer J. B. and Wiley R. M. (1962) Adv. Chem. Set. 34, 32. Vanderhofl" J. W., DiStefano F. V., EI-Aasser M. S., O'Leary R., Schaffer O. M. and Visioli D. L. (1984) J. Dispers. Sci. fechnol. 5, 323. Zhang Z. C., Jiang P. Y. and Zhang M. W. (1989) J. Radiat. Res. Radial. Process. 7, 45. Zhang Z. C., Wu X. Y., Jiang P. Y. and Zhang M. W. (1990) J. Radiat. Res. Radiat. Process. 8, 5.
~
Pergamon
0969-806X(94)00126-X
Copyright .4' 1995ElsevierScienceLtd Printed in Great Britain.All rights reserved 0969-806X/95 $9.50+ 0.00
KINETIC M O D E L FOR THE 6°Co-'~ RAY INITIATED INVERSE E M U L S I O N P O L Y M E R I Z A T I O N OF S O D I U M A C R Y L A T E SOLUTIONS PEI-YUN JIANG,? ZHI-CHENG ZHANG and MAN-WEI ZHANG Applied Chemistry Department, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China (Received 18 October 1993; accepted 13 September 1994)
Abstract--The conversion-time curves have been measured and treated quantitatively for the 6°Co-7 ray initiated inverse emulsion polymerization of aqueous sodium acrylate solutions on the basis of a monomer-droplet-nucleation mechanism. A method has been proposed to estimate the average number of polymerizing radicals in a droplet, ti, that characterizes the polymerization kinetics. For the system studied under the experimental conditions, the value of ri was derived as several hundreds, which is much larger than that for conventional emulsion polymerization.
I.
INTRODUCTION
Following the pioneering work of Vanderhoff et al. (1962), numerical studies have been carried out on the inverse emulsion polymerization of water-soluble monomers in nonaqueous media containing waterin-oil emulsifiers, more recently due to its main advantages of high polymerization rate and easy dissolution of the obtained polymers in water by phase inversion. The inverse emulsion polymerization of acrylamide solutions has been studied frequently, mainly on the nucleation mechanisms and the polymerization kinetics (Kurenkov et al., 1978, 1982; Trubitsyna et al., 1978; Dimonie et al., 1982; DiStefano et al., 1983; Reichert and Baade, 1984; Baade and Reichert, 1984, 1986; Vanderhoff et al., 1984; Pichot et al., 1985; Graillat et al., 1986; Glukhikh et al., 1987; Zhang et al., 1990). Recently we have studied the kinetics of the inverse emulsion polymerization of sodium acrylate solutions in kerosene containing Span 80 as the emulsifier with 6°Co-7 ray and potassium persulfate initiation (Jiang, 1988; Zhang et al., 1989; Jiang et al., 1990, 1995). Contrary to conventional emulsion polymerization, there seems no quantitative treatment for inverse emulsion polymerization. In our previous studies of the 6°Co-7 initiated emulsion polymerization of sodium acrylate solutions (Jiang, 1988; Zhang et al., 1989). we have proposed a monomer-dropletnucleation mechanism for this system under the experiment conditions investigated, which means that the polymerization proceeds in compartmentalized tAuthor to whom all correspondence should be addressed at: Radiation Laboratory. University of Notre Dame, Notre Dame, IN 46556, U.S.A. ~P~-455 ~
independent (by hypothesis) small systems, viz. monomer droplets. Based on this concept, the kinetics of the 6°Co-y initiated inverse emulsion polymerization of sodium acrylate solutions is treated quantitatively in this work.
2. EXPERIMENTAL Acrylic acid was distilled under reduced pressure just before use. Kerosene and Span 80 (reagent grade) and other chemicals (analytical grade) were used as supplied. Sodium acrylate solutions were prepared by neutralizing acrylic acid with sodium hydroxide (the pH was adjusted to 7.0 ___0.1) and were emulsified in kerosene containing Span 80 by stirring under nitrogen purging. The monomer emulsions were then vaccum-degassed. Polymerization was carried out at controlled temperatures with a 6 kCi ~Co-7 source, which provided dose rates in the range of 0.08-0.3 Gy s ~as determined by the Fricke dosimeter with G(Fe ~+ ) = 1.62/Jmol J ~, and was continuously followed with an automatic dilatometer remotely as described elsewhere (Jiang, 1988; Jiang et al., 1990). The monomer emulsions and the polymer latex were observed and their particle sizes estimated with an Olympus BX-2 optical microscope. 3. EXPERIMENTALRESULTS The volumetric contraction constant upon polymerization for sodium acrylate has been estimated as 1.59 × 10-2dm 3 mol ~ sodium acrylate at 303 K and as 1.59× 10--'-4.44x 10 5 ( T - 3 0 3 ) d m 3 m o l t a t a given temperature T (K) (Jiang, 1988; Jiang et al., 1995). The conversion of monomer was calculated by assuming that the volumetric contraction constant
825
Pei-Yun Jiang et al.
826
was unchanged with the emulsion ingredient under out experimental conditions. The conversion-time curves are generally S-shaped as shown in Fig. 1 and could be reproduced well. The rate of polymerization increases to maximum at around 20% conversion, showing no constant-rate-region that is typical for conventional emulsion polymerization (Smith and Ewart, 1948). Induction period was normally observed, typically 3-30 min depending mainly on the dose rate, presumably due to the existence of oxygen in the monomer emulsions, which was found to have no apparent effects on the rate of polymerization at conversions higher than about 10%. The monomer emulsions and the polymer latex were diluted with kerosene and observed by optical microscope. No apparent change in particle size was observed after polymerization. The particle diameters of the monomer emulsions and the polymer latex were roughly estimated as around 1/~m, without significant change with the emulsion ingredient and the polymerization conditions as observed by optical microscope. The distribution was rather narrow though no quantitative estimation was made. It is to be expected that the polymerization is initiated in the monomer droplets since the radiolysis of water in the droplets generates e~q, OH and H with G ( e ~ q + O H + H ) = 0 . 6 / ~ m o l J -~ in pure water (Buxton, 1987) (presumably significantly higher for the present system due to the scavenging effect of sodium acrylate), which react very rapidly with sodium acrylate, and the radiolysis of the continuous oil phase (kerosene, mixed alkanes) generates alkyl radicals with G ~ 0 . 5 # m o l J t typical for pure alkanes (Swallow, 1987; Tabata et al., 1991), which are water insoluble and thus of little importance in initiating polymerization since the monomer sodium
0.8
'
'
'
'
I
I
,
,
,
I
'
'
'
'
I
'
'
'
0.08
i
.$ )<
E
0.6
0.06
0.4
0.04
~
0.2
0.02
~
c o
acrylate is insoluble in the oil phase. The polymerization thus proceeds by a monomer-dropletnucleation mechanism, viz. in the compartmentalized monomer droplets independently, which is supported by the results that the particle size is almost unchanged after polymerization. In this sense the inverse emulsion polymerization of the present system resembles suspension polymerization except the smaller size of the droplets for the inverse emulsion system. 4. KINETIC T R E A T M E N T
Assuming that (1) the droplets do not coalesce or split during polymerization, (2) the droplets are of the same size, (3) the conversion is the same in all droplets, and (4) the average number of polymerizing radicals in a droplet reaches a constant steady-state value after the conversion reaches a certain value, the polymerization rate can be expressed by equation (1) by analogy with seeded conventional emulsion polymerization (Soh, 1980), where [M] is the monomer concentration (mol dm 3) in the droplets at time t, Vp the volume of a droplet (dm 3) at time t, t the polymerization time (s), r~ the average number of polymerizing radicals in a droplet, k r the propagation rate constant (din 3 mol ] s L), and No the Avogadro number.
-d([M]Vp)/dt = (ff/No)kp[M ].
(1)
Equation (1) is expressed in terms of conversion, x, to give equation (2) with [M] = ( 1 - x)[M]0/(l - ( x ) and Vp=(1--Ex)Vp~/(1--E), where V0~ is the volume (dm 3) of a droplet of 100% conversion, x the conversion of monomer to polymer, and the volume contraction coefficient given by E = (Vp0 - Vp~ )/1/'00 = K [M]0 with Vp0 being the volume (dm 3) of a droplet before polymerization, K the volumetric contraction constant (dm3mol ~) as indicated above, and [M]0 the monomer concentration ( m o l d m -3) in the droplets before polymerization. [Vp~_/(1 - ~)]dx/dt = (ff/No)kp(l - x ) / ( 1 - ~x).
(2)
c
8 E o a. 0
i
0.0
10
20
30
i
i
J
Assuming the ri and k v are constant in the steadystate, equation (2) is integrated to give equation (3) with the initial condition of x = x 0 at t = to, where to is the beginning time of the steady-state.
0
40
I / mln
Fig. I. Conversion of sodium acrylate (x) and rate of polymerization (Ax/At) as a function of polymerization time (t). Ingredient: aqueous phase (75wt%), 2.93 mol dm 3 sodium acrylate, pH = 6.94, d = 1.1 kg dm 3; oil phase (25wi%), 6.8 wt% Span 80 in kerosene, d = 0.78 kgdm 3; volume ratio w/o = 2.1 (all parameters are given for room temperature of around 296 K). Polymerization temperature T = 296 K. Dose rate = 0.188 Gy s for the dosimeter solution. Induction time = 3 rain.
~x/(l -- ~)-- In(I -- x) = A +[ffkp/(Vp~No)]t
(t >to)
(3)
A = o:0/( 1 - E) - In( 1 - .% ) - [vikp/( Vp, No )]t0.
(4)
Thus a plot of [~x/(1 - ~ ) - ln(I - x ) ] vs t should be linear with slope ~kp/(Vp, No) if fi reaches a constant steady-state value. The experimental results are shown in Fig. 2. When the conversion is over about 20%, [~x/(I - ~) - In(l - x ) ] is linear with the
Inverse emulsion polymerization model
~"
1.0
1.0
0.50
0.5
x
827
present model and analysis to the inverse emulsion polymerization of sodium acrylate solutions initiated by 6°Co-~, ray and potassium persulfate will be discussed elsewhere. Although the present ad hoc model is somewhat limited by the assumptions, it is of considerable interests to extend its application to other systems.
us
REFERENCES ~
0.(~
0.0
I
10
20
30
[
I
0
40
t / rain
Fig. 2. Plots of [~x/(l - ~) - ln(l - x)] and x vs t. See Fig. 1 for ingredient and polymerization conditions.
polymerization time t to give ~ k p / ( V p ~ N o ) = 7.7 × 10 4s ~, confirming our steady-state assumption for ft. Principally k o and Vo:~" can be obtained separately and thus fi can be estimated experimentally according to the above treatment. F r o m the optical microscope observation, the diameter d (dm) of the droplets is about 1/zm (I0 -5 dm), thus Vp_~= red3~6. The value ofkp has been reported as 650 dm 3 m o l - ~s- ' (Karaputadse et al., 1972; cited by Brandrup and Immergut, 1989) under the more or less similar experimental condition to that of the present study. Thus ti was estimated as around 370, which is 2 orders higher than that considered for conventional emulsion polymerization, e.g. ideally 0.5 for water-insoluble monomers (Smith and Ewart, 1948). The large ti value also suggests that there should be no basic difference between inverse emulsion polymerization and solution polymerization for sodium acrylate solutions (at least in the concentration range studied in the present work) when the conversion is higher than about 20%. The difference is at the initial stage of the polymerization where the termination of the polymerizing radicals is retarded by compartmentalization in inverse emulsion polymerization, leading to higher polymerization rate than in solution polymerization. Since ri is very sensitive to the droplet size d and rather sensitive to kp, the present estimation of fi is only qualitative and tentative due to the uncertainties in d and kp. Nevertheless, the above analysis provides a feasible way to estimate experimentally the value of ri that characterizes the polymerization process. Detailed examination and application of the
Baade W. and Reichert K. H. (1984) Eur. Polym. J. 20, 505. Baade W. and Reichert K. H. (1986) Macromol. (Twin. Rapid Commun. 7, 235. Brandrup J. and Immergut E. H. (1989) PoO,mer Handbook. Wiley, New York. Buxton G. V. (1987) Radiation Chemisto,: Principles and Applications (Edited by Farhataziz and Rodgers M. A. J.), Chap. 10. VCH. Dimonie M. V., Boghina C. M., Marinescu N. N., Marinescu M. M., Cincu C. 1. and Oprescu C. G. (1982) Eur. Polym. J. 18, 639. DiStefano F. V., Schaffer O. M., E1-Aasser M. S. and Vanderhoff J. W. (1983) J. Colloid Interl'ace Sci. 92, 269. Gtukhikh V., Graillat C. and Pichot C. (1987) J. Polvm. Sci. Polym. Chem. Ed. 25, 1127. Graillat C., Pichot C., Guyot A. and EI-Aasser M. S. (1986) J. Polym. Sci. Polym. Chem. Ed. 24, 427. Jiang P. Y. (1988) M.Sc. thesis, the University of Science and Technology of China. Jiang P. Y., Zhang Z. C. and Zhang M. W. (1995) Submitted to J. Polvm. Sci. Polym. Chem. Ed. Jiang P. Y., Zhang Z. C., Wu X. Y. and Zhang M. W. (1990) J. Radiat. Res. Radiat. Process. 8, 100. Karaputadse T. M., Kurilova A. I., Topchiev, P. A. and Kabanov V. A. (1972) I/vsokomol. Soedin. BI4, 323. Kurenkov V. F., Osipova T. M., Kuznetsov E. V. and Myagchenkov V. A. (1978) Vysokomol. Soedin. B20, 647. Kurenkov V. F., Verzhnikova A. S., Kuznetsov E. V. and Myagchenkov V. A. (1982) hit. J. Polvm. Sci. Technol. 9, 65. Pichot C., Graillat C. and Glukhikh V. (1985) Makromol. Chem. Suppl. 10/11, 199. Reichert K. H. and Baade W. (1984) Angew. Makromol. Chem. 123]124, 361. Smith W. V. and Ewart R. H. (1948) J. Chem. Phys. 16, 952. Soh S. K. (1980) J. Appl. Polym. Sci. 25, 2993. Swallow A. J. (1987) Radiation Chemisto,: Principles and Applications (Edited by Farhataziz and Rodgers M. A. J.), Chap. 11. VCH. Tabata Y., lto Y. and Tagawa S. (1991) CRC Handbook Of Radiation Chemistry, Chap. XII. CRC Press, Boca Raton, Fla. Trubitsyna S. N., lsmailov K. and Askarov M. A. (1978) Vysokomol. Soedin. A20, 2608. VanderhoffJ. W., Bradford E. B., Tarkowski H. L., Schaffer J. B. and Wiley R. M. (1962) Adv. Chem. Set. 34, 32. Vanderhofl" J. W., DiStefano F. V., EI-Aasser M. S., O'Leary R., Schaffer O. M. and Visioli D. L. (1984) J. Dispers. Sci. fechnol. 5, 323. Zhang Z. C., Jiang P. Y. and Zhang M. W. (1989) J. Radiat. Res. Radial. Process. 7, 45. Zhang Z. C., Wu X. Y., Jiang P. Y. and Zhang M. W. (1990) J. Radiat. Res. Radiat. Process. 8, 5.