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degrad of polymers

VIEWS: 7 PAGES: 51

  • pg 1
									Degradation of Polymers under

            Ultrasound

        And Microwave
                  A Report

    Submitted in Partial Fulfillment of the

       Requirement for the Degree of

      Μαστερ οφ Ενγινεερινγ

        in the Faculty of Engineering



                      By

              Jayanta Chakraborty




    Department of Chemical Engineering

      INDIAN INSTITUTE OF SCIENCE

         BANGALORE-560012, INDIA

                 JUNE 2004
ABSTRACT
       The ultrasonic degradation of polybutadiene and isotactic polypropylene in

solution was studied at different temperatures and in different solvents, degradation of

poly (ethylene oxide) of different initial molecular weights was studied at a fixed

temperature. The time evolution of molecular weight distribution was determined

experimentally through gel permeation chromatography. Degradation rate coefficients

were determined from a model based on continuous distribution kinetics and

assuming mid-point chain scission. The variation of rate coefficients for

polybutadiene and isotactic polypropylene with vapour pressure and kinematic

viscosity was investigated. The rate coefficient was calculated based on a previous

model. To model the effect of initial molecular weight, the ultrasonic rate coefficient,

κ, is assumed to be of the form, κ = kd ( x − xlim )λ , where x and xlim represent the

molecular weight and limiting molecular weight, respectively. A continuous

distribution model assuming midpoint chain scission and two different expressions for

the rate coefficient, where either kd or λ is assumed to be independent of the initial

molecular weight, was developed to satisfactorily model the experimental data. For λ

=1, the value of kd increased with increasing molecular weight while for constant kd,

the value of λ decreased with increasing initial molecular weight.

       The microwave assisted degradation of polyethylene oxide in the presence of

persulfate was investigated at different heating cycle times and with different

persulfate concentrations. A model based on continuous distribution kinetics with

time dependent rate coefficients was used to obtain the kinetic parameters by non-

linear regression of experimental data. The change in molecular weight distribution

with time was followed by gel permeation chromatography. The highest degradation
                                                                                      ii
was observed during 20 sec heating time and with 1 kg/m3 of persulfate concentration.

The activation energy was found to be 10.3 kcal/mol for the microwave-assisted

oxidative degradation of polyethylene oxide.




                                                                                   iii
CONTENTS
1. Introduction

      1.1 A Short Overview on Polymers                              1

      1.2 Polymer Degradation                                       1

      1.3 The Present Work                                          2

          References                                                3

2. Ultrasonic Degradation of Polymers

      2.1 Introduction                                              4

      2.2 Experimental

             2.2.1 Degradation Reaction                             6

             2.2.2 Polymer Analysis                                 8

      2.3 Model Used                                                9

      2.4 Result and Discussion                                     10

      2.5 Conclusion                                                13

         References                                                 14

3. Microwave Assisted Oxidative Degradation of Polyethylene Oxide

      3.1 Introduction                                              27

      3.2 Experimental Section

             3.2.1 Materials                                        29

             3.2.2 Microwave Reactor                                29

             3.2.3 Degradation Reaction                             29

             3.2.4 GPC Analysis                                     30

      3.3 Results and Discussion
                                                                        iv
            3.3.1 Theoretical Model       30

            3.3.2 Microwave degradation   33

      3.4 Conclusion                      35

         References                       36

4. Conclusion and scope for future work

      4.1 conclusion                      43

      4.2 future work                     44




                                               v
                                                                                       6

LIST OF FIGURES
2.1a.   Evolution of molecular weight of isotactic poly (propylene) in ODCB       17

2.1b.   Evolution of molecular weight of poly (butadiene) in ODCB                 18

2.2.    Variation of the limiting molecular weight with temperature in ODCB       19

        for isotactic polypropylene and polybutadiene.

2. 3a. Ln(H) vs. sonication time for isotactic poly(propylene) in ODCB            20

        at various temperature.

2.3b.   Ln (H) vs. sonication time for poly(butadiene) in ODCB at various         21

        temperature

2.4.    Vapor pressure of solvent vs. rate coefficient(k)                         22

2.5.    Kinematic Viscosity of the solvent vs. rate coefficient(k)                23

2.6.    Variation of the molecular weight with time, based on Eq 2.4.             24

2.7.    Variation of the non-dimensional number-average molecular weight          25

        with time(experimental data and model fit). Inset: variation of the

        molecular weight with time showing the limiting molecular weight.

2.8.    Variation of λ and kd with the initial molecular weight of the polymer.   26

3.1a.   Variation of Mn0/Mn with time with 0.2 kg/m3 of persulfate                38

3.1b    Variation of Mn0/Mn with time with 0.4 kg/m3 of persulfate                39

3.1c    Variation of Mn0/Mn with time with 1.0 kg/m3 of persulfate                40

3.2a    Theoretical prediction of persulfate concentration                        41

3.2b    Theoretical prediction of radical concentration                           42




                                                                                       6
                                                                                      7

CHAPTER 1

INTRODUCTION


1.1 A SHORT OVERVIEW ON POLYMERS

   Synthetic polymers are synthesized mainly from petroleum fractions like naptha,

natural gas etc. Polymers are one of the most important materials in the modern

world with a wide range of applicability. It is used as a substitute for metal and as an

artificial organ in human body. Polymeric materials are very popular because those

are light in weight, tough, relatively inert in environmental conditions and cheap.

   Chemically polymers are (poly=many; mar=unit) large molecules of high

molecular weight consists of repetitive units [1]. If the repetitive units are same then

it called homopolymer and if there is more than one set of unit repeats, then it is

called co-polymers. Generally the long chain consists of carbon atom, although it is

possible to synthesize a polymer that contains non-carbon backbone. Different

orientation of the chain or different side groups in synthetic organic polymers gives

rise to different useful properties. Another important concept in polymer physics is its

molecular weight distribution. Unlike other chemicals, polymers do not have a unique

molecular weight, but the molecular weight is distributed over a range. That means a

given sample of a specified polymer will always contain molecules of very different

molecular weights.     Therefore, a polymer is always has a molecular weight

distribution.

1.2 POLYMER DEGRADATION




                                                                                      7
                                                                                    8
Depending on the application, polymer may need to be degraded. In the study of

degradation, different methods of degradation are available, such as thermal and

catalytic degradation. Unconventional methods like ultrasound[2], UV, microwave[3],

photo catalytic are also important.

1.3 THE PRESENT WORK

       In this thesis, degradation by ultrasound and microwave has been considered.

Some typical features of ultrasound and microwave degradation have been discussed

in the following chapters. Experiments have been conducted to explore the effect of

different parameters on ultrasonic degradation. The effect of initial molecular weight

has been explored through experimental studies and a new model has been proposed.

The kinetics of microwave degradation has been studied through experiment and the

rate parameters have been determined.




                                                                                    8
                                                                                  4
REFERENCES:

  1. Billmeyer, F. W., Textbook of Polymer Science, Wiley, New York(2003).

  2. Price, G. J., “The use of ultrasound for the controlled degradation of polymer

     solutions,” Advances in Sonochemistry, Jai Press. (1990).

  3. Caddick, S., “Microwave Assisted Organic Reactions,” Tetrahedron, 51,

     10403(1995).
                                                                                          5

CHAPTER 2

ULTRASONIC DEGRADATION OF POLYMERS


2.1 INTRODUCTION

Polymers can be degraded thermally by pyrolysis [1] or in solution [2] but the

processes are energy intensive. The need for alternative techniques that would reduce

energy requirements for the degradation process is important. The use of ultrasound,

photo and chemical methods is less energy-intensive polymer degradation. Further, the

mechanism by which they interact with the polymeric systems can help in gaining

insight into the degradation pathways or mechanisms. Polymers undergo degradation

when they are subjected to ultrasound irradiation of high intensity. Several workers

have investigated the ultrasound degradation of polymers, which has been summarized

by Price [3]. The breaking of the chemical bonds is due to the cavitation in the medium.

Cavitation is the formation and violent collapse of small bubbles or voids in the liquid

as a result of pressure changes in the medium. This leads to shearing forces of sufficient

magnitude that they can cause the rupture of bonds. The sound waves do not directly

interact with the polymer but they act on the solvent causing the growth and rapid

collapse of micro-bubbles resulting in high shear gradient. It has been shown that this

shear force is roughly similar to the force required to break chemical bonds in polymers

[4-5]. Another unique feature of ultrasonic degradation is the fact that, in contrast to all

chemical and thermal decomposition reactions, the ultrasound depolymerization is a

non-random process which produces fragmentation at the mid-point of the chain [6].

The existence of limiting molecular weight, below which degradation by ultrasound
                                                                                        6
does not take place, has the additional effect in that the molecular weight distribution

initially broadens and before narrowing during degradation. The effect of various

parameters like temperature, ultrasound intensity, dissolved gases [7] and polymer

concentration [8] on the ultrasonic degradation of polystyrene has been investigated. A

primary factor in the ultrasonic degradation of polymers is the effect of solvent in the

degradation rate. While some workers [9,10]report no effect of solvent on the

degradation of cellulose nitrate and polyisobutylene, several investigators have found

an effect of solvent on the ultrasonic degradation of dextran [11], poly(ethylene glycol)

[12], hydroxypropyl cellulose [13], poly(alkyl methacrylate)s[14], poly(vinyl acetate)

[15] and polystyrene [8]. While the ultrasonic degradation is influenced by polymer

solvent interaction parameters like Florye-Huggins and Huggins constant [8], the major

factors that influence the degradation are the kinematic viscosity and vapour pressure of

the solvent [9].Though polybutadiene and polypropylene are important commercial

polymers, there are no studies on the ultrasonic degradation of these polymers. There is

no study on the ultrasonic degradation of isotactic polypropylene and polybutadiene

over an extensive temperature range or the effect of solvents on degradation of these

polymers.

       The importance of the initial molecular weight for the degradation kinetics is

well known because it provides insights into degradation mechanisms for

macromolecular reactions. The effect of molecular weight on the thermal degradation

kinetics has been investigated and a non-linear dependence of the degradation rate on

molecular weight was observed depending on the change in the molecular weight and

the initial molecular weight [22]. Thus it is apparent that a determination of the scaling

exponent is essential to a molecular understanding of the chain scission mechanism
                                                                                          7
[23]. The influence of molecular weight on the rate of ultrasonic degradation is not

clear. For example, a direct proportionality between the rate of ultrasonic degradation

and the molecular weight, x, was established for the degradation of dextran [24].

However, a quadratic dependence, κ= kd x2, was established for the ultrasonic

degradation of synthetic polymers like polystyrene [25-27]. Experimental data [23] for

both ultrasonic and elongational flow also showed that the degradation rate depends

non-linearly on molecular weight.

          The objective of this study is to present new experimental data for the ultrasonic

degradation of these polymers and determine the degradation rate coefficients using a

model developed earlier [16]. The variation of the rate coefficients with temperature is

attributed to the change in the kinematic viscosity and vapour pressure. The other

objective of the current investigation is to study the effect of the initial molecular

weight on the ultrasonic degradation of polyethylene oxide in water. A continuous

distribution model is developed to model the degradation kinetics and it is shown that

experimental results and theory demonstrate that the degradation rate of ultrasonic

degradation of polymers do not follow a linear dependence of the initial molecular

weight.

2.2 EXPERIMENTS

2.2.1 Degradation reaction:

          The reaction was carried out in a 100-ml beaker. Approximately 80 ml of

polymer solution (2 g/l) was taken each time and the beaker was held with a clamp-

stand assembly in a constant temperature water bath ( ±10 C ). Ultrasound was coupled

directly to the reaction system by a horn type sonicator (Vibronics, India) with voltage

and frequency of 180 V and 25 kHz, respectively. The beaker was wrapped with
                                                                                               8
aluminum foil to the sonic horn to minimize solvent evaporation. The experiments

were conducted by covering the beaker to ensure that no air entered the system during

degradation.      No   crosslinking   was   observed       because     the   Gel   Permeation

Chromatography (GPC) chromatograph did not show any molecular weight above the

initial molecular weight. Calculated amounts of solvents were added to maintain the

concentration of polymer solution constant inside the reaction system. Samples were

drawn at regular intervals through a syringe and analyzed by GPC.

           The ultrasonic degradation of polybutadiene was investigated at 32, 50, 60 and
     0
70       C with o-dichlorobenzene as solvent and in chlorobenzene, toluene, p-xylene,
                                                       0
chloroform, tetrahydrofuran and benzene at 32              C. The ultrasonic degradation of
                                                                                   0
isotactic polypropylene was investigated at 80, 90, 113, 133 and 155                   C with o-

dichlorobenzene as solvent. Because the initial molecular weight of polypropylene was
                                                                0
only 125,000, it was completely dissolved even at 70                C. This was confirmed by

dissolving the polymer at 70 0 C and 155 0 C. Both the solutions showed the exact same

GPC chromatogram confirming that polypropylene remained soluble in all

experimental conditions. Polyethylene oxide of different molecular weights was

degraded in an aqueous solution at a fixed temperature of 30 oC.

           The model to determine the degradation rate coefficient requires the limiting

molecular weight for the degradation of the polymer. Several experiments were

conducted for 10 h and no detectable change in the molecular weight was noticed after

6 h. Further, the experimental data indicated that the ratio of the limiting molecular

weight to the molecular weight after 120 min of degradation was approximately 0.8 in

all cases. This ratio determines the limiting molecular weight of the polymer for the

experiments conducted for only 3 h. The variation of the limiting molecular weights for
                                                                                         9
the polymers with reaction temperature was measured and the plot was linear (Figure

2.2). This observation was consistent with the observations reported in the literature [7]

for the variation of the limiting molecular weight with temperature for the ultrasonic

degradation of polystyrene in toluene. For the ultrasonic degradation of polyethylene

oxide, a constant limiting molecular weight of 16000 was observed experimentally.

2.2.2. Polymer analysis

       The molecular weight distributions of the polypropylene samples were

measured by Gel Permeation Chromatography(GPC). The HPLC-GPC system consists

of an isocratic pump (Waters, USA), mixed B columns(Polymer Labs, UK) and

evaporative light scattering detector (Polymer Labs, UK). The columns were
                     0
maintained at 150        C using a column heater (Eldex, USA) and the system was

calibrated with polystyrene standards. The flow rate of the eluent, o-dichlorobenzene,

was maintained at 0.7 ml/min and the flow rate of nitrogen to the light scattering

detector was maintained at 0.8 ml/min for enhanced sensitivity.

       The molecular weight distributions of the polybutadiene samples were

measured by Gel Permeation Chromatography (GPC system consisted of an isocratic

pump (Waters, Model R410), an injector (Rheodyne, 200microliter sample loop) and

three GPC columns. (HR 4, HR3 and HR 0.5 size: 300 mm 7.5 mm) of varying pore
                                                                                




sizes. Columns kept inside column heater (Waters, USA) maintained at 50 C. A 0.5

micrometer filter (Supelco) was placed at the column inlet to prevent any dirt particle

to entry. A differential refractive index (RI) detector (Waters, USA) was connected at

the outlet of the last column. Tetrahydrofuran (THF) was distilled twice and filtered

through 0.2 micrometer membrane filter (Millipore) and was eluent for the system and

pumped at a constant flow rate of 1.0 ml/min through the system to obtain the
                                                                                               10
chromatogram. These were converted to MWD with the help of calibration curve

made using six polystyrene standards of narrow distribution.

                     The molecular weight distribution of polyethylene oxide was monitored

by Gel Permeation chromatography. The GPC consisted of Waters Ultrahydrogel linear

SEC column measuring 7.8x300 mm maintained at 50°C. Double distilled deionised

water was used as eluent at a flow rate of 0.5 ml/min. The refractive index was

monitored continuously with a Waters 401 Differential Refractometer. About 800 µl of

sample was injected into the system to obtain a chromatogram and converted to

molecular weight by using narrow-distribution polyethylene oxide calibration

standards.

2.3 MODEL USED

Because the polymer breaks at the midpoint,

                                                       →
                                         P( x)  2 P( x / 2)
                                                k ( x)
                                                                                         (A)

P ( x) represents the polymer species and p ( x, t ) is the molecular weight distribution of

the species. No repolymerization of the degraded species was observed in the

experiments. This was confirmed by the GPC chromatogram that showed no molecular

weight products higher than the initial distribution. The population balance

equation for the above reaction (A) is [16]




            = − k ( x) p ( x, t ) + 2 ∫ k ( x) p ( x ' , t )δ ( x − )dx '
                                     ∞
∂p ( x, t )                                                        x'
                                                                                        (2.1)
   ∂t                                 x
                                                                   2

The degradation is assumed to be first order with the polymer concentration p ( x, t ) and

the degradation rate, k ( x ) , is assumed to be of the form k ( x) = k ( x − xl ) where the xl

represents the limiting molecular weight[16]. This ensures that the rate coefficient, k ,
                                                                                                                      11
is independentof x and becomes zero when x = xl and no further degradation takes


                                                              ∫
                                                                  ∞
place. Applying the moment operation                                  x n []dx to the above equation yields
                                                                  0



    dp ( n )
             = kp ( n +1) (21− n − 1) − kp ( n ) xl (21− n − 1)                                                (2.2)
     dt

                p (0) and p (1) represent the molar and mass concentrations of the polymer,

respectively and can be obtained by putting n = 0 and 1 in Eq. (2.2). For n = 0

    dp (0)
           = kp (1) − kp (0) xl                                                                                (2.3)
     dt

Solving equation (2.3) with initial condition p (0) (t = 0) = p0 , gives
                                                               (0)




     ( p (1) − p0 xl )
                            ¡




                 (0)
                          = e kxl t                                                                            (2.4)
¢                                   £




     ( p (1) − p (0) xl )
¤                           ¥




The number average MW, Mn is defined as p (1) / p (0) , and the above equation reduces

to

                    −1
           ( xl − M n 0 )
       ¦                §




ln                        = ln( H ) = kxl t                                                                   (2.5)
       ¨                        ©




                    −
           ( xl − M n 1 )
                       




2.4 RESULTS AND DISCUSSION

Figure 2.1a and 2.1b shows the molecular weight dynamics during the sonication

reaction. The sharp fall in molecular weight during the beginning of the process is

typical characteristics of ultrasonic degradation. The molecular weight curves steadily

approaches a limiting value depending on the nature of the reacting system. The

limiting molecular weight is found to be linear with temperature (Figure 2.2).

               Figure 2.3a and 2.3b shows the variation of H with time for the ultrasonic

degradation of isotactic polypropylene and polybutadiene, respectively. The semi-log

plots are nearly linear, confirming the validity of Eq.(2.5). The degradation rate
                                                                                          12
coefficients were determined from the regressed slopes. The rate coefficients, k

(×108 mol g −1 s −1 ) , for isotactic poly propylene decreased from 0.94 to0.28 as the

temperature increased from 80 to 155 0 C. The rate coefficients, k (×108 mol g −1 s −1 ) for

polybutadiene decreased from 0.76 to 0.25 as the temperature increased from 32 to

70 0 C. As the rate coefficients decrease with an increase in temperature, an Arrhenius

plot would yield negative activation energies and would not have any physical

meaning. The decrease of degradation rate with an increase of temperature is similar to

that observed for mechanical breakage of polymers. As the temperature of the solution

increases, a large

quantity of the solvent vapour enters the cavitation bubbles during their expansion and

exerts a cushioning. effect [3] during the collapse leading to diminishing of the

intensity of the shock wave, reducing the jet velocity [19]leading to reduced

degradation at higher temperatures. The same phenomena can be used to explain the

decrease of the degradation rate coefficients with an increase in the vapour pressure of

the solvent (Figure 2.4). While kinematic viscosity of the solvent was assumed to play

a role in the ultrasonic degradation [20,21], a more detailed study [16]indicated that

this could be a crucial parameter. Better transmission of the shock waves in solution of

higher kinematic viscosity [16] is a probable reason that explains the increase of

degradation rate coefficients with increasing kinematic viscosity (Figure 2.5).The

limiting molecular weight obtained for the degradation of polybutadiene and

polypropylene is similar to the limiting molecular weight obtained for the ultrasonic

degradation of polystyrene [7,8], poly(vinyl acetate) [15] and poly(methyl

methacrylate) [22].However, the degradation rate coefficients for polybutadiene and

polypropylene are higher than the degradation rate coefficients of polystyrene [8],
                                                                                        13
poly(vinyl acetate) [15] and poly(methyl methacrylate) [22].The variation of the rate

coefficients with increase in temperature, vapour pressure and kinematic viscosity is

consistent with the observations for other polymers in the literature [3,7,15,22].

       The effect of initial molecular weight on the degradation rate of polyethylene

oxide was investigated. Figure 2.6 shows this plot and the lines are obtained by simple

linear regression. The rate coefficient, kd, is directly obtained by dividing the slope of

the regressed line with the limiting molecular weight. The variation of the rate

coefficient, kd, with the initial molecular weight is shown in Figure 2.8. Though the rate

coefficient, kd, should be independent of the initial molecular weight, it is dependent on

the initial molecular weight and increases linearly with increasing initial molecular

weight (Figure 2.8). Another model is proposed in which the degradation rate, κ(x), is

assumed to be of the form κ(x) = kd (x-xl)λ but λ is not assumed to be a constant.

Instead, the rate coefficient, kd, is assumed to be independent of the initial molecular

weight and equal to 10-10 mol g-1 s-1. The governing population balance equation (2.2) is

solved numerically using the finite difference technique, as discussed in details in the

literature [28]. The value of         is determined from the non-linear regression of the

experimental data with the numerical solution of the theory. The theoretical fitting of

the experimental data indicates that the model fit is very good (Figure 2.7). The value

of is found to be dependent on the initial molecular weight and varies from 1.4 to 1.34
   




as the initial molecular weight of the polymer varies from 105 to 106, as shown in

Figure 2.3. The decrease of λ with increasing initial molecular weight is consistent with

the observation of experimental data for ultrasonic and elongational flow [23], wherein

it was observed that λ approaches zero for very large initial molecular weights. The

assumption of λ   ¡   1 for modeling the degradation kinetics for ultrasonic degradation is
                                                                                         14
consistent with the modeling the degradation kinetics for thermal degradation [22].

The non-linear dependence of the degradation rate on the initial molecular weight can

thus be directly accounted by varying the exponent (scaling factor), λ.

2.5 CONCLUSION

          The ultrasonic degradation of two commercially important polymers,

polybutadiene and isotactic polypropylene, has been investigated. The evolution of the

molecular weight was determined by gel permeation chromatography and a model

based on continuous distribution kinetics was used to determine degradationrate

coefficients. The degradation rate decreased with increasing temperatures, increasing

vapour pressure and decreasing kinematic viscosity of the solvents.

          The ultrasonic degradation of an aqueous solution of poly (ethylene oxide) of

different initial molecular weights was investigated at 30 oC. The ultrasonic rate

coefficient, κ, was assumed to be of the form, κ = kd ( x − xlim )λ , where x and xlim

represent the molecular weight and limiting molecular weight, respectively. For λ=1,

expressions were derived analytically and the experimental data was fitted to the theory

by linear regression. This indicated that the degradation rate coefficient, kd, was linearly

dependent on the initial molecular weight. Another approach was envisaged wherein kd

was assumed to be independent of the molecular weight and the value of λ was

determined by non-linear regression by solving the population balance equation

numerically. The value of λ exponentially decreased with increasing initial molecular

weight.
                                                                                  15
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 1. Jellinek, H. H. G., Editor. Degradation of vinyl polymers. New York: Academic

    Press (1955).

 2. Price, G. J., “The use of ultrasound for the controlled degradation of polymer

    solutions,” Advances in Sonochemistry, Jai Press. (1990).

 3. Thomas, G. R., “Sonic degradation of high polymers in solution” J. Phys.

    Chem., 63,1725 (1959).

 4. Okuyama, M., and Hirose, T. J., “Physicochemical approach to ultrasonic

    cavitation: Dynamics on ultrasonic cavitation from the viewpoint of

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 5. Pritchard, N. J., Hughes, D.E., and Peacocke, A. R., “Ultrasonic degradation of

    biological macromolecules under conditions of stable cavitation. I. Theory,

    methods, and application to deoxyribonucleic acid,”Biopolymers, 4, 259 (1966).

 6. Peacocke, Arthur R.; Pritchard, N. J., “Ultrasonic degradation of biological

    macromolecules under conditions of stable cavitation. II. Degradation of

    deoxyribonucleic acid”.Biopolymers, 6, 605 (1968).

 7. Thomas, B.B., and Alexender, W.J., “Ultrasonic Degradation of Cellulose

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 8. Nelkenbaum, Y.Y., Prokofrev, I.K., and Sangalore., Y.A., “Ultrasonic

    Degradation Of Poly Iso-Butylene,” Vyskomolek Soedin Ser A., 29, 2395

    (1986).

 9. Basedow, A.M., and Ebert, K.H., “Mechanism of Degradation of Polymers in

    Solution by Ultrasound,” Makromole. Chem., 176, 745 (1975).
                                                                                16
10. Basedow, A.M., Ebert, K.H., and Fosshag, E., “Ultrasonic Degradation of

   Polymers in Mixed Solvents,’ Makromole. Chem.., 179, 2565 (1978).

11. Malhotra, S.L., “Ultrasonic Degradation of Hydroxy propyl cellulose solutions

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   601(1982).

12. Price, G.J., Smith, P.F., “Ultrasonic Degradation of Polymer Solutions: III.

   Effect of Changing solvent and Solution Concentration, ” Polym. J., 29, 419

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13. Scmid, G. Z., “Effect of ultrasonic vibrations on the magnetic properties of

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14. McCoy, B. J., Madras, G., “Degradation Kinetics of Polymers in Solution:

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15. McCoy, B. J., Madras, G., “Oxidative Degradation Kinetics of Polystyrene in

   Solution,” Chem. Eng. Sci., 52, 2707 (1997).


16. Perry, R.H., and Chilton, C.H., Editors, Chemical Engineers Handbook,

   McGraw-Hill, New York (1973).

17. Brandrup J, Editor, Polymer handbook, John Wiley, New York (1975).

18. 'The properties of liquid and gas' Reid; R.C, Sherwood; T.K, Second Edition,

   McGraw -Hill Book Company 1965.

19. Jellinek, H.H. J., “Degradation of long chain molecules by ultrasonic waves.

   VII. Effect of viscosity and surface tension on cavitation” Polym. Sci., 22 149

   (1956)
                                                                                  17
20. Basedow, A. M., Ebert, K. H., “Determination of molecular weight

   distributions and mean values of the molecular weight of clinical dextrans,”

   Makromol. Chem., 176 745 (1975).

21. Madras, G., Chottopadhyay, S., “Effect of solvent on the ultrasonic degradation

   of poly(vinyl acetate),” Polymer Degradation and Stability , 71, 273 (2001).


22. Madras, G., Chung, G. Y., Smith, J. M., McCoy, B. J., “Mol. Wt. effect on the

   dynamics of polystyrene degradation,” Ind. Eng. Chem. Res., 36, 2019 (1997).

23. Nguyen, T. Q., Liang, Q. Z., and H. H. Kausch, “Kinetics of Ultrasonic and

   Transient Elongational Flow Degradation: A Comparative Study”, Polymer, 38,

   3783(1997).

24. Ederer, H. J., Basedow, A. M. and Ebert, K. H., in Modelling of Chemical

   Reaction Systems, ed. K. H. Ebert, P. Deuflhard and W. Jagger. Springer-

   Verlag, Berlin, 1981, p. 189.

25. Price, G. J., “The Use of Ultrasound for the Controlled Degradation of

   PolymerSolutions”. Mason T. J. Editor, Advances in Sonochemistry Vol I,

   Cambridge Jai Press, p 231 (1990).

26. Florea, M., “New use of size exclusion chromatography in kinetics of

   mechanical degradation of polymers in solution”, J. Appl. Polym. Sci, 50,

   2039(1993).

27. Mason, T. J. and Lorimer, J. P., Sonoehemistry: Theory, Applications and Uses

   of Ultrasound in Chemistry. Ellis Horwood, New York, 1989, Ch. 2



28. Madras, G., McCoy, B.J., “Molecular Weight Distribution Kinetics for

   Ultrasonic Reactions of Polymers,” AIChE. J 47, 2341(2001).
                                                                                        27



        140000


        120000


        100000


         80000
   Mn




         60000


         40000


         20000


            0
                 0   20       40       60          80       100       120   140   160
                                                Time(min)


Figure 2.1a. Evolution of molecular weight of isotactic poly (propylene) in ODCB
                                   ¡




                 Legends: 80°C 90°C 113°C 133°C 155°C
                                            ¢           £         ¤
                                                                                                28


     110000

     100000

      90000

      80000

      70000
Mn




      60000

      50000

      40000

      30000

              0   20    40    60       80       100       120       140   160       180   200
                                    Sonication time(min)



Figure 2.1b. Evolution of molecular weight with time for poly (butadiene) in ODCB
                                            ¡




                        Legends: 80 C 70 C 30 C 60 C 50 C
                                                      ¢         £         ¤      
                                                                               29


                    4
           5.0x10
                    4
           4.8x10
                    4
           4.6x10
                    4
           4.4x10
                    4
           4.2x10
                    4
           4.0x10
                    4
           3.8x10
    Mlim




                    4
           3.6x10
                    4
           3.4x10
                    4
           3.2x10
                    4
           3.0x10
                    4
           2.8x10
                    4
           2.6x10
                        20   40   60    80      100     120     140     160
                                                          0
                                   Reaction temperature( C)



Figure2.2. Variation of the limiting molecular weight with temperature in o-
dichlorobenzene for the ultrasonic degradation of isotactic polypropylene ( ) and
polybutadiene ( ).
                 
                                                                                     30




             2.0




             1.5
    log(H)




             1.0




             0.5




             0.0
                   0   20    40        60           80       100           120
                                      Time(min)



Figure2. 3a. Ln(H) vs. sonication time for isotactic poly(propylene) in ODCB
                                            ¡




                                   




at various temperature. Legends: 80 C 90 C 113 C 133 C 155 C
                                                 
                                                    ¢
                                                          
                                                             £
                                                                       ¢          
                                                                                           31


        3.0



        2.5



        2.0
Ln(H)




        1.5



        1.0



        0.5



        0.0
              0   20   40   60    80       100       120       140       160   180   200
                                    Time(min)


   Figure 2.3b. Ln(H) vs. sonication time for poly(butadiene) in ODCB at various
                                                 ¡




                                        




                   temperature. Legends: 32°C 50°C 60°C 70°C
                                                           ¢         £
                                                                                                                             32


                                            -7
                                       6x10
                                            -7
                                       5x10
                                            -7
       Rate coefficient (mol g min )
       -1                              5x10
                                            -7
                                       4x10
       -1




                                            -7
                                       4x10
                                            -7
                                       3x10
                                            -7
                                       3x10
                                            -7
                                       2x10
                                            -7
                                       2x10
                                            -7
                                       1x10
                                            -8
                                       5x10
                                            0
                                                         0.0    0.1        0.2         0.3   0.4        0.5      0.6
                                                                       Vapor pressure(bar)



Figure 2.4. Vapor pressure of solvent vs. rate coefficient(k) Legends: PP(ODCB) at                          




                                                 ¡




different temp. PB(ODCB) at different temp PB (Chlorobenzene) at 32°C              ¢                              £
                                                                                                                       PB(

Benzene) at 32°C                                     ¤
                                                         PB(THF) at 45°C   ¡   PB(Toluene) at45°C   ¢   PB(Chloroform) at

45°C     £                             PB(Xylene) at 45°C.
                                                                                                             33


                                      -7
                                   6x10
                                      -7
                                   6x10
                                      -7
                                   5x10
     min )
     -1
                                      -7
                                   5x10
                                      -7
                                   4x10
     -1
     Rate Coefficient (mol g


                                      -7
                                   4x10
                                      -7
                                   3x10
                                      -7
                                   3x10
                                      -7
                                   2x10
                                      -7
                                   2x10
                                      -7
                                   1x10
                                      -8
                                   5x10
                                      0
                                      0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
                                                                                   2
                                                             Kinematic viscosity(cm /sec)



                                                                                                          




Figure 2.5. Kinematic Viscosity of the solvent vs. rate coefficient(k)Legends:
                                                     ¡




PB(ODCB) at different temp.                              PB(Chlorobenzene) at 32°C.        PB(Toluene)

at45°C .                       £    PB(Xylene) at 45°C. PB(Chloroform) at 45°C.
                                                         ¤                         £       PB(THF) at

45°C. PP(ODCB) at different temp. ----- Linear fit for PB . —— Linear fit for PP.
                ¡
                                                                                     34



            1.4


            1.2


            1.0


            0.8
     ln H




            0.6


            0.4


            0.2


            0.0
                  0       50           100          150          200
                                           Time (min)



Figure2.6. Variation of the molecular weight with time, based on Eq 2.5. The lines

are obtained from linear regression and the slope corresponds to the degradation rate

coefficient, kd. See Figure 1 for legend
                                                                                                               35




              1.0                                           10




                                             5
                                                 M n x 10
              0.8
                                                            1

              0.6
     Mn/Mn0




                                                                 0     50    100     150   200     250
              0.4
                                                                     Sonication Time(min)

              0.2



              0.0


                    0           50          100                        150             200               250
                                        Sonication Time(min)


Figure 2.7. Variation of the non-dimensional number-average molecular weight with

time. The inset of the figure shows the variation of the molecular weight with time.

Legends             Mn0 = 105; ♦Mn0 = 2 x 105;    ¡    Mn0 = 6 x 105;         ¢    Mn0 = 106;    _______
                                                                                                           Model
                                                                                                    36


                                                                             5.4
         1.40
                                                                             5.2




                                                                                   -1
                                                                                   kd (x 10 ) mol g s
         1.39




                                                                                   -1
                                                                             5.0
         1.38
                                                                             4.8




                                                                                   -9
         1.37
   λ




                                                                             4.6
         1.36
                                                                             4.4
         1.35
                                                                             4.2
         1.34
                                                                             4.0
                0         2          4          6         8          10
                                                              5
                     Initial Molecular Weight (x 10 )

Figure 2.8. Variation of λ and kd with the initial molecular weight of the polymer.

The lines in the graph represent exponential decay and linear fit for the variation of λ

and kd with the initial molecular weight, respectively
                                                                                        37

CHAPTER 3

MICROWAVE ASSISTED OXIDATIVE
DEGRADATION OF POLYETHYLENE OXIDE


3.1 INTRODUCTION

       Growing     interest   in   non-conventional    methods        of   polymerization-

depolymerization has lead to research on applications of microwaves for these

processes. Microwave heating offers increased reaction rates and reduced electrical

consumption, compared to thermal heating, as observed in several organic synthesis

reactions [1-2]. There is a better distribution of heat in the sample and hence better

control over the process. Moreover, the efficiency of converting electrical energy to

thermal energy is over 85 % and the rate of heating is many times faster than thermal

heating [3]. Microwaves are known to enhance the solid-state polymerization of PET

and nylon 66 by increasing the overall diffusion rates and reducing the activation

energy for the diffusion process [4]. Improved polymerization of caprolactone

initiated by carboxylic acids was observed on microwave irradiation [5]. However,

lower Mw was obtained with increasing acidity of the initiator due to simultaneous

degradation of the formed polymer. Microwave polymerization of methyl

methacrylate showed marked dependence on microwave power. The reaction rate

increased with microwave power because of increased heating rate at comparable

temperature with thermal heating [6]. The emulsion polymerization of styrene was

studied in a microwave reactor. The results showed that the monomer-water ratio,

microwave power, volume of reaction mixture and geometry of vessel used were

important factors to be considered to accelerate heating rates [7].
                                                                                   38
        The pyrolysis of lignin and cellulose could be manipulated to improve

product selectivity by rapid homogenous heating by microwaves. The rate

enhancement during pyrolysis was also observed [8-9]. The surface oxidation of

polyethylene with permanganate was studied by FT IR when microwaves were made

to impinge on solid samples [10]. Starch degradation in microwaves was studied by

Khan et.al. [11]. The hydrolysis of starch occurred at high temperatures and pressures

produced in a sealed glass ampule, with increase in total acidity and a concurrent

decrease in pH. The thermo-oxidative degradation of edible fats by microwave and

conventional heating was studied. It was found that greater amount of alterations

occurred on microwave-heated samples as quantified by chromatographic techniques

[12].

        The microwave heating effect arises when polarizable molecules tend to

reorient and align themselves in an applied microwave field. The ability to convert

microwave energy to thermal energy depends on the dielectric constant and dielectric

loss associated with a material. Greater effects are observed when the material

involved has a greater dielectric constant at a given microwave frequency and power

[13]. The heating effect by microwaves is unique because heat is generated internally

within the material. Therefore, it heats the material from inside. There is

instantaneous heating, which is volumetric and specific to the material. Also it has

been found that microwave heating does not alter the composition of products

appreciably when compared to those produced by conventional heating techniques

[7]. Water couples with microwaves to a greater extent because of its high dielectric

constant. Hence reactions with water are expected to proceed at faster rates by

microwave heating over conventional thermal heating. Polymer degradation in
                                                                                     39
aqueous solutions is a viable approach to study the kinetics of the degradation

process by the application of microwave energy.

        In the present study we have aimed to look in to the oxidative degradation of

polyethylene oxide by persulfate under microwaves by changing cycle times and the

number of the cycles of irradiation. The effect of persulfate concentration on the

reaction kinetics was also investigated. Continuous distribution kinetics was used to

obtain the degradation rate parameters by non-linear regression of the experimental

data.

3.2 EXPERIMENTAL SECTION

3.2.1 Materials

        Polyethylene oxide (Aldrich Co) and potassium persulfate (S. D. Fine

Chemicals) were used as obtained.

3.2.2 Microwave reactor

        A domestic microwave oven with a magnetron source for microwave

generation was used (Essentia, India). The maximum power was 700 W with a

frequency of 2.45 GHz. All experiments were conducted at the maximum power of

the equipment.

3.2.3 Degradation experiments

        The polymer solution concentration taken was 2 kg/m3. The reaction vessel

was a glass beaker of 50 ml capacity. The volume of the solution taken was 40 ml for

all the experiments. Three different concentrations of persulfate were used. The

required persulfate was added and stirred to dissolve before starting the irradiation of

the sample polymer solution. The sample was placed at the center of the oven directly

below the magnetron source. Different microwave cycle times (th) were employed like
                                                                                      40
10, 15, 20 s and the number of cycles was fixed at 10 cycles. Therefore, for 10, 15

and 20 s cycles the total irradiated time was 100, 150 and 200 s. To ensure uniform

heating and to avoid temperature gradients, the sample was rotated on a turntable. The

temperature of the reaction mixture was monitored with a fluoro-optic thermometer

with an accuracy of ± 0.5 ºC. The irradiated sample was cooled to 22 ºC by immersing

in an ice-bath for a set time of 110 s (tc).

3.2.4 GPC Analysis

            The molecular weight distribution was monitored by Gel Permeation

chromatography. The GPC consisted of Waters Ultrahydrogel linear SEC column

measuring 7.8x300 mm maintained at 50°C. Double distilled deionized water was

used as eluent at a flow rate of 0.5 ml/min. The refractive index was monitored

continuously with a Waters 401 Differential Refractometer. About 800 µl of sample

was injected into the system to obtain a chromatogram and converted to molecular

weight by using narrow-distribution polyethylene oxide calibration standards.



3.3 RESULTS AND DISCUSSION

3.3.1 Theoretical model

The homolytic cleavage of persulfate in to two radicals can be written as

C2  2C •
      →
    p   k
                                                                            (3.1)

The rate of persulfate disappearance by dissociation is

dc p
       = −k p c p                                                           (3.2)
 dt
                                                                                         41
where cp denotes the molar concentration of persulfate. The hydrogen abstraction

from polymer chain occurs through these radicals resulting in the formation of

polymer tertiary radicals. This is written as follows

C • + P ( x )  CH + R • ( x )
               d( )
                    →
                             k    x
                                                                                 (3.3)

The population balance for the consumption of persulfate radicals can be written as


dc ( t ) dt = −2k p c p ( t ) − c ( t ) ∫ kd ( x ' ) p ( x ', t ) dx '
                                                       ∞
                                                                                 (3.4)
                                                           0




The temperature variation during microwave heating was found to vary linearly with

time. The temperature profile for each cycle can be assumed to be


                         Tpeak − Tw
               




                  Tw +                    t                    ∀t ∈ ( 0, th )
          ¡




          ¡




                                 th
T=                                                                               (3.5)
                            Tpeak − Tw
      ¢




          ¡




          ¡




                  Tpeak −                     ( t − th )        ∀t ∈ ( th ,τ )
                                 τ − th
              £




The initiation and termination steps for the polymer can be represented by a reversible

reaction


P ( x)                R• ( x ') + R• ( x − x ')                                  (3.6)
                  ¤




But since these steps are not frequent when compared with the propagation step they

can be neglected [14]. Hydrogen abstraction from the polymer chain can also occur

through a polymer radical. This is a reversible reaction and can be given by


P ( x ) R• ( x ')                                                                (3.7)


The propagation step occurs by the irreversible β-scission of the polymer chain and

can be written as
                                                                                                                      42
R • ( x )  R • ( x ') + P ( x − x ' )
           ks
              →                                                                                              (3.8)


The population balance equations for polymer and polymer radical are


∂p ( x, t ) ∂t = −kd ( x ) c ( t ) p ( x, t ) − kh ( x ) p ( x, t ) + k H r ( x, t )

                          + ∫ ks ( x ' ) r ( x ', t ) Ω ( x, x ' ) dx '
                               ∞                                                                             (3..9)
                                 x




∂r ( x, t ) ∂t = kd ( x ) c ( t ) p ( x, t ) + kh ( x ) p ( x, t ) − k H r ( x, t ) − k s ( x ) r ( x, t )

                        + ∫ k s ( x ' ) r ( x ', t ) Ω ( x, x ') dx '
                           ∞
                                                                                                             (3.10)
                           x




For random chain scission, the stoichiometric kernel is given by 1/x' [14]. Then by

applying moment operation we get


dp j                                                                k
     = −kd c ( t ) p ( j +1) ( t ) − kh p ( j +1) + k H r ( j +1) + s r ( j +1)                              (3.11)
 dt                                                                j +1


dr j                                                                     j ( j +1)
     = kd c ( t ) p ( n +1) ( t ) + kh p ( j +1) − k H r ( j +1) − k s      r                                (3.12)
 dt                                                                    j +1


Quasi-steady state approximation can be applied to equation (3.12) and the radical

concentration can be given by


                                       k d c ( t ) + kh
r ( j +1) = ( j + 1) p ( j +1)                                                                               (3.13)
                                     jk s + ( j + 1) k H


The simultaneous solution of equations (3.11) and (3.13) gives the jth moment in

terms of known quantities.
                                                                                    43
dp ( j)
                      kd c ( t ) + kh
    = − ( j − 1) ks                     p( j +1)                           (3.14)
 dt                 jk s + ( j + 1) k H


When j=0, the molar concentration of polymer can be known and equation reduces to


 dp ( 0)
         = k0 p (1)                                                        (3.15)
  dt


where the overall rate coefficient k0 is given by koxd c ( t ) + ktherm . The oxidative

degradation coefficient, koxd , is kd ks k H and the thermal degradation coefficient in

the absence of persulfate, ktherm , is kh ks k H . Since experimental observation shows

that no degradation occurred in the absence of persulfate, the contribution from

thermal degradation can be neglected, and therefore k0 = koxd c ( t ) . Thus equation

(3.15) becomes


dp ( 0)
        = koxd c ( t ) p (1)                                               (3.16)
 dt

The simultaneous solution of equation (3.16) along with equations (3.2) and (3.4)

gives the time evolution of number-average molecular weight with the initial set

conditions and temperature dependency. The rate coefficients and activation energies

for hydrogen abstraction and random oxidative chain scission can be found by non-

linear regression of experimental data.

3.3.2 Microwave degradation

          The microwave assisted oxidative degradation of polyethylene oxide was

studied at different heating cycle time varying from 10 to 20 sec cycles and at

different concentrations of persulfate ranging from 0.2 kg/m3 to 1.0 kg/m3. When the

polymer solution is exposed to microwave radiation in the presence of persulfate rapid
                                                                                                                 44
degradation occurs. No degradation occurred in the absence of persulfate. The

variation of Mn0/Mn with time for three different persulfate concentrations is shown in

Figure 3.1a, 3.1b and 3.1c. The rate of decrease is greater with greater concentration

of persulfate and the degradation was found to be rapid during the initial stages of

irradiation. The points are from experiment and the solid line is from theory. As seen

from the figures there is good agreement between theory and experimental data. No

degradation was observed at 10 sec cycle time with 0.2 kg/m3 concentration of

persulfate. The accelerated degradation by microwaves can be attributed to the

volumetric heating of the sample and the improved mixing of the solution due to

microstirring by the absorption of microwave energy by molecules. The rate of radical

formation is also enhanced because of inherently high temperatures produced in

shorter times thereby increasing the overall rate of the degradation. Degradation of

polyethylene oxide under similar conditions (for a fixed time, temperature and

concentration of persulfate) was done by thermal heating and it was found that the end

molecular weight obtained at the end of 5 min of thermal degradation was many times

higher than the molecular weight obtained after microwave degradation of the sample.

This clearly indicates that at comparable temperatures too there exists a definite

"microwave effect" which clearly enhances the rate of degradation.

         The kinetic parameters for the degradation can be obtained by non-linear

regression of the experimental data. Dependence of rate coefficient on temperature

was assumed to be of Arrhenius form. The rate coefficients for persulfate

decomposition, hydrogen abstraction and oxidative random scission are given by

               − E p / RT
k p = k p 0e                , kd = kd 0 e − Ed / RT and koxd = koxd 0 e− Eoxd / RT . Since the rate coefficients are

temperature dependent the temperature terms in the expressions were replaced by
                                                                                                        45
equation (3.5) The decomposition of persulfate is well known and the rate

coefficient for the homolytic cleavage is given by k p = 38.4e−33500 / RT [15]. The values

are for kd and koxd are obtained by solving equations (3.2), (3.4) and (3.16) by

incorporating the above expressions for rate coefficients. The initial conditions are set

       ( 0)
as p          ( t = 0 ) = p0( 0) ,   c p ( t = 0 ) = c p 0 and c ( t = 0 ) = 0 . The non-linearly regressed

values of rate coefficients are kd = 19.0e −7700 / T and koxd = 12.5e −5200 / T .

              The theoretical variation of persulfate and radical concentration with heating

and cooling time is shown in Figure 3.2a and 3.2b. The fit is for 0.4 kg/m3 of

persulfate concentration at 15 s heating cycle time and 110 s cooling time. The

persulfate concentration decreases rapidly during heating and slowly during cooling

times. The concentration of radicals is zero initially. It rises during heating cycle and

falls during cooling cycle. After the first cycle, the radical concentration variation

becomes periodic with time. The highest radical concentration is obtained during

heating cycle when the temperature is highest.



3.4. CONCLUSIONS

              The degradation of polyethylene oxide under microwave irradiation in the

presence of persulfate was studied at various heating times and concentrations of

persulfate. The kinetic parameters were obtained from model based on continuous

distribution kinetics, by non-linear regression of experimental data. The microwave

degradation was found to be faster and more efficient than degradation by

conventional thermal heating. Higher degradation was found at higher concentrations

of persulfate and higher microwave heating cycle times.
                                                                                  46




REFERENCES

1. Gedye, R., Smith, F., Westaway, K., Ali, H., Baldisera, L., Laberge, L., Rousell,

   J., “The Use of Microwave Ovens for Rapid Organic Synthesis,” Tetrahedron

   letters, 27, 279 (1986).

2. Giguere, R. J., Bray, T. L., Duncan, S. M., “Application of Commercial

   Microwave Ovens to Organic Synthesis,” Tetrahedron letters, 27, 4945(1986).

3. Ludlow-Palafox, C., Chase, H. A., “Microwave-Induced Pyrolysis of Plastic

   Wastes,” Ind. Eng. Chem. Res, 40, 4749(2001).

4. Mallon, F. K., and Ray, W.H., J. “The Effect of the Type of Purge Gas on the

   Solid-State Polymerization of Polyethylene Terephthalate,” App. Polym. Sci., 69,

   1203(1998).

5. Zhang, C., Liu, L. J., and Zhuo, R. X., J. Polym. Sci. Part A: Polym. Chem., 41,

   13(2003).

6. Jacob J, Chia LHL, Boey FYC, “Microwave Polymerization of poly(methyl

   acrylate): Conversion Studies at Variable Power”, J. App. Polym. Sci., 63, 787

   (1996).

7. Correa, R., Gonzalez, G., Dougar, V., “Emulsion Polymerization in a Microwave

   Reactor,” Polymer, 39, 1471(1998).

8. Chan, R. W. C., and Krieger, B. B., “Kinetics of dielectric-loss Microwave

   Degradation of Polymers: Lignin,” J. App. Polym. Sci., 26, 1533(1981).
                                                                                  47
9. Allan, G.G., Krieger, B. B., and Donald, W., “Dielectric Loss Microwave

   Degradation of Polymers: Cellulose,” J. App. Polym. Sci., 25, 1839(1980).

10. Mallakpour, S. E., Hajipour, A. R., Mahdavian, A. R., Zadhoush, A., and

   Hosseini, F. A., “Microwave assisted oxidation of polyethylene under solid-state

   conditions with potassium permanganate,” Eur. Polm. J., 37, 1199(2001).

11. Khan, A. R., Johnson, J. A., and Robinson, R. J., “Degradation of starch polymers

   by microwave energy,” Cereal Chemistry, 56,303(1979).

12. Albi, T., Lanzon, A., Guinda, A., Leon, M., Perez-Camino, M. C., “Microwave

   and Conventional Heating Effect on Thermooxidative Degradation of Edible

   Fats,” J. Agri. Food Chem., 45, 3795(1997).

13. Caddick, S., “Microwave Assisted Organic Reactions,” Tetrahedron, 51,

   10403(1995).

14. Kodera, Y., and McCoy, B., “Distribution Kinetics of Radical Mechanism:

   Reversible Polymer Decomposition,” AIChE J., 43, 3205(1997).

15. Bandyopadhyay, M., Konar, R. S., “Thermal Decomposition of Persulphate in the

   Aqueous Media,” J. Indian Chem. Society, 51,722(1974).
                                                                           xlviii


         3.5


         3.0


         2.5
Mn0/Mn




         2.0


         1.5


         1.0
               0    30      60      90      120     150     180      210
                                    Time (sec)



         Figure 3.1a. Variation of Mn0/Mn with time with 0.2 kg/m3 of persulfate
                                                                          xlix


         4.5

         4.0

         3.5

         3.0
Mn0/Mn


         2.5

         2.0

         1.5

         1.0
               0   30   60     90     120     150     180     210

                             Time (sec)



 Figure 3.1b Variation of Mn0/Mn with time with 0.4 kg/m3 of persulfate
                                                                           l


         7

         6

         5
Mn0/Mn


         4

         3

         2

         1
             0   30   60      90     120     150    180     210
                            Time (sec)



  Figure 3.1c Variation of Mn0/Mn with time with 1.0 kg/m3 of persulfate
                                                                                               li

                                             -3
                                        1.5x10

                                             -3
                                        1.5x10



         Persulfate conc.(cp),kmol/m3
                                             -3
                                        1.5x10

                                             -3
                                        1.5x10

                                             -3
                                        1.5x10

                                             -3
                                        1.5x10

                                             -3
                                        1.5x10

                                             -3
                                        1.5x10

                                                  0   200   400    600     800   1000   1200
                                                                  Time,s


Figure 3.2a Theoretical prediction of persulfate concentration with heating and

cooling cycles
                                                                                                lii


                                              18

                                              16




          Radical concentration (c) kmol/m3
                                              14

                                              12

                                              10

                                              8

                                              6

                                              4

                                              2

                                              0
                                                   0   200   400    600     800   1000   1200
                                                                   Time,s



Figure 3.2b Theoretical prediction of radical concentration with heating and cooling

cycles
                                                                                   liii

CHAPTER 4
CONCLUSIONS AND FUTURE WORK



4.1 CONCLUSION
      The ultrasonic degradation of two commercially important polymers,

polybutadiene and isotactic polypropylene, has been investigated. The degradation

rate coefficient has been calculated from a modle based on continuous distribution

kinetics. The rate coefficient is found to be decreased with increasing temperatures,

increasing vapour pressure and decreasing kinematic viscosity of the solvents.

       The ultrasonic degradation of an aqueous solution of poly (ethylene oxide) of

different initial molecular weights was investigated at 30 oC. The ultrasonic rate

coefficient, κ, was assumed to be of the form, κ = kd ( x − xlim )λ , where x and xlim

represent the molecular weight and limiting molecular weight, respectively. For λ=1,

expressions were derived analytically and the experimental data was fitted to the

theory by linear regression. This indicated that the degradation rate coefficient, kd,

was linearly dependent on the initial molecular weight. Another approach was

envisaged wherein kd was assumed to be independent of the molecular weight and the

value of λ was determined by non-linear regression by solving the population balance

equation numerically. The value of λ exponentially decreased with increasing initial

molecular weight.

       The degradation of polyethylene oxide under microwave irradiation in the

presence of persulfate was studied at various heating times and concentrations of

persulfate. The kinetic parameters were obtained from model based on continuous
                                                                                      liv
distribution kinetics, by non-linear regression of experimental data. The microwave

degradation was found to be faster and more efficient than degradation by

conventional thermal heating. Higher degradation was found at higher concentrations



4.2 FUTURE WORK

        Experiments and modeling can be done on ultrasonic degradation of polymers.

Although the mechanism of degradation is assumed to be mid point and it gives

reasonably good fit over experimental data, the nature of degradation is yet to be

explored completely. Some more experimentation may give insight into the actual

process. Dependence of rate constant on solvent parameters should be studied more

thoroughly. Effect of intensity and power on limiting molecular weight is an

interesting field of study.

        In terms of the simulation and theoretical study, ample scope can be found in

exploring the most suitable kinetics of ultrasonic degradation. The population balance

equation can be solved with different stoichiometric kernel and rate expression that

can be physically meaningful. The existence of limiting molecular weight and

nonlinear dependence made this problem more interesting.

        Like microwave assisted degradation, microwave assisted simultaneous

polymerization and degradation is an interesting phenomenon to study. That can be

studied and the kinetics can be explored. Study of effect of different parameters can

also be conducted.
lv

								
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