Appendices

Appendices -

List of Publications

1. Transpolt of styrene monomer through natural rubber Aji P. Mathew, S. Packirisamy, M.G. Kumaran and Sabu Thomas, Po/ymer 36(26), 4935 (1995)

2. Kinetics of diffusion if styrene monomer containing divinyl benzene through vulcanized natural rubber Aji P. Mathew, S. Packirisamy, A. S. Padmanabhan and Sabu Thomas, J. fblym. Eng., 17(5), 405 (1997)

3. Sorption and diffusion of acrybnitrile monomer through crosslinked nitrile rubber A.S. Aprem, A .P. Mathew, K. Joseph and S .Thomas J. Appl. Polym. 2i. (in press)

4. Morphology, mechanical properties and failure topography of semi-interpenetrating polymer networks based on natural rubber and polystyrene Aji P. Mathew, S. Packirisamy and Sabu Thomas, J, Appl. Pdym. Sci, (communicated)

5. Viscoebstic properties of nano-structured natural rubber/polystyrene interpenetrating polymer networks Aji P. Mathew , G. Groeninkoc, HJ. Raduxh, G.H. Michler and h b u Thomas, Polymer(communicated)

6. Izod impact behavior of natural rubber/polystyrene interpenetrating polymer networks Aji P. Mathew and Sabu Thomas, J. Mater. ki.(communicated)

7. Effect of initiating system, blend ratio and crosslink density on the mechanical properties and failure topography of nano-structured full-interpenetrating polymer networks from natural rubber and polystyrene Aji P. Mathew, S. Packirisamy, and Sabu Thomas, Eur, Powm. J. (communicated)

8. Studies on the thermal stability of Natural rubber/poh/styrene interpenetrating polymer networks: thermogravimebic analysis Aji P. Mathew, S. Packirisamy and Sabu Thomas, 77?ermodtim. Acta.(communicated)

9. Swelling Behaviour of Natural Rubber / Polystyrene (NR/PS) Interpenetrating Polymer Networks in Various Organic Solvents and Oils Afi P. Mathew S. Packirisamy, A. S. Padmanabhan and Sabu Thomas, J. Membr. 9;. (communicated)

10. Electrical properties of Natural Rubber / Polystyrene (NRIPS) Interpenetrating Polymer Networks Aji P. Mathew, Hima Varghese, 5. Packirisamy, and Sabu Thomas I. Macromol. ki. Phys. (communicated)

Curriculum Vitae

Aji P. Mathew

Date of Birth llm February 1971

Sex Female

Nationality Indian

Religion Christian

Marital Status Married

Permanent Address Pallikunnel House, Pmthakuzhy P. 0. Pampady, Kottayarn, Kerala-686521. Phone: (0481) 506344.

Experience

+ 5 years of research experience in the field of polymer technology.

Educational

M. Sc. (Applied Chemistry) First Clas & First Rank, Mahatma Gandhi Univetsity.

Awards

Senior Research Fellowship (Council of Scientific &Industrial Research).

Prof. Shankarlal Memorial Award for best paper presentation (IT, Kharagpur 1995).

Rerearch Interests

Interpenetrating Networks: lPNs and characterisation.

Polymer Mends: Characterisation and Properties.

Polymer composites: Fabrication and properties - polymer fiber interface adhesion, fiber surface modification and characterisation . Transport pmess through polymers, its kinetics and thermodynamics,

E I N E M A N N IF=-=- Polvmcr Val. 36 No. 26. pp. 4935-4942, 1995 Copyrighl 1 1995 Elsevier Sftence Ltd

Printed ~n Grca, Brilaln. All rights reserved 0032~386liYS:$IO.O0+0.00

Transport of styrene monomer through natural rubber

Aji P. Mathew. S. Packirisamy*, M. G. Kumarant and Sabu Thomas$ School of Chemical Sc~ences, Mahatma Gandhi University, Priyadarshini Hills PO, Kottayam 686 560, Kerala, India (Received 14 November 1994; revised 2 0 February 1995)

The diffusion and transport ol inhibitor-free styrene through crosslinked natural rubber (NR) have been studied at various lemperatures. N R has been vulcanized by conventional, efficient, peroxide and mixed vulcanization techniques The dependence of diffusion coefficient on the crosslinking system has been studied for all the systems. The influence of temperature on the sorption and the activation energies of sorption have been calculated. The interaction parameter, permeability, sorption coefficient and molecular weight between crasslinks ha\c heen evaluated using the diffusion data. The effect of degree of crosslinking on the sorption chari~cteristics US styrene through NR has also been investigated for the different crosslinking systemr l'he peroxkdc system showed lowest uptake and the conventional system showed highest uptake.

(Keywords: crosslinked natural ruhkr; diffusion; sorption)

INTRODUCTION istics of the rubber in monomers are to he studied in

The diffusion properties of ditferenl liquids in polymers have been studied extensively by several authors'-6.

-Often the diffusion of liquid5 through rubbery polymers can be described by Fick's law of diffusion. However, there are instances where deviation from Fick's law has been observed. The transport phenomena of various solvents and monomers through polymers have also been investigated. The sorption properties of rubbery poly- mers are controlled by polymer structure. crosslink density, type of crosslinking. temperature. etc. In the study on swelling characteristics of natural rubber (NR) in aromatic hydrocarbon liquids. Harogoppad et ul. investigated the dependence of tranbport phenomena on polymer structure. The effect of crosslink density on diffusion has been observed by Poh et ul.' The dependents of swelling and ahsorption of $~FF samples on temperature have also been investigated Harogoppad el a / . made use of the temperature dependence of the transport coefficients to cstimate the activation parameters from the Arrhenius plots1.

The swelling and sorption behaviours of NR in various liquids are of great interest. as NR is a well known polymer having extensive usc in everyday life. The swelling of natural rubber sanlples In the presence of monomers like styrene, methyl metha~.rylate. acryloni- trile, butyl acrylate. etc., is of great research interest, since it constitutes the preliminarq step in the pre drd Pi- ;L tion of interpenetrating polymer netuorks (IPN) To prepare a rubber-based IPN. the swelling character-

--- - - ~~~~ -~

* PSC Division. VSSC. Thiruvi!nanillapurm. Kcra1;i. lndca t Deputy Director. QC Division. RRI I . Kott'iyarn 9 Kcrnla. lndta *To whom corrcspondencc should hc oddscised

detail. A clear and accurate knowledge about the swelling rate of the polymer in the monomers helps in controlling the composition, morphology and properties of the resulting IPN. However, no detailed investigation has been made so far on the kinetics of diffusion and sorption of styrene through natural rubber crosslinked by different curing systems such as conventional (CV), efficient (EV), peroxide (DCP) and mixed systems.

In this paper the swelling of NR in styrene monomer has been studied in the temperature range of 25-45°C. This will be the primary step for the development of IPN based on NR and polystyrene (PS) having various morphological features and property profiles. The NR was vulcanized by different techniques. viz. conven- tional, efficient, peroxide and mixed vulcanization systems. The influence of different vulcanizing systems on diffusion properties is analysed. For each crosslinking system, samples were vulcanized at different cure times so as to attain samples of different crosslink densities. The effect of crosslink density on sorption has been investigated. Finally the temperature dependence of diffusion and rubber-solvent interaction parameter x are determined.

EXPERIMENTAL Materials

The natural rubber (NR) used was of ISNR-5 grade and was supplied by Rubber Research Institute of India (RRII). The styrene monomer is made free of inhibitor by washing with 0.1% NaOH and dried using sodium sulfate before use for diffusion experiments. The chemicals used in the various vulcanizing systems are of laboratory reagent grade.

POLYMER Volume 36 Number 26 1995 4935

Transport of styrene through rubber: A. P. Mathev! et al

Sample preparation The formulations for different mixes are given in Ezble

I . The mixing was done in a two-roll mixing mill, as per ASTM procedure. The rheographs are taken for each mix to obtain the cure times (Figure 1). The mixes are cured at different time intervals: tloo, tso. tso. From the rheograph, the time corresponding to the maxinum torque was taken as tloo. The optimum cure time, tso, refers to the time for obtaining 90% of the maxinum torque, i.e. 90% of tloo. The time corresponding to 80% of maximum torque was taken as I,,. The mre characteristics of the samples are given in Table 2.

Immer.~ion/w~eight-gain e.rperiments For the swelling experiments, circular samples are cut

from the different vulcanized sheets using a sharp steel die (diameter = 1.9cm). The thickness of the sample was

Table 1 Fannulatians for the mixes

Ingredient (phr)" CV EV D C P ~ Mired

NR 100 100 100 102 Stearic acid 1.5 1.5 -

Zinc oxide 5 5 -

MOR' 0.6 - 3.6 TMTD" - I -

CBS' - 1.5 -

DCP 4 1.5 Sulfur 2 0.6 I . ?

"Parts per hundred rubber by weight Dicumyl peroxide Morpholinebenzothialyl sulfenamide Tetramethylthiuram disulfide

N-Cyclohexyl-2-benrothiazyl sulfenamide

01 I I I I 0 5 10 I5 20 25

I _I

Time (rnin)

Figure I Rheographs of the mixes: A, DCP; B, mixed; C, EV; D. CV

Table 2 Cure characteristics of the mines

Cure characteristics CV EV DCP Mixed

Minimum torque (dNrn) 5.6 4.5 7 Maximum torque (dNm) 36 47.4 44.8 3?.8 Scorch time (min) 2.0 2.5 1.8 2 .4

measured by means of a screw gauge. The samples are weighed on an electronic balance and then kept immersed in inhihitor-free styrene monomer in test bottles. The samples are taken out of the liquid at specific time intervals, the monomer adhering to the surface rubbed off, and the samples weighed and replaced in the test bottles. This process was continued till equilibrium is reached (i.e. after about 50 h). The time for each weighing was kept to a minimum (at most 40 s) to make the error due to the escape of solvent from t h d sample negligible. The values obtained are found to be perfectly reproducible. When conducting the experi- ments at temperatures higher than room temperature, the samples were kept to a thermostatically controlled air oven.

The mole per cent uptake, Q,, for the monomer by 100g of the polymer was plotted against the square root of time and the results are analysedI5. The Q, value is defined by:

where M,(m) is the mass of monomer at equilibrium, M,(m) is the relative molecular mass of the monomer, and Mi(s) is the initial mass of the sample. When equilibrium was reached, Q, was taken as Q,, i.e. mole uptake at infinite time.

RESULTS AND DISCUSSION

To obtain conclusions from the diffusion experiments, the sorption curves were analysed. The Q , values are given in Table 3. Figures 2, 3 and 4 show the diffusion curves of NR crosslinked by the four vulcanized systems* having optimum cure (I,,) at three different tempera- tures, 25, 35 and 45°C. The figures show clearly that monomer uptake is higher in the case of conventional and mixed systems and lowest in the peroxide system. The efficient vulcanizing system takes an intermediate position. The difference in the Q , values for the various systems is partly due to the different types of crosslinking present in them. The structure of networks formed during vulcanization is shown in Figure 5. The poly- sulfidic linkages in conventional vulcanization impart high chain flexibility. In the mixed system both polysulfidic and C-C linkages are present. But as DCP is a slow curing reagent and as the cure time for the mixed system was IOmin, which is not enough to effect complete peroxide curing (the vulcanization time for the NRIDCP system is 25min (Table 2)), the linkages

Table 3 Values of 0- for different samoles

Temp. Cure ("c) time CV EV DCP Mined

O~timum cure time (min) 9 5 25 IC

4936 POLYMER Volume 36 Number 26 1995

Transport of styrene through rubber: A. P Mathew et a1

formed may be predominantly polysultidic. As a result the monomer molecules are more readily accommodated between the rubber chains in the case ol'conventional as well as mixed systems. The efficiently vulcanized samples with mono- and disulfidic linkages are comparatively less flexible and nlonomer uptake is lower in this case. In the case of DCP-cured system. lehs-flexible C C linkages are present and hence lowest Q , values are observed. The diffusion curves for undercured and overcured samples

*~ for the four systems were also analysed. In all cases and at different temperatures the same mend was observed

x Mined

0 cv A EV

0 DCP

Figure 2 Sorption curve showcng the oiole pvl cent uplakc of optimum cured CV. EV. mined and peroridc riimples .tt 25 C

x Mined

6 A EV

Figure3 Sorption curve showing the mole per ccnl uptakeof optimum cured CV. EV. mixed and peroxide samples at 35 C

Figure4 Sorptioncurve showing the mole per cent uptake ofoptimum cured CV, EV, mixed and peroxide samples at 45'C

7

-c- Predominatly C-C linkages

X Mixed

0 cv

u Predominatly mono or disulphidic linkages

Mixed linkages

- Predominatly polysulphidic linkages

Figure 5 Schematic representation of the crosslinks formed during curing: (a) peroxide. (b) efficient. (c) mixed and (d) conventional vulcanization

POLYMER Volume 36 Number 26 1995 4937

Transport of styrene through rubber: A. P. Mathew et al

Figure 6 Sorption

7

6 - 5

- - 4

E 6 3

2

I

0 1 I I 0 10 20 30 40 50

G e (mi")

curve showing the mole per cent uptake of conventional vulcanized samples with different cure times

Figure 7 Sorption curve showing the mole per cent uptake of efficient vulcanized samples with different cure times

(CV, mixed > EV > peroxide). The other major factor that contributes to the difference in the monomer upt:~ke is the crosslink density, which is discussed later on in I his paper.

Samples cured at different cure times ( t l w . tqo, t sa ) for the same vulcanizing system at the same temperature show different Q , values, which may he explained by the degree of crosslinking. The diffusion curves for CV samples with different cure times ( t l W , tgO, tag) at room temperature were analysed (Figure 6). The t l oo and samples show greater uptake than the optimum cured (tg0) samples. The same is the case with efficient, peroxide and mixed systems (Figures 7, 8 and 9). The t loo sam~~les are overcured and hence some of the crosslinks forned may undergo rupture. This facilitates higher mono~ner uptake. On the other hand, for t,, samples, the systern is

Figure8 Sorption curve showing the molc per cent uptake of peroxide vulcanized samples with different cure times

undercured and therefore the crosslinks may not be fully formed. Here also monomer uptake is made easy. In the I,, samples the crosslinks are optimum and complete for the best balance of properties. Therefore the monomer uptake is minimum in this case. We have also analysed the behaviour at different temperatures. The trend was exactly the same. Therefore, the same explanation holds good for all samples at different temperatures.

The volume fraction of rubber, $, in the solvent- swollen samples was calculated usingI6 :

A where wl is the weight of the rubber sample, pl the density of natural rubber, w2 the weight of styrene monomer in the swollen sample, and p2 the density of the monomer. The high value of 4 is an indication of high crosslinking density. The values are given in Table 4. The @ values of DCP-cured samples were found to be higher, showing high crosslink density and hence low monomer

4938 POLYMER Volume 36 Number 26 1995

Transport of styrene through rubber: A. P. Mathew et al

uptake. The o values are lowest for CV and mixed samples. whlch show high monomer uptake. For EV system the value comes in between those of CV and DCP systems, which shows the intermediate swelling characteristics. At high temperature (35 and 45°C) and

Figure 9 Sorplcon curve showinp the molc pcr ccnl uplake of' mixed vulcanized samples with diffcrcnl cure r l rnca

.- Table 4 Values of 6 for difcreni siirnplur - ~ ~

for different degrees of curing, the same pattern was followed.

The values of swelling coefficient (a) were calculated usingI7:

where M , is the mass of solvent (mass of swollen sample - original mass of polymer sample), p0 the solvent density and M, the mass of the polymer sample. The swelling coefficient a is a measure of the volume of solvent in unit mass of the polymer. The values are given in Table 5. The swelling coefficient is in the order DCP < EV < CV, mixed. The swelling coefficient is found to increase with temperature.

To understand the mechanism of sorption, the values obtained were fitted to the equation1':

log (Q,/Q,) = log k + n log t (4) where Q, is the mole per cent increase in uptake at time t , Q, the mole per cent increase in uptake at equilibrium, t the time and k a constant characteristic of the polymer, which indicates the interaction between polymer and solvent. The values of n and k were determined by linear regression analysis. In all cases the correlation coeffi- cients were found to he 0.99.

The value of n is equal to 0.5 for a Fickian diffusion mechanism. When the value falls between 0.5 and 1, the diffusion is anomalous. In this system, i.e. for NR and styrene, a slight deviation from the Fickian mode of diffusion is shown at all temperatures (Table 5). The values of k for different systems were also determined from equation (4) (Tuhle 5). From the swelling data the diffusion coefficient D was calculated usingh:

, . . . where 0 is the slope of the linear portion of the sorption curves and h is the initial thickness of the sample. The values of diffusion coefficients are given in Table 6. The peroxide system shows highest D value, as it has the lowest Q , values. The CV and mixed systems have lowest diffusion coefficients. Also, it is noticeable that, in each system, the value of D increases with temperature. The increase of diffusion with temperature invariably points out the activation of the diffusion process at higher temperature.

Table 5 Value5 of swelling coetlicicnt. , ,and h ;a1 d~f i ren t temperatures -- ~

~ - --

Snclllnp coclhc~cnl 1 k x 10'' (g/g min') Temp. Curr ~

( C) time CV t\' I ) C P Mined CV EV DCP M~xed CV EV DCP Mined - . - .~ ~-

25 I,,,,, 6.771 5.123 1 x 5 5 6913 0.6161 0.6192 0.6310 0.6627 3.05 3.19 2.66 2.12

I*, h 279 4 921 3 x 7 8 6.4186 0.5727 0.6344 0.5994 0.6300 3.83 3 1 5 2.96 2.62 I,,, 6.302 4 826 ;'llI>l h.3265 0.6334 0.6375 0.6537 0.5888 2.73 3.29 3.05 3.24

* 35 II~H, 6.899 5 051 3 '412 7.105 0.5452 0.5906 0.5564 0.5489 4.62 5.05 3.96 4.33

I,,, 6252 4'179 1x396 6472 0.5628 0.5986 0.6456 0.6810 3.86 4.13 3.18 2.36

I,,, 6.2668 4x25 4l l l lY 6.763 0.6638 0.6509 0.6732 0.6418 2.76 3.33 3.34 3.05

45 I,,,,, 7 4h7 X ?it I'iXl 7 1239 0.6075 0.5102 0.5840 0.5510 3.50 6.22 6.53 4.90 I,],, 6996 i J l l X 41122 65XO 0.6246 0.6035 0.6574 0.5798 3.35 4.50 3.06 4.21

I, , , 6.966 5 lh'i 4 11132 6.7109 0.6142 0.5938 0.5627 0.5673 3.40 4.76 5.93 4.75 - ~~

~ - -- ~

POLYMER Volume 36 Number 26 1995 4939

Transport of styrene through rubber: A. P. Mathew et al

Table 7 Value5 of M, and degree uicrosslinkcng -~ ~~ ~ p ~ ~ ~ - ~~

M, 10‘' Cure ~~ - -

System time 25 (. 35'C 45°C 25°C 35°C 45°C -p ~ ~

~pp - -~ CV ~ I , Y ) 13?i18.37 13840.5 15964.96 3.785 3.612 3.131

IYO 1 16844 12212.9 15019.18 4.279 4.094 3.329 1x0 11834.02 12378.2 14648.96 4.225 4.039 3.413

DCP XI 6772 7121.3 8049.8 7.382 6.737 6.21 13 (YO 6x33 6 7331.3 8330.6 7.316 6.82 6.0119 1x0 67877 7633.38 8008.43 7.366 6.550 6.243

Figure 10 Arrhcnlu, plots 01 In P i \ I I

. CV

r DCP

IOWIT K-'

Figure 11 Arrhenius plots of In D vs. IIT

Table 8 Values for activation energy

close to 0.99. The activation energy of permeation Ep is found to be greater than the activation energy of system

EP En AH8 (kJ mol-I) (kJ mol-I) (1 K-' mol-')

diffusion ED. The values of E, and ED are given in Table 8 . The values given are for the r,),, samoles for CV, Cv -. . 15.970 - -,, 1 1 . 7 6 -. 4.21 - ." EV. DCP and m~xed systems

The heat of sorptlon AH, 13 glven h)

E V 1 x 0 0 >. 14 Lli

DCP 24.805 23.34 1.465 Mixed 9.958 8.564 1.394

AH, = E p Ll1 (12)

The values of AH, are also given in Tuhlr 8 . The From the values of AH and AS the free energy AG has enthalpy and entropy of sorption have been calculated been calculated as: using the van't Hoff relation-': AG = A H - T A S 114) ~,

In K, = ASiR - AH,;KT ( I 3 ) The AG values are given in Table 9. It is interesting to The values obtained by the linear regression method are note that the AG values of all the systems are negative, given in Table 9. The values of AS and A H are positive. showing spontaneous sorption.

- POLYMER Volume 36 Number 26 1995 4941

-

Transport of styrene through rubber: A. P. Mathew ?t al.

Table 9 Therrnodynamtc funct~ons AH. A S and AG --

Curc AH A S -AF System rlmc (kl ma1 ') ( I K-' mol-I) (kl mol ' 1

DCP 1100 1.1548 ' 14.2 3.0708 YO 1.4436 15.35 31307 fa" 1.991 17.25 31495

Mixed liw 1.1596 15.83 3.5577 l,,o 1.076 18.24 4.359 lwn 1.9027 2l.05 4.370

CONCLUSION

From this study on the diffusion of styrene monolrer through natural rubber, it is clear that the crosslinkilg system has an important role in determining the diffusion coefficient. The uptake is in the order: peroxide < EV < CV. mixed. This has been ex~lained based on the

the Fickian mode of diffusion. The polymer-solvent interaction parameter x was calculated and decreased with temperature. The free energy of sorption was found to be negatjie for all systems, suggesting spontaneous sorption.

REFERENCES

1 Harogoppad, S. B., Aminabhavi, T . M. and Balundgi. R. H I 7 J . Appl. Polytn. Sci. 1991, 42, 1297

2 Harogoppdd, S. B. and Aminabhavi, T. M. Poh,mrr 1990. 31. 7746 -< ."

3 Berens, A. R. and Hopfenberg, H. B. Polymer 1978, 19,489 4 Sourirajan, S. Ind Eng. Chem.. Procem Der. DPV 1967,6, 154 5 Govindan. T. S. and Saurirajan, S. Ind. Eng. Chem., Proeer.~

DP.~. DPY. 1966, 5, 422 6 Haragoppad, S. B. and Aminabhavi, T. M. J. Appl Polyrn. Sci.

1991.42. 2329 ~~ ~ ~. -.

7 Harogoppad, S. B., Aminabhavi, T. M. and Balundgi, R. H. J. Appl. Polym. Sci. 1991.44. 1687

8 Pah, B. T., Adachi, K. and Kotaka, T. Mucromoleeulrs 1987,20, 2563

9 Mandema, W, and Zeldenrust, H. Polymer 1977, 18, 835 10 Khinnawar, R. S. and Aminabhavi, T. M. J Appl. Polb,nz. Sci.

1991,42,2321 I1 Saleem. M.. Asfour. A. A,. Dekee. D. and Harrei. B. J . Aool. . .

flexibility of the network and the crosslink density. The P O / ~ ~ . ' S C ~ . ' I ~ X ~ , 37, 617

presence of rigid C-C linkages and high dens ty 12 Das. B. and Gangopadhya~, T. Eur. P0ly.m. J . 1992.8,867 13 Das, B. and Gangopadhyay. T. Eur. Polym J . 1993.29, 57 of peroxide 'ystem account for the lowest 14 Donatelli, A. A,, Sperling, L. H. and Thomas, D. A. Macromol-

uptake in the peroxide-crosslinked system. On the otter ecules 1976, 9, 676 hand, the relatively flexible polysulfidic linkages present I5 Aithal, U. S., Aminabhavi, T. N. and Cassidy, P. E. Am. Chem.

in the CV and mixed systems and their low crossli~k Soc. Spmp. Ser. 1990,423, 351

density account for their high monomer uptake. .4s 16 Cassidy, P. E., Aminabhavi, T. M, and Thompson, C. M. Ruh- ber Cken~. Techno1 1983.56, 594

expected the EV system showed intermediate behaviollr. 17 Unnikrishnan, G. and T ~ O ~ ~ S , S. polymer 1994.35, 5504 Also. the extent of curing influences the diffusi'm 18 Fedors. R. F. Polvmer 1979.20. 1087 - . . char~cteristics, The uptake is lowest in tso samples a 1d 19 or ell;^. H. ' ~u6ber ~echnology and ~anu fac tu re ' ( ~ d . C. M.

Blow), Butterworth, London, 1975, p. 162 V it is high for both ti011 and t80, samples. It is found that the 20 Shanthamurthy, "., Aithal, and T, M, J , Appl. temperature activates the d~ffusion process in all c a m . Polym. Sci. 1991,42, 2837

The values of n are suggestive of a slight deviation frc~m

4942 POLYMER Volume 36 Number 26 1995

Kinetics of Diffusion of Styrene Monomer Containing Divinyl Benzene Through Vulcanized Natural Rubber

Aji P. Mathew, S. Packirisamy,* A.S. Padrnanabhan and Sabu ~homas"

School of Chemical Sciences. Mahatma Gandhi Universily. Priyadarshini Hills P. 0.. Kottoyom-686560; *PSC Division. Vihram Sarabhai Space

Centre, Thiruvananfhapuram; Kerala. India

ABSTRACT

Diffusion and sorption of styrene monomer containing divinyl benzene as

crosslinker through wlcanised natural ~ b b e r were studied in a temperature

range of 2545'C. this study is the primary step in the preparation of an interpenetrating network (IpN) based on natural rubber (NR) and polystyrene (PS) by the sequential technique, where NR is swollen in styrene

monomer and its crosslinker and initiator, which is then polymerised in sihr. The mechanism of diffusion was analysed and was found to follow an anomalous wend. The influence of the nature of crossLinks and crosslinking density of NR on the tmnqmrt properties was examined. The diffusion Mefficient was calculated and was found to be concentration dependent. Amhenius parameters for diffusion and permeation processes and other thermodynamic parameters of sorption were estimated. The influence of the cure system, the nature of crosslinks, crosslink density, and temperature on the diffusion process were examined in detail. In the presence of crosslinker,

the monomer uptake was lowered, whereas an increase in temperature

activated the diffusion process. Finally, the experimental sorption results

were compared with theoretical predictions.

" To whom correspondence should be addressed.

Kittetics ojDiflusiotr of Slyreno Mottonter Cotttoirtittg Divinyl Bcrrzene

I. INTRODUCTION

During the past few decades, the diffusion of aromatic and aliphatic hydrocarbons through various polymers has gained much attention in research and industrial areas. The transport of various solvents through

rubbery polymers, as well as crystalline and glassy polymers, has been

studied by many researchers 11-41. The diffusion process was found to

depend on many factors like temperature; the naaire of psnetrants, polymers,

and crosslinks; crosslink density 15.61; and others. Studies of diffusion and permeation are of great importance in the world today because of their

widespread application: separation processes, controlled drug release, encapsulations 7, and so on. In most systems, the mechanism of diffusion

can be explained by Fickian, non-Fickian, or anomalous modes of diffusion

171. Harogoppad and Aminabhavi 181 studied in detail the diffUsion of n- alkanes through different rubbery polymers. Permeation studies can serve as

tools for determining polymer StruchUe. The m s i o n process also gives a clear picture of the polymer-solvent interaction 19,101.

Diffusion studies are important in developing an interpenetrating polymer network (IF'N), which can be defined as multi-component systems in which at least one of the networks has been synthesized in the immediate presence of the other 111,131. In the preparation of sequential IPNs 114,151, the swelling of one component in the network of the other must be studied in detail to control the composition, morphology, and the properties of the

resulting P N 1161. The work canied out by Meyer and coworkers 1171

explains the Importance of tracing the styrene monomer uptake by polyurethane @U) membrane during the preparation of polyurethane1

polystyrene (PUiPS) sequential IPNs. In the present work, importance is given to the diffusion of styrene

monomer containing DVB through the natural rubber network, vulcanised

by four different techniques viz.. conventional, efficient, peroxide, and mixed vulcanising systems. this study aims at the preparation of IPN-based on M S . A detailed study of styrene uptake by hR systems was carried out previously 1181. The present work highlights on !he mechaniaijm, temperature dependence, effect of cure system, diffusion rate, etc. of -9yrene monomer containing divinyl benzene through NR. In fact, the DVB acts as the crosslinker for styrene. The crosslinker was incorporated into the monomer

406

A.1'. Marltrw. S l'uckinsomy. A.S. Jou~nal of Polynrer Et,gi,tecri,rg I'a~lmlmonahhon. S 7hontu.r

and, the mixture was used for diffusion studies. The amount of uptake was recorded at different temperahues by weighing at different time intervals. Various parameters were deduced from the diffusion rate. The rate constant,

concentration dependence of diffusion, enthalpy and entropy of the df i s ion

process, free energy, etc., were calculated using various equations. The experimental sorption curves were compared with theoretical predictions.

2. EXPERIMENTAL

2.1. Materials

The major substances used were nahlral rubber (Mo and styrene monomer. NR was ISNR-5 grade obtained from the Rubber Research Institute of India

(RRII), Kottayam. The styrene monomer was of reagent grade. Before use, the inhibitor was washed off with sodium hydroxide solution. The divinyl

benzene @VB) was of reagent grade and was supplied by Merck. All other ingredients used for vulcanisation were of reagent grade.

2.1. Sample preparation

The NR was compounded according to the recipe in a tulo-roll laboratory mixing mill. The formulation of the mixes are given in Table 1. The cure time of the mixes was determined from the rhwgraphs taken using a Monsanto Rheometer. The time to develop (a) maximum torque is denoted

as tlm , @) 90% of the maximum torque is taken as h , and (c) 80% of the maximum torque is taken as b ~ . The compounded sheets were cured in a hydraulic press at 160°C under a pressure of 25 tonnes to obtain t lm , h, and tM samples. The h samples were considered optimum cured, where tlm

were overcured and tso were undercured.

2.2. Immersiodweight gain experiments

C~rcular samples were punched out of the vulcaniscd sheets using a sharp steel die of 1.96 cm diameter. To the styrene monomer made free from

inhibitor was added 2% DVB, taken in the diffusion bottles, and samples were kept immersed in styrene monomer. The samples were taken out at different time intervals, wiped free of monomer, weighed, and replaced in

Kittetic.r of Diflusio~l of Styrene Monomer Containing Divinyl Benzene

Table 1 Formallon of the 1111xcs

- -.

lngredlents (phr) CV EV Peroxide Mixed

Natura I rubber

Zinc oxide

Stearic a c i d

CBS

T H T O

MOR

Sulphu,

OCP

DCP - Oicumyl peroxide MOR - Horpholine benzothiazyl sulphenamide THTD - Tetramethyl thiuram disulphide CBS - N cyclo hexyl-2-benzothiazyl sulphenamide phr - Parts per hundred rubber by weight

the bottles. The process was continued until equilibrium swelling was reached, whereafter the weight remained constant. The weighing was done on a highly accurate electronic balance, which is accurate up to 0.0001 g. To keep experimental error to a minimum, care was taken lo complete each weighing in 40 sec. To carry out experiments at higher temperatures (35'C and 45'C), we used a thermostatically controlled air oven.

3. RESULTS AND DlSCUSSlON

The results of W o n experiments were expressed as mol% uptake of the monomer by 100 g polymer. To obtain the sorption curves, we plotted the moi% uptake (Q,?/o) plotted against the square root of time in minutes. The mol% uptake Q, is given by

/I./'. hl~rr l t~,w, 3. I'ockiri.ran~y, A.S. f'a~lrnar~ahiaz,~, S. ??lomas

(Wt of monomer l&o up at time t )

Mol wt of monomer x 100 ,tialwtofsample

At equilibrium Q, was taken as QOOm. The various sorption curves

drawn showed an initial portion of slight curvature suggesting a concentrationdependent diffusion (Figs. 2 and 3). similar deviations were observed by other researchers also [S].

3.1 Effect of cure system, crosslink density, cure time and temperature

The samples vulcanised by four different vulcanizing systems were used

for diffusion studies. Fig. 1 shows the nature of crosslinks formed during vulcanisation. We investigated the effect of the nature of crosslinks on

ditfusion. Fig. 2 shows the effect of cure system on the monomer uptake.

The tso samples at 45'C were considered here. We found that conventional and mixed systems exhibited the maximum uptake, whereas the peroxide system showed the minimum uptake. the efficient system showed an intermediate position. The same trend was shown by the t lM and tgO samples at other temperatures also. This trend can be explained by considering the

flexibility of the crosslinks formed during vulcanisation as well as the crosslink density of the system.

The diierence in flexibility in different vulcanising systems can be understood from Fig. 1. The conventional system contains the most flexible polysulphilc linkages, which make the penetration of the solvent molecules through the network easier. On the contrary, the peroxide system with rigid -C-C-linkages hinders the monomer uptake, as indicated by a low value of monomer uptake. In the case of efficient systenls, mono- and disulphidic linkages are present. which shows moderate flexibiliw and as a result, the monomer uptake also shows an intermediate value. In the mixed system, all the different types of linkages viz.. polysulphidic, monosulphidic, disulphidic and -C-C-linkages are possible. Bat as the cure time is closer to the conventional system, most linkages formed may be the highly flexible polysulphidic type, resulting in a high value of monomer uptake, which is

due to the longer time taken for peroxide vulcanization. To study the effect of cmsslink density on monomer uptake, the

crosslink density of the. network ($I must be calculated. For the calculation

Pird<:mulantly mono or d~s~lphidrc linkagcj

MIXED

F i 1: The nature of cross links in natural rubber network under various modes of vulcanisation.

A,/>. Matllrw, S Paclurisamy. A S . Joun~nl of Polymer El~gineen'wg Padmanabha,#. S. Thomas

0 I 1 I I I J 0 10 20 30 40 50 60

J(rnin)

Fig. 2: The effect of cure system on diffusion.

of crosslink density, one must estimate the interaction pammeter (x) between the network and the solvent and the molecular weight between crosslinks M). The interaction parameter can be considered a measure of interaction between the polymer and the solvent. The interaction parameter has been calculated using the equation [20.21].

where V, is the volume fraction of rubber, 6.. and Sg are the respective solubility parameters of natural rubber and styrene monomer, T is the absolute temperature, and R is the gas constant. The respective x values obtained for the NRIstyrene system at 25OC, 35'C, and 45'C were 0.801,

0.786, and 0.773.

The molecular weight between the crosslinks in the polymeric material is an important factor aect ing the *ion process. The M. values are estimated using the following equation 1211.

where IS the density of the polymer, V is the molar volume of solvent, $ is

the volume fraction of polymer, and x is the interaction parameter. The values of M, obtained are presented in Table 2.

As seen, the M. values were maximum for conventional and mixed

systems, and minimum for the peroxide system, with the efficient system

Table 2 Values of inolecular weight between crosslinks (Mc) and crosslink density (4)

Tern- n, (g/mol) \ / x lo5 g mal/cc pera. C u r e --..--.---.---.-..-.---.---- t u r e t l m e CV E V Mixed Perox ide CV EV Mixed Perox ide

A I' hf<~lttew. S. Pockiri~oronty. A.S. Jozrmol of Polymer En~ngit~een'n~ I'<~,rlmo,tohhrr,t. S. Tlronmos

being intermediate. This trend was followed at all temperatures. In the

absence of DW?, also the M. value was in the order CV,

mixed > EV > peroxide /18/.The crosslink density 'I of the polymer.

calculated using the equation

Dves us an idea about the polymer network structure. The values of 4 were

shown in Table 2. The 'Ivalues were maximum for the peroxide system,

explaining the low monomer uptake. The highest monomer uptake was

shown by conventional and mixed systems, which in fact show the lowest

4 values. The efficient system with intermediate 'I values show intermediate

monomer uptake. Nevertheless, the contribution of both factors (flexibility of

crosslinks and crosslink density) toward monomer uptake could be separated out. Further experiments are in progress to analyse this problem.

We also observed the same trend in the absence of divinyl benzene 1181. But nevertheless, we noticed that the Qm values were lower for styrene that contained divinyl benzene. This was made clear through Table 3, which contains the Qm values of different cure systems with different cure times and different temperatures in the absence and presence of divinyl benzene in styrene. This lowering of monomer uptake upon the addition of divinyl benzene may be associated with the blockages fonned by the bulkier DW?

molecules in behveen the polymer chains, thereby reducing the monomer uptake.

The effect of cure time on diffusion was investigated, which is

demonstrated in Fig. 3. The CV samples at 45°C were compared. It was clear from the graph that the uptake is in the order tlm > tgo > tso. In the tlm samples, some linkages fonned may broken down from overturing, resulting

m more free volume within the network. This results in an increase in uptake. The L,, samples were optimum cured, and hence the network

structure is complete and thereby shows lower uptake than the tlm samples.

In the case of the too samples, the crosslinks are incompletely developed, so the monomers taken up were not retained in the network as desorption takes place. This results in lower Qco values. This trend is shown in all cases, especially at higher temperam.

Kinetic* qfD~gwion of Styrene Monomer Containing Divinyl Benzene

Table 3 Values of Q, for different samples

U i t h o u t O V B ,With DVB Tempe. Cure ...-....-.-.-.-----.----.- --.-.----------.------.--. r a t u r e t i m e CV EV DCP Mixed CV EV OCP M i x e d

In Fig. 4, the effect of temperature on the diffusion process has been shown. Conventionally vulcanised, o p t i m u m d samples were considered here. It was made very clear that as the temperature increases, the monomer uptake also increased, as indicated by the Qm values in Table 3. The uptake is in the order 45OC > 3 5 4 C 25OC. This trend was followed in all cases,

irrespective of the presence or absence of divinyl benzene. This shows that,

as e x p e w temperature activates the process of diffusion.

To determine the mechanism of diffusion, the diffusion data has been fit into the following equation 181.1

A.P. Marhew, S. Pockiri.ramy, A.S. Journal of Polymer Engineering I'adntanuhha,~, S. Thontos

0 10 20 30 40 50 60

Ji-(mi")

Fig. 3: The effect of cure time on diffusion.

where Q, is the mol% uptake at time t, Qm is the mol% uptake at equilibrium, and k and n are constants. The k depends on the structural

features of polymers and its interaction with the solvent and n gives an idea about the mechanism of sorption. If n =0.5, the mechanism is said to be

Fickian, and if n = 1, the mechanism is non-Fickian. If 0.5 < n< I, the mechanism is considered to be anomalous. Linear regression is used to determine the values of n and k. The slope and intercept of the curve give the respective values of n and k. The average correlation coefficient was found to H.001 in all cases. The values of n and k are presented in Table 4.

The n values indicated an anomalous mode of diffusion. The n values were more toward the Fickian mode in the abscnce of DVB than in the presence

KineN'cs of Dr//usio,r of Slyre~te Mortorner Conlairtirtg Divinyl Beruene

T ( m i n ) Fig. 4: The effect of temperature on diffusion.

of DVB. Several studies of anomalous d i i i o n in mbbexy polymers were reported previously 120,211. The values of k do not show any systematic Wend.

During the diffusion process, the solvent enters the polymer matrix,

causing a suuchual rearrangement in Ule polymer chains. Therefore, the flexibility of the chains and the crosslink density play vital roles in the kinetics study of sorption. Hence, considering this process as kinetically controlled is reasonable, and the rate of the diffusion can be, traced out by

using the first-order kinetic rate equation.

A / ' \l~irliew,. S. i'rrchivi,mnry, A.S. .loenrol oj'l'olynr~r E,rrrgit,reriw~ i'~rdn~~~~rah1~rrr~. S. Tltumos

Table 4 Values of 11 illid k a1 2SDC, 35'C, and 45'C for different vulcanising systems

Cure system

log (C, - CJ = log C, 4 U 2 . 3 0 3 (6)

where I is the time in minutes, C, and C, are the masses of monomer taken

up at equilibrium and at time I , respectively, and k is the rate constant 1211.

The slope of the straight line log (C, - C3 versus time gives the value of k.

The values are obtained by the linear regression method, in which the

uncertainty in the values gives was 33.001. The values obtained are

presented in Table 5. The cure systems did not exhibit any noticeable effect

on k values. The plots of log (C, - C3 versus time for different systems are

presented in Fig. 5.

It was interesting to study the influence of concentration on the diffusion

process. In all four vulcanising systems, viz., CV, EV, peroxide, and mixed

Kine1ic.r of DIJJ~IS~OII of Styrene Monomer Co~traitriw~ Divir~yl Benzene

Table 5 Values of rate constant (k)

Cure system Temperature

C V EV Peroxide Mixed

0.5 I 5 55 105 155 205 255 305

TIME (rnin) Fig. 5: Plot of log (G- Q vs time.

A 1'. Marlrew, S Pockirisan?y. A.S. Jounrol o/Po!vmcr Ertgi~ruerirtg l'adn,a,tabl,nt,. S. T1,ontos

systems, we observed a marked effect of concentration of the diffusion

coefficient. Figure 6 throws light on this. All the systems show a maximum value for diiusion coefficient, which was followed by a decrease in df i s ion

coefficient values. Aminabhavi and co-workers 1221 had previously observed a similar concentration dependence of diffusion in many systems. In the case of natural rubber and styrene monomer, the conventional, mixed, and

efficient systems show the maxima at relatively lower concentrations as compared with the peroxide system. This phenomenon may be due to the

relative ease of diffusion in CV. EV, and mixed systems as compared with

the peroxide system.

CONCENTRATION Fig. 6: Concentration dependence of d i i s ion .

3.3 Diffusion, sorption, and permeation

The diffusion cc&icient was calculated for the different systems at

different temperatures using the following equation 18.91:

where h 1s the initial sample thickness, 0 is the slope of the initial portion of

the sorption curve, and Qm is the mol% uptake at equilibrium. The values obtained are presented in Table 6. It can be noticed that the D values are highest in the case of peroxide samples, as the Qoo values are lowest. The

other three systems show comparatively similar values of D. Also, it can be

Table 6 Val~~cs of diffi~sion, sorption, and permeation coeficients

-- ~p ~~~p ~- --

S a m p l e Diffusion Sorption Permeation s p e c i f , coeff'ci nt coefficient coeff'ci nt 5 cation ( D X I O + cm /sl ( 5 ) (PXIO' 1 5 cm /SI

/ I 1'. ,t,ia.lurIrrw,. S. IJockiri.~anty, A.S. Jorcn~al ofPulynter E~~gi ,~cc!r i t !y I 'o~hatmblmt~. S. Thontas

seen that the temperature increase results in an increased D value in all cases, showing that the temperature activates the diffusion process.

Sorption can be referred to as the initial penetration and dispersal of the penetrant molecules through the polymer. The sorption coefficient (S) can be

calculated using the relation

where Mw is the weight of the solvent at equilibrium and M, is the initial polymer weight. The estimated values of S are presented in Table 6. Here the S values are minimum in the peroxide system, as the Ma values are the

lowest there. The sorption coefficient values follow the order CVC, mixed > EV > peroxide, which is the same as the monomer uptake at equilibrium swelling. Also, the temperahlre activation in this process can be observed

from the S values.

Permeation, which could be considered as the total effect of sorption and ditfusion, can be estimated from the permeation coefficient using the

equation

The values of permeation coefficient are presented in Table 6. The values of P are almost the same in all systems.

3.4 Activation energy nod thermodynamic parameters

The measure of the monomer uptake by the polymer could be estimated

from the thermodynamic sorption constant (Ks) 1211. The sorption constant was defined as

No. of moles of monomer sorbed at equilibrium K, :: (10)

Initial mass of the polymer

The values obtained are presented in Table 7. The Ks was found to be in the order CV. mixed > EV >peroxide, i.e., the values were in the order of

Table 7 Values of swelling coeelicie~~t (a) and sorption coefficient (Ks)

r a t u r e t i m e C V E V DCP M i x e d C V E V OCP Mixed -

2 5 O L ' !Do 6 024 5.022 3.899 6 . 1 7 9 5.25 4.379 3.401 5.398

monomer uptake. Also, as the temperature was raised, no noticeable change

was observed.

The swelling 6 c i e n t (a) is an indication of the swelling nature of a

polymer. The higher the value of a , the easier the swelling of the polymer.

The swelling coefficient could be calculated using the following equation

1211.

where Ms and Mo were the mass of monomer and mass of polymer,

respectively, and Ps the density of monomer. The values obtained by

calculation are presented in Table 7. As expected, the values were in the

order CV, mixed > EV > peroxide for all temperatures.

To determine the entropy and enthslpy of the diffusion process, in which

actually the monomer molecules were allowed to mix with the polymer

A.1'. Marhew. S. Packirisamy, A.S. Jountol ofPolymcr Engi,teeri,tg I'udmanabhan. S. tho ma.^

matrix, the van't Hoff relation I221 could be used. According to the van't Hoff equation

where & and AS0 are the standard enthalpy and entropy, respectively, T is the absolute tempemhlre, R is the gas constant, and Ks is the sorption

constant. The values of & and AS' were estimated from the plot of log Ks against 1K 1211. The plots are shown in Fig. 7. The slope gave the value of AS' and the y-intercept gave the AIf value, by linear regression analysis.

1 / T X I O - ~ ( K - ' ) Rig. 7: Plot of log Ks vs I n .

The cor~elauon coefficient was slightly lower than 0.99 in d l cases. The

values obtained for standard enthalpy and entropy at room temperature are presented in Table 8. The AS' values are negative for the conventional,

efficient, and peroxide samples, but positive for the mixed system. The

negative fl value is suggestive of an exothermic sorption process.

The free energy, AGO for the difbion process could be estimated using

the simple lhermodynamic formula

where T is the absolute temperature. The values obtained for the four

vulcanising systems at room temperature are presented in Table 8. The AG values are negative in all cases, suggesting spontaneous sorption, which

supports the experimental observations.

Also, the activation energy of the diffusion (ED) and permeation (E,) of the monomer through the natural rubber matrix was calculated using the

Arrhenius equation 121,221.

where X stands for D or P, Xo for DO or PO. Ex for ED or E, and T the

absolute temperature.

Table 8 'l'l~crn~odyn;~nl~c hinction AH. AS, AG and activation energies Ep and ED

C V E V P e r o x i d e M i x e d

t p i k J ) - 4 . 2 7 5 - 6 . 2 9 9 - 6 . 9 4 9 - 2 . 9 9 8

Lo i k J 1 - 3 . 3 2 5 -5 .751 -6 .694 - 3 . 1 6 3

AH, ( J ) -949 - 5 4 1 . 9 - 2 5 4 . 4 t 1 6 5 . 1

A S ' ( J ) - 2 2 . 2 1 -24 .73 - 2 7 . 3 0 - 2 5 . 1 9

A H ' { J ) - 9 0 7 . 3 3 -408 .3 - 2 4 8 . 8 t 1 3 2 . 6 3

Ati ( k J j - 7 . 5 2 5 -7 .777 -8 .384 - 7 . 3 7 4

A / ' Mnrhcw. .Y. I'nckirisan?y. A.S. Jounzrrl of l'olyntrr E,tginecrir,g I'o~fn#nlonobha,,. S, nlomos

It was observed that the plots of In P vs 1/T and in D vs 1 R (Figs. 8 and 9 ) were straight lines. The slope of these lines gave the values of the

activation energy of d i i s i o n (ED) and the activation energy of permeation (E,). The values were obtained by the linear regression method, and the correlation coeficients were slightly below 0.99. The values of ED and E, are presented in Table 8. Both the ED and the E, values were negative. The

heat of sorption (AHs) was given by the equation

l / T x l ~ ~ ~ ( K - ' ) Fig. 8: Arrhenius plot of In P vs 1R .

Kine1ic.r of D1;4uirsiorr of Sryref~e Motlomer Conlaini~~g Divinyl Betnewe

' - '-I

i *CV *EV * DCP +MIXED I

Fig. 9: Arrhenius plot of in D vs 1 f I

The values obtained are presented in Table 8. The AHs values obtained were negative, except for the mixed system. Also the values were more or less equal to the &value obtained from the van't Hoff equation.

3.5 Theoretical fitting

To determine the accuracy of the experiments, we compared the experimental results of diffusion with theoretical prediction. Fig. 10 shows the comparison. The theoretical curve was drawn using the following

equation 1201.

A/ ' . Malltew. S. Packirisamy, A.S. Journal of Polynlrr Engbtecring I'admanabhan. S. Thomar

A(rnin) Fig. 10: Comparison behveen experimental diffusion data of conventionally

vulcanised samples and theoretical values.

where Q, and Q= are the mole percent monomer uptake at time t and at equilibrium, respectively, and h is the initial sample thickness. The

theoretical w e represents a Fickian mode of diffusion. The diffusion data of conventionally Mllcanised optimum cured samples have been used in drawing the experimental curve. The curvature in the initial portion of the

experimental curve and its deviation from the theoretical curve indicates the anomalous Fickian behaviour. The same can be understood by the n values also (Table 4). Thus, all the factors were supportive of an anomalous mode of diffusion of styrene monomer containing DVB, through crosslinked natural rubber.

4. CONCLUSION

The monomer uptake by the natural rubber matrix was found to be. lowered by the addition of crosslinker in the monomer. In all cases, the Qm

was higher in the absence of DVB in the styrene monomer. The m e system

plays a signifmnt role in the swelling nature. The uptake is maximum for conventional and mixed systems, and lowest for the peroxide system with

the efficient system coming in behveen. This trend was explained by the

flexibility crosslinks and the crosslink density of the four vulcanising systems. The mechanism of diffusion of styrene in the presence of DVB was

found to deviate more from the Fickian mode than in the case where styrene

alone was used. Therefore, the mechanism followed in the presence of DVB

was of anomalous mode in nature. The values of the swelling coefficient (a), *ion coeff~cient (D), and sorption constant (K,) indicating increased

swelling at higher temperature show that temperature activates the process of diffusion. The rate constant, however, shows no sigruficant temperature dependence. The activation energy of permeation and diffusion were negative. The calculated negative value for free energy, AG, supports the spontaneous sorption that was observed experimentally. The diffusion

coefficient was found to be concentration dependent in all four wlcanising systems. The experimental values were compared with those of the theoretical ones, whereby a deviation from the normal Fickian mode was observed. This again supports the anomalous mode of diffusion, as suggested

by the n values. The diffusion data were observed to be. perfectly fit in the first order rate equation.

ACKNOWLEDGMENT

Two of the authors (APM and ST) are grateful to the Third World Academy of Sciences (TWAS) for the financial support

A.1'. Marlrcw. S, l'nckir;.ranty. A.S. I'a<lma,fiabhn,~. S. Ttjonta.~

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