gobinda gopal bar@w~shodhganga.inflibnet.ac.in/bitstream/10603/6468/19/19_appendices.pdf · gobinda...

ABOUT THE A UTHOR

Name

Aaiiress

Aaiiress for communication

Date of birth

Hobbies

Research interests

Gobinda Gopal B a r @ w ~

Solid Motors Group Vikrm Smabhai Space Cenlre ISRO P.O. Thinivananthapurmn 695 022

I11 A-02, YSSC Housing Colony St Xaviers College P. 0. Thiruvmumrhapurmn 695 586 Kerala, India

I st September, 1956

Dr M C BandypaYyq andMrs Pramila Devi

Indian

B Sc (Horn) in Chemrshy, Calcutta University, 1979 B Tech in Plastics and Rubber Technology, Calcutta Universjv, 1981 M Tech in Rubber Technology, Indian Institute of Technology, Kharagpur, 1983

Scientist, VSSC (since 1983) Present grade: Scientist~Engineer-'SF'

Insirumental music, clay modeling

- Multiphase polymer sysiemscharacterisation and modeling studies.

- Polymeric materials for space opplicafrons. - Polymer based Insulation systems in Solid Rocker Motors. - Solid propellants: rheological and ageing behaviour. - System Reliabiliiy.

VISCOELASTIC BEHAVIOR OF NBR/EVA POLYMER BLENDS: APPLICATION OF MODELS

G. G. BANDYOPADWAY,' S. S. BHAGAWAN,~ AND K . x. ?~IS.L\.$ V f u w S r u s s ~ l SPACE ~ N T R E . THIRUVANANTRAPUR*LI 695 022 1 x 0 1 ~

AND

S. THOMAS SCHDOL OF C H ~ I C N SCIENCES, hl. 6. UNIVERSITY. K O ~ A Y * Y 686 560 IXDL%

ABSTRACT

T h e vlvoclaab~c propenma of blend. b d on nitrile rubber (NBRI aad e thylent \~n?: uctate copolymer (EVA), n thcrrnoplruuc elulomcr. M invart~gsted in terms of storage modulu. and 1- iarsenc for different campuslrluna Thne smdl-strun dynamic mechanlcd properties have been e\duated u r n g a Rhcoribron Vis. coelaatume<rr covrrlng a wde temperature range. Attempts have beon m d c to fit the emcmrrnrri r a u l u with cvmpurstxanh hued on rn- field rhearkc, developed by Kernax. Ptcdict~one baxd on the d-te p a ~ i c l e model (which w u m n out of the urmponenrt of the blend to be the matrix and the other d b p n r c u ~nclunoiu) we found to bc rarrsfutory in thr uu. of 3(1/70 NBRIEVA blend bur nor 70130 and 5 0 5 3 b k d , The packed grain ntodrl ,wlnck -urn- ne~rher of the cornponenu to be the matrix but apprmsmats cocontmuour struc- Lure of thc two) prtd~crsonr do not asre with the experimental data on 50/50 blend far r z a cc-continuous n,urpholol~. vaa rrvcalrd rrr SE!4 o b u r n t ~ o n s .

Research on polymeric blends is an important area of materials developmen: The wide range of properties attainable with these systems were hitherto either impossible :G obtain from an individual polymer or rould involve costly development of new pol>mers. Hecm ix h imponant to predict the resultant properties, structure (morpholog).) and the blend Lriarior irom the properties of the individual components.

Polyrnerlc blends are vkcoelastic in nature and hence :heir michanicd &cd?&r L- dependent on time, temperature and frequency, in addition t o blend structure.'morphc.+ T;l,,rerical modelling studiw wbich ium at understanding and predicting the mechanical b e i ~ ~ r . ' m o r p h o l o g y of t h e blends from the individual component characteristics ha,? g G 4 isFrd;.z.'-' :,lodels thus developed will help in designing products wing these ma:er&.

kXCOELASTIC ANALYSIS

Dynamic mechanjcai analysis has proved to be an effective to01 especiall~ fm characterizing the dual viscous and elanic nature of polymeric materials. In an oscillatory 6eiL the viscwlastic material shows a phase between the imposed dynamic strain and the d>namic srress response or vice versa. The extent of phase lag is a measure of the viscous nature of the poiynerk body, or the deviation from elastic nature, so t o say. This, in turn, also depicts the i n t e r n d - ~ i r , ! ~ ~ p ~ i t ~ e capacity of the polymeric materials. For the linear viscoeiastic case, re. for a sdieiently small deformationjstrain level. stress bears a linear relationship wit!: *:a% and the impceed dynamic

*Solid Moiurr Prolect

Propellant Engineenas Division. amhor to whom correspondence should be a d d r d t Propellancl and Specid Chemicals Group.

. . . .-. ..... ,. .

~ ......... . . .

VlSCOEWSTIC BEHAVIOR OF BLEUDS ...C~.

,, :' . . . .

strain (c) and stnrs (a) Rkuom can be e x p d as6 ' . f'~'.yz< . . . ...... a = aoeY' . . F.?

= e0e,ld+6) .,.. ';$I ;;,!j ,i., ,.- ~ ,

The dynamic moduius response can be apressed as a complex quantity -::wtr.

... L z . 2- <?;

E' and F' are rekrred as st- and lass moduli, respectively. The ratio 6'/6, i.e. 1- & to storage modulus, is a me- of i n t d 6iction in the system. Thus the polymeric md.;IJI perturbed in this way s u m a portion of the energy elasticdly (corresponding to b2&& ulus F ) and dissipate a p w m in the form of heat (corresponding t o lcm modulus ratio of dissipation to s r o a e IE'/F = tan6) depends upon temperature and fngumcy + namic behavior d t!x r-"c (pohmeric) materials is a strong function of temp&$&. - transitions in moiecuiar Y ; Z ~ requiring higher energy are attributed to the p e h in h l ~ ;

moduli vs. temperature acd .an6 vs. temperature measurements. Dynamic me&ani&ia are panzcularly suited [or a d p i s of &component composites/blends by c o m k ' s . i m e n d data with ;&=:- 5 a 4 3- ..=+om models. These models assume diE-.& ..

geometryjstructiue for t h 5 h d s . ~.,; ..:- .. .:+, && The rnulticomponent t h e m e generated for ideal elastic system can be adapted for . .

marenals through elasrzc \&tic correspondence principle. Here the time-dependeni && .. . ..". constanls are replaced a mrreponding complex viscoelastic constants obtained h a d p a & expenrnents in the steady =sate harmonic condition. Steady state harmonic material *& . ,.- .-.? independent of the time {duration) of measurement.'-12 .....

:. 3: -.4. These models ha\? beem ~$4 earlier for predicting properties due to compositiond

However. w t h the advent oi $-namic mdan ica l testing techniques and the availabili6 h.* . enies over a wide temperature range, the models are used for predicting dynamic prop&t&ii .^* .... different temperatures. in adoition to maluating compositional changes. This has opened up mw 1 . .' , L. : vistas in understanding strucrureproperty relations in polymer systems/blends. .:.,:+::i y . . . . . ... ..% : . :,. -,+*;;; ..... . SHORT REVIEW OF .\IODELS T.: ... ..3.*..L<..$!. ..

Slcdels of importance in the study of pol.meric blend composites may be categorid m foUoa3:' - .....

I. .Ilechnntcnl couplzng models.- These models are empirical representation of -:,k terms oi constituent mechanicai properties through mechanical models. These modela &a comb .' nient framework for empirical curve Gtting; however they are neither morphologically nor ically realistic models for blend structural response. Takayanagi model^^^^" are typical ... . . . . . of this categov. , .?.. . . . . . .

2. Seif u)-tent rnodels/Mean field theories.- These models give single valued , '

based on analysis of deformation and stress about a representative inclusion. Them+,- this catezori are: Three obase model (or doublv embedded modell due to ~erner." VsmdPPdd - . . model.16 corrected and simplified by ~mith,".~' Christensen and'lol'; composik sph*:rpodd . . .: ........ due to Hashnzo and Christensen." ............ .la.&

3. Bounding or ltmtting models.- These models give probable modulus value rankr . .

composite for a given set of assumption.. These models are due to Hashin and ~htr ibnan?;~? and ill.'^ They give bounds on mechanical properties behavior without recourse to&.*. : .; ::., :. . . . ... geometry considerations. . . . . . . .!.. -

4. Semzemptncai models.- The complexities and inadequacies of the theoretied modds .-

been reduced using semiempirical relationships. There are a number of models under tm- -~ Examples of empirical modifications of theoretical models include the following: (a) fbaX- model modified by Nielsen'3~2'-26 using an empirical expression for effective ~.-.-*. the blend based on a maximum packing fraction for the filler; (b) a modilicatioo of .. the- ....dLd .d ' ~ . .- model by Ziegel and Romanov considering the effective volume fraction of 6Uer *:cI'5-Frz,

;. : .==>>$<*.<<:, <:. :::;&&*-;>

652 RUBBER CHEMISTRY AND TECHNOLOGY VOL. 70

immobilization of the soft polymer matrix at the hard filler ~ u r f a c e l ~ ~ ~ ' . ~ ~ ; (c) the Vander Poel model modified by ~ i c k i e ' ~ . ~ ' by incorporating a functional form of the eRective mlume M i o n term for the filler using an empirical curve fitting parameter and the diameter of the filler particle; (d) Halpin-Tsai3'-" presented a semiempirical model which is a general form of the Kerner and many other equations, considering such factors as the geometry of the filler and the Poisson ratio of the matrix. This last model has been further modified by Nielsen," Lewis and Nielsen", and later by McGee and McCullough8." based on the maximum padring fraction of the filler.

KERNER MODEL: DESCRIPTIOS A S D GOVERNING EQUATIONS

KernerI4 proposed expressions for gross bulk and shear moduli of multimmponent system of spherical particulate filled isotropic composites, with arbitrary values of modulus. Prwious calculations using the Kerner and Vander Poel equa~ion have been applied to hro types of heterogeneous polymer composites-particulate filled rubber and rubber modified t h e r m ~ p l a s t i o . ' ~ ~ ~ ' Application of these models for rubber-rubber blends appeared recently in the l i t e r a t ~ r e . ~ . ~ '

The two cases considered in Kerner's expressions are: composites with discrete dispersed particles in a matrix, and polyaggregates without any matrix In the first case, which assumes discrete particles dispersed in a continuous matrix, an arerage filier panicle/inclusion (spherical) is regarded as surrounded by a shell of matrix material which merges into a medium that has the elastic properties of the composite (see Figure 1). Particle adhere to the matrix but do not interact with one another. In the second case, knomn as the polyaggregatelpacked grain model, no matrix phase is postulated. The particles of each component of the composite are suspended in a matrix of a third unspecified component. As the concentration of the third component approaches zero, the particles of each component will pack together in the volume of the material. Many re- searchers have applied the above models for investigation of filler/polymer composites of rubber- rubber and plastic-rubber blends. Thermoplastic elastomers (TPEs) have gained importance in recent years since they posses propenies of both thermoplastics and rubbers. Very little work has been reported on the use of models for studying d:namic data of T P E systems.

In t h ~ s paper, we discuss models for predicting d?namic properties of NBRIEVA blends. These TPEs have found wide applications in footap~r . -hie; etc. An attempt is made to apply the Kerner model to andyzejpredict dynamic data for SSR'EVA blends. The governing equations of both the models, which were originally derived f?r elastic caws, are written for viscoelastic response through the use of correspondence principle 'Tbe correspondence principle s t a t e that t h e expressions for the complex moduli of the compcs;i:e may be obtained byreplacement of the

I. MATRIX SHELL

2. S X R l i C L I N t L U 3 3

3 CWPOSITE

FIG. 1.-Kerner model.

VISCOELASTIC BEHAVIOR OF BLEXDS 653

phase elastic moduli by the phase complex moduli in an eaa &on for the wrrerponding elastic moduli). The Kerner equation for shear modulrn for the discrete particle model for n components suspended in a matrix material is""

which,-for a b~nary blend, LC., one component dispersd in mrtm materid, transforms to

G - - - ( 1 - 4 i ) G m + ( ~ + o . ) G . G, (1 + u+i)G, u ( l - a ) G .

(4)

where:

G = shear modulus of blend,

G, = shear modulus of the matrix,

G. = shear modulus of the inclusion,

o. = volume concentration of inclusions,

u = a function of Poisson ratio of the mstrir: = 214 - 3 h ) / ( 7 - 5 ~ ~ ) .

pm = Poisnn ratio of the matrix.

Based on the correspondence principle for the viscoehmc case (mith implicit assumption that the Poisson ratio is a real constant). Equation (4) can be a p r d as

where the superscript denotes the corresponding dynamic shear modulus of the composite and the cornponenta.

The dynamic Young's modulus E' is related to the dynamic shear modulus G' through the reiatlon

where p' = p' - tp" is the viscoelastic Poisson ratio. .&uming p = p'. where p is the elastic Poisson ratlo. Equations (4) and (5) ~ield '

where 3 = (1 + p,)/(l + p,) and 7 = (1 + p)/(l + h ) . Dickie has shown that the error in assuming p a s a real quantity is negligible. This equation. due to Kerner, has been found to represent dynamic data reasonably well for a variety of systems of the soft inclusion/bard matrix type.'.','

The following assumptions were made in the derivation of the above model: phase surfaces were in direct contact; no slip o c c m at the phase interface; interactions between particles are ignored: and size and spatial distribution between matri~ and inclusions are random.

The Poisson ratio generally varies from 0.32 (gl- plastic zone ) to 0.5 (rubbery zone) for polymeric materials. Its variation with temperature is assumed to follow the relation,37

O.l7[log E1(glass) - log E1(T)1 p(T) = [log E1(glau) -log Ef(rubber)]

+ 0.32

For the Kerner packed grain model, the coupled governing equations for bulk modulus (K) and shear modulus (G) are


These equations are expressed in terms of complex dynamic Young's modulus (E') properties through the correspondence prinaple and the relations (6) and (11).

The transformed equations with complex parameters are resolved into real and imaginary parts. Equation (10) yields:

f (E') >> f (u) + ig(v) = 0 (12)

f (u) >> f (E', E") = 0

g(u) >> g(E',E") = 0

Similarly Equation (9) also yields a pair of equations for the real and imaginary parts. The Y e ~ t o n - R a ~ h s o n ~ ' . ~ ~ method is used to solve the simultaneous Equations (13) and (14).

The increments in E' and E", 1.c.. AE' and AE" are defined as

-

where D (Determ~nanti = df (u)/dE'.dg(v)/dE"-df(u)/dEr' dg(v)/dE' Convergence is attained w ~ t h the expresslonr

E ' j + I = E'j i A& (17)

l r ~ ~ t ~ a i estrmata ior E' and E" and p (assumed real) are attained From their d u e s weighted by their volume fraction. Temperature dependence of p for the componenrs in the blend are determtned from Equation (8). The values of E' and E" obtained from the Equations (13) and (14) are substituted in the real part of the Equation (9) to solve for a n e a \ d u e of p. The value of p which falls betawn 0.32 to 0.5 is used for the final convergence of all the \ariables E', E'', and p for the solution of the complex system of equations E'. E" azd -z: "r the biends are computed using FORTRAN programs. @

EXPERLMENTAL DETAILS

NBR (Aparene 2535 NS from Gujrat Aparene Polymers Lid.) h a r i i 3 2 -iocinile content and EVA (Piiene-1802 from PIL, hladras) having 18% vinyl content were used for preparation of the biends. The SBRIEVA blends of different compositions. x u . 33/50. 70.'30. 30!70 wight ratio. were prepared on a two roll mixing mill. The sheets were compremon molded at 150 OC for 2 minutes.

The sarnpies for dynamic mechanical analysis were cut out along the mill direction bom the molded sheet (size: 50 mm x 110 mm x 15 mm). Dynamic te t ing m a s carried ,out using a Rheovibron DDV-III-C Viscoelammeter a t an amplitude of 0.0025 an and a %&cy of 35 Hz over a temperature range of -50 OC t o 75 OC. The instrument provides tan6 \dues directly while the complex modulus (E') is obtained using6

E'= x 10" dynes/crn2 8ADW x t

where,

L) = dynanuc force reading,

L = specmen length,

VISCOELASTIC BEHAVIOR O F BLENDS

t = specimen thiclmcs

A = instrument parameter.

The storage and Ices moduli up then computed using, G = E' cos 6 and li? = E' ain6. For SEM innatigations. .WR was prefmntidly Ectnvted from M/70 and 50/50 blends using

toluene and EVA was extracted h m 70130 blend wing CCL. The solvent extracted samples were sputter coated with Au/Pd d o y and studied using the JEOGJSM-T330A Scanning Electron Microscope.

msXTS .\?? 2 L G S S I O N

The applicability of Kerner theory to cal& dynsmic mechanical properties of the blends of NBRIEVA over a tempenam -e of i n t a a t 8.c d e d . Attempts are also made to deduce possible structure ( r n o r p h o i ! of 7 . blends 6a1 a knowledge of experimental and computed results.

The dependence of d~~ W e s of the pure mmponenta and blends on temperature are shown in and Figures 2 and 3. > x R shows a sharp loss tangent peak at -7 'C w h e r w EVA shoas a broad lor+ transition "rh a peak around -10 OC. Similarly, NBR shows a sharp &' las, peak at -10 ' C wheres EVA sbo\3 a shoulder 9pe transition a t -20 "C. These characteristia for NBR and EV.4 are summarized in Table I.

Xlodel computations are carried out with polynomial best fit data for E' and tan6 for the components. The best tit Lines of the E' and tan6 are shown as d i d lines on the corresponding figures depicting the experimental data for the components, viz. Figures 2 and 3. Computed results based on Kerner discrete and polyaggregate models and the experimental data for storage modulus

Fla 2.--Dependence of storage modulus dn temperature for YBRIEVA blends including corresponding experimental data on individual components.

RUBBERCHEMISTRYANDTECHNOLOGY

- NBR FIT DATA . . .. . EVA EXPT DATA - EVA m DATA ==.-. NBR EXPT DATA ooooo NBR/NA 30 /70 . . * * * NBR/EVA 70 /30 ...-. NBR/EVA 50/50

FIG. 3 -Dependence of lass tangent on temperature for NBRIEVA blends including corresponding cxpmirnmul data on individual cornponenu.

and tan6 are compared in Figures 4-9 for the different blend compositions. SEM photographs are given in Figures 1&12 for the blends.

3 0 / i 0 SBRiEV.4 BLEXD

As evident from Figure 3, the tan6 expe r imed data for the blend are found to be closer t o that of EVA, wlth a comparatively narrower transition. The E' experimental data compared well with the computed data armming EVA to he the matrix (Figure 4). Computed ~ d u s of tan6 (Figure 5) show some mismatch with ~=q&menf below the T, region. However, beyond the transition region, the agreement is satisfactory. Pol.-e model computations are also found to closely match the e x p e r i m d daca D i -tck model computations, aauming an NEJR matrix, did not match the experimental da ta This is attributed to the lower volume fraction of NBR. The predicted data of '& &cre%e +-A& zwdei with an EVA continuum more or less agree with the experimental data over the temperature range investigated. Earlier investigations of the blend using a scanning elgtron rniarscope techniques showed particles of N B R embedded in a matrix of EVA in the form of well defined inclusions. A SEM photomicrograph of the blend is shown in Figure 10.

T~sre : DY.*A.\IIC PROPU(N TRAvSmON TUIPERATURES IN NBR AND EVA

System E" lors peak (shoulder) - -- tan 6 peak

NBR -7 ' C -10 OC EVA -10 OC -20 "C

VISCOELASTIC BEHAVIOR OF BLENDS

FIG. 4.-Cornpanron oi experimental and calculated norage znodulw data for 30170 NBR/EVA blend.

- - - - -

0

. O * * ' . rCX.!kEVA AS MATRIX *.".I W N B R AS MATRIX * * 1 * I WPOLYAGCRECATE ----A MPERlMEKlAL

, . , , ~ , , . , , , , , , , , , , r , ~ , . . . , , , . , , , , , , , , , , , , , , ,

Fic. j . -Cornpai~m of experimental and calculated ims tangent data for 30170 NBR/EVA blend

--30 - 10 10 30 50 70 TEMPERATURE (OC)

RUBBER CHEMISTRY AND TECHNOLOGY

0 1 , , , , , --30 - 10 1 1 1 1 1 1 1 1 1 1 , , , , , , , , , , 10 30 50

I 70

TEMPERATURE ( O C )

FI(; 6 - - G m ~ a r = n of expenmena and calculated storage modulus data for 50/50 ~VBR/EVA blend.

0 q 0 , . . , . , . . . . , I ~ ~ I I I I I I I I . , , , , , , , ,

a 30 -10 10 0 TEMPERATURE ( O C ) 50 70

FIG 7 Cornpanson of e r p ~ m e n t a l and calNkted loss tangent data for 50/50 NBR/EVA blend


- 0 1 ~ ~ ~ 5 ~ ' 1 " 1 1 ' 1 ' 1 1 1 1 1 * 1 1 0 1 1 1 r 1 .m -- 30 - 1 0 10 30 50 70

TEMPERATURE (OC)

0 - - E - 0 - 0- - U) >'& a-: C - % - -0 - V - W- o= - -

Fic : Cumpartson of experimental and calculated srarage modulus data for 70:30 SBR!EVA blend

a ..*.. CAU):EVA U MATRIX A ..-I. W N B R AS MATRIX A 9 t * r U P O C Y * C G R E G * T E . r r r r . aPmUENTM

7

1 . e o e o e CAU):FfA AS MAiRlX .+A- , = x. I -. CAU):NBR AS MATRIX . * r r r r t CALD:POLYAGGREGAE

r r r r r EXPERIMENTAL .I -- I I

-1 0 o ? , , , , , ~ ~ ~ ~ , ~ ~ ~ ~ ~ ~ ~ ~ ~ l ~ r ~ ~ . ~ ~ ~ ~ I ' " " " ~ ' I ' a " ~ " ~ ~ ~

-30 - 1 0 1 0 30 50 70 TEMPERATURE ( O C )

Flc 9 Como-n of expertmental and calculated loss tangent data for 70130 NBR/EVA blend

RUBBER CHEMISTRY AND TECHNOLOGY

Fm. 10.-SEM Photomicrograph of 30170 NBRjEVA blend.

.A5 po~nted out earlier. Kerner's discrete particle model is based on the assumption of rigid spher~cal partlcies being randomly distributed in a soft matrix. Rom the SEhl micrograph shown in Figure 10, it is clear that the morphology of 30170 NBR/EVA blend largely satisfies the assumptions. The agreement betawn computed data (assuming an EVA matrix) and experimental result, can thus be explained.

50150 NBR/EVA BLESD

Frum Ftgure 3, it 1s observed that the experimental tan6 data of the blend exhibit shift in glass transition toward EVA pol>mer. T h e computed storage moduli for the 50/50 blend are found to be closer to the experimental data, assuming an EVA matrix, over the temperature range studied (Figure 6). The discrete particle model computation, assuming an NBR matrix, doe, not a p e with the experimental data. However, quite contrary to theoretical expectation, polxaggegate model predictions do not match the experimental Endings. The scanning electron micrograph obsenations are s h m n in Figure 11. It is clear from this micrograph that EVA forms a .ccr.;inu.~uj matrix UnIike the 30/i0 NBR/WA blend, a number of NBR partides (dark regions)

Fic. 11.-SEM Photomicrograph of 50150 NBR/EVA blend.


FIG. 12.-SEM Photomicrograph of 70130 NBR/EVA blend

are found to be coalesced with a tendency to form a continuous structure. The polyaggregate model of Iierner assumes that the components of the b lend/compi te are packed so as to result in a mntinuous structure of the two in the blend. Since the continuity of the NBR p h e h only panial. the calculations based on polyaggregate model do not fit the experimental results. As diswsed above. EVA phase continuity exists in 50150 blend. Thw, the dcu la t ed values of modulus and loss tangent assuming an EVA matrix are closer t o the experimental results.

70/30 YBR/EVA BLEND

An eramlnatlon of Figures 8 and 9 reveals that none of the models fit the experimental da ta Howe\?r somewhat reasonable agreement between the data is obsened when EVA is chosen as matrix for the discrete particle model. Tan 6 computed with EVA as matrix showed agreement with the c~perimental data, only differing in the location of the peak/shoulder. However, the lower wlume fraction of EV.4 in this blend ( i .e. 30% EVA compared to 70% KBR) rules out EVA as the continuum. Theoretically speaking, the discrete particle model using XBR as the matrix should have matched the experimental d a t a The SEM micrograph in Figure 12 showed an NBR continuous phase with dispersed inclusions of EVA.

It has been shown earlierJo that 4,, the maximum volume fraction a filler can have in a blend, and K E . the Einstein Coefficient which takes into account the m e r geometry in the blend, are hm important parameters influencing the mechanical response of a blend. These parameters depend on the particle shape. state of agglomeration, structuring and orientation of the filler. Agglom- erates and nonspherical particles contribute to increase the Einstein Coefficient and g e n e d y have d e r @,, d u e s than spherical inclusions. For instance, in the case of randomly packed agglomerares of spherical particles K E approaches 6.76 vs. 2.5 for dispersed spherical particles." An inceass in h'~ or decrease in @, (as a result of nonsphericity of filler, state of agglomera- tionjc!usrenng) results in increase in modulus of the blend. Clustering of EVA particles forming larger domains can be seen in the Figure 12 micrograph; this was also reported by Varghese, et d3'

T h ~ e factors may- contribute to the deviation of the experimental data from the model PI+ dictions when considering NBR as the matrix in a 70130 NBRIEVA blend.

CONCLUSIONS

The Kerner equations for dscrete particle a&d polyaggregate models have been used for pre- ,

dicting storage rnodulus and loss factor for different blends of NBR/EVA over a wide temperature range. Comparison of the experimental data with the prediction made over the temperature range indicawd ;ood agreement on the 30170 NBR/EVA blend for the discrete particle model. Such a


sult is supported by SEM observations. For 70130 and 50150 blends, the agreement was poor. The possible causes for this lack of agreement are explained based on morphologicd considerations.

ACKNOWLEDGEMENT

One of the authors (GGB) wishes to thank Hima Varghese for providing the samples for dynamic mechanical studies and authorities of Vikram Sarabhai Space Centre for permission to carry ou t the studies

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1978. Ch 1

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'*R, hl Chrlstenaen and K. H. Lo. J . Zlcch. Phys. Sol& 27(4). 315 (1979).

' "2 . Hh\h>n. J. Appl. .!lcch 28. I43 :196?1. "2. Haahbn and S Shti~kman. J. .Ale& Phyr. Sol id . 11. 127 (1963).

,

"B. Paul. Tmru AI.$IEZIB. #36 i l W ) .

"R. Hill. J hlcch. P h y s Soti& 11. 357 (1963). "L. E Nielren. J Appi. Polym. S n . Appl. Palym. S y m p . no. 12, 249 (1969).

" L E Xielsen. J .Appi. Phys. 41. 4626 (1970).

'"T. B Lrwm and L E Nielsen. J. AWL Polym. Sci. 14. 1449 (1970).

"K. D Zkegel m d A. Rornanav. J. AppL Polym. Sci. 17, 1133 (1973).

"K. D Zicgel and A. Romano,.. J. Appl. Polym. S n 17. 1119 (1973).

"R. A D~ck~e . J Poiym. Scr., P o l y m Phys. Ed. 14. 2073 (1976).

"'L. E. Nlelscn and Roben F. Landel. "Yechanical Properties of Polymers & Compositer: 2nd EC. SL-d DeWrer. Inc. Sew Yxk. 1994. Ch. 7. p. 377.

"s. W TSI. US. Gox-r. Rept.. ADWff i1 (1968).

"J. E, hshton, J . C. Halpl". and P H. Petit, "Primer on Composite Analyris.' Technornic. Lan-er. Pa . 1969

'"J. C Ha\p>n. J. Compoa. Motn. 3. 732 (1969).

'"S. McCee and R. L. YcCullough. P o l p . Compob. 2. 149 (1981).

"R. A. Didr~e. J Appl. Paiy. Scl. 17, i 9 (1973).

"'K. A . hlaich. H K. Plummer, Jr.. >I. A. Sarnus. and P. C. Killogosr, Jr., J. Appl. Polym. Scl- 37. 157? (19891

"K A hlazich, P C. Killogoar. Jr., and J. A. Ingram. RUBBER CHEM. TECHNOL. 82. 305 (1989).

"'Brice Carnahan. H. .X Luther, and James 0. Willu. 'Applied Numerical hlethods,' John \Viley 6- Sam. Inc-. New York. 1969. -

3 9 ~ . Vaigiine S S Bhagawan. S. Sam-a Rao, and S. Thomar, Eur. Polym. J. 31, 95? (1995).

btdinn /onrital of Natllral Rubber Research, 9(2) : 100-105, 1996

MODELLING VISCOELASTIC PROPERTIES OF RUBBER-TPE BLENDS

S.S. Bhagawan and G.G. Bandyopadhyay

Bhd~awan. S.S. and Bandyopadhyay, G.G. (19%). Modelling rvmelasttc properties of rubber- TrE blends. I,,durr lounto1 o/Natarol Rlrbbn Rrsmrch. 9 0 ) : lLW105.

Blend? ol natural tubber (NR) and 1 2 polybutadiene (12 PBD) were evaluate~i for dynamtc m c ~ h a n ~ a l propennes such as storage modulus (E') and dampmg factor (tan S). Cornputat~ons have hwn made based on mean field theories of Kerner to predicl propemes of the blends. Tlrr d~3crrtc prrt~cle model predictions are found lo be moderatelv dare to expr~mental results !n the case of 70/30 1.2 PBD/NR blend assuming 12 PBD as matrix in the c a r of 9 / 5 0 blnnd h~vln): J co.conl~nuuus morphology as revealed by SEM e~aluation, predictions baser1 on polyaggregate model are found to be in agreement with experiment, with devlat~ons in the r a n ~ c ot 4ltC to OC which lies between the Tgs of the componma.

K d Natural rubber, 1.2 Polybutarliene. Storage modulus. Therrnopl.~\t~c. t4.wtorncr. Blmris, Vircwlastic properties, Kemer :nodels.

5 5 Bhasw.ln (lor cnnespandence). Propellant Eng~neenng Dvaion. and G.G. Bandyopdhyav. 5111~1 hlotors Propct. Vlkrarn Sarabhai Space Centre. Trivandrurn - 695 022. Kerala, India.

The importance of viscoelastic properties tor characterising modulus and damping behav~our of rubbers is well known (hfurayama, 1978; Dickie, 1978 ; Ferry, 1980). These time/temperature dependent properties oi elastomers subjected to cyclic deformation are expressed in terms of

and tan i, = E" / E' (2)

where E', E' and E" are complex, storage and loss moduli respectively. The terminology and methods of measurement have been discussed zlsewhere (Murayama, 1978).

The ~rucial role of dynamic mechanical analysis m understanding the behaviour of rubber blends is wldely accepted. Dy- namlc rneihcmcc~i properties are zdeally

suited for analysis of multicomponent com- positeslblends by comparing experimental results with predictions based on various models (such as the Kerner model). Multicomponent theories generated for ideal elastic systems can be adapted for viscoelastic materials through elastic/ viscoelastic correspondence principle. Here the timedependent elastic constants are replaced with the corresponding complex viscoelastic constants obtained from dynamic experiments. Earlier, the models have been used for predicting compositional changes Ockie, 1973; 1978). With the advent of sophisticated test machines for measuring properties over a wide range of temperature and frequency, the models are also used for predicting dynamic properties at different temperatures (Dickie, 1978; Mazich et al., 1989b; Nielsen and Landel, 1994; Shick and Ishida 1994; Ya Goldman, 1994).

MODELLING VlSCOELASTlC PROPERTIES OF BLENDS

Kerner (1956) proposed expressions for gross bulk and shear moduli of multicomponent systems of spherical

filed isotropiccomposites. These models have been recently applied for predicting dynamic properties of rubber- rubber blends (Mazich eta!., 1989a. b). Very little work has been reported on the use of these models for rubber-WE (thermoplastic elastomer) blends (Bandyopadhyay et al., 1997). In this paper, an attempt has been made to apply the Kerner model for prediction of dynam~c properties of 1.2 PBD/NR blends.

The models

The two cases considered in Kerner's expressions are the discrete particle model and packed gram model. In the first case, a filler particle/inclusion is regarded as surro~lnded by a shell of matrix material which merges into a medium that has the elastic properties of the composite. Parti- cles adhere to the matrix but do not interact with one another. In the packed grain (polyaggregate) model, no matrix is postulated. The particles of each component of the composite are suspended in a matrix of a third unspecified component. As the concentration of the third component ap- roaches zero, the particles of each component pack together in the volume of the material.

In the case of d~screte particle model, for a binary blend the Kemer equation for Young's modulus can be written as.

where E', E'," and E,' are the dynamic young's moduli of blend, matrix and inclusion and Q, is the volume concentration of inclusions. The parameters ~ . p and y are functions of poisson ratio ( w ) given by

This equation was found to represent dynamic data for a variety of systems of the type soft inclusion/hard matrix reasonably well (Dickie, 1973; 1978). Poisson ratio usually varies from 0.32 to 0.5 for polymeric materials. Its dependence on temperature is incorporated in the computations as suggested by Mazich et al. (1989b).

In the case of the packed grain model, the two coupled governing equations for bulk modulus (K) and shear modulus (G) are

and

These equations are expressed in terms of complex Young's modulus (E') through

K' = E' / 3 (1-2 p) (6)

and F = 2 G ' ( l + p ) (7)

The transformed equations with complex parameters are resolved into real and imaginary parts. The numerical analysis technique of Newton-Raphson (Camahan et al., 1968) was applied to solve the simultaneous equation obtained from Equation (5) for the blend moduli. Initial estimate for E', E and p were made from the weighted volume fractions of the components for each temperature. The temperature dependence of p is computed as mentioned above. The values of E' and E" thus obtained are substituted in the real part of Equation (4) to derive a new value of p.

102 BHAGAWAN and BANDYOPADHYAY

Value of LL wh~ch falls within 0.32 and 0.5 (Bhagawan, 1987 and Bhagawan and was used for final convergence of all the Tripathy, 1987). variables E', E" and p for solution of the complex system of equations. Suitable RESULTS AND DISCUSSION programmes were developed for carrying out computations related to Equations (3), (4) and (5).

Experimental details

NR was obtained from the Rubber Research Institute of tndia, Kottayam while 1.2 PBD was from Japan Synthetic Rubber Co., Tokvo. Details relating to preparation of the blends using a Brabender plasticorder and determination of storage modulus and loss tangcrrt uslng a Rheovibron \ . i<corL l . i~ t<,~ l i t t t~~r \\'pre reported earlier

Temperature (C)

F . 1.5:orage inc~~lulus and I < , - * tangent data as a function of temperature for cornponenu (1.2 PBD!\[R) at 35 Hz

The storage modulus and loss tangent data for the components at different temperatures at 35 Hz are shown (Fig.1). It is observed that NR undergoes changes in E' and loss tangent at temperatures much lower than in the case of 1,2 PBD. Based on tan 6_, the Tg (glass transition temperature) of NR occurs around -55°C and that of 1.2 PBDat 5°C. The characteristic difference in magnitude of tan 6_, values between rubber and thermoplastic rubber is also evident (Fig. 2).

."-.NRas matrix ... "". 1 2 PBD as matrix ' . ...a. pdyaggregate model

East (70130 1.2PBDNA) C - m C

-70 -45 -20 5 30 Temperature (C)

Fig. 2. Co~npanwn of computed and rxperlmcntal data (loss tangent and storage modulus versus temperature) for 70/30 1. 2 PBD/KR blend

MODELLING VISCOELASTIC PROPERTIES OF BLENDS 103

70130 1,2 PBDlNR blend

The experimentally determined properties of 70/30 1,2 PBD/NR blend are compared with computed data for both discrete particle and polyaggregate models (Fig. 2). It is observed that predictions based on discrete particle model assuming 1.2 PBD as matrix are somewhat closer to the exper~mental results. Large differences between the prediction and the exoerimen- ~-~

tal data are observed in the temperature range of -30 "C to 5 "C. in the case of loss tangent data, the models predict hvo septi- rate trans~tion peaks whereas experimental. data uidicatt: shoulder for transition corresponding to NR and peak corresponding to that of 1,2 PBD (larger component). Predic- tions assuming NR as matrix and based on polyaggregate model are similar to those by discrete part~cle model with 12 PBD as matrix. I t mav be noted that earlier investigations (Bhagawan and Tripathv, 1987) of the blends based on scanning electron micrograph~ (SEM) indicated NR to be dispersed in a matrix of 1.2 PBD.

50150 1,2 PBDINR blend

An examinat~on of modulus-temperature data (Fig. 3) for the blend indicates that discrete particle model calculations (assuming either 1.2 PBD or NR as matrix) do not agree with experimental results. Calcula- tions of E' at different temperatures based on polyaggregate model are comparatively closer to the experimentally determined values. In this case the agreement between computed and actual modulus values is good at temperatures below 4 5 "C and above 0 ,'C. Predictions by polyaggregate model are lower than experimental values in the temperature range of -45 "C to -25 OC and higher than experimental data in the temperature range -25 T to 0 "C. In the case of loss tangent-temperature data (Fig.3), computed values are different from experimental results. Relatisely speaking, predic-

tions based on polyaggregate model are somewhat nearer. However, considerable differences are observed in the temperature range of -50 "C too"€. Earlier investigations (Bhagawan and Tripathy, 1987) of solvent etched samples by SEM indicated 1,2 PBD to form the continuous phase in the case of 50/50 1,2 PBD/NR blend. Thus, the polyaggregate model needs to be modified for more accurate predictions.

30170 1,2 PBDlNR blend

A comparison of predicted values and experimental results for storage modulus as well as loss tangent versus tempera-

.----NRasmatrix ' - - . .1.2 PBDasmatrix

:. ..--a polyaggregate model . Expt (W50 1.2 PBDiNR) C

. . . . , , , . , , , . , . , , . . -70 -45

I -20 5 30

Temperature (C)

Fig. 3. Comparison of computed and experimrnbl data (loss tangent and storage modulus versus temperature) for 50/50/ 1.2 PBD/NR blend

IIU BHAGAWAN and BANDYOPADHYAY

1 ..... NR as matrix 1 , . . polyapgregate model

PBDMR) I

I ;; i i . ~ # I > ~ ' , w " o ~ I i ' l I,>ILLII,I~LI~ and L . x ~ . c ~ I I ~ ~ P ~ I ~ I ~iat,, (itorage m~xlulus and loss tangent versus temperature) for 30/70 1, 2 PBDlNR blend

ture tor 30/70 1.2 PBD/NR blend (Fig.4) indicates that none of the models is suitable. Previous invesfigation on morphology of the blend (Bhagawan and Tripathy, 1987) revealed that 1.2 PBD forms the continuous matrix even in the case of 30/70 1.2 PBD/ hX blend. h.lodifications of the model are required for better agreement with experimental data.

The agreement between experimental and calculated values is good below 4 0 "C and above 5 "C and poor in the intermediate temperature ranges. For the j0/50 blend polyaggregate model predic-. tions are closer (than discrete particle model

predictions) to experimental results indicat- ing a co-continuous morphology. Model predictions for the 30/70 blend are poor and do not support previous SEM results based on solvent etching. Modifications of the model are required to improve predictions in the temperature range of -40 .C to 0 c.

Bandyopadhyay, G.G.. Bhagawan, SS., Ninan, K.N. and Thomas. S. (1997). Viwoelastic behaviour of SBRIEVA p o l p e r blends: Application of mhfels. Rubbn Cltenrirlry and Trclrnnlo~, (In pr65).

Bhagawan. IS. (1987). Tlm~1oplusticr~~sIonr?3 Lwd to,,

svvuwluclrc I.? julybt,tudi.,a. Ph.D. Thesis, lndwn Institute of Technolow, Kh.~rafipur. Indw.

Bhagawan. 5.S. and Tnpathy, D.K. (19117). M'rpljc~l- ogy and mechanical behav~our 01 1.2 pc,iibutadienmatural rubber blends. Malrnul Cl int~sly urld Plz~s~cs. 17 : 415-02.

C~rna l~an . 0.. Luther. H.A. and Wtlkes. 1.0. (1968) Appltnl numerrcal methods. John Wlley. Nrw York. pp. 319.331.

D~ckie, R..i.(1973). Heterogeneous plymer-polymer comp~sites : 1. Thmry of vtscoelasltc proper- lies and uquivalenl mrrhantcal rn<xkl?.. 1s.r- ttvl .! App1,t.d Pofyr,,t.r Sc,c-;rrrtcr. 17 : 45-61.

Dtckie. R..A. (1978). Mechanical properties (small deformation) of multiphase polymer blends. In: Polyntn Blmdr. Vol. I. (Eds. D.R. Paul and S. Sewman), Academic Press, New York.

Ferry, J.D. (1980). Vixoelastic properties of polymers. John Wiley. New York, pp. 33-55.

Kerner, E.H. (1956). The elastic and thennoelastic pmperties of composite media. Procrcdilrgs of Plrsicol Society. 690 : 8W613.

Maz~ch. L A . , Plummer. H.K., Samus. M.A.Jr. and Kilhgoar, P.C. (1989a). Mean field calculations of the dynamic mechanical pmpertles of two- phase elastamer blends : Included oarticla in a matrix phase. loen,ul of A ~ f i c d P01yrrr.r SC:?ICP, 37 : 187-1888,

Mazich, L A . . Killigoar. P.C. Jr. and Ingram, ].A. (1554b). Mean-field calculations of the dynamic mechanical properties of heterogenous elastomer blends. R u b h Cltm#isfry anrl Tt,clr- ni ...qy, 62 : 305.314.

MODELLING VlSCOELASnC PROPERTIES OF

Murayama, T. (1978). Dynamicmechanical analysisof polyrnerac marerials Ekevier Publishers, NEW York.

Ntelsen. L.E. and Lrutel. R.F. (1994). Mechanical pmpen~esofpulyme~andcompos1te5. Marcel Dekker. New York.

Shack. R. A and lshcda, H. (1994). Elastic' and vl.;c<xlastxc behavtour of composites. In: Char-

BLENDS 105

act~is~t1011 of Compsitc nrolwlals (Eds. Habuo Ishida and L.E. Fibpatrick). Butterworth- Heinemann. Boston, pp. 147-183.

Ya Goldman (1994). Viwoelastic behaviour of pol"- meric and composite materials and the prino- ole of orediction. In: Predictio~t d f L r DrfurmD ;ion &pertin of Polymrnc ~ont)wsite ~ ~ t c r i a l r American Chemical Society. Washington D.C..

Dynamic Properties of NR/EVA Polymer Blends: Model Calculations and Blend Morphology C. C . BANDYOPADHYAY,' 5 . 5. BHACAWAN,' K. N. NINAN,' S. THOMAS4

' Solids Motors Croup. Vikram Sarahhai Space Centre, Thiruvananthapuram 695 022, lndia

Vropellan~ Engjneertng Dtb~rton Vtkram Satahhat Space Centre. Th~ruvananthapuram 695 022, lndta

' Propellant and Swia l Chemtcalr Croup. Vikram Sarabhai Space Centre, Thiruvananthapuram 695 021 . lndia

"~hhool oi Chern~cai S< lencn. \I ti. University. Konayam 686 560, lndia

Received 2 Februan 1998; accepted 19 August 1998

ABSTRACT: The d.mamic mechanical properties of blends of natural rubber (NR) and the ethylene-vinul acetate mpolymer (EVA), a thermoplastic elastomer, were investigated in terms of the storage modulus and loss tangent for different mmpositions, using dynamic mechan~cal thermal analysis (DMTAI eovering a wide temperature range. Mean-field t h m n c ~ developed by Kerner were applied to these binary blends ofdifferent comparitions. Thmreucal calcuivtlons were compared with the experimental small strain dynamic me- chanlci~l pmpertles of the blends and their morphological characterizations. Predictions based on the discrete particle model (which considers one of the components as a matrix and the other dispersed as well-defined spherical i,nclusions embedded in the matrix1 agreed well with the experimental data in the case of 30R0 NR'EVA but not in the case of 70130 YF3BV.A blends. A 50150 blend. where a comntinuous morphology was revealed by SEN studies. was found to be approximately modeled by the plyaggregate model (where no matrix phase but a cocontinuous structure of the hvo is postulated). 0 1999 John Wile? & So-. Inc .I Appl Poi?m Sci 72: 165174, 1999

Key words: polymer blends; dynamic mechanical properties; NBR, EVA, Kerner model. polyaggregate model morphology; viscoelastic behavior

Polymers and the blends made from them are viscoelastic i n nature . Hence, t h e investigation of viscoelastic properties plays a major role i n characterizing pol-mer blends regarding thei r mechanical behavior. structure-property relationships, a n d so on. Dynamic mechanical analysis has proved to he a n effective tool in the characterization studies of viscoelastic materials. In a cyclic deformation field, the oscillatory strain wave results in a n oscillatory stress response

--- . -- . Correspondence to 5 S Bhaparan.

J O U ~ ~ I o i ~ p p i i p d P U I ? ~ ~ rune. i. : : 2 . ipi ; t 1999, 0 1999 J a b Wer & .%m 1 7 ~ iY'C W21SP9M9/0201Gi0

with a p h a s e l ag (8 ) i n between, which is a mea- s u r e of t h e viscous contribution. The result ing viscoelastic parameters a r e expressed as'

E * (complex modulus) = E' (elastic modulus)

+ iE" (loss modulus)

tan 6 = E"IE'

Presently, application of theoretical models which aim at unders tanding a n d predicting t h e mechanical behavior and morphology of t h e blends from t h e individual component characteristics h a s gained importance.'-' Dynamic mechanical anal - ysis has proved to be an effective tool i n th i s

regard. The computation technique to predict the viscoelastic properties is based on the analogy between viscosity and elasticity. The multicomponent theories generated for elastic systems have been adapted for viscoelastic materials through the elastic-viscoelastic correspondence principle.

A number of approaches are found in the liter- ature to determine the composite properties from those of the components. Each approach has its merits and demerits. The empirical methods are based on the approximation of experimental data like analytical curve fitting. The hydrodynamic approach does not reflect the dependence of the effective properties on the elastic properties of the filler, the latter being assumed to be completely rigid. Methods of elasticity theory and geometri- cal models of the composite medium constitute the most widely accepted approach.' For polymeric materials, dynamic mechanical analysis has proved to be an effective tool because the theories for elastic systems can be easily adapted for viscoelastic materials in the case of a steady- state harmonic condition. For the linear viscoelastic matrix and inclusion, the tlme-dependent elastic constants are replaced with corresponding complex viscoelast~c constants obtained from dynamic experiments in the steady-state harmonic condition. When dvnamic experiments are carried out at constant frequency. the steady material resoonse is independent of the time tduration) of the measurement."-IS

Models of importance in the study of polymeric blends and composites can be categorized as mechanical coupling models, self-consistent models, and bounding and semiemp~rical models. Self- consistent models, namely. Kerner and Vander Poel and the empirical modifications thereof, al- low study of the mechanical behavior with respect to the morphology/st~cture and, hence, find importance in mechanical properties versus morphological in~estigations.'~"~'

The models have lately been used for predicting dynamic mechanical properties with respect to morphological aspects of the rubberhbber blends.3638 Thermoplastic elastomers ITPE) have gained importance in recent years since they possess properties of both thermoplastics and rubbers. Very little work has been reported on the use of models for studying the dynamic data of TPE systems. In this article, tie discuss the applicability of Kerner's models for predicting the dynamic properties of NWEVA blends. In our earlier article. we examined the a p plicability of the models to the NBR/EVA and hW 12-PBD systems.".'0

THEORETICAL

The two cases considered in Kerner's expres- s i o n ~ ' ~ are composites with discrete particles in a matrix and polyaggregates without any matrix. The polyaggregate or the packed grain model where no separate matrix phase is postulated is assumed to represent a cocontinuous morphology of the blends.

Discrete Particle Model

The assumptions underlying this model are that spherical inclusions of varying size are randomly distributed in the volume of the matrix. The phase surfaces are in direct contact [bonded phys- ically or chemically), that is, there is no slip a t the phase interface, hut interactions between particles are ignored. The model gives the overall av- erage response of the material to loads (or deformation) rather than localized variation in material characteristics.

The Kerner equation for the shear modulus for a multicomponent system is given by

which for a binary blend of viscoelastic materials can be adapted for the complex Youngs modulus through the correspondence principle and the relation E* = 211 + r*JG', where p* ( = p' + ip") is the viscoelastic Poisson ratio. Here. p* is assumed as p ( a real quantity), that is. the elastic Poisson ratio. Dickieg showed that the error in assuming p as a real quantity is negligible.

The transformed equation is represented as

where a = 2(4-5w,J1(7-5pm); p = ( l+p,~l ( l+pi) and y = (l+p)/(l+p,,,); E' is the complex Young's modulus of the blend; E', the complex Young's modulus of the matrix; E i, the complex Young's modulus of the inclusion; +,, the volume fraction of the inclusion; p, the Poisson ratio of the blend; p,, the Poisson ratio of the matrix. and pi, the Poisson ratio of the inclusion. p generally varies from 0.32 to 0.5 (glassy plastic to rubbery zone);

D\%.AMIC PROPERTIES OF NWEVA POLYMER BLENDS 167

its variation with temperature, taken into consid- (% - If*)+, (e - K*)& eration for computations, is as was used by (3KT + 4G*) + (3% + 4G*) = (4) Mazich e t al.:IH The relation is gwen below:

(G* - GT)+,

0.17{(logE'1.glassi - log E'iT)] ( 7 - 5p)GX + (8 - 1OP)GT piT) = .-

{log E'iglass) - log E ' ( ~ b b e r ) ] + 0.32 + (G* - G;)& (3) (7 - 5p)G* + (8 - 1 0 ~ ) G , * = 0 (5)

E', E". and tan b for the blends are computed Equations (4) and (5 ) are expressed in terms of using a Fortran program. The equation due to the dynamic Young's modulus (E*) through the Kemer has been found to represent dynamic data equations E' = 2(1 + p*)G' and K = E*/3(1 on a variety of systems of the so& inclusions/hard - 2p). The transformed equations with complex matrix parameters are resolved into real and imaginary

parts a s follows:

Polyaggregate Model Eq (4): f(E*) = g ( E ' , Em, and p~

Here, no separate matrix phase is contemplated. Particles of each component are suspended in a + i h ~ E ' , E", and fi) = 0 (6 )

third component As the concentration of the third component approaches zero, particles of Eq 15): f(E*) = u(E', E", and P I

each component will pack together in the volume + iu(E', E". and p) = 0 (7 ) of the material

Themodel is represented by hvomupledgoveming From eqs. (6 ) and (71, we have four sets of equa- equations for the hulk (M and the shear modulus IG): tions by equating the real and imaginary parts of

0- i--, - :,ill. , l l l l l l l l . l , , , , , , , , i l , , , , , , , -8C -6C -43 -20 0 20

TE?'?ERATURE ( ' C )

Figure 1 Temprrarure dependence of storage modulus of NWEVA blends inclu&ng pur? ' omponent.

4 - EXPTL NR DATA - - U P T L EVA DATA ****. n P r L NR/WA 70/x DATA ..... EXPTL NR/EVA 50/50 DATA

1 A A A ~ A UPTL NR/NA )o/m DATA

1 22

Figure 2 T,.mper:iture dependence of loss tangent of NR/EVA blends including pure c o r n ~ ~ x l u n t s .

each to zero. Thcse cquatluns are functions of E', E , andp. Since is ;~ssurned to be real. we have only three variables to solve ~i.e., E' . E, and pl. For this reason, we ignore the i m a g i n a ~ part of eq. (41 or (6). leaving three equations to solve. The Newton-Raphson was used to solve the simultaneous equations from 17).

The increments in E' and E , that is. AE' and 1E" are defined ;is

where

Convergence is attained with the expressions

The real part of eq. (61 is expressed as quadratic in I*. The values ofE' and E obtained from eq. (7) are substituted in the real part of eq. (6) to solve for a new value of F . The value of p thus obtained (generally it falls between 0.32 and 0.5) is used for the final convergence of E', E , a n d p for subse- quent iterations t o converge. Solution of the coupled system of eqs. (4) and ( 5 ) was obtained by convergence of all variables E', E , and p.

Initial estimates for E', E", and p (assumed real) are obtained from the values of the components, weighted by their volume fractions. The temperature dependence of I*, of the components, that is, p, (n and p2 (n in the blend, is determined from the relation as mentioned earlier in eq. (3). The details of the procedure have been dealt with in our earlier article.39

EXPERIMENTAL

The details of the experimental methods of blend preparation and the determination of the storage

DYNAMIC PROPERTIES OF N W V A POLYMER BLENDS 169

0 I ' " ' ' " " I " ~ ~ ~ " " " " " ' ' 1 " " ~ ~ I -*. ." -60 -40 - 20 0 20

TEMPERATURE ( " C )

Figure 3 Computed and experimental storage modulus data for 30170 SRIEVA blend

modulus and loss tangent have been described elsewhere.'Vhe blends were prepared in a labo- ratory model intermix ishaw Intermix KO) a t a temperature of 60°C using a rotor speed of 60 rpm. The composit~ons chosen for the present study were 30170. 50150, and 70130 NRIEVA.

Dynamic mechanical measurements were carried out on a DhlTA machine (Polymer Laborato- ries) consisting of a temperature programmer and controller. This Instrument measures the dynamic moduli (both storaee and loss moduli) and

rise in the loss tangent and drop in E' corresponding to the glass transition of the material. EVA does not show any such abrupt rise or fall in the tan S value or E' a t its characteristic glass transition zone. In the case of EVA, a rise in tan S occurs followed by plateauing and E' exhibits a gradual decrease around the T, region.

The blends exhibit two transitions corresponding to each of the components as shown below:

~~ ~ "

the damping of a specimen under an oscillatory N m V A TB,, (*C) TSN, (OC) load as a function of temperature. The experi-

~~ ~

ments were conducted m a uniaxial tension mode loolo -46.3 - 70130 -46.3 - from -80 to 20°C at a frequency of 10 Hz. Further 50150 -50.0 details of the raw materials. mlxing, and property -10.9 30FO -51.7 -10.1

evaluation are as reported earlier.42 O/IOO - -100

RESULTS AND DISCUSSION 30170 NWEVA Blend

The experimental data for viscoelastic parame- . When the experimentally obtained properties of ters are shown in Figures 1 and 2. Based on the the 30170 NBR/EVA blend are compared with the peak values of tan 8, the T2 of NR was found to computed data for both discreteparticle andpoly- occur around 1 6 ' C and ;hat of EVA around aggregate models, it is observed from Figures 3 -10°C. The homopolyner XR showed a sharp and 4 that predictions based on the discrete par-

n n ~ a a NR AS MATRIX o o o o * N1 As MATRIX - - WLY*GCREDTE

8 O-6 -60 -41 -20 o a

TEMPERATURE ( ' C )

Figure 4 Cumputcd and experimental loss tangent data for 30170 NR/EVA blend.

tick model assumlng EVA os the matrix provide a close match to the experimental data for both E' and tan 8. Differences between the predicted and experimental data are observed at temperatures above -30'C. that is, from the low-temperature through the transition-temperature regions, the model has worked well. At the very low temperature zone, the molecular movements are frozen and both the components behave like elastic solids. In the transition-temperature region past the glass transition temperature. the segmental mo- bility of the pol>-mer backbone only sets in. Thus, a t both low temperature and in the transition zone, a good match is observed; deviation occurs a t a higher temperature where long-range ~ b - bery relaxations also are expected to contribute. We observe that the discrete particle model (EVA as the matrix, predicts storage modulus values slightly higher than does the experimental data a t temperatures above -30°C. A satisfactory match between the experimental data and the predictions has also been reen in the case of the polyaggregate model. It is interesting to note that the discrete particle model assuming either EVA or NR as the matrk~ and the polyaggregate model predictions give excellent ageement with the experimental data below the T~

In the case of the loss tangent data also, the discrete particle model (assuming EVA as the matrix) approximately matches the experimental data. The match is excellent below T,, and a t T,, there is a small difference in the location of the peak. The experimental peak occurs a t a slightly higher value than the predicted one. Although the predicted values are marginally lower than the experimental data, they clearly indicate the trend of the experimental results, tha t is, the two transitions corresponding to the NR and EVA peaks around -52 and around -1O0C', respectively, in the blend. I t may be noted that earlier investigations" based on SEM analysis of a 40160 NFYEVA blind indicated NR particles dispersed in a matrix of EVA, and beyond 50-60 parts of NR in the blend, a cocontinuous morphology of the two resulted. Thus, a larger volume fraction of EVA in the 30170 NRIEVA blend coupled with the SEM findings supports the prediction tha t EVA is the matrix in which particles of NR are dispersed. Hence, the predictions of the discrete particle model with EV.4 a s the matrix are quite satisfactory. The lack of fit assuming NR (having a low volume fraction and a high melt vis-

DYNAhIIC PROPERTIES OF NR/EVA POLYMER BLENDS 171

. . . I . EXPTL W T A n n ~ n n NR AS MATRIX * o O O O EVA AS MATRIX - - POLYAGGREGATE

A A A

P - - - - . .

. I

" " " " " ' I ~ " " = ~ " " ' ~ ~ ~ ' ~ ~ ~ " ' ~ ~ ~ ' ~ ~ " ~ ~ ' ~ ~ ' ~ -80 -.

-0 - -4a -20 0 20

TEMPERATURE ( ' C )

Figure 5 ('ornputcd :~nd experimental storage modulus data for 50150 NlUEVA blend.

anAnn NR AS MATRIX o o o o o EVA AS W T R I X - - WLYAGGREWTE

Figure 6 Computed and experimental loss tangent data for 50150 NIUEVA blend

I I.. EXPTL DATA A n n A n NR AS MATRIX * o o Q O N A AS MATRIX - - POLYAGGREGATE

F~gurt. 7 ('omputed and expenmental storage modulus data for 70130 NRJEVA blend

c o s ~ t y ~ a s the matrix IS in accordance with ex- pectations.

For the 30170 hlend. ~t is also observed that except for the tr:insitii~n region the polyaggregate model's predictions are as good as those of the discrete particle model assuming EVA as the matrix. The polyaggregate model predicts a shift in the transition peak as compared to the experimental tan 8 data and slightly overestimates the experimental data. However. the closeness of the polyaggregate calculations to the experimental da ta is difficult to reconcile on the basis of SEM findings that suggest that the 30170 blend would be a dispersed-phase morphology. A possible explanation is the volume fraction of the "packed grains" of the major component, namely, EVA. The number of grains of EV.1 are sufficiently large enough to form a matrix for the grains of NR.

50150 NRIEVA Blend

The data for the 50150 blend is in conformity with increase in the XR content a s revealed in the storage modulus and loss tangent values compared to 30170 I\;R/EVA blend (Figs. 1 and 2;. The

loss tangent data show a higher NR peak, but no appreciable change in the shoulder corresponding :a EVA as compared to 30170 NWZVA blend. The- oretical calculations of the dynamic properties based on packed grain and discrete particle models are presented in Figures 5 and 6.

It is observed that discrete particle model calculations considering either EVA or NR as the matrix are markedly different from the experimental data. Calculations based on the polyag- pegate model are somewhat closer to the experimental results. Up to -20°C, the polyaggregate predictions for the E' data are lower than the experimental data. Above -20°C. the reverse is m e . Similar trends are observed in the case of loss tangent data. Earlier studies by Alex et a]." udicated a cocontinuous morphology for the .SO150 NIUEVA blends. In view of the assumptions for the polyaggregate model, the greater agreement with the experimental observations indicates the applicability of this model. However, the ~x ta l l deviations below and above -3VC need to k rationalized.

It may be noted from the tan &temperature c m e (Fig. 6 ) that the discrete particle model with EVA as the matrix matched reasonably well to

D'LVA\IIC PROPERTIES OF h'IbE1-A POLI1IER BLENDS 173

Figure 8 Computed and experimental loss tangent data for 70130 NWEVA blend

the experimental dnta, but underestimated the tan b values above T,. The latter model also predicted the location of the tan 6 peak to within a few dcgrecs. Howcvcr, con~pnriwun of L11c prcdic- tions of the models and experin~cntnl dnta for the storage modulus indicated a closer match for the polyaggregote model for the 50150 blend.

70130 N R EVA Blend

The expenmental data for the 70130 NWEVA blend (Figs. 1 and 2) refl6ct the increase in the volume fraction of the NR phase compared to the 50150 blend. This is manifested in lower E' values and a higher tan 6,,, for the NR phase. hioreover, there is no shift in the T, value (-46.3'C) for the component NR in the blend as shown above.

Considering the larger volume fraction of NR in the blend. the discrete particle model with NR as the matrix should match the data. Also, previous investigation of the morphology of the blend revealed aggregates of EVA domains dispersed in a matrix formed by NR?'

The predicted values and experimental results for the storage modulus and loss tangent a t direrent temperatures for the 7 W 0 NIUEVA blend for

direrent models are given in Figures 7 and 8. A comparison of the predicted values and experimental results for thc storngc modulus ns well nu the 1c~s.s Lnrlgmt Tor the 7M10 NIVEVA blend indicnlcs that discrclc particlc mdc l predictions arc in clovo agreement to the experimental data, especially from low temperature to the T, region. Above tho T*. tlic niiikli in ptwr fix 1~1th Llie nk~rllgo i i~~dulun nnd tan 6. The predictions for Lhe tun ti data mnkh the location of the T, but gives a lugher peak value compnred to the experimental data.

The discrete porticle model predicts higher tnn 6 values a t the transition region and lower values a t the temperature region around -30°C onward. Whereas the polyaggregate model matches the experimental data a t both below and above the T, region, the model overestimates the tan 6 data at T,. but to a lesser extent when compared to the discrete particle model. Calculations assuming EVA a s the matrix do not match the experiment01 results. The minor deviation ofthe model with NR as the matrix can be explained from morphologi- cnl considcrations. In tho blend. npgrcgote~ of EVA are distributed in a matrix fornled by NR. I t may be recalled that the model assumed single- dispersed spherical particles.

CONCLUSIONS

T h e Kerner models for discrete particle a n d polyaggregate s y s t e m s were used to predict t h e vis- cwlas t ic properties of N R E V A polymer blends over a t e m p e r a t u r e r ange encompassing the glass transit ion t e m p e r a t u r e regions of t h e individual components. Comparison of t h e experimental d a t a a n d the predictions indicated good agree- men t for t h e 30170 NlUEVA blend in the case of the discrete particle model. T h i s i s suppor ted by SEM studiea. For the 50150 composition, t h e polyaggregate model provided a closer match, indicat- ing i t s applicability for t h e blend. S E h l s tudies revealed cocontinuous morphology for t h e blend. For t h e 70130 NWEVA blend, discrete particle predictions d id not ag ree with t h e expcr i~nen ta l d a t a beyond the glass t rans i t ion region. T h e deviations are explained on the bas is of l a rge r do- ma ins of EVA particles dispersed in t h e NR matrix.

Oneoftheauthors(G.G.B.i wishes to thank the authorities of the Vikram Sarnbhni Space Centre for permission to carry out the studies.

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