Multiphase Polymers: Blends and Ionomers - ACS Publications

Chapter 6

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Phase Transitions in Simple Flow Fields J. Lyngaae-Jørgensen IKI, The Technical University of Denmark, 2800 Lyngby, Denmark

A theoretical expression for the depression of the melting point of polymers with low degree of crystallinity is derived for simple shear flow at constant rate of deformation using a thermodynamically approach. The last surviving crystallite aggregate is treated as a body consisting of many single polymer molecules held together by a crystalline nucleus. The theory is tested with data for PVC, copolymers of ethylene and polypropylenes. An analogical approach has been applied to blokcopolymers and polymer blends in order to predict transitions from two-phase to one phase melt state during simple flow. Two-phase flow of polymer systems i s of increasing importance because of the increased application of blockcopolymers, blends and a l l o y s . Most polymers are immiscible with other polymers of d i f ferent molecular structure (1) because the entropy of mixing converges to zero with increasing molecular weight. The properties of an immiscible blend depend on the two-phase structure or morphology of the blend, the interface structure etc. I t i s therefore important to be able to control the two-phase structure of the blend. This d i s c i p l i n e : c a l l e d structuring, which i s governing of the two-phase or multiphase structures by proper selection of processing prehistory, i s of increasing i n d u s t r i a l and academic i n t e r e s t . One p o s s i b i l i t y for obtaining materials with special morphologies a f t e r processing, often i n a reproducible way, i s to provoke phase transitions i n flowing systems. The purposes of this contribution are; 1. to b r i e f l y review some of the papers dealing with interactions between, e.g. shearing stresses i n flow and phase behavior, and 2. to develop models for 0097-6156/89/0395-0128$07.25A) o 1989 American Chemical Society

Utracki and Weiss; Multiphase Polymers: Blends and Ionomers ACS Symposium Series; American Chemical Society: Washington, DC, 1989.

6.

LYNGAAE-JORGENSEN

Phase Transitions in Simple Flow Fields129

phase transitions i n simple flow f i e l d s . The focus here i s on transitions to "homogeneous" melt states i n simple flow f i e l d s . Two cases for phase transitions i n simple flow f i e l d s w i l l be treated, 1. a t r a n s i t i o n involving melting of c r y s t a l l i n e areas i n polymers with low degree of c r y s t a l l i n i t y , and 2. a t r a n s i t i o n to a homogeneous state of an o r i g i n a l l y phase separated blend of two polymers. This case represents an attempt to extend the solution developed for case 1; consequently the ideas are presented with emphasis on melt theory i n flow f i e l d s as well as an evaluation of the theoretical predictions. The published work on polymer blends (18) w i l l be only b r i e f l y summarized i n this paper. E a r l i e r findings. The subject i s broad because interactions between stresses and, say, the melting temperature may be encountered i n many different situations e.g. during necking of c r y s t a l l i n e polymers (2). In simple flow f i e l d s as i n c a p i l l a r y flow i t i s normally reported that c r y s t a l l i n i t y i s provoked by flow (3). However, for polymers with low degree of c r y s t a l l i z a t i o n i t was assessed that the melting point was depressed at high shear stresses (4). Shear induced melting has been t h e o r e t i c a l l y predicted from non-equilibrium molecular dynamic simulations (5, 6); at higher shear rates a t r a n s i t i o n to a new ordered state was predicted. The question of interaction between shear flow and phase structure was studied by Silberberg and Kuhn (7) i n 1952. They reported that a homogeneous one-phase solution r e s u l t s i f a v e l o c i ty gradient i s maintained i n a stable two-phase system of p o l y styrene, e t h y l c e l l u l o s e and benzene. Rangel-Nafaile, Metzner and Wissbrun (8) reviewed studies on s o l u b i l i t y phenomena i n deforming solutions and developed an expression for stress-induced phase separation i n polymer s o l u tions. Other recent studies i n this f i e l d were published by Wolf et a l . (9-13) by Mazich and Carr (14) and by Vrahopoulou-Gilbert and McHugh (15). There i s no general consensus as to the influence of stress during flow on phase e q u i l i b r i a at present, and i n fact observations from d i f f e r e n t sources are c o n f l i c t i n g . Most observations of d i l u t e solutions with upper c r i t i c a l solution temperatures indicate that phase separation may be provoked by mechanical deformation (8) or, stated d i f f e r e n t l y , that the c r i t i c a l s o l u b i l i t y temperature i s increased by flow. Wolf et a l . (9-12), however, developed a theory which predicts that the s o l u b i l i t y temperature may decrease by flow i n accordance with Silberberg*s (7) observations. Wolf et a l . calculated the equilibrium size of droplets formed i n a phase-separated system. From a force balance, he derived an expression indicating that the equilibrium droplet size r i s a decreasing function of shear rate and that when r approaches the radius of gyration of the polymer molecules, r e d i s s o l u t i o n w i l l have occurred. Recently Kramer and Wolf have generalized the approach and formulated simple c r i t e r i a for solution, respectively demixing (16).


130

MULTIPHASE POLYMERS: BLENDS AND IONOMERS

Only a few investigations on shear flow induced changes i n s o l u b i l i t y phenomena i n polymer blends have been reported. However, Lyngaae-Jorgensen and Semdergaard (17, 18) d i d advance a hypothesis predicting that a homogeneous melt should be formed at suff i c i e n t l y high shear stresses for nearly miscible blends. Experimentally, such a t r a n s i t i o n was observed for simple shear flow for blends of SAN and PMMA (19). Winter observed a t r a n s i t i o n to homogeneous state i n u n i a x i a l extensional flow for a blend of PS and PVME (20) at high extensional

strains e = et ^ 44 Hencky.

Melting of C r y s t a l l i t e s i n Polymers with Low Degree of C r y s t a l l i n i t y i n Simple Flow F i e l d s We considered a linear polymer with c r y s t a l l i z a b l e sequences. The molecules of the polymer consist i n p r i n c i p l e of a l t e r n a t i n g blocks of c r y s t a l l i z a b l e and n o n - c r y s t a l l i z a b l e sequences. Examples of such chains would be nearly a t a c t i c homopolymers and random copolymers. Poly(vinylchloride) produced at temperatures between 40°C and 60°C are only s l i g h t l y c r y s t a l l i n e and i t may be assumed that only syndiotactic sequences c r y s t a l l i z e . Polymers where only sequences with a stereospecific configuration can c r y s t a l l i z e may, i n the context of this paper, be considered as copolymers. The melting point of a polymer i s defined as the temperature where the l a s t trace of c r y s t a l l i n i t y disappears. Only the most stable c r y s t a l l i t e s existing i n the material exist i n the melt at the melting point. It i s assumed that i n a shear flow f i e l d the l a s t surviving "structures" showing c r y s t a l l i n i t y consist of a c r y s t a l l i n e nucleus acting as a giant branching point with n branches (a c r y s t a l l i t e aggregate). This assumption i s based on the fact that the last surviving c r y s t a l l i t e aggregate i n d i l u t e solution has this structure (21). A key concept used i n this work i s that of "entanglements" even though i t i s an i n t u i t i v e and rather i l l - d e f i n e d one. Entanglements here are considered to r e present regions where neighbouring molecules are looped together one after another and thereby offer high resistance to deformation for a time (22). A number of assumptions are made: random c o i l e d linear polymer molecules, isothermal conditions, constant volume, molecular weights (M) much larger than the c r i t i c a l molecular weights (M ) for entanglement formation, constant segment concent r a t i o n , n e g l i g i b l e i n e r t i a l forces ( e t c . ) c

At isothermal steady state conditions, we assume that the melt behaves as a l i g h t l y crosslinked network with non-permanent network points. The effect of destroying c r y s t a l l i n e aggregates i s evaluated as the removal of "extra" entanglements i n a continuous phase with non-permanent crosslinks (entanglements). That i s , c r y s t a l l i n e aggregates are considered and measured i n entanglement units. The free energy of a closed system without flow i s a function of state and may be expressed as a function of intensive state parameters including temperature, T, pressure, P and composition.


6.

Phase Transitions in Simple Flow Fields131

LYNGAAE-JORGENSEN

The number of degrees of freedom, n, i n the system i s given by n = k + 3 - f

(1)

where f i s the number of phases, k the number of components. Eq. 1 states that the melting temperature i s therefore a function of e.g. shear rate (or shear stress) and pressure. If solvent i s present we may express the melting temperature as a function of e.g. p r e s sure, shear stress and solvent volume f r a c t i o n . A Theory for T r a n s i t i o n to a Monomolecular Melt state at Constant Shear Rate (Simple Shear Flow). A c r i t e r i o n for a t r a n s i t i o n from a two phase state to a monomolecular melt state may be formulated as follows. The t o t a l change i n free energy (AGj,) by removing one c r y s t a l l i t e aggregate from a melt at constant shear rate may be considered to consist of the c o n t r i butions: AGL = AG + AG . + AG . i melt mix el ^melt

c o r r e s

P°

n c

^

s

t

o

v

(2) '

tbe change i n the free energy observed when

pure c r y s t a l l i n e phases are melted. Since the systems considered are o r i g i n a l l y two-phase systems (for shear stress: T = 0), ^ G ^ m e

t

i s always p o s i t i v e . The action of a domain i n a polymer melt i s assumed to be equivalent to the action of a giant c r o s s l i n k i n a rubber. Removing one "crosslink" i s accompanied by a negative free energy change ( A G ^ ) . If solvent i s present i n the mixture one need to include the term A G ^ ^ , which corresponds to the change i n the free energy observed when pure phases are mixed. At steady state a condition for equilibrium between a two-phase structure and a homogeneous melt structure i s that the chemical potential of a repeat unit i n the c r y s t a l l i n e phase

i s equal to the chemical

p o t e n t i a l of a repeat unit i n the melt state

=

"A cr

ref

»k ~»k J

" A ref ^ A ^ A

{

3

)

, ^ A

(

4

)

ref

i s a suitably chosen reference state. For pure polymers ref A with the same molecular structure as the sample. If solvent i s present the reference state may of convenience be chosen as the chemical potential of a homogeneous amorphous melt of the same composition i n the mixture considered. J


132


Expressions for the l e f t and the right hand side of Eq. 4 are derived i n appendix. For pure polymer melts, into Eq. 4 gives:

i n s e r t i o n of Eqs. 5 and 12 from appendix

1 T, dyn

r

T m

2

(13)

Q T? dyn

where 2 c

4

RAH

A

Q = a

2

p

2

M H A

2

M

c

dyn where T

m

i s the s t a t i c melting temperature and

i s the melting

temperature at constant shear rate i n simple shear flow, a i s a constant, p i s polymer density, i s the molecular weight of a repeat u n i t , H = M^^/M i s the r a t i o between the average molecular n

weight by weight and by number, respectively,

M i s the average e

molecular weight between entanglements. In the calculations we use an estimate M ^ 2 M , M i s the molecular weight at the i n t e r c e c section of two lines defined by the equation 7) = K q

where b

changes from ~1 to ~3.5; c i s polymer concentration, R i s the gas constant, = T i s the shear stress and AH^ i s the enthalpy of melting per repeat u n i t . The s t a t i c melting temperature i s depressed by solvent. The change may be written (23):

where T

m

1

1

m

m

R V

A

2

i s the s t a t i c melting temperature of polymer-solvent mix-

ture, T° i s the melting temperature of the pure polymer,

and

the molar volume of a repeat unit and solvent molecule, respectively, Vj i s the solvent volume f r a c t i o n and \ the i n t e r a c t i o n parameter. The f i n a l expression for the dynamic melting temperature may again be cast i n the form of eq. 13 i f T i s defined as the m melting temperature of the polymer-solvent mixture.


6.

LYNGAAE-JORGENSEN

Phase Transitions in Simple Flow Fields 133

The Gel Destruction Temperature T ^

1 1

i n a Shear Flow f i e l d below

the S t a t i c Gel Destruction Temperature T^.

The gel destruction

temperature may be defined as the temperature where enough c r y s t a l l i n e areas (which act as crosslinks) are melted to prevent an effective i n f i n i t e network of c r y s t a l l i n e areas to exist i n the melt (threshold percolation structure). In this respect, gel formation i s analogous to the gel point during condensation polymerization. Below the gel destruction temperature T^ the material i s i n a rubb e r l i k e s o l i d state. If a rubberlike s o l i d ( l i k e PVC p a r t i c l e s below T j ) i s sheared i n a shear flow f i e l d i t w i l l deform u n t i l the adhesion to the walls of the equipment f a i l s , the gel structure i s broken or melted or a slippage mechanism involving e.g. a p a r t i c l e flow mechanism such as Nooney flow as proposed by Berens and Volt (25-27) i s established. The derivation of a r e l a t i o n between T and r i s equivalent d

to the derivation i n the preceding section. C r y s t a l l i n e network c r o s s l i n k s , w i l l melt i f one transfers d i f f e r e n t i a l amounts of r e p e t i t i o n units from the c r y s t a l l i n e to the amorphous state i n such a way that the free energy change i s always negative or zero, or

" ( ^ V ? ) )

+ (H -HA)

= 0

A

(15)

el

H

< >

given by F l o r y . The change of free energy by melting of a c r y s t a l l i n e crossl i n k i n a deformed rubbery state i s :

e A

where X

c r

cr

T.P.T

(or evt. T )

i s the number of r e p e t i t i o n units between c r o s s l i n k at T^

and N the number of c r y s t a l l i n e c r o s s l i n k .

If we consider a

material being deformed at constant shear rate*, (nr = t t ) : AG

e l

= | N R T (4t)

T

= NRT -rt

2

(18)

(19)


134

MULTIPHASE POLYMERS: BLENDS AND IONOMERS For a momentary t r a n s i t i o n M X = L = X ; N = — cr M w ir o H c

f

RT =

RT 2\

~

F

T

n H . T.P.,

2

RT 2

(NKT) "

2X 4 M W

r

2

2

X

* w

2

M

.

"

O"W

t 2

1

2

2 c RT

2

w (20)

Insertion of Eq. 16 and Eq. 20 into Eq. 15: 2c

2

RAH.

where Q = T ,Q d

J

(21) M. M A w

Thus the gel destruction temperature may be evaluated as a function of shear stress by Eq. 21. According to Eq. 21, the stresses necessary to depress T^ are so large, (at least for r i g i d compounds) that melt fracture or p a r t i c l e slippage takes place before any change i n T^. Melt fracture i n a c a p i l l a r y corresponds to constant shear stress at the w a l l . It can be seen by analogy with the derivation i n the preceding section that at constant stress T^ i s expected to increase. Thus Eq. 21 predicts that the o r i g i n a l p a r t i c l e structure cannot be destroyed below the gel des t r u c t i o n temperature for r i g i d and concentrated compounds. Experimental Sample Materials. Vinnol H 60d, Vinnol Y 60, and Vinnol E 6Qg are commercial polyvinylchlorides from Wacker, produced by suspension, bulk, and emulsion polymerization techniques, respectively. A l l materials have nearly the same molecular weight d i s t r i b u t i o n (MWD) as S o l v i c 226 which, (with our SEC c a l i b r a t i o n ) gave: M" = 74.000, w

M^ = 35,000.

The samples used i n this investigation i n the Vinnol

60 series had molecular weights i n the range M^ = 72,000 ± 2000 and M = 34,000 ± 2000. n

Vinnol H 70 d: M = 110.000 and M = 54,000. w n

Vinnol H 80 F: M = 166,000, M = 80.000. w n

Four parts of l i q u i d t i n *^


6.

LYNGAAE-JORGENSEN


s t a b i l i z e r , Okstan X-3 (from Otto Barlocher GmbH, Munich), were used i n a l l compounds. The s t a b i l i z e r was chosen because of i t s high thermostabilizing effect and compatibility. 25, 50, 100 and 200 pph of p l a s t i c i z e r : DOP (Di-2-ethylhexyl phthalate) were used. Alathon E/VA 3185 from Du Pont, an ethylene-vinyl acetate copolymer with 33 wt % v i n y l acetate M = 79800, M = 19800 as described i n w n Ref. 28. J

Methods. The molecular weight d i s t r i b u t i o n was determined by size exclusion chromatography SEC as described elsewhere (4). Rheometrv. The following rheometers were used i n this study: An Instron c a p i l l a r y rheometer, a Rheometries mechanical spectrometer, used i n both cone and plate mode as well as i n the b i c o n i c a l mode, and a Brabender Plastograph (4). Results. It i s seen from eq. 13 that the parameter Q can be c a l culated i f corresponding values of and T are measured and T

m

i s found either by independent measurements or from rheological data. Q has been determined by 1. p l o t t i n g logT against 1/T with nr as discrete variable and curve f i t t i n g . The v i s c o s i t y of a homogeneous melt can be approximated by 17 = A exp(E*/RT)(22), where E^ i s the a c t i v a t i o n energy at constant shear rate and A and R are constants. A plot of logT against 1/T with nr as discrete v a r i a b l e i s thus a straight l i n e for a homogeneous melt. A melt containing c r y s t a l l i t e s with a d i s t r i b u t i o n of c r y s t a l l i t e sizes "melts" over a broad range of temperatures. Crys t a l l i t e aggregates acts as very large branched structures. Destruction of c r y s t a l l i t e aggregates causes a decrease i n the viscosity. Thus below the melting temperature but above the gel destruction temperature a temperature increase w i l l involve two contributions the "normal" descrease i n v i s c o s i t y given by Eq. 22 and a decrease caused by c r y s t a l l i t e melting. So below the melting temperature a curve through corresponding points i n a delineation of logT against 1/T r e f l e c t s the more stable part of the c r y s t a l l i t e size d i s t r i b u t i o n (a melting curve). At the melting temperature the melting curve and the straight l i n e representing homogeneous melt behaviour crosses. The intersection points represent corresponding values of T , and T . T can be found as the l i m i t dyn m ing value of for small r values. Such plots are shown on F i g . 1 and 2 for PVC compounds, on F i g . 3 for EVA and on F i g . 4 for ethylene propylene copolymers, respectively (see next section). On these plots Eq. 13 i s shown as the f u l l drawn curve. This curve represents the geometrical place for the points where the last c r y s t a l l i t e s disappear; consequently the straight lines representing homogeneous melt behaviour should intersect the measured logT Y curves on the f u l l drawn curve. 2. a l t e r n a t i v e l y Q can be estimated as shown i n F i g . 5.

If "recry3

s t a l l i z a t i o n " i s a slow process corresponding values of T**™ and T


136


i i i I 1i i i i 1i I I I | i i I i | l I I I |l i I i 1I I l

i i 1i i i i I i i i i I I 2.00

2.05

2.10

2.15 3

2.20

2.25

2.30

1

10 -1/T(K" )

F i g . 1. Delineation of logarithmic shear stress against r e c i procal temperature with shear rate as discrete v a r i a b l e . Shear 1

rates: 1.8 , 9, 18 , 36 , 72, 108, 180 and 270 sec" , respectively. Material: Vinnol H70/D0P/stab: 100/50/4. F i l l e d points c o r r e o * spond to data where samples were "premelted" at 210 C at nr= 36 sec to steady state. F u l l heavy drawn curve: best estimate of Eq. 13 r e l a t i o n . Dotted curve calculated from Eq. 13 with a = 7.7. 1


6.

LYNGAAE-JORGENSEN

10

2l I I 2.00

Phase Transitions in Simple Mow Fields

I 1 I l I I I

2.05

III I 2.10

i i I i i M

2.15

3

10 VT ( K F i g . 2.

I I l

1 I 2.25

I I i I i i I

2.30

)

A p l o t of logT against 1/T with nr as discrete v a r i a b l e

for Vinnol H60/D0P/stab 100/50/4. 144,

_1

1 i 2.20

1

180, 234 and 270 sec" .

and 108 sec = 7.7.

1

.

v'- 1.8 , 9, 18 , 36 , 72,

108,

F i l l e d points: premelting at 205°C

F u l l drawn curve: best estimate.

Dotted curve: a


137

138


I

I

I

I

2.80

I

I

I

I

I

U 1

2.90 3

I

I

I

I

I

I

I

3.00 1

1/T-10 (K' ) F i g . 3.

LogT against 1/T with shear rate as discrete v a r i a b l e

for E/VA 3185 (33 (W%) vinylacetate). -Y:0.01, 0.016, 0.025, 0.04, 0.063, 0.1, 0.16, 0.25, 0.4, 0.63, 1.0. 1.6, 2, 5 and 10 sec

respectively.


6.

LYNGAAE-JORGENSEN


F i g . 4. A p l o t of logT against 1/T with nr as discrete variable for EP copolymer with 66 (mol%) propylene. F u l l drawn curve calculated from Eq. 13 with a = 8.


140

Fig.


5.

Plot of shear stress against shear rate at 190°C for the 1

sample used i n F i g . 2. -r = 1.8 • N (sec" ) and T = 60»M (Pa). The c i r c l e s are measured s t a r t i n g with the lowest rates. The cubes are measured when the shear rates are decreased.


6.

LYNGAAE-JQRGENSEN


may be found from the intercept of the two curves found by f i r s t increasing and then decreasing the shear rate. These curves are measured again after annealing without flow. F i g . 6 shows a double logarithmic plot of Q against concent r a t i o n (c) for FVC samples. The slope i s within experimental uncertainty equal to the theoretical value 4 given i n Eq. 13. The average value of the constant a i s found to be 7.7. = 8 . F i g . 7 shows a delineation of Eq. 13 and Eq. 21 i n a p l o t of logT against reciprocal temperature for a r i g i d compound with = 72000.

Values for stress g i v i n g melt fracture at the wall are

shown too. For steady state measurements F i g . 7 shows that normal molecular melt flow, where the single polymer molecules constitute the flow u n i t s , i s predicted i n area A. In area B i t i s predicted that stable crystallite-aggregates exist i n the melt. In area C the material i s i n a l i g h t l y cross linked rubbery state. Discussion (Comparison with L i t e r a t u r e data). F i g . 1-4 show a rasonably accordance with eq. 13. From such plots T can be m

assessed as the l i m i t i n g value of 1/T for small values of shear stress. From corresponding values of and T , Q may then be evaluated from Eq. 13. The p r e d i c t i o n that Q depends of the concentration to the fourth power i s tested i n F i g . 6. The uncertainty on a single estimate of Q i s r e l a t i v e l y large because Q r e f l e c t s uncertainties on both T , and r (standard deviation on Q: ±15%). However, m

i f we p l o t the average values for each concentration i n DOP determined by either method 1 or 2, and a single point where t r i c r e s y l phosfate (TTP) were used as p l a s t i c i z e r , we find a slope i n a p l o t of logQ against logc equal to 3.97. This slope i s d e f i n i t e l y not s i g n i f i c a n t different from the theoretical value 4. The concentrations were calculated at T . Some of the Q data have been m published (4, 28 and 29). From the experimental Q values the constant a i s found to be 7.7 ^ 8. In F i g s . 3 and 4, Eq. 13 i s plotted as the heavy f u l l drawn curve. The data used for the variables i n Eq. 13 i n F i g s . 1-4 are shown i n Table 1. The data for copolymers of ethylene-propylene copolymers (measured by c a p i l l a r y rheometry) are transplotted from Vinogradov (30). Since the model describes different systems of polymers with low degree of c r y s t a l l i n i t y within experimental uncertainty, i t i s concluded that the model described i n Eq. 13 cannot be rejected based on our test data. Dramatic changes i n rheological response of PVC compounds taking place at c h a r a c t e r i s t i c temperatures (T ) have been reported by many groups (4, 31-36). The most elegant technique which permits an evaluation of Q by determination of corresponding values of and T i s described m

by V i l l e m a i r e and Agassant (37 , 38). They constructed an ingenious piece of equipment which allows material to be processed i n Couette flow under variable conditions and immediately thereafter to be extruded through a c a p i l l a r y rheometer. Their findings are i n dicated i n F i g . 8 and 9 (by courtesy of Villemaire and Agassant).


142


-0.6

-0.4

-0.2 log C

0.0 0.2 (log(gycm )) 3

F i g . 6. Log Q vs. log c for PVC compounds. O : Based on Vinnol H60D/D0P/stab mixtures. Q, : Vinnol H70d/D0P/stab: 100/50/4, JO : Vinnol H80F/D0P/stab: 100/100/4, • : Vinnol H60d/Tricresylphosphate/stab: 100/100/4.


Phase Transitions in Simple Flow Fields

LYNGAAE-JORGENSEN

_

I

I

I

I

I

I

I

I

I

I

I

I I I .

I

•

•

~

_

-

a

10

/

A

5

Q_

-

10

I

H

1.95

i 1/T

C

B

/

M

i

i

i

I

2.05

2.15 3

I 1/T

D

I

"

I

2.25

1

1/T-10 (K' )

F i g . 7. LogT against 1/T as predicted by Eq. 13 and Eq. 21 wi melt fracture data plotted i n the same delineation for a PVC sample with M = 72000 and PVC/stab: 100/4. w



4

A

V

(4)

3

_1

(Pa «K -10~ )

2

1

2

1

9

7

K" 10 - >

3.

2.

1.

7.7

68

fl

In X with AH. PP A

7.5

6.4

930

3

(2)

8.3:17

8

7.8

8

3.3< >

40.9

6400

9,84 ,R = ' mol '

30

60

8

7.7 4.9

4.0

36.13

5700

5.7

950

393 9.207

341 7.533

— mol'K

Mol Fraction propylen (1) X 0,67

10-20% crystallinity p

EPM

E/VA 3185

2.1

44.65

11500

11.5

1280

1390

3.285

481.46

708

792

Vinnol H70d PPH PVC 100 DOP 50 XOC 4

V

V = A

M

A ^

•XOC

20°C

1070

m From M = 3.8*V where V = M *v and M i s the average molecular weight of a stretched chain e g g g s p g (44) which i s 2.5 A long. V i s the s p e c i f i c volume of polymer (45) Estimated from v i s c o s i t y - shear rate data

R AH

1

\°

7.5

4.9

7.7 54

2.1

44.65

2.1

Estimated from the equation •

(Pa •K" -10" )

2

((dyn/cm )

2

Qexperimental

U

n

H = M /M w n a calculated ( e q . 14)

7

(m /mol) -10"

3

(g/mol)

(cm /mol)

c

44.65

11.5 11500

11.5 11500

M (kg/mol)

M

c

1280

1280

1390

1390

p(220°C)(kg/m )

3

p(20°C)(kg/m )

3

3.285

3.285

A

708 474.16

1208 503.15

K

m ° A H (KJ/mol)

3

T

(220°C)(kg/m

c

792

1325

3

(20°C)(kg/m )

Vinnol H60d PPH PVC 100 DOP 50 XOC 4

Vinnol H60D PPH PVC 100 XOC 4

Variables used i n Eq. 14

c

Sample

TABLE 1.

6.

LYNGAAE-JORGENSEN


From plots l i k e that i n F i g . 8 and TXT corresponding values m of T and T^^ may be evaluated as the point of conversion of a l l 11

curves irrespective of prehistory. Q can be calculated from Eq. 13. V i l l e m a i r e and Agassant interpreted their results as caused by melting of c r y s t a l l i t e aggregates. According to the gel destruction temperature hypothesis i n Eq. 21 the prehistory effects can only be observed for T >T>T,. This i s documented by V i l l e m a i r e and m a Agassant as shown i n f i g . 9; a c t u a l l y the figure allows of both T

d

and T . m

For a r i g i d sample with ^

estimation

^ 70000, T j * 180°C

and T ^ 2 3 0 ° C . The average Q values estimated from V i l l e m a i r e and m Agassant's data and an estimation of significance i n t e r v a l are shown on F i g . 6. The data are within experimental uncertainty i n accordance with our data. Singleton et a l . (39) have published data for FVC with 40 p . p . h DOP which may be s i m i l a r i l y interpreted as those published by Villemaire and Agassant. The calculated Q data are shown i n F i g . 6. It i s thus concluded that Eq. 13 i s reasonable for samples where > T^. It can be shown (40) that the gel destruction temperature T , i s related to the melting temperature T

by

(f -constant) T, = — = T d f m where £

i s the sequence length of c r y s t a l l i t e s melting at T^.

Consequently, as the c r y s t a l l i z a b i l i t y increases,

T^ and T

m

converge. For polymers with regular stereospecific configuration or block copolymers with well-defined block lengths T^ = T as may m

be shown for polypropylene model systems and Hytrel block copolymers.

T^ predictions for PVC compounds are compared with e x p e r i -

mental data i n Ref. 40. Phase Transitions i n Polymer Blends and Block Copolymers A d e r i v a t i o n analogous to the derivation i n this paper has been extended to diblock copolymer systems (41) and to immiscible (at T = 0) polymer blends (18). T h e o r e t i c a l l y , i t i s predicted that a homogeneous state may be formed during simple flow above a c r i t i c a l shear stress, which depends primarily on the m i s c i b i l i t y of the two polymers. Light scattering measurements on a (nearly miscible) model system consisting of mixtures of SAN and PMMA were applied during flow i n order to evaluate the p r e d i c t i o n that a phase trans i t i o n to a homogeneous state could be provoked by a p p l i c a t i o n of a c r i t i c a l shear stress. At conditions within the spinodal range of the phase diagram i t was shown (19) that above the stress r =80


146


1 P.V.C. A

• •

!

Fig.

8.

10s 108

I30s-b I30s-I

190°C 210°C

10 100 1000 Shear r a t e s-1

Influence of mechanical and thermal h i s t o r y on the v i s -

c o s i t y of PVC A a t 190°C (M^

70000).

(Reproduced with permission

from r e f . 37. Copyright 1984 Elsevier.)

-

P .V.C. A She a r

!0s-A

rate:

-

S

407.

-

—

w 207.

£

180

190 Temperature

Fig.

9.

200

210

°C

Evolution of the f a l l of v i s c o s i t y with measurement

temperature of PVC A for a shear rate of 10 s

.

(Reproduced

with permission from r e f . 37. Copyright 1984 Elsevier.)


6.


LYNGAAE-JORGENSEN

kPa the t o t a l scattering i s ~ zero and the anisotropic scattering pattern disappears. When the shearing i s stopped the scattering pattern i s independent of scattering angle and shows maxima i n a p l o t of scattering intensity as a function of scattering angle(42). The structure formed i s an interpenetrating cocontinuous structure. The melt i s o p t i c a l l y clear above and milky below. Thus i t has been documented that a phase t r a n s i t i o n to homogeneous state may be provoked by shearing. However, even though s u r p r i s i n g l y good predictions of m i s c i b i l i t y of polymer blends may be obtained based on e.g. group contribution models (43), such methods can at best give an order of magnitude estimate for a c r i t i c a l shear stress (T" ). Consequently the p r e d i c t i v e v a l i d i t y of c

expressions for

i n polymer blends i s of limited value with the

present accuracy of predictive schemes. Acknow1edgment s The author wish to express h i s gratitude to the Danish Council for S c i e n t i f i c and Industrial Research for f i n a n c i a l support of the project. Appendix The expression^

"A

R

- "A -

~

( 5 )

r> m

has been successfully used by Flory (23) and w i l l be accepted here. AH^ i s the enthalpy of melting per repeat unit and T i s the s t a t i c m

melting temperature ( i n contrast to the dynamic melting point i n troduced be1ow). A c r i t i c a l condition for a t r a n s i t i o n from a two-phase system to one single homogeneous phase i s that we can transfer d i f f e r e n t i a l amounts of the components from the two-phase system to a homogeneous phase i n such a way that the contribution to the fre energy i s always negative or zero, or that: ref ^A'^A

1

1

where O ^ " ! ] ^ ) ing with A G

e l

el (eq.

*

s

t

n

e

J

+

el

^

U

cr ref A ~A ^ U

Multiphase Polymers: Blends and Ionomers - ACS Publications

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