Domain Flow in Two-Phase Polymer Systems - Advances in Chemistry

28 Domain Flow in Two-Phase Polymer Systems

Downloaded by NORTH CAROLINA STATE UNIV on May 8, 2015 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0176.ch028

A Study of the Flow Properties of a Styrene— Methylmethacrylate Diblock Copolymer and SBS Triblock Copolymers J. LYNGAAE-JØRGENSEN, N A R A S A I A H ALLE, and F. L. MARTEN Instituttet for Kemiindustri, The Technical University of Denmark, DK-2800 Lyngby, Denmark

Based on thermodynamic considerations, criteria for the existence of domains in the melt in simple shearfieldsare developed. Above a critical shear stress, experimental data for the investigated block copolymers form a master curve when reduced viscosity is plotted against reduced shear rate. Furthermore the zero shear viscosity corresponding to data above a critical shear stress follow the WLF equation for temperatures in a range: T + 100°C. This temperature dependence is characteristic of homopolymers. The experimental evidence indicates that domains exist in the melt below a critical value of shear stress. Above a critical shear stress the last traces of the domains are destroyed and a melt where the single polymer molecules constitute the flow units is formed in simple shear flow fields. g

A

number of investigations concerning the morphology of A B and A B A block copolymers have shown that these systems normally exhibit phase separation if the blocks consist of sufficiently long chains. One block type often is found to constitute a dispersed phase in a continuous matrix of the second block type. A thermodynamic treatment of phase separation i n block copolymers has been given by Krause (1,2). As is the case with blends of homopolymers, phase separation i n block copolymers is caused b y a positive free energy of mixing. Meier (3) has presented a treatment of micro0-8412-0457-8/79/33-176-541$05.00/0 © 1979 American Chemical Society In Multiphase Polymers; Cooper, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.


542

MULTIPHASE

POLYMERS

phase separation and domain formation and obtains a relation between domain size and chain length of the block. Furthermore, Meier gives a basis for estimation of critical block chain length for phase separation and domain morphology. Previous investigations (4,5,6,7,8) have shown that block copolymers exhibit unusual melt rheological properties such as a very high viscosity, elasticity, and non-Newtonian behavior even at very low shear rates which are all attributed to the multiphase structure resulting from the incompatibility between the two copolymer units i n the melt state. The purpose of this research project was to investigate whether single polymer molecules could constitute the flow units ( in the following referred to as a monomolecular melt) i n melts of a diblock copolymer and a triblock copolymer, respectively. If a monomolecular melt does exist, under what conditions w i l l it be formed? Experimental Sample Materials. A styrene-butadiene—styrène ( SBS ) triblock copolymer from Phillips Petroleum named Solprene 414C was studied i n the investigation. The material and information on molecular weight data were kindly suppliedJby Κ Η. Burr, Phillips Petroleum C o . : M = 129,000, M = 107,000, M /M„ = 1.21, styrene content 40% by weight. (Our own G P C measurements showed styrene content 3 9 % and M / M = 1.38 without correction for band spreading. ) SBS and SB materials caused problems because of thermal (and possibly mechanical) degradation. A diblock copolymer model material with blocks of methylmethacrylate (approximately 2 5 % ) and styrene was prepared since this sys tem should be thermally stable. The diblock copolymer was prepared using a technique described by Rempp et al. (9,10) with slight modifi cations. The following amounts were used: methylmethacrylate 50 g (0.5 m o l ) , styrene 150 g (1.44 mol), solvent T H F 1,000 m L , and n-butyllithium 2.5 · 10 mol (anionic catalyst). Reaction temperature, —55°C. The monomers were vacuum distilled three times and dried with C a H . T H F was refluxed over C u C l (5 h r ) , refluxed five times over C a H (8 h r ) , distilled, and finally refluxed over L i A l H . A l l treatments were carried out under nitrogen. Before the monomers were added, a drop of styrene was added to the solvent which was titrated with n-butyl lithium until the weakly red, styrylic anion color was stable. The solution was diluted with cyclohexane, a solvent for polystyrene and a nonsolvent for polymethylmethacrylate, and the product thereafter precipitated by addition to methanol; THF/cyclohexane/methanol = 1:2:10 (by volume). The product was finally dried to constant weight. Characterization of Molecular Structure. The molecular weight distribution ( M W D ) was determined before and after processing using a G P C with two detectors. The method is described by Runyon et al. (II). The G P C apparatus was Waters Assoc. Model 200. The column combination was 10 , 2 · 10 , 10 , 10 A polystyrene gel. The G P C i n w

n

w

w

u

3

2

2

2

4

e

4

4

3

In Multiphase Polymers; Cooper, S., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1979.

28.

LYNGAAE-JORGENSEN

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Domain Flow

AL.

543

strument was run under the following conditions: flow rate: 1 m L / m i n ; injection volume: 2 m L ; sample concentration: 2.5 · 10" g/mL. T H F was used as the solvent. The columns were calibrated with polystyrene standards from Pres sure Chemical Co. and from National Bureau of Standards under the above mentioned conditions except for the injection volume which was 0.5 m L . The calibration found for PS standards was used directly i n the cal culations since intrinsic viscosity-molecular weight relations for PS and P M M A samples in T H F do not deviate significantly, [rj_ = 1.17 * 10" · M for PS i n T H F (12) and [ ] = 1.28 · H T · M [cm /g] for P M M A in T H F (13) (the last relation is based on very few points with quite large scatter). The styrene content was determined to 74% by_ weight with_5% _of the total mass as pure polystyrene, M = 91,000, M = 50,000, M / M = 1.82. Except for a low-molecular-weight tailing of pure polystyrene (5% ), no deviation from the average composition was observed. N o sig nificant changes in M W D were o_bserved after processing except for the two highest temperatures, where M dropped to ~ 80,000. Rheometry. Melt-flow properties at low shear rates in a steady state rotational mode were determined by using a Rheometrics Mechanical Spectrometer on a cone and plate set up ( D D C - 1 ) and ( D D C - 2 ) be tween 160° and 250°C. The details of the geometry were: disks, diameter = 25 and 50 mm, respectively; cone angle, 0.040 rad; gap, 0.050 mm. After loading the material, measurements were performed i n succession starting with low and thereafter increasing shear rates. Additional meas urements on the triblock copolymer were performed on a Brabender Plastograph and a Rheometric's rheometer in a bicone geometry as cov ered by Ref. 14. Theoretical (Basic Hypothesis). The purpose of this part is to de rive a criterion for the transition from a two-phase melt state to a monomolecular melt state. The basic idea behind the derivation is as follows. The total change in free energy ( A G r ) by removing one domain from a melt at constant shear stress (τ) would consist of two contributions, AG = AG -)- a G . One contribution A G corresponds to the change in the free energy of mixing. Since the systems considered are originally two-phase systems (for τ = 0), AG is always positive. The action of a domain in a polymer melt ( at constant shear stress ) can be shown to be equivalent to the action of a giant crosslink i n a rubber. Removing of one "crosslink" is accompanied by a negative "freeenergy change" ( A G ). The conditions where the last domain vanishes is found as follows. A condition for equilibrium between a two-phase structure and a homo geneous-melt structure is that the chemical potential of a repeat unit i n the domain Μ and i n the monomolecular melt state Μ are the same: 3


2

w

0

7 1 7

2

v

w

w

0 6 9

n

3

w

n

w

T

m i x

2

m i x

mix

2

Α

Ό

Α

ΜΧ

Ό

= ft A Or fi A

—

M A

D

=

0


(1)

544

MULTIPHASE

POLYMERS

The chemical potential of a repeat unit i n a domain at shear stress τ can be written as the identity:

ΜΑ

where Μ ° is the chemical potential of a repeat unit of pure amorphous polymer A . Downloaded by NORTH CAROLINA STATE UNIV on May 8, 2015 | http://pubs.acs.org Publication Date: June 1, 1979 | doi: 10.1021/ba-1979-0176.ch028

Α

Μ

_

Α

Ό

Μ

ΜΑ

Α

Μ° -

(Μ »

Α

Α

-

Μ °) Α

=

0

where Μ — Μ ° is equal to the positive change i n chemical potential on mixing and — (Μ — Μ °) is equal to the negative change i n chemical potential realized when a domain acting as a giant crosslink is removed. That is, Α

Α

Ώ

Α

Α

(ΜA -/*A°)mix = MA° - ΜΑ°.

(2)

( μ A ~~>A°)mix is found by partial differentiation with respect to the num ber of polymer repeat units found i n domains ( U ), from the expression for the Gibbs free energy change on domain destruction found by Krause (2). A

S. Krause's thermodynamic treatment of the Gibbs free-energy change of mixing on domain destruction for the whole system of N copolymer molecules occupying volume V gives c

àG /kT=

(V/V )v v (l

mix

r

A

= 2/z) +

BXAB

- 2 Ne (m - 1) (AS /R) dis

N ln(v *AV *B) c

A

B

+ N ln(m - 1)

(3)

c

where V is the total volume of the system, V is the volume of a lattice site, V and V are the volume fractions of monomer A and Β i n the copolymer molecule, respectively, ζ is the coordination number of the lattice, χ Β is the interaction parameter between A units and Β units, m is the number of blocks i n the block copolymer molecule, A S / R is the disorientation entropy gain on fusion per segment of polymer which is again related as A S / R = In [(z — l)/e], where e is the base of the r

A

B

Α

di8

di8


28.

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545

Domain Flow

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natural logarithms, k is the Boltzman constant, and Τ is the absolute tem perature. O n differentiating Equation 3 with respect to polymer repeat units in a domain (C7 ), A

( μ A — μ Α ° ) m i x == / d ^ O m X


\

P ^ A

=

Τ,Ρ,ϋΒ

/

+ 1η(ν ^ · ν ·.)1 - 2 J Xn Δ

(

Β

_

m

1 }

+

1 Xn

K

l

n

(

m

1 }

)

( 4 )

)

for a copolymer with molar volumes V , V and mole fractions n and n » V = n V + B V , v is the volume fraction of repeat units found i n domains, υ = 1 — υ and X is the degree of polymerization. As shown in a later publication, A

A

N

B

B

B

A

B

A

Β

Α

n

(MA

-

D

ΜΑ°)

=

(5)

where τ is the shear stress, Τ absolute temperature, and Q is a constant depending on the molecular structure of the material (calculated as 0.166 (erg mol/cm K ) for the P S - P M M A block copolymer). 6

F M *H c

2

where α is approximately equal to the ratio between the second and the first normal stress difference ( approximately 0.1), ρ is the melt density, R is the gas constant, V is the average molar volume of the repeat units, M is the critical molecular weight where the exponent a i n the equation η = Κ · M changes from 1 to 3.5, and Η is the heterogeneity of the sample: H = M / M . Substituting Equations 4 and 5 into Equation 2 and simplifying, the following expression is found: c

w

a

w

n

ZÇ-A'T

for

where a and β are constants, disappear, and

T * C R

X A B

+ B'

=

a+|,

(6)

(7)

is the shear stress where the last domain


546

MULTIPHASE

A' = Q y { Rv

( 1 -

2

B

-

fj a+ R/X

n

(m - 1) (AS /R)

(2R/X ) n

m

POLYMERS

[ i n Ï / ^ B + Î , In

^ ]

b

+ = - ln(m - 1 ) |


*'-Q^w(l-?)-* Since A ' and B ' are constants for a given copolymer and the possible temperature interval is relatively limited, a transition is predicted at an approximately constant shear stress. Melt transitions have i n faot been reported at approximately constant shear stresses for styrene-butadienestyrene triblock copolymers (4). However, this behavior was certainly not observed for the styrene methylmethacrylate diblock copolymer. A possible explanation for the observed behavior is given as follows. The exact movement of a domain i n a shear flow field is difficult to describe if the domain is a viscoelastic liquid because the domain w i l l deform. However, whether a domain is " r i g i d " or deformable it has to rotate i n order to constitute a flow unit. The force holding the domain together is the "chemical potential force" opposing mixing of A and Β segments. However, if flow processes occur inside a domain it may break up before the conditions derived above are reached. The following hypothesis could serve as a first approximate rationalization of the ob served behavior. The probability Ρ that a part of a polymer molecule belonging to a domain w i l l be "torn" out by flow processes is assumed to be proportional to the ratio between the energy which is actually transmitted by the melt to that which is theoretically necessary for destruction of a domain. F is furthermore inversely proportional to the "domain viscosity." That is

P«

Domain Flow in Two-Phase Polymer Systems - Advances in Chemistry

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