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2014 | OriginalPaper | Chapter

7. Rheology of Polymer Alloys and Blends

Authors : Musa R. Kamal, Leszek A. Utracki, A. Mirzadeh

Published in: Polymer Blends Handbook

Publisher: Springer Netherlands

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Abstract

This chapter presents an overview of some of the important principles and characteristics associated with the rheological behavior of polymer blends. Initially, the chapter reports the observations and the scientific laws that illustrate and govern the rheological behavior of classical suspensions and emulsions of simple non-polymeric liquids. It is indicated that one of the main characteristics that differentiates the rheological behavior of polymer blends from that of simpler liquids is the viscoelastic nature of polymers and their blends. The discussion also points out the relationship between blend morphology and rheology and the importance of surface energy effects, such as interparticle and interfacial interactions. The general rheological characteristics of miscible polymer systems are considered. However, since the majority of polymers are immiscible, the rheological behavior of immiscible polymer blends is considered in more detail, with allowance for both thermodynamic and morphological factors. The influence of flow on morphology, as in phase separation, drop deformation, breakup, and fiber formation are discussed. Both viscous and viscoelastic characteristics of blend behavior are described, under the influence of shear and elongational flow fields. Various examples are presented, based on the study of rheological behavior of blends in both rheological testing devices (parallel plate, rotational, steady state, oscillatory, capillary, elongational, etc.) and processing equipment (extruders, mixers, molds, dies, etc.). In many cases, the observed rheological behavior is compared to the predictions of theoretical, computational, or empirical models.

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previous chapter Interpenetrating Polymer Networks

next chapter Morphology of Polymer Blends

Notations (Roman Letters)

a, b, k, K, n, u, β

Equation constants

Interfacial area density

BAB

Reduced binary thermodynamic interaction parameter, B_AB = χ_ABRT/V

Droplet width

Segment length

Lee and Park relaxation parameters

Deformation

Droplet diameter

Equilibrium droplet diameter

D, DM, Ds

Diffusion, inter diffusion and self diffusion coefficient, respectively

Particle diffusion coefficient

E+

Threshold energy of coagulation

EDK

Macroscopic bulk breaking energy

Intrinsic thermodynamic function

Frequency

G*, G′, G″

Complex, storage and loss shear modulus, respectively

H(τ)

Relaxation time spectrum

\( \tilde{\mathbf{H}}\left(\boldsymbol{\upomega} \right) \)

Reduced frequency relaxation spectrum

\( {\tilde{\mathbf{H}}}_{\mathbf{G}}\left(\boldsymbol{\upomega} \right) \)

Gross’ frequency relaxation spectrum

Hmax

Maximum of the relaxation spectrum

Critical separation distance

Boltzmann constant

Droplet length

Onsager-type mobility factor

Mn, Mw, Mz

Number, weight and z-average molecular weight, respectively

N1 = σ11 − σ22

First normal stress difference

No,N

Initial and final number of particles respectively

No, N+

Number of coagulating drops, initially and at t = t_c

Total number of collisions per unit time

Number of particles

Number of moles unit volume

Pressure

Peclet number

Probability that two particles that have collided result in coalescence

Wave vector, or sinusoidal distortion

Ideal gas constant

Reynolds number or real part of a complex function

R(q)

Fluctuation function

\( \overline{\mathbf{r}} \)

Reduced drop radius

〈r Θ 2 〉1/2

Unperturbed, average radius of gyration

rad

Radian

Radius of the critical nucleus

S(q), S0

Virtual structure function

So, S

Interfacial area per unit volume of the blend for monodispersed spherical particles before and after coalescence, respectively

Spinodal

Absolute temperature

Glass transition temperature

Time

Necessary time for breakup of droplets

tb*

Dimensionless breakup time

Coalescence time

UCST

Upper critical solubility temperature

Volume

Vx/V

Volume fraction of emulsion undergoing uniform shear

Reduced frequency, f · τ

Notation (Greek Letters)

Orientation angle

αo

The distortion at t = 0

β12

Interlayer slip factor

χAΒ

Binary thermodynamic interaction parameter between polymers A and B

Thermodynamic distance from the spinodal; Δ ≡ 2((χ_AΒN)_s− (χ_AΒN)

ΔΕ

Activation energy, e.g., of flow: ΔΕ_η

ΔGm

Gibbs free energy of mixing

ΔHm, ΔSm

Enthalpy and entropy of mixing, respectively

ε, \( \dot{\boldsymbol{\upvarepsilon}} \)

Hencky strain and Hencky strain rate in extension, respectively

ϕ1, ϕ2

Volume fraction of dispersed and matrix phase, respectively

ϕc

Volume fraction of the cross-linked monomer units

ϕi

Volume fraction of phase i at phase inversion

ϕm

Maximum packing volume fraction

ϕperc

Percolation threshold

γ, \( \dot{\boldsymbol{\upgamma}} \)

Shear strain and rate of shearing, respectively

Viscosity

ηo

Zero-shear viscosity

ηr

Relative viscosity

[η]

Intrinsic viscosity

η′

Dynamic viscosity

η*

Complex viscosity

η1, η2

Viscosity of dispersed and matrix phase, respectively

κ = σιφd/ν12

Capillary number

κcrit

Critical capillary number

Distortion wavelength

λ = η1/η2

Viscosity ratio

λs

Wavelength

ν 12 o

Interfacial tension in a quiescent blends

ν12

Interfacial tension coefficient between phase 1 and 2

Density

ρd

Droplet density

Stress

σ11

Extensional stress

σ11 − σ22 = N1

First normal stress difference

σ12

Shear stress

Stress in the matrix phase

σy

Yield stress

σy o

Permanent yield stress

Relaxation time

Mean relaxation time

Ω(Λ, λ)

Tabulated function for capillary instability

Angular frequency

ωmax

Frequency at which \( \tilde{H}\left(\omega \right) \) is maximum

ωx

Crossover frequency

ψ1, ψ2

First and second normal stress difference coefficient, respectively

Abbreviations

ABS

Acrylonitrile-butadiene-styrene

EFM

Extensional flow mixer

EPDM

Ethylene-propylene-diene terpolymer

EPR

Ethylene-propylene rubber

EVAc

Ethylene-vinyl acetate copolymer

HDPE

High density polyethylene

HIPS

High impact polystyrene

IPN

Interpenetrating networks

LDPE

Low density polyethylene

LLDPE

Linear low density polyethylene

Nucleation and growth

Natural rubber

Polyamide

PAA

Polyacrylic acid

Polybutadiene

Polycarbonate

PCL

Polcaprolactone

Polyethylene

PEO

Polyethylene oxide (or polyethyleneglycol, PEG)

PEMA

Poly(ethyl methacrylate)

Phenoxy

Polyhydroxyether of bis-phenol A

PMMA

Polymethylmethacrylate

PnBA

Poly(n-butyl)acrylate

Polypropylene

PPE

Polyphenyleneether

PS, PSD

Polystyrene, deuterated PS

PSF

Polysulfone

PVC

Polyvinyl chloride

PVME

Polyvinylmethylether

RMS

Rheometrics Mechanical Spectrometer

RSR

Rheometrics Stress Rheometer

SBR

Styrene-butadiene rubber

SBS

Styrene-butadiene-styrene three block copolymer

Spinodal decomposition

SEBS

Styrene-ethylene/butene-styrene three block copolymer

SEC

Size exclusion chromatography

SIN

Simultaneous interpenetrating polymer networks

SSE

Single-screw extruder

Thermoplastic resin

Thermoset resin

TSE

Twin-screw extruder

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Title: Rheology of Polymer Alloys and Blends
Authors: Musa R. Kamal
Leszek A. Utracki
A. Mirzadeh
Publisher: Springer Netherlands
Book: Polymer Blends Handbook
Print ISBN: 978-94-007-6063-9

Electronic ISBN: 978-94-007-6064-6

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-94-007-6064-6_9

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