ISSN 2277 7164 Original Article Polydimethylsiloxane ...urpjournals.com/tocjnls/1_14v4i3_2.pdf ·...

43 Advances in Polymer Science and Technology: An International Journal 2014; 4(3): 43-51

ISSN 2277 – 7164

Original Article

Modeling of Young’s Modulus of Thermoplastic Polyurethane and

Polydimethylsiloxane Rubber Blends Based on Phase Morphology

Jineesh Ayippadath Gopi · Golok Bihari Nando*

Rubber Technology Centre, Indian Institute of Technology Kharagpur, West Bengal, India, 721302

*Corresponding author email: [email protected]

Author email: [email protected]

Received 17 August 2014; accepted 09 September 2014 Abstract

Young’s modulus of blends of Thermoplastic polyurethane (TPU) and Polydimethylsiloxane rubber (PDMS) are measured

throughout the composition range. Comparison and evaluation between the experimental results and the theoretical

predictions based on different developed models for the Young’s modulus have been presented based on both

droplet/matrix and co-continuous morphology. Both two dimensional (parallel, series, Takayanagi, Davies and Coran-Patel

models) and three dimensional (Barentsen and Nijhof) models were selected for predicting Young’s modulus of the blends.

Emphasis was given to the tensile strain behavior of weak PDMS phase and the stiff TPU phase in each blend and the

dependence of their behavior in the Young’s modulus values predicted by the models. The blends with finely dispersed

PDMS phase in TPU matrix show relatively comparable Young’s moduli as predicted by Takayanagi parallel model, and

Barentsen series model of parallel parts due to equal elongation for both the phases and the very small strain gradient

between the parallel parts in the model. Young’s moduli of the blends with dispersed TPU in PDMS major matrix show

comparable results as predicted by Takayanagi series model and Barentsen parallel model of serial parts because of the

weak PDMS matrix and the limited influence of the strain on the stiff dispersed TPU domains. Experimental Young’s

modulus of the blends with co-continuity in its morphology is similar to the predicted values as per Nijof and Coran-Patel

model which are based on co-continuous morphology.

© 2014 Universal Research Publications. All rights reserved

Key Words: phase morphology, thermoplastic polyurethane, polydimethylsiloxane rubber, polymer blends, scanning

electron microscopy

Introduction

Synthesis of new polymers with specific end use properties is an

expensive and time consuming process as it involves several tedious

and hazardous manufacturing steps. The process of blending of

polymers to develop new materials commenced in late part of the

20th century has become very popular in the area of polymer science

and engineering. Blending of two or more different polymers with

wider range of properties became an effective and inexpensive route

to produce new materials with specific end use properties. The

properties of a multiphase polymer system cannot be deduced from

the properties of the individual phases. Instead, the properties

depend on many factors, such as the spatial organization of each

phase and the nature of the interface. Most of the polymer blends

are often produced by melt-mixing technique, which generates

different types of morphology. Factors governing the morphology

of the blends are composition, interfacial tension, processing

conditions and rheological characteristics of the components [1-3].

In general, polymer blend morphology can be

divided into different classes, i.e. dispersed, stratified and

co-continuous morphology. Dispersions of droplets of the

minor phase in a matrix of the major phase are most

common and are characterized under dispersed

morphology. When the content of the minor phase

increases, it is possible that both the components may

present in a continuous network, which is known as the co-

continuous morphology. Stratified morphology is made up

of alternate layers of the two phases. The types and scales

of the morphologies determine the blend characteristics [4-

5].

Among various parameters, mechanical properties

are useful for deducing the morphology or phase continuity

in multiphase polymer blend systems. One of the key

factors for achieving the desired properties is the control of

the type and dimensions of the morphology. Droplet–

matrix morphology can improve the impact properties,

fibrillar morphology may result in better tensile properties,

blends with lamellar structures enhance barrier properties

and co-continuous morphology show a combination of the

characteristics of both the polymer components [6-10]. The

blend component with the lowest viscosity and highest

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volume fraction forms the continuous phase, whereas the

blend component with the highest viscosity and lowest

volume fraction forms the dispersed phase. The continuity

of phases has a great impact on the resultant macroscopic

properties of the blends.

Percolation theory deals with the development of

continuity in the polymer blends. According to this theory,

at lower concentrations of the phase, dispersion of particles

occurs in the other phase which is the continuous matrix. A

gradual change in structure, from dispersed to co-

continuous, occurs in heterogeneous polymer blends with

increasing volume fraction of the minor phase component

[11]. The co-continuous morphology can exist over a range

of compositions, depending on the blending conditions.

Beyond this range, at still higher volume fractions of that

components, the phase network of the erstwhile matrix

component starts breaking down until finally the said

component becomes dispersed and the process is known as

‘phase inversion’[12]. Understanding the development of

morphology of blends is very much critical in designing a

polymer blend system for a specific end use.

During the past several decades, thermoplastic

polyurethanes (TPU) have received considerable attention

from among both the academia and industry. Thermoplastic

polyurethanes are extensively used as high performance

elastomers and tough thermoplastics in a wide variety of

applications requiring high impact strength, abrasion

resistance, solvent and oil resistance, good adhesion and so

on. TPU finds applications in automobile, biomedical,

footwear, wire and cable coatings, adhesives and so on [13-

14]. In recent years extensive research on the blending of

TPU, with the other polymers are in vogue and very

interesting results have been reported [15-19]. Blends of

TPU, with polyolefins as well as ethylene–propylene–diene

elastomer have been investigated for technological,

economical, and environmental reasons by many

researchers [20-21].

In the present paper, a detail study on phase

morphology of the blends of thermoplastic polyurethane

and poly dimethylsiloxane throughout the composition

range have been reported and attempts have been made to

correlate the Young’s modulus with the existing models

based on the phase morphology of the blends. Both two

dimensional and three dimensional geometry models have

been selected for the proper understanding of stress-strain

behavior. The suitability of each model has been studied by

considering the high strength and modulus behavior of TPU

and low strength and modulus behavior of PDMS.

Materials and Methods

Materials

TEXIN® RxT85A is aromatic polyether based

thermoplastic polyurethane has been generously given by

Bayer Material Science LLC USA. Specific gravity is 1.12

and the melt flow index is 4g/10 min at 190°C/8.7kg.

PDMS grade, silastic WC-50TM having specific gravity

1.17 was procured from Dow Corning Inc. (Midland, MI,

USA).

Preparation of blends

Blends of TPU and PDMS rubber at blend ratios

varying from 100:0 to 0:100 have been prepared by melt

mixing technique in a Brabender® Plastograph®

EC(digital 3.8-kW motor, a torque measuring range of 200

Nm, and a speed range from 0.2 to 150 min-1) at optimized

processing conditions determined by the Taguchi

methodology[22]. The mixing temperature was 190°C, the

rotor speed was 80 rpm and the mixing time was

maintained at 2 minutes. Sheet specimens of thickness

about 2 mm for all the compositions were prepared using

compression molding press (Moore Press, GE Moore and

Son, Birmingham, UK) at 190°C for 3 min at a pressure of

7 MPa.

Measurement of Tensile properties

The dumbbell specimens were punched out of the molded

tensile sheets and tensile properties were measured using a

Zwick/Roell BX1‐EZ005.A4K‐00 universal testing

machine at ambient temperature. In this test 0.2% plastic

strain with 50mm/min cross head speed was applied to

determine the Young’s modulus of the sample. A load cell

of 1kN has been used to test the samples to get more

accurate results.

Phase morphology of the blends.

A JEOL-JSM-5800 scanning electron microscope was used

to study the phase morphology of the TPU-PDMS blends.

The samples were prepared by cryogenically fracturing the

blends in liquid nitrogen. The PDMS phase was extracted

preferentially using toluene as the solvent for TPU rich

samples (equal to and more than 50% TPU) whereas the

TPU phase was extracted preferentially using dimethyl

formamide for PDMS rich samples (PDMS content is

higher than 50%). The extracted specimens were dried at

room temperature and then in an oven at 70 °C and then

sputter coated with a thin layer of gold in a vacuum

chamber before examining under the scanning electron

microscope.

Results

Scanning electron microscopy (SEM) study:

Figure 1 shows the SEM photomicrographs of the blends at

different blend ratios. Fig. 1(a) to 1(c) clearly shows

dispersed domain morphology of PDMS rubber within the

major matrix phase of TPU whereas Fig. 1(d) for

TPU:PDMS (60:40) blend ratio shows highly elongated

elliptical PDMS phase within TPU matrix give an

indication of onset of co-continuity. Figure 1(e) [blend ratio

of 50:50] shows dispersed domains of elliptical

morphology with a significant amount of co-continuous

morphology. When the PDMS weight proportion in the

blend reaches 60% (Fig.1(f)) phase inversion takes place

and the PDMS becomes the major matrix phase, and TPU

becomes dispersed phase. Beyond this weight proportion,

TPU remains in the dispersed phase till TPU:PDMS

(10:90) as showed in Fig. 1(g) to 1(i). The dispersed

domain sizes of all the blends have been calculated using

the Matlab image processing toolbox and presented in

Table 1.

In the blends containing higher proportions of

TPU (higher than 70% TPU content) the PDMS domains

are uniformly distributed within the TPU matrix and the

size of PDMS domains varies from 0.1-0.2 microns.

However the dispersion of TPU phase in the PDMS matrix

(where TPU content is less than 50%) do not show similar


Figure 1. (a) to (e) show the SEM photo micrographs of TPU-PDMS blends from 90:10 to 50:50 ratios etched in toluene.

Figure (f) to (i) show the SEM photo micrographs of TPU-PDMS blends from 40:60 to 10:90 ratio etched with dimethyl

formamide.

Table 1. Size range of dispersed phases in TPU-PDMS blends and the type of morphologies

Blend ratio

(TPU:PDMS) Type of phase morphology Dispersed phase

Domain size

range (µm)

90:10 Dispersed/matrix morphology PDMS 0.09 - 0.12

80:20 Dispersed/matrix morphology PDMS 0.10 – 0.15

70:30 Dispersed/matrix morphology PDMS 0.15 – 0.2

60:40 Highly elongated elliptical dispersed phase PDMS 0.25 - 0.4

50:50 Co-continuous morphology Both TPU and PDMS -

40:60 Dispersed /matrix morphology TPU 0.35 – 0.5

30:70 Dispersed /matrix morphology TPU 0.26 - 0.5

20:80 Dispersed /matrix morphology TPU 0.17 -0.23

10:90 Dispersed /matrix morphology TPU -

Table 2. Young’s modulus of neat TPU, PDMS and TPU-PDMS blends

Blend Ratio( TPU:PDMS) Young’s modulus (MPa)

100:0 12.30

90:10 10.50

80:20 9.45

70:30 8.51

60:40 6.53

50:50 4.20

40:60 2.07

30:70 1.51

20:80 1.38

10:90 1.22

0:100 1.07


uniformity in the dispersion and the domain sizes of TPU

which fall in the range of 0.5- 1 microns. Interestingly the

TPU:PDMS blend with 10:90 ratio shows a morphology

similar to a single phase matrix with some undulations and

irregularities on the surface because of the etching of TPU.

(Fig. 1(i)).

Mechanical Properties of TPU-PDMS blends

The average Young’s modulus of virgin polymers

and their blends are reported in Table 2. Virgin TPU

exhibits a Young’s modulus of 12.30 MPa and virgin

PDMS exhibits a very low Young’s modulus value of 1.07.

The blends with a dispersed PDMS phase in a TPU domain

matrix show comparatively good mechanical properties.

But as the matrix changes from TPU to PDMS the

mechanical properties are drastically reduced. This is quite

obvious that the major matrix used to take the stress on

elongation during tensile test and when PDMS becomes the

major phase and it can’t take much stress and it lead to a

low tensile strength values.

Study of different models based on dispersed/ matrix

phase morphology

The mechanical properties of the blends depend on

the degree to which they are homogenous. In these blends

two parameters must be defined and they are a) shapes of

the inhomogeneity b) their degree of orientation. As far as

the classical theory of elasticity concerned the dimensions

of the phases present in the blends are irrelevant. But when

higher strains are involved and when yield and fracture

processes are being considered, the dimensions become

very vital. The physical properties of the blends depend

strongly on the phase dimensions.

For modeling the polymer blend system, due

emphasis is being given to Young’s modulus and its

dependence on phase morphology. The importance of

mechanical properties in understanding the behavior of

polymer blends is well understood and the dependence of

mechanical properties on the phase morphology vis-à-vis

processing properties was studied by several authors earlier

[23-26].

Mechanical models have been developed in the

past for understanding the phase behavior, continuity in the

morphology and its effect on mechanical properties of the

polymer blend systems particularly those are heterogeneous

in nature. Predicting the elastic moduli of two-component

systems from the mechanical properties of the individual

components has been the subject of intense investigation.

There has been no general principle based on which this

problem could be solved, but it is certain that moduli are

affected by the morphology of the systems. That is the

juxtaposition and the shape of the individual components in

space, and the way they are bonded together, play a major

role in imparting the physic-mechanical properties. The

basic difficulty always remains a fact that one does not

know the priori, which is how stress and strain are

transmitted through the system [27-32].

Several theories have been propounded to predict

the tensile properties based on various parameters. These

theories are classified into two broad categories: (1) The

theories based on composition and (2) and that based on

morphology [33]. Most of these theories assume perfect

Figure 2. Models for two phased TPU-PDMS system. φ1

and φ2 are the volume fractions. (a) an iso-strain model, (b)

an iso-stress model, (c) and (d) are combinations of iso-

strain and iso-stress model of Takayanagi.

adhesion between the phases in a macroscopically

homogeneous and isotropic specimen.

There are series and parallel models for polymers

containing two separate phases. The applications of these

models require the knowledge of the experimental data on

mechanical property for the neat components, for example

TPU and PDMS. These two simple models, the so-called

parallel and series models represent the upper and lower

bounds of the tensile property predictions respectively. In

parallel model (Fig. 2(a)) an iso-strain condition exists and

the total stress on the system is the sum of all the stresses,

and the mechanical properties of the system [34] is given

by

EU = E1φ1 + E2φ2 (1)

In the series model (Fig. 2b) an iso-stress condition exists,

and the strains are additive. Then the mechanical property

of the blend is obtained by averaging the strains in the

individual phases as per the equation given below;

EL = (φ1/ E1 + φ2/ E2)-1 (2)

Where EU is the tensile property of the blend in the upper

bound parallel model, and EL is the tensile property of the

blend in the series model. E1 and E2 are the mechanical

properties of components 1 and 2, respectively; and φ1, φ2

are their corresponding volume fractions. For both these

models, no morphology is required, but strain or stress

should be continuous across the interface, and Poisson’s

ratio should be the same for both phases. Since neither of

these bounds generally describes the behavior of a two-

phase composite, Takayanagi developed a combined series-

parallel model for the tensile property E, by introducing a

degree of parallelinity into the series model [35]. It is a

phenomenological model consisting of a mixing rule

between two simple models involving connection in series

(Reuss prediction) or in parallel (Voight prediction) of the

components. It was assumed that the two-phase material

can be treated as a combination of series and parallel

elements. The equation for Takayanagi parallel model

(Fig. 2(c) is given as

E=[ (φ /(λE2+(1-λ) E1))+((1- φ )/E1)]-1 (3)

and for series model (Fig. (2(d)) is

E=λ[(φ /E2)+((1- φ )/E1)] -1 +(1- λ) E1 (4)

E1 is the property of the matrix phase; E2 is the property of

the dispersed phase. Quantities λ and φ are geometry

factors representing phase morphology in the Takayanagi

model, whereas the product λφ is the volume fraction of the


dispersed phase and is related to the degree of series

parallel coupling. The degree of series parallel coupling of

the model can be expressed by

% parallel = [φ(1-λ)/(1- φλ)]*100 (5)

Parameters λ and φ vary with composition and with the

change in the state of dispersion. For spherical particles

independently and homogeneously dispersed in a matrix, it

can be assumed that λ is equal to φ.

Figure 3. Barentsen Three-dimensional models for the

calculation of the moduli of dispersed polymer blends (a)

series model of parallel parts (b) parallel model of serial

linked parts.

A combination of parallel and series elements for

three-dimensional geometries in a droplet/matrix blend

system has been proposed by Barentsen[36]. Barentsen’s

model can either be described as a series model of parallel

parts (Fig.3(a) and Eq. (6)) or a parallel model of serial

linked parts (Fig. 3(b) and Eq. (7)). The unit cubes, as

shown in Fig. 3(a) and 3(b), can be used for modeling of

polymer blends with a droplet/matrix morphology when the

dispersed particles are evenly distributed in the matrix.

E=Em[((λ2) Ed+(1- λ2)Em)/((1- λ) λ2Ed+(1- λ2+ λ3)Em)] (6)

E=(1- λ2)Em+[( λ2EmEd)/( λ Em+(1- λ) Ed)] (7)

Where E is the property of the blend according to the

model, Em and Ed are the property of the matrix and

dispersed phase respectively, and the value of λ can be

determined using the equation

λ3= φd =1- φm (8)

where φd and φm are the volume fractions of the dispersed

phase and matrix respectively

Figure 4. Comparison and variation of the theoretically

predicted (based on droplet/matrix morphology) and

experimental Young’s modulus of the TPU-PDMS blends

as a function of volume fraction of the TPU.

Figure 4 shows the comparison and the variation

of the theoretically predicted (based on droplet/matrix

morphology) and experimental Young’s modulus of the

TPU-PDMS blends as functions of volume fraction of the

TPU.

Study of different models based on co-continuous phase

morphology

A co-continuous morphology is a non-equilibrium

morphology that is generated during melt mixing of two

polymers. As such, it is an unstable morphology, and it

starts changing through filament break-up and retraction as

soon as the melt comes out of the mixer. However, the

blend may remain co-continuous, if it is frozen fast. The

co-continuous morphologies are mainly not formed at

single volume fractions, such as the point of phase

inversion, but rather over a range of volume fractions. This

range of volume fractions very much depends upon the

processing conditions and the rheological properties of the

blend components [37]. In particular, in blends with

thermoplastic elastomers (TPEs) co-continuous

morphologies may form over a wider composition range

[38].

s

Figure 5. Three dimensional model for a co-continous

polymer blend (a) – Nijhof series model of parallel parts,

(b) Nijhof parallel model of serial-linked parts

In a co-continuous morphology, the dispersed

phase does not form of separate domains in the matrix

phase, but the so called domains are interconnected

facilitating formation of elongated domains extended

throughout the matrix. To visualize co-continuity, a model

was proposed by Nijhof consisting of three orthogonal bars

of first polymer component embedded in a unit cube where

the remaining volume is occupied by the second polymer

component [39]. Repeating this unit cube in three

dimensional set up shows that first component has the same

framework as the second component, i.e. both the

components are interconnected. Relations for a series

model of parallel parts (Fig. 5(a)) is given in equation 9 and

the relation for parallel model of serial-linked parts (Fig.

5(b)) is given in equation 10.

E=[(a4+2a3b)E12+2(a3b+3a2b2+ab3)E1E2+(2ab3+b4)E2

2]/[

(a3+a2b+2ab2)E1+(2a2b+ab2+b3)E2 (9)

E=[a2bE12+(a3+2ab+b3)E1E2+ab2E2

2]/[bE1+aE2] (10)

Where E1 and E2 are the properties of the first and second

components in the blend respectively, ‘a’ is related to the

volume fraction of first component

3a2-2a3= φ1 (11)

And ‘b’ is related to the volume fraction of the second

component by the equation


b=1-a (12)

The parallel model of serial-linked parts for co-continuity

proposed by Nijhof is comparable to the COS model

proposed by Kolarik [40].

A dual phase continuity model proposed by

Davies [41], which accounts for the phase interaction, is

E1/5 = E11/5 φ1+ E2

1/5 φ2 (13)

where, E is the tensile property. Ei and φi are tensile

property and volume fractions of each component. This

relation assumes that the blend needs to be macroscopically

homogeneous and isotropic. Then it can be applied for co-

continuous structures without any details being specified.

The phase continuity and phase inversion in

polymer blends can be studied by using the relation for the

tensile moduli of the blend constituents to composite

moduli. Coran and Patel[42,43] proposed an equation

which is intended to account for phase inversion at a certain

composition of the blend. The modulus is expressed as a

function of the upper and lower bounds using a fit

parameter n, which is considered to depend on wettability

and compatibility and to give the point of phase inversion

as

φ= (n-1)/n (14)

Coran–Patel model represents a phenomenological

adjustment between the parallel and series models and

characterized as one-parameter model given by;

E= φHn(nφs+1)(EU-EL)+EL (15)

Where EU is the upper bound and EL is the lower bound

value and n is an adjustable parameter related to the change

in phase morphology as a function of hard phase H. φH is

the volume fraction of the hard phase and φS is the volume

fraction of the soft phase.

Figure 6. Comparison and variation of the theoretically

predicted (based on co-continuous morphology) and

experimental Young’s modulus of the TPU-PDMS blends

as functions of volume fraction of the TPU.

Figure 6 shows the comparison and variation of the

theoretically predicted (based on co-continuous

morphology) and experimental Young’s modulus of the

TPU-PDMS blends as functions of volume fraction of the

TPU. Discussion

The experimental Young’s modulus values are in

between the values obtained by upper bound parallel model

Figure 7. The representation of the morphology of the

blends with dispersed PDMS in TPU matrix. (a) before

elongation (b) during elongation

and lower bound series model. As it is well understood that

almost all blends show neither pure iso-stress nor iso-strain

condition, that means neither the strain nor the stresses are

additive. The actual nature of the blends will be in between

or in combination of the component’s nature. At higher

TPU content (>70%), the Young’s moduli of the blends are

comparable with those predicted using droplet/matrix

models like Takayanagi parallel mode (Figure 2(c)), and

Barentson series model of parallel parts (Figure 3(a)). The

reason for this can be easily explained from the

morphology of these blends. Scanning electron

micrographs of the blends containing 70% by weight of

TPU or higher (Fig. 1(a) to 1(c)) show a uniformly

dispersed PDMS phase in the TPU matrix. Even though the

major matrix (TPU) is taking a major part of the load

during tensile strain, the strain on TPU will induce a strain

on the surface of the droplets of PDMS. PDMS is weak and

therefore the domains of the PDMS will also be elongated

by the induced strain from the TPU matrix. This can be

represented by the Figure 7. From Figure 7 one can

understand that both the phases undergo a similar degree of

strain (isostrain) during the extension. In practice the

matrix will have the same elongation throughout the

composition in these blends and the strain gradient between

the parallel parts will be smaller. Hence the Barentson

series model of the parallel parts model [Fig. 3(a)] seems to

be more appropriate for these blends. That means in this

system isostrain behavior is predominant and this condition

is related to Takayanaki parallel model and Barenstson

series model of parallel parts where these models also

include an isostrain predominant element.

At higher PDMS content (>60% by weight),

scanning electron micrographs (Fig. 1(f) to 1(i)) show

dispersed phase morphology of TPU in PDMS matrix. The

Young’s modulus of the blends are comparable with the

values predicted using droplet/matrix models of

Takayanagi series model (Figure 2(d))and Barentson

Parallel model of serial parts (Figure 3(b)). In these blends

PDMS is the major matrix and they show different

behavior on extension than the blends with TPU as the

major matrix. If applied tensile strain in the blends where

PDMS is the major matrix, the PDMS matrix will take the

load and it will be elongated. But being a weak phase it

can’t impart enough stress on the surface of the higher


Figure 8. The representation of the morphology of the

blends with dispersed TPU in PDMS matrix. (a) before

elongation (b) during elongation

modulus TPU matrix to be elongated in the direction of the

strain. This behavior can be represented in the Figure 8.

Here the strains in the both the phases are not similar (no

iso-strain characteristics), Therefore the system is more

similar to the Takayanagi series model and Barentson

Parallel model of serial parts where these models have an

iso-stress predomination.

If the dispersed phase is TPU (blends having less

than or equal to 40% TPU), the matrix will be weak and the

influence of the stiff dispersed phase in the direction

perpendicular to the applied force direction will be limited.

Then according to the model depicted in Fig. 3(b), the stiff

dispersion shall force a part of the weak matrix that is

coupled in series with it to an elongation that is much

longer than the elongation of the rest of the matrix. This is

in agreement with reality because in real blends the weak

matrix in the blend will deform most at the interface

between the stiff droplets and the weak matrix (relative

high strain gradients in the weak matrix do not cost so

much energy). Therefore, the model as depicted in Fig. 3(b)

is more appropriate when the weak PDMS component

dominates. Fig. 4 is in agreement with the above

observation.

The predicted and experimental Young’s moduli

values are completely different in the blends where TPU

content is about 60 & 50% by weight. This is quite obvious

as these blends do not show perfect droplet/matrix

morphology (Fig. 1(d) and 1(e)). T60P40 blend shows a

highly elongated elliptical dispersed PDMS phase in TPU

matrix, and the morphology is intermediate between the

droplet/matrix and is co-continuous. This means the onset

of co-continuous phase formation can be seen in T60P40.

T50P50 shows a significant amount of co-continuity in the

phase morphology. The predicted Young’s moduli for these

two blends are pretty much higher than that of the

experimental values. In these blends, TPU and PDMS are

in co-continuous phase and the applied stress is distributed

through both the matrices. Since the PDMS matrix cannot

withstand high stress as it has low modulus, the blends with

co-continuous morphology exhibit lower Young’s modulus

using the models of droplet/matrix morphology where

PDMS is considered as the dispersed phase.

Co-continuity occurs around the phase inversion

point, where a dispersion of the first component in a matrix

of second component will change into a dispersion of the

second component in a matrix of the first component.

Figure 6 gives comparisons between experimental results

and predicted theory for Young’s modulus obtained with

the aforementioned equations of co-continuity. From

Figure 6 the aforementioned equations cannot give a proper

evaluation of the moduli of the blends over the entire

composition range. From the scanning electron

micrographs, co-continuity is observed in the blend at a

blend ratio of 50:50 and also a highly elongated elliptical

morphology with some onset of co-continuity is observed

in T60P40. The experimental value of T60P40 almost fits

well with the predicted values using the Nihjof Parallel

model of serial linked parts which incorporate the dual

phase interconnectivity. Coran & Patel model also fit well

with a fit parameter n=2.5 which predicts the tensile

strength is closely similar that obtained experimentally for

the T60P40 blend. This value corresponds to VH =0.6 as the

hard phase volume fraction, which corresponds to the phase

inversion of the blends from a dispersed phase to a co-

continuous phase. This observation is in agreement with

our experimental observations from mechanical and

morphological properties. In the micrographs of T60P40,

the transition from droplet/matrix morphology to co-

continuous morphology through the highly elongated

elliptical morphology of the PDMS phase in the TPU

matrix is observed.

Conclusions

A comparison and evaluation between the

experimental results and the theoretically predicted values

based on different developed models for the Young’s

modulus of Thermoplastic Polyurethane and

Polydimethylsiloxane rubber have been presented based on

both droplet/matrix and co-continuous morphology. The

following conclusions may be drawn from the present

study;

1.In the blends where the weak PDMS is uniformly

dispersed in TPU matrix (where TPU content is more than

70%), the matrix will have the same elongation throughout

in these blends, because of the strain imparted by TPU on

the surface of PDMS and the strain gradient between the

parallel parts is small. Therefore the experimental Young’

modulus is similar to the values obtained by Takayanaki

parallel model and Barenstson series model of parallel parts

where these models also include an iso-strain

predomination.

2. In case of the blends where TPU is uniformly dispersed

in the PDMS matrix (where PDMS content is more than

60%), the matrix is weak and the influence of the strain on

the hard dispersed TPU phase in the direction perpendicular

to the applied force direction are limited. Because of this

reason the experimental Young’s modulus of these blends

is in agreement with the theoretical predictions by

Takayanagi series model and Barentson Parallel model of

serial parts where these models are almost similar to this

present condition of these blends.

3. The experimental Young’s modulus of T60P40 fits well

with the theoretical values obtained using the Nihjof

Parallel model of serial linked parts which incorporate the

dual phase interconnectivity even though this blend show

an elongated elliptical morphology with some onset of co-


continuity. Coran& Patel model fit well with a fit parameter

n=2.5 which predicts the tensile strength closely in similar

to that obtained experimentally for the T60P40 blend. This

value corresponds to VH =0.6 as the hard phase volume

fraction, which corresponds to a phase inversion of the

blends from a dispersed phase to a co-continuous phase and

it is in agreement with the scanning electron microscopy

studies.

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Source of support: Nil; Conflict of interest: None declared

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