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CHAPTER 8

DYNAMIC MECHANICAL ANALYSIS Abstract

Linear viscoelastic properties of Barium Sodium Niobate-Polystyrene

nanocomposites and Yttrium Barium Copper Oxide -Polystyrene

microcomposites were investigated with special reference to the effect of

filler loading, frequency and temperature. Dynamic mechanical analysis

showed significant increase in storage modulus in the glassy and rubbery

region .The (tanδ) peak temperature showed a right shift and, the peak

intensity was lowered for the composites. The composites showed a shift

in cross over frequency to the lower frequency region suggesting a

delayed relaxation of the molecular chains in the presence of fillers and

this shift was found to depend on the content of filler. The enhancement

in storage modulus was correlated with the morphological observations.

The compatibility of the composites was observed through the Cole-Cole

plots.

The results of this chapter have been communicated to publish in Journal

of Thermal Analysis and Calorimetry.

228 Chapter VIII

8.1 Introduction

DMTA [Dynamic Mechanical Thermal Analysis] measures the stiffness

and mechanical damping or internal friction/thermal dissipation of a

dynamically deformed material as a function of temperature. Specifically it

is used to study transitions in materials that occur on the molecular level.

The most conspicuous of the transition characteristics of amorphous and

semicrystalline polymers is the alpha or glass transition temperature (Tg).

Below this temperature an amorphous polymer is a glass. At Tg, micro-

Brownian motion of molecular segments begins where short range

diffusion can take place. At temperature less than Tg, thermal energy is

insufficient to cause rotational and translational motions of segments

[1-5]. The viscoelastic response of the polymeric materials can be

monitored with respect to time, temperature and frequencies. DMTA is an

extremely versatile thermal analysis method, and no other single test

method provides more information about the physical properties of a

sample in a single test. This supplies an oscillating force, causing a

sinusoidal stress to be applied to a sample which generates a sinusoidal

strain. By the measurement of the magnitude of the deformation at the

peak of the sine wave and the lag between the stress and strain waves,

properties such as modulus, glass transition temperature and damping can

be measured.

For solids that behave ideally and follow Hooke’s law, the stress is

proportional to the strain amplitude, and the stress and strain signals are in

phase. The stress signal generated by a viscoelastic material can be

separated into two components: an elastic stress in phase with the strain,

and a viscous stress90°out of phase with the strain. The elastic stress

Dynamic Mechanical Analysis 229

measures the degree to which the material behave as a solid and the

viscous stress, measures the degree to which the material behaves as an

ideal fluid [6].

The elastic and viscous stresses are related to material properties through

the ratio of stress to strain, the modulus. The ratio of the elastic stress to

strain is the elastic (or storage) modulus G’ which signifies the stiffness of

the polymer; the ratio of the viscous stress to strain is the viscous (or loss)

modulus G”, which implies the dissipated energy and the damping is

given by the ratio of loss modulus to storage modulus. Storage modulus

(G′), loss modulus (G″) and loss tangent (tan∂= G″/ G′) are presented as a

function of temperature and frequency for polystyrene and the

composites. The presence of nanofillers modifies all the above properties

of polystyrene.

The first objective of this research is to evaluate the value of (Tg) using

the three different techniques(1) the onset of the change in the slope of the

storage modulus (G’) curve,(2) the maximum loss modulus (G”) on loss

modulus-temperature curve and(3) the maximum loss tangent (tanδ ) in

the (tanδ)- temperature curve. Comparing the (Tg) values obtained from

the above calculations one can predict the applicability of the composites

for various electrical & electronic purposes.

Even though DMTA is used extensively in Tg calculation, uncertainties

still exist regarding the proper methods of accurate determination. The

procedures described in several standards and recommendations can result

in significantly different values of the same data, as discussed in detail by

Wolfurm et al. [7]. Tg represents a range of temperature over which the

glass transition takes place [8]. The five regions of viscoelastic behavior

230 Chapter VIII

typical of a thermoplastic polymer [9, 10] are presented in Figure8.1. The

glass-transition range is characterized by a sharp decrease in the elastic

modulus of the polymer and is dependent on the state of the polymer and its

thermal history [11]. In an effort to simplify the determination of Tg, it is

commonly defined as the maximum of the damping ratio, (G”/G’), (tanδ ),

or the maximum of G”. Several researchers however, had found that a

more accurate determination could be derived from the onset of the

change in the slope of the G’ curve [12, 13]. Tg values computed with the

onset of change in the slope of the G’ curve were obtained by plotting the

derivative of G’ as a function of temperature. Tg was then determined to

be the average of two slopes from that curve. The first slope was selected

at a temperature before the modulus drop step; the second slope was

selected at a temperature indicating the middle point of the modulus drop.

The intersection of the two slopes is to be taken as the value of Tg. If Tg

is used for engineering design, that is, the determination of maximal end-

use temperatures, we believe that a conservative estimate of ( Tg )is

warranted . Therefore, in this work, one method of Tg calculation was

based on the temperature at which mechanical properties began to be

compromised, that is, the onset of the glass transition range, as

determined by the onset of the change in the slope of G’. It can be

measured from the peak point of the plot, derivative of storage modulus

versus temperature. Also the value of( Tg ) based on the maximum

damping ratio and by the tan(δ) peak is also reported. The last value

represents the end of the transition period. The three values give an

indication of the size of the transition period as in fig 8.2


Figure 8.1 Five regions of thermoplastic polymer viscoelastic behavior:

(1) glassy region, (2) glass-transition region, (3) rubberyregion, (4) rubbery flow region, and (5) liquid flow region.

Figure 8.2 Tg determined by the onset of the (G’) change, the maximum

of (G”) and the maximum of (tan δ). Clearly, the above methods can produce different values for the same set of data

232 Chapter VIII

8.2 Results and discussion

DMA of the samples were carried out at frequencies 0.1Hz, 1Hz and 10Hz. A detailed discussion of the results of ‘Tg’ variations is neatly presented. The enhancement in storage modulus is seen in the case of glassy and rubbery regions of the composites. The compatibility is expressed in terms of Cole-Cole plot.

8.2.1 Storage modulus

Fig 8.3, 8.4, 8.5, &8.6 give the graphical representation of storage modules change in PS and composites by dynamic mechanical thermal analysis at different frequencies. An enhancement in storage modulus is observed in all composites. The enhancement in storage modulus is the presence of dispersion of homogeneous fillers in Polystyrene matrix and the better reinforcement of the matrix and the filler [14]. The effectiveness of fillers on the modules of the composites can be represented by a coefficient ‘C’ such as

C= ( '/ ')( '/ ')

Gg Gr compositeGg Gr polystyrene

(8.1)

Table 8.1 The value of the constant C Serial no Name of the sample Value of constant

1 BNN10 0.58 2 BNN20 0.43 3 BNN30 0.30 4 BNN40 0.28 5 YBCO10 0.61 6 YBCO20 0.55 7 YBCO30 0.46 8 YBCO40 0.35


Where 'Gg and 'Gr are the storage modulus values in the glassy and

rubbery regions respectively [15]. The lower the value of C, the higher is the effectiveness of the filler. The measured G’ values at 30 and 1200C for the polymer and the composites were employed as 'Gg and

'Gr respectively. The values obtained for different systems at frequency 10 Hz are given in table8.1. The effectiveness of the composites is gradually increasing with filler content and the highest is for 40% filler loading. It is important to mention that modulus in the glassy state is determined primarily by the strength of the intermolecular forces and the way the polymer chains are packed. The stiffness at high temperature is determined by the amorphous regions, which are very compliant above the relaxation transition. However, the difference between modules of the glassy state and rubbery state is smaller in composites than in PS.

20 40 60 80 100 120 1405.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

log(

G')

( Pa)

Temperature(0C)

PS BNN10 BNN20 BNN30 BNN40

Fig 8.3 Variation of storage modulus of BNN-PS composites with temperature at a frequency of 10Hz

234 Chapter VIII

20 40 60 80 100 120 1405.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

log(

G')

( Pa)

Temperature(0C)

PS YBCO10 YBCO20 YBCO30 YBCO40

Fig 8.4 Variation of storage modulus of YBCO-PS composites with

temperature at a frequency of 10Hz

Fig8.5 Derivative of storage modulus of BNN-PS composites with

temperature at a frequency of 0.1 Hz


Fig 8.6 Derivative of storage modulus of YBCPO-PS composites with temperature at a frequency of 0.1 Hz

The peak points of fig 8.5 and fig 8.6 are the change in slope of G’ curve is

the measure of onset change in slope of storage modulus .This is found out

from the plot of 8.5 and 8.6 and reported in the third column of table 8.3

0 10 20 30 40

1.50E+009

2.00E+009

2.50E+009

3.00E+009

3.50E+009

4.00E+009

Storage modulus at 300CStorage modulus at 1200C

Volume% of BNN

Stor

age

mod

ulus

(Pa)

0

1000000

2000000

3000000

4000000

5000000

6000000

7000000

8000000

9000000

Storage m

odulus (Pa)

Fig 8.7 Variation of storage modulus at glassy and rubbery region of BNN-PS at 10Hz

236 Chapter VIII

0 10 20 30 40

1.60E+009

1.80E+009

2.00E+009

2.20E+009

2.40E+009

2.60E+009

2.80E+009

Storage modulus at 300C Storage modulus at 1200C

Stor

age

mod

ulus

(Pa)

Volume% of YBCO

Stor

age

mod

ulus

(Pa)

1000000

1500000

2000000

2500000

3000000

3500000

4000000

Fig 8.8 Variation of storage modulus at glassy and rubbery region of

YBCO-PS at 10Hz

In the glassy state, the polymer shows higher storage modulus and it

decreases with increasing temperature. Similar behavior is observed for

the composites of BNN and YBCO for different loadings. The storage

modulus below Tg maintains a plateau for PS as well as both of its

composites. However, above Tg, in the rubbery region, the storage

modulus of the nanocomposites was greater than that of micro

composites. The energy storage capacity increased in the rubbery state,

where as the molecular motions are elevated which suggests that BNN

had a much more significant effect, resulting in the retention of a high

proportion of the storage modulus in the rubbery region and that the

dispersion of nano fillers in the polymer plays a vital role in altering the

molecular motions at high thermal energy as in fig 8.7and fig 8.8 [16].


8.2.2 Theoretical modeling

The simplest equation for the prediction of storage modulus of a material

by the inclusion of filler is rule of mixtures and the equation is [17]

1(1 )Gc Gm v= + (8.2)

where CG and mG are the storage modulus of composite and matrix

respectively. Einstein had developed a better approach and by

Einstein’s model [18], the equation is

1(1 1.25 )Gc Gm v= + (8.3)

Table 8.2 Theoretical predictions of storage modulus at room temperature.

Name of the sample

Rule of mixtures(GPa)

Einstein Equation(GPa)

Guth Equation(GPa) Experimental(GPa)

Polystyrene 1.59 1.59 1.59 1.59

BNN10 1.74 1.78 2.01 1.99

BNN20 1.91 1.98 2.88 2.55

BNN30 2.06 2.18 4.21 2.95

BNN40 2.23 2.38 5.97 3.66

YBCO10 1.74 1.78 2.02 1.71

YBCO20 1.91 1.98 2.88 1.82

YBCO30 2.06 2.12 4.20 2.19

YBCO40 2.22 2.35 5.97 2.51

238 Chapter VIII

v1 is the volume fraction of filler. This model has been used to investigate

adhesion between spherical filler and an incompressible matrix and is valid

only at low concentration of filler particles. Many researchers modified this

equation. According to Guth [19] the prediction is

21 1(1 1.25 14.1 )Gc Gm v v= + + (8.4)

The experimental and theoretical modulus values are given in table 8.2. It

can be seen that the experimental value lie between the two theoretical

predictions. This signifies the chemical non reactivity of filler and

polymer.

8.2.3 Glass transition Region The glass transition is detected as a sudden and considerable (several

decades) change in the elastic modulus and an attendant peak in the (tan δ)

curve. This underscores the importance of the glass transition as a

material property, for it shows clearly the substantial change in rigidity

that the material experiences in a short span of temperatures.

There is a large fall in modulus with increasing temperature in the unfilled

system The storage moduli drops from~ 109 to~106 Pa in the glass

transition region of PS .The drop in the modulus on passing through the

glass transition temperature is comparatively less for filled composites

than that of unfilled one as in fig 8.9and fig 8.10.


Fig 8.9 Effect of temperature on tan (δ) of BNN-PS

composites at 0.1Hz

Fig 8.10 Effect of temperature on tan (δ) of YBCO-PS composites

at 0.1Hz

240 Chapter VIII

8.2.4 Magnitude of tan (δ) peak

Magnitude of tan (δ) peak value is indicative of the nature of the polymer

system. The tan (δ) peak value, which signifies the dissipation of energy due

to internal friction and molecular motions decreased with increasing filler

content for the composites as shown in fig 8.9&8.10 and the results are

reported in the fourth column of table 8.4. Since the damping peak occurs in

the region of glass transition where the material changes from rigid to more

elastic state, is associated with the movement of small groups and chains of

molecule within the polymer structure, all of which are initially frozen in. In

a composite system damping is affected through the incorporation of fillers.

This is due mainly to shear stress concentrations at the filler surface in

association with additional viscoelastic energy dissipation in the matrix

material. The lowering of tan (δ) peak values for the composites can be

ascribed to the confinement of Polystyrene by fillers and this confined

fraction changes as the content of fillers changed; similar behaviour has been

reported for other micro and nano composites [20] Improvement in

interfacial reinforcement in the composites occurs as observed by the

lowering of tan(δ) values. Damping at the interfaces depends upon the

adhesion between filler and PS. High damping is seen in the case of YBCO

composites. This is associated with the poorer adhesion between YBCO and

PS. Based on the above studies it is concluded that YBCO- dissipate more

energy than that of BNN-PS. At high filler content when strain is applied to

the composite, the strain is controlled mainly by the filler in such a way that

the interface, which is assumed to be the more dissipative component of the

composite is strained to a lesser degree [21].The observed reduction in tan (δ)

values are attributed to the presences of interfacial reinforcement between PS


matrix and filler and to the increased hindrance for energy dissipation and

relaxation of polymer chains in the presence of filler.

8.2.5 Shifting of tan (δ) peak

The glass transition temperature of the nanocomposites, based on the

temperature of the tan (δ) peak, was found to be shifted slightly towards

higher temperature as that of pristine polymer with respect to the content

of BNN and YBCO as shown in fig 8.9 and fig 8.10 and the respective

values are reported in the last column of table 8.3.

Table 8.3 Tg by different methods at a frequency 0.1Hz

Serial No

Name of the sample

By Slope of storage modulus

(0C)

By Loss Modulus ( 0C)

By (tanδ) peak (0C)

1 Polystyrene 84.18 96 108.875

2 BNN10 85.43 96.8 109.23

3 BNN20 86.8 97.2 110.4

4 BNN30 87.8 98 110.75

5 BNN40 88.8 98.5 112.57

6 YBCO10 84.6 96.5 110.01

7 YBCO20 85.12 97.1 110.23

8 YBCO30 86.03 97.7 111.06

9 YBCO40 87.4 98 111.6

In an unfilled system, the chain segments are free from restraints.

Addition of fillers show a positive shift to the Tg values stressing the

242 Chapter VIII

effectiveness of the filler as the reinforcing agent. This effect is more

prominent in BNN-PS composites than that of YBCO-PS composites. The

shifting of Tg to higher temperature can be associated with the decreased

mobility of the chains by the addition of fillers and the increased

interfacial reinforcements [22].

8.2.6 Theoretical predictions of dissipation factor (tan (δ))

The prediction of damping behavior is important for a polymer technologist

both academically and industrially. Composite damping property results

from the inherent damping of the constituents. Rigid fillers usually lower

the damping behavior and this can be represented as [24]

tan tan tanc f f m mV Vδ δ δ= + (8.5)

But in the case of rigid particulate fillers sintered at a high temperature,

the first term in the RHS can be neglected and therefore the equation

becomes [25]

tan tanc mVmδ δ= (8.6)

where the subscripts c and m represents the composite and matrix, Vm is

the volume fraction of the matrix.

However, the variation in the composite modulus resulting from the

differences in the processing conditions must be accounted by the

equation. This is mainly due to the additional constraints or stiffness

imposed on the matrix is similar to increased number of crosslinks. This

in turn can further reduce the tanδ values. So the equation must have a

stiffness term. It is assumed that the matrix in the presence of fillers offers


stiffness equivalent to the minimum elastic modulus of the composite and

the above equation can be modified as [26]

tan tanc mGmVmGc

δ δ =

(8.7)

where G is the storage modulus m and c represents the matrix and composite

respectively. The experimental values are partially matching with both the

predictions (table 8.4).

Table 8.4 Theoretical predictions of tan δ at a frequency 0.1Hz

Name of the sample Eq 8.6 Eq.8.7 Experimental

Polystyrene 2.75 2.75 2.75

BNN10 2.475 1.96 2.34

BNN20 2.20 1.746 2.01

BNN30 1.92 1.031 1.78

BNN40 1.65 0.728 1.451

YBCO10 2.475 2.31 2.5

YBCO20 2.2 1.84 2.18

YBCO30 1.92 1.388 1.86

YBCO40 1.65 1.049 1.51

8.2.7 Loss modulus

The loss modulus G”, is defined as the viscous response of the material.

The loss factors are most sensitive to the molecular motions (fig 8.11)

&8.12). The modulus value increases with filler content at Tg. The loss

modulus peak value shows a regular decrease with decrease of filler

244 Chapter VIII

content at glass transition region. The loss modulus peak value is reported

in the fourth column of table 8.3.Another result is the broadening of the

loss modulus peak with filler content.

The damping is low below glass transition region because the chain segments

are frozen in. Below Tg, the deformations are thus mainly elastic and

molecular slip resulting in viscous flow is low. As temperature increases,

damping goes through a maximum near Tg, in the transition region and then

a minimum in the rubbery region. Above Tg, where rubbery region exists,

the damping is also low because molecular segments are very free to move

about and there is only very little resistance for flow. Thus, when the

segments are either frozen in or are free to move, damping is low. The peak

is seemed to be broadened with the increment in filler content at glass

transition region. The observed broadening may be explained as due to the

difference in the physical state of the matrix surrounding the filler to the rest

of the matrix. The higher the volume fraction of the filler, the more restraints

are present at the interfaces. The different physical state of the matrix

surrounding the filler hinders the molecular motions. The greater constraints

on the amorphous phase could give rise to the higher and broader glass

transition behavior [27, 28]


Fig 8.11 Effect of temperature on loss modulus of (a) BNN-PS

composites at a frequency of 0.1Hz.

Fig 8.12 Effect of temperature on loss modulus of YBCO-PS

composites at a frequency of 0.1Hz.

246 Chapter VIII

8.2.8 Effect of frequency

The storage modulus, loss modulus and damping peaks have been found

to be affected by frequency. The variation of G’, G” and tan (δ) with

frequency of neat PS and one of the composites as a function of

temperature is shown in fig(8.13-8.18). Increase of frequency has been

found to increase the modulus values. Frequency has a direct impact on

the dynamic modulus especially at higher temperature. The modulus

values are found to drop at a temperature around 850C. The drop in

modulus value continues steadily till the temperature of 1150C is reached.

The molecular motion can be believed to be set in at 800C. If a material is

subjected to a constant stress, its elastic modulus will decrease over a

period of time. This is due to the fact that the material undergoes

molecular rearrangement in an attempt to minimize the localized stresses.

Modulus measurement performed over a short time (high frequency)

result thus in higher values whereas, measurements taken over longer time

(low frequency) result in lower values [29]

The tanδ peak is found to shift to higher temperature with increase of

frequency as in fig 8.17 &8.18. The damping peak is associated with

partial loosening of the polymer structure so that the groups and small

chain segments can move. Fig 8.15&fig 8.16 show the effect of frequency

on the loss modulus values of PS and composites. The peak of loss

modulus is seen to be shifted to higher temperature with increase of

frequency. The G” peak of the composite is broader revealing the

morphological rearrangement resulting in a highly rigid high modulus

region and also improved interaction between the filler and the polymer.


Fig 8. 13 Storage modulus versus temperature of PS with frequency

Fig 8. 14 Storage modulus versus temperature of BNN10 with frequency

248 Chapter VIII

Fig 8.15 Loss modulus versus temperature of PS with frequency

Fig8.16 Loss modulus versus temperature of BNN30 with frequency


Fig 8.17 tan δ versus temperature of PS with frequency

Fig 8.18 tanδ versus temperature of YBCO10 with frequency

250 Chapter VIII

8.2.9 Cross over Frequency

From figures (8.13-8.18) it is clear that at 1000C, in the lower frequency

region PS composites showed more liquid like behaviour.(G’<G”)

compared to solid like behaviour in the higher frequency region(G’>G”).

The frequency at which the cross over between (G’) and (G’’) occurs is

considered as the transition from liquid-to- solid like behavior of the

matrix. A shift in cross over frequency of the composites towards the

lower frequency side with increasing filler content was clearly discernible

from fig8.19 and fig 8.20. The shifting of cross over frequency towards

the lower side signifies the delayed relaxation of the polymeric chains

[30]. At 1000C, the crossover occurs at a frequency for BNN10 is 1.3Hz.

The value is further shift to low frequency side i.e. 0.47 for BNN30. At

1000C, BNN30 is its solid like behaviour. Same result is seen in the case

of YBCO-PS composites and the results are reported in table 8.5

The cross over frequencies of PS and composites are temperature

dependent. To compare the relaxation behavior, the thermal slopes of G’

can be used [31]. As the temperature is increased due to the enhanced

motion of the polymeric chains the slopes also increased. In fig 8.5& 8.6,

it is seen that as temperature increases, the curves become more and more

straight indicating a higher slope for the composites than the matrix.


0 2 4 6 8 10

0.00E+0002.00E+008

4.00E+008

6.00E+0088.00E+008

1.00E+0091.20E+009

1.40E+0091.60E+009

1.80E+0092.00E+0092.20E+009

2.40E+009

2.60E+0092.80E+009

3.00E+009

G' &

G'' (

Pa)

Frequency ( Hz)

Storage modulus BNN10 Loss modulus BNN10 Storage modulus BNN30 Loss modulus BNN30

Fig 8.19 Cross over frequency for BNN-PS composites

0 2 4 6 8 10

0.00E+000

5.00E+008

1.00E+009

1.50E+009

2.00E+009

2.50E+009

3.00E+009

3.50E+009

4.00E+009

4.50E+009

5.00E+009

5.50E+009

G'/G

''(Pa

)

Frequency (Hz)

Loss modulus YBCO10 Storage modulus YBCO10 Loss modulus YBCO30 Storage modulus YBCO30

Fig 8.20 Cross over frequency for YBCO-PS composites

252 Chapter VIII

Table 8.5 Cross over frequency

Name of sample Cross over frequency(Hz)

BNN10 1.52

BNN30 0.47

YBCO10 1.36

YBCO30 0.34

8.2.10 Cole-Cole (like) plots

Structural changes taking place in polymers after filler addition to

polymeric matrices can be studied using Cole-Cole method. The dynamic

mechanical properties when examined as a function of temperature and

frequency are represented on the Cole-Cole complex plane.

G”= f (G’) (8.8)

Cole-Cole plots (imaginary part of the storage modulus is plotted against

real part) are generally used to observe the compatibility and relaxation

behavior of the two constituents of the composite. Smooth, semicircular

arcs imply compatibility of the components [32]. Figures 8.21 &8.22

show the nanocomposites and the microcomposites have same nature of

plots compared to pristine PS.


0.00E+000 5.00E+008 1.00E+009 1.50E+009 2.00E+009 2.50E+0090.00E+000

2.00E+008

4.00E+008

6.00E+008

8.00E+008

1.00E+009

G''(

Pa)

G' (Pa)

PS BNN40 BNN20 BNN30 BNN10

Fig 8.21 Cole-Cole plot for BNN-PS composite

0.00E+000 5.00E+008 1.00E+009 1.50E+009 2.00E+009 2.50E+0090.00E+000

2.00E+008

4.00E+008

6.00E+008

8.00E+008

1.00E+009

G''(

Pa)

G'(Pa)

PS YBCO40 YBCO20 YBCO30 YBCO10

Fig 8.22 Cole-Cole plot for YBCO-PS composite

254 Chapter VIII

8.3 Conclusions

Dynamic mechanical properties of ceramic powder reinforced PS

composites are greatly dependent on the volume fraction of filler. This

analysis showed significant improvement in storage modulus of PS in the

glassy and rubbery region and is correlated with the morphological

behaviour. Different test methods and oscillation frequencies can result in

different Tg values as in Table8.3. Therefore, the values found in Table

8.3 should be viewed qualitatively because values from different studies

cannot be compared directly. This gives the beginning and end of the

transition period. The Tg values calculated in this chapter, therefore,

support the trends found by others. The presence of rigid filler into a

polymer matrix is generally responsible for the increase of glass transition

temperature. The glass transition temperature is shifted positively on the

addition of filler. Increase of frequency shifts the ‘Tg’ to higher

temperature. This results are justified by the homogeneity of dispersion of

the nanofiller into Polystyrene, as revealed by SEM analysis, and by the

enormous interfacial area of the nanoparticles, as a strong interconnection

between the two phases, reduces the mobility of Polystyrene chains.

The cross over frequency of the nanocomposites shifted towards the lower

frequency region with increasing BNN & YBCO content, signifying the

elastic behaviour and the delayed relaxation of the composites because of

the incorporation of BNN & YBCO. The (tanδ) peak temperature showed

a right shift and, the peak intensity was lowered for the composites.


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