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Heat capacity, entropy and enthalpy of silicone-poly(styrene butadiene) rubber blends from 80 to 300 K
Heat capacity, entropy and enthalpy of silicone- poly(styrene butadiene) rubber blends from 80 to 300 K T. Bhowmick, B.R. Gupta* and S. Pattanayakt Cryogenic Engineering Centre, Indian Institute of Technology, Kharagpur-721302, India *Rubber Technology Centre, Indian Institute of Technology, Kharagpur-721302, India
Received 12 July 1991; revised 19 November 1991 Measurements of the variation of heat capacity, entropy and enthalpy of silicone and poly(styrene butadiene) rubber blends of composition O - 1 0 0 % , 2 0 - 8 0 % , 4 0 - 6 0 % , 8 0 - 2 0 % and 1 0 0 - 0 % from 80 to 300 K are reported. It is observed that the heat capacities of blends have two clear anomalies which correspond to the glass transition temperature regions of silicone and styrene butadiene rubber (SBR). It is also found that the change of heat capacity with blend composition becomes reversed at around 200 K. The experimental values of heat capacity for the entire blend composition are empirically correlated by a single polynomial equation for the above temperature zone in the form: C(T) = A1T + A2 T2 - A 3 T3 where the constants A1, A2, A 3 are functions of composition (F). The values of the constants also change after 200 K when a reversal of the change of heat capacity with composition occurs. This empirical equation fits well with the experimental values throughout the range except in the transition regions. The change of entropy and enthalpy thus obtained from heat capacity are also correlated by a similar set of empirical equations of the form S or H = B~T + B2T2 + B3T3+ constant. These parameters also increase with temperature, with a sudden rise near the transition temperature of SBR only. The average standard deviation is found to be 5% maximum.
Keywords: heat capacity; entropy; enthalpy
The rapid development of materials science in recent years has stimulated interest in the investigation of the thermal properties of polymers and their blends in the cryogenic temperature region. They are an emerging class of materials increasingly replacing conventional materials in the design of cryogenic components. Though impressive progress has been achieved in recent years1-5, much remains uncovered. The serviceability of these materials at cryogenic temperatures depends not only on their mechanical properties, but also on their thermal properties, such as heat capacity, entropy and enthalpy. The efficiency of the thermal design of a cryogenic system depends on the accurate estimation of such properties. Study of the variation of heat capacity thus helps to make an efficient and optimized design. Similarly the variation of entropy and enthalpy with temperature will be helpful to understand the intermolecular interactive phenomena, the different vibrational modes of the molecules and their arrangements in the different temperature regions and the calculation of various thermodynamic functions. Furthermore, study *To w h o m
correspondence s h o u l d
be
addressed
0 0 1 1 - 2275/92/070616 - 0 7 © 1 9 9 2 B u t t e r w o r t h - H e i n e m a n n Ltd
616
Cryogenics 1992 Vol 32, No 7
of all these parameters will be extremely helpful for different heat transfer and cooling load calculations for the thermal design of any cryogenic component and for the determination of different state points. When a blend is cooled gradually from ambient conditions, the various modes of molecular motions, viz. (i) translational motion of the entire chain, (ii) three-dimensional cooperative vibration of about 10 to 50 carbon atoms in length, (iii) small segmental (five to six carbon atoms) and side group movements and (iv) vibration of atoms about equilibrium position 4 in it will begin successively to be frozen. Motions (i) to (iv) occur in order of decreasing activation energy. Below glass transition temperature, motions (iii) and (iv) dominate whereas above it the first two types are predominant. Each mode of such frozen molecular motion is associated with a specific relaxation process. With amorphous polymers like rubbers these types of relaxation process are dominant, being related to the transition from melt to rubbery, rubbery to leathery and leathery to glassy states 6. The transitions occur mainly owing to the freezing of the segmental mobilities of the microBrownian type and lead to a marked change in all types of properties. According to Hoffman et al. 6, transi-
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. tions appear in the form of folding motion, changes in voids and reorientation of polymeric chains. These mobilities are caused by large kinetic units of molecular chains. The end chain effects which have low energy motional state have at best little influence upon the thermal properties above 0.4 K 7. It has been established 8 that at low temperatures if the dominant phonon wavelength of the interchain modes of an elastomer is of the order of the crosslink distance, it will greatly influence the low temperature properties. The entanglement would further restrict the interchain mobility and needs different modes for explanation. Hindered rotational motion of side groups has been used to explain the variation of thermal properties between 4 K and 150 K 9. At low temperature the interchain phenomenon is not predominant. The transitions due to such effects may be singlet, doublet or multiplet 8. The orientation effect, end effect and effect of bulkiness of side chains may also be associated with the glass transition of the amorphous region 8. Thus the frozen modes of vibration will leave their imprint on the thermal properties such as the heat capacity, entropy and enthalpy. The temperature dependence of these parameters gives much valuable information regarding the structure, heat transfer mechanism and serviceability of the elastomers. It is highly improbable that a method can be derived for the calculation of accurate values of changes in entropy and enthalpy by the simple addition of the group contribution. In view of this the development of a method based on experimental work for the prediction of these parameters is desirable. Elastomeric blends have attracted much interest in recent years 4 for their improved mechanical properties, but very little information regarding their thermal behaviour at cryogenic temperatures is available in the literature. These blends play a crucial role for optimization of different thermal properties and in some cases are used as a replacement for the conventional material with effective reduction in cost and improvement of properties. The effect of crosslinking as a correlation of chemical structure with physical properties is well known. The variations of many properties can be understood by molecular anisotropy of the binding forces. Strong covalent and weak Van der Waals forces act along and transverse to the main chain respectively. Furthermore, silicone rubber is found to have very good low temperature properties. As this rubber is very costly, its blending with comparatively cheap commercially available rubber may retain its properties within acceptable limits. With this idea in mind, a series of blends of silicone rubber-SBR have been used for investigating the variation of heat capacity, entropy and enthalpy with varying composition from 0 to 100% over a temperature range from 80 to 300 K. The heat capacity is calculated from the equation Cp = d Q / m d T where dT is temperature rise of the specimen for the heat input dQ. The variation of heat capacity with temperature for the calorimeter and its assembly is obtained from an initial experimental run with an empty calorimeter. This heat capacity, which varies from 0.27 J g-t K -t to 0.45 J g - ' K -~, is subtracted from the total C v to obtain its value for the sample. The change of entropy and enthalpy at different
temperatures is calculated from the heat capacity as S(T) = l T2 Cp(T)dT 3 T, T
(1)
and
H(T) =
Cv(T)dT
(2)
TL
where Cp(T) is the temperature-dependent heat capacity function, TI is the initial reference temperature and T2 is the final temperature.
Sample preparation and experimentation The specifications and compositions of the samples are shown in Table 1. Co-axial samples of 6.00 mm outer diameter and 3.00 mm inner diameter are used in the measurement of heat capacity of the blend samples. The blending is performed in a two-roll mill at a temperature of 45°C. The time required for blending each sample is 40 min. Once the blend is thoroughly mixed, it is sheeted out from the mill. The sample is then moulded to the desired shape on an electrically heated press with a mild steel mould at a temperature of 115°C. The sample is cut into small pieces, and force packed in the mould by means of a cover plate. The mould is then heated with its cover plates and pressed in the press. To avoid the material sticking to the mould surface, aluminium foil is used. The mould is then cooled and the samples taken out, and cut to the required size to fit into the copper calorimeter. The samples are weighed in a single pan scientific balance to an accuracy of 0.1 mg. The weights of different samples used for the measurement are shown in Table 1.
Table 1
Sample specifications, composition and weight of the silicone rubber-SBR blends Specification Silicone rubber
Source: M/S Dow Coming Corporation, USA Classification: VMQ Density: 1.28 g cm 3
Styrene butadiene rubber (SBR)
Source: M/S Synthetics and Chemicals, India Density: 0.980 g c m -3
Composition of the sample Blend no. Blend Blend Blend Blend Blend Blend
1 2 3 4 5 6
silicone rubber (%)
SBR (%)
Weight of sample (g)
1O0 80 60 40 20 0
0 20 40 60 80 100
6.035 5.752 5.469 5.186 4.904 4.621
Cryogenics 1992 Vol 32, No 7
617
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. The principle of adiabatic calorimetry with the transient heating technique 1° was used for the measurement of heat capacity of the sample. The adiabaticity between the surfaces of the shield and calorimeter is maintained in the order of 0.01 K. The weight of addenda is 1.243 g and the temperature is measured by a 36 gauge copper- constantan thermocouple earlier calibrated with reference to the fixed points. The systematic error introduced represents an accuracy within 3 to 5 %.
Results and Discussion
Figure I shows graphically the variation of experimental values of heat capacity for blends 1 to 6 (Table 1) in the temperature region from 80 to 300 K. From the experiment it is seen that the heat capacity of silicone rubber is higher than that of SBR at 80 K. This difference of heat capacity gradually diminishes to zero at about 200 K and then the heat capacity of SBR increases more rapidly with temperature than silicone rubber. There are anomalies in the behaviour of the heat capacity of blends corresponding to the Tg of pure gum, i.e., at 148 K for silicone rubber and near 213 K for SBR. As two peaks are observed, we can say that the two rubbers are incompatible with each other. These anomalies can be explained theoretically 8. At the glass transition temperature, there is a sudden absorption of energy because of the phase transition, which is reflected as the sudden rise in heat capacity. The rate of change of heat capacity near glass transition temperature should be appreciably higher than that at any other region.
Moreover, SBR with its heavy styrene component as a side group will impart more influence on the entire mechanism of the change of heat capacity of the blends. This is clearly demonstrated in all the experimental values of the blends as the cross-over point (at 200 K) is closer to the Tg of SBR than that of silicone rubber. Table 2 shows the rate of change of heat capacity of these blends near their glass transition temperatures and with increasing SBR percentage. Near the respective glass transition temperatures both the materials have higher rates of change of heat capacity, which also change with composition of SBR. The rate of change of heat capacity is governed by the closeness of Tg of the predominant composition. From Table 2, it is seen that
Table 2 Rate of change of heat capacity of silicone r u b b e r - SBR blends at different temperatures Rate of change of heat capacity (J g i K-1 K - l ) Sample
At 140 K
At 205 K
Silicone rubber 100% SBR 2 0 % SBR 4 0 % SBR 6 0 % SBR 8 0 % SBR 100%
0.067 0.055 0.043 0.030 0.018 0.006
0.003 0.013 0.023 0.032 0.043 0.053
2.8l 2.4
2.0
i v
T
1.6
1.2
"1-
0.8
0.4
01 80
l 100
I 120
I 140
I 160
I 180
I 200
I 220
I 240
I 260
I 280
I 300
Temperature ( K ) Figure I Variation of heat capacity of silicone r u b b e r - SBR blends with temperature: • , silicone rubber (SBR 0%); 20%; [3, SBR 4 0 % ; x, S B R 6 0 % ; • , S B R 8 0 % ; O , S B R 1OO%
618
Cryogenics 1992 Vol 32, No 7
A , SBR
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. the quantity is decreasing at 140 K (closer to silicone Tg) and increasing at 205 K (closer to SBR Tg) with the increase of SBR percentage. It is also seen that heat capacity generally increases with temperature. The blending is a physical entanglement and does not involve any chemical reaction. Thus the physical properties of blends are observed to be additive in nature. A third degree polynomial is found to fit excellently with the experimental values of Cp as a function of temperature. The constants are different before and after the temperature where the reversal occurs. This single empirical equation surprisingly gives very satisfactory predictions of heat capacity for any composition of blends within the experimental range. The empirical equation is as follows
developed empirical equation based on experimental data. The variations of heat capacity of blends with compositions below and above the cross-over point (200 K) are shown in Figures 2 and 3 respectively. It is observed that below 200 K the heat capacity decreases linearly with increased percentage of SBR content up to 200 K, beyond which the trend is reversed. This may be due to the glass transition temperature of the dominant SBR phase. The change of entropy and enthalpy may be calculated by integrating the following equations
I
S(T) =
Cp(T) = (7.04 × 10 -3 + 1.13 × 10-3T)T
T2 % 0 3 T]
dT
T
+ (1.87 × 10 -7 + 1.57 x 10-SF)T 2 - (2.61 × 10 -8 - 9.95 × 10-8F)T 3
2.ot
(3)
for the range 80 to 230 K, and Cp(T) = (7.04 x + (1.87
10 -3 +
7.9 × 10-3F)T
× 10 -7 -
1 . 6 t ~
5.06 X 10-SF)T 2
- (2.61 × 10 -8 - 6.57 × 10-8F)T 3
(4)
for the range 230 to 300 K. The percentage deviation of empirically predicted values from experimental ones is found to be not greater than 5% in any case. The deviations at 100, 180 and 260 K for all the blends are shown in Table 3. Both the elastomers used are highly branched polymers with heavy side chains. The variation of their heat capacity can be explained qualitatively with the help of Tarasov's theory, taking into consideration the characteristic group vibrations arising out of stretching, twisting, bending, wagging and rocking of the covalent bonds by Einstein's concept of heat capacity contribution. Considering these characteristic group vibrations and the vibrations due to interchain, interlayer interaction by Tarasov's model, a theoretical model is developed. It is found that heat capacity is a function of T, T 2 and T 3 terms for one-, two- and threedimensional cases. The values obtained from these theoretical equations show the same trend as that of the
~
1.2
~" 0.8
0.q
1
I
I
I
I
20
q0
60
80
100
Composition (~o SBR) 2 Variation of heat capacity with composition of silicone rubber-SBR blends: O, lOOK; 1:3, 12OK; • , 13OK; & , 14OK; x, 1 4 5 K Figure
t
3 Percentage deviation of the values of heat capacity obtained from empirical equations (3) and (4) with the experimental results
Table
Deviation of empirical values from experimental (%) Sample
1O0 K
180 K
260 K
Silicone rubber SBR 20% SBR 40% SBR 60% SBR BO% SBR 100%
1.48 1.67 1.68 1.87 2.02 2.11
4.9 4.9 1.1 3.34 2.72 2.05
1.23 0.43 0.80 0.69 0.86 0.32
? cn
1.2
Q.
0.8
-1-
0.4
0
I
I
I
I
I
20
40
60
80
100
Composition (~ SBR) 3 Variation of heat capacity with composition of silicone rubber-SBR blends at different ttemperatures: O, 230 K; • , 250 K; • , 27OK; x, 280 K; [ ] , 29OK Figure
Cryogenics 1992 Vol 32, No 7
619
Heat capacity of silicone-poly(styrene butadiene) rubber b/ends: T. Bhowmick et al. 1.6
1,4
1.2
1.0 J~
D3 -7 0.8 >. o_
o
ua 0.6
0.4
0.2
0 60
I 80
I I00
I 120
I 140
I, 160
I 180
I 200
I 220
I 240
I 260
I 280
I 300
I 280
I 300
Temperature (K] Figure
4
Variation
of entropy
with
temperature
for
silicone
rubber-SBR
blends. S y m b o l s as in
Figure 1
280
240
200
i
o~
160
>oc LU
120 -
80
40
60
I 80
~"
I 100
I 120
I 140
I 160
I 180
I 200
I 220
I 240
I 260
Temperature ( K ) Figure 5
620
Variation
of enthalpy
with
temperature
Cryogenics 1992 Vol 32, No 7
for silicone
rubber-SBR
blends. S y m b o l s as in
Figure 1
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. and
300
H(73 ;
Cp(~dr T~
250
where Cp(T) is the heat capacity represented by Equations (3) and (4), and T 2 and T 1 a r e the final and initial temperatures, which are 290 and 80 K in this case. The final empirical equation for the change of entropy and enthalpy becomes S(T) = (7.04 x 10 -3 + 1.13 × 10-3F)T
2oo~ 7o~ ~ 1so' .~
Ca
+ (0.935 × 10 -7 + 0.79 × 10-~F)T 2
,,5 100i
- (0.87 × 10 -8 - 3.32 X 10-8F)T 3 , ..----...._.~
- (0.559 + 0.125F)
(5)
so
for the range 80 to 230 K, and
(:>--'---~
z>-----------o
4>--
S(T) = (7.04 × 10 _3 + 7.9 × 10-3F)T
I 20
I 60
I 80
I 100
Composition
(~ S B R }
+ (0.94 x 10 -7 - 2.53 × 10-SF)T 2
I 40
Figure 7 Variation of enthalpy with composition for silicone rubber- SBR blends. Symbols asin Figure 6
- (0.87 × 10 -8 - 2.19 × 10-SF)T 3 - (0.559 + 0.125F)
(6)
for the range 230 to 300 K. For enthalpy it is H(T) = (3.52 × 10 -3 + 0.56 × 10-3F)T 2 + (0.62 × 10 -7 + 0.53 × 10-SF)T 3 - (0.65 × 10 -8 - 2.49 × 10-SF)T 4 - (22.293 + 5.275F)
(7)
for the range 80 to 230 K, and H(T) = (3.52 × 10 -3 + 3.63 × 10-3F)T 2 + (0.62 × 10 - 7 - 1.69 x 10-SF)T 3 - (0.65 × 10 -8 - 1.64 × 10-8F)T 4 - (22.293 + 5.275F)
(8)
Figures 4 and 5 show the variations of entropy and enthalpy with temperature for the blends. The important observation is that the SBR and blends with high SBR content show considerable increase in the rate of change in entropy and enthalpy with temperature beyond the Tg of SBR, whereas silicone rubber does not show any change in rate around its Tg. This again confirms that SBR, being the rubber with heavier side group has predominance on the change of all physical properties. Figures 6 and 7 graphically represent the variation of the change of entropy and enthalpy versus composition curve. It shows that both entropy and enthalpy decrease linearly with increase in SBR content and that the slope of the lines is higher at higher temperatures and vice versa, which is obvious because at higher temperatures the different vibrational modes become more activated causing higher absorption of energy.
for the range 230 to 300 K. Conclusion 1.8
1.4
qtn
1.0
o 0.6 LU
~
0.2 I 20
I 40
I 60
~o
o--
I 80
I 100
References
Composition (~ SBR)
Figure
6 Variation of e n t r o p y with c o m p o s i t i o n r u b b e r - S B R blends: O , 1 2 0 K; zx, 1 6 0 K ; [ ] , 240K; •, 28OK
1 Heat capacity variation with temperature shows two distinct peaks at the glass transition temperatures of pure gum rubbers, indicating that the two rubbers are incompatible with each other. 2 There is a cross-over point at around 200 K in the variation of Cp with temperature. This cross-over temperature being closer to T~ of SBR shows that the influence of SBR molecular structure in the blend is more pronounced than that of silicone rubber. 3 Empirical polynomial equations relating Cp, S and H with temperature and percentage o f SBR content have been developed (Equations (2) to, (8)). 4 Co, S and H all vary linearly with SBR composition in the blends.
for silicone 20OK; •,
I Bu H.S., Aycock, W. and Wunderlich, B. Polymer (1987) 28 1165 2 Freeman, J.J. and Greig, D. Adv Cryog Eng (1982) 30 105 3 Scheibner,W. and Jackel, M. Phys Stat Sol (a) (1985) 87 543
Cryogenics 1992 Vol 32, No 7
621
Heat capacity of silicone-poly(styrene butadiene) rubber b/ends: T. Bhowrnick et al. 4 Rosen, S.L. Fundamental Principles of Polymeric Materials Wiley, New York (1982) Ch 8 5 Pattanayak, S. and Bhowmick, T. Proc Low Temperature Engineering and Cryogenic Conference 1990 Southampton, UK, article no. 9.3. Institute of Cryogenics, University of Southampton, UK 6 Hoffman, J.D., William, G. and Pasaglia, E. in Transition and Relaxation in Polymers (Ed Buyer, R.) Interscience, New York, USA (1966)
622
Cryogenics 1992 Vol 32, No 7
7 Choy, C.L., Hunt, R.G. and Salinger, G.L. J Chem Phys (1972) 52 3629 8 Perpechko, I. in Acoustic Methods of Investigating Polymers Mir, Moscow (1975) 9 Stephens, R.B., Cieloszyk, G.S. and Salinger, G.L. Phys Lett A (1972) 38 (3) 215 10 Bhowmick, T. and Pattannyak, S. Cryogenics (1989) 29 (4) 463
Received 12 July 1991; revised 19 November 1991 Measurements of the variation of heat capacity, entropy and enthalpy of silicone and poly(styrene butadiene) rubber blends of composition O - 1 0 0 % , 2 0 - 8 0 % , 4 0 - 6 0 % , 8 0 - 2 0 % and 1 0 0 - 0 % from 80 to 300 K are reported. It is observed that the heat capacities of blends have two clear anomalies which correspond to the glass transition temperature regions of silicone and styrene butadiene rubber (SBR). It is also found that the change of heat capacity with blend composition becomes reversed at around 200 K. The experimental values of heat capacity for the entire blend composition are empirically correlated by a single polynomial equation for the above temperature zone in the form: C(T) = A1T + A2 T2 - A 3 T3 where the constants A1, A2, A 3 are functions of composition (F). The values of the constants also change after 200 K when a reversal of the change of heat capacity with composition occurs. This empirical equation fits well with the experimental values throughout the range except in the transition regions. The change of entropy and enthalpy thus obtained from heat capacity are also correlated by a similar set of empirical equations of the form S or H = B~T + B2T2 + B3T3+ constant. These parameters also increase with temperature, with a sudden rise near the transition temperature of SBR only. The average standard deviation is found to be 5% maximum.
Keywords: heat capacity; entropy; enthalpy
The rapid development of materials science in recent years has stimulated interest in the investigation of the thermal properties of polymers and their blends in the cryogenic temperature region. They are an emerging class of materials increasingly replacing conventional materials in the design of cryogenic components. Though impressive progress has been achieved in recent years1-5, much remains uncovered. The serviceability of these materials at cryogenic temperatures depends not only on their mechanical properties, but also on their thermal properties, such as heat capacity, entropy and enthalpy. The efficiency of the thermal design of a cryogenic system depends on the accurate estimation of such properties. Study of the variation of heat capacity thus helps to make an efficient and optimized design. Similarly the variation of entropy and enthalpy with temperature will be helpful to understand the intermolecular interactive phenomena, the different vibrational modes of the molecules and their arrangements in the different temperature regions and the calculation of various thermodynamic functions. Furthermore, study *To w h o m
correspondence s h o u l d
be
addressed
0 0 1 1 - 2275/92/070616 - 0 7 © 1 9 9 2 B u t t e r w o r t h - H e i n e m a n n Ltd
616
Cryogenics 1992 Vol 32, No 7
of all these parameters will be extremely helpful for different heat transfer and cooling load calculations for the thermal design of any cryogenic component and for the determination of different state points. When a blend is cooled gradually from ambient conditions, the various modes of molecular motions, viz. (i) translational motion of the entire chain, (ii) three-dimensional cooperative vibration of about 10 to 50 carbon atoms in length, (iii) small segmental (five to six carbon atoms) and side group movements and (iv) vibration of atoms about equilibrium position 4 in it will begin successively to be frozen. Motions (i) to (iv) occur in order of decreasing activation energy. Below glass transition temperature, motions (iii) and (iv) dominate whereas above it the first two types are predominant. Each mode of such frozen molecular motion is associated with a specific relaxation process. With amorphous polymers like rubbers these types of relaxation process are dominant, being related to the transition from melt to rubbery, rubbery to leathery and leathery to glassy states 6. The transitions occur mainly owing to the freezing of the segmental mobilities of the microBrownian type and lead to a marked change in all types of properties. According to Hoffman et al. 6, transi-
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. tions appear in the form of folding motion, changes in voids and reorientation of polymeric chains. These mobilities are caused by large kinetic units of molecular chains. The end chain effects which have low energy motional state have at best little influence upon the thermal properties above 0.4 K 7. It has been established 8 that at low temperatures if the dominant phonon wavelength of the interchain modes of an elastomer is of the order of the crosslink distance, it will greatly influence the low temperature properties. The entanglement would further restrict the interchain mobility and needs different modes for explanation. Hindered rotational motion of side groups has been used to explain the variation of thermal properties between 4 K and 150 K 9. At low temperature the interchain phenomenon is not predominant. The transitions due to such effects may be singlet, doublet or multiplet 8. The orientation effect, end effect and effect of bulkiness of side chains may also be associated with the glass transition of the amorphous region 8. Thus the frozen modes of vibration will leave their imprint on the thermal properties such as the heat capacity, entropy and enthalpy. The temperature dependence of these parameters gives much valuable information regarding the structure, heat transfer mechanism and serviceability of the elastomers. It is highly improbable that a method can be derived for the calculation of accurate values of changes in entropy and enthalpy by the simple addition of the group contribution. In view of this the development of a method based on experimental work for the prediction of these parameters is desirable. Elastomeric blends have attracted much interest in recent years 4 for their improved mechanical properties, but very little information regarding their thermal behaviour at cryogenic temperatures is available in the literature. These blends play a crucial role for optimization of different thermal properties and in some cases are used as a replacement for the conventional material with effective reduction in cost and improvement of properties. The effect of crosslinking as a correlation of chemical structure with physical properties is well known. The variations of many properties can be understood by molecular anisotropy of the binding forces. Strong covalent and weak Van der Waals forces act along and transverse to the main chain respectively. Furthermore, silicone rubber is found to have very good low temperature properties. As this rubber is very costly, its blending with comparatively cheap commercially available rubber may retain its properties within acceptable limits. With this idea in mind, a series of blends of silicone rubber-SBR have been used for investigating the variation of heat capacity, entropy and enthalpy with varying composition from 0 to 100% over a temperature range from 80 to 300 K. The heat capacity is calculated from the equation Cp = d Q / m d T where dT is temperature rise of the specimen for the heat input dQ. The variation of heat capacity with temperature for the calorimeter and its assembly is obtained from an initial experimental run with an empty calorimeter. This heat capacity, which varies from 0.27 J g-t K -t to 0.45 J g - ' K -~, is subtracted from the total C v to obtain its value for the sample. The change of entropy and enthalpy at different
temperatures is calculated from the heat capacity as S(T) = l T2 Cp(T)dT 3 T, T
(1)
and
H(T) =
Cv(T)dT
(2)
TL
where Cp(T) is the temperature-dependent heat capacity function, TI is the initial reference temperature and T2 is the final temperature.
Sample preparation and experimentation The specifications and compositions of the samples are shown in Table 1. Co-axial samples of 6.00 mm outer diameter and 3.00 mm inner diameter are used in the measurement of heat capacity of the blend samples. The blending is performed in a two-roll mill at a temperature of 45°C. The time required for blending each sample is 40 min. Once the blend is thoroughly mixed, it is sheeted out from the mill. The sample is then moulded to the desired shape on an electrically heated press with a mild steel mould at a temperature of 115°C. The sample is cut into small pieces, and force packed in the mould by means of a cover plate. The mould is then heated with its cover plates and pressed in the press. To avoid the material sticking to the mould surface, aluminium foil is used. The mould is then cooled and the samples taken out, and cut to the required size to fit into the copper calorimeter. The samples are weighed in a single pan scientific balance to an accuracy of 0.1 mg. The weights of different samples used for the measurement are shown in Table 1.
Table 1
Sample specifications, composition and weight of the silicone rubber-SBR blends Specification Silicone rubber
Source: M/S Dow Coming Corporation, USA Classification: VMQ Density: 1.28 g cm 3
Styrene butadiene rubber (SBR)
Source: M/S Synthetics and Chemicals, India Density: 0.980 g c m -3
Composition of the sample Blend no. Blend Blend Blend Blend Blend Blend
1 2 3 4 5 6
silicone rubber (%)
SBR (%)
Weight of sample (g)
1O0 80 60 40 20 0
0 20 40 60 80 100
6.035 5.752 5.469 5.186 4.904 4.621
Cryogenics 1992 Vol 32, No 7
617
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. The principle of adiabatic calorimetry with the transient heating technique 1° was used for the measurement of heat capacity of the sample. The adiabaticity between the surfaces of the shield and calorimeter is maintained in the order of 0.01 K. The weight of addenda is 1.243 g and the temperature is measured by a 36 gauge copper- constantan thermocouple earlier calibrated with reference to the fixed points. The systematic error introduced represents an accuracy within 3 to 5 %.
Results and Discussion
Figure I shows graphically the variation of experimental values of heat capacity for blends 1 to 6 (Table 1) in the temperature region from 80 to 300 K. From the experiment it is seen that the heat capacity of silicone rubber is higher than that of SBR at 80 K. This difference of heat capacity gradually diminishes to zero at about 200 K and then the heat capacity of SBR increases more rapidly with temperature than silicone rubber. There are anomalies in the behaviour of the heat capacity of blends corresponding to the Tg of pure gum, i.e., at 148 K for silicone rubber and near 213 K for SBR. As two peaks are observed, we can say that the two rubbers are incompatible with each other. These anomalies can be explained theoretically 8. At the glass transition temperature, there is a sudden absorption of energy because of the phase transition, which is reflected as the sudden rise in heat capacity. The rate of change of heat capacity near glass transition temperature should be appreciably higher than that at any other region.
Moreover, SBR with its heavy styrene component as a side group will impart more influence on the entire mechanism of the change of heat capacity of the blends. This is clearly demonstrated in all the experimental values of the blends as the cross-over point (at 200 K) is closer to the Tg of SBR than that of silicone rubber. Table 2 shows the rate of change of heat capacity of these blends near their glass transition temperatures and with increasing SBR percentage. Near the respective glass transition temperatures both the materials have higher rates of change of heat capacity, which also change with composition of SBR. The rate of change of heat capacity is governed by the closeness of Tg of the predominant composition. From Table 2, it is seen that
Table 2 Rate of change of heat capacity of silicone r u b b e r - SBR blends at different temperatures Rate of change of heat capacity (J g i K-1 K - l ) Sample
At 140 K
At 205 K
Silicone rubber 100% SBR 2 0 % SBR 4 0 % SBR 6 0 % SBR 8 0 % SBR 100%
0.067 0.055 0.043 0.030 0.018 0.006
0.003 0.013 0.023 0.032 0.043 0.053
2.8l 2.4
2.0
i v
T
1.6
1.2
"1-
0.8
0.4
01 80
l 100
I 120
I 140
I 160
I 180
I 200
I 220
I 240
I 260
I 280
I 300
Temperature ( K ) Figure I Variation of heat capacity of silicone r u b b e r - SBR blends with temperature: • , silicone rubber (SBR 0%); 20%; [3, SBR 4 0 % ; x, S B R 6 0 % ; • , S B R 8 0 % ; O , S B R 1OO%
618
Cryogenics 1992 Vol 32, No 7
A , SBR
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. the quantity is decreasing at 140 K (closer to silicone Tg) and increasing at 205 K (closer to SBR Tg) with the increase of SBR percentage. It is also seen that heat capacity generally increases with temperature. The blending is a physical entanglement and does not involve any chemical reaction. Thus the physical properties of blends are observed to be additive in nature. A third degree polynomial is found to fit excellently with the experimental values of Cp as a function of temperature. The constants are different before and after the temperature where the reversal occurs. This single empirical equation surprisingly gives very satisfactory predictions of heat capacity for any composition of blends within the experimental range. The empirical equation is as follows
developed empirical equation based on experimental data. The variations of heat capacity of blends with compositions below and above the cross-over point (200 K) are shown in Figures 2 and 3 respectively. It is observed that below 200 K the heat capacity decreases linearly with increased percentage of SBR content up to 200 K, beyond which the trend is reversed. This may be due to the glass transition temperature of the dominant SBR phase. The change of entropy and enthalpy may be calculated by integrating the following equations
I
S(T) =
Cp(T) = (7.04 × 10 -3 + 1.13 × 10-3T)T
T2 % 0 3 T]
dT
T
+ (1.87 × 10 -7 + 1.57 x 10-SF)T 2 - (2.61 × 10 -8 - 9.95 × 10-8F)T 3
2.ot
(3)
for the range 80 to 230 K, and Cp(T) = (7.04 x + (1.87
10 -3 +
7.9 × 10-3F)T
× 10 -7 -
1 . 6 t ~
5.06 X 10-SF)T 2
- (2.61 × 10 -8 - 6.57 × 10-8F)T 3
(4)
for the range 230 to 300 K. The percentage deviation of empirically predicted values from experimental ones is found to be not greater than 5% in any case. The deviations at 100, 180 and 260 K for all the blends are shown in Table 3. Both the elastomers used are highly branched polymers with heavy side chains. The variation of their heat capacity can be explained qualitatively with the help of Tarasov's theory, taking into consideration the characteristic group vibrations arising out of stretching, twisting, bending, wagging and rocking of the covalent bonds by Einstein's concept of heat capacity contribution. Considering these characteristic group vibrations and the vibrations due to interchain, interlayer interaction by Tarasov's model, a theoretical model is developed. It is found that heat capacity is a function of T, T 2 and T 3 terms for one-, two- and threedimensional cases. The values obtained from these theoretical equations show the same trend as that of the
~
1.2
~" 0.8
0.q
1
I
I
I
I
20
q0
60
80
100
Composition (~o SBR) 2 Variation of heat capacity with composition of silicone rubber-SBR blends: O, lOOK; 1:3, 12OK; • , 13OK; & , 14OK; x, 1 4 5 K Figure
t
3 Percentage deviation of the values of heat capacity obtained from empirical equations (3) and (4) with the experimental results
Table
Deviation of empirical values from experimental (%) Sample
1O0 K
180 K
260 K
Silicone rubber SBR 20% SBR 40% SBR 60% SBR BO% SBR 100%
1.48 1.67 1.68 1.87 2.02 2.11
4.9 4.9 1.1 3.34 2.72 2.05
1.23 0.43 0.80 0.69 0.86 0.32
? cn
1.2
Q.
0.8
-1-
0.4
0
I
I
I
I
I
20
40
60
80
100
Composition (~ SBR) 3 Variation of heat capacity with composition of silicone rubber-SBR blends at different ttemperatures: O, 230 K; • , 250 K; • , 27OK; x, 280 K; [ ] , 29OK Figure
Cryogenics 1992 Vol 32, No 7
619
Heat capacity of silicone-poly(styrene butadiene) rubber b/ends: T. Bhowmick et al. 1.6
1,4
1.2
1.0 J~
D3 -7 0.8 >. o_
o
ua 0.6
0.4
0.2
0 60
I 80
I I00
I 120
I 140
I, 160
I 180
I 200
I 220
I 240
I 260
I 280
I 300
I 280
I 300
Temperature (K] Figure
4
Variation
of entropy
with
temperature
for
silicone
rubber-SBR
blends. S y m b o l s as in
Figure 1
280
240
200
i
o~
160
>oc LU
120 -
80
40
60
I 80
~"
I 100
I 120
I 140
I 160
I 180
I 200
I 220
I 240
I 260
Temperature ( K ) Figure 5
620
Variation
of enthalpy
with
temperature
Cryogenics 1992 Vol 32, No 7
for silicone
rubber-SBR
blends. S y m b o l s as in
Figure 1
Heat capacity of silicone-poly(styrene butadiene) rubber blends: T. Bhowmick et al. and
300
H(73 ;
Cp(~dr T~
250
where Cp(T) is the heat capacity represented by Equations (3) and (4), and T 2 and T 1 a r e the final and initial temperatures, which are 290 and 80 K in this case. The final empirical equation for the change of entropy and enthalpy becomes S(T) = (7.04 x 10 -3 + 1.13 × 10-3F)T
2oo~ 7o~ ~ 1so' .~
Ca
+ (0.935 × 10 -7 + 0.79 × 10-~F)T 2
,,5 100i
- (0.87 × 10 -8 - 3.32 X 10-8F)T 3 , ..----...._.~
- (0.559 + 0.125F)
(5)
so
for the range 80 to 230 K, and
(:>--'---~
z>-----------o
4>--
S(T) = (7.04 × 10 _3 + 7.9 × 10-3F)T
I 20
I 60
I 80
I 100
Composition
(~ S B R }
+ (0.94 x 10 -7 - 2.53 × 10-SF)T 2
I 40
Figure 7 Variation of enthalpy with composition for silicone rubber- SBR blends. Symbols asin Figure 6
- (0.87 × 10 -8 - 2.19 × 10-SF)T 3 - (0.559 + 0.125F)
(6)
for the range 230 to 300 K. For enthalpy it is H(T) = (3.52 × 10 -3 + 0.56 × 10-3F)T 2 + (0.62 × 10 -7 + 0.53 × 10-SF)T 3 - (0.65 × 10 -8 - 2.49 × 10-SF)T 4 - (22.293 + 5.275F)
(7)
for the range 80 to 230 K, and H(T) = (3.52 × 10 -3 + 3.63 × 10-3F)T 2 + (0.62 × 10 - 7 - 1.69 x 10-SF)T 3 - (0.65 × 10 -8 - 1.64 × 10-8F)T 4 - (22.293 + 5.275F)
(8)
Figures 4 and 5 show the variations of entropy and enthalpy with temperature for the blends. The important observation is that the SBR and blends with high SBR content show considerable increase in the rate of change in entropy and enthalpy with temperature beyond the Tg of SBR, whereas silicone rubber does not show any change in rate around its Tg. This again confirms that SBR, being the rubber with heavier side group has predominance on the change of all physical properties. Figures 6 and 7 graphically represent the variation of the change of entropy and enthalpy versus composition curve. It shows that both entropy and enthalpy decrease linearly with increase in SBR content and that the slope of the lines is higher at higher temperatures and vice versa, which is obvious because at higher temperatures the different vibrational modes become more activated causing higher absorption of energy.
for the range 230 to 300 K. Conclusion 1.8
1.4
qtn
1.0
o 0.6 LU
~
0.2 I 20
I 40
I 60
~o
o--
I 80
I 100
References
Composition (~ SBR)
Figure
6 Variation of e n t r o p y with c o m p o s i t i o n r u b b e r - S B R blends: O , 1 2 0 K; zx, 1 6 0 K ; [ ] , 240K; •, 28OK
1 Heat capacity variation with temperature shows two distinct peaks at the glass transition temperatures of pure gum rubbers, indicating that the two rubbers are incompatible with each other. 2 There is a cross-over point at around 200 K in the variation of Cp with temperature. This cross-over temperature being closer to T~ of SBR shows that the influence of SBR molecular structure in the blend is more pronounced than that of silicone rubber. 3 Empirical polynomial equations relating Cp, S and H with temperature and percentage o f SBR content have been developed (Equations (2) to, (8)). 4 Co, S and H all vary linearly with SBR composition in the blends.
for silicone 20OK; •,
I Bu H.S., Aycock, W. and Wunderlich, B. Polymer (1987) 28 1165 2 Freeman, J.J. and Greig, D. Adv Cryog Eng (1982) 30 105 3 Scheibner,W. and Jackel, M. Phys Stat Sol (a) (1985) 87 543
Cryogenics 1992 Vol 32, No 7
621
Heat capacity of silicone-poly(styrene butadiene) rubber b/ends: T. Bhowrnick et al. 4 Rosen, S.L. Fundamental Principles of Polymeric Materials Wiley, New York (1982) Ch 8 5 Pattanayak, S. and Bhowmick, T. Proc Low Temperature Engineering and Cryogenic Conference 1990 Southampton, UK, article no. 9.3. Institute of Cryogenics, University of Southampton, UK 6 Hoffman, J.D., William, G. and Pasaglia, E. in Transition and Relaxation in Polymers (Ed Buyer, R.) Interscience, New York, USA (1966)
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Cryogenics 1992 Vol 32, No 7
7 Choy, C.L., Hunt, R.G. and Salinger, G.L. J Chem Phys (1972) 52 3629 8 Perpechko, I. in Acoustic Methods of Investigating Polymers Mir, Moscow (1975) 9 Stephens, R.B., Cieloszyk, G.S. and Salinger, G.L. Phys Lett A (1972) 38 (3) 215 10 Bhowmick, T. and Pattannyak, S. Cryogenics (1989) 29 (4) 463