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Transport Properties of Crosslinked Acrylonitrile Butadiene
Rubber/Poly(ethylene-co-vinyl acetate) Blends
HIMA VARGHESE, S. S. BHAGAWAN,* SABU THOMAS
School of Chemical Sciences, Mahatma Gandhi University, Priyadarshini Hills P.O., Kottayam-686 560, Kerala, India
Received 9 September 1998; revised 1 April 1999; accepted 2 April 1999
ABSTRACT: The diffusion and transport of organic solvents through crosslinked nitrile
rubber/poly(ethylene-co-vinyl acetate) (NBR/EVA) blends have been studied. The diffusion of cyclohexanone through these blends was studied with special reference to
blend composition, crosslinking systems, fillers, filler loading, and temperature. At
room temperature the mechanism of diffusion was found to be Fickian for cyclohexanone–NBR/EVA blend systems. However, a deviation from the Fickian mode of diffusion is observed at higher temperature. The transport coefficients, namely, intrinsic
diffusion coefficient (D*), sorption coefficient (S), and permeation coefficient (P) increase with the increase in NBR content. The sorption data have been used to estimate
the activation energies for permeation and diffusion. The van’t Hoff relationship was
used to determine the thermodynamic parameters. The affine and phantom models for
chemical crosslinks were used to predict the nature of crosslinks. The experimental
results were compared with the theoretical predictions. The influence of penetrants
transport was studied using dichloromethane, chloroform, and carbon tetrachloride.
© 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1815–1831, 1999
Keywords: acrylonitrile butadiene rubber; poly(ethylene-co-vinyl acetate); morphology; diffusion; crosslinking
INTRODUCTION
Diffusion and transport of organic solvents
through polymeric materials have been a subject
of fundamental interest1–5 and the technological
importance of the molecular transport of solvents
in polymers plays a vital role in a variety of applications such as separation process,6 food packaging,7 controlled drug release,8 reverse osmosis,9
and microelectronics.10 As far as these applications are considered, it is quite essential to evaluate the dimensional stability of the polymeric
materials in the presence of aggressive liquids.
* Present address: Propellant Engineering Division,
V.S.S.C., Thiruvananthapuram, 695 022, Kerala, India
Correspondence to: S. Thomas (E-mail: [email protected]
vsnl.net.in)
Journal of Polymer Science: Part B: Polymer Physics, Vol. 37, 1815–1831 (1999)
© 1999 John Wiley & Sons, Inc.
CCC 0887-6266/99/151815-17
The sorption behavior in polymer blends was
first reported by Cates and White.11–13 They investigated the water sorption characteristics of
polyacrylonitrile (PAN)/cellulose, PAN/silk, and
PAN/cellulose acetate blends. The sorption of water in PAN/cellulose and PAN/cellulose acetate
varied linearly with blend composition, whereas
the blend of PAN/silk exhibited a complicated
sorption behavior. Hopfenberg et al.14 –17 systematically examined the effects of temperature, penetrant activity, blend composition, and thermal
history on the sorption kinetics of n-hexane in
polystyrene/poly(2,6-dimethyl 1,4-phenylene oxide). The effect of fillers on the sorption behavior
of elastomers is also reported extensively.18 –20 It
is observed that the presence of an active filler
reduces the extent of equilibrium swelling compared to the corresponding gum sample.
Stannett and coworkers attempted to combine
the properties of glassy polystyrene and cellulose
1815
1816
VARGHESE, BHAGAWAN, AND THOMAS
Table I. Details of Materials Used
Materials
Nitrile rubber—
(Aparene
N553 NS)
Poly(ethylene-covinyl acetate)—
Pilene (1802)
Characteristics
Source
Volatile matter (%)
Antioxidant (%)
Organic acid (%)
Soap (%)
Mooney viscosity
(ML114 100°C)
Bound acrylonitrile (%)
Intrinsic viscosity (dl/g)
Melt flow index (g/10 min)
Density (g/cc)
Vicat softening point (°C)
Vinyl acetate (%)
Intrinsic viscosity (dl/g)
acetate by grafting styrene to cellulose acetate in
a variety of configurations.21,22 These grafting
techniques improved the compaction resistance of
cellulose acetate. Although the excellent permselectivity of cellulose acetate was retained, the
water sorption and, in turn, permeability to water
were reduced. A membrane for the desalination of
sea water was successfully prepared from blends
of cellulose triacetate and cellulose diacetate by
Saltonstall et al.23 These blend membranes have
exhibited rejections in excess to 99.9% to aqueous
feeds containing approximately 3.5% dissolved sodium chloride.
Masuhara et al.24 developed a membrane from
poly(vinyl pyrrolidone) and polyurethane blend
suitable for dialysis. The dialysis rate was found
to be approximately twice as high as rates normally achieved with conventional cellophane dialysis membranes. Gregor and coworkers prepared polymer blend membranes from poly(styrene sulfonic acid) and poly(vinylidene fluoride)
as ultrafiltration membranes for concentration of
biological proteins,25 purification of primary sewage effluents,26 and purification of effluents from
pulp and paper mills.27 Gregor et al.28 –30 also
reported the synthesis and properties of ion-selective blend membranes prepared from a polyelectrolyte component and an uncharged, second
polymeric component. Hollow fiber dialysis membranes from a complicated blend of quaternized
acrylonitrile–methyl vinyl pyridine copolymer
and an acrylonitrile–vinyl acetate copolymer was
reported by Sayler et al.31 Molecular transport of
alkanes32 and haloalkanes33 through blends of
ethylene–propylene random copolymer and isotactic polypropylene has been reported by Amin-
:
0.130
:
1.400
:
0.250
:
0.004
: 40.000
: 34.000
:
1.527
:
2.000
:
0.937
: 59.000
: 18.000
:
0.170
Gujarat Apar
Polymers Ltd.,
Mumbai
Polyolefins
Industries Ltd.,
Chennai
abhavi et al. The sorption, desorption, resorption,
and redesorption characteristics were influenced
by the nature of the liquid and the temperature.
The blends of nitrile rubber (NBR) and poly(ethylene-co-vinyl acetate) (EVA) combine the excellent oil resistance of NBR and the ozone resistance and mechanical properties of EVA. In our
earlier studies,34,35 we have reported the morphology, mechanical properties, viscoelastic behavior, failure mechanism, and reprocessability
of NBR/EVA blends. The aim of the present work
is to investigate the diffusion and sorption behavior of organic solvents through crosslinked nitrile
rubber/poly(ethylene-co-vinyl acetate) (NBR/
EVA) blends. The effects of blend composition,
crosslinking systems, filler type, loading, temperature, and nature of penetrants on the diffusion
process have been investigated.
EXPERIMENTAL
Materials
NBR (Aparene-N 553 NS), with a bound acrylonitrile content of 34%, was supplied gratis by Gujarat Apar Polymers Ltd., Mumbai. EVA (Pilene1802), with a vinyl acetate content of 18%, was
procured from Polyolefins Industries Ltd., Chennai. The basic characteristics of NBR and EVA
are given in Table I. The rubber chemicals such as
dicumyl peroxide, zinc oxide, stearic acid, mercaptobenzothiazyl disulfide (MBTS), sulfur, and fillers such as high-abrasion furnace black (HAF)
and semireinforcing furnace black (SRF) were of
commercial grade. Solvents (laboratory grade re-
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1817
Table II. Compounding Recipe for NBR/EVA Blends
Ingredients
(phr)a
Peroxide
System
(P)
Sulfur
System
(S)
Mixed
System
(M)
10
S
10
C
10
BS
10
BH
20
BH
30
BH
Polymer
Zinc oxide
Stearic acid
MBTSb
Sulfur
DCPc
Silica
Clay
SRF
HAF
100
—
—
—
—
4.0
—
—
—
—
100
5.0
1.5
1.5
1.5
—
—
—
—
—
100
5.0
1.5
1.5
1.5
4.0
—
—
—
—
100
—
—
—
—
4.0
10.0
—
—
—
100
—
—
—
—
4.0
—
10.0
—
—
100
—
—
—
—
4.0
—
—
10.0
—
100
—
—
—
—
4.0
—
—
—
10.0
100
—
—
—
—
4.0
—
—
—
20.0
100
—
—
—
—
4.0
—
—
—
30.0
a
Parts per hundred rubber by weight.
Mercaptobenzo thiazyl disulfide.
c
Dicumyl peroxide.
b
agent) used were cyclohexanone, dichloromethane, chloroform, and carbon tetrachloride. The
solvents were dried over anhydrous calcium chloride before use.
Blend Preparation
The blends of NBR/EVA with different crosslinking systems and blend ratio were prepared on a
two-roll mixing mill of friction ratio 1 : 1.4. The
compounding recipes of the blends are given in
Table II. The different crosslinking systems used,
namely, peroxide system (DCP), sulfur system
(S), and mixed system (DCP 1 S) are indicated
using letters P, S, and M, respectively. Dicumyl
peroxide can be used for the crosslinking of both
NBR and EVA; hence, in the peroxide-cured system both NBR and EVA phases are crosslinked
and interwoven, resulting in the formation of a
full interpenetrating network. But sulfur can
crosslink only NBR and not EVA due to its saturated backbone structure. So in the sulfur-cured
system only one phase, i.e., NBR is crosslinked
and results in the formation of a semi-interpenetrating network. A mixed-cure system, containing
both peroxide and sulfur, was also selected for an
effective curing of both the phases. The mixedcure system also results in the formation of a full
interpenetrating network. The compounds containing a mixed-cure system are designated as
N0M (pure EVA), N30M (30/70 : NBR/EVA), N50M
(50/50 : NBR/EVA), and so forth. The subscript
indicates the weight percentage of NBR in the
blend. The peroxide-cured 50/50 : NBR/EVA
blend (N50P) was selected for studying the effect
of fillers. The different fillers used were HAF,
SRF, silica, and clay and are designated as BH,
BS, S, and C, respectively. The loading is indicated by prefixing numbers, that is, 10 BH indicates a 10 phr HAF loaded system; 20 BH, a 20
phr loaded system; and so on. The compounded
blends were compression molded at 160°C for the
optimum cure. Circular samples (diameter ' 2
cm) were punched by means of a sharp-edged die
from the molded sheets. The thickness of the samples was measured using a micrometer screw
gauge.
Diffusion Experiments
Samples were immersed in the solvent taken in
the test bottles. The samples were withdrawn
periodically from the solvent; any solvent adhering to the surface was rubbed off. The samples
were weighed on a highly sensitive electronic balance and then replaced in the test bottle. This
process was continued till equilibrium was
reached. To minimize the error due to the evaporation of solvent from the sample, the time for
weighing was kept to a minimum of 30 s in all the
experiments. For the experiments above room
temperature, the samples were kept in a thermostatically controlled air oven. The mol % uptake
(Q t ) for the solvent by 100 g of the polymer was
plotted against the square root of time and the
results were analyzed. When equilibrium was
reached, Q t was taken as Q ` , i.e., mol % uptake at
infinite time.
1818
VARGHESE, BHAGAWAN, AND THOMAS
expected for the dispersed phase. The sorption
behavior of N70P, where NBR is the continuous
phase, is similar to that of NBR (N100P). Again,
the sorption behavior of EVA rich blend (N30P) is
Figure 1. Sorption curves of NBR/EVA blends.
RESULTS AND DISCUSSION
The swelling behavior of NBR/EVA blends in cyclohexanone as a function of blend composition,
crosslinking systems, filler type, and filler loading
is studied. The effect of blend composition on the
sorption behavior of a peroxide-crosslinked system is presented in Figure 1. From Figure 1, it is
observed that EVA has the lowest equilibrium
uptake. There is an increase in the equilibrium
uptake with the increase in NBR content. This
can be related to the morphology of the system.
The scanning electron micrographs of NBR/EVA
blends is given in Figure 2. In N30 and N70, the
major component tends to be the continuous
phase. The N50 exhibits a cocontinuous morphology. In the case of crosslinked samples, the extraction of the rubber phase was rather difficult;
therefore, SEM analysis of the morphology of the
system is difficult. The morphology of the
crosslinked systems is speculated based on the
morphology of uncrosslinked systems and is given
in Figure 3. When N30 (Fig. 3a) is crosslinked, a
particle size reduction is expected for the dispersed NBR phase. In N50 (Fig. 3b), when sulfur
is the curing agent, only NBR is crosslinked and
results in the formation of a semi-interpenetrating network. For the peroxide and mixed-cure
systems, both phases are crosslinked, resulting in
the formation of a full-interpenetrating network.
In N70 (Fig. 3c), a particle size reduction is also
Figure 2. Scanning electron micrographs showing
the morphology of (a) N30, (b) N50, and (c) N70.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1819
Figure 3. Schematic model for the morphology of crosslinked NBR/EVA blends.
similar to that of EVA (N0P). The N50P, where
both phases are continuous, exhibits an intermediate sorption behavior between those of the pure
components. This clearly indicates that one can
study the phase continuity from transport studies. But N70P (i.e., 70/30 : NBR/EVA) exhibits a
higher equilibrium uptake than N100P. This can
be explained on the basis of crosslink density. The
crosslink density of the samples was calculated
from the tensile measurements using the equation:
n5
F
2A 0r pRT~ a 2 1/ a 2!
(1)
where F is the load; A 0 , cross-sectional area of the
sample; r p , density of the polymer; R, gas con-
1820
VARGHESE, BHAGAWAN, AND THOMAS
Table III. Crosslink Density (n) and Volume
Fraction of Rubber (f) in Swollen Mass of NBR/EVA
Blends
Samples
f
n 3 104 (gmol/cc)
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
0.72
0.48
0.38
0.19
0.22
0.39
0.40
0.44
0.44
0.45
0.46
0.48
0.49
3.69
3.02
2.18
1.44
1.68
2.27
2.31
5.54
5.23
5.59
6.44
7.52
8.57
stant; T, the absolute temperature; and a, the
extension ratio. The crosslink density values are
given in Table III. The higher equilibrium uptake
of N70P is due to its lower crosslink density than
N100P. The equilibrium uptake is also affected by
the crystallinity of the sample. EVA (N0P), which
is crystalline, shows the lowest equilibrium uptake. As NBR is added to EVA, the crystallinity is
reduced and the equilibrium uptake increases accordingly.
Volume fraction of rubber f in the solvent
swollen sample was calculated using the equation36:
f5
W1
r1
W1 W2
1
r1
r2
Table IV. Dependence of Equilibrium Uptake (Q ` )
on Temperature for NBR/EVA Blends
Samples
27°C
40°C
50°C
60°C
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
0.39
1.05
1.61
3.81
3.39
1.54
1.46
1.14
1.19
1.17
1.12
1.01
0.92
0.69
1.56
2.03
3.89
3.40
1.82
1.84
1.42
1.50
1.42
1.45
1.24
1.11
1.59
3.16
4.09
5.60
4.28
2.84
2.80
1.99
2.28
2.16
2.18
1.92
1.77
2.33
5.39
5.32
7.52
5.05
4.23
3.82
3.12
3.59
3.02
3.45
2.60
2.03
bility of the solvent in the polymer. The difference
in solubility parameters of the solvent and the
polymer ( d s 2 d p ) is plotted against the equilibrium uptake and is given in Figure 4. It is clear
from the figure that as ( d s 2 d p ) increases, equilibrium uptake decreases. The higher equilibrium
uptake of N70P has been discussed earlier. The
equilibrium uptake values of different NBR/EVA
blends at various temperatures are given in Table
IV. As expected, the equilibrium values increase
with temperature. Figure 5 shows the sorption
(2)
where W 1 the weight of the rubber sample; r1, the
density of the rubber; W 2 , the weight of solvent in
the swollen sample; and r2, density of the solvent.
A high value of f is an indication of high crosslink
density. The f values are given in Table III. The
f value also supports the higher equilibrium uptake of N70P.
In spite of its higher equilibrium uptake value,
N70P shows a lower initial rate of uptake than
that of N100P. This is due to the difference in
solubility parameters (d) of the samples, i.e., d(cyclohexanone) 2 d(N70P) 5 0.36 and d(cyclohexanone) 2 d(N100P) 5 0.12. The greater the difference in solubility parameter, the lesser the solu-
Figure 4. d s – d p vs. equilibrium uptake curve of NBR/
EVA– cyclohexanone system.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1821
sample; r p , the density of the polymer; r s , the
density of the solvent; and A s , the amount of
solvent absorbed. For an unfilled system, f 5 0.
Substituting this in eq. (4), we get the expression
for the volume fraction of rubber in the solventswollen unfilled sample (V r0 )
V r0 5
Figure 5. Sorption curves of various crosslinked
NBR/EVA blends.
V r0/V rf 5 1 2 [email protected]/1 2 f#
(5)
Since eq. (3) has the general form of an equation
for a straight line, a plot of V r0 /V rf as a function of
f/1 2 f should give a straight line, whose slope
(m) will be a direct measure of the reinforcing
ability of the filler used. According to the theory
developed by Kraus20 for highly reinforcing carbon blacks, negative higher slope values indicate
a better reinforcement. A constant C, characteristic of the filler, is also calculated using the equation:
C5
curves of N50P with different crosslinking systems. Here the mixed-cure system shows the lowest equilibrium uptake and the peroxide-cure system the highest. The sulfur-cure system takes the
intermediate position. The lowest equilibrium uptake of the mixed-cure system is due to its high
crosslink density (Table III). The sorption curves
of various filled systems (10 phr loading) and unfilled (N50P) are given in Figure 6. The presence of
fillers reduced the equilibrium uptake values considerably due to reinforcement. Among the various fillers, the HAF black filled system (10 BH)
with the highest crosslink density shows the lowest equilibrium uptake. The equilibrium uptake
of all the other filled systems (SRF black, silica,
and clay) are comparable.
The extent of reinforcement is assessed using
Kraus’s equation.20 According to this equation:
d r 21
p
d r 1 A sr 21
s
21
p
m 2 V r0 1 1
1/3
3~1 2 V r0
!
(6)
The Kraus plots for various fillers are shown in
Figure 7 and the values of slope and C are given
in Table V. It was observed that the amount of
solvent absorbed ( A s ) decreases as the filler loading increases. This results in an increase in the
(3)
where V rf is the volume fraction of rubber in the
solvent-swollen filled sample and is given by the
equation:
V rf 5
~d 2 fw! r 21
p
21
~d 2 fw! r 21
p 1 A sr s
(4)
where d is the deswollen weight; f, the volume
fraction of the filler; w, the initial weight of the
Figure 6. Sorption curves of unfilled and various
filled NBR/EVA blends.
1822
VARGHESE, BHAGAWAN, AND THOMAS
Figure 7. Plots of V r0 /V rf vs. f/1 2 f for various filled
N50P.
V rf values (with filler loading) calculated using
eq. (4). Since V r0 remains constant, the ratio V r0 /
V rf decreases with the filler loading, resulting in a
negative slope (Figure 7). It is observed that the
negative slope value, which is a direct measure of
the reinforcing ability of the fillers, decreases in
the order of HAF . SRF . silica . clay. This
shows that as far as the extent of reinforcement is
concerned, HAF is superior to other fillers; thus,
the lower uptake of the HAF-filled system is supported by its reinforcing ability.
With filler loading, there is a decrease in equilibrium uptake value (Figure 8). This is due to the
increase in reinforcement upon loading. A schematic representation of the unfilled and filled
blend before and after swelling is given in Figure
9. During mixing, carbon black forms bound rubber in the blend. Bound rubber represents the
amount of polymer insolubilized by the carbon
black. The decrease in equilibrium uptake of the
Figure 8. Effect of filler loading on the sorption
curves.
filled system is due to the formation of bound
rubber. As the reinforcement increases, the bound
rubber content also increases. The effect of tem-
Table V. Values of Negative Slope and C for Filled
N50P
Fillers
Negative Slope
C
HAF
SRF
Silica
Clay
0.72
0.23
0.19
0.17
1.44
0.94
0.90
0.88
Figure 9. Schematic representation of unfilled and
filled blends before and after swelling.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1823
Table VI. Values of n and k for NBR/EVA Blends
k 3 10 2 (min2n )
n
Samples
27°C
40°C
50°C
60°C
27°C
40°C
50°C
60°C
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
0.45
0.43
0.42
0.45
0.51
0.44
0.43
0.53
0.52
0.55
0.54
0.53
0.57
0.50
0.54
0.55
0.54
0.62
0.56
0.57
0.53
0.57
0.56
0.55
0.56
0.57
0.58
0.57
0.61
0.63
0.65
0.62
0.64
0.56
0.54
0.55
0.49
0.52
0.50
0.56
0.65
0.62
0.60
0.59
0.62
0.52
0.65
0.64
0.60
0.62
0.58
0.56
1.8
2.1
2.0
1.2
2.0
1.9
1.8
1.5
1.4
1.3
1.2
1.4
1.4
2.0
1.6
1.4
1.3
1.5
1.4
1.5
1.6
1.4
1.3
1.4
1.3
1.4
1.3
1.0
0.8
0.9
1.3
1.2
0.9
1.5
1.6
1.6
1.8
1.7
1.9
1.5
0.6
0.7
0.9
1.5
1.2
1.6
0.8
0.8
1.0
1.1
1.2
1.5
perature on the sorption curves of N50P is shown
in Figure 10. The rate of diffusion and equilibrium uptake increase with increase in temperature. This behavior is attributed to the increase in
free volume and segmental mobility at higher
temperature.
To follow the mechanism of sorption, the values obtained were fitted to the equation37:
log~Q t/Q `! 5 log k 1 n log t
blend systems. However, a deviation from the
Fickian mode of diffusion is observed as the temperature increases. This is due to the increased
rate of diffusion of the penetrant molecules at
higher temperatures. No systematic trend is observed for the values of k at room temperature as
well as at higher temperatures.
From the swelling data, the diffusion coefficient D was calculated using the equation38:
(7)
where Q t is the mol % increase in uptake at time
t; Q ` , the mol % increase in uptake at equilibrium; t, the time; k, a constant characteristic of
the polymer, which indicates the interaction between polymer and solvent; and n indicates the
mechanism of sorption. The values of n and k
were determined by linear regression analysis
and are given in Table VI.
If value of n is 0.5, it means that the rate of
diffusion of penetrant molecules is much less than
the rate of relaxation of polymer chains. This
mode of transport is termed as Fickian. On the
other hand, if the value of n is unity, the mode of
diffusion is termed as non-Fickian, where the rate
of diffusion of penetrant molecules is much faster
than polymer relaxation. When the rates of both
processes are similar, the values of n will fall
between 0.5 and 1, presenting an anomalous behavior. From the table, it is observed that the
values of n range from 0.42 to 0.65. For all the
systems, the n value is close to 0.5 at room temperature. This suggests the mode of diffusion is
close to Fickian for cyclohexanone–NBR/EVA
D 5 p ~h u /4Q `! 2
Figure 10.
curves.
(8)
Effect of temperature on the sorption
1824
VARGHESE, BHAGAWAN, AND THOMAS
Table VII. Values of Intrinsic Diffusion, Sorption, and Permeation Coefficients for NBR/EVA Blends
D* 3 10 7 (cm2 sec21)
P 3 10 6 (cm2 sec21)
S
Samples
27°C
40°C
50°C
60°C
27°C
40°C
50°C
60°C
27°C
40°C
50°C
60°C
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
0.63
1.43
2.11
5.52
17.27
2.04
1.95
4.79
4.86
4.93
4.91
4.49
4.77
4.04
9.04
13.23
34.11
63.69
12.44
14.85
9.94
9.66
9.72
9.96
9.53
9.40
18.64
24.50
42.18
124.82
121.62
45.47
39.11
24.79
21.91
23.83
19.32
18.80
15.87
24.06
66.44
67.15
174.79
118.94
97.88
52.89
48.67
41.38
41.29
62.35
37.11
30.17
0.38
1.03
1.58
3.75
3.32
1.51
1.42
1.11
1.17
1.14
1.09
0.98
0.90
0.67
1.53
1.98
3.81
3.31
1.78
1.87
1.38
1.47
1.39
1.42
1.21
1.09
1.56
3.09
4.00
5.48
4.20
2.78
2.85
1.94
2.23
2.12
2.13
1.87
1.73
2.29
5.28
5.22
7.36
4.94
4.14
3.74
3.06
3.51
2.95
3.38
2.55
1.99
0.02
0.15
0.33
2.07
5.73
0.31
0.28
0.53
0.57
0.56
0.53
0.44
0.43
0.27
1.38
4.62
12.99
21.08
3.02
2.77
1.37
1.42
1.28
1.41
1.15
1.02
2.91
7.57
16.87
68.40
51.08
12.64
11.15
4.81
4.89
5.05
4.11
3.52
2.69
5.51
35.08
35.06
128.64
58.75
40.52
19.78
14.52
14.52
12.18
21.07
9.46
6.00
where u is the slope of the sorption curves before
attainment of 50% equilibrium and h is the initial
thickness of the sample. The value of D depends
on the polymer segmental mobility. Equation (8)
holds for systems without appreciable swelling.
For considerable swelling, a correction for the
swelling of the polymer can be made by incorporating f, the volume fraction of the polymer in the
swollen mass, thus giving the intrinsic diffusion
coefficient, D*. 39
D* 5
D
f 7/3
where M ` is the mass of the solvent taken up at
equilibrium swelling and M p is the mass of the
polymer sample. The permeability coefficient (P),
which implies the net effect of sorption and diffusion, is given by the relation36:
P 5 D*S
(11)
The values of S and P are also given in Table VII. A
similar trend as that of D* is observed for S and P
values with the change in blend composition,
(9)
The values of intrinsic diffusion coefficients are
given in Table VII. It is observed that the D*
value increases with an increase in NBR content
in the blend. For the different crosslinking systems, the peroxide-cured system (N50P) exhibits
the highest D* value. Among the filled systems,
the silica-filled system (10 S) shows a low D*
value as the filler loading increases. For all the
systems, the D* value increases with an increase
in temperature, which indicates the activation of
diffusion process at higher temperatures.
The permeability of a penetrant in a polymer
membrane depends on the diffusivity as well as
solubility or sorption of the penetrant in the polymer membrane. Therefore, the sorption coefficient that is related to the equilibrium sorption of
the penetrant is calculated using the equation40:
S5
M`
Mp
(10)
Figure 11. Variation of S with the weight percentage
of NBR.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1825
P d 1 2P m 2 2 f d~P m 2 P d!
P d 1 2P m 1 f d~P m 2 P d!
(14)
P# c 5 P m
where the subscripts d and m correspond to dispersed phase and matrix, respectively.
Robeson extended42 Maxwell’s analysis to include the continuous and discontinuous characteristic of both phases at intermediate compositions and expressed the equations,
F
P# c 5 x aP# 1
P# 2 1 2P# 1 2 2 f 2~P# 1 2 P# 2!
P# 2 1 2P# 1 1 f 2~P# 1 2 P# 2!
F
1 x bP# 2
Figure 12. Variation of D* and P with the weight
percentage of NBR.
G
P# 1 1 2P# 2 2 2 f 1~P# 2 2 P# 1!
P# 1 1 2P 2 1 f 1~P# 2 2 P# 1!
G
(15)
where x a and x b are fractional contributions to
continuous phase so that x a 1 x b 5 1.
Figure 13 shows the variation of permeation
coefficient with volume fraction of NBR. The experimental values are close to the Maxwell model
crosslinking systems, filler type, loading, and temperature. The variation in sorption coefficient (S)
with the weight percentage of NBR is given in Figure 11. The value of S increases with NBR content.
The effect of weight percentage of NBR on intrinsic
diffusion (D*) and permeation (P) coefficients is
shown in Figure 12. D* and P increase regularly up
to 50 wt % of NBR. Beyond that the properties
increase sharply. This can be attributed to the
phase inversion in morphology of the system.
In the case of heterogeneous blends, the permeability can be interpreted in terms of various
theoretical models. Robeson’s two limiting models
(i.e., series and parallel models) are generally
used in the case of polymer blends.
According to the parallel model
P c 5 P 1f 1 1 P 2f 2
(12)
and by the series model
P c 5 P 1P 2/~ f 1P 2/ f 2P 1!
(13)
where P c , P 1 , and P 2 are the permeation coefficients of blend, component I, and component II,
respectively, and f1 and f2 are the volume fractions of components I and II, respectively.
Further, for a conducting spherical filler, the
overall composite permeation coefficient is given
by Maxwell’s equations as41,42
Figure 13. Theoretical modeling for the permeation
coefficient of NBR/EVA blends.
1826
VARGHESE, BHAGAWAN, AND THOMAS
Table VIII. Activation Energies for Permeation and
Diffusion of NBR/EVA Blends
Samples
E P (kJ mol21)
E D (kJ mol21)
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
96.9
95.9
90.7
90.8
50.9
99.8
85.5
59.9
55.2
56.4
62.8
53.6
46.2
144.2
139.4
122.1
108.5
61.5
124.3
110.7
85.4
83.1
80.3
91.5
78.6
67.7
up to fNBR 5 0.6; beyond that, it is close to the
Robeson model.
The temperature dependence of transport coefficients (D*, S, and P) can be used to calculate
the energy of activation for the processes of diffusion and permeation from the Arrhenius relationship40:
X 5 X 0exp~2E x/RT!
(16)
where X is D*, S, or P; X 0 represents D *0 , S 0 , or
P 0 , which are constants; E x , the activation energy; R, the universal gas constant; and T, the
absolute temperature. The values of activation
Table IX. Thermodynamic Parameters
Samples
DH (kJ mol21)
DS (Jmol21 k21)
N0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
47.2
42.4
32.2
17.8
10.5
26.1
25.1
25.3
25.1
24.5
28.5
24.7
21.5
110.6
102.4
72.3
45.6
6.5
51.1
47.9
46.2
55.8
44.1
56.8
43.3
32.1
energy of permeation (E p ) and the activation energy of diffusion (E D ) are given in Table VIII.
Pure EVA (N0P) exhibits the highest activation
energy for both permeation and diffusion. This is
because of the crystalline nature of EVA. The E p
and E D decrease as the wt % of NBR increases. As
the NBR content is increased, the crystallinity of
the sample is reduced and hence the blends exhibit a drop in activation energies. This is evident
from the X-ray diffraction patterns given in Figure 14. The X-ray diffraction patterns were separated into two parts, crystalline and amorphous,
by taking nitrile rubber as fully amorphous. The
areas under the crystalline and amorphous portions were measured in arbitrary units, and the
degree of crystallinity X c of the samples was calculated using the relation:
Table X. Comparison of Network Structure
Figure 14. XRD patterns of NBR/EVA blends.
Sample
M c (chem.)
M c (affine)
M c (phantom)
N 0P
N30P
N50P
N70P
N100P
N50S
N50M
10S
10C
10BS
10BH
20BH
30BH
296
960
1761
8324
5295
1658
1536
1214
1243
1169
1098
998
985
288
935
1715
8101
5153
1557
1411
1116
1142
1073
1008
867
813
96
311
572
2700
1717
579
470
371
381
358
336
289
271
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
1827
Figure 16. Sorption behavior of NBR/EVA blends in
dichloromethane.
The enthalpy and entropy of sorption have
been calculated using the van’t Hoff relation38
Figure 15. Comparison of theoretical and experimental sorption curves.
Xc 5
Ic
Ic 1 Ia
(17)
where I c and I a represent the integrated intensities corresponding to the crystalline and amorphous phases respectively, i.e., the areas under
the respective curves. The degree of crystallinity
(X c ) of N0P, N30P, N50P, and N70P is 35, 23, 20,
and 8%, respectively.
Usually the activation energies for permeation
and diffusion increase with loading of filler. But
in the case of N50P, as the carbon black loading is
increased from 10 BH to 30 BH, it is seen that
there is a decrease in E P and E D . This is due to
the presence of polar groups on the surface of
carbon black, which enables a high interaction
with cyclohexanone, a polar solvent. As the loading is increased, the number of filler particles per
unit volume increases, thereby increasing the
sites of interaction. However, the equilibrium uptake exhibits the normal trend, that is, it decreases with filler loading as observed earlier.
ln K s 5
DS DH
2
R
RT
(18)
The values obtained by the linear regression
method are given in Table IX. It is found that the
values of DH and DS are positive for the different
NBR/EVA systems.
Determination of the Network Structure
The investigation of swelling equilibrium can
help to elucidate the structure of the polymer
network. Flory and Rehner43 relations were developed for a network deforming affinely, i.e., the
Table XI. Solubility Parameters (d) of Solvents and
Polymers
Reference
d (cal/cm3)1/2
Dichloromethane
Chloroform
Carbon tetrachloride
N0 (pure EVA)
N50 (50/50 : NBR/EVA)
N100 (pure NBR)
9.7
9.3
8.6
8.99
9.38
9.78
1828
VARGHESE, BHAGAWAN, AND THOMAS
Figure 17. Sorption behavior of NBR/EVA blends in
chloroform.
components of each chain vector transform linearly with macroscopic deformation and the junction points are assumed to be embedded in the
network without fluctuations. Then the molecular
weight between crosslinks (M c ) for the affine
Figure 18. Sorption behavior of NBR/EVA blends in
carbon tetrachloride.
Figure 19. d s – d p vs. equilibrium uptake curve for
NBR/EVA– dichloromethane system.
limit of the model [M c (aff)] was calculated by the
formula,44
S
D
m 1/3
n
n 2m
M c~aff! 5
2
2~ln~1 2 n 2m! 1 n 2m 1 xn 2m
!
2/3 1/3
r V sn 2c
n 2m 1 2
(19)
Figure 20. d s – d p vs. equilibrium uptake curve for
NBR/EVA– chloroform system.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
Table XII. Values of Q ` in Different Solvents
Samples
Dichloromethane
Chloroform
Carbon
Tetrachloride
N0
N50
N100
2.38
5.28
6.77
7.03
7.45
5.87
4.95
2.41
1.08
where V s is the molar volume of the solvent; m
and n are called the number of effective chains
and junctions; n 2m , the polymer volume fraction
at swelling equilibrium; n 2c , the polymer volume
fraction during crosslinking; and r, the polymer
density. James and Guth45 proposed the phantom
network model, where the chains may move freely
through one another. According to the theory, the
molecular weight between crosslinks for the
phantom limit of the model [M c (ph)] was calculated by44
S
D
2
2/3 1/3
r V sn 2c
n 2m
f
M c~ph! 5
2
2~ln~1 2 n 2m! 1 n 2m 1 xn 2m
!
12
(20)
where f is the junction functionality.
Mc(aff) and Mc(ph) were compared with Mc(chem) and the values are given in Table X. It is
seen that Mc(chem) values are close to Mc(aff).
This suggests that in the highly swollen state,
the chains in NBR, EVA, and the blends deform
affinely.
The experimental diffusion results were compared with theoretical predictions in order to find
the deviation from the regular Fickian mode described by the equation46
Mt
8
512 2
M`
p
1829
trants. The sorption curves as a function of blend
composition are given in Figure 16 –18. In dichloromethane N0P (pure EVA) exhibits the lowest
uptake (Figure 16). The rate of diffusion as well
as the equilibrium uptake increase with the increase in NBR content. This can be explained on
the basis of solubility parameters of the solvent
and polymers. The closer the solubility parameters, the greater will be the solubility of the solvent in the polymer. The solubility parameters of
the solvents and polymers are given in Table XI.
In the case of chloroform (Figure 17) the equilibrium uptake is higher for the blend than that of
the pure components. This is because of the closeness in solubility parameters of N50P and chloroform. In carbon tetrachloride, the rate of diffusion
as well as the equilibrium uptake increase with
the increase in EVA content (Figure 18). The values of Q ` in different solvents are given in Table
XII The equilibrium uptake of the blends in dichloromethane, chloroform, and carbon tetrachloride is plotted against the difference in solubility
parameters of the solvent and polymer in Figure
19 –21,. The greater the difference, the lesser the
equilibrium uptake.
The sorption curves of N50P for different penetrants are shown in Figure 22. Here, too, the
solubility parameter is the deciding factor for the
rate of diffusion and equilibrium uptake.
The mechanism of sorption was followed by
fitting the values obtained in eq. (7). The values of
O ~2n 11 1! expF 2D~2nh1 1! p tG
n5`
2
2
2
2
n50
(21)
The given equation represents a Fickian mode
of diffusion. Figure 15 shows the experimental (at
room temperature) and theoretical sorption
curves. This is an excellent fit at the early stages
of diffusion, indicating Fickian behavior.
Effect of Penetrants
Dichloromethane, chloroform, and carbon tetrachloride were used to study the effect of pene-
Figure 21. d p – d s vs. equilibrium uptake curve for
NBR/EVA– carbon tetrachloride system.
1830
VARGHESE, BHAGAWAN, AND THOMAS
Figure 22. Sorption curves of N50P in different solvents.
Figure 23. Sorption-desorption-resorption-redesorption curves of N50P in carbon tetrachloride.
n and k are given in Table XIII. The values of n lie
between 0.5 and 1 for all the solvents, indicating
a deviation from a Fickian mode of diffusion.
In order to understand the stability of the
blends, the sorption– desorption–resorption– desorption pattern of N50P in carbon tetrachloride
was followed and is presented in Figure 23. The
figure reveals that the rate of desorption (desorption and redesorption) is greater than that of
sorption (sorption and resorption). In the sorption
process, the solvent molecules have to penetrate
into the tightly packed network and hence the
rate of the sorption process is low. While in the
desorption process, the escape of solvent molecules from the relaxed polymer chain takes place
more easily. So the rates of the desorption processes are greater than those for sorption processes.
Table XIII. Values of n and k in Different Solvents
Samples
Dichloromethane
Chloroform
Carbon tetrachloride
N0
N50
N100
N0
N50
N100
N0
N50
N100
n
k 3 10 2
(min2n )
0.55
0.62
0.68
0.65
0.66
0.63
0.64
0.57
0.54
4.1
3.1
4.6
1.4
1.8
4.0
0.9
1.4
2.1
CONCLUSIONS
The diffusion of organic solvents through
crosslinked NBR/EVA blends has been studied.
The influence of blend composition, crosslinking
systems, filler type, loading, temperature, and
penetrants on the diffusion process has been
analyzed. At room temperature, the mode of
diffusion was found to be Fickian for the cyclohexanone–NBR/EVA blend systems. At higher
temperatures a deviation from the Fickian
mode of diffusion is observed. The sorption behavior of the blends was related to the morphology of the system. The variations in the equilibrium uptake values were explained on the
basis of the blend morphology, volume fraction
of polymer in the swollen mass, crosslink density, and crystallinity. The equilibrium uptake
of the filled system decreases upon loading due
to reinforcement. The extent of reinforcement
was assessed using the Kraus equation. The
transport coefficients increase with the increase
in NBR content. The activation energies for the
processes of diffusion and permeation were
estimated.
TRANSPORT IN CROSSLINKED NBR/EVA BLENDS
Thermodynamic parameters were determined
using van’t Hoff’s relationship. Chemical crosslinks
were determined using affine and phantom models
and it was found that the experimental values lie
close to the affine model. For different solvents, the
variations in the equilibrium uptake were explained using their solubility parameter values. The
mechanism of sorption for chlorinated hydrocarbons also deviates from the Fickian mode.
One of the authors (H.V.) is grateful to the Council of
Scientific and Industrial Research, New Delhi, for financial assistance.
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