Post on 19-Oct-2020
Chapter 5
Transport of Organic Solvents through Natural Rubber/Nitrile Rubber /Organically Modified
Montmorillonite Nanocomposites
Abstract
The chapter describes the transport phenomenon of some commonly used
laboratory organic solvents which differ in their solubility parameter value of the
polymer blend nanocomposites membrane prepared by melt mixing. The three
solvents that were used are hexane, toluene and xylene, which differed widely in
their solubility parameter values. This study was done to understand the effect of
solubility parameter on the diffusion transport characteristics of NR/NBR (natural
rubber /nitrile rubber) blends. The solvent uptake, diffusion, sorption and
permeation constants were investigated and were found to decrease with
organically modified montmorillonite (O1Mt) content at lower loading. The mode
of transport through NR/NBR nanocomposites was found to be anomalous. The
difference in solubility parameter value greatly influenced the transport properties.
The dependence of various properties on O1Mt content was supported by
morphological analysis. The effects of blend ratio, solvent size and O1Mt loading
on the diffusion of aromatic and aliphatic solvents through NR/NBR blend systems
were investigated. The swelling coefficient values also decreased upon the addition
of fillers, indicating the presence of hindered path for solvents to diffuse into the
polymer matrix. The better reinforcement at lower filler loading was confirmed
from the crosslink density values and mechanical properties. The transport data
obtained was applied to mathematical models, for predicting the
diffusion behaviour through nanocomposite membranes and to elucidate the
physical mechanism of transport.1
1 The results of this chapter has been published in Journal of Material Science
2013, Volume 48, Issue 15, pp 5373-5386 DOI 10.1007/s10853-013-7332-7
166 Chapter 5
5. 1. Introduction
Polymer composite science and technology is a very large and rapidly growing
area. Although the polymer composites may not corrode via the same
mechanisms as metals, when exposed to moisture, hazardous solvents, UV
radiation etc polymer composites have a tendency to undergo plasticization and
degradation. This results in deterioration of mechanical properties and reduction
in the life of composite structures. Polymer nanocomposites, made by dispersing
nanosized particles, can solve this problem to a great extent by reducing the
diffusivity of moisture and other molecules in polymer composites. One of the
unique properties of nanocomposites, especially layered silicate filled
nanocomposites, are their resistance to penetration of solvents and gases, which
make it applicable/usable in many fields. Solvent resistant membranes have a
strong potential for a variety of applications. This can be used as a technique to
elucidate the relationship between processes of mass transport and polymer
structure. The transport of small molecules through polymer membrane occurs
due to random molecular motion of individual molecules1. Therefore, the
transport behaviour of various organic solvents and gases through polymers, is
of great technological importance and it plays a vital role in a variety of barrier
applications2.
The effect of fillers on the transport characteristics of polymers has been of
immense interest to scientists. A lot of works are reported regarding the
transport properties in polymer blends and blend nanocomposites34,5,6 The
effect of fillers on the diffusion and sorption processes has been reported7,8.
The sorption of chloroform by an epoxy resin was lowered by about 70 %,
when 5% filler was incorporated9. The study of diffusion, sorption and
permeation in blend structures provide valuable means for additional
characterization of polymer blends10. Blend composition, miscibility and
Diffusion studies of ………. 167
phase morphology are the main determining factors of transport properties
through polymer membranes. For immiscible blends, the nature of the two
polymers and the interface influence the transport properties. Solvent resistant
properties of nano-structured layered silicates filled blend of NR, and
carboxylated styrene butadiene rubber (XSBR) were investigated by Stephan
et al.11,12. The study of barrier properties through poly (ethylene-co-vinyl
acetate) /clay nanocomposites with different organic modification revealed
that the incorporation of O1Mt in the polymer increased the barrier
properties13,14. The swelling properties of filled natural rubber/linear low-
density polyethylene blends was investigated by Ahmad et al. and was found
that the swelling index decreased with increase in filler loading 15.
The present work was motivated by a desire to know how the nanoparticles in
an immiscible blend system affect its transport properties. No reports are there
to our knowledge, regarding the transport properties in NR/NBR elastomer
blend system, where O1Mt act as a reinforcing and compatibilizing agent.
Organic solvents are harmful to humans and are identified as carcinogens,
especially when it comes into contact with the skin. Thus the transport studies
in NR/NBR blend nanocomposites are of much interest from many points of
view, especially the potential use of this blend in glove manufacturing
industry. The presence of fillers in the NR/NBR blend system further
enhances the properties of gloves, by improving its transport properties and
mechanical properties. The potential application of these blend
nanocomposites in glove manufacturing industry will be a matter of future
study. The discussion in this chapter involves the work undertaken to
investigate the transport characteristics of NR/NBR blend nanocomposites in
commonly used laboratory organic solvents, based on the difference in their
solubility parameter values. The effect of O1Mt on the blend composition,
168 Chapter 5
and clay loading, were also taken into account while investigating the transport
properties of these blend nanocomposites.
5.2 Results and discussion:
The sorption data of different solvents into NR/NBR blend nanocomposites at
different blend composition and filler loading, with different solvents were
determined. It is expressed as the molar percentage uptake (% Qt) of solvent
per gram of NR/NBR blends, and was calculated using (Eq. 5.1)
%�� = �����
� �� × 100 − − − − − (5.1)
M t is the mass of the sample at time t, Mo is the initial mass of the sample and
Mw is the molecular weight of the solvent. The molar percentage uptake
(%Qt) for the solvent was plotted against the square root of time (√t). The
sorption curves (% Qt moles of solvent sorbed per 100 g of rubber vs. √t) are
shown in Fig. 5.1 & 5.2. The diffusion of solvent through a composite
depends on the geometry of the filler (size, shape, size distribution,
concentration, and orientation), properties of the matrix, and interaction
between the matrix and filler.
5.2.1 Effect of blend composition
A significant initial increase in uptake was shown for the entire blend
nanocomposite studied. This is due to the high concentration gradient of
solvent molecules with the polymer. Also this initial solvent absorption rates
in polymers have been explained in terms of rapid cavitations, which expose
a greater surface area, thus enhancing solvent percolation16. On the other
hand, after a time period of 24hrs at equilibrium, the solvent uptake is counter
balanced by solvent release from the polymer. From both Fig 5.1 (a & b), it
is observed that NBR has the lowest equilibrium uptake. Also, there is a
Diffusion studies of ………. 169
decrease in the equilibrium uptake with the increase in NBR content. This is
due to the high resistance of NBR to gas, organic solvents and oil, and also
due to the higher cohesive energy of NBR. Difference in solubility parameters
between the matrix and solvent is another reason for the decreased
permeability in NBR. The uptake was fastest in pure NR, followed by that of
70/30 and 50/50 NR/NBR blends. The preferential migration of O1Mt
towards NBR due to its polarity match further enhanced the solvent resistance
for the blend composition with higher NBR content. These layers increase the
path length for diffusion of solvent molecule to pass through the polymer. The
increased path length predicted better barrier properties for nanocomposites.
The uptake of solvent could be practically neglected for neat NBR and for
nanocomposites of NBR.
0 5 10 15 20 25 30 35 40
0.0
0.2
0.4
0.6
0.8
1.0
Qt
(mo
l%)
t 1/2 (min1/2 )
100/0(0) 70/30(0) 50/50(0) 0/100(0)
a
170 Chapter 5
Figure 5.1 Percentage uptake of solvent against time of different NR/NBR /O1Mt
blends nanocomposites in hexane a) at zero loading b) at 5 phr loading.
5.2.2 Effect of clay loading
For all the blend nanocomposites, the solvent uptake was found to get reduced
than the gum blend with increased O1Mt content as compared to gum samples.
(Fig 5.2). There is a decrease in solvent uptake with increase in filler loading
up to 1 phr. This can be explained based on the fact that even after
vulcanization, the local mobility of the polymer17 gets restricted by
reinforcement of nanofillers and improves the solvent resistance. Thus, the
reinforcement of blend by nanofiller improves the solvent resistance to a good
extent.
0 5 10 15 20 25 30 35 40
0.0
0.2
0.4
0.6
0.8
1.0Q
t (m
ol%
)
t1/2 (min1/2)
100/0(5) 70/30(5) 50/50(5) 0/100(5)
b
Diffusion studies of ………. 171
Figure 5. 2 Percentage uptake of solvent against time of 50/50, NR/NBR blends nanocomposites in hexane with different clay loading.
The diffusion of the penetrant solvent also depends on the concentration of
free space available in the matrix to accommodate the penetrant molecule. The
addition of O1Mt reduces the availability of free spaces (Fig 5.3a&b) and also
creates a tortuous path for transport of solvent molecules.
Figure 5.3 Schematic showing a) NR/NBR blend without O1Mt b) with O1Mt
172 Chapter 5
The uptake of solvent molecules was thus reduced for O1Mt filled composites
compared to unfilled rubber. However, after a filler loading of 1 and 2 phr
there was an increase in solvent uptake. The mechanical properties (Fig. 5.4
& 5.5) also show the reinforcement by clay, at lower filler loading followed
by a levelling off of at higher loading. The modulus of the all the
nanocomposites was also improved except for 70/30 blend nanocomposites
This can be a result of the exfoliated morphology of the blend nanocomposite
at lower loading and the presence of agglomerates at higher filler loading
which forms filler –filler network that should have improved the modulus.
The exceptional behaviour in the case of 70/30 can be due to the presence of
O1Mt tactoids in the dispersed NBR phase which reduces the possibility of
filler –filler interaction.
Figure 5. 4 Tensile strength of 50/50 NR/NBR blend nanocomposite with different
clay loading.
Diffusion studies of ………. 173
Figure 5.5 Modulus value for 50/50 NR /NBR blend at different filler loading
The mode of dispersion of the nanoclay was analysed through XRD and is
given in Fig. 5.6. The nanocomposites with 2 phr clay loading is
predominantly exfoliated and enhanced the polymer/ filler interactions. The
intercalated and exfoliated morphology of the blend nanocomposites hinders
the movement of penetrant molecules. Hindered movement of the penetrant
molecules in the presence of O1Mt platelets are already reported 4. The TEM
image in Fig. 5.7 further clarifies this, showing an exfoliated morphology at
lower loading and agglomerated O1Mt at higher loading.
174 Chapter 5
Figure 5.6 XRD pattern for 50/50 NR /NBR blend at different filler loading.
Figure 5.7 TEM images of NR/NBR (01Mt) nanocomposites, a) 50/50 (2) b) 50/50 (10)
Diffusion studies of ………. 175
5.2.3 Effect of solvent
On comparing the two aromatic solvents, (Fig.5.8) there is a decrease in
solvent uptake when xylene is used as the solvent. The solubility parameter
difference between the blend nanocomposites and the solvents varied with the
solvents used. Hexane having a larger difference in solubility parameter from
the blend nanocomposites, showed lesser diffusion compared to other
solvents. The increase in molecular size of the penetrant xylene molecule,
rather than that of toluene 18-19 also contributes to the lesser diffusion. The
extremely low penetration of hexane compared with that of aromatic solvents
can be attributed to the higher molar volume of hexane compared to the two
aromatic solvents20 . For each blend nanocomposite, diffusion decreases when
the solvent is hexane. Fig.5.9 shows the difference in solubility parameter
values of the solvent with that of the blend nanocomposites. The plot of
solubility parameter vs. swelling of elastomers was made based on the concept
that materials with similar solubility parameter mix well, while swelling of
polymers in solvents with very high difference in solubility parameter can be
considered negligible. We have plotted the equilibrium swelling of selected
blend nanocomposites against the resultant solubility parameter determined by
Eq. (5.2) where ΦNR, ΦNBR δNR & δNBR are the volume fraction and solubility
parameter of NR and NBR respectively. The plot clearly explains the trend,
that, as the value of solubility parameter of the solvent (δs) lies away from that
of the polymer blends system, it produces a very small change in equilibrium
swelling. For hexane, the δs (14.4) value is much different from that for the
blend system (∼18) and the equilibrium swelling is very low when hexane is
used as the solvent. Table 5.1 gives the difference in solubility parameter
values of the solvent with that of the equilibrium uptake and, it can be seen
176 Chapter 5
that as the solubility parameter difference increases, the equilibrium swelling
decreases.
δeffective= ΦNR .δNR + ΦNBR .δNBR…………………(5.2)
0 5 10 15 20 25 30 35 400.0
0.6
1.2
1.8
2.4
Hexane
Xylene
Qt(
mo
l%)
t1/2 (min1/2)
Toluene Xylene Hexane
Toluene
Figure 5. 8 Percentage uptake of solvent against time of 70/30(1), NR/NBR blends nanocomposite with different solvents
Figure 5. 9 Plot of solubility parameter difference vs equilibrium uptake in three solvents for different NR/NBR nanocomposites with 0phr and 5 phr clay loading
-2 -1 0 1 2 3 4 5
0.0
0.4
0.8
1.2
1.6
2.0
2.4
(hexane)
(toluene)
δ δ p- δ c (MPa
1/2 )
Qα
(m
ol%
)
toluene(for 0%) xylene (for 0%) hexane(for 0%) toluene(for 5%) xylene(for 5%) hexane(for 5%)
(xylene)
Diffusion studies of ………. 177
Table 5.1 The change in equilibrium uptake for 70/30(1),NR/NBR(O1Mt) with solubility parameter difference
The plot of interaction parameter (blend- solvent) vs equilibrium uptake also
shows that, for hexane, as the interaction parameter increases the equilibrium
swelling decreases (Fig.5.10). The interaction parameter χ expressed as a
function solubility parameters of the polymer blend system and of the solvent,
by Eq. (5.3)
χ = ���� × (δ�−δ �)� ....... (5.3) Where of δA and δB denote the solubility parameters of the polymer blend
system and of the solvent, Vr is the molar volume, R is the universal gas
constant and T is the absolute temperature.
178 Chapter 5
Figure 5.10 Plot of interaction parameter vs equilibrium uptake in three solvents for different NR/NBR nanocomposites with 5phr clay loading.
5.2.4 Mode of transport
The mechanism of transport can be computed from the diffusion data using
Eq. (5.4)
���� = . �
! ……………(5.4)
where k indicates the interaction between the penetrant and the polymer and n
represents the mode of transport. Taking log on both the sides, we get Eq.
(5.5) 21 . The value of n and k are obtained from Eq. 5.5.
"#$�%/�' � "#$ ( )"#$t ………….(5.5)
For normal Fickian mode of transport, where rate of polymer chain relaxation
is higher compared to the diffusion of penetrant, an n value of approximately
0.5 have been reported 22 . The Fickian diffusion, actually, refers to a situation
where solvent penetration is less than the polymer chain relaxation. When n=1,
the transport approaches non-Fickian behaviour, where chain relaxation is
Diffusion studies of ………. 179
slower than the liquid penetration. If the value of n is in between 0.5 and 1, the
mode of transport is classified as anomalous. Nevertheless, when the solvent
penetration is much below the polymer chain relaxation, it is possible to record
the n values below 0.5. This situation, which is still regarded as Fickian
diffusion, is named "Less Fickian23, or ‘Quasi Fickian’. This mechanism
indicates that the solvent diffuses slowly, through the swollen matrix and free
spaces in the nanocomposite sample24.
The estimated values of n and k for 70/30 and 50/50 blend nanocomposites are
given in Table 5.2. With a change in blend composition, the value of ‘n’ varies
from Fickian diffusion to that of an anomalous transport of the penetrant
molecules. Anomalous transport occurs due to the coupling of Fickian and
non-Fickian transport mechanisms. Here the diffusion is considered because
of two processes. Variation from Fickian sorption is associated with the time
taken by rubber segments to respond to swelling stress and rearrange them to
accommodate the solvent molecules4. The reinforcement with the filler
particle imparts a high degree of restriction to the rearrangement of rubber
chains. The polymer chain mobility of both NR and NBR chains gets
restricted due to the interaction of the O1Mt with them. While the interaction
between NBR is due to the polarity factors, the NR phase also shows some
interaction with the O1Mt due to the presence of HT which is rich in alkyl
groups. Thus the observed anomalous diffusion can be because of the
counteraction between the ability of rubber segments to rearrange in the
presence of solvents and the restriction imparted to this by the reinforced filler
particles. In the Fickian mode of transport by 70/30, the k values decrease for
lower filler loading, indicating less diffusion. The value of k indicates the
degree of rubber interactions with the solvent. When polymer-filler interaction
is good or when there is good dispersion of filler in the polymer, there will be
180 Chapter 5
less interaction between the solvent and the polymer. The higher difference
in solubility parameter value also decreases the interaction of the solvent with
the blend system.
Table 5.2: Values of n and k for different clay loading of NR/NBR blend nanocomposites
Composition n k ( 102 min-1)
70/30 (0) 0.68 1.2
70/30 (1) 0.68 1.19
70/30 (2) 0.65 1.13
70/30 (5) 0.69 1.25
70/30 (10) 0.68 1.35
50/50(0 0.56 1.15
50/50(1) 0.54 1.15
50/50(2) 0.56 1.23
50/50(5) 0.56 1.24
50/50(10) 0.56 0.93
5.2.5 Diffusion coefficient (D)
The diffusion coefficient or the diffusivity ‘D’ of a solvent molecule through
a polymer membrane can be calculated using Eq. (5.6) obtained using Fick’s
second law 25-26.
* = π (ℎθ /4�')� … … … … … … ...…….(5.6) where h is the blend thickness, θ is the slope of the initial linear portion of the
plot of % Qt against √t, and Q∞ is the equilibrium absorption. As we increase
the NBR content, the diffusion coefficient decreases (Fig.5.11) because of the
high resistance of NBR to gas, organics and oil. NBR is having high cohesive
energy density because of the functional groups present in it. Therefore, the
blend nanocomposites exhibit lower diffusivity value at higher NBR content.
It has also been reported that the presence of polar or bulky groups influences
Diffusion studies of ………. 181
the diffusion properties27. The sluggish motion of the polymer chains caused
by the presence of nitrile group in NBR can be another reason for the low
permeability.
0 20 40 60 80 100
0.0
6.0x10-5
1.2x10-4
1.8x10-4
2.4x10-4
3.0x10-4
Dif
fusi
on
co
effi
cen
t (c
m2 /
sec)
NR (wt %)
0phr 1phr 2phr 5phr 10phr
100 80 60 40 20 0NBR (wt %)
Figure 5.11 Diffusion coefficient in hexane for different blend nanocomposites with different phr clay loading.
The addition of O1Mt will reduce the availability of space and restrict the
mobility of chain segments. On analyzing the blend nanocomposites with
different clay loading, a sharp decrease in diffusion coefficient for 50/50
NR/NBR blend with 2phr is observed and this can be a result of the exfoliated
morphology of the blend nanocomposite, which is confirmed from the XRD
data given in Fig. 5.6. While the d-spacing was found to be 19.6 Aºfor neat
clay, the value was shifted to 23.42 Aº for 5 and 10phr O1Mt, where an
intercalated morphology was observed. Thus, the nanocomposites with 1 and
2phr clay loading were predominantly exfoliated and for 5 and 10 phr it was
intercalated. The intercalated and exfoliated morphology of the blend
nanocomposites hinders the movement of penetrant molecules. The TEM
182 Chapter 5
images of 2 phr also confirm this. (Fig 5.7). Hindered movement of the
penetrant molecules in the presence of nanoclay platelets are already
reported 4,10. The comparatively less rate of diffusion coefficient value for
1and 2phr explains the better dispersion of clay in this compositions.
On comparing the diffusion coefficient for two solvents Fig .5.12 a) and b), a
decrease in diffusion coefficient is observed by changing the solvent from
toluene to hexane for every system. Also this can be attributed to the higher
molecular volume of hexane and of the higher solubility parameter difference28.
The solubility parameter of hexane shows good difference from that of NR and
NBR, while for toluene it is nearer to the solubility parameter value of both the
rubbers. Diffusivity is thus greatly dependent on the size solubility parameter
of the penetrant molecules. Many investigators 29,19 have reported a decrease in
equilibrium penetrant uptake with increasing penetrant chain length. The shape
of penetrant also plays a role in determining diffusion process.
Figure 5. 12a Diffusion coefficient of 50/50 NR/NBR blend with different clay
loading
Diffusion studies of ………. 183
Figure 5. 12b Diffusion coefficient in hexane and toluene for 50/50 and 70/30
blend with different clay loading
5.2.6 Permeability coefficient (P)
The permeability coefficient (P) of toluene in the rubber blend was
. = * ∗ 0 ..……..(5.7) where D is the diffusion coefficient and S is the sorption coefficient.
The values of P are shown in Table 5.3. For both aliphatic and aromatic
solvents, the same trend was shown but the magnitude was different, due to
the difference in penetrant properties. For different NR/NBR blends with 5phr
filler loading it was shown that the permeation coefficient decreases on adding
filler, and this can be well explained as due to the tortuous path that the clay
have made in the blend. While its strong polarity match influences the
migration towards NBR, the presence of HT causes the clay to migrate towards
the NR phase and the interface. The presence of clay at the interface, and in
both the NR and NBR phases hinders the movement of solvent molecules. For
50/50 blends with different clay loading, at 1phr loading permeability of
aliphatic penetrant increases, while for aromatic it increases at 2phr loading.
184 Chapter 5
This, as discussed earlier, the process was found to be related to the structural
difference between the two penetrant molecules and the diffusion path in the
polymer intercalated clay network, which paves way for the hexane molecule
to penetrate easily at 2 phr loading. Thus, it was shown that permeability
followed the same trend as the diffusion coefficient and that diffusion process
controls the permeability.
Table5.3: Values of permeation coefficient
5.2.7 Swelling parameters
The extent of swelling behaviour of the blend nanocomposites were inferred
from the swelling parameters like swelling index, swelling coefficient etc.
Swelling coefficient is an index of the ability with which the sample swells.
In order to assess the blends reinforced with O1Mt, the swelling coefficients
(β) have been calculated by Eq. (5.8). The extent of swelling, interface
strength, and degree of dispersion of fillers in the elastomer matrix can be
Diffusion studies of ………. 185
inferred from the swelling parameter value 30,31. The swelling behaviour of
the blend nanocomposites was assessed (Table 5.4 using Eq. (5.8) 32.
123""4)$ 5#366453)� 7 � �8' � 89�/89 � ρ:……..(5.8)
where Mo and M∞ are mass of the sample before swelling and after swelling
respectively and ρs is the density of the solvent. Swelling index which is
another parameter of transport properties is calculated by the Eq. (5.9)
123""4)$ 4);3< % � �8' � 89�/89 � 100 ……(5.9)
From Table 5.4 it can be observed that the swelling coefficient and swelling
index of the NR/NBR blend nanocomposites values (Table 5.4), it can be
observed that the swelling coefficient decreases to a good extent due to the
presence of fillers that hinders the path of penetrant molecules to an otherwise
free path.
Table 5.4: Mol. wt between crosslink (Mc), crosslink density, (ν) swelling coefficient (β) and swelling index of the NR/NBR blend nanocomposites
186 Chapter 5
5.2.8 Crosslink density
The crosslink density (Eq. 2.9) can be determined from the Flory Rehner
equation33 (Eq. 2.10) by calculating the molecular weight between two
successive crosslinks (Mc) by making use of the swelling data.
The calculated result of molecular mass (Mc) and the crosslink density υ are listed
in Table 5.5. As we increase the NBR content in the blends, a decreasing
tendency of Mc is observed. This may be attributed to the difference in nature of
the two elastomers 34. The slight increase in cross link density with NBR content
indicates the better reinforcing effect of polar cloisite 10A with NBR matrix. This
reinforcement, due to better interaction between polymer and clay, reduces the
penetration of solvent molecules. The schematic in Fig. 5.13a&b shows how the
filler at lower concentration reduces the penetration by forming a network, and
how at high concentration the clay agglomerates together, reducing the interaction
between clay and polymer.
Figure 5.13 Schematic showing the clay network a)at lower loading and b) aggregates at higher loading
To compare with the theory, the molecular weight between the cross links was
compared with the affine limit of the model [Mc(aff)] and the phantom
Diffusion studies of ………. 187
network model proposed by James and Guth using the Eq. 35,36 (5.10) and
(5.11) respectively.
85(=66) = >? @∅ BCBD ∅ BE
FDGHIJK∅ BE
FDL
(IMN(HI OBE )P OBE PQ OBE B .........(5.10)
85(Rℎ) = (HI�/Q) >?@∅ BCBD ∅ BE
FD
[IMN(HI OBE )P OBE PQ OBE B] ............(5.11)
where µ and υ are the number of effective chains and junctions,37 φ2m is the
polymer volume fraction of swelling at equilibrium, and φ2c, the polymer volume
fraction during crosslinking. The polymer chains may move freely through one
another where χ is the junction functionality38. The calculated Mc values along
with the experimental values are detailed in Table 5.5.
Table 5.5 : Values of Mc (Exp). Mc (ph).and Mc (aff).in/cm3
It was found that the Mc values of phantom network model showed moderate
agreement with the experimental values rather than affine limit of the model.
188 Chapter 5
Here the chain can move freely through one another, ie, the junction points
fluctuate over time around their mean position without any hindrance from the
neighbouring molecules.
5.2.9 Kinetic modelling of diffusion
The major objectives of mathematical modelling are the prediction of
diffusion behaviour through polymers, optimization of the diffusion kinetics
and elucidation of the physical mechanism of transport by comparing diffusion
data using mathematical models39. Here we have used the diffusion models
like, first order kinetic equation, Higuchi model, Korsmeyer Peppas model and
Peppas-Sahlin equation to predict the diffusion behaviour. All these models
are based on the process in which penetrants migrate from the initial position
in the polymeric system to the polymer’s outer surface40. This is affected by
factors such as the physico-chemical properties of the penetrant, the structural
characteristics of the material system etc. Applying these models in polymeric
system is thus justified. Also it has been reported that, penetrant diffusion,
polymeric and matrix swelling are suggested to be the main driving forces for
transport of penetrants containing polymeric matrices. Specifically, Fick’s
law of diffusion provides the basis for the description of all these models. The
equation and the corresponding fitting parameters are given in Table 5.6. First
order kinetics can be expressed by the Eq. (5.16)41.
log Qt = log Q∞ -k t/2.303. (5.12)
where, Q∞ is the concentration of solvent at equlibrium , k is the first order
rate constant, and t is the time. The data obtained are plotted as log Qt/ Q∞ vs.
time (Fig 5.14). From the plot it is clear that the diffusion of solvent is not
proportional to the amount remaining in the polymer matrix as the curve is not
fitted well.
Diffusion studies of ………. 189
0.1
1
0 200 400 600 800 1000 1200
50/50(1)50/50(10)
Qt/Q
o(m
ol)
t 1/2(min)1/2
Figure 5.14 Model fitting of the solvent permeation through NR/NBR blend nanocomposites using first order Kinetics.
Higuchi equation tries to relate the release rate based on simple laws of
diffusion. The equation (Eq.5.12) describes the release/diffusion processes
under Fickian mechanism, or through non Fickian mechanism. In the case of
Fickian mechanism, the rate of diffusion is much less than that of polymer
relaxation. For Case II system or non Fickian, the rate of diffusion is much
larger than that of polymer relaxation. The Higuchi model41 is represented as
�� = UV ∗ �H/� …… (5.13) where Kh is the Higuchi dissolution constant, t is the time and Qt is the molar
percentage uptake. Power Law Equation is a more comprehensive, very simple
and semi-empirical equation developed by Korsmeyer- Peppas42. From the
equation it can be observed that the fractional diffusion is exponentially related
to diffusion time (Fig.5.15). The data obtained were plotted as Qt/Q∞ versus
square root of time.
190 Chapter 5
Another analysis of the mechanism is that which considers diffusion in
polymer matrices as a result of two processes, i.e. diffusion into the swollen
polymer and matrix relaxation. This was carried out by fitting the data to the
model proposed by Peppas and Sahlin43 given by the Eq. 5.13
�%
�' = UW�X + UY��X ………(5.14) where Mt/M∞ is the fraction of solvent released at time t, Kf is the diffusion
Fickian contribution coefficient, Kr is the relaxation contribution coefficient
and m is the purely Fickian diffusion exponent. When Kf > Kr the release is
mainly controlled by diffusion, and when Kr > K f, the diffusion is mostly due
to matrix swelling. When K f = Kr, the diffusion is a combination of diffusion
and polymer relaxation. The selection of the appropriate model to ensure the
effectiveness can be found out from correlation coefficient (R) (Table 5.6) and
it is found that the experimental value fitted quite well into the model.
0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35
Qt/Q
o(m
ol %
)
t 1/2 (min)1/2
Peppas Sahlin
Kosmeyer Peppas
Haguchi
Experimental
Figure 5.15. Model fitting of the solvent permeation through NR/NBR blend nanocomposites using Peppas – Sahlin, Haguchi and Korsmeyer-Peppas
Diffusion studies of ………. 191
Table 5.6: Correlation coefficient (R2) and constant (K) of different kinetic models
5.3. Conclusion
The transport properties of organically modified montmorillonite filled
NR/NBR blends were investigated. The addition of layered structured
nanofillers enhanced the barrier property of the elastomer blend
nanocomposites. It was found that blend composition and clay loading played
a significant role in determining the diffusion parameters like solvent uptake,
diffusion, and permeation coefficients. For neat polymer, the diffusivity was
high. Nevertheless, the presence of O1Mt showed lower diffusion at lower
filler loading due to the fine dispersion leading to good polymer/filler
interactions. The claim was supported by the XRD data, where an exfoliated
morphology was shown. The mechanical properties also supported the
diffusion behaviour of nanocomposites. The slower diffusion was associated
with the increase in tortuosity. At higher loading of O1Mt, overall diffusion
was increased due to poor polymer/filler interactions caused by O1Mt
agglomeration. These assumptions tally with the observations from the TEM
analysis. The shape and size of the solvent also played a considerable role in
determining the diffusion parameters. The dimension of the filler plays a
considerable role in determining the diffusion parameters. The high l/d ratio
can improve the barrier properties if dispersed properly. Cloisite 10A is having
a higher aspect ratio as the thickness of Cloisite is 10 to 50 times smaller than
other clay like nanokaolin44. The fully exfoliated silicate platelets of cloisite
192 Chapter 5
clays are only 1 manometer thick. This special structure of the clay layers
results in an exceptionally high aspect ratio of more than 100 for cloisite 10A.
The high aspect ratio makes cloisite clay to have superior barrier
properties to mercapto silane modified clay which is having a thickness of
60nm (chapter 2)
The cross link density, an important characteristic influencing the properties
of cured rubber was also determined and an increase of the same was found at
lower filler loading. The experimental values were fitted with mathematical
models and showed rather fine agreement with theoretical values. Among the
mathematical models used for determining the molecular weight between the
crosslinks, the phantom model shows more agreement with the experimental
values. At the same time, Kinetics of diffusion fitted well for Peppas Sahlin
model where diffusion was considered to be a combination of Fickian
diffusion and polymer relaxation process.
Diffusion studies of ………. 193
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44 BYK additives and instruments, Technical information Technical
Information B-RI 10 cloisite-nanocomposites addtives for halogen free
flame retardants.
http://www.byk.com/fileadmin/byk/additives/product_groups/rheology/f
ormer_rockwood_additives/technical_brochures/BYK_B-
RI10_CLOISITE_EN.pdf.