Chapter 5 Transport of Organic Solvents through Natural...

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


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


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.


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)


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)


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


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


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


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


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


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.


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


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.


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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.

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