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CHAPTER 7

SORPTION AND DIFFUSION OF ORGANIC

PENETRANTS INTO DICARBOXYLIC ACIDS BASED CHAIN EXTENDED

POLYURETHANES

This chapter is divided into two sections Part - A and Part – B. Part - A deals

with the molecular transport of a series of n-alkanes into TDI based CEPUs (MA and

CA) and Part B covers the transport behavior of substituted aromatic penetrants into

HDI based CEPUs (MA and CA). Molecular transport of a series of organic probe

molecules through prepared CEPU membranes have been studied in the temperature

range 25–60 °C using sorption-gravimetric method. The Fickian diffusion equation

was used to calculate the sorption (S), and diffusion (D) coefficients, which were

dependent on the size of the probe molecules and temperature. Sorption data is

correlated with the solubility parameter of solvents and polymer. It was found that

solvents of comparable solubility parameter with CEPUs interact more and thus there

is an increase in sorption. In all the liquid penetrants, the transport phenomenon was

found to follow the Fickian mode of transport. From the temperature dependence of

diffusion and permeation coefficients, the Arrhenius activation parameters such

activation energy for diffusion (ED) and permeation (EP) processes have been

estimated. Furthermore, the sorption results have been interpreted in terms of

thermodynamic parameters such as change in enthalpy (∆H) and entropy (∆S).

7.1 Introduction

The diffusion of small molecular liquids into polymers is a subject of intense

study. This type of diffusion process plays an important role in several important

areas of engineering and industry [1-2]. Membrane separation of liquids in the

industry has become wide spread as more traditional methods are based on

absorption, pressure-swing adsorption or cryogenic. The membrane process has

certain benefits compared to the cryogenics process, for example, lower investment

cost and easier operation.

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The effects of interaction between polymers and small molecules are of practical interest to chemical engineers, because of the inherent sorption and transport of liquid penetrants present in most processes they encounter.

Now-a-days polymer membranes are increasingly used in various barrier

applications. Molecular transport of organic liquids through polymer membranes has been the subject of investigations over the past several years [3-8]. Such studies are necessary due to the production of innumerable polymer membranes of commercial importance [9-10]. The total amount of liquid sorption in polymeric materials is fundamental for applications such as pharmaceuticals, food packaging, electronic and medical components.

Research studies are focused on three major areas of transport mechanism of

polymeric materials. These may be designated as diffusion, sorption and permeation. Diffusion studies are concerned with transport of low molecular weight materials. The diffusion coefficient is a more fundamental quantity, which describes molecular mobility in the absence of a driving force in the same operating conditions. In packaging the transport is most commonly expressed in terms of permeability or permeation rate also known as transmission rate. These two important physical properties can greatly influence performance on the materials characteristics.

Depending on polymer compositions, the structure and morphology relative to

the physico-chemical nature of the penetratant materials is determined to elucidate mechanisms of transport and sorption process and molecular details of polymeric structure and morphology. Hence, it is necessary to analyze the transport behaviors, which have been widely studied by various researchers [11-16]. In all these studies, it has been pointed out that the rate of solvent transport with in polymer matrix, depends upon the nature of the functional group and its interaction with the polymer chain segments. Structural characteristics of the polymer are also important factors which leads to an increased understanding about the molecular transport phenomenon into elastomeric system.

Several studies have been reported in the literature regarding the transport and

sorption of liquids into polymer membranes. Kim et al [17] studied the transport of aromatic and aliphatic liquids into crosslinked polystyrene (PS). Lipscomb [18] reported the thermodynamic analysis of sorption in rubbery and glassy material. In

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recent years, Vergnaud et al [19-21] and Goto et al [22] employed numerical/mathematical procedures to study diffusion of liquids into polymeric membranes. Kendaganna Swamy and Siddaramaiah [23] have investigated the transport behavior of diol based chain extended PU (CEPU) membranes.

In view of the importance of PU in several areas such as biomedical

applications, coating, adhesives, etc., it is important to know its transport

characteristics with respect to organic solvents. The sorption of CEPUs depends very

much on their chemical structure and morphology. The structure and molecular

weight of the reactants of CEPU significantly influence the phase separation behavior.

Polyurethane elastomers are known to exhibit unique mechanical properties,

primarily as a result of two phase morphology [24]. These materials are alternating

block copolymers made of hard segments from the diisocyanate/chain extender and

soft segments from the polyol (ether or ester, castor oil). The hard and soft segments

are chemically incompatible and microphase separation of the hard segments into

domains dispersed in a matrix of soft segment can occur in varying degrees. In view

of the importance of PU as a barrier material in several engineering sectors [25-26], it

is important to know its transport characteristics with respect to common organic

solvents. Thus, knowledge of the transport mechanisms as manifested by sorption,

diffusion and permeation of organic liquid penetrants in PU matrix is helpful for

establishing the structure- properties relationships under severe application

conditions.

Although some previous studies [27-29] have been made on solvent transport

through PU membrane more experimental data are still needed for a better

understanding of the thermodynamic interactions between polymer and solvent. A

CEPU membrane has been chosen in this study because of its good mechanical

properties and wide variety of industrial engineering and biomedical applications.

However, acceptability of PUs for any specific applications depends on its

performance requirements before these materials seek commercial or engineering

applications. Aromatic solvents have been chosen as probe molecules as these have

diverse applications in process industries and in manufacture of perfumes, dyes, bulk

drug formulations etc.

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Siddaramaiah et al have studied [30-33], and investigated the sorption and

diffusion behavior of castor oil-based PU. Its IPNs and diol based CEPU have been

studied for molecular transport with several organic liquids. They found that transport

behavior does not merely depend on the size of the penetrants but also on the nature

of liquid molecules and membranes. These studies are extremely important for the

design of new polymer materials, which would greatly benefit the development of

high performance membranes. Polyether-based PU foam are being studied by many

scientists for the isolation of heavy metal ions like cobalt and antimony and

absorption of phenol compounds in aqueous solutions [34-36]. The penetration of the

solvent into the polymer membrane depends on the length of storage and nature of the

solvent. The behaviour of the solvent with the membrane for a considerable length of

time has to be studied. Hence, sorption of solvents is very essential to know the

diffusion and permeation characteristics of polymer membranes.

The principle objective of this chapter is to investigate the transport behaviour

of aromatic liquids and n-alakanes (C6-C9) through dicarboxylic acid based CEPU

(MA and CA) membranes. It is expected that a systematic change in solvent power

would lead to results which could be interpreted by considering the possible

interactions with soft and hard segments of the polymer. Transport properties viz.,

sorption (S), diffusivity (D) and permeability (P) have been studied over an interval of

temperatures from 25 to 60 oC to predict the Arrhenius parameters for each of the

transport processes involved.

7.2 Molecular transport

7.2.1 Sorption

Sorption in polymers is a topic of great relevance in several industrial

applications. Liquid, vapour or gas sorption in a polymer matrix depends on the

concentration or pressure of the sorbed species and the nature of the polymer. A

number of theories have been developed to study the polymer penetrant interactions

during sorption experiments and these will be summarized in the forth coming

section.

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7.2.2 Diffusion

Diffusion is a molecular process in which molecules drift as a result of random

thermal motion from the region of higher concentration to one of lower concentration.

The transport of a liquid is the similar process. This section is concerned with the

theories of mass transfer for polymer-penetrant systems. To describe diffusion of

small molecules through rubbery polymers a number of molecular and free volume

models have been proposed. The molecular models are based on the analysis of

specified motions of penetrant and of polymer chains related to each other taking into

account the inter- molecular forces. The free volume models originated from

statistical mechanical considerations and they do not offer a detailed microscopic

description of the phenomenon.

7.2.3 Molecular models

All the molecular models are based on the experimental observation that the

penetrant transport in polymer follows Arrhenius relation. Here, diffusion is regarded

as thermally activated process (called activated diffusion) with the assumption that the

micro cavities of different sizes are continuously formed and destroyed within the

polymer matrix due to the random movement of polymer segments. Three of the main

theoretical models have been distinguished and these exist often in more than one

version as described below.

First one is the molecular relaxation model, which takes into account the

molecular rearrangement in the polymer necessary to accommodate a change in

penetrant content. Near or below Tg, such molecular relaxations are very slow on the

time scale of diffusion process. Different versions of the model have been applied to

systems where the penetrant is a good swelling solvent to the polymer. Perhaps the

difficulty of these models lies in the use of "initial state" which poorly characterize

physically and introduce a significant number of adjustable parameters.

The second model is concerned with connective diffusion. When a glossy

polymer is strongly swollen by the penetrant, zero order absorption kinetics is noticed.

More detailed absorption reveals sharp (discontinuous) penetrant fronts which

separate the highly swollen outer region from the inner glassy core and advances in a

constant velocity, "V". Such processes, called non-Fickian, are completely rate

201

controlled by the swelling stress. A more precise and detailed physical picture of the

phenomenon is still lacking. A phenomenological model of non-Fickian diffusion has

also been proposed in which the Fickian and non-Fickian mechanisms are combined

additively through the equation;

(∂C/ ∂t) = (∂/∂x) [D (∂C/∂x) - VC] (1)

Assuming D as constant can solve this equation and the treatment has proved

particularly useful for the description of sorption kinetics of solvents including binary

mixtures.

The third model, the differential swelling stress model, is based on the

consideration that uneven distribution of penetrant across the polymer film during

diffusion caused a correspondingly uneven swelling tendency along the plane of the

membrane. Assuming the polymer to exhibit linear viscoelasticity, later refined this

model. It should be noted that each of the models above has special characteristics,

which enhance its utility for certain applications. However, the molecular relaxation

model has been used more extensively than the other two.

7.2.4 Free volume model

A number of free volume theories have been advanced to study the diffusion

in polymers. The term free volume refers to the empty space between the molecules

of the substance and has been discussed at various levels of sophistication [37-44].

One of the most promising and earliest free volume models developed by Fujita

[45-46] in the nearly sixties enjoyed popularity for a long time. This approach

employed the William-Landel-Ferry (WLF) modification of the Doolittle equation

[47-48]. Fujita [45-46] suggested the molecular transport as a result of redistribution

of free volume and not the thermal activation. Based on the Cohen and Turnbull

formalism [49], Fujita suggested a relation between the thermodynamic diffusion

coefficient [DT = D (d lnC/d ln a)] and the fractional free volume of a penetrant-

polymer system. The validity of Fujita's theory has been tested for a number of

organic vapours-amorphous polymer systems wherein strong dependence of D on

penetrant concentration was found [45-46, 50-52]. A brief mention may be made here

of some of the earlier theories concerning free volume concepts. These include

Wilkins and Long [53], who considered the diffusion of local regions of high free

volume in the mixture. Peterlin [54] invoked the Hildebrand concept of fractional free

202

volume and used Flory-Huggins equation to develop a relation for solubility

coefficient in terms of polymer-solvent interaction parameter.

Later developments in this area have been attempted by Vrentas and Duda

[55-56]. In order to account for the difference between the diffusion behaviour of

gases and organic solvents in amorphous polymers, Vrentas and Duda have proposed

a new version of the free volume theory [56]. Their theory is based on the earlier

models of Cohen and Turnbull [49], Fujita [45-46] and Bearman [57] between the

mutual diffusion coefficient and the friction coefficient and makes use of the

thermodynamic theory of Flory [58] and the entanglement theory of Bueche [59].

Their formalism was used to calculate the concentration and temperature dependence

of the mutual diffusion coefficient [60].

7.2.5 Permeation

Penetrant permeation through polymer membrane is an extremely complex

phenomenon for which no satisfactory theory exists. Several models have been

proposed and used to interpret the experimental results, yet only a few of them met

with limited success. Some models took into account the details of the postulated

mechanism transport of liquids while others describe the overall phenomenon without

proper mechanism. Most of the existing models tried to answer the question as to

what is the nature flow of liquid through the membrane. The immediate answer would

be that the flow is either viscous or diffuse or a combination of the two; the latter

seems to be more logical.

The broad subject of polymer permeability has been classified into three topics

representing three conceptual approaches. The first topic focuses on the actual

mechanism of penetration, where heavy emphasis is given to the question related to

transport kinetics and to diffusion phenomenon discussed earlier. The second topic

concerns the study of dimensional response of the polymer termed hygroelasticity,

where, one is confronted with problems of swelling, internal stresses, etc. The theme

of the third topic deals with the environmental and ecological effects on the properties

of polymers.

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7.2.6 Kinetics and mechanisms of the solvent sorption in polymers

In order to understand the phenomenon of small molecules in polymers, it is

necessary to elucidate the mechanism of diffusion on a microscopic level. Fick's

relations are the starting points for first studies. If diffusion is restricted to x-direction

such as in the case of thin polymer film absorbing a liquid where, diffusion into the

edges of the film can be ignored then Fick's second law of diffusion is written as [61];

∂C/∂t = D (∂2C/∂x2) (2)

where, t is the sorption time, C is the liquid concentration within the membrane

materials and D is the concentration independent diffusion coefficient. Equation (2)

was solved to calculate the values of D by the sorption method. The solution of this

equation is based on the assumption that the concentration within the membrane is

initially uniform and that surface concentrations are instantaneously brought to

equilibrium. The relation for Fick’s second law is;

∞

Mt/M∞ = 1-8/ π2 ∑1/(2n+1)2 exp (-(2n+1)2 π 2 td)/h2) (3)

n=o

where, Mt and M∞ referred to the cumulative masses sorbed from the polymer sample

at time t and t∞ respectively. The values of M∞ can be obtained from the plots of

(Mt/M∞) versus t1/2 or t1/2/h. There is also a limiting case equation before 50%

completion of equilibrium sorption and according to this equation (3), D can be

calculated as;

D= π [h θ /4M∞]2 (4)

where, θ and h are the initial slope and thickness of the specimen and M∞ is the mass

obtained at equilibrium. Equation (4) is generally used to estimate D of a penetrant in

a polymer from the slope of the straight line portion of the sorption curve. A method

of studying diffusivity and solubility of a polymer- penetrant system is to determine

the rates of sorption and desorption of penetrant by the gravimetric method [62-63].

In the absence of complicating polymer relaxation rate behaviour, plots of

(Mt/M∞) versus t1/2 or t1/2/h are generally linear from the origin upto about 55% of the

total concentration. Above the linear portions, the curves are bending and then show

asymptotic behaviour. When the diffusion process is Fickian, the value of t/h2 for

which Mt/M∞ = 0.5.

(t/h2)0.5 = 1 (1/ π 2 D) ln [ (π 2 /16)-1/9(π 2 /16)9 ] (5)

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So that,

D=0.04939 / (t/h2)0.5 (6)

The average values of D as calculated from equation (6) have been expected as a better approximation to the value of D than the individual values. When

Mt/M∞>0.4, the sorption rate equation can be written as;

ln (1- Mt/M∞) = ln (K/T2) - DT2 (t/h2 ) (7)

Thus D may be computed from the limiting slope of a plot of ln (1-Mt/M∞) versus t or t/h2. In order to investigate the type of diffusion mechanism the sorption data of all the penetrant polymer systems have been fitted to the following equation [64-65];

log (Mt/M∞)= log K + n log t (8)

The values of n tell us something about the type of transport mechanism, Fickian or non-Fickian, k is a system parameter which depends on structural features of polymer and solvent.

From least square analysis of the log (Mt/M∞) data verses log t the values of K and n have been calculated. The slope of the straight line gives n and y-intercept gives log K. The permeability coefficient, P is calculated by the following relation [66];

P = D x S (9)

Thus, the P values are considered as estimates of the permeability coefficients. Liquid ingression into a polymeric material is a phenomenon of great technological importance. In many instances, it is necessary to know the penetration depth of liquids into polymer. In most application areas, the liquid penetration rates are calculated in terms of liquid concentration profiles. These are extremely useful to predict the self-life of the polymer while in contact with the liquids 7.2.7 Thermodynamic and activation parameters The temperature dependence of transport coefficients (P, D and S) have been used to compute the activation parameters ED and EP for the process of the diffusion and permeation respectively from the consideration of the Arrhenius relationship;

X = X0 exp (-Ea/RT) (10)

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Here, X is P, D or S, and X0 represent the constant term. Ea is activation energy, R is

the molar gas constant and T is absolute temperature. From least square analysis of

ln D or ln P verses l/T plot, the values of X0 and Ea are calculated.

Temperature dependent thermodynamic equilibrium sorption constant Ks

values are used to evaluate standard enthalpy (i.e., heat of sorption) (∆H) and standard

entropy of sorption (∆S) by using van't Hoffs relation;

ln Ks = (∆S/R) - [(∆H/R) (1/T)] (11)

From the least square analysis of ln Ks verses l/T, ∆H and ∆S are calculated.

The percentage weight gain Qt of the soaked polymer membrane is calculated using

equation;

Qt = [(Mt - Mi) / Mi] x 100 (12)

where, Mi is initial weight of the membrane and Mt is the weight at time t. The weight

gain during sorption process is expressed as moles of solvent uptake by 100 g of

polymer sample (Ct);

M

XW

WWmolC t

t100%)(

0

0

−= (13)

where, W0 is the initial mass of the sample; Wt is the mass at time t, that is the

immersion period; and M is the molar mass of the liquid.

The transport properties such as diffusion, sorption, permeation and

thermodynamic parameters are discussed in detail for interaction of aromatic organic

solvent in CEPU systems.

7.2.8 Present research problem

A survey of the literature reveals that the molecular transport behavior of

dicarboxylic acid based CEPUs has not been studied. But the sorption and diffusion

behaviour of PU membranes have been studied by many researchers [67-81]. In this

research programme dicarboxylic acid based CEPUs membranes have been selected,

206

because of its potential applications. In all these application areas, it is likely that

these membranes may come in contact with penetrants such as organic solvents, salt

solutions and oils which may affect the performance of the PU membranes.

The main goal of the present thesis is to achieve comprehensive understanding

of the transport characteristics of organic penetrants like n-alkanes and aromatic

penetrants through CEPU membranes. The sorption experiment was performed at 25,

40 and 60 oC. These results are discussed in terms of the nature of the polymer-

solvent interaction, molecule size and viscosity of the penetrants.

7.3 Experimental

7.3.1 Specimen preparation

The MA and CA based CEPU membranes were prepared as per procedure

given in chapter 3 using two diisocyanates like, TDI and HDI. The prepared CEPU

membranes have been investigated for molecular transport with n-alkanes and

aromatic solvents.

7.3.2 Sorption measurements

These CEPU membranes were exposed to the n-alkanes for a definite period

of time and the changes in mass of the membranes are monitored. The mass uptake of

the penetrants by the PU membranes depends upon the polymer network structure. In

these experiments, mass gain due to sorption is accurately measured as a function of

time. From these results S and D values have been calculated for the organic probe

molecule through the PU membranes [23, 67, 82-83].

Sorption experiments were performed at 25, 40 and 60 oC using an electrically

controlled oven maintained at the desired temperature with in the accuracy of ±0.5 oC.

The CEPU samples were cut circularly (diameter =1.5 cm) using sharp edged steel

die. The initial thickness of the specimens was measured at several points (Mitutoyo,

Japan with precision of ± 0.001) and then dried in a dessicator for one day before the

experiment. Dry weights of specimens were recorded before immersion into the

penetrant. The cut specimens were immersed into the organic solvents taken in a

207

screw tight metal cap bottle, kept in a temperature controlled oven. At specified

intervals of time, the membrane was removed from the containers; surface adhered

liquid drops were removed by using soft filter paper and then weighed immediately

using analytical balance. The sample was then placed back immediately into the test

liquid and transferred to the temperature-controlled oven. The total time spent by the

CEPU membrane outside the penetrant was within 20-30 sec in order to minimize the

possible experimental error. The weighing of the samples continued until the

equilibrium value was reached. After the membrane attained equilibrium sorption, no

more mass gain occurred and this did not change significantly by keeping the samples

inside the liquids for a further period of one or two days. The time until no more

liquid uptake by the polymer was observed (equilibrium sorption taken for the

attainment of equilibrium for different liquids varied from 70 to 90 h. Two

independent readings were taken and an average value was used in all the

calculations. Sorption coefficients were expressed as wt % and mol % and are

calculated using eqs. (12) and (13).

PART A - Transport characteristics of carboxylic acids based chain

extended PU membranes with n-alkane penetrants

In this section citric acid (CA) and maleic acid (MA) based CEPU membranes

have been subjected to studying the molecular transport of n-alkanes. The n-alkanes

such as hexane, heptane, octane and nonane of AR grade were distilled before use.

Some physical properties of solvents used as penetrants are given in Table 7.1.

Table 7.1. Some physical properties of n-alkane penetrants at 25 oC

Penetrants Mol. Vol. (cm3/mol)

Density (g/cc)

Sol. Parameter

(cal /cm3)1/2 ε

Dipole moment (debye)

Polaris ability (10-24 cm-1)

BP (oC)

Visco-sity

(cSt)

Hexane 115.2 0.625 7.10 1.84 0.02 -- 68 0.401

Heptane 131.6 0.660 7.27 1.88 0.02 6.34 98 0.511

Octane 163.5 0.704 7.57 1.95 0.02 8.43 125 0.645

Nonane 147.5 0.683 --- -- -- 7.38 150 0.807

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7.4 Results and Discussion

7.4.1 Sorption kinetics

Two CEPU membranes were selected in this study and they are; TMA

(CO+TDI+MA) and TCA (CO+TDI+CA). Sorption and diffusion of n-alkanes into

different membranes of dicarboxylic acid based CEPUs have been studied. The total

amount of n-alkane molecules absorbed by polymeric materials is the fundamental to

measure the sorption values. During initial sorption stages, the penetrant uptake

increased linearly with t½. Later due to equilibrium, the sorption curves for all

penetrant attained plateau regions at all temperatures. All CEPU membranes have

reached equilibrium almost at the same time.

Sorption studies can be easily understood by interpretation in terms of mass

increase per 100 g of the polymer sample verses square root of time t½. Comparison of

sorption tendencies of both TMA and TCA based CEPUs with octane at 25 oC is

shown in Figure 7.1. From the figure it was noticed that MA based PU has more

interaction with octane than TCA based PU. This is due to TCA (the functionality of

CA is three- two dicarboxylic acid groups and one hydroxyl group) being a highly

polar membrane as compared to TMA. The sorption results of all the n-alkane

penetrants such as hexane, heptane, octane and nonane at room temperature (25 oC)

for TMA and TCA based CEPUs are presented in Figures 7.2 (a) and (b) respectively.

These membranes in all alkane penetrants showed almost identical sorption

tendencies. Here, sorption (S) values increases with increase in molecular size of the

penetrant. There is a competition between size of the penetrant and the degree of

interaction between PU membrane and solvent [82-83]. This can also be attributed to

the solubility parameter factor of membrane and probe molecules. Differences in

solubility parameters overcome the molecular size and hence, influence the sorption

[83]. The sorption process of all penetrants followed the sequence; nonane > octane >

heptane > hexane. The molecular size, solubility parameter and dielectric constant of

probe molecules also followed same trend of sorption.

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Figure 7.1. Percentage mass uptake (Qt) versus t1/2 for MA and CA based CEPUs

with octane at 25 ºC

Figure 7.2. Percentage mass uptake (Qt) versus t1/2 for (a) MA and (b) CA based

CEPUs with different n-alkanes at room temperature

t1/2 (min1/2)

Qt (

%)

t1/2 (min1/2)

Qt (

%)

t1/2 (min1/2)

Qt

(%)

(b)

(a)

210

For a Fickian type behavior, the plots of Qt versus t½ should increase linearly

up to about 50 % sorption. Deviation from the Fickian sorption is associated with the

time taken by the polymer segments to respond to swelling stress and rearrange them

to accommodate the solvent molecules [83]. This usually results in the sigmoidal

shapes of the sorption curves. Thus non-Fickian diffusion involves the tension

between swollen (soft segment) and unswollen (hard segments) parts of PU, as the

latter tends to resist further swelling. Molecular transport of liquids through the

polymeric membranes depends on temperature and thus we have studied the effect of

temperature on sorption. Such dependency is typically shown in Figure 7.3 for citric

acid based CEPU with n-hexane. From the figure it was noticed that as temperature

increases the sorption values also increased. This effect follows the conventional

theory that at higher temperature the free volume increases due to an increased

movement of the chain segments of the CEPUs [84]. Sorption capacity increases with

increase in temperature. However, sorption at higher temperature attains equilibrium

much more quickly and uptake values are also higher than those observed at lower

temperatures.

Figure 7.3. Percentage mass uptake (Qt) versus t1/2 for CA based CEPU in

hexane at different temperatures

In order to know about the type of transport mode, the estimated values of n

and K were calculated [85-86]; where, parameter K is a closely related function of

polymer type and nature of the solvent molecules. Further, it has been shown to be

related to the diffusion parameters and polymer –solvent interaction [3-5, 12, 15].

t1/2 (min1/2)

Qt (

%)

211

Figure 7.4. A plot of ln Mt/M∞ versus ln t for CA based CEPU with hexane at

different temperatures

Table 7.2. Sorption data for MA and CA based CEPUs in n-alkanes

n K (102 g/g. min n) Solvent

25 oC 40 oC 60 oC 25 oC 40 oC 60 oC

MA

Hexane 0.53 0.57 0.54 0.87 1.26 1.86

Heptane 0.57 0.55 0.53 2.19 2.82 3.55

Octane 0.54 0.52 0.54 1.21 2.55 3.08

Nonane 0.59 0.48 0.53 2.86 3.15 3.14

CA

Hexane 0.51 0.51 0.57 2.12 2.24 2.64

Heptane 0.52 0.55 0.48 1.01 3.48 3.98

Octane 0.51 0.53 0.57 2.12 2.76 2.88

Nonane 0.52 0.50 0.51 1.23 5.61 5.84

The magnitude of n decides the transport mode. For instance, a value of

n = 0.5 suggests the Fickian mode and for n = 1, a non- Fickian diffusion mode is

predicted. In order to determine K and n plots of ln (Mt/M∞) versus ln (t) were

constructed, and it is shown in Figure 7.4. The calculated empirical parameters n and

K are given in Table 7.2. From the table, it was noticed that n-values lie in the range

0.48 – 0.59 for the investigated temperature interval 25-60 oC, which indicates a

ln t

ln M

t/ M

∞

212

Fickian mode of transport. The results of n are not dependent on temperature. K value

increases with increase in temperature and lies in the range 0.87 x 10-2 - 5.84 x 10-2

g/g minn. The temperature dependence of K for all the penetrants suggests that it

increases with increase in temperature. Furthermore, K appears to depend on the

structural characteristics of the penetrant molecules. Thus, it appears that, K not only

depends on the structural characteristics of polymer and penetrant molecules, but also

on solvent interactions with PU chains [23].

7.4.2 Sorption

The calculated sorption values of all CEPUs are tabulated in Table 7.3. From

the values of sorption data, all the CEPUs showed different sorption values. This may

be due to different chemical structure and morphology of different dicarboxylic acid

based CEPUs. The morphology of the CEPU membranes depends on the nature of the

chain extender/crosslinker, state of compatibility and micro phase segregation

between the hard and soft segments. But there is no systematic variation in S values

among the PU membranes. Molecular migration of each penetrant differs depending

upon their size, polarity and solubility parameter and nature of polymeric membranes,

thus showing the effect on the structure and/or its morphology. From this result it is

evident that the molecular transport depends on the structure and/or morphological set

up of the membrane material and the polymer penetrant interactions may be a

physical type rather than a chemical interaction.

7.4.3 Diffusion and permeation coefficients

Diffusion coefficient (D) of the polymer-solvent systems is a key parameter in

many engineering areas. The transport of small molecules through the polymer

membranes generally occurs by a solution diffusion mechanism. That is the penetrant

molecules are first sorbed by the polymer followed by the diffusion [12]. The

diffusion through the polymer depends on the amount of the penetrant molecules

between the two surfaces. Diffusion coefficient was calculated using Fick’s

equation (4) [87].

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Table 7.3. Sorption (S), diffusion (D) and permeation (P) coefficients of MA and CA based CEPUs in n- alkanes

MA CA n-

Alkanes Properties 25 oC 40 oC 60 oC 25 oC 40 oC 60 oC

S x102 (g/g) 6.79 12.90 16.60 6. 68 12.58 17.58

Dx107 (cm2/s) 4.06 5.53 6.23 3.08 3.98 4.51 Hexane

P x 107 (cm2 /s) 27.56 69.59 103.41 20.57 51.35 77.61

S x102 (g/g) 10.62 15.91 17.60 10.05 14.82 22.99

Dx107 (cm2/s) 3.17 4.51 5.01 2.14 2.95 3.37 Heptane

P x107 (cm2 /s) 30.11 71.75 88.19 21.50 43.74 64.40

S x102 (g/g) 11.22 16.00 18.10 10.44 15.23 18.01

Dx107 (cm2/s) 2.84 3.07 4.22 1.49 2.03 2.40 Octane

P x 107 (cm2 /s) 31.86 49.13 76.49 15.55 30.88 67.08

S x102 (g/g) 12.51 17.60 20.02 12.44 15.02 20.09

Dx107 (cm2/s) 1.74 2.21 3.26 1.14 1.61 2.07 Nonane

P x 107 (cm2 /s) 21.76 39.01 65.40 14.18 24.31 64.42

Figure 7.5. Plots for ln D versus 1/T for CA based CEPU for different n-alkane

penetrants

l/T X 103 (K−1)

ln D

214

Calculated values of D for all CEPUs are given in Table 7.3. The variation of

D depends upon the nature of the penetrant molecules in addition to the structural

characteristics of CEPUs. Diffusion coefficient decreased with increasing molecular

volume of their migrating liquids. The sequence of variation of D with respect to

penetrants is; hexane > heptane > octane > nonane. The D values also increases with

increase in temperature. Such dependency of D on molecular volume of n-alkanes

suggest that larger molecules in a related series of liquids occupy larger free volumes,

leading to hindered diffusion through the polymer matrix [88].

Molecular transport of probe molecules into the polymer membranes is

dependent upon several factors [89-91] such as; (i) micro voids for free diffusion

(ii) the construction resulting from alternately small and large pores in the transport

path (iii) the construction resulting from the very close approach of the boundaries of

the limiting pore within the transport path and (iv) the tortuosity imparted by the

membrane material. The diffusion of solvent molecules into the dense polymer

expands the network of matrix and thereby weakens the molecular interaction

between the neighboring polymer segments. A highly cross-linked and crystalline

polymer inhibits diffusion of liquid molecules more than a linear uncross linked

polymer.

The permeation of small molecules through polymers generally occurs

through a solution diffusion mechanism, i.e., the penetrant molecules are first sorbed

by the polymer followed by diffusion through the polymer. The net transport through

the polymer depends on the difference in the amount of penetrant molecules between

the two surfaces. 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. The calculated ‘P’ [92] values also followed the same trends as those of

diffusion with reference to temperature and molecular size of the penetrant molecules

(Table 7.3).

215

7.4.4 Activation parameters

The Arrhenius activation parameters, viz., ED and EP for the processes of

diffusion and permeation have been computed from a consideration of the

temperature variation of P and D respectively. The Arrhenius plots namely

ln D verses 1/T and ln P verses 1/T are presented in Figures 7.5 and 7.6 for TCA

based CEPU for different penetrants respectively. Arrhenius plots exhibit linearity

and this suggests that values of activation energy are roughly constant over the

investigated range of temperature. The activation energy (ED and EP) has been

calculated from the slope of Arrhenius plot (Table 7.4). The values of ED and EP are in

the range 8.19- 28.6 kJ/mol and 20.61-35.88 kJ/mol respectively. Activation energy

will be greater for the larger liquids and for the rigid polymer chain with stronger

cohesive energy. On the other hand, the heat of sorption is a composite parameter,

which involves contribution from Henry’s law mode with the endothermic reaction

contribution and Langmuir’s (hole filling) type sorption giving the exothermic heats

of sorption. This is due to the degree of interaction between PU-alkane being different

for different membrane - penetrant systems. Activation energy, EP will be higher as

compared to ED for PU-penetrant systems, because of higher degree of cohesive

energy in polymer chain. Those liquids, which exhibit lower values of D have shown

higher values of activation parameter ED and vice versa.

Figure 7.6. Plot of ln P versus 1/T for CA based CEPU for different n-alkane penetrants

l/T X 103 (K−1)

ln P

216

Table 7.4. Activation energy for diffusion (ED, kJ/mol), permeation (EP, kJ/mol), enthalpy of sorption (∆H, kJ/mol ± 4) and entropy of sorption (∆S, J mol-1 K-1 ± 1)

for MA and CA based CEPUs with n-alkane systems

Property n-Alkanes Sample

ED EP ∆H ∆S

MA 9.88 32.70 22.82 -22.82 Hexane

CA 8.19 30.86 22.67 -21.96

MA 10.50 24.80 14.30 -14.21 Heptane

CA 10.60 25.58 14.98 -14.99

MA 9.49 20.61 11.12 -11.12 Octane

CA 11.00 34.42 23.42 -23.36

MA 14.80 23.39 8.59 -8.57 Nonane

CA 28.60 35.88 7.28 -22.05

7.4.5 Thermodynamic parameters

The equilibrium sorption constants Ks, were calculated from the following

equation;

KS = Number of moles of penetrant sorbed / Unit mass of the polymer (14)

The calculated Ks values are given in Table 7.5. A systematic decrease in Ks values

with increasing molecular volume of n- alkanes was observed, suggesting an inverse

dependency of Ks on molecular volume of n- alkanes. This is because larger size

occupies more free volume than smaller molecules. A plot of ln Ks versus 1/T for

both CEPUs in octane is shown in Figure 7.7. It was noticed that the plots are linear

within the temperature interval of 25-60 oC. The values of ∆H and ∆S were calculated

from the figure and they are given in Table 7.4.

The enthalpy of sorption is calculated from the equation;

∆HS = EP − ED (15)

∆HS is a composite parameter involving the contribution from, (i) Henry’s law

needed for the formation of a site and the dissolution of the species into that site, the

formation of the site involves an endothermic contribution and (ii) Langmuir’s (hole

filling) type sorption mechanism, in which case the site already exists in the polymer

matrix and sorption by hole filling gives exothermic heat of sorption.

217

Figure 7.7. van’t Hoff’s plot of ln KS versus 1/T for both CEPUs in octane

The positive ∆HS values for CEPUs suggest a Henry’s type sorption and the

negative ∆HS value suggests a Langmuir type sorption. There is no systematic

variation of ∆HS with respect to penetration size. The calculated ∆S values from the

van’t Hoff plots are negative for all PU-alkane systems suggesting that solvent

molecules retain their liquid-state structure even in the sorbed state.

Table 7.5. Equilibrium sorption constant (KS) of CEPUs in n-alkanes

Ks x 102 (m mol/g) Sample

Temp. (oC) Hexane Heptane Octane Nonane

25 7.22 9.52 9.82 12.96

40 14.27 15.91 14.03 13.75 MA

60 19.03 17.63 15.87 15.66

25 7.74 10.05 9.15 9.71

40 15.00 14.82 13.35 11.73 CA

60 19.98 22.24 24.57 24.28

7.5 Conclusions

The work described in this section, summarizes the molecular transport of n-alkane penetrants into two carboxylic acids (CA and MA) based CEPU membranes by the gravimetric sorption method in the temperature intervals at 25, 40 and 60 oC. The sorption and diffusion tendencies of both CEPUs are different for different

ln K

S

l/T X 103 (K−1)

218

penetrants. The Fickian model has been used to estimate the diffusion coefficient transport data. The values of n lie in the range 0.48 – 0.59 suggesting that the molecular transport is Fickian mode. It was observed that factors such as solvent type, the chemical structure and morphology of the PU seem to exert tremendous influence on the transport characteristics. It was also observed that the diffusion mechanism followed the Fickian trend and that the kinetics of sorption is of the first order. Diffusion data and related activation parameters for the process of diffusion follow the principle of Eyring’s theory of activated diffusion of molecules into the PU network structures. It is also observed that, the sorption-coefficient values for both PU membranes increases with increasing molecular volume of penetrants and the

sequence is; nonane > octane > heptane > hexane. The estimated ∆HS values are

positive and lie in the range 22.82-7.28 kJ/mol. The ∆HS values of CEPUs suggest that the sorption process is dominated by Henry’s law mode. Furthermore, such studies are useful for a preliminary screening of the polymers before their intended applications in technological and engineering sectors.

PART B - Molecular transport behaviour of substituted aromatic solvents with CEPUs

In this section, molecular transport characteristics of hexamethylene diisocyanate (HDI) based CEPU (HCA and HMA) membranes with substituted aromatic penetrants (benzene, chlorobenzene and nitrobenzene) have been reported in the temperature range 25–60 °C. Molecular migration depends on the nature of the organic solvent, membrane–solvent interaction, temperature, solubility parameter, molecular volume and free volume available within the polymer matrix. Typical properties of aromatic solvents are given in Table 7.6.

Table 7.6. Some of the characteristic properties of the aromatic solvents

Penetrants Molecular Formula

Molecular weight

Molar volume

(cm3/mol)

Boiling point (oC)

Viscosity (MPa s)

Solubility parameter

(cal/cm3)1/2

Benzene C6H6 78 88.7 80.09 647 9.2

Chlorobenzene C6H5Cl 112 101.3 132.0 830 9.7

Nitrobenzene C6H5NO2 123 102.2 210.0 1980 10.0

219

7.6 Results and Discussion

7.6.1 Transport behavior

Transport behaviour of substituted aromatic penetrants such as benzene,

chlorobenzene and nitrobenzene into CA and MA based CEPU membranes has been

studied at 25, 40 and 60 oC on an immersion weight gain method. The weight gain

during sorption process is expressed as moles of solvent uptake by 100g of the

polymer sample (Ct, mol %) and it was calculated using equation (13). The solvent

uptake was monitored until the specimens attained the equilibrium values. Some

typical plots of sorption curves for CA and MA based CEPUs in nitrobenzene at 25,

40 and 60 oC are presented in Figure 7.8.

The sorption behaviour is a thermodynamic parameter, which depends on the

strength of the interaction in polymer-probe molecule and describes the initial

penetration and diffusion of probe molecules into the polymeric membranes. The

sorption (S) i.e., maximum mass uptake (obtained from the plateau region of the

sorption plots) of CA and MA based CEPUs in nitrobenzene follow the order;

CA>MA. A similar behavior was observed for all penetrants and temperatures. This

could be due to the presence of additional polar groups like -COOH and –OH groups

in CA based CEPU as compared to MA based CEPU, which leads to more interaction

with the polar solvent and hence higher penetrant uptake. During initial sorption

stages, i.e., up to 50% of the completion of the sorption penetrant uptake increased

linearly with t1/2 values.

Deviations from the Fickian sorption are associated with the time taken by the

polymer segments to respond to swelling stress and to rearrange themselves to

accommodate the solvent molecules [68]. This usually results in the sigmoidal shapes

for the sorption curves. Thus, non-Fickian diffusion involves the tension between

swollen (soft segments) and the unswollen (hard segments) parts of CEPU as the

latter tend to resist further swelling. However, during early stages of sorption, the

samples may not reach the true equilibrium concentration of the penetrant and thus,

the rate of sorption builds up slowly to produce slight curvatures as shown in Figures

7.8-7.9.

220

0 20 40 600.0

0.2

0.4

0.6

0.8

1.0 25 OC

t1/2 (min1/2)

Ct/1

00 (m

ol%

) HMA HCA

0 20 40 600.0

0.4

0.8

1.2

1.6 400C

Ct/1

00 (m

ol%

)

t1/2(min1/2)

HMA HCA

0 20 40 60 800.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0 60 0C

t1/2(min 1/2)

Ct/1

00 (m

ol %

)

HMA HCA

Figure 7.8. The mol % uptake versus square root of time for HCA and HMA in

nitrobenzene at different temperatures

221

This is an indication of the departure from the Fickian mode and is further

confirmed from an analysis of sorption data. At later stages of the sorption

experiments, due to the saturation equilibrium, the sorption values for all penetrants at

all temperatures attained plateau regions and values given in Table 7.7.

From the figure, it can also be observed that, the initial portion of the sorption

curves are linear after which the mechanism changes. According to Southern and

Thomas [93], when a polymer interacts with solvents, the surface of the polymer

membrane swells immediately, but the swelling will not take place in the underlying

un swollen material. Thus, a two dimensional compressive stress is exerted on the

surface. The swelling stresses are either relaxed or dissipated by further swelling and

rearrangement of the segments. Diffusion of low molecular weight probe molecules

were found to lead typical phenomena of membrane swelling and physical relaxation.

The dynamic sorption curves of MA and CA based CEPUs with different

aromatic probe molecules at 60 oC are shown in Figure 7.9 respectively. A persual of

the sorption curves given in Figure 7.9 suggests a systematic trend with respect to

molecular volume of penetrants in the sorption behaviour of aromatic probe

molecules. The sorption curve in benzene is found to be lower compared to other

penetrants. This can be attributed to nonpolar nature of benzene which leads to less

interaction with polar CEPU membrane. The sorption and the diffusion process are

influenced by the factors such as molecular size, interaction parameter between the

polymer and solvent and the solubility parameters of the membranes and the solvents.

Here sorption increases with increase in molecular size of the penetrant. There is a

competition between size of the penetrants and the interaction between polymers and

the solvents [67-69]. This is attributed solubility parameter factor. Difference in

solubility parameters overcomes the molecular size and hence, influences the sorption

process [94]. The equilibrium mol % uptake for sorption as a function of molecular

volume and solubility parameter of probe molecules is shown in Figures 7.10 (a)–(b)

respectively.

222

0 10 20 30 40 50 60 700.0

0.4

0.8

1.2

1.6H M A

t1/2(m in 1/2)

Ct/1

00 (m

ol %

)

Benzene Chlorobenzene Nitrobenzene

0 10 20 30 40 50 60 700.0

0.5

1.0

1.5

2.0

2.5

Ct/1

00 (m

ol%

)

t1/2(min 1/2)

HCA

Benzene Chlorobenzene Nitrobenzene

Figure 7.9. Mol % uptake versus square root of time for HMA and HCA in

different solvents at 60 oC

As the solubility parameter of nitrobenzene is closer to the solubility parameter of CEPU the equilibrium mol uptake of nitrobenzene into the CEPU is more. Similarly benzene with low solubility parameter exhibits less sorption into the polymer network. The sequence of sorption behaviour with reference to penetrants is; benzene < chlorobenzene < nitrobenzene. In this experimental investigation significant dependence (linear behaviour) of the solubility parameter of the solvent on the solvent uptake behaviour was noticed. This indicates that there are more interactions between solvent and polymer, which lead to solvation followed by diffusion into membrane.

Recently Siddaramaiah et al [95-96] observed a correlation between sorption coefficient and solubility parameters of probe molecules for IPN-aromatic penetrants. Aithal et al [97] also made a similar kind of observation for PU system. The pattern of curves in Figure 7.10 indicates that there is clear-cut interaction between CEPU and probe molecules that depends on solubility parameter and molecular size.

223

Figure 7.10 (a)-(b). Sorption coefficient (S) as a function of molar volume and solubility parameter of probe molecules for CEPU membranes

Sorption data also serve as a guide to study the effect of temperature on the

observed transport behaviour. The effect of temperature on mol % uptake of

nitrobenzene for CA based CEPU is shown in Figure 7.11. The rate of diffusion and

permeation increases with increase in temperature [98]. The same observation was

noticed for all CEPU-penetrant systems. This effect follows the conventional theory

that at higher temperature an increase in free volume occurs due to an increased

movement of the chain segments of the polyurethane [99-101]. Increase in

temperature reduces the tortuous route of the solvent and also reduces the time

required to attain equilibrium.

(a)

0

30

60

90

120

87 92 97 102

Molar volume (cm3/mol)

Sx10

0 (%

)HCA

HMA

0

30

60

90

120

9.2 9.7 10

Solubility parameter of pobe molecules (cal/cm3)

Sx10

0(%

)

HCA

HMA

224

Figure 7.11. Mol % uptake versus square root of time for HCA in nitrobenzene at different temperatures

From the slope, θ of the initial linear portion of the sorption curves i.e.,

Qt verses t1/2, the diffusion coefficients have been calculated by using equation (4).

The values of D determined in this manner can be regarded as independent of

concentration and are thus applicable for Fickian mode of transport [67, 71, 73-74,

82]. A triple evaluation of D from sorption curves gave us D values with an error of ±

0.004 units at 25 oC ± 0.0048 units at 40 oC and ± 0.0057 units at 60 oC for all

polymer-penetrant systems. These uncertainty estimates regarding diffusion

coefficients suggest that the half times were very reproducible (to within a few tens of

seconds). The calculated values of D are tabulated in Table 7.7 for all CEPU-solvent

pairs. The variation in the diffusion coefficient also depends on the nature of the

penetrant molecules in addition to the structural characteristics of the CEPUs.

The calculated sorption (S), diffusion (D) and permeation (P) coefficients

under investigated temperatures for CEPU-aromatic penetrant systems are given in

Table 7.7. The sorption and diffusion coefficients of MA based CEPU were lower as

compared to CA based CEPU. The sorption values increased with increase in

temperature for all solvents. The sorption and diffusion coefficient values for CEPUs

followed a sequence; benzene < chlorobenzene < nitrobenzene. This can be attributed

0 10 20 30 40 50 60 700.0

0.4

0.8

1.2

1.6

2.0 HCA

Ct /

100

(mol

%)

t1/2 (min1/2)

25oC 40oC 60oC

225

to the increase in molecular volume of the penetrants (Table 7.6). As is well known,

the diffusion process is a thermally activated process. An increase in temperature was

found to increase the diffusion coefficient of the penetrant molecule. It can also be

attributed to the development of micro cracks/voids on the surface and in the bulk of

the materials [102].

Table 7.7. Diffusion (D), sorption (S) and permeation (P) coefficients of CA and MA based CEPUs

The transport of small molecules through polymers generally occurs through a

solution diffusion mechanism, i.e., the solvent molecules are first sorbed by the

polymer followed by diffusion through the polymer. The net diffusion through

polymer depends on the difference in the amount of penetrant molecules between the

two successive layers. Permeation is a collective process of diffusion and sorption and

consequently the permeability of liquid molecules into polymer membrane depends

upon both diffusivity and sorptivity. The calculated permeability coefficient (P)

values are tabulated in Table 7.7 and it follows the order of S, D and P values for

nitrobenzene is highest whereas for benzene it is lowest. This indicates that, solubility

parameter of probe molecules play an important role in P values and thus affinity of

CEPU is more towards nitrobenzene. From Tables 7.6 and 7.7 it is observed that the

sequence of variation of permeability coefficient and solubility parameter of solvents

is in the order: nitrobenzene > chlorobenzene > benzene.

Benzene Chlorobenzene Nitrobenzene

Samples Temp. (oC)

D x 106

± 0.04 (cm2/ sec)

S x

102

(mol %)

P (cm2/ sec mol %)

Dx106

±0.04 (cm2/ sec)

S x 102 (mol %)

P (cm2/ sec)

mol %

D x 106

±0.04 (cm2/ sec)

S x 102 (mol %)

P (cm2/

sec mol %)

25 2.50 0.66 1.67 3.23 0.93 3.04 3.93 0.97 3.93

40 4.52 1.22 5.53 5.05 1.37 6.95 5.72 1.50 8.62 HCA

60 4.90 1.71 8.42 5.72 1.82 10.48 6.12 1.87 11.5

25 2.11 0.37 0.8 3.19 0.66 2.11 3.72 0.78 2.92

40 3.37 1.02 3.45 3.62 1.32 4.79 4.0 1.34 5.37 HMA

60 3.94 1.30 5.19 4.15 1.39 8.30 5.1 1.58 7.98

226

To investigate the type of diffusion mechanism, an attempt was made to

estimate the values of ‘n’ and ‘K’ [86-87]. In order to determine K and n the plots of

ln (Mt/M∞) versus ln t were plotted (Figure 7.12). Figure 7.12 represents a typical plot

for CEPUs in nitrobenzene. The estimated values for the empirical parameters n and

K are given in Table 7.8. The average uncertainty in the estimation of n and K are

around + 0.007 and + 0.009 respectively. The magnitude of n denotes the transport

mode.

40 oC

-2

-1.6

-1.2

-0.8

-0.4

0

4 4.5 5 5.5 6

ln t

ln M

t / M

∞

HMAHCA

Figure 7.12. The plots of ln Mt/M∞ versus ln t for HMA and HCA with

nitrobenzene penetrant at 40 oC

For a normal Fickian mode of transport, where the rate of polymer chain

relaxation is higher compared to the diffusion rate of the probe molecules, the value

of n is 0.5. When n = 1, (non Fickian mode of transport) chain relaxation is slower

than the liquid diffusion. For the Fickian modes of transport, the rate of diffusion of

probe molecules are much less than the relaxation rate of the polymer chains.

Generally rubbers and semi crystalline polymers exhibit the Fickian mode of diffusion

[103]. A general variation of n from a minimum value was observed indicating the

process to be nearly Fickian type. The n values for sorption process lie in the range

0.44-0.54. The lower value of n clearly indicates that the mechanism of molecular

transport of CEPU - aromatic penetrant systems is in the nearly Fickian mode. The

increase of K values with increase in temperature reveals that the interaction of probe

molecules with the polymer is high.

227

Table 7.8. Values of n and K for CA and MA based CEPUs at different temperatures

Penetrant Temp. (oC) Samples n ± 2 Kx102 ± 0.04

(g/g minn)

CA 0.54 3.6 25

MA 0.45 3.5

CA 0.46 5.2 40

MA 0.48 4.0

CA 0.50 7.1

Benzene

60 MA 0.51 5.3

CA 0.45 4.5 25

MA 0.46 3.7

CA 0.45 5.7 40

MA 0.45 4.0

CA 0.51 7.9

Chlorobenzene

60 MA 0.45 5.1

CA 0.53 3.5 25

MA 0.53 3.0

CA 0.52 4.0 40

MA 0.49 3.6

CA 0.44 8.1

Nitrobenzene

60 MA 0.48 5.0

7.6.2 Activation parameters

Temperature plays a very important role in the diffusion of penetrants through

polymeric membrane. As observed elsewhere [96], both D and P are found to increase

with increase in temperature. This is mainly attributed to the creation of additional

free volume because of increase in segmental motion of the polymer chain upon

increase in temperature. Calculation of the activation energy for diffusion (ED) and

permeation (Ep) processes which is estimated from the Arrhenius relation was

prompted by this effect. The Arrhenius plots of ln D and ln P versus 1/T are shown in

228

Figures 7.13 and 7.14 respectively. These plots exhibit linear dependency for all

system. From the Arrhenius plots, the values of activation energy for permeation (EP)

and diffusion (ED) were calculated using the regression analysis (Table 7.9).

Higher ED and EP values were noticed for MA based CEPU as compared to

CA based CEPU. Higher ED values for benzene and lower values for nitrobenzene

sorption process were noticed. The ED and EP sorption process values lies in the range

1.24 -2.79 kJ/mol and 4.46-8.4 kJ/mol respectively. It is also observed that activation

energy (Ep) will be greater for all liquids, because of the higher degree of cohesive

energy in polymer chain.

HCA

-13.2

-12.8

-12.4

-12

-11.6

2.9 3 3.1 3.2 3.3 3.4

1/T X 103 (K-1)

ln D

(cm

2 /sec

)

NitrobenzeneChlorobenzeneBenzene

HMA

-13.2

-12.8

-12.4

-12

2.9 3 3.1 3.2 3.3 3.41/T X 103 (K-1)

ln D

(cm

2 /sec)

NitrobenzeneChlorobenzeneBenzene

Figure 7.13. A plot of ln D versus 1/T for CA and MA based CEPUs in different

aromatic penetrants

229

Figure 7.14. A plot of ln P versus 1/T for CA and MA based CEPUs in different aromatic penetrants

Table 7.9. Values of activation energy for diffusion (ED, kJ/mol), permeation (EP, kJ/mol), enthalpy of sorption, (∆H, kJ/mol ± 3) and entropy of sorption

(∆S, J mol-1 K-1 ± 2) for CA and MA based CEPUs with aromatic probe molecules

Samples Benzene Chlorobenzene Nitrobenzene

ED 2.79 2.37 1.84

EP 6.72 5.14 4.46

∆H 3.90 2.31 2.70 HCA

∆S -47.85 -41.04 -38.87

ED 2.59 1.09 1.24

EP 8.4 5.69 4.64

∆H 5.19 3.08 2.95 HMA

∆S -53.22 -44.74 -40.18

HMA

-14.5

-13.5

-12.5

-11.5

2.9 3 3.1 3.2 3.3 3.4

1/T X 103 (K-1)

ln P

(cm

2 /sec

)

NitrobenzeneChlorobenzeneBenzene

1

HCA

-14

-13

-12

-11

2.9 3 3.1 3.2 3.3 3.41/T x103 (K-1)

ln P

(cm

2 /sec)

NitrobenzeneChorobenzene

Benzene

230

HMA

-6.5

-6

-5.5

-5

-4.5

-4

-3.5

-3

2.9 3 3.1 3.2 3.3 3.4

1/TX103(K-1)

Ln

Ks

BenzeneChlorobenzeneNitrobenzene

-5.5

-5

-4.5

-4

-3.5

-3

2.9 3 3.1 3.2 3.3 3.4

1/TX103(K-1)

Ln

Ks

BenzeneChlorobenzeneNitrobenzeen

HCA

7.6.3 Thermodynamic parameters

The values of ∆H and ∆S are obtained by regression analysis of the plot of ln

Ks versus 1/T (Van’t Hoff plots) (Figure 7.15). These plots are linear within the

temperature interval of 25-60 oC. The calculated values of ∆H and ∆S are given in

Table 7.9. The average estimated error in ∆H is about ± 4 J/mol, whereas for ∆S is

about ± 1 J/mol/K. The ∆H values for all solvent–polymer systems are positive,

suggesting that sorption may be dominated by Henry’s law mode giving an

endothermic contribution. The heat of sorption is a composite parameter, which

involves contribution from Henry’s law mode with the endothermic reaction

contribution and Langmuir’s hole-filling type sorption giving the endothermic heats

of sorption. The ∆S values for all membrane–solvent systems are negative and it lies

in the range -38.87 to -53.22 J/mol K. This suggests that the structure of the solvent

molecules is retained in the sorbed state [68].

Figure 7.15. Van’t Hoff’s plot of ln Ks versus 1/T for all penetrants for (a) MA

and (b) CA based CEPUs

ln K

S ln

KS

231

7.7 Conclusions

The experimental investigation results of sorption and transport of substituted

aromatic penetrants into structurally different CEPUs are reported here. It was

observed that factors such as solvent type and chemical nature of the CEPU seem to

exert tremendous influence on the transport characteristics. The sorption and diffusion

coefficients of substituted aromatic solvents into CA based CEPU is higher compared

to MA based CEPU. The diffusion coefficient (D) and permeation coefficient (P)

were found to increase with increase in molecular volume of the penetrants and

temperature. The solvent uptake values are found to be highest for nitrobenzene at all

temperatures. The effects of solubility parameters of solvents on the transport

phenomenon have been studied. It is found that as the difference in solubility

parameter of solvents and polymer membranes are less, there is an increase in

sorption and permeation coefficients. This indicates that there are more interactions

between solvent and polymer, which lead to solvation followed by diffusion into the

membrane. The values of ‘n’ lie in the range 0.44-0.54 clearly revealing that the

mechanism of transport of aromatic penetrant-CEPU is Fickian mode. The increased

K values with increasing temperature for all penetrants show more interaction

between penetrant and PU membrane.

The diffusion coefficient result suggests that when CEPU membrane is used as

a barrier for aromatic probe molecules, sorption behaviour depends on several factors,

such as nature of membrane, molecular volume, solubility parameter of probe

molecules, temperature and its compatibility with CEPU membranes and their

chemical characteristics.

The activation energy for diffusion (ED) and permeation (EP) were calculated.

The enthalpy (∆H) and entropy (∆S) of sorption values for CEPU – aromatic solvents

were lies in the range 2.31 to 5.19 kJ/mol and -38.87 to -53.22 J mol-1K-1

respectively. For all CEPU- penetrant systems positive ∆H values are observed. The

positive ∆H values indicate that, the sorption is an endothermic process and is

dominated by Henry’s mode, i.e., the sorption proceeds through creation of new sites

or pores in the polymer. The negative values of ∆S implied that solvent structures

were retained even in the sorbed state.

232

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