water sorption and diffusion through saturated polyester and their nano composites synthesized from...

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Water sorption and diffusion through saturated polyester and their

nanocomposites synthesized from glycolyzed PET waste with

varied composition

Sunain Katoch a, Vinay Sharma b, P.P. Kundu a,b,

a Department of Chemical Technology, Sant Longowal Institute of Engineering and Technology, Sangrur, Punjab 148106, Indiab Department of Polymer Science and Technology, University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India

a r t i c l e i n f o

Article history:

Received 7 July 2009

Received in revised form

29 January 2010

Accepted 29 March 2010Available online 1 April 2010

Keywords:

Water transport

Diffusion

Sorption

Glycolyzed PET

Pseudo-Fickian transport

Activation energy

Heat of sorption

a b s t r a c t

A new system of saturated polyester and their nanocomposites synthesized from glycolyzed PET with

varied composition is investigated for the sorption and diffusion studies in water. The kinetics of

sorption is studied by using the equation of transport phenomena. The values of n from transport

equation are found to be below 0.5, showing the non-Fickian or pseudo-Fickian transport in the

polymer. The dependence of diffusion coefficient on composition and temperature has been studied for

all polymeric samples. The diffusion coefficient of saturated polyester samples decreases with an

increase in glycolyzed PET contents. The nanocomposite samples show less diffusion coefficient than

pristine polymer and it decreases with an increase in nano-filler up to 4 wt%. The diffusion coefficient

increases with an increase in temperature for all the samples. The sorption coefficient shows a little

change with variation in composition as well as temperature for all the samples and it is in a range of 1.

The activation energy for diffusion and permeation is positive for all the samples. The heat of sorption is

also positive for all the samples, indicating Henry type mode of sorption.

& 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Usual reactants for the saturated polyesters are a glycol and an

acid or anhydride. It is the family of polyesters in which the

polyester backbones are saturated and hence unreactive as

compared to the more reactive, unsaturated ones. Saturated

polyesters consist of low molecular weight liquids used as

plasticizers and as reactants in forming urethane polymers, and

linear, high molecular weight thermoplastics such as polyethy-

lene terephthalate (Mylar and Dacron). Poly(ethylene terephtha-

late) (PET) is a semicrystalline polymer, with only minor

differences in molecular weight and modifications, PET is used

in textiles (clothes, curtains, and furniture upholstery), reinforce-

ment of tires and rubber goods, and food and beverage packaging(water, soft drink and isotonic beverage bottles, sauce and jam

jars, etc.) (Imai et al., 2002). The incorporation of clay into PET can

result in outstanding property improvement in terms of decreasing

water permeability in food packaging, increasing flame resistance

in textiles, and increasing the modulus in injection molded parts.

This can be done with less clay content than used in most

conventional composites. Conventional fillers have been used to

improve properties and reduce cost; however, there are limitations

in their application due to phase separation, particle agglomera-

tion, and heterogeneous distribution in the product (Carrado,

2003). Small size of clay minerals and clay surface treatments

with chemicals in order to create an affinity between the clay

surface and the polymer, can reduce those problems. According

to Tsai (2000) the addition of layered silicates in PET acts as a

heterogeneous nucleating agent, which increases the overall

crystallisation rate and the crystalline fraction. The fact that clay

particles are impermeable is also expected to improve barrier

properties of the PET nanocomposite to gases and water vapour

(Wang et al., 2004).

When water in liquid or vapor form is absorbed into the

polymer; water molecules fill the voids that are formed betweenpolymer chains and then induce relaxation, or swelling of the

polymer (Adhikari and Majumdar, 2004; Kondratowicz et al.,

2001; Buchold et al., 1999; Pradas et al., 2001; Turner, 1982).

Water affects polymers in ways that are unique in comparison to

any other substance (Pradas et al., 2001; Nogueira et al., 2000).

The study of water sorption in polymers is important for many

applications. For example, polymers are used in the coatings

industry. Coatings are also important in the food industry (Lange

and Wyser, 2003; Chirife and Buera, 1996; Arvanitoyannis, 1999).

Water is probably the single most important factor in governing

microbial spoilage in foods. Therefore polymers that are excellent

barriers for water are needed for packaging.

ARTICLE IN PRESS

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/ces

Chemical Engineering Science

0009-2509/$- see front matter & 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ces.2010.03.050

Corresponding author at: Department of Polymer Science and Technology,

University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India.

E-mail address: [email protected] (P.P. Kundu).

Chemical Engineering Science 65 (2010) 43784387
http://-/?-http://www.elsevier.com/locate/ceshttp://dx.doi.org/10.1016/j.ces.2010.03.050mailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.ces.2010.03.050http://www.elsevier.com/locate/ceshttp://-/?-


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Sorption and diffusion of the solvents in and through polymers

have been widely investigated from both theoretical as well as

experimental point of view (Gouanve et al., 2007; Hansen, 2004;

Tanigami et al., 1995; Lobo et al., 1996; Valente et al., 2005;

Pereira et al., 2009). The swelling technique is a commonly used

method to determine various coefficients such as diffusion,

sorption, and permeability coefficient (Zhu et al., 2006; Detallante

et al., 2002; Kumar et al., 1985; Han et al., 1995; Singh et al.,

2005). In swelling experiments, the polymer of known dimensionis dispersed in a solvent, and the solvent mass uptake versus time

is recorded and the data are used to calculate the various

coefficients. These coefficients give an idea about the use of

polymers in various applications, such as membranes, ion-

exchangers, controlled release systems, packaging, microchip

manufacturing, etc. There are very few patents on the application

of PET nanocomposites for barrier properties (Barbee et al., 2000;

Williamson et al., 2006).

In the present study, the saturated polyester synthesized from

glycolyzed PET with varied compositions and their nanocompo-

site are studied using Fickian model. The activation energy for

diffusion (ED) and for permeation (EP) is calculated by using

standard Arrhenius relationship. The variation in sorption is

studied with respect to time and temperature. The objective of the

present work is to study the sorption and diffusion. Kinetics of the

saturated polyester synthesized from glycolyzed PET waste and

their nanocomposites with an alteration in the composition and

clay contents. The effect of various parameters on the polymer

samples are studied by using transport equation and Arrhenius

relationship.

2. Experimental

2.1. Materials

Discarded PET bottles from soft drinks were procured from

scrapers, cleaned thoroughly and cut into small pieces (6 mm 6

mm). Zinc acetate, minimum assay 99%, ethylene glycol (EG),

diethylene glycol (DEG) and styrene were procured from E. Merck

(India) Pvt. Ltd., Bombay. Phthalic anhydride (TA) was obtained

from CDH (India). Montmorillonite (K-10), dodecyl trimethyl

ammonium bromide (DTAB), cetyl-trimethyl ammonium bromide

(CTAB) were purchased from Aldrich Chemical Company (Mil-

waukee, MI) and used as received.

2.2. Synthetic work

2.2.1. Modification of montmorillonite

Montmorillonite was modified by the same method used in

previous study (Sharma et al., 2008). Cetyl trimethyl ammonium

bromide (CTAB) or dodecyl trimethyl ammonium bromide (DTAB)was used for the modification of clay. The CEC (cation exchange

capacity) calculated from the titre value for CTAB was 29.92 and

for DTAB 152.84 meq/100 gm of clay.

2.2.2. Glycolysis of PET waste

Glycolysis of PET scrap has been done in a 1000 mL five-necked

reactor equipped with a reflux condenser, an inert gas inlet, a

mechanical PTFE blade stirrer and a thermocouple linked to a

temperature regulation device. Molar ratio of PET repeating

unit to glycol has been taken 1:2, respectively. The mixture of

diols DEG:EG was charged in the ratio 50:50, respectively.

Zn(CH3COO)2 was used as trans-esterification catalyst. Then, the

reactants were heated in the temperature range from 120 to

1401

C for first 3h and then at 1801C for subsequent 5h. The

whole reaction was carried out in inert atmosphere (argon

atmosphere) under reflux with constant stirring.

2.2.3. Synthesis of saturated polyester from glycolyzed PET

Initially, a reference resin (blank) was synthesized by direct

esterification (Samant and Ng, 1999; Yang et al., 1996; Ravin-

dranath and Mashelkar, 1982a,b; Chegolya et al., 1979; Kemkes,

1970; Mellichamp, 1970). This reaction was a heterogeneous

reaction with monomers of phthalic anhydride and ethyleneglycol. The mixture of monomers was charged as slurry, because

TA was hard to dissolve in EG. The TA:EG molar ratio used is

1:1.12 and the reaction temperature was usually 150180 1C.

The reaction was carried out in a five-necked reaction kettle

equipped with a mechanical stirrer, inlet to inert gas (argon),

thermometer, and condenser. The reactor was purged with argon

for 15 min, before heating was switched on. Then, the contents

were heated under argon atmosphere to 1801C until approxi-

mately 15 mL of water were collected. In the commercial reaction,

some PET prepolymer (BHET) is added in order to shorten the

reaction time. Pre-polymer produced from the direct esterifica-

tion reaction was gradually heated to 200 1C. In this step, EG was

collected as a byproduct. The overall reaction time, including the

esterification and the polycondensation processes, was long andusually varies from 5 to 10h (Ravindranath and Mashelkar,

1982a, b; Chegolya et al., 1979).

The above experiment was repeated by replacing the ethylene

glycol with glycolyzed PET (GPET) by 100:0, 80:20, 60:40, 50:50, and

40:60 percent, respectively. The nomenclature used in this work is

based on the original composition of reactants (shown in Table 1).

2.2.4. Synthesis of saturated polyester/clay nanocomposites

The saturated polyester nanocomposites (GPET waste) were

prepared by heating the desired mixture of phthalic anhydride,

ethylene glycol, GPET and modified montmorillonite clay in a five

necked reaction kettle. The modified nano-filler of a predeter-

mined quantity was dispersed in a reaction mixture. The detailed

compositions are reported in Table 1. The dispersion wasmaintained by constant mechanical stirring at 500 rpm (overnight

for proper intercalation). The mixture was heated at 120 1C for 3h,

followed by at 150200 1C for 34 h. The whole mass was

transferred to an appropriate mould. The photographs of the

nanocomposite prepared are shown in Fig. 1.

2.2.5. Swelling experiments

The samples were cut into circular form using a die of 10 mm

diameter. The thickness of the sample was measured by means of

a screw gauge. The dry samples were weighed on an electronic

balance (Citizen, CX 220) and then kept in the solvent in screwed

bottles. The samples were taken out of the solvent at specific

intervals and the excess solvent was rubbed off. The samples were

then weighed and again immersed in the solvent till equilibriumwas attained (i.e. 72 h). The time for measuring weight of the

sample was kept minimal (about 30 s), so that the escape of the

solvent from the sample remains negligible. Equilibrium swelling

experiments were carried out at 20, 30, 40 and 50 1C (71 1C) to

study the effect of temperature on the swelling. For temperatures

higher than room temperature, the samples were kept in a

microprocessor controlled hot air oven.

The mole percent uptake (Qt) at each time interval was

calculated by using (Ajithkumar et al., 1998).

Qt MtMr

100

Mi1

where Mt is the mass of the solvent taken up at time t, Mr is the

relative molecular mass of the solvent and Mi is the mass of the

S. Katoch et al. / Chemical Engineering Science 65 (2010) 43784387 4379


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dry sample. The mole percent uptake at 72 h is taken as swelling

at infinite time (QN

).

3. Results and discussion

3.1. Swelling of polymer samples

The mole percent uptake of the solvent is plotted against

square root of time. The plot for the mole percent uptake is shown

in Fig. 2 for saturated polyester with varied GPET composition at

25 1C. It is observed that the swelling of the saturated polyester

decreases with an increase in the GPET contents. The sample

containing 50% GPET shows a minimum swelling, whereas the

neat sample (without GPET) shows a maximum swelling. In the

present case, the decrease in the water uptake with an increase in

the GPET contents can only be explained by an increase in the

rigid part with an increase in the GPET content, resulting in more

rigid chains. It is well known that incorporation of rigid bulky

groups such as an aromatic ring in the chain makes the polymer

more stiff and rigid. Moreover, the bulky group resulted in a great

hindrance to the chain rotation and thus, reduced the chain

flexibility. Depolymerization of PET with ethylene glycol (EG)

(Baliga and Wong, 1989; Goje and Mishra, 2003; Campanelli et al.,1994; Kao et al., 1997; Chen and Chen, 1999; Chen et al., 2001)

leads to bis hydroxy ethyl terephthalate (BHET) and PET

oligomers. The insertion of depolymerized PET, which is the

mixture of hydroxyl terminated monomer and oligomers, results

in more rigid and stiff backbone of resulting polymeric chain. It is

observed that beyond 50% GPET content the water uptake starts

increasing. It is possibly due to the decrease in the extent of

reaction with increase in the GPET content beyond 50%.

Fig. 3 shows the sorption curves for the nanocomposite

samples at 251C. Fig. 3a shows sorption for the saturated

polyester samples with varying GPET contents at 4% modified

montmorillonite clay. The maximum and minimum water uptake

is shown by samples having 60% and 50% GPET content at 4%

nano-clay (CTAB modified), respectively. The remaining samples

Table 1

Detailed composition of the saturated polyester and their nanocomposite with varied glycolyzed PET content.

Sample ID Glycolyzed PET/(%) Ethylene glycol/(%) Montmorillonite Clay/(%)

STD PET 0 100 0

GPET20 20 80 0

GPET40 40 60 0

GPET50 50 50 0

GPET60 60 40 0

GPET50(2)CTAB 50 50 2(CTAB)GPET50(3)CTAB 50 50 3(CTAB

GPET50(4)CTAB 50 50 4(CTAB




GPET(60)4CTAB 60 40 4(CTAB

GPET50(4)DTAB 50 50 5(DTAB)

Fig. 1. The photographs of prepared nanocomposites.

Fig. 2. The sorption curve for saturated polyester with varied GPET composition at

25 1C.

S. Katoch et al. / Chemical Engineering Science 65 (2010) 437843874380


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show intermediate swelling. Fig. 3b shows the sorption curves for

the samples with varying montmorillonite contents from 0% to 5%

at similar composition. For the samples containing varying nano-

clay at 50% GPET composition, the maximum and minimum

swelling is observed for the samples with 5% and 4% clay content

(modified by CTAB), respectively. It is observed that a sample with

5% nano-filler shows high solvent uptake. This may be due to

the high nano-clay content, resulting in the accumulation of

clay at the interface, hence, reducing the barrier properties ofthe nanocomposite. The clay (montmorillonite) is modified by

two surfactants, cetyl trimethyl ammonium bromide (CTAB) and

dodecyl trimethyl ammonium bromide (DTAB). The sample

modified by CTAB (surfactant) shows relatively less swelling

than GPET50 (4) modified by DTAB. It is because of inserting long

chain surfactant (CTAB) into the hydrophilic galleries of the native

clay, the interlayer distance increases, and the surface chemistry

of the clay is modified. These newly rendered organophilic

galleries show less affinity to water.

It is evident from Figs. 2, 3a and 3b, for all polymeric samples a

two stage sorption is followed (a non-Fickian diffusion case). It is

due to a quasi-equilibrium, which first reaches rapidly at the

polymer surface and then by simple diffusion throughout the

polymer sample (Bagley and Long, 1955). The second stage of

sorption is associated with an increase in surface concentration,

which occurs slowly compared to the diffusion process and is the

rate-determining factor for sorption. The concentration is vir-

tually uniform throughout the sheet and increases at a rate,

independent of the thickness. From recent works, a better

rationalization of these anomalous behaviors has been achieved,where contributions from the effect of macroscopic elastic

constraints arising during the swelling process (geometrical

effects) in adsorption experiments have been pointed out (Rossi,

1996). Initially, the sample is completely dry and immersed in the

wet environment (penetrant). The diffusion of penetrant starts

instantaneously and the sample starts swelling. The dry (non-

swollen) core of the sample exerts a compressive stress on the

outer wet (swollen) layers, hindering the diffusion (Samus and

Rossi, 1996). Since the core is still dry, the only direction to which

the sample is allowed to swell is perpendicular to the surface

(stage I). This is proved by the fast increase in thickness of the

sample, compared to the square root increase of the area. As the

diffusion front penetrates the sample, the reducing force is less

prominent and ultimately disappears, when the diffusion front

reaches middle of the sample. At this point, the swelling of the

sample is free to commence in all directions (stage II) and the

diffusion rate increases, until it levels off (close to the dissemina-

tion point).

Fig. 4 shows the sorption curve for STDPET, sample with 50%

GPET content and its nanocomposite at different temperatures.

For STDPET sample the water uptake is a maximum at 55 1C

and decreases with decrease in temperature. The GPET-50%

sample shows a minimum swelling at 251C and a maximum

swelling at 551C. It is observed that the swelling increases with an

increase in temperature. This is due to the fact that the polymer

chain shows higher segmental mobility with an increase in

temperature, hence accommodating higher amount of the solvent.

The nanocomposite sample GPET-50-4% shows reverse order for

swelling with an increase in the temperature. It has maximum

swelling at low temperature and minimum swelling at high

0 1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Qt/(mol%)

(Time)1/2 / hr

STDPETGPET20-4 (CTAB)GPET40-4 (CTAB)GPET50-4 (CTAB)GPET60-4 (CTAB)GPET50-4 (DTAB)

0 1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Qt/(mol%)

GPET50

GPET50-2 (CTAB)

GPET50-3 (CTAB)

GPET50-4 (CTAB)

GPET50-5 (CTAB)

GPET50-4 (DTAB)

(Time)1/2 / hr

Fig. 3. The sorption curves for nanocomposite samples at 25 1C. (a) For samples

with variation in GPET composition, and (b) for samples with variation in clay

contents.

0 1 2 3 4 5 6 7 8 9 10

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

GPET50-4-@25C

GPET50-4-@35C

GPET50-4-@45C

GPET50-4-@55C

GPET50@25C

GPET50@35C

GPET50@45C

GPET50@55C

STDPET@25C

STDPET@35C

STDPET@45C

STDPET@55C

Qt/(mol%)

(Time)1/2 / hr

Fig. 4. The sorption curve for saturated polyester (STDPET, GPET50), and

nanocomposite sample (GPET50-4) at different temperatures.



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temperature. It is due to fact that the layered nano-fillers have

platelet like structure, which improves the barrier properties of

the polymer (Lu and Mai, 2005). The platelets due to the rise in

temperature are then evenly distributed into the polymer matrix,

creating multiple parallel layers. These layers force the solvent

molecules to flow through the polymer in a torturous path,

forming complex barriers to the solvent molecules. The detailed

process is shown in Scheme 1. The filler platelets are

impenetrable for the diffusing solvent molecules. Therefore,

when compared to the parent polymer, a decrease in the

diffusion of the solvent in the nanocomposites is observed.

In order to find out the mechanism of swelling, the diffusion

data are fitted into an empirical equation (Eq. (3)), George et al.

(1999) derived from the equation of transport phenomena(Ajithkumar et al., 1998)

QtQ1

ktn 2

lnQt

Q1 ln k n ln t 3

where Qtand QN are the mole percent uptake of solvent at time t

and at infinity or equilibrium. k is a constant, which depends

upon the solvent-polymer interaction and the structure of the

polymer. For all the samples, the regression coefficient (r) varies

between 0.95 and 0.99. The values of constant k and n obtained

from the Eq. (3) and QN

are reported in Tables 2 and 3. The value

of n gives an idea of the mechanism of sorption (Crank, 1975).For the value of n as 0.5, the mechanism of swelling is termed as

Fickian transport. This occurs, when the rate of diffusion of

solvent is smaller than polymer segmental mobility. If the value of

n is not equal to 0.5, then the transport is considered as non-

Fickian. In particular, if n1, the transport is called case II

transport (Crank, 1975). It is a special case, where the solvent

front moves with constant velocity. If n lies between 0.5 and 1,

then it is called anomalous transport (Crank, 1975). For non-

Fickian transport, diffusion is more rapid than the polymer

relaxation rate. For anomalous transport, the diffusion and

relaxation rates are comparable (Crank, 1975). If sorption is less

than 0.5, then it is termed as pseudo-Fickian transport. It is

characterized by initial curvature of the Qt versus t1/2 plots out of

the origin concave to the time axis (Rogers, 1985; Windle, 1985).

From Tables 2 and 3, the values of n are below 0.5, indicating

the transport as non-Fickian or pseudo-Fickian transport.

In glassy polymers, deviations from this ideal Fickian behavior

are often observed. These deviations are generally believed to

arise as a consequence of the finite rate of polymer structure

reorganization in response to penetrant-induced swelling during

the sorption-diffusion process (Rogers, 1985). The penetrant may

sorb in the polymer in two stages, an initial Fickian-like stage

d

LW

Solvent

Scheme 1. The schematic representation of tortuosity-based model to describe

the solvent diffusion in the nano-clay filled polymer composite. ( Wis the width or

thickness and L is the length of the filler platelet. d is the thickness of the polymer

matrix, through which the solvent molecules diffuse).

Table 2

Values of mole percent uptake at infinite time ( QN), n, k and standard deviation

(SD) for different samples at 25 and 35 1C.

Temperature/(1C) Sample ID QN /(mol %) n K SD

25 STD PET 0.667 0.168 0.721 0.029

GPET20 0.659 0.173 0.752 0.036

GPET40 0.648 0.175 0.767 0.032

GPET50 0.505 0.141 0.599 0.014

GPET60 0.587 0.140 0.595 0.023GPE T50(2)C TAB 0.497 0.158 0.677 0.016

GPE T50(3)C TAB 0.460 0.151 0.635 0.022

GPE T50(4)C TAB 0.454 0.149 0.666 0.030

GPE T50(5)C TAB 0.505 0.09 8 0.423 0.015

GPE T20(4)C TAB 0.645 0.180 0.773 0.026

GPE T40(4)C TAB 0.562 0.139 0.575 0.018

GPE T(60)4C TAB 0.676 0.09 3 0.386 0.008

GPE T50(4)DT AB 0.460 0.09 4 0.394 0.014

35 STD PET 0.723 0.177 0.791 0.033

GPET20 0.689 0.178 0.789 0.042

GPET40 0.675 0.182 0.806 0.032

GPET50 0.525 0.141 0.599 0.013

GPET60 0.623 0.158 0.667 0.028

GP ET50(2) CTAB 0.46 5 0.177 0.749 0.020

GP ET50(3) CTAB 0.44 5 0.153 0.648 0.022

GP ET50(4) CTAB 0.42 3 0.160 0.716 0.036

GP ET50(5) CTAB 0.48 7 0.098 0.421 0.013GP ET20(4) CTAB 0.65 4 0.176 0.752 0.026

GP ET40(4) CTAB 0.53 4 0.135 0.563 0.022

GP ET(60)4 CTAB 0.65 7 0.123 0.530 0.012

GP ET50(4) DTAB 0.44 7 0.102 0.439 0.010

Table 3

Values of mole percent uptake at infinite time ( QN

), n, k and standard deviation

(SD) for different samples at 45 and 55 1C.

Temperature/(1C) Sample ID QN

/(mol %) n K SD

45 STD PET 0.754 0.176 0.808 0.041

GPET20 0.695 0.172 0.752 0.037

GPET40 0.687 0.180 0.800 0.034

GPET50 0.556 0.133 0.572 0.011GPET60 0.654 0.158 0.666 0.029

GPE T50(2)C TAB 0.447 0.178 0.754 0.022

GPE T50(3)C TAB 0.427 0.148 0.622 0.025

GPE T50(4)C TAB 0.411 0.141 0.633 0.031

GPE T50(5)C TAB 0.456 0.09 8 0.419 0.012

GPE T20(4)C TAB 0.634 0.182 0.783 0.029

GPE T40(4)C TAB 0.511 0.126 0.517 0.021

GPE T(60)4C TAB 0.648 0.117 0.497 0.016

GPE T50(4)DT AB 0.412 0.104 0.432 0.010

55 STD PET 0.767 0.176 0.819 0.045

GPET20 0.721 0.179 0.805 0.041

GPET40 0.697 0.182 0.799 0.034

GPET50 0.565 0.141 0.619 0.016

GPET60 0.667 0.157 0.651 0.031

GP ET50(2) CTAB 0.42 3 0.185 0.782 0.025

GP ET50(3) CTAB 0.401 0.150 0.628 0.025

GP ET50(4) CTAB 0.38 7 0.151 0.681 0.037GP ET50(5) CTAB 0.43 2 0.097 0.410 0.012

GP ET20(4) CTAB 0.61 2 0.191 0.835 0.040

GP ET40(4) CTAB 0.49 8 0.138 0.574 0.015

GP ET(60)4 CTAB 0.66 7 0.121 0.541 0.021

GP ET50(4) DTAB 0.39 8 0.093 0.407 0.012



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followed by a protracted drift towards a final equilibrium value

(McDowell et al., 1999). In another departure from Fickian

sorption kinetics, the penetrant weight uptake may be a linear

function of contact time until equilibrium is reached ( Moaddeb

and Koros, 1995). When penetrant sorption is accompanied

by significant swelling of the polymer, any time dependent

resistance to changes in the volume of the polymer can lead to

non-Fickian sorption kinetics. As the penetrant swells the

polymer, local stresses are built up when the chains disentanglefrom each other. These stresses can be quite high, and can, infact,

cause mechanical failure in the polymer.

The rate limiting step for penetrant diffusion is the creation

of transient gaps in the polymer matrix via local scale

polymer segmental dynamics involving several polymer chains

(Muller-Plathe, 1994). Penetrant molecules vibrate inside local

cavities in the polymer matrix at frequencies much higher than

the frequency of polymer chain motion required to open a gap of

sufficient size to accommodate the penetrant. These steps are

shown schematically in Scheme 2. In 2A, a penetrant molecule is

shown dissolved in a polymer matrix. The penetrant vibrates

inside a gap or molecular scale cavity in the polymer matrix

at very high frequency (ca. 1012 vibrations/s or 1 vibration/

picosecond) (Muller-Plathe, 1994). The polymer molecules do not

occupy the entire volume of the polymer sample. Due to packing

inefficiencies and polymer chain molecular motion, some of the

volume in the polymer matrix is empty or free and this so-

called free volume is redistributed continuously as a result of the

random, thermally stimulated molecular motion of the polymer

segments (Ghosal and Freeman, 1994).

In 2B, local polymer segmental motion has opened a connect-

ing channel between two free volume elements in the polymer

matrix and the penetrant molecule can, as a result of its own

Brownian motion, explore the entire corridor between the initial

free volume element which it occupied and the second free

volume element which is connected to it via the opening of a

transient gap in the polymer matrix. Eventually, local segmental

motion of the polymer segments closes the connection between

the two free volume elements and if the penetrant happens to be

away from its original position, as shown in 2C, when the gap in

the polymer matrix is closed, the penetrant will be trapped in

another free volume element in the polymer matrix and will have

executed a diffusion step. The process shown in Scheme 2 has

been called the Red Sea mechanism of penetrant transport in

dense polymers (Muller-Plathe, 1994).

The swelling data are used to calculate the diffusion coefficient(D), which is a measure of the ability of the solvent molecules to

move through the polymer and the sorption coefficient (S), which

gives an idea about the equilibrium sorption. The diffusion

coefficient (D) is calculated as (Ajithkumar et al., 2000)

D phy

4Q1

24

where p3.14; h is the thickness of the dry sample and y is the

slope of the initial linear portion of the curve QtversusOt; and QNis the mole percent uptake of the solvent at infinite time.

The sorption coefficient (S) is calculated as (Ajithkumar et al.,

2000)

S

M1

Mp 5

where MN

is the mass of the solvent uptake at equilibrium and Mpis the mass of the dry sample. The sorption and diffusion

coefficients are used to calculate permeability coefficient (P) of

the samples, which is given by (Ajithkumar et al., 2000)

P D S 6

The values of these coefficients are reported in Tables 4 and 5.

It is observed that for saturated polyester samples synthesized by

varied GPET content, STDPET sample shows the highest and the

GPET50 sample shows the lowest diffusion coefficient. The

diffusion coefficient of the vary GPET samples decreases with an

increase in the GPET content from 20% to 50% (Tables 4 and 5). It

is due to an increase in the rigid part with an increase in the GPET

content (a mixture of monomer and oligomer), resulting in more

rigid chains thereby, decreasing the diffusion of solvent in

the polymer network. The diffusion coefficient increases with

an increase in the temperature for all varied GPET samples.

The decrease in the diffusion coefficient is due to the insertion of

phthalic anhydride moiety in the polymer chain. An increase in

the GPET content, results in incorporation of rigid bulky groups,

such as an aromatic ring in the chain makes the polymer stiffer

and rigid, hence shows less affinity to water. The sorption

coefficient values decrease with an increase in the GPET

content. Likewise, diffusion coefficient, the sorption coefficient

values increase with an increase in the temperature. The increase

in sorption is quite small and almost equal to one for all samples

at all temperatures. This indicates that there is very less change in

the sorption properties with variation in GPET contents as well astemperature. The permeability in the samples shows the same

trend as that for diffusion coefficient.

For the nanocomposite samples with varied GPET content at

fixed organically modified nano-clay (4%), the diffusion coefficient

decreases with an increase in GPET content (Tables 4 and 5). It is

observed that a maximum and a minimum diffusion coefficient

values are shown by the samples GPET60(4) (CTAB modify), and

GPET50(4), respectively. The sorption coefficient decreases with an

increase in the GPET content up to 50% and increases with an

increase in the temperature. The permeability in the samples is

observed to show a similar trend as that for the diffusion coefficient.

For the nanocomposite samples with varied nano-clay from 0%

to 5% at fixed GPET content, the diffusion coefficient decreases

with an increase in the nano-clay content up to 4%. GPET50(5)

Scheme 2. The schematic representation of the penetration of solvent molecules

in the polymer matrix.



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ARTICLE IN PRESS

(CTAB modify) shows a maximum and GPET50(4) shows a

minimum diffusion coefficient. With an increase in the nano-

clay, the decreasing values of the diffusion coefficient are due to

the incorporation of the nano-clay that increases the barrier

properties. The platelet like structure with a high aspect ratio can

be expected to improve the resistance towards low molecular

weight solvent molecules. It is expected that a high loading of

nano-clay is more effective for the solvent resistance, but the

polymer with 5% filler shows high diffusion coefficient value even

more than that for the sample without clay (GPET50). This may be

due to the high nano-clay contents, resulting in the accumulation

of clay at the interface. This behavior is just like ordinary filler.

The higher filler contents (5%) reduce the barrier properties of the

nanocomposite. Therefore, the sample shows distortion, instead

of swelling after 12 h.

An increase in the temperature results in an increase in the

diffusion coefficient for all the samples. The sorption coefficient

for all the samples shows a decrease with an increase in GPET

content up to 50% and 4% nano-clay content. This indicates that

the solvent assimilation or the ability to absorb solvent decreases

due to the incorporation of nano-filler. This indicates the good

compatibility of the nano-clay and polymer matrix. The perme-

ability coefficient shows similar trends as is for diffusioncoefficient.

Diffusion and permeation are thermally activated processes,

and their temperature dependence can be used to calculate the

activation energy for the process of water absorption. The

activation energy for diffusion (ED) and for permeation (EP) is

calculated by using standard Arrhenius relationship (Eq. (8))

(George and Thomas, 2001; George et al., 1996).

XXoe-EX=RT 7

logX logXo-EX=2:303:RT 8

where X represents either D or P, Xo is a constant representing

either Do or Po. EX is either ED or EP, which depends upon the

swelling process under consideration. From the linear plot of logX

Table 4

Diffusion coefficient (D), sorption coefficient (S) and permeability coefficient (P) in

water for different samples at 25 and 35 1C.

Temperature/(1C) Sample ID D/(107 cm2/s) S (g/g) P/(107 cm2/s)

25 STD PET 33.50 0.120 4.02

GPET20 33.10 0.118 3.90

GPET40 31.32 0.116 3.63

GPET50 31.13 0.091 2.83

GPET60 32.46 0.105 3.40GPET50(2)CTAB 29.48 0.089 2.62

GPET50(3)CTAB 29.16 0.082 2.39

GPET50(4)CTAB 27.63 0.081 2.23

GPET50(5)CTAB 33.02 0.090 2.97

GPET20(4)CTAB 31.39 0.116 3.64

GPET40(4)CTAB 30.77 0.101 3.10

GPET(60)4CTAB 32.01 0.121 3.87

GPET50(4)DTAB 30.32 0.082 2.48

35 STD PET 33.89 0.130 4.40

GPET20 33.56 0.124 4.16

GPET40 31.81 0.121 3.84

GPET50 34.76 0.094 3.26

GPET60 47.66 0.112 5.33

GPET50(2)CTAB 30.00 0.083 2.49

GPET50(3)CTAB 29.87 0.080 2.38

GPET50(4)CTAB 29.65 0.076 2.25

GPET50(5)CTAB 33.54 0.087 2.91GPET20(4)CTAB 31.90 0.117 3.73

GPET40(4)CTAB 32.96 0.096 3.16

GPET(60)4CTAB 33.55 0.118 3.95

GPET50(4)DTAB 33.21 0.080 2.65

Table 5

Diffusion coefficient (D), sorption coefficient (S) and permeability coefficient (P) in

water for different samples at 45 and 55 1C.

Temperature/(1C) Sample ID D/(107 cm2/s) S (g/g) P/(107 cm2/s)

45 STD PET 34.32 0.135 4.63

GPET20 34.42 0.125 4.30

GPET40 31.98 0.123 3.93

GPET50 35.89 0.100 3.58

GPET60 47.95 0.117 5.61

GPET50(2)CTAB 30.43 0.080 2.43

GPET50(3)CTAB 31.38 0.076 2.38

GPET50(4)CTAB 30.61 0.073 2.23

GPET50(5)CTAB 38.44 0.082 3.15

GPET20(4)CTAB 33.19 0.114 3.78

GPET40(4)CTAB 34.08 0.091 3.10

GPET(60)4CTAB 34.73 0.116 4.02

GPET50(4)DTAB 34.57 0.074 2.55

55 STD PET 35.77 0.138 4.93

GPET20 34.51 0.129 4.45

GPET40 32.57 0.125 4.07

GPET50 37.76 0.101 3.81

GPET60 48.47 0.120 5.81

GPET50(2)CTAB 31.64 0.076 2.40

GPET50(3)CTAB 33.34 0.072 2.40


GPET20(4)CTAB 33.73 0.110 3.71

GPET40(4)CTAB 33.52 0.089 2.98

GPET(60)4CTAB 31.09 0.120 3.73

GPET50(4)DTAB 35.12 0.071 2.49

0.0030 0.0031 0.0032 0.0033 0.0034

-5.50

-5.45

-5.40

-5.35

-5.30

LogD

STDPETGPET20GPET40GPET50GPET60

0.0030 0.0031 0.0032 0.0033 0.0034

-6.55

-6.50

-6.45

-6.40

-6.35

-6.30

-6.25

Log

P

STDPETGPET20GPET40GPET50GPET60

1/T / (K-1)

1/T / (K-1)

Fig. 5. The plot of log D and log Pversus inverse of temperature (1/T) for saturated

polyester with varied GPET composition.



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ARTICLE IN PRESS

versus 1/T, the values of EX can be calculated. Figs. 57 give the

plot of log D and log P versus 1/T for different polymer samples.

The values of ED and EP calculated from Figs. 5 and 6 are shown

in Table 6. The regression coefficient values in estimation

are between 0.92 and 0.99. The heat of sorption (DHS) is also

calculated by using the Eq. (9) (George and Thomas, 2001; George

et al., 1996)

DHS EP-ED 9

The values of DHS provide additional information about the

transport of solvent molecules through the polymer matrix. Thevalues of DHS are given in Table 6. All the values are positive,

indicating Henry type sorption in the majority (endothermic

contribution to the sorption process) (Aminabhavi et al., 1996).

This type of sorption is concerned with the formation of a hole of a

molecular size in the polymer matrix (Aminabhavi et al., 1996).

The activation energy for diffusion is the energy needed to enable

the dissolved molecules to jump into another hole. The positive

activation energy of diffusion for all the polymer samples

indicates a high energy requirement to jump from one hole to

another. It is observed that for polyester samples with an increase

in GPET content, the activation energy goes on increasing. STDPET

sample has the lowest and GPET60 sample has the highest values

ofED. For nanocomposite samples at fixed GPET (50%) content, ED

value increases with an increase in the clay loading.

4. Conclusion

A new system of saturated polyester and their nanocomposites

synthesized from glycolyzed PET with varied composition is

investigated for the sorption and diffusion studies in water. The

kinetics of sorption is studied by using the equation of transport

phenomena. The values of n in solvent transport equation are

found to be below 0.5, showing the non-Fickian or pseudo-

Fickian transport in the polymer. The dependence of diffusion

0.0030 0.0031 0.0032 0.0033 0.0034

-6.8

-6.6

-6.4

-6.2

-6.0

-5.8

-5.6

LogP

STDPETGPET20-4 (CTAB)GPET40-4 (CTAB)GPET50-4 (CTAB)GPET60-4 (CTAB)GPET50-4 (DTAB)

1/T / (K-1)


polyester with varied GPET content at 4% nano-clay.

0.0030 0.0031 0.0032 0.0033 0.0034

-5.56

-5.54

-5.52

-5.50

-5.48

-5.46

-5.44

-5.42

-5.40

L

ogD

GPET50GPET50-2 (CTAB)GPET50-3 (CTAB)GPET50-4 (CTAB)GPET50-5 (CTAB)GPET50-4 (DTAB)

0.0030 0.0031 0.0032 0.0033 0.0034

-6.8

-6.6

-6.4

-6.2

-6.0

-5.8

-5.6

LogP

GPET50

GPET50-2 (CTAB)

GPET50-3 (CTAB)

GPET50-4 (CTAB)

GPET50-5 (CTAB)

GPET50-4 (DTAB)

1/T / (K-1)

1/T / (K-1)


polyester with varied nano-clay content at fixed composition.

Table 6

Arrhenius parameters and heat of sorption for different polymers in water.

Sample ID ED/(102 kJ/mol) EP/(10

2 kJ/mol) DHS/(102 kJ/mol)

STD PET 5.04 16.09 11.05

GPET20 5.07 10.42 5.35

GPET40 8.98 8.90 5.92

GPET50 15.01 23.98 8.97

GPET60 22.78 24.79 2.01

GPET50(2)CTAB 5.44 10.65 5.21

GPET50(3)CTAB 10.86 15.49 4.63

GPET50(4)CTAB 11.94 79.98 68.04

GPET50(5)CTAB 15.11 17.69 2.58


GPET(60)4CTAB 8.016 37.74 29.724

GPET50(4)DTAB 11.76 12.24 0.48



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ARTICLE IN PRESS

coefficient on composition and temperature has been studied for

all polymeric samples. The diffusion coefficient in saturated

polyester samples decreases with an increase up to 50%

glycolyzed PET content. The nanocomposite samples show less

diffusion coefficient than pristine polymer and it decreases with

an increasing in nano-filler up to 4% by weight. The diffusion

coefficient increases with an increase in temperature for all

polymer samples. The sorption coefficient shows a little change

with variation in composition as well as temperature for all thesamples and it is in a range of 1. STDPET sample has the lowest

and GPET60 sample has the highest values of ED. For nanocompo-

site samples at fixed GPET (50%) content, ED value increases with

an increase in the clay loading. The activation energy for diffusion

and permeation is positive for all the samples. The heat of

sorption is also positive for all the samples, indicating Henry type

mode of sorption.

From the diffusion studies it can be concluded that these

polymer nanocomposites can find numerous applications in the

food processing industries, the barrier to the vapors is a

prerequisite. These nanocomposites can be used in rigid food

and beverage containers due to their barrier properties, proces-

sibility and formability, ecological and toxicological character-

istics, and economics.

Appendix A. Supplementary material

Supplementary data associated with this article can be found

in the online version at doi:10.1016/j.ces.2010.03.050.

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