Permeability of Polymer Clay Nano composites

European Polymer Journal 45 (2009) 967–984

Contents lists available at ScienceDirect

European Polymer Journal j o u r n a l h o m e p a g e : : w w w . e l s e v i e r . c o m / l o c a t e / e u r o p o l j

Macromolecular Nanotechnology – Review

Permeability of polymer/clay nanocomposites: A review G. Choudalakis Choudalakis , A.D. Gotsis *

Department of Sciences, Technical University of Crete, GR-73100, Hania, Greece

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 26 June 2008 Received in revised form 12 January 2009 Accepted 14 January 2009 Available online 30 January 2009

This is a review of the existing studies on the permeability of gas molecules in nanocomposite materials that consist of inorganic platelet-shaped fillers in polymeric matrices. We describe the dominant mechanisms for the transport of small molecules in polymers and polymer nanocomposites, as well as the procedures for the measurement of the permeability and the diffusivity. The emphasis is given on the various models that have been proposed posed for the prediction prediction of permeability permeability in polymer–cl polymer–clay ay nanocompos nanocomposites. ites. The influence influence of the characteristics of the inorganic particles on the barrier properties of the composite membrane is discussed and tested using the model and the available experimental data. Some aspects on the methods of improving the barrier properties of the nanocomposite are examined and a few applications applications of these materials materials as gas barriers are presented.  2009 Elsevier Ltd. All rights reserved.

Keywords: Gas permeability Barrier properties Permeation models Nano-clay Nanocomposite

Contents

1. 2.

3.

4.

Introd Introduct uction ion:: Nanocom Nanocompos posite itess with phyll phyllos osili ilicat cate e reinfor reinforcem cement ent and and polymer polymeric ic matrix matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The The meas measur urem emen entt of the the per perme meab abil ilit ity y............. .............. ................ .............. .............. 2.1. 2.1. Dire Direct ct mea measu sure reme ment nt in in a cell cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. 2.2. Sorpt Sorptio ion/ n/de deso sorp rpti tion on exp exper erim imen ents. ts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Mass tra trans nspo port rt in pol polym ymer ers. s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. 3.1. Free Free volum volume e and dif diffu fusi sion on in in amorp amorpho hous us pol polym ymer erss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. 3.2. Semi Semicr crys ysta talli lline ne pol polym ymer erss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The The perm permea eabi bili lity ty of of nano nanoco comp mpos osit ites es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. 4.1. Regu Regula larr arran arrange geme ment nt of of paral paralle lell nanop nanopla late tele lets ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. 4.2. Rand Random om spa spati tial al posi positi tion onin ing g of para parall llel el plat plates es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. 4.3. Arrang Arrangeme ements nts at angles angles  90  to the the main main diffu diffusi sion on dire direct ctio ion n. ..... .... .... ..... .... ..... .... .... ..... .... 4.4. 4.4. Infl Influe uenc nce e of the the int inter erfa faci cial al reg regio ions. ns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. 4.5. Infl Influe uenc nce e of the the par parti ticl cle e aggr aggreg egat atio ion n....................... ............... .............. ............... 4.6. 4.6. Expe Experi rime ment ntal al and and nume numeri rica call valid validat atio ion n of the the mode models. ls. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Using Using PALS PALS to study study the the permeab permeabili ility ty of polym polymers ers and and nanoco nanocompo mposit sites. es. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Meth Method odss to infl influe uenc nce e the per perme meab abil ilit ity y of the the nano nanoco comp mpos osit ite e.... ..... ..... ..... ..... ..... .... ..... .... .... ..... . 6.1. 6.1. Electr Electrica ically lly modul modulate ated d permeab permeabili ility ty using using side-c side-chai hain n liquid liquid crysta crystalli lline ne polyme polymers. rs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. 6.2. Improv Improving ing the the barrier barrier prope propertie rtiess using using reactiv reactive e additiv additives es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low permea permeabil bility ity nano nanocom compos posite ite coat coating ingss and othe otherr applica applicatio tions ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conc Conclu lusi sion onss and and reco recomm mmen enda dati tion ons. s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ackn Acknow owle ledg dgem emen ents ts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Refe Refere renc nces es . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6¼

5. 6.

7. 8.

*

Corresponding author. E-mail address: gchoudalakis [email protected] @isc.tuc.gr (G. (G. Choudalakis).

0014-3057/$ - see front matter  2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.eurpolymj.2009.01.027

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Y G O L O N H C E T O N A N R A L U C E L O M O R C A M

968

G. Choudalakis, A.D. Gotsis / European Polymer Journal 45 (2009) 967–984

1. Introduction: Nanocomposites with phyllosilicate reinforcement and polymeric matrix


Nanocomposites materials are two phase systems that consist of a polymeric matrix and dispersed inorganic particles of nanometer scale. The most common inorganic particles belong to the family of 2:1 phyllosilicates. Their crystal structure (Fig. 1) [1] consists of an aluminium or magnesium hydroxide octahedral sheet sandwiched between two silicon oxide tetrahedral sheets. The layer thickness of each platelet is around 1 nm, and their lateral dimensions may vary from 30 nm to several microns. The layers are located on top of each other like the pages of a book. Van der Waals gaps are created between the layers, called galleries. The isomorphic substitution of the tetrahedral or octahedral cations, e.g. the substitution of Al3+ with Mg2+ or Fe2+ with Li1+, generates negative charges that are counterbalanced by alkali and alkaline earth cations located inside the galleries. In the case of tetrahedral substitution, the negative charge is located on the surface of the silicate layers and, thus, the polymer matrices can interact more readily with tetrahedral than with octahedral substituted material. Two particular characteristics of layered silicates play an important role in the creation of nanocomposites: the first is the ability of silicate sheets to disperse into individual layers, and the second is the possibility to modify their surface chemistry through ion exchange reactions with organic and inorganic cations. The simple mixing of polymer and layered silicates does not always result in the generation of a nanocomposite, as this usually leads to dispersion of stacked sheets. This failure is due to the weak interactions between thepolymer and theinorganic component. If these interactions become stronger, then the inorganic phase can be dispersed in the organic matrix in nanometer scale. The layered phyllosilicate particulates usually contain Na+ or K+ ions and are only compatible with hydrophilic polymers, such as poly(vinyl alcohol). To render the layered silicates compatible with non-polar polymers one must convert the hydrophilic silicate surface to organo-

philic. This can be achieved by ion exchange reactions with cationic surfactants including primary, secondary, tertiary, and quaternary alkylammonium cations or phosphonium cations which contain various substituents. At least one of these substituents must be a long carbon chain of 12 carbon atoms or more, in order to make the clay mineral compatible with the polymer [2–4]. The alkylammonium cations lower the surface energy of the inorganic reinforcement, improve the wetting characteristics of the polymer matrix, and result in larger interlayer spacing (swelling). Additionally, the alkylammonium cations can provide functional groups that react with the polymer matrix or, in some cases, can initiate the polymerisation of monomers to form the polymer in-situ [5]. The phyllosilicate particles present a very high aspect ratio of width/thickness, in the order of 10–1000. For very low concentrations of particles, the total interface between polymer and layered silicates is much greater than that in conventional composites. Depending on the strength of the interfacial interaction, four types of morphology are possible in nanocomposites (Fig. 2) [1]: aggregated; intercalated; flocculated; and exfoliated. The main goal for the successful development of claybased nanocomposites is to achieve complete exfoliation of the layered silicate in the polymer matrix. The three most common methods that are used for the preparation of a polymer-nanocomposite are: (1) Intercalation in a suitable monomer and subsequent in situ polymerisation that leads to exfoliation. (2) Intercalation of polymer from solution and exfoliation. (3) Polymer melt intercalation and exfoliation. Recent reviews of the methods that are used for the synthesis of polymer–clay nanocomposites can be found in [6,7]. The nanocomposites have become an area of intensive research activity. The first reason for this development is

Fig. 1. The crystal structure of the phyllosilicates [1].

969


Fig. 2. Schematic representation of three types of polymer/clay nanocomposites [1].

their high mechanical properties. The complete dispersion of clay nanolayers in a polymer optimises the number of available reinforcing elements that carry an applied load and deflect the evolving cracks. The coupling between the large surface area of the clay and the polymer matrix facilitates the stress transfer to the reinforcing phase allowing for the improvement of the tensile stress and toughness [8–10]. The second major advantage of the nanocomposites is their enhanced barrier properties. The impermeable clay layers force a tortuous pathway for a permeant transversing the nanocomposite. It is reported that gas permeability through polymer films can be reduced by 50–500 times even with small loadings of nanoclays. The relevant research on polymer–clay nanocomposite concerns mostly oxygen, carbon dioxide and nitrogen barrier films, a.o., for packaging food and carbonated drinks. Other applications include gas tanks and coatings.

tion of the gas in the membrane, c x; t , reaches a steady distribution, J t reaches the steady state flux, J 1 . In a flat membrane of thickness d, J 1 depends on the (constant) gas pressure, P 0 :

ð Þ

ðÞ

¼ K P d : 0

J 1

ð2:2Þ

The constant of proportionality, K , is the permeability coefficient. Eq. (2.2) is a special case of the fundamental law of diffusion:

ð Þ ¼ Drc ð ; t Þ;

J r ; t

ð2:3Þ

r

When the flux density and the concentration vary with time, one has to solve also the time dependent diffusion (Fick’s) equation in a semi-infinite body:

D

r c ð ; t Þ ¼ c ð t ; t Þ : 2

o

r

r

ð2:4Þ

o

The 1D solution applicable in the experiments shown in Fig. 3 is subject to the following conditions [11]:

2. The measurement of the permeability

The permeation of gases through an organic membrane, such as a polymer film, is a complex process that consists of four processes: the sorption of gas molecules on the surface of the membrane; the dissolution of the gas inside the membrane; the diffusion through it; and, finally, the desorption of gas from the other surface of the membrane. The permeability coefficient, K (in mol Pa1 m1 s1), is the product of the diffusion coefficient, D (in m2 s1), and the sorption coefficient or solubility, S (in mol m3 Pa1):

K D S :

¼ 

t 0 The entire cell is initially under vacuum. The gas is introduced suddenly, at t 0, into the volume V 0 at pressure P 0 ; thus c x; t 0 0 (Fig. 3). t > 0 The compartment V 0 is kept at constant pressure, P 0 . The solubility of the gas in the membrane is the ratio of its concentration to the external gas pressure, when these two phases are in equilibrium. The

¼

¼ ð ¼ Þ ¼

x=0

ð2:1Þ

The permeability can be measured directly using a permeation cell, or indirectly in sorption/desorption experiments.

P0 ,V 0

2.1. Direct measurement in a cell

A c0

For the direct measurement of the permeability, one can use an arrangement such as shown in Fig. 3. A membrane separates the cell into two compartments. The gas is introduced in the compartment V 0 (left hand side in Fig. 3) under constant pressure P 0 . The flux density J t (in mol m2 s1) of the gas in the other compartment is monitored at constant temperature. The evolution of J t reflects the non-steady state process. When the concentra-

ðÞ ðÞ

P0 ,V

x=d

P0

P0

c0

cd (t)

cd (t) c(x,t) d

x

Fig. 3. Experimental cell for the measurement of the permeability. A membrane, with thickness d and area A, divides the cell in two chambers. The gas is introduced in volume V 0 under constant pressure, P 0 . The concentration of the test gas is c 0 on the left surface of the membrane and c d t on the right surface.The concentration of the gas inside the membrane is c x; t .

ðÞ

ð Þ


970


surface of the membrane that is exposed to the gas under pressure P 0 will absorb or dissolve the gas, until the concentration of dissolved gas reaches the saturation value, c 0 , given by Henry’s equation; thus c x 0 ; t c 0 S P 0 .

cd (t)

ð ¼ Þ ¼ ¼ 

The boundary value of c at the surface of the membrane on the side of volume V is considered zero, so c x d; t 0. A solution of (2.4) for a flat membrane is [12]:

ð ¼ Þ ¼

c x; t

"

x d

ð Þ ¼ SP 1   0

2 1 1 mp x sin exp p m¼1 m d



X

2

d

steady state

#

m2 p2 Dt

:

ð2:5Þ

At x d Eq. (2.3) for 1D gives the flux of the gas that permeates the membrane:

¼

ð Þ ¼ DSP d

0

J t


" X þ 1

1

2cos mp exp



m 1

¼



#

m2 p2 Dt 2

d

t0

Fig. 4. Typical diagram of experimental measurements. The time lag is estimated from the extrapolation of the steady state line.

ð2:6Þ

:

t

Eq. (2.6) becomes at steady state ( t

J 1

! 1):

P 0 DS ; d

J t

ð Þ ¼ 2SP 

ð2:7Þ

¼ 

which gives back Eq. (2.1) when compared to Eq. (2.2). By integrating Eq. (2.6) from time 0 to t , and since J t dc = Adt , with A the area of the membrane, one obtains the concentration, c d t (in mol/m3), at the right hand side of the experimental cell:

ðÞ¼

2

2

d 2d t  ð Þ ¼ ADSP  Vd 6D p D 0

c d t

2

1

X  ð Þ m 1

¼

1

m

2

ðm p Dt =d

exp

2

m2

2

# Þ

ð2:8Þ

For long times Eq. (2.8) becomes:

ð Þ ¼ ADSP ðt  t Þ Vd 0

c d t

0

with

t 0

¼

ð2:9Þ ð2:10Þ

The characteristic time t 0 is a measure of the time that is required to establish a constant flow. If we plot c d vs. t for sufficiently long times to reach a linear response, then we can determine the time lag, t 0 , as shown in Fig. 4, and the diffusion coefficient D from Eq. (2.10). The slope of the line gives the product D S , i.e. the permeability coefficient. This is a simple and direct way for the determination of the coefficients D , S and K . In practise, it is only necessary to introduce gas in volume V 0 , and record the mass flux in volume V as a function of time, until a straight line appears. Then the straight line is extrapolated and the time lag is determined. In spite of the simplicity of the calculations, the above method has practical difficulties because t 0 is very large in many cases. Indeed, the diffusion coefficient for small gas molecules in most polymers is about 10 6–109 cm2/ s. For polyethylene or polystyrene the diffusion coefficient is about 108 cm2/s and a membrane of these polymers with 1 mm thickness requires approximately two days to reach steady state. An alternative solution for Eq. (2.3) was proposed by Rogers et al. [11]:





2

d 2m 4Dt

ð þ 1Þ

2

#

ð2:11Þ

:

:

ln t 1=2 J t

f  ð Þg ¼ ln

"  #  2SP 0

D

p

1=2

2

d : 4Dt

ð2:12Þ

Plotting the left hand side of Eq. (2.12) against the reciprocal time we obtain a straight line. The diffusion coeffi2 cient can be calculated from the slope of this line ( d =4D). The permeability measurements are often conducted in a Wicke–Kallenbach device similar to the cell in Fig. 3 [13]. A mixture of gases (e.g. CO 2 and N2) is introduced in the left chamber, while the right chamber is fed with a pure, reference gas (e.g. N 2). Both chambers remain at the same pressure. The outlet stream from the right chamber consists of the reference gas i.e. N 2, and the test gas, i.e. CO2, that permeates through the membrane. This stream is fed to a mass spectrometer or analyser in order to determine the permeate concentration. Two types of experiments can be established. First, if the time lag is relatively small (i.e. diffusion coefficient in the order of 10 6 cm2 =s, or membrane thickness in the order of 100 lm, or both) one can perform the steady state experiment using Eq. (2.9). Otherwise a transient experiment should be performed using Eq. (2.12). It has been reported [14] that the diffusion coefficient measured at steady state differs from the one that is extracted from transient experiments because of the existence of deadend pathways in the membrane. In some cases the permeation measurements are conducted using pressure difference between the two compartments of the cell in order to accelerate the process. The diffusion coefficient calculated from this kind of experiments does not reflect the actual diffusion process due to the existence of an external driving force.



2

d : 6D

D 1 exp pt m¼1

For short times Eq. (2.11) can be approximated by ignoring all but the first term of the sequence. Multiplying then with t 1=2 and taking the logarithm on both sides one gets:

ðÞ

"

0

r ffiffi ffi X "

971


2.2. Sorption/desorption experiments

Sorption/desorption experiments are used to measure both the diffusion coefficient and the solubility and, therefrom, the permeability using Eq. (2.1). In the simplest form of such an experiment, the membrane remains initially under vacuum and the gas is introduced and maintained at constant pressure. The gas is dissolved and diffuses into the membrane, and the weight gain is estimated with a balance. The fractional mass uptake is reported as a function of time. Assuming a flat membrane of thickness d and uniform concentration of the gas in the membrane there are two possible solutions for Eq. (2.4) [15]: M t M 1 M t M 1

s ffiffi ffi " X  !# ffiffi þ ð Þ ð Þ p ¼ " ð þÞ # X ¼    Dt 1

8

2

p

2

d

1

md

m

1 ierfc

m 0

¼

8 1 1 1 exp 2 p m¼0 ð2m þ 1Þ2

4 Dt

2

1 p t

D 2m

2

d

ð2:13Þ

;

1=2

2

;

ð2:14Þ

where M t and M 1 are the mass uptakes at times t and , and ierfc is the error function integral. Eq. (2.13) converges rapidly for short times and can be approximated then by:

1

M t M 1

8

¼p

1=2

Dt



1=2

2

d

ð2:15Þ

:

p ffiffi

By plotting M t =M 1 against t =d we obtain a straight line until t 1=2 , the half life time when M t =M 1 1=2 (Fig. 5). The diffusion coefficient is calculated from the slope of this line. Alternatively, Eq. (2.14) converges rapidly for long times. Keeping, then, only the first term and taking the logarithms on both sides one obtains a straight line in the form:

¼

M t M 1

8

   ¼   

ln 1

ln

p

2

p2 Dt 2

d

:

ð2:16Þ

By plotting the right hand side against t we can calculate D from the slope of this line.

Applying the above methods, the diffusion coefficient can be determined in isothermal and isobaric sorption/ desorption experiments. These methods present, however, an uncertainty in the time interval over which they are valid. A more detailed description of methods that are used to extract the diffusion coefficients from gravimetric data is presented in [16,17]. The solubility coefficient is found by measuring the concentration ofthe solublegas asa functionof pressure.In general, the total concentration, C , of gas molecules absorbed in a macroscopicallynon-porousglassypolymer consistsof the gas molecules in the dissolved state or Henry’s population, C d , and the Langmuir population, C H , which represents the adsorption of gas molecules into the micro-voids or freevolume holes that exist in the glass [18]:

C C d

¼ þ C

H

C d

¼ k P ;

:

H

ð2:17Þ

with k d the solubility coefficient, P the partial pressure of the gas, and C 0H and b the hole saturation and hole affinity constants. Henry’s law, which describes the sorption behaviour of C d , is similar to the case of swelling in rubbers, where solvent molecules dissolve among the polymer chains and swell the polymer matrix. The Langmuir holes, on the other hand, are considered to be non-equilibrium defects and their sizes and numbers depend on the thermal history. The coefficients k d , b and C 0H can be determined by fitting the experimental isotherms with Eq. (2.17) [19].

3. Mass transport in polymers 3.1. Free volume and diffusion in amorphous polymers

Gas permeation in a membrane is a complex process and has two main stages: initially the gas molecules are adsorbed on the surface of the membrane, and then they diffuse through the membrane. During adsorption, the gas molecules are positioned in the free volume holes of the polymer that are created by Brownian motions of the chains or by thermal perturbations. The diffusion process occurs by jumps through neighbouring holes. Thus, it depends on the number and the size of these holes (static free volume) and on the frequency of the jumps (dynamic free volume). The static free volume is independent of thermal motions of the macromolecules and is related to the gas solubility, while the dynamic free volume originates from the segmental motions of the polymer chains and is related to the gas diffusivity. Thus, the diffusion coefficient is a kinetic factor that reflects the mobility of the gas molecules in the polymeric phase, while the solubility coefficient, S , is a thermodynamic factor related to the interactions between the polymer and the gas molecules. The latter is associated with the specific free volume, v f [20]:

  ¼ qS ;

v f

v

v 0

g

Fig. 5. Typical diagram of sorption/desorption experimental measurements. The curve is linear in the initial stage until t 1=2 which is the half time for sorption.

d

0

¼ 1C þbP ; bP

C H

ð3:1Þ

where v is the specific volume, v 0 is the occupied specific volume and q g is the density of sorbed gas. The fractional free volume is defined as:


972


¼ ¼ qS v f

f

v

v

g v

ð3:2Þ

:

The average radius of the holes, R, can be calculated assuming identical spherical holes arranged in a cubic lattice with constant a :

R

¼ a

r ffiffi ffi ffi 3

3 f : 4p

ð3:3Þ

v

The fractional free volume can be determined experimentally, e.g. by Positron Annihilation Lifetime Spectroscopy (PALS) [21]. Some details on the use of this method to study the permeability in polymers and nanocomposites are given in Section 5. The diffusion coefficient of a gas in a polymer depends on the free volume in the matrix, the molecular diameter of the gas, a , and the velocity of the gas molecules, u, [22]:

D ¼ ga  u exp


cv 0

  v f

ð3:4Þ

;

where g is a geometric factor and c is a factor related to the overlap of free volume, i.e. the degree to which more than one molecules may access the same free volume. Regrouping the constants Eq. (3.4) can be written in the form:

D

¼ A exp

B : f

 

ð3:5Þ

v

The temperature dependence of D and S is of the Arrhenius type:

D

¼ D

0

E d ; kT

 

exp

S S 0 exp

¼

DH s

  kT

;

ð3:6Þ

where E d is the activation energy for diffusion and DH s is the heat of sorption. Therefore, for the permeability:

K K 0 exp

¼



E d

þ DH

s

kT



:

þ

¼ pnr RT Ds‘DP ; 2

K

ð3:8Þ

where n is the number of pores, r is their radius, s is the tortuosity factor, ‘ is the membrane thickness and DK is the Knudsen diffusion coefficient given by:

DK

r ffiffi ffi ffi ffi

¼ 0:66r

8RT ; pM

In semicrystalline polymers, the size and the shape of the crystallites, the crystal structure and the degree of crystallinity have an important influence on the permeation process. The basic assumption is that the crystallites consist of a phase impermeable for gas molecules and the diffusion occurs only in the amorphous phase. The adsorption of gases in amorphous polymers is described by Henry’s law:

c SP :

ð3:9Þ

with M the molecular weight of the gas. From Eq. (3.9) it can been seen that the diffusion coefficient is inversely proportional to the molecular weight of the gas. Thus, membranes where Knudsen flux is dominant are used for gas separation.

ð3:10Þ

¼

For semicrystalline polymers:

S S 0 1 /c ;

ð3:11Þ

¼ ð  Þ

where S 0 is the solubility coefficient of the amorphous phase, and /c is the volume fraction of the crystalline phase. Obviously, for purely crystalline phase, S 0. Eq. (3.11) is applicable to most semicrystalline polymers. It is assumed in this case that the presence of crystallites leaves the amorphous phase unaffected [24]. The crystallites have two different effects on the diffusion process. They act as impermeable barriers to the gas molecules, forcing them to follow longer paths. This is included in the tortuosity factor, s. Additionally, the presence of the crystals can immobilise side-chains in the amorphous phase and, thus, reduce the free volume there, resulting in higher activation energies for diffusion. This influence can be included in an immobilisation factor, b, [25]:

¼

D

¼ Dbs : 0

ð3:12Þ

In combination with Eq. (3.5) this gives

D

ð3:7Þ

where E d DH s is the total activation energy for permeation. Since DH s is often negative, the permeation activation energy is less than the E d . The free volume theory neglects the diffusion through the pores. When the pore size is between 0.002 and 0.05 lm, then the main transport mechanism is Knudsen flux [23]:

J K

3.2. Semicrystalline polymers

¼ bAs  e

B f v

ð3:13Þ

The chain segment immobility factor b is given by:

¼ exp

b

h   p ffiffi ffi i k d

/L =2

2

ð3:14Þ

where k is independent of the penetrant, d is the diameter p ffiffiffiffiffi of the penetrant and /L =2 is approximately equal to the mean unoccupied distance between two chain segments. Increasing the crystallinity leads to an increase in the factor b because the mean unoccupied distance decreases. 4. The permeability of nanocomposites

The mass transport mechanism of gasses permeating a nanoplatelet reinforced polymer is similar to that in a semicrystalline polymer. In most theoretical treatises the nanocomposite is considered to consist of a permeable phase (polymer matrix) in which non-permeable nanoplatelets are dispersed. There are three main factors that influence the permeability of a nanocomposite: the volume fraction of the nanoplatelets; their orientation relative to the diffusion direction; and their aspect ratio. It is generally accepted that the transport mechanism within the polymer matrix follows Fick’s law, and that the matrix maintains the same properties and characteris-

973


Fig. 6. Influence of the degree of delamination on the tortuosity factor and the aspect ratio of nanoplatelets [26]. W is the thickness of the stacks.

tics as the neat polymer. Therefore, a decrease of the solubility is expected in the nanocomposite due to the reduced polymer matrix volume, as well as a decrease in diffusion due to a more tortuous path for the diffusing molecules. The reduction of the diffusion coefficient is higher than that of the solubility coefficient. Indeed, the volume fraction of nanoplatelets is low and, thus, the reduction of the matrix volume is small. The major factor, then, is the tortuosity, which is connected directly to the shape and the degree of dispersion of the nanoplatelets. The degree of dispersion of the nanoplatelets is determined by the degree of delamination of the clay. The fully delaminated (exfoliated) nanocomposite presents much higher values for the tortuosity factor and the aspect ratio in comparison with the partially delaminated (intercalated) nanocomposite (Fig. 6) and it is much more effective to be used in barrier membranes for gasses. The terms intercalated and exfoliated layered silicate nanocomposites are often used to describe two extreme states of silicate layer organisation in the composite morphology. Intercalation implies the insertion of polymer chains in the galleries of the initial layered tactoids. This leads to a longitudinal expansion of the galleries. Exfoliation implies complete breakage of the initial layer stacking order and homogeneous dispersion of the layers in the polymer matrix. Several models have been developed in order to describe the mass transfer within the nanocomposites. Most models assume that the platelets have a regular and uniform shape (rectangular, sanidic or circular) and form a regular array in space. They are either parallel to each other or have a distribution of orientations with the average orientation at an angle to the main direction of diffu-

sion of the gas molecules. Some of these models are outlined in the following. 4.1. Regular arrangement of parallel nanoplatelets

One of the first attempts to describe the permeability of membranes, where a second phase is dispersed in a regular arrangement, was made by Barrer and Petropoulos [27]. These authors calculated the diffusion through a regular array of parallelepipeds of a second phase dispersed in a matrix with a different diffusion coefficient. When this approach is applied in the case of dispersed impermeable thin plates, the change of the permeability is found to be proportional to the fractional cross section (slit) that is available for the diffusant to move forward and depends on the tortuosity of the path. A simple permeability model for a regular arrangement of platelets has been proposed by Nielsen [28] and is presented in Fig. 7. The nanoparticles are evenly dispersed and considered to be rectangular platelets with finite width, L , and thickness, W . Their orientation is perpendicular to the diffusion direction. The solubility coefficient of this nanocomposite is:

S S 0 1 / ;

¼ ð  Þ

ð4:1Þ

where S 0 is the diffusion coefficient of the neat polymer, and / is the volume fraction of the nanoplatelets that are dispersed in the matrix. In this approximation the solubility does not depend on the morphological features of the phases. The platelets act as impermeable barriers to the diffusing molecules, forcing them to follow longer and more tortuous

Fig. 7. Regular arrangement of orthogonally shaped platelets in a parallel array with their main direction perpendicular to the diffusion direction.


974


paths in order to diffuse through the nanocomposite. The diffusion coefficient, D, is influenced by the tortuosity, s:

¼ Ds ; 0

D

ð4:2Þ

where D0 is the diffusion coefficient of the matrix. The factor s depends on the aspect ratio, the shape and the orientation of the nanoplatelets, and it is defined as

s

‘ 0 ‘

ð4:3Þ

where ‘ 0 is the distance that a solute must travel to diffuse through the membrane when nanoplatelets are present and ‘ is the membrane thickness. From Eqs. (2.1), (4.1) and (4.2):

K composite K matrix


¼ 1 s / :

ð4:4Þ

The prolonged diffusion length ‘0 is estimated as follows: Each nanoplatelet contributes to the enhancement of the diffusion length by L =2 on the average. If N is the mean number of nanoplatelets that a solute encounters as it diffuses through the membrane, then:

h i

‘0

¼ ‘ þ hN i L2 :

ð4:5Þ

h i ¼ ‘/=W , the factor s becomes:

Since N

s ¼ 1 þ

L /: 2W

ð4:6Þ



Eq. (4.4), then, gives:


¼ 11þ a // ;

ð4:7Þ

2

where a L =W is the aspect ratio of the nanoplatelets. This equation shows that the permeability of the nanocomposite decreases with the increase of / and a . In practise however, the limit for its validity is / 6 10%, because the particles have a tendency to aggregate, which increases with /. From the most common nanoparticles, such as synthetic mica, montmorillonite, laponite and vermiculite, the last one is believed to have the highest aspect ratio and is the most efficient for the reduction of K composite. The predictions of this model for different values of the aspect ratio, a, are shown in Fig. 8. The diffusion through a multiperforated single laminae was studied by Wakeham and Mason [29]. These authors found that the resistance to diffusion through such a membrane had a contribution from the need of the diffusant to enter the constriction into the pore/slit, and a contribution due to the length of the pore. This approach was extended by Cussler et al. [30] to multiple layers of parallel platelets of infinite third dimension, separated by slits. The result was:

¼


¼



1

da s a b

2

d b a b

þ ð þ Þþ ð þ Þþ

/ is the volume fraction of the plateda= d s a b lets, d =a a is the particle aspect ratio and s =a r is the slit aspect ratio. Cussler et al. [30] neglected the second term of Eq. (4.8), since it is relatively much smaller, and suggested for narrow slits ( r 1) the following simpler expression for the enhancement of the barrier properties of the membrane:

½ð þ Þð þ Þ ¼ ¼

¼




¼



1

a 2 /2

þ 1  /

!

1

ð4:9Þ

:

This model predicts a rapid reduction of the relative permeability at small values of / [30], in contrast with the model of Nielsen (Eq. (4.7)) [28], which needs either high volume fraction or high aspect ratio for the same reduction. This is probably attributed to the different regions over which the above models are applicable. Two variations of Eq. (4.8) were given by Falla et al. [31] based on Aris [32] and Wakeham and Mason [29]: K composite K matrix K composite K matrix

 ¼ þ  þ  ¼

1

 !  !

4a/ pa2 / a2 /2 a/ 1 ln þ rð1  /Þ 1 / r pð1  /Þ 1 1/ a2 /2 a/ 1þ þ þ 2ð1  /Þ ln 2r/ 1/ r

;

ð4:8Þ where, l is the thickness of the membrane, and the other dimensions are shown in Fig. 9. In this arrangement,

ð4:10Þ ð4:11Þ

The fourth term in Eq. (4.10) was derived from arguments presented in [32]. The same term in Eq. (4.11) was derived based on [29].

1

 !

2b d ln l 2s

Fig. 8. Predictions of Nielsen’s model for the relative permeability as a function of platelets volume fraction for different particle aspect ratios.

Fig. 9. Ribbon arrangement and characteristic parameters.

975


The second term of equations (4.10) and (4.11), that involves a 2 , reflects the contribution of the tortuous path of the diffusant through the plates. The third term is due to the resistance to diffusion of the slits and depends on their aspect ratio, r. The last part represents the constriction from the wide space between the plates into the narrow slits and it should depend on the constriction ratio, a=r, as it is the case in Eq. (4.10). Hexagonal flakes arranged in regular parallel arrays were examined by Moggridge et al. [33]. The same arguments as for Eq. (4.9) were used:


¼



1

2

2 a / þ 27 1  / 2

1

!

ð4:12Þ

The difference due to the specific platelet-shape is reflected by the coefficient (2/27), which reduces the effectiveness of the barrier. 4.2. Random spatial positioning of parallel plates

To describe the actual positioning of parallel platelets in the form of ribbons Brydges et al. [34] used the stacking parameter c x =2d ( x and 2d are defined in Fig. 9, and c < 1). This parameter expresses the deviation from the periodicity, by defining the horizontal offset of each ribbon layer with respect to the layer underneath it. The value c 1=2 represents the case when the ribbons in one layer are centered over the gap in the layer below. Obviously, c 1=2 gives the lowest permeability, while for c 0 the permeability is maximum. Brydges et al. [34] calculated the different mass fluxes around the platelets. In the cases where the aspect ratio is very large a 2d=a > 100 and 2s a this model gives:

¼

¼ ¼

¼

ð ¼




¼



1

a 2 /2

þ 1  / cð1  cÞ

Þ

1

!

ð4:13Þ

This expression has a form analogous to the equation of Cussler (Eq. (4.9)), except for the factor c 1 c . Cussler et al. [30] also examined the case of slits formed between randomly positioned parallel platelets of infinite third dimension and suggested the following expression for the permeability:

ð  Þ


¼



1

2

þ l1a // 0

2

!

1 ;

ð4:14Þ

where l 0 is a combined geometrical factor, characterising also the randomness of the porous media. Some ideas on the calculation of this parameter are described by Aris [32]. In a similar case, Lape et al. [35] considered rectangular nanoplatelets of the same aspect ratio arranged randomly but parallel to each other and perpendicular to the diffusion direction. The permeability of the nanoplatelet reinforced membrane is reduced then from that in the pure polymer by the product of the reduced area and the increased path length.


A f A0

    ¼  ‘ ‘0

ð4:15Þ

The distance that the solute molecule diffuses through the nanocomposite, becomes in this case:

‘0

¼ ‘ þ hN ihdi:

ð4:16Þ

which is the same with Eq. (4.5), except that L=2 is replaced by d , the average distance the solute must travel to reach the edge of platelet. Using simple statistical considerations d can be estimated considering that the molecule hits the platelet at a random point along its length, and that the resistance to mass transfer is proportional to the length of the path travelled. Thus ‘ 0 becomes:

h i

hi

1 ‘0 ¼ 1 þ a/ ‘:





3

ð4:17Þ

Eq. (4.17) differs from Eq. (4.6) by a factor 2=3, which is due to the randomness of the positions of the nanoplatelets. The area available for diffusion, A f , can be determined by dividing the volume available for diffusion by the distance travelled to cross the membrane:

A f A0

ð V  V Þ=‘0 ¼ ; m

f

ð4:18Þ

V m =‘

where V m is the total volume of the membrane and V f is the volume of all platelets. The relative permeability then becomes:


¼

1

 þ  1

/

a

3

/

2

:

ð4:19Þ

The case where the nanoplatelets are circular disks with radius R, thickness W and aspect ratio a R =W (Fig. 10) was examined by Fredrickson and Bicerano [36] using multiple scattering theory. When, the disks were spaced by an average distance exceeding R (dilute regime), the following expression for the diffusion coefficient was derived:

¼

Dcomposite Dmatrix

¼ 1 þ1ja/

ð4:20Þ

where j p= ln a. This case corresponds to low values of the volume fraction and the aspect ratio of the nanoplatelets (a/ 1), and presents a form similar to Nielsen’s equation (Eq. (4.7)). For low values of / but high values of a (a/ 1), the disks are overlapping (semi-dilute regime) and the relation becomes:

¼





Dcomposite Dmatrix

¼ 1 þ l1a / ; 2

2

ð4:21Þ

2

where l p2 =16ln a. This equation has a similar form with the equation of Cussler (Eq. (4.9)). In a different approach, Gusev and Lusti [37] developed a 3D computational model for a random array of parallel circular disks. This model is based on the solution of the Laplace equation for the local chemical potential:

¼

rK ð Þ  rl ¼ 0 r

ð4:22Þ

with a space dependent local permeability coefficient. The latter is assumed to have a value of zero inside the platelets and K matrix anywhere else. The proposed expression for the global permeability becomes:


976


Picard et al. [38] modified the model of Lape et al. [35] (Eq. (4.26)), considering not only the polydispersity of the width of the filler but also the polydispersity of its thickness:


¼

1

2 P   3 64 þ P 75 /

2

1

1 / 3

ni

2

ð4:28Þ

;

wi t i

w

ni t i i

Fig. 10. (a) The dilute regime of concentration in an oriented disk composite a / 1. The disks are spaced by a mean distance that exceeds the disks radius R. (b) The semi-dilute regime a/ 1. The disks are strongly overlapping due to their great aspect ratio, creating a tortuous path.







¼ exp

"  #  b

a/

x0

ð4:23Þ

:

The parameters b and x0 are usually evaluated by fitting experimental data [37]. The values of b 0 :71 and x0 3:47 were used by Picard et al. [38] in order to obtain similar results as with the model of Nielsen (Eq. (4.7)) for the diffusion of several gasses in nylon-6/montmorillonite composites. All the models above assumed nanoplatelets of uniform size. If, instead, there is a continuous distribution of sizes, g R , e.g. Gaussian of average size R and deviation r 0 :

¼

¼

ðÞ

g R

1

ð Þ ¼ p 2pr0 exp

ffiffi ffi ffi



 ðR  RÞ

2

2r02

!

;

ð4:24Þ

and constant thickness, W , then the mean number of nanoplatelets of size 2R encountered by the solute becomes [35]:

hN ðRÞi ¼ /W ‘  1g ðg RðÞRRdR ÞRdR

ð4:25Þ

R 0

This gives:


¼

1 1

þ

2 / 3 WR

 / : ðR þ r0 Þ 2

2

ð4:26Þ

If one compares this case with the case of nanoplatelets with a uniform size R R , then:

¼

K uni K polydisp

2 2

"  #  þ 1

r0 R

:

ð4:27Þ

Increasing the polydispersity of the size distribution, increases the standard deviation and reduces the permeability. Thus the barrier properties of the nanoplatelets with polydispersed sizes are better than these of monodispersed of the same mean size.

where w i and t i are the width and the thicknesses of the fractions i of the platelets. This model [38] is more appropriate for the cases of high loading of the impermeable phase, where, due to the presence of agglomerates, there is a distribution in the values of the aspect ratio. The comparison of the models that have been presented so far is not straightforward because the definition of the aspect ratio of the platelets is not common in all the models. Some authors define this ratio as the half width to thickness ratio, while others as the width to thickness ratio. Adopting the latter as the typical definition of the aspect ratio, some of the models should be modified accordingly. This is included in the curves of Fig. 11, which compares the predictions of the models. In the model proposed by Fredrickson–Bicerano (Eqs. (4.20) and (4.21)), where the platelets are considered to have a circular disk shape, another modification of the aspect ratio is needed. The relation between the disk aspect ratio and the rectangular platelet aspect ratio can be derived by comparing the area of a disk ( pR2 ) to the area of a rectangular platelet ( L2 ). ffiffiffiffi Thus, adisk a = p. The coefficients j and l should also be modified accordingly. Fig. 11 compares the predictions of some models as functions of the platelet volume fraction and for different aspect ratios. Two important observations can be made in this figure: first that all models require (relatively) large volume fractions or large aspect ratios for a large reduction of the permeability. Second that the predictions for the trend of this reduction are different between the several models mainly in the area of low volume fractions and aspect ratios. The best way to compare the predictions of the models, then, is to use the product a/ as the significant parameter of the membrane. Fig. 11 shows that in the dilute regime the models of Cussler (Eq. (4.9)), Fredrickson–Bicerano (Eq. (4.21)) and Gusev (Eq. (4.23)) present similar behaviour for low particle aspect ratios (Fig. 11a, a 10). The models of Nielsen (Eq. (4.7)) and of Fredrickson–Bicerano (Eq. (4.20)) indicate a stronger effectiveness of the platelets in reducing the permeability under these conditions. In semi-dilute systems and for intermediate aspect ratios ( a 100), however, the model of Fredrickson–Bicerano (Eq. (4.21)) seems to underestimate the barrier properties, while Cussler’s model overestimates them ( Fig. 11b, a 100). For higher aspect ratios (Fig. 11c, a 1000) Gusev’s model predicts almost zero permeability for a/ > 30. As this product goes to higher values (e.g. a/ > 60 in Fig. 11c) the absolute values of the permeability predicted by all the models become very low, in the range of 1–3% of the value of the unfilled polymer.

¼ p

¼



¼

¼

977


a

quate to describe the reduction of the relative permeability. An example of the effect of the aspect ratio, a , on the predictions of Nielsen’s model is shown in Fig. 8.

1.0 0.9

m

4.3. Arrangements at angles h –90 to the main diffusion direction

0.8

K /

p 0.7 m o c

K

0.6 0.5 0.4 0.00

eq. 4.7 eq. 4.9 eq. 4.20 eq. 4.23 eq. 4.21 0.02

0.04

0.06

0.08

0.10

¼ 12 h3cos h  1i;

vol. fraction

S 0

1.0

b

eq. 4.7 eq. 4.9 eq. 4.23 eq. 4.21

0.8

m 0.6

p m o c 0.4

ð4:29Þ

where h is the angle between the diffusion direction and the unit vector normal to the surface of a platelet, and the average is taken over all platelets with all possible orientations. When all platelets are parallel to the direction of 1=2. diffusion (h 0), then the order parameter is S 0 When h p=2, the orientation of the platelets is perpendicular to the diffusion direction and S 0 1. For random orientation S 0 0 (see Fig. 12). For non-uniform orientation Nielsen’s equation takes the following form [26]:

¼

¼ 

¼

¼

K

0.2

0.0 0.00

K composite K matrix 0.02

0.04

0.06

0.08

0.10

vol. fraction 1.0

eq. 4.21 eq. 4.7 eq. 4.23 eq. 4.9

0.8

m 0.6

K /

p m o c 0.4

K

0.0 0.00

0.02

0.04 0.06 vol. fraction

0.08

0.10

Fig. 11. Predictions of the relative permeability as a function of platelets volume fraction for different models, for a particle aspect ratio: (a) a 10; (b) a 100; and (c) a 1000.

¼

¼

¼ 1 þ a 1 S /0 þ 2 2 3

1 2

 

/

ð4:30Þ

:

Obviously, the case S 0 1 corresponds to the maximisation of the tortuosity factor and, therefore, to the greatest reduction of the permeability. The term 23 S 0 1=2 ( cos2 h from Eq. (4.29)) gives the factor 1=3 for S 0 0. The predictions are then similar to the ones of the models of Lape et al. [35] and Fredrickson and Bicerano [36] for random spatial positioning of clay layers. An empirical relation for the prediction of the permeability in nanocomposites with randomly (3D) oriented platelets has been proposed by Maksimov et al. [39] in the form of:

¼

¼h

K composite

0.2

¼

2

¼

K /

c

The tortuosity, s, is the highest when the nanoplatelets are aligned perpendicular to the diffusion direction. For other orientation angles Nielsen’s equation should be modified accordingly. For non-uniform orientation of the platelets an order parameter, S 0 , is introduced to quantify the degree of their orientation around the diffusion direction [26]:

ð þ

i

¼ 13 K k þ 2K



matrix



ð1  /Þ ;

¼

Þ

ð4:31Þ

where K k is the permeability of the nanocomposite as given by the model of Nielsen for oriented platelets. The second term corresponds to the permeability of the composites with platelets oriented parallel to the diffusion direction and it is assumed to be equal to the permeability of the matrix corrected for its volume fraction. 4.4. Influence of the interfacial regions

From a practical point of view, complete exfoliation is difficult to be achieved at high clay fractions and the actual aspect ratios are much lower than what is needed for efficient enhancement of the barrier properties. For intermediate cases, and given the comparisons with the few available experimental data in the following sections, we could conclude that the simple model of Nielsen is ade-

In many cases, the permeability of the nanocomposite can be affected by the existence of interfacial regions between the matrix and the inorganic particles. Such domains may enhance the diffusion coefficient. The interfaces are caused either by the surfactant that is used for the modification of the particles or/and are due to the formation of voids between the different phases.


978


Fig. 12. Values of the order parameter for three orientations of the platelets [26].

The relative diffusion coefficient in such cases has been expressed by Sorrentino et al. [40] as:


Dcomposite Dmatrix

0

¼ as ;

ð4:32Þ

where a0 is a factor that quantifies the effect of the interfacial regions:

a0

¼ 1 þ b0 /:

ð4:33Þ

The parameter b 0 is given by:

0 ¼ V s  D s  V s þ V f :

b

V f D0

ð4:34Þ

V f

Ds , V s are the diffusion coefficient and the volume of the interfaces, D 0 is the diffusion coefficient for the neat polymer and V f is the volume of the nanoplatelets. If V s =V f is negligible, then b0 1 and a0 1 /. However, the parameters D s , V s are not easily measurable. The value of the parameter b has a strong effect on the diffusivity for all concentrations of the impermeable phase.

¼ 

¼ 

4.5. Influence of the particle aggregation

A crucial factor that affects the permeation properties of the nanocomposite is the aggregation of silicate layers which leads to a decrease of the aspect ratio of nanoparticles. Manninen et al. [19] indicated that the processing path taken to prepare the nanocomposites may result in agglomeration of the organoclay layers. These agglomerates may cause the formation of large scale holes (pores) in the matrix, which can act as low resistance pathways for gas transport within the nanocomposite. In such a case the diffusion becomes mostly of the Knudsen flux type. For high clay contents, it is difficult to keep a high degree of platelet dispersion and avoid the presence of intercalated structures. Nazarenko et al. [41] modified Nielsen’s equation to take into account the case of stacks of layers (aggregates) dispersed homogeneously in the polymer matrix and oriented perpendicular to the diffusion direction. The proposed expression is:


¼ 11þa // 2N

ð4:35Þ

where N is the number of layers in the layer stack. Obviously, the value N 1 corresponds to complete layer delamination (exfoliation). Again, the larger the degree of stacking, i.e. the higher the value of N , the less efficient is the enhancement of the barrier properties. One observes that Eqs. (4.30) and (4.35) have a similar form. The former accounts for the orientation of the platelets, while the latter for their degree of stacking. Therefore, by combining these two equations we can obtain a single equation that might predict the change in permeability as a function of the volume fraction, the geometry, the orientation and the degree of stacking of the nano-platelets: K composite 1 / 4:36 : a K matrix 1 3N S 0 12 /

¼

¼ þ  þ

 

ð

Þ

4.6. Experimental and numerical validation of the models

A common feature in all the models that were presented above is the dependence of the permeation properties of the nanocomposite on the volume fraction and the aspect ratio of the reinforcing inorganic phase. In fact, the predictions of all the models are similar. When used in the reverse way, i.e. to predict the aspect ratio from the measured permeation properties, however, these models give different results. Some such predicted results for a number of the above described methods has been tabulated by Picard et al. [38] as applied in a nylon-6/montmorillonite system. The average aspect ratio of the particles is difficult to determine experimentally and, therefore, the comparison of the models is not straightforward. It has been observed that during the preparation of the nanocomposites the obtained aspect ratio depended on the volume fraction. In chlorobutyl/montmorillonite nanocomposites, e.g., the obtained aspect ratio decreased with increasing /, using either modified or non-modified particles [42]. Obviously, increasing / results in a reduction of the degree of delamination and, consequently, in the reduction of the final particle aspect ratio. The decrease of the relative permeability is attributed in all models mainly to the inorganic phase. If their aspect ratio and volume fraction are the same, the particles will in-

979


duce the same relative reduction of the permeability in any matrix they are dispersed, provided that the same degree of delamination is obtained. Further, if there are no special interactions between the solute gas and the particles, the relative enhancement of the barrier properties is not affected by the kind of the gas that is used [43,44], (Fig. 13). In other words, the improvement of the barrier properties of the material are determined solely by the dispersed inorganic phase. Fig. 14 gives the predictions of Eq. (4.7) for some published data, with the corresponding values of a for best fit. The figure shows that the model of Nielsen (Eq. (4.7)) gives reasonable predictions for most experimental data, such as butyl rubber/vermiculite composites [14], poly(ecaprolactone)/MMT [45], siloxane modified epoxy resin/ MMT [43], PLA/MMT [46]. Each fitting curve requires a different value of the aspect ratio. In Fig. 14a and c the clay particles are the same but the matrices in which they are dispersed are different. The variation of the aspect ratio seems to be the result of the different degrees of exfoliation of MMT in these matrices. In Fig. 14d a value of a 150 for the vermiculite particles seems logical as these particles have greater aspect ratio than montmorillonite.

¼

The reduction of the permeability in the platelet-reinforced nanocomposites is attributed to the lowering of the diffusion coefficient due to a more tortuous path for diffusing molecules, and to the decrease in solubility due to a reduced polymer matrix volume. An enhancement in solubility with the addition of inorganic particles has been reported by Ogasawara et al. [47], with the permeability, D S , remaining unchanged. This appeared to be the result either of gas adsorption at the surface of the inorganic particles or it might be caused by defects in the nanocomposite. None of these effects is accounted for by the mentioned models. An almost linear reduction of the relative permeability has been reported in some cases, e.g. H 2 O vapour or C O2 in nanocomposites of the type PE/HDPE-g-MA20/MMT [44] and poly(e-caprolactone)/mica [48] (Fig. 15). This linear reduction cannot be predicted by any of the models and is probably attributed to the behaviour of the solubility coefficient. These experimental results indicate that the tortuous path model may not be enough to cover all permeation processes. On the other hand, the permeability of water vapour in montmorillonite/styrene-acrylate copolymers was found by Maksimov et al. [39] to follow Nielsen’s model (Eq. (4.7)) at low weight fractions for a 210. At / > 0:03 incomplete exfoliation and decrease of the particle aspect ratio of the montmorillonite lead to a reduction of the efficiency of the barrier properties. Assuming that Nielsen’s model holds at / 0:07 (wt.), an average stacking index of 1.8 can be calculated from the data of [39] using Eq. (4.35). Comparisons of the results of Eqs. (4.10) and (4.11) with Monte Carlo calculations for the diffusion through membranes containing impermeable flakes were conducted by Falla et al. [31] and Swannack et al. [49]. Both papers reported rather good agreement between the theoretical and the simulation results, verifying the tortuous paths around the flakes and the effects of the constrictions into the slits and the diffusion through them. Falla et al. [31] showed that Eq. (4.10) is in general more sensitive to changes in the flake arrangement that will influence the diffusion mechanism, and can predict more accurately the resulting changes in the permeability of the membrane. Swannack et al. [49] indicated the need for 3D calculations and showed that Eq. (4.10) over-predicts the barrier effect of the membrane in this case, as the transverse slits are omitted.



¼

¼

5. Using PALS to study the permeability of polymers and nanocomposites

Fig. 13. Experimental results of relative permeability measurements for different gases [43,44]. (a) Nitrogen and oxygen in epoxy/MMT; (b) Oxygen and carbon dioxide in PE/HDPE-g-MA20/MMT.

The molecular transport through a polymer membrane depends also on the amount of the existing free volume. The free volume is created by the inefficient chain packing of the polymer generated by chain segment rearrangement. The increase of the free volume facilitates the diffusion process because of the creation of easier pathways for the solutes. In polymer-nanocomposite membranes the presence of the inorganic phase can influence the size and the number of the free volume holes, especially at the interfaces. Consequently, the change in the permeability of such


980



Fig. 14. Predictions of Eq. (4.7) for the relative permeability of gasses compared to experimental results taken from [43,45,46,14]: (a) oxygen in epoxy/MMT (b) water vapour in poly( e-caprolactone/MMT nanocomposite; (c) carbon dioxide in butyl rubber/vermiculite nanocomposite; (d) oxygen in PLA/MMT nanocomposite. Each fitting curve corresponds to a selected value for the aspect ratio L=W .

systems is a balance between the barrier properties of the impermeable nanoplatelets and the possible increase of the free volume of the matrix. Therefore, the nanoplatelets may not always promote efficiently the final barrier properties of the material. Positron Annihilation Lifetime Spectroscopy (PALS) is a nondestructive technique that provides an effective approach for the study of the free volume in the solid state. It is based on the localisation of the positronium ( Ps) in the free volume holes because of their repulsion by the surrounding atoms. Generally, the annihilation spectra in polymers consist of three exponentially decaying components that correspond to the three main processes of their annihilation [21]. Each of these processes is characterised by the mean life time and the probability of annihilation (intensity). The longest life time corresponds to the annihi-

lation process of o -Ps in the free volume holes. This is the process that is used to estimate the free volume in amorphous polymers. The size of the free volume holes, R , in the polymer can be determined from the measured lifetime, soPs , using the semi-empirical equation:

soPs ¼

1 1 2



R R0

þ

1 2pR sin 2p R0

1

 

:

ð5:1Þ

The relative intensity gives the probability for the formation of o-Ps, which is proportional to the number of holes, i.e. the overall free volume [21,50]. Plotting the measured life time of the o-Ps and the intensity as a function of clay particles loading, one can estimate any variation in the polymer free volume that may be caused by the presence of the nanoclay particles [51].

981


The interactions between the polymer matrix and the inorganic particles may cause the creation of distinct interfacial layers. These interfaces provide a favourable area for positron trapping and annihilation, even in the absence of extra free volume. Thus, the results of the PALS method conducted in nanocomposites can be complicated to interpret, because the o -Ps intensity may not reflect always directly the free volume hole concentration [52,53]. Despite these difficulties, Garcia et al. [23] have found that the presence of the nanoplatelets increased the amount of free volume in Nylon 6=SiO2 nanocomposites and, therefore, compromised the reduction of the permeability. Thus, in some cases the presence of the inorganic particles may even act destructively in the barrier properties of the membrane. On the other hand, in the case of coatings reinforced with laponite, the free volume was found not to depend on the volume fraction of the clay [51]. It seems, therefore, that every system should be studied separately.



a

experimental points H O 2

1.0

0.8

m

0.6

p m o c

0.4

K / K

0.2

0.0 0.00

0.01

0.02

0.03

0.04

6.1. Electrically modulated permeability using side-chain liquid crystalline polymers

Because the orientation of the impermeable barriers (crystallites, platelets etc.) is paramount for the efficient enhancement of the barrier properties of the material, attempts have also been reported of changing this orientation by means of external fields. An example is the use of an electric field to modulate the orientation of liquid crystalline (LC) polymers and control, thus, the barrier properties of the material [54]. Side-chain liquid crystalline polymers (SCLCP) present a similar picture for their permeability with that of semicrystalline polymers. Here the LCP side-chains may form LC domains by association, which can be impermeable to the gas and are the equivalent of the crystallites in the semicrystalline polymer. There is a significant difference, however, in that the impermeable LC domains can become aligned by the application of an external electric field [54]. These domains have strong dielectric anisotropy. Thus, if the external electric field strength exceeds a threshold, the domains can become oriented parallel or perpendicular to its direction, depending on the sign of their dielectric anisotropy. Due to their dense structure, the LC domains can be considered as barriers for the diffusion of other molecules. Therefore, depending on their orientation, more or less tortuous paths are created for the gas molecules within the LCP and the permeability of the material is affected accordingly. Let us suppose that the LC domains have orthogonal shape of length L and thickness W , they are aligned parallel to each other and at an angle h to the diffusion direction. Using the schematic model of Fig. 16 Ly and Cheng [55] estimated the tortuosity factor as:

0.05

clay volume fraction

b

6. Methods to influence the permeability of the nanocomposite

s ¼ F ða; rÞ 

experimental points CO2 1.0

1 ; sin h

ð6:1Þ

where F a; r is a function of the aspect ratios of the impermeable domains, a L =W , and the diffusion channels, r d=W . The polarisation, P , induced by the external electric field, E , is the dipole moment, l, per unit volume in the direction of the field::

ð

Þ

¼

¼

m

K / 0.8

¼ ð  e1 ÞE ¼ N lhsin hi;

P e0 e

p m o c

where e 0 is the dielectric permittivity of vacuum, e and e 1 are the dielectric and the optical dielectric constants of the material, N D is the number of dipoles per unit volume and h is the angle between l and E . This gives:

K

0.6

0.00

ð6:2Þ

D

!

0.05

0.10

0.15

0.20

clay content (wt%) Fig. 15. Relative permeability of the nanocomposites versus clay volume fraction or clay content: (a) poly(e-caprolactone)/mica [48] for H2O vapour, and (b) PE met /HDPE-g-MA20/MMT [44] for CO2. An almost linear reduction is observed, probably due to the contribution of the solubility coefficient. The line does not correspond to any of the described models.

!

hsin hi ¼ e ðeN  le1ÞE : 0

ð6:3Þ

D

From Eqs. (6.1) and (6.3) it seems that s 1= sin h and sin h E so s 1=E . Therefore, depending on the strength and the orientation of the applied field we can adjust the tortuosity factor and consequently the permeability of the SLCP.








982


a

where c 1;0 and c 2;0 are the initial concentrations of the gas and the additive respectively, m is the stoichiometric coefficient for the reaction between gas and additive, and H is the partition coefficient of the gas. Setting ‘0 equal to the membrane thickness, we can estimate the time lag:

LC domains

2

n o i t c e r i d d l e i f

b

diffusion direction

t 0

¼

t 0 t 0ðwithoutÞ

Fig. 16. (a) Uniform and parallel LC domains with an angle h to the diffusion direction. (b) Alignment of the LC domains due to the external applied electric field. This arrangement corresponds to the maximum tortuosity factor. (c) Minimisation of the tortuosity factor due to the horizontal electric field. The arrows indicate the dipole moment of each domain.

6.2. Improving the barrier properties using reactive additives

The barrier properties of the nanocomposites may further be improved by the addition to the membrane of a substance which either has higher affinity or can react with the penetrating gas molecules, stopping them from advancing their diffusion. The additive must preferably be immobilised inside the membrane and distributed in channels with low resistance to permeation. In this way an increase may be accomplished in the needed time lag, t 0 . The process is delayed, thus, while the steady state properties remain unchanged. Let us suppose that the reaction between the gas molecules and the additive material is very fast and irreversible. While the additive molecules are immobilised, the permeating gas reacts and consumes them. The reaction occurs at a front in depth ‘0 t , which propagates deeper in the membrane [33]. If the quantity of the additive material is considerable, this front will move slowly. We assume a quasi-steady state for the diffusion of the gas molecules from the surface to the front:

ðÞ

2

2

dz

¼ 0;

ð6:4Þ

where z is the distance from the surface of the membrane where the gas molecules enter. This equation is solved for the appropriate boundary conditions to give the penetration depth, ‘ 0 t :

‘0

¼

s ffiffi ffi ffi ffi ffi ffi ffi ðffi ffiÞffi

2mDHc 1;0 t ; c 2;0

¼

¼ m3c Hc

2;0

ð6:7Þ

:

1;0

Since H is a property of the polymer, the key parameter that can be adjusted is the concentration of the additive: the more the better.

field direction

d z

ð6:6Þ

:

After this time the flux comes to steady state. The model fails for c 2;0 0, as it gives gives t 0 0 then. This is attributed to the approximation of the pseudo-steady state that was used. If one compares the time lag for the membrane with and without additives, then:

diffusion direction

D

2;0 1;0

c


¼ 2m‘DH  c c

ð6:5Þ

7. Low permeability nanocomposite coatings and other applications

Low permeability nanocomposite materials can be used in a variety of applications especially in liquid and food packaging. Generally, polymers present many advantages in comparison with conventional glass containers, such as, e.g., low weight and mechanical strength. Polyethylene (PE), Polypropylene (PP) and poly(ethylene terephthalate) (PET) are widely used in bottles and containers. However, their limited barrier properties to oxygen make them inappropriate for products requiring long self life. Polyester nanocomposites offer superior barrier properties to oxygen and high transparency and are suitable for use in the manufacture of closed containers [56]. Nanoplatelets reinforced blends are also used for barrier properties to oxygen and to organic solvents, as they also offer high mechanical properties [57,58]. Materials for hydrogen storage tanks is another area of applications for organoclay compositions [59]. The use of the microbial barrier properties of the organoclays in polymers has been studied by [60]. The working time, t acti e for such a packaging film is given by Cussler [61]: v

2

t active

¼

d film ; D film

where d film is the thickness of the film and D film its diffusion coefficient. If the latter is reduced, according to any of the models described in this review, then the working time of the film will increase accordingly. e.g. [31]: 2

t active

¼



d film 1 D0

a 2 /2

2 þ 1  / þ ar/ þ pð41a/ /Þ ln rðp1a/ /Þ



! ð7:1Þ

If, further, use is made of reactive additives (Eq. (6.7)), then the working time of the composite film becomes:


¼ m3c Hc

2;0

t active

1;0



2 d film

D0



a2 /2

a/ pa2 / 4a/ þ þ 1þ ln 1  / r pð1  /Þ rð1  /Þ



!

ð7:2Þ Another area of research on this subject is the development of coatings incorporating nano-platelets. While this is mostly done to improve the mechanical properties (e.g. ‘‘chipping” of automobile paint) [62–64], the improvement of the barrier properties has not gone unnoticed. Polymeric nanocomposite coatings is an alternative inexpensive oxygen barrier material [65]. Such anticorrosive coatings can be used on zinc-steel plates for automobiles [66]. Asphalt nanocomposite based coatings can be useful for materials for building components such as shingles [67]. One such project that examines the utilisation of nanoplatelets with different aspect ratios for the development of coatings with exceptional gas barrier properties is currently under way at the Technical University of Crete. The research uses this method aiming to reduce the permeability of coatings used for the long time protection of large marble and stone surfaces against polluting gasses. 8. Conclusions and recommendations

The addition of inorganic impermeable nanoplatelets improves the barrier properties of polymers. This is attributed mostly to the lengthening of the diffusion path of the permeating gas molecules due to the increase of the tortuosity. Increasing the aspect ratio of the platelets and their volume fraction improves these properties. The addition of solute scavengers enhances these properties, at least by prolonging the induction period for permeation. Most of the proposed models for the estimation of the gas permeability of organoclay reinforced polymers deal with the ideal case of full exfoliation and assume that the physical characteristics of the polymer remain unchanged with the addition of the inorganic particles. The common feature in all the models is the dependence of the relative permeability on the volume fraction, the aspect ratio and the orientation of the platelets, something that is verified by the experiments. The reduction of the relative permeability is correlated to and determined by the inorganic phase and seems to be independent of the nature of the polymer matrix and the gas species. The experimental validation of the models and their comparison is not simple, because the actual aspect ratio and orientation of the platelets in the composites is difficult to estimate. When the geometric parameters of the clay/polymer system are known, it seems that the model proposed by Nielsen, which is the simplest, does a reasonable job in predicting the permeability. In fact, things may be more complicated because the nanocomposites present a variety of morphological features. Different kinds of interactions between the polymer and inorganic platelets may affect the free volume in the matrix, the interfacial regions between the two different phases and the degree of delamination of the silicate layers. It seems that an accurate enough prediction for the

983

barrier properties of a general nanocomposite that will lead to the appropriate selection of the nanocomposites composition is still wanted. In some cases the orientation of the platelets can be measured and controlled using electric or magnetic fields or mechanical stresses. The barrier properties can be further improved by using nanoplatelets that have polydisperse size distribution or/and by using reactive additives, which can obstruct the diffusion process, at least in the initial stages. More systematic measurements are required to clarify the effects of the inorganic particles on the permeation process. For example, it will be useful to establish permeability measurements for samples containing the same matrix with different inorganic particles, in various concentrations, or/and different matrices with the same dispersed particles. PALS measurements may also be useful to reveal the influences of the nanoplatelets on the free volume and the interfacial regions. Further, it may be worth finding out if the addition of a polar material through the low resistance diffusion channels (if such exist) can improve the barrier properties, at least in the case of (also) polar penetrants. Making the diffusion channels more polar can also be useful for the indirect estimation of the slit aspect ratio via dielectric measurements. Acknowledgements

We thank ELKE (the Research Funds Financial Administration) of the Technical University of Crete for partially supporting the research project of G. Choudalakis. We also thank the unknown (to us) reviewer who suggested the form of Eq. (4.36). References [1] Ray SS, Okamoto M. Polymer/layered silicate nanocomposites: a review from preparation to processing. Prog Polym Sci 2003;28:1539–641. [2] Usuki A, Kawasumi M, Kojima Y, Okada A, Karauchi T, Kamigaito O. Swelling behavior of montmorillonite cation exchanged for x-amino acids by e -caprolactam. J Mat Res 1993;8(5):1174–8. [3] Lagaly G. Interaction of alkylamines with different types of layered compounds. Solid State Ionics 1986;22:43–51. [4] Yoon K, Sung H, Hwang Y, Noh S, Lee D. Modification of montmorillonite with oligomeric amine derivatives for polymer nanocomposite preparation. Appl Clay Sci 2007;38(1–2):1–8. [5] Yano A, Usuki A, Okada A, Karauchi T, Kamigaito O. Synthesis and properties of polyimide-clay hybrid. J Polym Sci Part A: Polym Chem 1993;31:2493–9. [6] Usuki A, Hasegawa N, Kato M. Polymer–clay nanocomposites. Adv Polym Sci 2005;179:135–95. [7] Nguyen QT, Baird DG. Preparation of polymer–clay nanocomposites and their properties. Adv Polym Tech 2006;25:270–85. [8] LeBaron PC, Wang Z, Pinnavaia TJ. Polymer-layered silicate nanocomposites: an overview. Appl Clay Sci 1999;15:11–29. [9] Powell CE, Beall GW. Physical properties of polymer/clay nanocomposites. Curr Opin Solid State Mater Sci 2006;10:73–80. [10] Jordan J, Jacob K, Tannenbaum R, Sharaf M, Jasiuk I. Experimental trends in polymer nanocomposites-a review. Mat Sci Eng A 2005;393:1–11. [11] Rogers WA, Buritz RS, Alpert D. Diffusion coefficient, solubility and permeability for helium in glass. J Appl Phys 1954;25:7. [12] van Amerongen GJ. The permeability of different rubbers to gases and its relation to diffusivity and solubility. J App Phys 1946;17. [13] Wicke E, Kallenbach R. Die oberflächendiffusion von kohldioxyd in aktieven kohlen. Kolloid-Z 1941;97:135–51.


984



[14] Takashi S, Goldberg HA, Feeney CA, Karim DP, Farrel M, OLeary K, et al. Gas properties of butyl rubber/vermiculite nanocomposite coatings. Polymer 2006;47:3083–93. [15] Neogi P. Diffusion in polymers. Marcel Dekker Inc.; 1996. [16] Wong B, Zhang Z, Handa P. High precision gravimetric technique for determining the solubility and diffusivity of gases in polymers. J Polym Sci B: Polym Phys 1998;36:2025–32. [17] Ballik CM. On the extraction of diffusion coefficients from gravimetric data for sorption of small molecules by polymer thin films. Macromolecules 1996;29:3025–9. [18] Kemp DR, Paul DR. Gas sorption in polymer membranes containing adsorptive fillers. J Polym Sci Part B: Polym Phys 1974;12:485–500. [19] Manninen A, Naguib H, Nawaby A, Day M. Co2 sorption and diffusion in polymethyl methacrylate-clay nanocomposites. Polym Eng Sci 2005;45:904–14. [20] Hiltner A, Liu RYF, Hu YS, Baer E. Oxygen transport as a solid state structure probe for polymeric materials: a review. J Polym Sci Part B: Polym Phys 2005;43:1047–63. [21] Pethrick R. Positron annihilation – a probe for nano-scale voids and free volume. Prog Polym Sci 1997;22:1–47. [22] Cohen MH, Turnbull D. Molecular transport in liquids and glasses. J Chem Phys 1959;31(5):1164–9. [23] Garcia M, Barsema J, Galindo RE, Gangialosi D, Turiel J, Van Zyl WE, et al. Hybrid organic inorganic Nylon-6/SiO2 nanocomposites: transport properties. Polym Eng Sci 2004;44:1240–6. [24] Mogri P, Paul DR. Gas sorption and transport in side-chain crystalline and molten poly(octadecyl acrylate. Polymer 2001;42:2531–42. [25] Michaels AS, Bixler HJ. Flow of gases through polyethylene. J Polym Sci L 1961:413–39. [26] Bharadwaj RK. Modeling the barrier properties of polymer-layered silicate nanocomposites. Macromolecules 2001;34:9189–92. [27] Barrer RM, Petropoulos JH. Diffusion in heterogeneous media: lattice and parallelepipeds in a continuous phase. Br J Appl Phys 1961;12:691–7. [28] Nielsen LE. Models for the permeability of filled polymer systems. J Macromol Sci A 1967;1:929–42. [29] Wakeham WA, Mason EA. Diffusion through multiperforate lamninae. Ind Eng Chem Fundam 1979;18(4):301–5. [30] Cussler EL, Hughes SE, Ward WJ, Aris R. Barrier membranes. J Membr Sci 1988;38:161–74. [31] Falla WR, Mulski M, Cussler EL. Estimating diffusion through flakefilled membranes. J Membr Sci 1996;119:129–38. [32] Aris R. On a problem in hindered diffusion. Arch Ration Mech Anal 1986;12:83–91. [33] Moggridge GD, Lape NK, Yang C, Cussler EL. Barrier films using flakes and reactive additives. Prog Organ Coat 2003;46:231–40. [34] Brydges WT, Gulati ST, Baum G. Permeability of glass ribbonreinforced composites. J Mater Sci 1975;10:2044–9. [35] Lape NK, Nuxoll EE, Cussler EL. Polydisperse flakes in barrier films. J Membr Sci 2004;236:29–37. [36] Fredrickson GH, Bicerano J. Barrier properties of oriented disk composites. J Chem Phys 1999;110:2181–8. [37] Gusev AA, Lusti HR. Rational design of nanocomposites for barrier applications. Adv Mater 2001;13(21):1641–3. [38] Picard E, Vermogen A, Gerard J, Espuche E. Barrier properties of nylon-6 montmorillonite nanocomposite membranes prepared by melt blending: influence of the clay content and dispersion state: consequences of modelling. J Membr. Sci 2007;292:133–44. [39] Maksimov RD, Gaidukov S, Zicans J, Jansons J. Moisture permeability of a polymer nanocomposite containing unmodified clay. Mech Comp Mat 2008;44(5):505–14. [40] Sorrentino A, Tortora M, Vittoria V. Diffusion behavior in polymer– claynanocomposites.J Polym SciPart B: Polym Phys2006;44:265–74. [41] Nazarenko S, Meneghetti P, Julmon B, Qutubuddin S. Gas barrier of polystyrene montmorillonite clay nanocomposites: effect of mineral layer aggregation. J Polym Sci Part B: Polym Phys 2007;45:1733–53. [42] Sridhar V, Tripathy DK. Barrier properties of chlorobutyl nanoclay composites. J Appl Polym Sci 2006;101:3630–7. [43] Yeh JM, Huang HY, Chen CL, Su WF, Yu YH. Siloxane modified epoxy resin–clay nanocomposite coatings with advanced anticorrosive

properties prepared by a solution dispersion approach. Surf Coat Technol 2006;200:2753–63. [44] Jacquelot E, Espuche E, Gerard JF, Duchet J, Mazabraud P. Morphology and gas barrier properties of polyethylene-based nanocomposites. J Polym Sci Part B: Polym Phys 2006;44:431–40. [45] Tortora M, Vittoria V, Galli G, Ritrovati S, Chiellini E. Transport properties of modified montmorillonite-poly(-caprolactone) nanocomposites. Macromol Mater Eng 2002;287:243–9. [46] Ray SS, Bousmina M. Biodegradable polymers and their layered silicate nanocomposites: in greening the 21st century materials world. Prog Mater Sci 2005;50:962–1079. [47] Ogasawara T, Ishida Y, Ishikawa T, Aoki T, Ogura T. Helium gas permeability of montmorillonite/epoxy nanocomposites. Comp Part A 2006;37(12):2236–40. [48] Messersmith PB, Giannelis EP. Synthesis and barrier properties of poly (-caprolactone)-layered silicate nanocomposites. J Polym Sci Part A: Polym Chem 1995;33:1047–57. [49] Swannack C, Cox C, Liakos A, Hirt D. A three-dimensional simulation of barrier properties of nanocomposite films. J Membr Sci 2005;263:47–56. [50] Eastmond GC, Daly JH, McKinnon AS, Pethrick RA. Poly(ether imide)s: correlation of positron annihilation lifetime studies with polymer structure and gas permeability. Polymer 1999;40: 3605–10. [51] Choudalakis G, Gotsis AD, Schut H, Picken SJ. unpublished data, 2008.. [52] Wang ZF, Wang B, Qi N, Zhang HF, Zhang LQ. Influence of fillers on free volume and gas barrier properties in styrene-butadiene rubber studied by positrons. Polymer 2005;46:719–24. [53] Wang SJ, Liu LM, Fang PF, Chen Z, Wang HM, Zhang SP. Microstructure of polymer–clay nanocomposites studied by positrons. Radiat Phys Chem 2007;76:106–11. [54] Ly YP, Cheng YL. Electrically-modulated variable permeability liquid crystalline polymeric membrane. J Membr Sci 1993;77:99–112. [55] Ly YP, Cheng YL. Diffusion in heterogeneous media containing impermeable domains arranged in parallel arrays of variable orientation. J Membr Sci 1997;133:207–15. [56] Barbee R, Matayabas C. Nanocomposites for high barrier 2009 applications 2000. United States Patent WO0078855, 28.12.2000, European Patent EP 0 670 058 B1, 08.07.1998, Canadian Patent CA 2,149,891, 15.02.2000, Finnish Patent FI 952480, 13.12.2002. [57] Frounchi M, Dadbin S, Salehpour Z, Noferesti M. Gas barrier properties of pp/epdm blend nanocomposites. J Membr Sci 2006;282(1–2):142–8. [58] Myung-Ho Kim, Si Ho Lee, Nanocomposite blend composition having excellent barrier property 2006. JP2006328426 (07.12.2006). [59] Jang Bor Z. Nanocomposite compositions for hydrogen storage and methods for supplying hydrogen to fuel cells 2006. US2006030483 (09.02.2006). [60] Wang Xiaoying, Du Yumin, Yang Jianhong, Wang Xiaohui, Shi Ying Hu Xiaowen. Preparation, characterization and antimicrobial activity of chitosan/layered silicate nanocomposites. Polymer 2006;47(19):6738–44. [61] Cussler EL. Mass transfer in fluid systems. Cambridge University Press; 1984. [62] Nobel ML, Mendes E, Picken SJ. Acrylic-based nanocomposite resins for coating applications. J Appl Polym Sci 2007;104(4):2146–56. [63] Nobel ML, Picken SJ, Mendes E. Waterborne nanocomposite resins for automotive coating applications. Progr Org Coat 2007;58(2– 3):96–104. [64] Nobel ML, Mendes E, Picken SJ. Enhanced properties of innovative laponite-filled waterborne acrylic resin dispersions. J Appl Polym Sci 2007;103(2):687–97. [65] Kothapalli Venkata Raju, Kattimuttathu Suresh. Oxygen barrier material for packaging 2005. US2005145138 (07.07.2005). [66] Young Chul Lee, Myeong Jun Kim. Organo clay containing anticorrosive coating composition and preparation method 2007. WO2007055498 (18.05.2007). [67] Vinay Mehta, Brian Kanze. Asphalt nanocomposite-based roofing products 2007. WO2007109314 (27.09.2007).

Permeability of Polymer Clay Nano composites

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