[membrane science and technology] membrane contactors: fundamentals, applications and potentialities...

Chapter 2. Membrane materials

I. Introduction

The membrane itself represents the core of any membrane process. A large variety of

membranes exists, depending on their structure, transport properties and separation mechanism; all

those different characteristics are generally originated by dissimilar raw materials or preparation

methods. The class of synthetic membranes includes organic (polymeric) and inorganic membranes.

Due to the possibility to modulate their intrinsic properties (thermal, mechanical and chemical

stability, selectivity and permeability etc.), polymeric membranes have attracted much more

interest. A large part of membranes in use for membrane contactors applications are polymeric; the

most significant exception probably concerns the use of ceramic membranes in the emulsification

process.

The microstructure of a membrane is also a critical subject, and strictly depends on the

preparation procedures: commonly, one can discriminate between symmetric and asymmetric

membranes. Symmetric membranes may be dense or have straight or sponge-like pores: such a kind

of microporous structures are widely employed in membrane distillation and related operations, in

membrane absorption, stripping and extraction processes, as support for liquid membranes, in

membrane emulsification technology. Asymmetric membranes show a thin dense skin layer with or

without pores on the top of a high porous sublayer: the thickness of the selective skin offers the

advantage of a low resistance to the transport through the membrane. In phase transfer catalysis, if

pores in the dense layer are small enough to retain the catalyst- but large enough to freely pass

substrates and products - asymmetric membranes provide an interesting support for its

immobilization.

Membrane Materials 41

In the next paragraphs, a survey on some polymeric and inorganic materials and on the

preparation and characterization techniques for membranes used as contactors is presented. It is

beyond the scope of this book to give details on this extremely complex matter, and readers are

referred to specific handbooks in this field.

Information on commercial modules used in membrane contactors applications are furnished in

Chapter 3.

2. Membrane polymers

When producing porous membranes, the selection of the material is mainly driven by the

necessity to achieve a high chemical and thermal stability. Microporous polymeric membranes are

prepared by various techniques: sintering, stretching, track-etching, phase inversion. The processing

requirements and related characteristics of the resulting membrane also determine and limit the

choice of the polymeric materials.

Typology and main characteristics of the polymers frequently used as material for microporous

membranes are given in table 1.

3. Preparation methods

Different methodologies are available to prepare membranes. This paragraph will provide a brief

description of sintering of powders, stretching of films, track-etching and template leaching

techniques. The most common method for preparing porous membranes, the phase inversion

process, is discussed with more details.

42 Chapter 2

Table 1. Frequently used materials for microporous membranes

Polymer Chemical structure Main

characteristics

Polycarbonate

Cellulose acetate

Nylon

Polysulfone

o\ \ )?-o-o \ - ' - ~ / CH 3 \ - - - - - /

CH2OAc

o

OAc

H

I N ~ (CH2) s ~ C

\ -- I CH 3 \ -- I \ - I

High wet/dry strength; mechanical properties suitable for track-etching preparation method Very hydrophilic; sensitive to thermal and chemical degradation; low tensile strength

Inherently wettable; subject to hydrolytic degradation; better chemical stability when using aliphatic polyamides pH and temperature resistant; poor hydrocarbon resistant


Polyethersulfone High thermal and chemical stability

Polyetherketone

Polyetheretherketone

Polyimide

Polypropylene

Polyvinylidenefluoride

F

t o , O - ~

0 0

/c c\ N X C//N 0

c ,, 0 0

H CH3 1 I I C--C H H

F H I I C - - C I I F H

High thermal and chemical resistance

High thermal and chemical resistance; only soluble at room temperature in concentrated inorganic acids. Excellent thermal stability; good chemical resistance

Chemically resistant; hydrophobic

High temperature resistant; inherently hydrophobic

44 Chapter 2

Polytetrafluoroethylene

F: F I I

t 2 - - C I I F F

High temperature and chemical (acid) resistant; cannot be irradiated; inherently hydrophobic

3.1. Sintering

Sintering is a simple technique: a powder of polymeric particles is pressed into a film or plate

and sintered just below the melting point. The process yields to a microporous structure having

porosity in the range of 10-40% and a rather irregular pore size distribution (figure 1). The typical

pore size, determined by the particle size of sintered powder, ranges from 0.2 to 20 ~tm.

Figure 1. Scanning electron micrograph of a PTFE membrane prepared by sintering.

3.2. Stretching

Microporous membranes can be also prepared by stretching a homogeneous polymer film made

from a partially crystalline material. Films are obtained by extrusion from a polymeric powder at

temperature close to the melting point coupled with a rapid draw-down. Crystallites in the polymers

are aligned in the direction of drawing; after annealing and cooling, a mechanical stress is applied

perpendicularly to direction of drawing. This manufacturing process gives a relatively uniform


porous structure with pore size distribution in the range of 0.2-20 ~tm and porosity of about 90%

(figure 2).

Figure 2. Gore-Tex PTFE membrane prepared by stretching (pore size ~ 0.2 ~tm).

3.3. Track-etching

Microporous membranes with uniform and perfectly round cylindrical pores can be obtained by

track-etching. Homogeneous thin films, usually with thickness of 5-15 ~tm, are exposed to the

irradiation of collimated charged particles, having energy of about 1 MeV. These particles damage

the polymeric matrix; the film is then immersed in an acid or alkaline bath, where the polymeric

material is etched away along the tracks so leaving perfect pores with a narrow size distribution

Figure 3). Typical pore size ranges between 0.02 and 10 ~tm; however, the surface porosity

generally is below 10%.

Figure 3. Polycarbonate membrane prepared by track-etching.

46 Chapter 2

3.4. Template leaching

Porous structures can be obtained by leaching out one of the component from a film. This

technique allows producing porous glass membranes suitable for emulsification process. A

homogeneous melt of three components (i.e. SiO2, B203, and Na20) is cooled from 1300-1500~

down to 500-800~ As a consequence, demixing is induced in the system that splits into two

phases: one consisting mainly of Si02 which is not soluble in mineral acids, and the other phase is

richer in B203, that is subsequently leached out of the structure resulting in a microporous matrix.

Porous alumina membranes made by anodic oxidation contain parallel circular pores with a narrow

pore size distribution. They are formed by an electrochemical process involving the oxidation of

high purity aluminium foils in presence of an acid electrolyte, followed by etching in a strong acid

bath. In this process, an electrical circuit is established between a carbon cathode and a thin film of

aluminium which serves as the anode, resulting in the oxidation of the aluminium to form alumina

according to the reaction:

2AI + 3H20 --~ Al202 + 3H 2 (1)

In appropriate electrolyte solutions, the film that is formed has a uniform columnar array of

hexagonally close packed alumina cells, each containing a circular pore (figure 4). Pores form in the

oxide film because of field assisted dissolution of the alumina from the base of each pore. With

appropriate process conditions, membranes can be formed with pore diameters between 0.01 and

0.3 pm, pore densities between 108 and 10 II cm "2 and thicknesses up to 200 ~tm (figure 5).


Figure 5. A microporous aluminum membrane prepared by anodic oxidation.

Microlithography and reactive ion etching is a further technique to produce porous membranes.

A silicon nitride coating (= 1 ~m) is deposited on a silicon wafer by chemical vapor deposition. By

spin-coating, on the top of the nitride layer a photosensitive lacquer is applied. The lacquer is then

exposed to UV radiation and developed in a NaOH solution resulting in a print of the mask pattem

in the lacquer layer; perforations are extended to silicon nitride layer by reactive ion-etching. The

48 Chapter 2

resulting membranes are characterized by a narrow pore size distribution, with pore diameters

typically in the range of 0.5-10 pm. Alternatively, the exposed polymer layer can be degraded by

irradiation with X-rays (figure 6).

Figure 6. A silicon microsieve prepared by X-ray lithography process.

3.5. Phase inversion technique

Membranes are prepared by phase inversion technique from polymers that are soluble at a

certain temperature in an appropriate solvent or solvent mixture, and that can be precipitated as a

continuous phase by changing temperature and/or composition of the system. These changes aim to

create a miscibility gap in the system at a given temperature and composition; from a

thermodynamic point of view, the free energy of mixing of the system becomes positive.

The formation of two different phases, i.e. a solid phase forming the polymeric structure

(symmetric, with porosity almost uniform across the membrane cross-section, or asymmetric, with a

selective thin skin on a sub-layer) and a liquid phase generating the pores of the membrane, is

determined by few and conceptually simple actions:

1. by changing the temperature of the system (cooling of a homogeneous polymer solution

which separates in two phases): temperature-induced phase separation technique (TIPS);

2. by adding non-solvent or non-solvent mixture to a homogeneous solution: diffusion-

induced phase separation (DIPS);


3. by evaporating a volatile solvent from a homogeneous polymer solution prepared using

solvents with different dissolution capacity.

Although these procedures are practically dissimilar, the basic of membrane formation

mechanism is governed, in all cases, by similar thermodynamic and kinetic concepts: variations in

the chemical potential of the system, diffusivities of components in the mixture, Gibbs free energy

of mixing and presence of miscibility gaps.

TIPS and DIPS processes, often utilized also in combination to prepare membranes, are

discussed in details in the following paragraphs.

3.5.1. Phase separation: a thermodynamic description

Free Gibbs energy of a system is defined as a state function of enthalpy (H) and entropy (S)"

G = H - TS (2)

where T is the temperature of the system.

In general, G depends on temperature, pressure and number of moles ni of each components in the

system:

G = G ( r , P , nl ,n 2 ..... nk) (3)

and the change in Gibbs free energy for a multi-component systems is given by:

dG = OG dT + dP + dn~

P ,n i T ,n, i=1 T ,P ,nj (4)

In equation (3)"

= ~t~

" ~ P,n, = - S " ~ T,ni = V ~ T,P,nj (5)

and, therefore:

k dG = - S d T + VdP + ~ l.tidn i (6)

i=l

50 Chapter 2

For a two-component mixture, being T and P constant, the Gibbs free energy per mole Gm is given

by the sum of the chemical potentials of both components 1 and 2:

G m = Xl,s -'b X2,L/2 (7)

When nl moles of component 1 are mixed to n2 moles of component 2, the change in the free

energy of mixing AGm per mole of mixture is:

A G m = x1A]. I 1 + x2A,L/2 (8)

For an ideal solution, the chemical potential of each component is expressed by:

/.ti =/.t o + R T In x~ (9)

where/.t o is the molar free energy of pure components.

This circumstance is graphically illustrated in figure 7.

G m

0

~10

x 2

~2

Figure 7. Gibbs free energy of mixing for a two-components system at constant T and P.


From equation (8) follows that:

A/~ i = R T l n x i (10)

and

A G m = R T ( x I In x I + x 2 In X 2 ) (11)

Since lnxi is negative (being xi<l), AGm is consequently negative and an ideal mixture always

mixes spontaneously.

In order to describe the behavior of a real mixture, it is convenient to express the Gibbs free energy

of mixing in terms of the enthalpy of mixing AHm and the entropy of mixing ASm:

A G m = A n m - T A S m (12)

For polymer/solvent systems, an expression of AHm valid for small apolar solvents is [2]:

AHm= Vm (~11 -. ~/~/2 r r )

(13)

where Vm, Vl and V2 are the molar volumes of the solution and the two components, AE the energy

of vaporization, and r the volume fraction.

The solubility parameter 8 is defined as the square root of the cohesive energy density AE/V. The

cohesive energy per unit volume is the energy necessary to remove a molecule from its neighboring

molecules. For the polymer/solvent system, if 81~82, the value of AHm tends to zero and polymer is

miscible in the solvent.

The solubility parameter consists of three contributions [3]:

62 =SJ +82 +8~ (14)

where 6d is the solubility parameter due to dispersion forces, 8p is the solubility parameter due to

polar forces, and 8h is the solubility parameter due to hydrogen bonding.

52 Chapter 2

The entropy of mixing ASm can be described using the lattice model proposed by Flory [4].

Referring to the lattice of figure 8, it is assumed that macromolecules consist of segments identical

in size, each occupying a site. If co is the number of segments of a macromolecule, n2 the number of

polymeric chains, and nl the number of solvent molecules, the total number of molecules N is

therefore:

N = n 1 + con 2 (15)

gENBEELI~~,'ltslmt'IB gEr~wEEEEI~Ir-'~-~-s |EEEEFIWEEI~IEEED lr r mmr |mmmEmEmn OEIEEIEIr -'nmmEIEEIEIlf l lEIEEEEI. I~~."IEI ' I I lE D~IIEIIEllEIEllE~JEI[ |E l )mE ,'JC:.'IWWI~II~IllE[ )NLI~D ,IW[ )GIWGImwwrJEE[ )D 'lEt )WWWWWWWEE[ )E , IW~~~."IWEIWWWB )E gHWHIH~raEEC-~-LII~

Figure 8. A lattice representation of a polymer-solvent mixture.

Statistical considerations suggest that the total number of possible combinations f~ to arrange all the

molecules in the lattice is given by:

~2 = r"2 (F - 1) n2(•-2) N_(~,_x),,, [ ',2 (N / ~r~t ]" rt2 .t o-nz ~ ( r t l / ~ ) t J (16)

where ~ is a constant (=2 for asymmetric macromolecules), and F is the degree of coordination (= 4

for a bi-dimensional lattice).

Using the Boltzmann equation (S=kln~) to calculate the entropy of the solution, and subtracting the

entropy of the single components, the entropy of mixing ASm results:

ASm = -R(?'/1 #'/~1 "+" n2 h'102) (17)

where


~1 - - nl and ~2 = m n 2 nl + tO"/'/2 HI + ~r/'/2

(18)

Under the hypothesis that AHm =0, the Gibbs energy of mixing is:

NRTAG--"~m = - Z~mR = (~l l ln~bl + (~2 3 ln#2 (19)

In this case, it can be shown that athermal polymer solutions never demix. Demixing occurs in

presence of a positive enthalpy term AHm>0. In the most general case of AHm:/:0, the expression for

Gibbs free energy of mixing is generalized by including an enthalpic contribution (nl~b2Z):

A G m = RV(n 1 ln~bl + n 2 lnqk2 + HI{~2X ) (20)

Z is the Flory interaction parameter.

Figure 9 shows diagrams of AGm versus ~b and its derivatives up to the second order at a given

temperature and pressure for a bi-components system. The mixture is stable over a certain

composition range if

0 G m ~ < 0 (21)

The first derivative becomes zero when the binodal curve is reached, and reaches a positive

maximum when the spinodal curve is attained. In this region, the mixture is metastabile: there is not

a driving force to a spontaneous demixing.

A thermodynamic instability is observed when

OZGm 0r 2

< 0 (22)

and the system will demix spontaneously. The critical point is individuated by a zero value of the

first derivative and a minimum in the second derivative.

54 C h a p t e r 2

Figure 9. Plot of the Gibbs free energy of mixing as a function of the composition, referred to a system

exhibiting a miscibility gap.


3.5.2. Diffusion-induced phase separation

In a DIPS process, the membrane is formed by polymer precipitation caused by concentration

variations due to diffusive interchange between the solvent and the non-solvent. The final structure

of the membrane is determined by the rate of polymer precipitation. A low precipitation rate results

in the formation of a symmetric structure, whereas a high precipitation rate leads to an asymmetric

membrane, with large voids, spongy sublayer and/or finger-like cavities below a microporous or

dense upper layer.

From a practical point of view, the diffusion-induced phase separation process is routinely used

to prepare integral asymmetric membranes. This process is articulated in few simple steps:

1. dissolution of the polymer in an appropriate solvent to form a solution typically containing 10-

30% wt% of polymer;

2. casting the solution on a suitable support into a film of 100-500 ~m thickness;

3. quenching of the film in the non-solvent (typically water or an aqueous solution), or evaporation

of the solvent to increase the polymer concentration.

During the third step, the homogeneous polymeric solution demixes into two phases: a polymer-

rich solid phase, which forms the structure of the membrane, and a solvent-rich liquid phase, which

results in the formation of liquid-filled membrane pores.

For a more quantitative explication of the DIPS process, let us consider the equilibrium diagram

of the ternary system polymer/solvent/non-solvent reported in figure 10. The three-component

mixture exhibits a miscibility gap in a certain composition range; under these conditions, the system

splits into two distinct phases. Starting from an homogeneous mixture (point A), if the solvent is

completely evaporated, the final composition of the system will be represented by the point B. Here,

the system consists of only two components (polymer and non-solvent) and it is distributed in two

phases, whose compositions are indicated by point B' (polymer-rich phase, solid membrane

structure) and point B" (non-solvent rich phase, liquid-filled pores).

56 Chapter 2

Figure 10. A three component system isothermal diagram showing the formation of a membrane by solvent

evaporation.

Figure 11 illustrates the formation of the m e m b r a n e - based on the assumption of

thermodynamic equilibrium - for a phase separation process induced by addition of a non solvent to

a homogeneous polymer solution. Starting from the point A on the solvent-polymer axis, if the

solvent is completely removed from the mixture at about the same rate as the non-solvent enters, the

final composition of the system will be represented by point B.

Liquid-liquid demixing occurs when the line A-B intersects the binodal; the polymer concentration

in the polymer-rich phase is high enough to be considered as solid when the line A-B intersects the

tieline in correspondence of the vitrification point.


Figure 11. A three component system isothermal diagram showing the formation of a membrane by addition

of non-solvent.

Thermodynamic information about the system are useful but not sufficient to predict the

resulting morphology of the membrane, the pore size distribution and the occurrence of symmetric

or asymmetric structure.

A complete understanding of membrane formation is difficult because of the high number of

involved mechanisms and phenomena, i.e. thermal effects, demixing kinetics, eventual presence of

additives, mutual interaction parameters between polymer/solvent/non-solvent, temary diffusivities,

initial and boundary conditions etc.

Referring to the thermodynamic approach proposed in the previous paragraph, the solubility

parameters for some polymers and solvents are reported in tables 2 and 3, respectively.

58 Chapter 2

Table 2. Solubility parameters of some polymers (* expressed in MPa 1/2 [5]; ** expressed in cal/cm 3 [6]) Polymer ~d ~p 6h 6

Polyvinylidene 17.2 12.5 9.2 23.2

fluoride*

Polyethylene** 8.6 0 0 8.6

Nylon 66** 9.1 2.5 6.0 11.6

Polysulfone** 9.0 2.3 2.7 9.6

Polyacrylonitrile** 8.9 7.9 3.3 12.3

Cellulose 7.9 3.5 6.3 10.7

acetate* *

Poly(phenylene 9.4 1.3 2.4 9.8

oxide)**


Table 3. Solubility parameters of some solvents (expressed in MPa 1/2 [5])

Solvent t~ d t~p 8h t~

N,N-dimethylacetamide 16.8 11.5 10.2 22.7

(DMA)

N,N-dimethylformamide 17.4 13.7 11.3 24.8

(DMF)

Dimethylsulphoxide 18.4 16.4 10.2 26.7

(DMSO)

Hexamethylphosphoramide 18.4 8.6 11.3 23.2

(HMPA)

N-methyl-2-pyrrolidone 18.0 12.3 7.2 22.9

(NMP)

Tetramethylurea (TMU) 16.8 11.5 9.2 22.3

Triethyl phosphate (TEP) 16.8 16.0 10.2 22.3

As practical case, cloud point data at 20~ for PVDF-solvent-water systems are illustrated in the

ternary phase diagram shown in figure 12 [5]; at fixed concentration of polymer, the amount of

water required to precipitate PVDF increases with the following order for different solvents:

HMPA> DMA> DMF> TEP> TMP.

60 Chapter 2

Figure 12. Ternary phase diagram at 20~ for PVDF-solvent-water system. After [5].

A typical asymmetric structure of PVDF membrane prepared by DIPS technique is shown in figure

13.

Figure 13. Cross section of a PVDF membrane prepared by immersion precipitation.


The morphology of the membrane is determined by the properties of the system used to form the

membrane itself. Polymer-solvent interactions have been widely investigated by various authors

[7,8,9]. In general, lower interactions correspond to a higher rate of polymer precipitation, thus

resulting in the formation of finger-like structures. The compatibility of polymer and solvent can be

evaluated in terms of the three component of the solubility parameter ~ (see equation 13):

(23)

where subscripts P and S indicate the polymer and the solvent, respectively.

The tendency of a solvent to mix with the non-solvent also affects the membrane porosity and

structure [9, 10, 11, 12, 13]. For asymmetric membranes prepared by immersion in water, in most

cases the higher the difference of the solubility parameter of solvent and water (Sw = 47.8 MPa 1/2

[5]), and hence the lower tendency to mix, the higher the membrane water content.

A low solution viscosity generally determines the occurrence of cavities in the membrane. On the

contrary, an increase of the solution viscosity due to and increase of polymer concentration

obstructs the penetration of the nonsolvent during the immersion step.

The rate of phase separation depends on the degree of penetration in the demixing gap. An

instantaneous liquid-liquid demixing results in the formation of porous membranes. When a delay

in liquid-liquid demixing occurs, dense membranes are produced. Particularly during the first

moments subsequent to the immersion of the casting solution in the precipitation bath, mass transfer

(solvent and nonsolvent interdiffusion) could become the controlling mechanism for skin formation.

It has been evaluated that, for a solvent-nonsolvent diffusivity in the order of 10 -5 cm2/s and a

typical skin thickness of about 0.1 ~m, the characteristic time for mutual diffusion td is 10 -5 sec

[ 14]. Modeling studies report that, when the value of the solvent-nonsolvent diffusivity increases,

the concentration path in the temary diagram should lead to entry into the demixing gap at higher

polymer concentration [ 11, 15].

62 Chapter 2

3.5.3. Thermally -induced phase separation

Thermally-induced phase separation gives rise to solid-liquid phase separation by removing

thermal energy from the system. TIPS process basically consists of four simple steps [ 16]"

1. formation of a homogeneous solution by melt-bending the polymer with a high-boiling, low-

molecular weight diluent;

2. casting of the solution;

3. cooling of the cast solution to induce phase separation and solidification of the polymer;

4. removal of the diluent (typically by solvent extraction) to produce the membrane structure.

TIPS can be applied to a wide range of polymers, also if their low solubility prevents the use of

non-solvent induced phase inversion. This preparation technique allows to obtain isotropic

microporous structures. The formation of a membrane can be explained by referring to appropriate

equilibrium phase diagrams, and to the theory of phase equilibria in polymer systems.

For binary polymer-solvent systems in which the polymer is semi-crystalline, the melting point of

the polymeric compound is related to the mixture composition as follows [4]:

1 1 R V 2 . 2~'q~ #~) (24)

where Tm and T ~ are the melting temperatures of the crystalline polymer in solution and the pure

crystalline polymer, respectively; V1 is the molar volume of the solvent, V2 is the molar volume for

the repeating unit, ~2 is the volume fraction of the solvent, AHf is the enthalpy of fusion and Z is

the Flory-Huggins interaction parameter.

Solving equation (23) for Tm:

1 r m = (25)

~ z Vl r ~

and plotting it as function of the volume fraction of the polymer r (1 - ~b2 ) , it is possible to derive

a temperature-composition diagram for a semi-crystalline polymer-diluent system. A qualitative


version is reported in figure 14 for polypropylene and three diluents having different strengths of

interaction with the polymer.

-i- m

+

0

0 1 r

Figure 14. Temperature-composition phase diagram for polypropylene- diluent system. After [ 16].

As shown in figure 14, the temperature at which phase separation occurs is increased in presence

of lower strength of interactions polymer-solvent (X increases).

Equation (24) also shows that, all parameters being constant, the smaller the molar volume of the

solvent with respect to that of the polymer, the larger the melting point depression.

Referring to figure 15, let us to consider an homogeneous polymer-solvent solution (point A) at

temperature TA. If the solution is cooled at the same composition, the system loses its stability and a

solid-liquid separation occurs. At the point B (final temperature TB) the system separates in a

polymer-rich phase- the composition of which is indicated by the point B", and in a solvent-rich

phase - represented by the point B'. According to the classical lever rule, segments B'-B and B-B"

64 Chapter 2

represent the ratio of the amounts of the two phases in the mixtures, from which it is possible to

estimate the porosity of the membrane.

TA

(D

~._ B (D c~

E (D i--

HOMOGENEOUS LIQUID PHASE

r ~ LIQUID-LIQUID DEMIXING

\ Membrane composition

SOLID-LIQUID DEMIXING

solvent polymer

Figure 15. The phase diagram for a polymer-solvent binary system as a function of temperature.

The polymer-rich phase forms the solid membrane structure, and the solvent-rich phase the liquid

filled pores.

Table 4 lists some physicochemical properties of polymeric materials usually employed in TIPS

process.


Table 4. Polymers for membrane prepared by TIPS. After [16]

Polymers Density (g/cm 3) Average molecular Melting point (~

weight (Da)

Polypropylene (Himont 0.903 243,000 176

Pro-fax 6723)

High density polyethylene 0.954 224,000 130

(American Hoechst

Hostalen GM-9255-F2)

Polychlorotrifluoroethylene, 2.050 N.A. 197

(Kel-F, 3M Company,

Grade 6300)

Poly (4-methyl- 1-pentene) 0.835 N.A. 230

(Mitsui Chemicals, Grade

RT-18)

Poly(vinylidene fluoride) 1.780 N.A. 169

(Soltex Solvey 1011)

Diluent Density (g/cm 3) Average molecular Initial boiling point

weight (Da) (~

Mineral ,oil (Plough Inc., 0.866 N.A. - 320

Nujol)

Kel-F oligomineral oil (3M 1.930 630 270

Company, KF-3)

Dibutyl phthalate (Aldrich 1.043 278.4 340

Chemicals)

66 Chapter 2

The diagram of solid-liquid phase separation for polypropylene-mineral oil at different polymer

concentrations is reported in figure 16 [16]. Crystallization curves are affected by cooling rates,

since TIPS preparation method is a non-equilibrium process. Results in figure 16 show that the

temperature of demixing significantly decreases if the cooling rate is increased" the solution may

cool to temperatures below its corresponding equilibrium crystallization temperature prior to the

actual crystallization of the polymer from solution. A scanning electron micrograph of a

microporous polypropylene membrane prepared by TIPS is shown in figure 17.

120

0 o

v

f l )

E !-

110

100

90

80

70

60

0.0

cooling rate:

20 ~

~

80 ~

I 0.2 0.4 0.6 0.8 1.0

Weight Fraction Polymer

Figure 16. Crystallization temperature-concentration curves for PP-mineral oil at cooling rates indicated in the diagram. After [ 16].


Figure 17. Microporous polypropylene membrane obtained by thermally induced phase separation technique.

4. Membrane modification

A large part of commercial microporous polymeric membranes available in capillary and flat-

sheet forms that are used for membrane contactors applications were originally manufactured and

optimized for microfiltration purposes. The possibility to prepare new membranes for specific

operations is recently increasing in interest, and some significant results reached in the preparation

and modification of polymeric membranes have provided to an increase of the reliability of

membrane contactors technology.

4.1. Additives in the casting solution

The use of additives to the casting solution, e.g. in the form of water-soluble polymers such as

polyvinyl pirrolidone (PVP), polyethylene glycol (PEG) or inorganic salts (LiC1), represents a

practical way to modulate the structure of a membrane. This aspect has been investigated in the

preparation of microporous PVDF membranes for membrane distillation (MD) applications, where

high porosity is requested in order to obtain a significant flux [ 17, 18, 19]. In particular, it has been

observed that the addition of significant amounts of LiC1 increases the rate of PVDF precipitation

during the immersion step: this causes the formation of an open structure with large macrovoids and

68 Chapter 2

cavities. The accelerated precipitation is related to the high tendency of the additive to mix with

water and to the interactions of the additive with polymer and solvent [20]. The effect of LiC1

content on the porosity and mean pore size of membranes prepared from DMA/PVDF = 88/12 is

illustrated in figure 18. Porosity progressively increases from 79 to 83 % in the range of 1-7 wt.% of

additive, while the mean pore size achieves a maximum of 0.04 ~tm in correspondence of 3.5 wt.%

LiC1 concentration. On the other hand, membranes prepared by using high amounts of LiCI

exhibited low values of water entry pressure with a consequent increase of the risk of wettability.

86 4

3.6 84

3.2 x,~

82 .~

2.8 -~ o

80 2.4 ~;

78 2 2 4 6

LiCl concent ra t ion (wt.%)

Figure 18. Effect of LiCl concentration of the porosity and mean pore size of the membrane. After [18].

4.2. Use of copolymers

It is not mandatory to use a single type of monomer when preparing a membrane. Copolymers of

tetrafluoroethylene (TFE) and 2,2,4-trifluoro-5-trifluoromethoxy-l,3-dioxole (TTD), commercially

known as HYFLON AD, have been used to obtain asymmetric and composite membranes showing

a high hydrophobic character and contact angles to water higher than 120 ~ [21 ].

Asymmetric hydrophobic microporous membranes from the copolymer of PTFE and PVDF have

been prepared by phase inversion process [19]. According to the experimental analysis, these


membranes exhibit excellent mechanical properties (stretching strain and extension ratio at break

approximately 6-8 times higher PVDF) and good hydrophobicity (contact angle to water of about

870).

4.3. Composite membranes

Composite membranes generally show an asymmetric structure, generated by the deposition of a

thin toplayer on a porous sublayer of a different material. Composite membranes have the

advantage that the properties of each layer can be modulated and optimized independently to obtain

the required selectivity, permeability, chemical and thermal stability etc.

The preparation procedures for composite membranes can be grouped in four classes:

1) casting of the thin layer separately (e.g. by spreading a very dilute polymer solution on the

surface of a water bath) and then laminating it on a microporous support;

2) coating of the microporous support by a polymer, a reactive monomer or a pre-polymer

solution (e.g. by immersion in an appropriate solution with low solute concentration- often

less than 1%) followed by drying, heat treatment or radiation (figure 19);

3) plasma polymerization (figure 20);

4) interfacial polymerization of reactive monomers on the surface of the microporous support

(figure 21).

Details about each of these techniques can be found elsewhere [6]. Some specific examples related

to the preparation of composite membranes for membrane contactors applications are reported

below.

J IMMERSION IN GRAFT POLYMER

POLYMERIC FILM RADIATION MONOMER BATH CHAIN

Figure 19. Grafting by radiation.

70 Chapter 2

Q ?-J VACUUM PUMP v ~ . . , . ~

M e m b r a n e

�9 . . . . .

REACTOR

Monomer(s)

DISCHARGE COIL

Figure 20. Plasma polymerization reactor.

K / / / / / / Z f / / / / / / / /

V / / / / / / /

[ / / / / / / / / ,

Y / / / / / / / , POROUS SUPPORT

V//////,~ V//////A~

(/'//////,~ ~//////',,~I

IMMERSION IN IMMERSION IN A AQUEOUS SOLUTION WATER IMMISCIBLE INTERFACIAL

POLYMERIZATION AND OF REACTIVE SOLVENT WHERE FORMATION OF THE MONOMER OR PRE- ANOTHER REACTIVE

POLYMER MONOMER IS COMPOSITE DISSOLVED MEMBRANE

Figure 21. Interfacial polymerization.

The work of Xu and colleagues [22] showed that hydrophobic PTFE membranes with a

protective hydrophilic sodium alginate coating were resistant to wet-out at least for 300 minutes

during osmotic distillation tests using feeds containing 0.2, 0.4, and 0.8 wt.% orange oil. The

reduction in the overall mass transfer coefficient due to the coating was less than 5%.

In order to prepare a hydrophilic/hydrophobic composite membrane, the surface of hydrophilic

porous cellulose acetate was treated via radiation graft polymerization of styrene by Wu et al. [23].


Low pressure plasma polymerization permits to apply a thin layer upon a porous sublayer: this

generally results in a change of the chemical composition and properties of a material, such as

wettability, dyeability, refractive index, hardness, etc.

Plasma is obtained by ionising a gas using high frequency (up to 10 MHz) electrical discharges.

The pressure inside the reactor varies between 0.1 and 10 mbar. Collisions between monomers and

ionised gas generate radicals: the products of the resulting reactions precipitate on the membrane

when their molecular weight is high enough.

A very high hydrophobicity, somewhat higher than that of PTFE, was achieved by fluorinated

coatings also named "Teflon-like" [24]. Kong and co-workers [25] have modified hydrophilic

microporous cellulose nitrate membranes by plasma polymerization of octafluorocyclobutane. The

performance of these membranes, tested in membrane distilation applications, was found

comparable with that of usual hydrophobic polymers.

4.4. Surface modifying molecules

Generally, an increase of membrane porosity and pore size improves the flux. The analogous

effect can be obtained if membrane thickness and tortuosity is decreased. When considering thermal

driven membrane contactors operations, such as in the case of membrane distillation, the conductive

heat loss increases for thinner membranes and the efficiency of the process is therefore reduced. In

order to resolve the conflict between the requirements for high mass transfer and low heat transfer

through the membrane, composite microporous hydrophobic/hydrophilic membranes can be

prepared: the top hydrophobic thin layer is responsible for the mass transport, while the hydrophilic

sublayer increases the resistance to the conductive heat flux. Khayet et al. [26] have modified the

surface of hydrophilic membranes by adding oligomeric fluoropolymers synthesized by

polyurethane chemistry and tailored with fluorinated end-groups.

During membrane formation, surface-modifying molecules (SMMs) migrate to the air-film

surface according to the thermodynamic tendency to minimize the interfacial energy. These

72 Chapter 2

modified membranes exhibit low surface energies, good mechanical strength and high chemical

resistance [27].

5. Inorganic membranes

Inorganic membranes have received limited attention for applications as membrane contactors,

except that in membrane emulsification.

The preparation of glass membranes by leaching has been briefly considered in paragraph 4.

Ceramic membranes, being aluminium oxide (T-A1203) and zirconium oxide (ZrO2) are usually

obtained by sintering or by sol-gel processes.

Sol-gel process is usually carried out by following two different procedures: the colloidal

suspension route and the polymeric gel route (figure 22). In both cases, a precursor for hydrolysis

and polymerization reactions is commonly employed: it is often an alkoxide (such as aluminium tri-

sec butoxide) in case of colloidal dispersion. In the polymer gel route, the precursor is selected with

a low hydrolysis rate.

After the partial hydrolyzation of the alkoxide by addition of water, the reaction of condensation

leads to the formation of a polyoxometallate. The sol is peptized by addition of an inorganic acid;

the viscosity of the solution can be further increased by addition of polyvinylalcohol (PVA). A gel

is formed when the concentration of particles becomes sufficiently high. After drying, the

membrane is sintered at a definite temperature in order to stabilize the final morphology.

More extensive and detailed information on the preparation of inorganic membranes can be

found in [28].

colloidal gel

colloidal gel

ALKOXI DE PRECURSOR

polymer gel

colloidal particles

o o o

o ~ o o o

0 0 0 0

SOL

inorganic polymer

%

GEL

polymeric gel


DRYING AND SINTERING

Figure 22. Schematization of the sol-gel process. From [6] with kind permission of Springer Science and Buniness Media.

6. Membrane characterization

It is well known that the transport phenomena in membrane contactors are strictly related to the

structure of the membrane. In next chapters, correlations between transmembrane flux, energetic

efficiency, permeate or product characteristics, and structural membrane properties such as

thickness, porosity, pore size distribution etc. will be described in details for each membrane

operation considered in this book. The knowledge of such correlations permits to predict and to

optimize the membrane performance for a given application.

Membrane characterization procedures allow to determine the structural and morphological

properties of a membrane. The characterization of the surface chemistry is a critical issue in

membrane contactors technology, since their performance depends on hydrophobicity or

hydrophilicity character, surface charge, interactions between membrane and solutes or solvents,

etc.

Different membranes (porous, non porous, organic, inorganic etc.) require different procedures of

characterization. In this section, the most familiar methods used for microporous membranes will be

described. In particular, attention will be focused on the determination of structure-related

74 Chapter 2

parameters. Usual methodologies aiming to evaluate the permeation-related parameters (pure-water

flux under hydrostatic pressure gradient, solute retention, molecular-weight cut-off, bacteria

challenge test etc.) are not included in this section.

6.1.Contact angle measurements

The contact angle measurement is a traditional method to describe the hydrophobic or

hydrophilic behaviour of a material. In principle, it provides information about the wettability of an

ideal surface. In most cases, the intrinsic value of contact angle is perturbed by surface porosity and

roughness, heterogeneity, etc.

The value of the contact angle made by a liquid droplet deposited on a smooth surface (figure 23) is

greater than 90 ~ if the affinity between liquid and solid is low; in case of water, the material is

considered hydrophobic. Wetting occurs at 0 ~ when the liquid spreads onto the surface.

Figure 23. Contact angle (0) of a liquid droplet deposited on the surface of a solid. Representation of the

thermodynamic equilibrium at the triple point C.

At the triple point C where solid-liquid vapour interfaces are in contact, the thermodynamic

equilibrium is expressed by the Young's equation:

YLv cosO = Ysv -YsL (26)


where ]tLV , "[SV , and ]tSL are the surface tension for liquid-vapour, the surface energy of the

polymer, and the solid-liquid surface tension, respectively.

Surface tension values "}tLV for different test liquids are reported in table 5.

Table 5. Surface tension values ~'LV for different test liquids

Test liquid '}tLV (mJ/m)

Water 72.8

Glycerol 64

Ethylene glycol 48

Formamide 58

Dimethylsulfoxide 44

Chloroform 27.2

Diiodomethane 50.8

A-bromonaphthalene 44.4

Because surface tensions involving a solid cannot be measured directly, a second equation is

required to determine the hydrophobicity of the material, as given by the surface energy 7sv.

Using a thermodynamic approach, Newmann [29] established the following equation of state to

relate the three interfacial tensions:

YsL = YSV + YLV - 24YsvYLV exp[- fl(YSV - YLV )2 ] (27)

and, combining it with the Young's equation:

cos (9 = - 1 + 2x/'ys v/"YLv exp[- fl(Ysv - YLV )2 ] (28)

where 13 is a parameter independent of the solid and liquid used.

The Young's equation is rigorously applicable if the solid substrate is smooth, if the surface is

homogeneous and rigid, chemically inert and insoluble to contacting liquids. The effect of surface

76 Chapter 2

heterogeneity on contact angle is generally established by relation (29) that predict the contact

angle 0* of a rough surface from the contact angle 0 of the equivalent smooth surface [30]:

cos O* = fl cos 0 - f2 (29)

where fl and f2 are the fractions of liquid-solid and liquid-air surfaces, respectively.

Courel et al. [31 ] demonstrated that the application of Young's equation to a porous surface leads to

an expression similar to (29), where fl = y and f2 = l-y, being y the fraction of membrane surface

made of solid material.

For MD membranes with surface porosity lower than 0.5, it is generally assumed 1-y = ~/z, where

is the porosity and T the pore tortuosity. For PTFE membranes, a more specific model has been

developed:

costg* = y2 costg_ (l_y)2-2y(1-Y)IYsv?'I~V -cost9 (3o)

Under the assumption that the contact angles on the three-phase lines both on the outer drop border

and over the pores are equal (as exemplified in figure 24), Troger and colleagues [32] have obtained

a general relation between the observed contact angle 0' and the ideal one 0 (to be observed on

ideally smooth surface):

4e cosO'+l cos 0 = cos 0 ' - - - (31)

1 - e cosO'-I

where e is the porosity of the porous material; the validity of equation (31) has been tested on

porous PTFE membranes with appreciable results.


Figure 24. The assumption that the contact angles on the three phase lines occurring in the porous structure are equal. After [32].

6.2. Good-van Oss-Chaudhury method

The Good-van Oss-Chaudhury method [33] represents a more complex approach to the

determination of the surface tension components by contact angle measurements. In this case, three

reference liquids (typically water, di-iodomethane, and glycerol) are used to determine the apolar

Lifshitz-vane der Waals component yLW, the acid- base component yAB , the acid (electron

acceptor) y+, and the base (electron donor) component y- of the surface energy.

For instance, di-iodometane (apolar test liquid) allows the evaluation of the Lifshitz-van der Waals

component y LW of the membrane surface tension reflecting the dipole interactions"

(1- oso) y., = (32)

4

Subscripts s and 1 indicate solid (membrane) and liquid, respectively. Other components are

calculated by the following equations:

Ycv(l +c~ 2 [I ,~vy~w - + (33)

yAB 2 4 - § (34) = y , y ,

78 Chapter 2

Typical contact angle of water are close to 120 ~ on PP [34] and are about 108 ~ and 107 ~ on PTFE

and PVDF, respectively [35]. Additional data conceming various polymeric membranes are

reported in table 6.

Table 6. Contact angles in water (W), glycerol (G) and diiodomethane (D), and surface tension

parameters of different polymeric membranes: yLw =Lifshitz-van der Waals component, y -=

electron donor component, 7 '*= electron acceptor component, y,~e= acid-base component of the

liquid surface tension 7'. After [36] Membrane g~ (o) 6~ W (o) gG (o) yLw 7'- Y+ yA~ y

(mJ/m 2) (mJ/m 2) (mJ/m 2) (mJ/m 2) (mJ/m 2)

Nylon 24• 49• 75• 47 57 4 29 75

Polyester 41+2 75• 81+1 39 15 0.9 72 67

Polyethersulfone 30.4+ 1 54+ 1 69+2 44 41 1 14 58

Polyurethane 35+3.6 94.4+1.4 100.9+1.6 42.0 9.0 5.52 14.1 56

Polyetheretherketone- 24.6+2.4 69.9+2.2 69.5+1 46.3 15.7 0.32 4.5 51

WC-20

Polyetheretherketone- 26.2• 71.2+2.8 68.4• 45.7 13.7 0.15 2.9 49

WC-60

Collagen 52+1.3 82+2 .2 67+7.6 33.4 2.3 1.1 3.2 37

6.3.Contact angle and wettability

Comparing experimental results and theoretical calculations, Franken and colleagues [30]

concluded that contact angle measurements on homogeneous smooth materials are not suitable for

an accurate description of the membrane wetting phenomenon in MD. Wettability criteria based on

the concept of penetration surface tension Y~ (defined as the surface tension of the liquid on the

verge of penetrating a porous medium, and measured by penetrating drop method) provided more


satisfying results. Table 7 collects some values of y~" as obtained by Franken for two porous

hydrophobic polymers, PVDF and PP, and measured using various aqueous solutions.

6.4. The breakthrough pressure

In membrane contactors operations, in oder to efficiently work, the interface between phases

must carefully controlled. Generally, non-wetting fluid does not pass through pores as long as the

pressure is kept below a critical threshold known as breakthrough pressure. The Laplace' s equation

offers a relationship between the largest pore radius of the membrane rp.max and the breakthrough

pressure APentry:

2| A P e n t r y - - - ~ (35)

rp,max

where y is the interfacial tension, | is a geometric factor related to the pore structure (equal to 1 for

cylindrical pores), and 0 the liquid-solid contact angle. This angle increases with increasing polarity

difference between the polymeric membrane and the liquid.

8 0 C h a p t e r 2

It is reported that, for a typical water-hydrophobic membrane contact angle of 130 ~ the

penetration pressure of a cylindrical pore with 1 mm diameter is only 185 kPa [37]. Breakthrough

pressure data for several membranes types and fluids can be found in literature [38]" in the most

part of considered cases, AP values range between 100 and 400 kPa (figure 25).

v

L_ C~

C"

L

10 ' ' ' ' ' ' ' ' I

o+.~.. ~ +

++~ �9

�9 J i g + +

0.1

PP-Accurel

PVDF-Accurel

PTFE-Poreflon

PTFE-Gore Tex

I I I I I I I I I

1

Maximum pore size (tam)

+ +

+

�9 -

Figure 25. Water pressure entry for different membranes as a function of the maximum pore size. After [39].

The breakthrough pressure is drastically reduced in presence, even at trace level, of detergents

and surfactants (because they reduce the surface tension), or solvents that exhibit the same

behaviour. Experimental investigations [40] demonstrated that, once a membrane is wetted by the

penetrating liquid, a decreasing in hydrostatic pressure is not able to restore the original un-wetted

condition. For mixtures of water and ethanol, Gostoli and Sarti [41 ] observed that the liquid entry

pressure decreased linearly with alcohol concentration until the membrane was completely wetted at

ethanol concentration of 75 wt%.


If the liquid penetrates through the micropores, a reduction of the hydrostatic pressure does not

restore the un-wetted condition of the membrane. This phenomenon is illustrated in figure 26: the

liquid floods the largest pores if the pressure o v e r c o m e s APentry; as the pressure is increased further,

all the pores are flooded and the transmembrane flux N obeys the Darcy's law:

N = kAP (36)

being k a constant. Experimental investigations [40] showed that, if the applied pressure is reduced,

the flux decreases linearly.

F--

Hydrostatic pressure (AP)

Figure 26. The characteristic trend of the liquid transmembrane flux versus pressure drop in microporous hydrophobic membranes. After [37].

6.5. Microscopic techniques

Microscopy observation and image processing of micrographs directly furnish visual

information about the membrane morphology. Various microscopic techniques are used to

82 Chapter 2

investigate the structure of a membrane; three of them will be considered: the Scanning Electron

Microscopy (SEM), the Transmission Electron Microscopy (TEM) and the Atomic Force

Microscopy (AFM).

In SEM, a beam of electrons (with kinetic energy of 1-25kV) is produced at the top of the

microscope by heating of a metallic filament. The electron beam passes through electromagnetic

lenses which focus and direct it down towards the membrane sample. Once it hits the sample,

secondary electrons are ejected from the surface of the sample. Detectors collect the secondary or

backscattered electrons, and convert them to a signal that is sent to a viewing screen. SEM has a

resolution up to 5 nm. Membrane can be damaged by the electron beam; to prevent it, the sample

needs to be pre-treated by coating with a conducting layer.

Obtaining the pore size distribution from SEM micrographs is an extremely time consuming work;

a more convenient method was developed by Manabe et al. [42] for membranes with pore size

larger than 10 nm. They adopted some geometrical pore models and derived theoretical equations

relating the pore radius distribution function N(r) to the distribution function F(x) of the length x of

test lines cut off by pores in an electron micrograph. For straight-through cylindrical pores:

oo N(r) )dr F(x)= Xx/2I 4(4r 2 _ x 2

(37)

In TEM, a tungsten filament (the cathode) is heated and a high voltage (40- 100,000 kV) in order

to emit electrons. These negatively charged electrons are accelerated to the anode to form an

electron beam that is focussed onto the specimen by electro-magnets and double condenser lenses.

As result, some electrons are scattered whilst the remainder are focused by the objective lens either

onto a phosphorescent screen or photographic film to form an image. TEM has a resolution of 0.4-

0.5 nm; however, this technique requires a complex preparation procedure [43].

AFM (figure 27) operates by measuring attractive or repulsive forces between a tip and the

sample. In the repulsive "contact" mode, the instrument lightly touches a tip at the end of a leaf

spring or "cantilever" to the sample. As a raster-scan drags the tip over the sample, and detection


apparatus measures the vertical deflection of the cantilever, which indicates the local sample height.

In non-contact mode, the AFM derives topographic images from measurements of London-van der

Walls forces; the tip does not touch the sample. Membranes can be scanned in air without pre-

treatments. AFM has a resolution of about 1 nm and offers useful information about the mean

surface roughness Ra, that represents the mean value of the surface relative to the center plane for

which the volumes enclosed by the images above and below this plane are equal.

This parameter is calculated by [44]:

L Lv

(38)

where f(x, y) is the surface profile relative to the centre plane and Lx and Ly are the dimensions of

the surface in the x and y directions, respectively.

Surface profile (f)

Direction (x

Cantilever f ............................ ~ " 7 deflecti~ ~ / , ~ / /

Tip

Surface

Figure 27. Schematic representation of the AFM technique.

84 Chapter 2

6.6. Pore size distribution of microporous membranes

The knowledgement of the mean pore size and pore size distribution of a microporous

membrane is necessary for an accurate prediction of the transmembrane flux.

6. 6.1. Bubble point test

The bubble point test is a simple method for determining the size of the largest pore in a membrane

by measuring the pressure needed to blow air through a liquid-filled membrane. It is based on the

equation that gives the pressure p needed to displace one fluid by another through a pore diameter

dp:

4ycosO p = ~ (39)

dp

where 7 is the interfacial tension of the air-liquid interface, and 0 is the wetting angle with the solid

matrix of the membrane.

From a practical point of view, the membrane is in contact with the liquid (which wets the

membrane) on the top, while the gas flows at the bottom at increasing pressure (figure 28). The air

bubble penetrates through the membrane pores when its radius equals the pore radius; this means

that the contact angle is 0 ~ If using water, a pressure of 1.4 bar has to be applied for penetrating a

pore radius of 1 ~tm, and 14.5 bar for a pore radius of 0.1 p.m. In order to avoid the use of high

pressures, other liquids with low surface tensions (e.g. ethanol, iso-propanol, n-propanol etc.) are

preferentially used.


Figure 28. The principle of bubble-point method.

According to the same principle of the bubble-point method, the pore size distribution of a

membrane can be obtained by gas-liquid displacement technique. For further details, readers are

referred to the specific literature (e.g. [45]).

6. 6. 2. Mercury intrusion porosimetry

In mercury porosimetry, an amount of mercury is forced through the pores of a membrane at

increasing pressures. The required pressure corresponds to a certain pore diameter, according to

equation (39), and the total amount of mercury that disappears in the membrane allows evaluating

the total volume of pores.

Hysteresys of the extrusion-intrusion path and no- loop closing due to some portion of mercury

retained by the sample are common features present in the porograms. In polymeric membranes,

only pores having a diameter greater than 2 ~tm can be reliably detected. As disadvantage, this

technique does not distinct between dead-end pores and interconnective pores.

86 Chapter 2

6.6.3. Liquid permeation

The liquid permeation technique - in conjunction with appropriate mathematical models -

represents one of the most reliable methods for effectively determining pore size distribution.

This technique is based on measurements of the flux of a non-wetting fluid as a function of the

applied transmembrane pressure. At the beginning, pores are completely dry and the application of

a low pressure drop does not cause the flooding of the membrane pores with the non-wetting fluid.

If the applied transmembrane pressure exceeds a threshold value (APmin), liquid starts to penetrate

through largest pores. Further increases in pressure drop give rise to increases in flow, acoording to

the typical behavior shown in figure 26.

With the aim to minimize numerical problems, a smooth curve through experimental flow-pressure

data is required. For this purpose, a smoothing spline S is used:

b

a

(40)

subjected to the constraint:

.

(41)

where a and b are the boundaries abscissa of data, S" is the second derivative of S (geometrically,

its curvature), n the number of data points, wi the weights given to data, and cy the smoothing

parameter.

In order to perform the analysis of the flow-pressure curve according to the method proposed by

Grabar and Nikitine [46], let us consider a normalized function f ( r ) representing the pore size

distribution. If NTOT is the total number of pores, rmax is the radius of the largest pore flooded first,

and r(AP) the radius of the smallest flooded pore, the number of flooded pores N is given by"

N

NTOT

rm~

~ = If(x)dx (42) r(ae)


From a mathematical point of view, the fraction of pores N/NTOT that are flooded at pressure AP is

represented by the shaded area reported in figure 29.

Figure 29. A Gaussian pore size distribution. The number fraction of pores with radii between r and rmax is

represented by the shaded area.

When assuming that pores have a circular shape, the Cantor's equation allows to correlate the radius

of the smallest loaded pore to the flooding pressure AP:

r(AP)= 2yLc~ =~f~' (43) AP AP

where ~/L is the liquid surface tension, 0 is the contact angle, AP is the transmembrane pressure and

~i a constant for a given membrane-liquid pair.

In case of cylindrical pores having a tortuosity x, the Hagen-Poiseuille's equation can be used to

quantify the flowrate Q through the membrane pores:

# r 4 AP Q = ~ (44)

8~t6r

where g is the fluid viscosity, 8 is the thickness of the membrane and r the pore diameter.

Under the hypothesis of uniform membrane thickness, the total transmembrane flow Q at a given

AP>APmin is:

88 Chapter 2

rmax rmax ~ x 4 A p _z \ _

Q= I Xr~ -8ft6-rr :['x)dx:n2AP I X4 f(x)dX r(AP) r(AP)

(45)

Derivative of equation (44) with respect to AP, with opportune rearrangements and substitutions

give the final expression for the pore size distribution function (mathematical details in [47]):

f(r)= d(AP) AP 2 (46)

In equation (45), constants ~'~1~"~2 take into account information about the structural properties of the

membrane, the testing fluid properties and the fluid membrane interactions.

For a normalized distribution, the n-th moment (r") is mathematically defined as:

rmax

rmm (47)

where rmin and rmax are the radii of the smallest and largest pores in the membrane.

The first moment of the distribution corresponds to the average pore radius.

As disadvantage, the characterization method shows a loss in resolution in the pore size distribution

(that can be offset by opportune adjustments of the weighting factors) as the pore sizes decrease to

values well below the largest pore size. Moreover, this method needs an appropriate pore model

describing the membrane structure (eq. (46) is valid for non-interconnecting, cylindrical pores).

Liquid-liquid displacement represents a variant of the method above described. In this case,

membrane pores are filled by a liquid that is displaced by a second immiscible liquid. A typical

liquid pair is water/iso-butanol. Pores with diameters in the range of 5-100 nm can be adequately

detected. With respect to gas-liquid displacement, liquid pairs are characterized by lower interfacial

tensions compared to gas-liquid pairs, and reduced pressures are needed to penetrate pores with the

same size. Further details can be found in literature [45, 48, 49].


6. 6. 4. Perporometry

Perporometry is based on the phenomenon of capillary condensation of liquid in micropores.

The vapour pressure of a liquid depends on the radius of curvature of its surface, according to

Kelvin's equation:

ln P_fl_ - = 27"V cosO (48) Po RTrk

where p and p0 are the vapour pressures in the capillary and under standard conditions, respectively,

y is the surface tension between the capillary liquid and air, V is the molar volume of the liquid, 0

the contact angle, R the gas constant, T the absolute temperature and rk the Kelvin radius, little

smaller than the actual pore radius due to the presence of an absorbed layer of condensable gas.

By applying a partial pressure difference across the membrane, pores can be blocked with liquid

by capillary condensation; this principle is coupled to the measurement of the free diffusive

transport through the open pores.

A scheme of the experimental set-up is reported in figure 30. A mixture of oxygen and nitrogen

(e.g. air) is applied on the feed side, while nitrogen flows on the permeate side as carrier gas. This

creates a concentration gradient of oxygen across the membrane. On both lines, an organic

compound (e.g ethanol) is also applied as condensable gas; in order to avoid swelling phenomena,

the organic vapour should exhibit a low affinity with the membrane. At both sides of the membrane,

the absolute pressure is 1 atm and the relative pressure of the organic vapour is the same.

Evaporator

N2, Ethanol

N2, O 2, Ethanol

Evaporator

Figure 30. A permporometry setup.

I . [

DIFFUSION CELL

Membrane

IP GC Analysis

90 Chapter 2

The size distribution of active pores is therefore obtained by measuring the gas flow through the

membrane. For pore radii of 1-25 nm and at atmospheric pressure, the flux of the i-th component

through a pore with radius ri, determined by Knudsen diffusion, can be expressed as:

j , = 2 [ 8~ Ap n,r, (49)

3V MwRT A mr 6

where Mw is the molecular weight of the gas, R the gas constant, T the absolute temperature, Ap the

partial pressure gradient across the membrane, Am the membrane surface area, x the tortuosity of

pores, 8 the membrane thickness, and ni the number of pores having radius ri.

Integrating over the entire distribution of pore radii, few manipulations allow obtaining the pore

size distribution:

-d-~-~ rnun L drm,n -3V 8---~ Apr3mm (50)

Quantitative analysis are preferentially carried out during desorption process, since it is more

difficult to reach equilibrium during adsorption process: the gas (oxygen, in the discussed case) flux

as a function of the Kelvin radius through Nucleopore membranes (pore size given by

manufacturer: 15 nm) is reported in figure 31.


i

E ~ 3

6

' I ' I ' i '

i I i I i

4 8

Kelvin radius (nm)

0 I

0 12 16

Figure 31. Oxygen flux versus Kelvin radius for a Nucleopore membrane. After [45 ].

This technique characterizes only active pores in the range of 2-40 nm. More details are in [50, 51,

52,53].

6.6.5. Thermoporometry

Thermoporometry is based on the calorimetric measurement of a solid-liquid transition in a porous

material in order to determine the pore size distribution [54, 55, 56, 57].

In pores totally filled with a liquid, the curvature of the liquid-solid interface Cs is related to the

change of temperature T by:

r~ ,

92 Chapter 2

where V is the volume of the pore, AS is the surface area of the solid-liquid interface, ), is solid-

liquid surface tension.

The liquid-solid interface is almost spherical and its curve Cs is:

2 Cs " - ~

r - t where t is the thickness of the layer of condensate fixed to pore wall.

(52)

Equations (51) and (52) link the pore radius r to a decrease in solidification temperature T-T0. In

case of water, in the range of-40<T-T0<0 and considering t=0.8 nm as a typical value, Nakao [45]

reports the following relation for melting:

r(nm)= 32.33 - ~ + 0 . 6 8 (53) T-To

The energy of solidification W is related to undercooling AT by �9

W = -0.155.10 -2 AT 2 - 11.39AT- 332 (54)

The differential change of pore volume dV corresponding to d(AT) is given by:

1 dW dV = - - ~ ( 5 5 )

p W

where 9 is the water density.

Differentiating eq. (53) and coupling with (55), the equation that permit to calculate the pore

volume distribution function from water thermograms is derived:

dV _ (AT) 2 dW (56) ~ m

dr 64.67pWd(AT)

For practical analysis, the heat flux required for melting is measured by Differential Scanning

Calorimetry (DSC), and equation (56) is more conveniently used in the form:

d___V_V = ( A T ) ~ q (57) dr 64.67pW d(AT)/dt

where q is the heat flux obtained by DSC and d(AT)dt is temperature changing rate.


Thermoporometry is suited to characterize pores with diameters in the range of 2-50 nm; all pores,

also those not active, are included in the characterization.

7. The influence of pore size distribution on the transmembrane flux

An inadequate knowledge of the morphology of a microporous membrane can lead to inaccuracy

when modelling the mass transfer [58]. A good agreement between theoretical and experimental

results was obtained by Martinez-Diez and Vazquez-Gonzalez [59] using pore sizes measured by

mercury porometry and liquid displacement methods.

The attention to the structural properties of microporous polymeric membranes involved in MD

operations is today increasing significantly.

If f(r ) is the normalized distribution, and J(r ) the transmembrane flux through all pores with radii

equal to r, the total flow rate JT (r') through the membrane is obtained by the following integral

relation:

oo

Jr = IJ(r')~r(r')2 f(r') dr' (58) 0

Typically, a lognormal distribution in the form reported above, is sufficiently accurate to model the

size distribution of membrane pores:

_ , e x p f ( r ) = SD, ogr.~_~ 7L SD,og J (59)

where f(r) is the number of pores with pore radius r, ~ the mean pore radius, and SDiog the standard

deviation of lognormal function.

Figure 32 depicts the pore size distribution of a PP Accurel| hydrophobic membrane, frequently

used in membrane contactors experiments.

94 Chapter 2

0

0

d) t'~

E t -

or-

800

600

400

200

I ' I '

m

0.2 0.4 0.6

Pore diameter (gin)

Figure 32. Pore size distribution of an Accurel| PP membrane. After [60].

Laganh and coworkers [61] studied the effect of the shape of pore size distribution with

Gaussian (symmetric) and logarithmic (asymmetric) distribution functions; in this investigation,

non-symmetrical distribution achieved better agreement with the experimental results. Several

mathematical models aiming to examine the influence of both pore size distribution and air flux in

DCMD were presented by Phattaranawik et al. [62]. In particular, the log-normal distribution was

used to represent the shape of pore size distribution. In conclusion of their work, authors reported

that the predictions of the fluxes and MD coefficients showed good agreement with the

experimental results for GVHP-PVDF (Millipore, 0.22 mm) and excellent agreement for HVHP-

PVDF (Millipore, 0.45 mm) and PTFE (Sartorius, 0.2 mm). Additionally, the models predicted

fluxes with less than 8% discrepancy.

The investigation carried out by Martinez-Diez and colleagues [63] on three commercial

membranes frequently used in MD applications showed that the MD water vapour transfer

coefficients, calculated considering the pore size distributions, are similar to the ones obtained


assuming an average pore size model, and the permeabilities calculated from air-liquid

displacement measurements agree well with those obtained in literature MD models.

8. Estimation of the membrane distillation coefficient

For characterization purposes, a number of works involved flat membranes assembled in the

Lewis test cell having stirring capabilities (figure 33).

Figure 33. Schematic representation of a Lewis test cell.

Another common configuration considers the recirculation of both (hot) feed and (cold)

permeate streams through flat membranes using channel devices (figure 34).

96 Chapter 2

Permeate Permeate inlet outlet

Feed inlet /1

/1

Membrane

Feed outlet

Figure 34. Schematic representation of a flat channel test cell.

In thermal membrane distillation, the mass transport process through a microporous hydrophobic

membrane can be described by the following equation [64]:

cFdp ] (60 J = -~t"ffT-jrATm

where J is the molar flux per unit area, fi is the membrane thickness, C the membrane distillation

coefficient, APv the vapor pressure difference across the membrane, and ATm the temperature

difference between the membrane interfaces.

The value of ATm is related to bulk temperature difference ATb:

M e m b r a n e Mater ia ls 97

1 AT m = - - - - -~ AT b (61)

l + - - h

where

km H = CA dPv + ~ (62) dT 6

being H the overall heat transfer coefficient, ;~ the latent heat of vaporization, km the thermal

conductivity of the membrane, and 5 the membrane thickness.

Combining the previous equations:

l + k m ATb eta 1

J,~ c,~ dev h dT

(63)

Plotting the experimental data in terms of AT b / d2 vs. 1/(dP v / dT) , h can be evaluated from the

intercept (1/h) and C is obtained from the slope (1/CL)/(1 +km/Sh).

As example, figure 3 5 refers to the calculus of membrane coefficient C and heat transfer coefficient

h operated by Martinez-Diez and colleagues [65] starting from permeation experiments with a

PTFE membrane conducted by using a flat membrane module with channels for recirculation of hot

and cold water.

98 Chapter 2

E

d X

<1

I i I i

h = 1515+ 90 Wm-2K -~ C(x107)=21.0_+1.1 kg m-2s-~Pa -~

I , I , I

2 4 6

l/(dPv/dT) x 10 3, K/Pa

Figure 35. A plot of ATb/JX versus 1/(dPv/dT) corresponding to results obtained by [65] with a recirculation rate of 9.0 cm3/s.


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