[membrane science and technology] membrane contactors: fundamentals, applications and potentialities...
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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
Membrane Materials 43
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
Membrane Materials 45
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).
Membrane Materials 47
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);
Membrane Materials 49
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.
Membrane Materials 51
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
Membrane Materials 53
~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.
Membrane Materials 55
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.
Membrane Materials 57
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)**
Membrane Materials 59
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.
Membrane Materials 61
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
Membrane Materials 63
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.
Membrane Materials 65
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].
Membrane Materials 67
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
Membrane Materials 69
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].
Membrane Materials 71
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
Membrane Materials 73
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)
Membrane Materials 75
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.
Membrane Materials 77
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
Membrane Materials 79
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%.
Membrane Materials 81
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
Membrane Materials 83
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.
Membrane Materials 85
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)
Membrane Materials 87
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].
Membrane Materials 89
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.
Membrane Materials 91
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.
Membrane Materials 93
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
Membrane Materials 95
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.
Membrane Materials 99
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