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HERARY
Michigan State Th t fy h h
. :' _; is is ocerti t att e
U n ‘Vers 'iy thesis entitled

 

Size-selective Transport of Uncharged Solutes through
Multilayer Polyelectrolyte Membranes

presented by

Xiaoyun Liu

has been accepted towards fulﬁllment
of the requirements for the

MS. degree in chemistry

 

 

“mu/0 ﬂux“

'Major professor’s Signatare

8/13/03

Date

MSU is an Afﬁrmative Action/Equal Opportunity Institution

 

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
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6/01 c:/ClFlC/DataDuo.p65-p.15

Size-selective Transport of Uncharged Solutes
through Multilayer Polyelectrolyte Membranes

By

Xiaoyun Liu

A THESIS

Submitted to
Michigan State University
in partial ﬁllﬁllment of the requirements
for the degree of

MASTER OF SCIENCE
Department of Chemistry

2003

Abstract

Size-selective Transport of Uncharged
Solutes through Multilayer Polyelectrolyte Membranes

By
Xiaoyun Liu

Several recent studies demonstrated highly selective ion transport through
multilayer polyelectrolyte membranes. This thesis examines the transport of neutral
molecules through multilayer polyelectrolyte ﬁlms and shows signiﬁcant size-based
discrimination among organic analytes. Simple 7-bilayer poly(styrene sulfonate)
(PSS)/poly(allylamine hydrochloride) (PAH) ﬁlms deposited on porous alumina exhibit a
glucose/sucrose selectivity of ~1 50 in both diffusion dialysis and nanoﬁltration.
However, selectivity among smaller solutes is fairly low (methanol/glycerol z 2 and
glycerol/glucose z 8). High selectivity in nanoﬁltration by PSS/PAH membranes is
accompanied by relatively high solute rejections. Although such high rejections will
preclude the use of these membranes in sugar separations, they may prove useful in
applications such as removal of organic pollutants from water. The high water ﬂux
through PSS/PAH ﬁlms (0.9 m3m'2d'l at 4.8 bar) would also be important in water
puriﬁcation. Capping PSS/PAH ﬁlms with a few bilayers of poly(acrylic acid)
(PAA)/PAH increases glycerol/glucose diffusion-dialysis selectivity from 8 to 75. Thus,
controlling ﬁlm composition may allow tailoring of membrane properties for speciﬁc
separations. Simulations of nanoﬁltration and diffusion dialysis data for 7-bilayer
PSS/PAH membranes suggest that these ﬁlms have a porosity of 2 to 3% and pores with

radii of 0.4 to 0.5 nm.

ACKNOWLEDGEMENTS

First of all, I want to thank my advisor, Dr. Bruening. I have really enjoyed the two
years’ research under your guidance. Being with you is a great pleasure and working
with you is a process of having fun. I am impressed by your thoughtful insight into
scientiﬁc problems, your determination to ﬁgure out any puzzle, your great sense of
humor and. . .. Thank you so much.

Also, I would like to thank all my group members, past and present. Jinhua, Yingda,
and Wenxi, thank you so much for helping me get through the hard times. A smart guy,
Dan, I want to thank you for your help on technical problems, both for me and for the
group. Anagi, Bo, Brian, Christin, J in, Keith, Lei, Mat, and Sri, nice to work with you.

Last, I want to thank my loved parents and sister on the other side of the earth (I miss
you so much), and all my loved ﬁiends both here and in China. I am here because of all

ofyou!

iii

TABLE OF CONTENTS

List of Tables
List of Figures
Chapter 1. Introduction and Background

1.1 Membranes

1.2 Introduction to Membrane Processes

1.3 Nanoﬁltration: Signiﬁcance and Applications

1.4 Ultrathin Organic Films and Multilayer Polyelectrolyte Membranes
1.5 Transport through Porous and Nonporous Membranes

1.6 Motivation behind this Research

Chapter 2. Size-selective Transport of Uncharged Solutes through Multilayer
Polyelectrolyte Membranes

2.1 Introduction
2.2 Experimental Section
2.2.1 Materials
2.2.2 Film Deposition
2.2.3 Transport Studies
2.3 Results and Discussion
2.3.1 Diffusion Dialysis through PSS/PAH Membranes
2.3.2 Diffusion Dialysis through Hybrid PSS/PAH/PAA Membranes
2.3.3 Nanoﬁltration with PSS/PAH Membranes
2.3.4 Theory for Modeling of Transport
2.3.5 Determination of Effective Pore Sizes

Chapter 3. Conclusions and Future Work

References

iv

vi

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19

19
20
20
2O
21
27
27
31
34
37
42

46

47

LIST OF TABLES

Table 1. Typical Pressures, Permeabilities, and Solute Sizes Associated
with Different Pressure-driven Membrane Separations

Table 2. Molecular Weights, Diffusion Coefﬁcients (D) and Stokes’
Radii (rs) of Several Neutral Solutes

Table 3. Normalized Fluxes (mol cm'2 s’l/ M) and Selectivities in
Diffusion Dialysis through Bare Porous Alumina and Alumina
Coated with Polyelectrolyte Films

Table 4. Percent Rejections, Water Fluxes (in m3m'2d'l), and
Selectivities from NF Experiments with Multilayer Polyelectrolyte
Membranes and Solutions Containing Several Neutral Molecules

Table 5. Parameters and Fluxes (mol cm'2 5") Relevant to the
Simulation of Diffusion Dialysis through a 7-bilayer PSS/PAH
Membrane Assmning a Membrane Pore Radius of 5.28 X 10'8 cm

Table 6. Parameters and Rejections Calculated in the Simulation of
Nanoﬁltration with a 7-bilayer PSS/PAH Membrane Assuming a
Membrane Pore Radius of 4.2 X 10'8 cm

18

30

35

43

43

LIST OF FIGURES

Figure 1. Schematic representation of a membrane-based separation process.

Figure 2. Schematic diagram of layer-by-layer deposition of oppositely
charged polyelectrolytes on a porous substrate.

Figure 3. Krasemann and Tieke model for rejection of several different
ions by a multilayer polyelectrolyte ﬁlm.

Figure 4. Some characteristic pore geometries found in porous membranes.
Figure 5. Schematic representation of the cell used in diffusion dialysis.
Figure 6. Schematic diagram of the cross-ﬂow nanoﬁltration apparatus.
Figure 7. Gas-chromatography calibration curve for methanol.

Figure 8. Typical chromatogram of glycerol (peak 1), glucose (peak 2)
and sucrose (peak 3) in LC analysis.

Figure 9. Normalized permeate-phase concentrations of glycerol (squares),
glucose (triangles), and sucrose (diamonds) as a function of time in
diffusion dialysis through a 7-bilayer PSS/PAH membrane. The inset
shows an expanded view for glucose and sucrose.

Figure 10. Normalized permeate-phase concentrations of methanol
(squares), glycerol (triangles), and glucose (diamonds) as a function of
time in a diffusion dialysis experiment with a S-bilayer PSS/PAH

+ 1.5-bilayer PAA/PAH ﬁlm. The inset shows the expanded

view of glycerol and glucose transport across the membrane.

Figure 11. Schematic diagram of the analyte concentration proﬁle

in a membrane composed of a polyelectrolyte ﬁlm on a porous
alumina support.

vi

10

ll

22

23

25

26

28

32

38

Chapter 1

Introduction and Background

1.1 Membranes

A membrane is deﬁned as a selective barrier between two phases. These barriers
can be thick or thin, and their structure can be homogeneous or heterogeneous.
Additionally, membranes can be natural or synthetic, neutral or charged. Although
membranes can be classiﬁed from different points of view, morphological
classiﬁcation is probably most pertinent to this thesis. Generally speaking, there are
two types of membrane structures: symmetric and asymmetric. Symmetric
membranes consist of a homogeneous ﬁlm whose thickness is generally relatively
large (10 to 200 um). Because ﬂux through a membrane is usually inversely
proportional to membrane thickness, transport through symmetric membranes is often
unacceptably slow.

The development of asymmetric membranes revolutionized industrial applications
of membranes. These structures consist of a very dense skin layer (thickness of 0.1 to
0.5 pm) on a porous substrate (thickness of 50 to 150 pm). The skin layer provides
selectivity, while the porous support affords mechanical stability."2 Even though the
skin layer may be highly size-selective, its minimal thickness still allows high ﬂux.
Because the support is highly porous, resistance to mass transfer is largely determined

by the thin skin layer.

1.2 Introduction to Membrane Processes

Membrane processes are designed to achieve speciﬁc separations. Paramount in
any process is the capability of the membrane to allow faster transport of one
component than another. Differences in transport rates result from differences in
physical (size) or chemical properties of the transporting compounds. Driving forces
behind transport include electrical potentials, pressure, and concentration gradients
(Figure 1). Usually the transport rate, or solute ﬂux, is proportional to the driving
force. For instance, in diffusion dialysis, the ﬂux is proportional to the concentration
gradient as shown by F ick’s law (equation 1).

j. = -D.-————' (1)
In this equation, j,- represents solute ﬂux, D,- is the solute diffusion coefﬁcient in the
membrane, and dc,-/dx is the concentration gradient.

Membrane-based separations are applied in a wide variety of processes including:
microﬁltration (MF), ultraﬁltration (UF), nanoﬁltration (NF), reverse osmosis (R0),
electrodialysis, diffusion dialysis, gas separation, pervaporation and membrane
distillation. Among these processes, MF, UF, NF, and R0 are all pressure-driven
processes that involve the separation of solutes. Classiﬁcation of these processes is
generally based on solute size and operating pressure. For the sake of comparison,
Table 1 lists the solute sizes, operating pressures, and membrane permeabilities in MF,

UF, NF, and R0.

membrane

 

 

 

 

 

 

 

 

 

’
o . > o
0 O .. > .
feed 0 .O > O Eermeate
O O o > o
. O > .
O 0. t
O >

 

 

 

Driving force AC, AP, AT, AE

Figure 1. Schematic representation of a membrane-based separation process.

Table 1. Typical Pressures, Permeabilities, and Solute Sizes Associated with

Different Pressure-driven Membrane Separations 3

 

 

membrane process pressure range (bar) (Ipenrrpiabitlityl) 30121:“ :ize
microﬁltration 0. 1 -2.0 >50 >100
ultraﬁltration 1.0-5.0 10-50 5-100
nanoﬁltration 50-20 1 .4-12 0.1-8
reverse osmosis 10-100 0.05-1.4 <1

Application requirements generally dictate membrane structure.3 For example,
retention of particles with diameters >100 nm (microﬁltration) can occur with a highly
porous structure, while separation of macromolecules (molecular weights ranging
from about 104 to more than 106) in ultraﬁltration necessitates somewhat denser
membranes. Separation of low molecular weight compounds in applications such as
pervaporation and gas separation calls for the use of dense, nonporous membrane
materials. NF and R0 membranes, which are employed for separation of inorganic
ions or small organic molecules from solvent, have a structure that is intermediate
between open, porous membranes (MF/UF) and dense, nonporous membranes

(pervaporation and gas separation).

1.3 Nanoﬁltration: Signiﬁcance and Applications

Nanoﬁltration (NF) is becoming an increasingly important membrane process for
separations in areas such as water puriﬁcation, treatment of pulp and paper mill
efﬂuents, fractionation/puriﬁcation of protein, cheese-whey desalting, and sulfate
removal from oil-well injection water.4 Since the properties of NF membranes fall
between those of UF and R0 systems, the separation mechanism in NF can involve
both steric (sieving) and electrical (Donnan) effects. The electrical effect can play a
very important role in electrolyte separations. However, for neutral molecules such
as sugars, mass transport through NF membranes is controlled primarily by steric
factors.5 The advantage of NF over RO is operation at moderate pressures along with
a relatively high ﬂux. Thus, in applications such as water softening, NF membranes
can provide puriﬁed water at a lower operating cost. However, analytes separated by
NF are generally larger than those separated by RC. NF membranes can remove
essentially 100% of suspended particles, but they will not remove as many dissolved
substances as RO membranes, especially small inorganic ions like Na+ and Cl: One
can think of a NF membrane as a more “porous” R0 system, although according to the
“solution-diffusion” theory often applied to R0 membranes, there are no actual
“pores”.

The largest users of NF technology are municipal drinking water plants, and the
state of Florida is, by far, the greatest user of NF in the United States. It is estimated

that Florida NF operations will soon be capable of producing more than 100 million

gallons per day of NF permeate.6 There are existing plants that process more than 10

million gallons of water per day.

1.4 Ultrathin Organic Films and Multilayer Polyelectrolyte Membranes (MPMs)

The key to further enhancing the utility of NF is the development of membranes
that exhibit high ﬂux and selectivity as well as durability and resistance to fouling.7‘8
Synthesis of such membranes typically requires formation of an ultrathin, defect-free
ﬁlm on a highly permeable support in order to achieve sufﬁcient ﬂuxes in highly

1.2.9-1 1

selective systems. However, conventional techniques of ﬁlm preparation are

not capable of forming ultrathin, defect-free separating layers. Solution casting, for
example, is limited to the preparation of layers with thicknesses > 1 pm.12
Preparation of thinner separating layers requires more sophisticated deposition
techniques. In this regard, methods that allow thickness control at the nanometer
level, (e.g., self-assembly and Langmuir-Blodgett (LB) techniques13 '17) would clearly
be advantageous. More than 20 years ago, researchers tried to prepare composite
membranes using the LB technique to deposit multilayers of amphiphiles or

amphiphilic polymers on porous supports. '8

However, the LB separation layers did
not provide high permeability and selectivity because they consisted of densely packed
aliphatic chains with poor molecular mobility and low ﬂexibility. Even the use of
amphiphilic polymers with short alkyl side groups did not substantially improve the

separation efﬁciency. More recently, Regen and coworkers employed calixarene

amphiphiles to form selective membranes by the LB technique.” Although Regen’s

membranes are very impressive, fabrication of these materials on a large scale will
likely be very difﬁcult.

”'2' reported preparation of thin

About a decade ago, Decher and co-workers
polymer ﬁlms using electrostatic layer-by—layer assembly of cationic and anionic
compounds on a solid substrate. In a typical process, a negatively charged substrate is
dipped into a dilute aqueous solution of a positively charged polyelectrolyte so that the
polymer adsorbs on the substrate surface to form a molecularly thin ﬁlm and reverse
surface charge. After careful washing, the coated substrate is dipped into an aqueous
solution of a negatively charged polyelectrolyte so that this polymer adsorbs on top of
the previous one and again reverses surface charge. Repetition of the adsorption steps
yields a polyelectrolyte multilayer assembly in a simple, environmentally clean, and
elegant procedure.

Soon after the ﬁrst report on molecular ﬁlms prepared by alternating
polyelectrolyte deposition (APD), Stroeve and co-workers22 applied this technique to
the preparation of composite membranes. Polyelectrolytes were successively
adsorbed on hydrophilized, porous surfaces to form a skin layer as schematically
outlined in Figure 2. Films prepared by APD are attractive materials for membrane
skins for several reasons. First, their minimal thickness should allow high ﬂuxes.23
Film thickness can be controlled on the nanometer scale simply by varying the number
of deposited bilayers. Second, nearly any polyelectrolyte can form these ﬁlms, and
24-31

thus one can easily tune a separation through proper selection of ﬁlm constituents.

In addition, variation of deposition conditions such as solution

 

@769
‘6)

 

‘@

 

Figure 2. Schematic diagram of layer-by-layer deposition of oppositely charged

polyelectrolytes on a porous substrate.

35-38

pH32'34 and supporting electrolyte concentration also allows optimization of ﬁlm

properties. Finally, recent studies suggest that some polyelectrolyte ﬁlms resist cell

growth and protein adhesion and thus, may be somewhat resistant to fouling.”40

Over the past few years, a number of groups examined the capabilities of

22.41-43

multilayer polyelectrolyte membranes (MPMs) in gas separation, pervaporation

separation of alcohol/water mixtures,4446 and microﬁltration of protein solutions4749.
Additionally, MPMs are especially attractive for separating ions with different

0-54

valences.5 Krasemann and Tieke demonstrated Cl'/SO42' selectivity as high as 45

using poly(allylamine hydrochloride) (PAH)/poly(styrene sulfonate) (PSS) ﬁlms and
suggested that selectivity is due to greater Donnan exclusion of the divalent $042253
Their model of ion rejection,S3 which is represented in Figure 3, implies that ion
separation should become progressively more effective as the number of adsorbed
polyelectrolyte layers increases. However, fundamental studies of polyelectrolyte
ﬁlms suggest that polycations and polyanions are highly intertwined and that the bulk
of these ﬁlms does not contain a layered structure. Farhat and Schlenoff showed that
diffusion through multilayer polyelectrolyte ﬁlms on electrodes depends on analyte

55.56

charge, and we recently reported enhancement of the ion-transport selectivity of

MPMs through cross-linking, hybridization, and control over charge density.5 1'57’59
Preliminary simulations suggest that both selective diffusion and Donnan exclusion

play a role in effecting selectivity. Donnan exclusion occurs primarily at the ﬁlm

surface.

anionic
cationic
anionic
cationic

 

 

Figure 3. Krasemann and Tieke model for rejection of several different ions by a
multilayer polyelectrolyte ﬁlm (Taken from reference 52, with permission from the
American Chemical Society, copyright 2000).

1.5 Transport through Porous and Nonporous Membranes.

Figure 4 gives a schematic representation of several geometries that are possible in
porous membranes. The particular geometry in a membrane must be taken into
account in any model of transport. However, if pore geometry is approximately
known, transport models can demonstrate which structural parameters govern ﬂux and
suggest how to improve membrane performance.

The simplest representation of pore geometry is an assembly of parallel cylindrical
pores that extend completely through the membrane (see Figure 4a). Assuming that
all the pores have the same radii, r, equation (2) provides an expression for volume

ﬂux, JV, through a membrane.

(a)
(b)

 

Illll

Figure 4. Some characteristic pore geometries found in porous membranes.3

JV ___ rza‘AP
877rAx

 

(2)

This equation shows that solvent ﬂux is proportional to the driving force, i.e. the
pressure drop (AP) across the membrane, and inversely proportional to the solution
viscosity, I] , and the membrane thickness Ax. Other variables that affect ﬂux include
membrane porosity (a), which is the fractional pore area, and r, which is the pore
tortuosity. (For cylindrical pores, the tortuosity is equal to unity)

The Hagen-Poiseuille equation (equation (2)) gives a good description of transport
through membranes consisting of a number of parallel pores. However, very few
practical membranes possess such a structure. Structures similar to a system of closed
packed spheres (Figure 4b), are more common in sintered inorganic membranes or in
the nodular top layer of membranes prepared by phase inversion. The
Kozeny-Carman relationship describes the volume ﬂux through such membranes as
shown in equation (3),3

83 AP
Jv = 2 2 —
KnS (l—y) Ax

 

(3)

where 7 is the volume ﬁaction of the pores, S is the internal surface area and K is the
Kozeny-Carman constant, which depends on the shape of the pores and the tortuosity.

Some membranes prepared by phase inversion have a sponge-like structure, as
schematically shown in Figure 4c. Either the Hagen-Poiseulle or the Kozeny-Carman
relationship can describe the volume ﬂux through these membranes, although the
morphologies implied by the two models are quite different.

Nonporous materials constitute another important class of membranes. When the

12

sizes of molecules to be separated are in the same order of magnitude as oxygen,
nitrogen or hexane, porous membranes cannot effect a separation, and nonporous
membranes are necessary. However, the term nonporous is rather ambiguous because
pores (permanent or transient) must be present on a molecular level or no transport
would occur. Free volume theory provides a good description of the existence of
dynamic molecular pores and allows modeling of diffusion coefﬁcients in non-porous
membranes. The solution-diffusion mechanism describes the overall process of
transport through nonporous materials and satisfactorily explains the transport of gas,
vapor or liquid through a dense, nonporous membrane. This is also the most p0pular
model for reverse osmosis systems. Equations (4) and (5) comprise the essence of the
solution diffusion model. Flux is proportional to the permeability coefﬁcient, P, and
the pressure drop across the membrane, Ap, and inversely pr0portional to the
membrane thickness, Ax. The permeability coefﬁcient is a function of the solubility
coefﬁcient, S, for a transporting species as well as the diffusion coefﬁcient, D, of this
species.

Flux (j) = Permeability (P) X Ao/Ax (4)

Permeability (P) = Solubility (S) X Diffusivity (D) (5)

The solubility coefﬁcient is a thermodynamic parameter and gives a measure of the
amount of solute absorbed by the membrane under equilibrium conditions. Henry’s
law applies to the low solubility of gases in elastomeric polymers, and S is a constant.
However, with organic vapors or liquids, which are not as ideal as permanent gases, S

is a more complicated function of concentration. Diffusivity is a kinetic parameter

13

that indicates how fast a solute transports through the membrane. The diffusion
coefﬁcient depends on the geometry of the solute and decreases with increasing solute
size. For solutes that are capable of swelling the membrane, diffusion coefﬁcients
will also depend on concentration.

Quantitative methods for predicting performance in membrane-based separations
will facilitate the optimization of existing systems and broaden the range of membrane
applications. Modeling of transport requires data that describe membrane properties
as well as a fundamental mathematical description of the transport process. This
thesis focuses on NF, and the properties of NF membranes required for simulations
include pore density and geometry and electrical parameters such as the surface charge
density or the volumetric charge density. Since NF membranes have nm-sized pores,
and macroscopic descriptions of hydrodynamics may fail at these dimensions, it is
especially challenging to decide whether to model these membranes as porous or dense,
homogeneous materials. The assumption of a porous membrane necessitates the
description of solute transport inside pores with radii that are only a few times larger
than the radii of water molecules. This, in turn, leads to the question of whether one
can truly apply macroscopic descriptions of hydrodynamic and charge interactions to
NF membranes. Providing an answer to this question is difﬁcult because no existing
analytical or physical techniques can probe the structure of NF membranes with
conﬁdence. Most models of transport through NF membranes have thus far assumed
such membranes to consist of bundles of capillary tubes. Essentially, the

macroscopic models that were used for large pores have been adapted to describe NF.

14

The extended Nernst-Planck equation (equation (6)) forms the basis for modeling
the ﬂux, j,-, of ions and neutral solutes through porous membranes. In this equation,
dCi _ 21C: Di Fgl/i

j,’ =_Dl_

+ . v 6
dx RT dx CrJ ()

diffusive ﬂux is proportional to the diffusion coefﬁcient, D,-, and the concentration
gradient, dci/dx, while ﬂux due to migration is proportional to the potential gradient,
d l/I/dx, solute charge, 2,, solute concentration, c,-, the diffusion coefﬁcient, Di, and
several standard fundamental constants. The convective term, which is proportional
to the volume ﬂux of solvent, J... and the solute concentration, c,-, represents solute
being dragged through the membrane with solvent. When coupled with a suitable
description of the partitioning of solutes between solution and membrane, the extended
Nernst-Planck equation provides a complete description of transport. For uncharged
solutes, only the diffusive and convective ﬂows contribute to transport, so the
expression for ﬂux can be simpliﬁed to equation (7).

j. =—D,%+C.Jv (7)

In the case of very small pores, both diffusion and convection are hindered by drag of
the solute on the pore wall. Bowen and Mukhtar accounted for the hindered nature of
diffusion and convection of the solutes inside the membrane with the terms KM and
Km respectively, in equation (8).

. dc' ZiCiKirlD! (191/
.=— ,., ,—'-———'—F—+ .-..- . 8
J, KJDdx RT dx K.cJ ()

These hindrance factors are often calculated using the hydrodynamic coefﬁcients K],
the enhanced drag, and G, the lag coefﬁcient, for a spherical solute moving inside a

cylindrical pore of inﬁnite length.

15

A number of previous studies examined transport models for NF membranes.

The separation of charged solutes in NF membranes has been interpreted using the
extended Nernst-Planck equation combined with the Teorell—Meyer-Sievers
assumption (TMS model)"‘”’2 or the space-charge pore (SCPM) model."2 The TMS
model assumes that the membrane is homogenous, that the distribution of ﬁxed charge
density inside the membrane is uniform and that ion transport may be quantiﬁed using
bulk diffusivities. Donnan equilibrium is employed to calculate concentrations at
membrane-solution interfaces. Wang et al.63 employed the TMS model to estimate
the effective charge density in several NF membranes by using the effective
thickness/porosity values obtained from separate experiments on uncharged solutes.
The SCPM model takes into account the charge distribution inside of small pores as
well as the Poiseuille ﬂow proﬁle.

Bowen and Mukhtar 64 proposed a hybrid model based on the extended
Nemst-Planck equation to describe the transport of salts. The model assumed that the
membranes were homogenous but included hindrance factors for diffusion and
convection (mentioned above) to allow for the transport of ions in the membrane
taking place within a conﬁned space. The effective pore radius was estimated by
ﬁtting the rejection data for NaZSO4 and NaCl. In a subsequent paper, Bowen et al."5
used a similar model to interpret experimental data for the rejection of three salts with
a common co-ion and ﬁve uncharged solutes. Additionally, they attempted to make
direct measurements of surface pore radius and surface porosity by AFM.

Comparison of the results of these techniques allowed an evaluation of the

16

appropriateness and applicability of three possible descriptions of transport and
rejection in NF membranes i.e. a hybrid model (HM) without a solute velocity
distribution in pores, a porous ﬂow model (radial variation in velocity within a pore)
(PM), and a pore model with a full description of the space charge in the pores
(SCPM). Comparison of the characterization parameters obtained with HM and PM
models with salts and uncharged solutes suggested that PM gave results in better
agreement than the HM. It was probably due to the fact that the derivation of
hindrance factors inherently assumed a velocity distribution of the solute inside the
pores. Additionally, calculations of the potential distribution across pores indicated
that the variation of potential is less than 3 mV for membranes with a pore radius < 2.0
nm. Thus, for most nanoﬁltration membranes, the added complexity of the SCPM

model which describes the potential distribution is not necessary.

1.5 Motivation behind this Research

The main objective of this work is to better understand transport through
multilayer polyelectrolyte ﬁlms by studying the diffusion of various neutral molecules
across MPMs. The use of neutral analytes eliminates Donnan effects and allows us to
focus exclusively on size-based selectivity. In addition to providing fundamental

insight, neutral molecule studies will be important for potential applications of MPMs

66-71 72,73 74,75

such as controlled release, water puriﬁcation, and salt/sugar separations.
We chose to investigate transport of methanol, glycerol, glucose, and sucrose because

these molecules differ in size (Table 2) and yet have similar functional groups and

17

hydrophilicities.°5‘76

Diffusion dialysis studies with these molecules show that MPMs
can exhibit very high size-based selectivities (glucose/sucrose selectivity reaches 150)
that depend on membrane composition. Selectivities are maintained in high-ﬂux NF,
but rejections are also high. Even with the smallest molecule, methanol, rejection by

PSS/PAH ﬁlms is 70%. These high rejections suggest that PSS/PAH membranes

may be useful in removal of organic pollutants from water.

Table 2. Molecular Weights, Diffusion Coefﬁcients (D) and Stokes’ Radii (r,) of

Several Neutral Solutes 65‘"

 

 

solute MW D (m2 s'1 X 10'9) rs (nm)
methanol 32 1.56 0.157
glycerol 92 0.95 0.260
glucose 180 0.69 0.355
sucrose 342 0.52 0.471

18

Chapter 2

Size-selective Transport of Uncharged Solutes through Multilayer

Polyelectrolyte Membranes

2.1 Introduction

Recently, several studies demonstrated that alternating electrostatic adsorption of
cationic and anionic polyelectrolytes on porous supports is a versatile method to
prepare composite membranes with an ultrathin, defect-free separation layer.22’23’33’52
Careful choice of the polyelectrolytes and the porous substrate and optimization of
processing parameters afford composite membranes that exhibit high ion-transport
selectivities as well as high ﬂux. However, transport through polyelectrolyte ﬁlms is
still not well understood, partly because ion-transport selectivity is determined by both
size and electrostatic exclusion. Through studying the transport of several neutral
molecules, this work shows that typical poly(styrene sulfonate) (PSS)/poly(allylamine
hydrochloride) (PAH) membranes have pore sizes of 0.4-0.5 mm. Glucose/sucrose
selectivity through these ﬁlms is about 150, but size~selectivities among molecules
with sizes similar to common inorganic ions are minimal. In addition to providing
fundamental insight about pores in multilayer polyelectrolyte ﬁlms, this thesis reports

nanoﬁltration experiments that suggest that PSS/PAH ﬁlms may be useful for

removing organic pollutants from water or for separation of salts from sugars.

19

2.2 Experimental Section

2.2.1 Materials. Poly(styrene sulfonate) (PSS) (Aldrich, Mw = 70,000),
poly(allylamine hydrochloride) (PAH) (Aldrich, Mw = 70,000), poly(acrylic acid)
(PAA) (Mw = 90,000, 25 wt % solution, Alfa Aesar), MnClz (Mallinckrodt), NaBr
(Aldrich), NaCl (Mallinckrodt), methanol (CCI, ACS grade, anhydrous), glycerol
(CCI, ACS grade, anhydrous), glucose (Aldrich), and sucrose (Aldrich) were used as
received. The porous alumina supports (Anodisc 0.02 pm membrane ﬁlters) were
purchased from Whatrnan and subjected to UV/03 cleaning (Boekel UV__Clean model
135500) for 15 min before ﬁlm deposition. Deionized water (Milli-Q, 18.2 MQcm)
was used for rinsing and preparation of the polyelectrolyte solutions. The pH of

polyelectrolyte solutions was adjusted with dilute NaOH or HCl.

2.2.2 Film Deposition. A cleaned porous alumina support was ﬁrst placed in an O-ring
holder so that only the top of substrate would be exposed to polyelectrolyte solutions.
Polyelectrolyte deposition began with immersion of the alumina support in 0.02 M
PSS (pH 2.1, 0.5 M MnClz) for 2 min. (Polymer concentrations are always given
with respect to the repeating unit.) The substrate was rinsed with deionized water for
1 min before a 5-min immersion in 0.02 M PAH (pH 2.3, 0.5 M NaBr for PSS/PAH
bilayers and pH 4.5, 0.5 M NaCl for PAA/PAH bilayers) and subsequent rinsing.
Additional bilayers were deposited similarly. Supporting electrolytes and pH values

2,34,78

were chosen to follow literature procedures. Capped ﬁlms were synthesized

through deposition of a 5-bilayer PSS/PAH ﬁlm followed by deposition of FAA/PAH.

20

The PAA deposition step involved a 5-min immersion in 0.02 M PAA (pH 4.5, 0.5 M

NaCl). Films were dried with N2 only after deposition of all layers.

2.2.3 Transport Studies. A home-built dialysis apparatus (see Figure 5) was used to
study the transport of neutral molecules. The apparatus consists of two glass cells
(100 mL) connected by a 2.5-cm-long neck in which the membrane was sandwiched
between the feed and permeate sides. The exposed membrane area was 2.3 cm2, and
both feed and permeate sides were stirred vigorously to minimize concentration
polarization at the membrane-solution interface. The permeate side was initially
ﬁlled with deionized water, and the feed side contained 0.2 M methanol and 0.005 M
glycerol; 0.005 M glycerol and 0.005 M glucose; or 0.005 M glucose and 0.05 M
sucrose. Feed concentrations were chosen based on ﬂuxes and analysis limitations
for each analyte. (Experiments with uncoated porous alumina employed lower
analyte concentrations to avoid dilution prior to analysis, i.e., 0.1 M methanol, 0.0005
M glycerol, 0.0005 M glucose, and 0.0005 M sucrose.) In each dialysis run, a l-mL
aliquot was removed from both the source and receiving solutions after 5 min, and six
more l-mL aliquots were taken at 10-min intervals for one hour. Flux values were
normalized by dividing by the concentration in the feed side.

NF was performed using the cross-ﬂow apparatus represented in Figure 6. The
system was pressurized with Ar to 70 psi, and a centrifugal pump circulated the

analyte solution through the system and across the membrane. A stainless steel ﬁit

21

 

 

 

   

 

 

 

 

receiving phase source phase

membrane

Figure 5. Schematic representation of the cell used in diffusion dialysis.

22

 

 

 

 

 

 

 

 

 

 

Figure 6. Schematic diagram of the cross-ﬂow nanoﬁltration apparatus. (1) Ar tank,
(2) stainless steel feed tank, (3) centrifugal pump, (4) preﬁlter, (5) ﬂowmeter, (6)
pressure gauges, (7) membrane cells, and (8) graduated cylinders. (Taken from

reference 78, with permission from the American Chemical Society, copyright 2003)

23

(Mott Corporation) was used as a preﬁlter to remove any rust or particulate matter
from the feed stream. The volume of the feed solution (2 L) was about 30-times
greater than the total permeate, so the feed composition (0.002 M methanol and 0.0001
M glycerol; or 0.0001 M glycerol, 0.0002 M glucose and 0.005 M sucrose; or 0.0001
M glycerol, 0.0002 M glucose and 0.025 M sucrose) was essentially constant. To
avoid concentration polarization, the ﬂow rate across the membrane was kept at 18
mL/min and monitored by a ﬂowmeter located between the pump and membrane cell.
The membranes were placed in a home-built stainless steel cell, and the membrane
area exposed to the analyte solution was 1.5 cm2, which was determined by performing
nanoﬁltration with 0.1% Congo red dye and then measuring the stained area. Several
pressure gauges were used to insure that no signiﬁcant pressure drops occurred across
the membrane cells. The permeate was collected with a graduated cylinder after a
10-h equilibration period. Aliquots were taken at 30 min intervals for 1.5 h aﬁer the
equilibration period, and no signiﬁcant change in permeate composition was observed
after an additional 6 h of NF.

Methanol was analyzed by gas chromatography (Shimadzu, GC-17A, Version 3)
using a 30-m-long capillary column (Restek, RTX-BACI, ID 0.53 mm, ﬁlm thickness
3 pm). In the actual analysis, isopropanol with a speciﬁc concentration was chosen as
the internal standard. Thus, the calibration curve was made by plotting the methanol
concentration as a function of the ratio of methanol peak area to isopropanol peak area
(see Figure 7). Each methanol sample taken from diffusion dialysis or nanoﬁltration

was mixed with an equal volume of isopropanol solution and then injected into the GC

24

for analysis. The injection volume was maintained at l uL. The initial column
temperature stayed at 60 °C for 2 min, and then the column was heated to 250 0C at a

rate of 20 °C /min. The temperature was raised to drive all the solvent (water) out of

 

the column.
0.005
y = 0 .0029X - 0.0004
0.004 - R2 = 0.9961

0.003 ‘

0.002 "

0.001 "

Concentration of methanol (M)

 

 

0 l l l ,
0 0.5 1 1.5 2

 

Methanol/isopropanol peak area ratio

Figure 7. Gas-chromatography calibration curve for methanol.

Glycerol, glucose, and sucrose were analyzed by liquid chromatography (Dionex,
DX-600, CarbonPac PA-lO column, 100 mM NaOH eluent) coupled with integrated
amperometric detection (Dionex, ED-50). The concentrations were determined using
a group of standards bracketing the expected sample concentrations throughout the

running period. In this case, standard concentrations versus their corresponding peak

25

 

areas were used as calibration plots. A typical chromatogram of a solution containing

glycerol, glucose, and sucrose is shown in Figure 8.

Current (nC)

 

 

 

 

 

80.0 1 -1.617
40.0‘
2-5.117
3- 9.150
-10.0 .. I lrl"l I I Fl I I“
0.0 2 0 4.0 6.0 8 0 10.0

Retention time (min)

Figure 8. Typical chromatogram of glycerol (peak 1), glucose (peakv2) and sucrose

(peak 3) in LC analysis. Numbers next to peak labels are retention times.

26

2.3 Results and Discussion

2.3.1 Diffusion Dialysis through PSS/PAH Membranes. To examine the selectivity
of PSS/PAH ﬁlms, we initially employed diffusion dialysis. In these experiments, a
porous alumina substrate separates a permeate phase (initially deionized water) from
an aqueous source phase that contains the analytes of interest. By monitoring analyte
concentrations in the permeate phase as a function of time, one can measure the rate of
transport across the membrane. Because analyte concentrations in the permeate phase
are negligible compared to those in the source phase, the concentration gradients
across the membrane are essentially constant, and permeate-phase concentrations
increase linearly with time.

Figure 9 shows permeate-phase concentration as a function of time for the
difﬁrsion of glycerol, glucose and sucrose through porous alumina coated with a
7-bilayer PSS/ PAH ﬁlm. Glycerol transport is about 8-times faster than glucose
transport, and remarkably, the ﬂux of glucose across the membrane is ISO-fold greater
than that of sucrose (See Table 3). Corresponding selectivities for bare porous
alumina are <1 .5. As all of these analytes are neutral and hydrophilic, selectivity
must be based primarily on size.

In ion transport through PS S/PAH ﬁlms, terminating a membrane with PAH rather
than PSS gives a 2-fold increase in the ﬂux of 8042' and Ni(CN)42’ but has little effect
on C1' transport.52 In contrast, the ﬂux of sucrose decreases 2-fold on going from a
6.5-bilayer ([PSS/PAH]6PSS) to a 7-bilayer ([PSS/PAH]7) ﬁlm (Table 3), and the

ﬂuxes of glycerol and glucose also decrease slightly (~20%). The signiﬁcant

27

 

A
C ‘ I
,2 0001 ‘ I
E 0015 i ‘
E A .
° 0W
2 0 20 40 60 80 I
8 001
'U I I
Q I
.5 l,
E I I
g 0.005 > I
z
I
I A A ‘
o —+ 4 . t a . o o—-—o—————J
0 20 40 60 80

Time (min)

Figure 9. Normalized permeate-phase concentrations of glycerol (squares), glucose
(triangles), and sucrose (diamonds) as a function of time in diffusion dialysis
through a 7-bilayer PSS/PAH membrane. The inset shows an expanded view for

glucose and sucrose.

Concentrations were normalized by dividing by the

source-phase concentration, and data are from experiments using feed solutions
containing 0.005 M glycerol and 0.005 M glucose or 0.005 M glucose and 0.05 M

sucrose. Glucose ﬂux was similar for both feed solutions.

28

decrease in sucrose ﬂux probably results from a tighter surface packing when the top
layer is PAH.79 Surface packing should have little effect on the transport of 8042' and
Ni(CN)42' because the Stokes’ radii of these molecules are less than that of glycerol.80
Thus, in the transport of divalent anions, changes in Donnan exclusion are the primary
result of changing the surface layer to a polycation, and ﬂux increases when
terminating ﬁlms with PAH. In contrast, with neutral molecules Donnan exclusion is
not operative, and addition of a PAH layer yields a decrease in ﬂux due to tighter

surface packing and/or a thicker membrane.

29

Table 3. Normalized Fluxes (mol cm'z s'I/ M) and Selectivities in Diffusion
Dialysis through Bare Porous Alumina and Alumina Coated with Polyelectrolyte

Films '

 

.. methanol glycerol glucose sucrose methanol/ glycerol/ glucose/
ﬁlm composrtron

 

ﬂux ﬂux ﬂux ﬂux glycerol glucose sucrose
b 3.6><10'7 2.6><10'7 1.8x10'7 1.3><10'7 1.36 1.45b 1.35
are (6x109) (8x 10") (1x103) (1 x 108) (0.05) (0.11) (0.02)
PSS/PAH PSS 3.5><10'7 2.1><10'7 2.7><10'8 3.4x10"° 1.96 6.4 80
[ 1" (4x108) (5x109) (2x109) (5x10'”) (0.05) (0.4) (7)
PSS/PAH] 3.0><10'7 1.7><10‘7 2.2><10'8 1.5x10"° 2.0 7.8 150
[ 7 (1 x108) (5x 10") (2x10"’) (4x 10'1 l) (0.1) (0.9) (40)
PSS/P 2.4><10‘7 7.3><10'8 9.1x10"° , 3.5 75
l “”5 -3 _, _,, <4.5x10"~ >200
[PAA/PAH]PAA (2x10) (6x10) (3x10 ) (0.6) (20)
[PSS/PAH], 2.8X10'7 1.3><10'7 1.4><10'8 1.0><10'lo 2.35 10.2 133
[PAA/PAH]2 (5x109) (2x108) (7x10"°) (6XI0"2) (0.03) (0.3) (6)

3The values in parentheses represent the standard deviations of at least three
measurements.

bIn this case, the selectivity was obtained by dividing the ﬂux of glycerol (from the
experiment with methanol/glycerol as the feed solution) by the ﬂux of glucose (from
the experiment with glucose and sucrose as the feed solution). In all other cases,
analytes were examined competitively in the same solution, and selectivity values are
an average of the selectivities in three experiments.

30

2.3.2 Diffusion Dialysis through Hybrid PSS/PAH/PAA Membranes. Simple
PSS/PAH membranes are highly selective for glucose over sucrose, but the selectivity
for glycerol over glucose is fairly low. Our previous work showed that capping of a
5-bilayer PSS/PAH precursor ﬁlm with 1.5 bilayers of PAA/PAH yields dramatic
increases in Cl'/SO42'selectivity without greatly hindering Cl- ﬂux,5 1 so we attempted
to use this strategy to enhance selectivity in neutral molecule transport. The ﬂux of
glycerol through 5 bilayers of PSS/PAH capped with 1.5 bilayers of PAA/PAH is
about one third of that through 6.5-bilayer PSS/PAH ﬁlms, but glucose ﬂux is 30-fold
lower through the capped ﬁlms. Thus, the overall glycerol/glucose selectivity
increases from 6.4 to 75 when using the capping layers (See Figure 10 and Table 3).
With ﬁlms capped with 1.5 bilayers of PAA/PAH, the concentration of sucrose in the
permeate is below the detection limit of our analysis (~2><10'7 M), and thus, we can
only establish a minimum glucose/sucrose selectivity, which is 200.

The methanol/glycerol selectivity of 3.5 with [PSS/PAH], [PAA/PAH]PAA ﬁlms is
signiﬁcantly less than that for glycerol over glucose, indicating that the pores in
capped membranes are still too large to effectively separate small molecules. This
again suggests that the high selectivity in previous ion-transport studies was primarily
due to electrostatic effects. The Cl'/SO42' selectivity of [PSS/PAH]5[PAA/PAH]PAA
ﬁlms is 70,5 I even though 8042' has a smaller Stokes’ radius (0.23 nm) than glycerol.

The selectivity of capped membranes decreases dramatically when the

polyelectrolyte ﬁlms terminate in PAH rather than PAA (Table 3). Upon going from

31

 

 

 

.5 l 1 I A ‘ l '

i; l I A i .

‘3 0.004 A A . I Q

3 l A l l

5 o W I I

g 0.01 0 20 40 60- 80 l
N

'7'; A I

A

Z I A l

A i

0 wt 4 14 e I e o a J

0 20 40 60 80

Time (min)

Figure 10. Normalized permeate-phase concentrations of methanol (squares),
glycerol (triangles), and glucose (diamonds) as a function of time in a diffusion
dialysis experiment with a 5-bilayer PSS/PAH + 1.5-bilayer PAA/PAH ﬁlm.
The inset shows the expanded view of glycerol and glucose transport across the
membrane. Glycerol/glucose selectivity is 75. Concentrations were
normalized by dividing by the source-phase concentration.

32

a 1.5-bilayer to a 2-bilayer PAA/PAH cap, glycerol/ glucose selectivity decreases from
75 to 10, and methanol/glycerol selectivity decreases from 3.5 to 2.4. Presumably,
the ﬁlm with PAA as the terminal layer has a tighter surface structure than the ﬁlm
with PAH as the top layer. (This trend is opposite to that for PAH and P83 and may
reﬂect the fact that carboxylates are less hydrated than sulfonates.8') Although
selectivity among small molecules decreases when capped ﬁlms terminate with PAH,
such membranes still exhibit a selectivity of 130 for glucose over sucrose, and glucose
ﬂux through [PSS/PAH]5[PAA/PAH]2 ﬁlms is 15-fold greater than that with a
1.5-bilayer PAA/PAH capping layer. Such wide variations in transport properties

should be beneﬁcial for developing membranes for speciﬁc applications.

33

2.3.3 Nanofiltration with PSS/PAH Membranes. Table 4 shows percent rejection
values, selectivities, and water ﬂuxes (in m3 m'2 d'l) from NF experiments with 6.5-
and 7-bilayer PSS/PAH membranes and solutions containing several neutral
molecules. Water ﬂux through these ﬁlms is 20-60% lower than our previously
published results with 4.5- or 5-bilayer PSS/PAH membranes,79 presumably because
of the greater thickness of 6.5- and 7-bilayer ﬁlms. However, water ﬂuxes are still
similar to those of commercial NF membranes.”83
PSS/PAH membranes show impressive NF selectivities that correlate well with

results from diffusion dialysis. In NF, selectivities are calculated according to

equation ( l),
Selectivity = (100-R/)/(100-R2) (l)

where R represents percent rejection. Glucose/sucrose selectivities for 6.5-bilayer
and 7-bilayer PSS/PAH membranes are 70 and 140, respectively, and the

corresponding values in diffusion dialysis are 80 and 150.

Methanol/glycerol and glycerol/glucose selectivities are also similar to those
determined in diffusion dialysis. Compared to 7-bilayer PSS/PAH, 6.5-bilayer
PSS/PAH membranes exhibit lower selectivities for both glycerol/glucose and
glucose/sucrose. However, water ﬂuxes through 7-bilayer and 6.5-bilayer ﬁlms are
about the same. If the higher selectivities of 7-bilayer ﬁlms were due to tighter

surface packing, we would expect to see a slightly lower water ﬂux with these ﬁlms.

34

A small difference in water ﬂux could, however, be obscured by the experimental error

in our measurements.

Table 4. Percent Rejections, Water Fluxes (in m3m‘2d'l), and Selectivities from

NF Experiments with Multilayer Polyelectrolyte Membranes and Solutions

Containing Several Neutral Molecules

 

 

ﬁlm glycerol/ glucosc/
. _ methanol glycerol glucose sucrose water ﬂux
composrtron glucose sucrose
871:3“ 98.3i0.2“ >99.99a 0.90:1:008a 7.7:i:0.9a >100a
[PSS/PAHL 97.4:E0.4b 99.13202b 99.993001" 0.70mb 2.8i0.4b 144511"
70:t5c 88thc 0.910. lc
[PSS/ PAH ], a , a a a a
PSS - 90.7i0.4 97.4i0.6 99.963001 0.89i005 3.73:0.7 68i5

a‘Experiment conducted with a feed solution containing 0.0001 M glycerol, 0.0002 M
glucose, and 0.005 M sucrose. With 7-bilayer ﬁlms, sucrose concentration in the
permeate was near the instrument detection limit.
bExperiment conducted with a feed solution containing 0.0001 M glycerol, 0.0002 M
glucose, and 0.025 M sucrose.
cExperiment conducted with a feed solution containing 0.002 M methanol and 0.0001
Methanol/glycerol selectivity was 2.6:i:0.9.

M glycerol.

35

In spite of high selectivities, PSS/PAH membranes will probably not be useful for
the separation of small organic molecules because of their high rejection values. As
shown in Table 4, with 7-bilayer PSS/PAH membranes, methanol, glycerol, glucose
and sucrose rejections are 70%, 88%, 98.3% and 99.99%, respectively. Nevertheless,
these high rejections could be very beneﬁcial in salt/sugar separations or removal of

5

organic pollutants from water.7 In the former case, rejection of sugars and high

passage of salts should allow selective concentration of oligosaccharides.

The high rejection of sucrose resulted in permeate concentrations near the
detection limit of our chromatograph. Because of this, we performed NF with a
glycerol/glucose/sucrose solution that contained 0.025 M sucrose rather than 0.005 M
sucrose (Table 4). Rejection of both glycerol and glucose increased with the higher
sucrose concentration, presumably because sucrose blocked pores‘ at the membrane
surface. A decrease in water ﬂux also suggests the presence of adsorbed sucrose,
although increased osmotic pressure (9 psi) due to the higher sucrose concentration
probably accounts for much of the ﬂux reduction. Sucrose rejection was similar for

0.025 and 0.005 M feed solutions, but rejection was very high in both cases.

36

2.3.4 Theory for Modeling of Transport. Figure 11 shows schematically the
concentration proﬁle of a solute diffusing through a multilayer polyelectrolyte/porous
alumina membrane. To model diffusion dialysis through such a membrane, we
utilized F ick’s ﬁrst law (equation (2)) in both the alumina and the polyelectrolyte ﬁlm.
1.: -D.% (2)

In this equation, j.- represents solute ﬂux, D,- is the solute diffusion coefﬁcient in a

particular medium, and dci/dx is the concentration gradient. Because ﬂux is at steady

state (see Figures 9 and 10 for evidence of steady-state transport), Fick’s law can be

rewritten as

. AC:

- = - Dr _ 3
J, ( )

where Ax is the thickness of either the porous alumina or the polyelectrolyte ﬁlm and
Ac,- represents the total drop in concentration within the apprOpriate layer. There are
also concentration changes at the alumina/polyelectrolyte and polyelectrolyte/ feed
interfaces due to partitioning into the MPM. (Because the pores in the alumina are
large (20-200 mm), there should be no concentration change at the alumina/permeate
interface.) With the assumption that the polyelectrolyte ﬁlm behaves like an

assembly of small cylindrical pores,(’3“""84'85

equation (4) describes the relationship
between the concentration at the surface of the polyelectrolyte ﬁlm, c4, and the
concentration in the feed, C5 (Figure 11). The partition coefﬁcient, (D, is a function of

the ratio of Stokes’ radius to pore radius, 2.. A similar relationship should exist at the

polyelectrolyte/alumina (C3 /cz) interface.

37

 

concentration

Porous alumina Polymer ﬁlm
C5

Permeate Feed

C1

 

 

 

\ J J

Ax1 Ax2

Figure 1]. Schematic diagram of the analyte concentration proﬁle in a membrane
composed of a polyelectrolyte ﬁlm on a porous alumina support.

Ax): thickness of the porous support

AX22 thickness of the polyelectrolyte ﬁlm

C]:
Cz.‘
C32
C41
C52

analyte concentration in the permeate

analyte concentration in the alumina support at the support-ﬁlm interface
analyte concentration in the ﬁlm at the support-ﬁlm interface

analyte concentration in the ﬁlm at the ﬁlm-solution interface

analyte concentration in the feed

38

¢=c4/C5 = 63/62 = (I —l)2 (4)

Assuming that the concentration in the permeate phase, c), is negligible compared to
C3, we can calculate c; from the experimental ﬂux value using equation (5). We
obtained D I, the diffusion coefﬁcient in the porous alumina, from diffusion dialysis
data with a bare porous alumina support, and Ax I is thickness of the alumina (~60 um).
C3 =j,-Ax;/D1 (5)

For transport through the polyelectrolyte ﬁlm, substitution of equation (4) and

equation (5) into equation (3) plus rearrangement yields the expression for ﬂux in

 

equation (6).
. _ c5 6
.li — sz +ﬂ ( )
020—0 D.

However, D3, the diffusion coefﬁcient in the MPM, is a function of the hindrance
factor for diffusion in small pores, Km, the ﬁlm porosity, e, and the diffusion
coefﬁcient in free solution, Dinf, as shown in equation (7)."5

D: = Din/Kw 8 (7)

Using correlations for KM as a function of A. (see below), one can write the ﬂux j)
through the MPM in terms of two variables, 1 and e. To estimate ﬁlm porosity, we
utilized measurements of water ﬂux in NF. Assuming that all the pores in a ﬁlm have
the same radii, volume ﬂux in NF can be described by equation (8), where Jv is the
volume ﬂux, r is the pore radius, AP is the pressure drop across the ﬁlm, 77 is the
solvent viscosity, and z'is the pore tortuosity. (For straight cylindrical pores, the

tortuosity is equal to unity.)

39

rZEAP
J. =
SnrAx

 

(8)

With water-ﬂux data from NF and solute-ﬂux data from diffusion dialysis, equations
(6) (with substitution of equation (7)) and (8) can be solved iteratively for r and e if the
radius of the solute is known. In our actual calculation of r, we ﬁrst assumed a value
of r and calculated a from equation (8) and D2 from equation (7) and the correlations
given below for Kw. Finally, we calculated ﬂux from equation (6). We optimized
the value assumed for r to minimize the sum of least squares of percent error in the
ﬂuxes of methanol, glycerol, glucose and sucrose.

In the case of NF, the expression for solute ﬂux contains both diffusive and
convective terms. The treatment that we followed to simulate transport is similar to
that developed by Bowen et a1."5 Addition of convection to Fick’s law yields
equation (9), where J, is the volume ﬂux of the solvent.

1,: -D.% + K...c.J. (9)

The hindered nature of convection and diffusion inside membrane pores is accounted
for by Kim, the hindrance factor for convection, and KM (equation (7) for 02), the
hindrance factor for diffusion, which are functions of A. If one assumes a homogenous
velocity across very small membrane pores, KM and K), are respectively equivalent to
K 7,1,0), the enhanced drag coefﬁcient, and GM, 0), the lag coefﬁcient.64’65 Bungay
and Brenner ﬁtted the enhanced drag and lag coefﬁcients to equations (10) and
(11).“87 Other correlations for drag and lag coefﬁcients gave similar results in our

. . 6 ‘8
Simulations. 5 6

40

-l = 2 2 _ —2.5 +_‘7_7_2_93 .—

— 22.5083 — 5.6117/1 — 0.3363/12 — 1.216613 + 1.647/14}

0(4,0)={2n2ﬁ(1—2)‘2-5[1+67_0_(1 ,1)— 2227 (1—2) 1+40180_ 397881
4 50400 (11)
-1
4.921522 +4.39223 +5.00624}6K_(_4:»_0_)
7!

Integration of equation (9) over the polyelectrolyte ﬁlm with the boundary conditions
listed in equation (12) (CV and cm, are the solute concentrations in the feed and
permeate, respectively) yields the expression for rejection, R, in equation (13). In this
equation, the Peclet number, Pem is deﬁned as shown in equation (14).

Ci,.r=0 = mCif and Ci..r=Ar = ci.p (12)

') 1'ch
R: _"'_-I=1_ K- (13)
C1.f 1" exp(-Pe..)(1-K,-,.)

 

_ Kim JvAx
Km! Dung

Fe

m

 

(14)

Equations (13) and (14) provide an expression for rejection as a function of A and e.

In the actual procedure for determining the porosity and pore radius from NF data,
we ﬁrst assumed a value for pore size and calculated porosity from equation (8). We
then determined the hindrance factors for both diffusion and convection using
equations (10) and (11), and subsequently calculated rejection with equation (13).
Iterations on this procedure yielded a best-ﬁt pore radius through minimization of the
sum of least squares for the percent error in (l-R) for methanol, glycerol, and glucose.

We note that for cross-ﬂow NF, we assumed partition equilibrium only at the
feed-side interface. The polyelectrolyte/alumina interface is not stirred so we

assumed that the concentration on the alumina side of this interface is the same as the

41

concentration in the polyelectrolyte. We also neglected mass-transport resistance due
to the alumina support. This is an appropriate assumption in NF because water ﬂux

through bare alumina is >100 times larger than ﬂux through PSS/PAH-coated alumina.
In diffusion dialysis, however, the alumina support provides a signiﬁcant resistance to

mass transport.

2.3.5 Determination of Effective Pore Sizes. The models described above allow
estimation of effective pore sizes and porosity in polyelectrolyte ﬁlms, and these
parameters will be important for prediction of selectivity and ﬂux in speciﬁc
separations. Table 5 shows simulated ﬂuxes for diffusion dialysis and the important
variables used to calculate these ﬂuxes. Mimization of the percent error in the ﬂux of
the different solutes gave an effective pore radius of 0.53 nm and a porosity of 1.8%.
Calculated ﬂuxes of all four solutes were within at least 32% of the measured values.
However, effective pore size depends greatly on the value of Dinf chosen for the
calculation. We utilized the effective diffusion coefﬁcient (uncorrected for porosity)
in porous alumina as the value of Dim: If we correct this value for the alumina
porosity determined from NF experiments (21%), the calculated pore size in the
polyelectrolyte ﬁlm decreases to 0.45 nm and porosity increases to 2.5%.88 We

utilized the uncorrected value for the difﬁision coefﬁcient because we thought that

42

'2 8") Relevant to the Simulation of

Table 5. Parameters and Fluxes (J, mol cm
Diffusion Dialysis through a 7-bilayer PSS/PAH Membrane Assuming a Pore

Radius of 5.28 x 104’ cm ‘

 

A (1-2..)2 Dinf.(cmzs'1) D2(cmzs") Jcalculated Jmeasured

 

methanol 0.30 0.49 2.1><10'6 1.6x10'8 6.3 x 10‘8 6.0 x 10‘8
glycerol 0.49 0.26 1.6x10" 4.8X10‘9 8.0 x 10-10 8.7 X 10.10
glucose 0.67 0.11 1.1><10'6 9.9x10"° 1.5 x 10'10 1.1 x 10'10

sucrose 0.89 0.012 8.0><10'7 3.7><10‘ll 7.2 x10'12 73 x 10'12

3A porosity of 1.8% was calculated from equation (8) using nanoﬁltration data at 70

psi that yielded a water ﬂux of 0.001 cm3cm'zs'l. The polyelectrolyte ﬁlm thickness

was assumed to be 30 nm based on ellipsometric measurements.

Table 6. Parameters and Rejections Calculated in the Simulation of

Nanoﬁltration with a 7-bilayer PSS/PAH Membrane Assuming a Pore Radius of

 

 

4.2 x 10'8 cm '
A W K" K... «i‘i‘EJ-‘iﬁiii. %"IZ§ZZI?.1.
methanol 0.37 0.39 0.31 0.89 61.4 70 i 5
glycerol 0.62 0.15 0.078 0.76 87.5 88 :1: 2
glucose 0.85 0.024 0.0067 0.60 98.5 98.3 i 0.2
sucrose >1 - - - 100 99.99 i 0.01

3A porosity of 2.8% was calculated from equation (8) and nanoﬁltration data at 70 psi
that yielded a water ﬂux of 0.001 cm3cm'zs". The polyelectrolyte ﬁlm thickness was

assumed to be 30 nm.

43

diffusion through the ﬁlm would not occur to nonporous areas of the alumina surface.
(This assumption implies that lateral diffusion at the polyelectrolyte/alumina interface
is insigniﬁcant.) The calculated diffusion coefficient, D3, for sucrose (MW =342) is
similar to that measured by Ibarz et al. for ﬂuorescein (MW = 332) diffusion through
annealed polyelectrolyte capsules.89

Simulation of NF (Table 6) resulted in a pore size of 0.42 nm and a porosity of
2.8%. Calculated rejections were within 12% of measured values. We should note
that the simulations assume a uniform pore size, while, in fact, there is certame a
distribution of pore sizes, and thus, effective pores sizes are only rough
approximations. This may explain why a small amount of sucrose passes through the
membrane even though its Stokes’ radius is larger than the effective pore radius. The
calculated pore size in NF is 0.1 nm less than the value from diffusion dialysis, and this
may reﬂect the approximate nature of the simulations or the choice of diffusion
coefﬁcient in the diffusion dialysis calculation. However, compaction due to the
pressure applied in NF could also decrease pore sizes.

Effective pore sizes are consistent with the fact that the approximate molecular
weight cutoff (90% rejection in NF) of these membranes is around 92, the molecular
weight of glycerol. The Stokes’ radius of glycerol is 0.26 nm, and molecules larger
than this should be highly rejected from the membrane, primarily due to the partition
coefﬁcient, which is a function of the ratio of Stokes’ radius to pore radius (equation

(4)). In fact, the NF model suggests that partitioning is the primary factor behind

44

selectivity with the molecules examined, although there is a small effect from hindered
convection.

One of the reasons for performing this work was to determine if there was a
size-based selectivity in ion separations, e.g., Cl' and 8042'. Because the Stokes’ radii
of these ions are signiﬁcantly less than the pore radius, size selectivity should be <2
with PSS/PAH membranes. However, other polyelectrolyte systems may pack more
tightly and allow for size discrimination among small ions. Additionally, electrostatic
interactions between ions and polyelectrolytes can result in selective diffusion, as
shown by Farhat and Schlenoffss‘56 Our future work aims at controlling pore size in

MPMs by carefully selecting constituent polyelectrolytes.

45

Chapter 3

Conclusions and Future Work

MPMs are highly selective for neutral molecules in both diffusion dialysis and NF.
These membranes demonstrate glucose/sucrose selectivity as high as 150, and size
exclusion is the main factor behind such selectivities. Modeling of solute and solvent
ﬂuxes as well as rejection values suggests that PSS/PAH membranes contain pores
with radii of 0.4 to 0.5 nm. The high rejections of glucose and sucrose by PSS/PAH
membranes along with a high water ﬂux suggest that these materials may be applicable
in salt/sugar separations or removal of organic pollutants from water. In contrast to
neutral molecules, however, selective transport of small ions such as CT and 8042'
through PSS/PAH ﬁlms should not be based on size because the Stokes’ radii of these
ions are signiﬁcantly smaller than ﬁlm pores.

Although this thesis clearly demonstrates the potential of MPMs, further work will
be necessary prior to practical separations with these materials. The porous alumina
support for MPMs is quite fragile, so large-scale applications will likely require
methods for preparation of ﬁlms on polymeric substrates. These methods will need to
be optimized to achieve both high water ﬂux and high selectivities. For separation of
sugars in NF, as we already suggested, we need to lower rejections substantially while
maintaining high selectivities. This could be achieved by careful selection of

constituent polyelectrolytes or tuning of deposition conditions.

46

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51

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52