Salt transport in polymeric pervaporation membrane

Journal Pre-proof Salt transport in polymeric pervaporation membrane

Dihua Wu, Aoran Gao, Xianshe Feng PII:

S1004-9541(19)30927-9

DOI:

https://doi.org/10.1016/j.cjche.2019.11.009

Reference:

CJCHE 1589

To appear in:

Chinese Journal of Chemical Engineering

Received date:

24 June 2019

Revised date:

7 November 2019

Accepted date:

21 November 2019

Please cite this article as: D. Wu, A. Gao and X. Feng, Salt transport in polymeric pervaporation membrane, Chinese Journal of Chemical Engineering(2019), https://doi.org/10.1016/j.cjche.2019.11.009

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© 2019 Published by Elsevier.

Journal Pre-proof Dihua Wu1,2 a, Aoran Gao2 a, Xianshe Feng2*

Salt transport in polymeric pervaporation membrane

Abstract

of

The salt transport in a PEBA membrane used in pervaporative desalination was studied. The

ro

concentration profile of salt in the membrane during pervaporation was investigated

-p

experimentally using a multilayer membrane. The salt was found to be sorbed in the membrane

re

but was not removed during the pervaporative desalination process, and the salt concentration in the membrane varied linearly with position. High purity water was obtained as the permeate as

lP

long as the permeate side was kept dry under vacuum. The accumulated salt uptake in the

na

membrane follows the order of MgCl2 > NaCl > Na2SO4. The solubility of salt in the membrane follows the order of MgCl2 > NaCl > Na2SO4. Both the permeability and diffusivity of salt in the

ur

membrane follow the order of NaCl > MgCl2 > Na2SO4. The permeability of salt in the

Jo

membrane is not influenced by the feed salt concentration. It is mainly determined by the diffusion coefficients.

Key words: Concentration profile, Pervaporative desalination, Salt transport

1

Dr. Dihua Wu, College of Materials and Environmental Engineering, Hangzhou Dianzi University, Xiasha Higher Education Zone, Hangzhou, 310018, Zhejiang Province, China 2 Dr. Dihua Wu, Aoran Gao, Prof. Dr. Xianshe Feng, Department of Chemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, N2L 3G1, Ontario, Canada a The two authors contributed equally to this paper. *Corresponding author. Tel.: +1 519 888 4567; E-mail: [email protected] (X.Feng).

1

Journal Pre-proof

Highlights The salt concentration profile in the membrane was determined experimentally



The salt was found to be sorbed into the membrane but would not be removed during the pervaporative desalination



The permeability coefficient of the salt was determined by the mass balance method



The permeation of the salt in the membrane is mainly determined by the diffusion

Jo

ur

na

lP

re

-p

ro

of



2

Journal Pre-proof 1. Introduction Desalination is one of the most important technologies for obtaining fresh water from seawater and brackish water. Currently, reverse osmosis (RO) is still the dominant membranebased technology for the treatment of seawater and brackish water and accounts for 60% of desalination plants. However, the main limitation for RO is the high osmotic pressure caused by the salinity of the solution. Pervaporative desalination and membrane distillation (MD) have

of

been considered as alternative technologies for the production of ultrapure water. Both these two

ro

processes are energy-saving as they do not have the concern about the high osmotic pressure.

-p

Pervaporative desalination is generally performed by a dense and hydrophilic membrane. Water

re

molecules adsorbed onto the membrane surface diffuse through the membrane and vaporize on

lP

the permeate side. Pervaporative desalination is driven by the partial pressure differences of water on the two sides. On the contrary, MD is carried out by a hydrophobic microporous

na

membrane as a barrier for the liquid water while allowing vaporous water to pass through the pores. The salt rejection can be achieved at nearly 100% in both these two processes regardless

ur

of salinity. MD has a higher flux than pervaporation desalination. However, membrane fouling

Jo

and wetting are main problems in MD [1], which causes the decline of water flux and salt rejection, even the damage and degradation of the membrane materials [2]. Such problems can be mitigated in pervaporation desalination because it uses hydrophilic materials. The electrical energy required for pumping the feed and permeate for pervaporative desalination is generally 2 kWh.m-3 [3], which is the lowest value RO can achieve now [3]. The water flux of pervaporative desalination can be enhanced to a comparable value of RO about 40 kg.m-2.h-1 by increasing the feed temperature and tailoring the membrane materials [4]. The energy needed for elevating the feed temperature for pervaporative desalination can be helped by

3

Journal Pre-proof the renewable solar energy, though the capacity is small. Therefore, pervaporative desalination is a promising candidate for desalination in terms of energy consumption, especially for the smallscale processes. Different hydrophilic materials have been used for pervaporative desalination. Zeolite [5] and silica [6] are the two main inorganic materials, and poly(vinyl alcohol) (PVA) [7,8] is an excellent organic material for pervaporative desalination. Recently, two-dimensional materials,

of

such as graphene oxide [9] and MXene nanosheets [10], have been employed as new materials

ro

for pervaporative desalination. Many studies have focused on developing new membrane

-p

materials and tailoring the membrane properties to obtain a better separation performance. Little

re

attention has been paid to the intrinsic transport of salt through the membrane. Salt is almost fully retained by the membrane in the pervaporation process due to its nonvolatility. However,

lP

this does not mean that the membrane is fully impermeable to salt. Therefore, determining the

na

permeability and diffusivity of salt in the membrane is significantly meaningful for insight into salt transport in the membrane during the pervaporative desalination process.

ur

A mass balance is the most general method for evaluating these permeabilities based on the

Jo

concentration variations of salt in the donator and receiver sides of the membrane [11,12]. This method is minimally restricted by the experimental conditions. The basic hypotheses of this method are as follows: (1) the amount of permeant remaining in the membrane is negligible, and (2) the permeant is receipted on the receiver side immediately after leaving the donator side. In some circumstances, such as gas permeation [13] and drug release [14] through polymeric films, a transient permeation happens in the beginning stage of the diffusion and causes a “time-lag (θ)”, during which a concentration profile in the membrane is established. After the transient permeation elapses, the diffusion reaches the pseudo-steady state as soon as difference of the

4

Journal Pre-proof transmembrane concentration is constant. Then, an unsteady state appears when the concentration on the receiver side is high enough, and the permeation stops when there is no concentration difference across the membrane. However, in the mass balance method, the “transient” stage of permeation is neglected, and the data at the initial stage, which are significantly influenced by the “transient” permeation, are excluded. Apparently, the accuracy of the kinetic parameter so determined is compromised.

of

A new approach that considers the characteristics of both the mass balance and time lag was

ro

developed to determine the permeability and diffusivity coefficients [15]. In this method, the

-p

permeation data in short time are evaluated by the time-lag method, and the permeation data in

re

long time are evaluated by the mass balance technique. The modified method for determination of permeability coefficient is briefly described in the Supporting Information.

lP

In view of the above, the concentration profile of salt in the membrane during the

na

pervaporative desalination process was investigated. To our knowledge, this is the first time that the concentration profile of salt in the membrane was determined experimentally. The

ur

permeability and diffusivity coefficients of salts in the polymeric membrane were evaluated by

Jo

the modified method. A poly(ether-block-amide) (PEBA) membrane was used for pervaporative desalination [16] due to its hydrophilicity.

2. Experimental 2.1 Membrane preparation and characterization The PEBA copolymer was kindly provided by Specialty Polymers, Arkema Inc. (Philadelphia, PA). The solution-casting method was used to prepare the homogeneous membranes with specific thicknesses, and the details have been described before [16]. 5

Journal Pre-proof The surface charge property of the PEBA membrane was studied by means of streaming potential. The measurements were taken by an Anton Paar zeta potential analysis meter (Austria). A membrane sample was placed in the measuring cell and the KCl solution with a concentration of 0.001 M, at pH=2-9 and temperature of 25 °C was circulated through the cell at. The average values based on at least three repeated tests are presented.

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2.2 Pervaporation with multilayer membranes

ro

The experimental setup for pervaporative desalination is similar to that in our previous

-p

study [16]. To determine the concentration profile of salts in the membrane, multilayer

re

membranes were used for pervaporative desalination. Five sheets of membranes with the same

lP

thickness and area (40 µm and 22.05 cm2) were laminated tightly and placed together in the membrane cell, and the total membrane thickness was approximately 200 µm. Pervaporative

na

desalination was conducted using feed solutions with various salt concentrations (from 2 to 20 wt%) at 25 °C continuously for 10 h. After the pervaporation process, these five membrane

ur

sheets were separated immediately, and each membrane was put into 100 mL of deionized water

Jo

to extract the salt from the membrane. The amount of salt dissolved in the membrane equals that dissolved in the water. It was determined by measuring the salt concentration in water using a conductivity meter. This procedure is shown in Fig. S1 for a clear illustration.

2.3 Sorption/desorption Sorption and desorption experiments were carried out to investigate the solubility of water and salt in the membrane. The dried membranes with a thickness of 56 μm were immersed in aqueous solutions of NaCl, MgCl2 and Na2SO4 at concentrations of 1, 5, 10, 15, and 20 wt%. 6

Journal Pre-proof The membrane samples were submerged in these solutions at 25 °C for 24 h to reach the sorption equilibrium. The total sorption weights of water and salt in the membrane was calculated from:

(1) where

and

respectively, and

are the weights of the membrane sample before and after sorption, is the total weight of water and salt sorbed in the membrane.

of

To calculate the respective weights of water and salt in the membrane, the membrane

ro

sample after sorption was placed in a vacuum oven at 60 °C for 24 h to achieve complete

is the weight of water sorbed in the membrane, and

(2) is the weight of the dry

lP

where

re

-p

desorption of water from the membrane. Thus, the sorption uptake of water can be calculated as:

membrane sample after water desorption, Mw is the molecular weight of water. Then, the

(3) where

Jo

ur

na

sorption uptake of salt can be expressed as:

is the weight of the salt sorbed in the membrane, Ms is the molecular weight of salt.

Each experiment was repeated at least twice.

2.4 Swelling The membrane swelling experiments were carried out using membrane samples with sizes of 3 cm × 3 cm. By measuring the thickness, length and width of the membrane, the volume of the membrane can thus be determined. The membrane swelling was expressed as:

7

Journal Pre-proof (4)

where

and

are the volume of the membrane before and after the sorption experiment,

respectively.

2.5 Diffusion/permeation

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The diffusivity and permeability of salts in the membrane were investigated by permeation

ro

experiments. Fig. S2 shows the experimental apparatus, which comprises a compartment with a

-p

capacity of 100 ml as the donor and a compartment with a capacity of 1500 ml as the receiver. The membrane was fixed at the bottom of the donor compartment and suspended on the top of receipting compartment. Stirrers were equipped in both the source and receiving

re

the

lP

compartments to eliminate the boundary layer effect. Before the experiment started, 950 ml

na

deionized water filled in the receiver compartment, and then 50 ml salt solution at a certain concentration (i.e., 1, 5, 10, 15, or 20 wt%) filled in the donator compartment to induce salt

ur

diffusion and permeation through the membrane. The salt concentration in the receiving

Jo

compartment was measured by the conductivity meter in real time. The membrane thickness used in this study was the same as that used in the sorption/desorption experiments (i.e., 56 μm), and the effective membrane area for permeation was 11.34 cm2. The experiment was carried out at 25 °C.

3. Results and discussion 3.1 Concentration profile of salts in membrane during pervaporation

8

Journal Pre-proof The concentration profile of salts in the membrane during the pervaporation process was determined using five sheet membranes that were laminated together. The salt contents in every sheet and the accumulative sorption amount are shown in Fig. 1 for NaCl, Figs. S3 and S4 for MgCl2 and Na2SO4, respectively. The salt amount in the membrane decreases from the first layer of the membrane (i.e., the layer nearest to the feed side) to the last layer (i.e., the layer furthest from the feed side). The accumulative salt in the laminated membrane sheets increases, but the

of

increase becomes less significant along the direction from feed to permeate side. By increasing

ro

in the salt concentration, the uptake of salt in every single membrane sheet increases, and the

-p

accumulative amount of salt uptake in the membrane sheets also increases. The accumulative

re

amount of salt uptake in the membrane accounts for only 0.036 - 0.24% of the total salt in the

lP

feed solution.

20% 10% 2%

ur

1.0

NaCl (wt%)

0.8

Jo

Salt in membrane / 10-3 mol.g-1

(a)

na

1.2

0.6

0.4

0.2

0.0 Feed

side

20

60

100

140

Position measured from feed side /m

9

180 Permeate side

Journal Pre-proof 3.5

NaCl (wt%) 2% 10% 20%

3.0 2.5

363 0.00 + 3X

2.0

6 0.01 + X 10  1 44 -3.3 = 63 Y + 0.009 X 1 6 7 0.00 -5 2 0 X + 1  4 1 46 Y = -1. + 0.0068 -5 2 X + 0.002791X Y = -6.4799  10 -5

1.5

of

1.0

2

0.5

ro

Accumulated mass of salts in membrane -3 -1 / 10 mol.g

(b)

0

20

40

60

-p

0.0

80

100

120

140

160

180

200

re

Total membrane thickness / m

na

lP

Fig. 1 Amount of NaCl in each membrane sheet (a) and the accumulated amount of salt in the laminated membranes at different positions (b).

It may be hypothesized that the salts are sorbed in the membrane by the following possible

ur

mechanisms: (1) Under the pressure difference applied across the membrane during

Jo

pervaporation, both water molecules and salt ions were dragged into the membrane. (2) Following the solution-diffusion model, both the water and the salt molecules diffuse into the membrane. Regardless of how the salts enter the membrane, they are left at a local position because of their nonvolatility while the water molecules permeate through the membrane. The accumulated salt amounts in the membrane as a function of position (Fig. 1, Figs. S3 and S4) were found to be well represented mathematically by a polynomial function, and a differential was taken with respect to the position, which is shown in Fig. 2, depicting the concentration profile of the salts in the membrane. Here, l is the total thickness of the five sheets

10

Journal Pre-proof membranes laminated together, x is the thickness of the membrane at a certain point of the five sheets. The following observations can be made: (1) The amount of salt in the membrane varies linearly with the local position. Note that in pervaporation, where the permeate side is under vacuum, it is expected that the membrane gradually becomes dryer in the direction of pervaporation mass transport. The linear relationship over the entire membrane thickness indicates that the change in membrane “wetness” across membrane thickness has no effect on

of

salt distribution in the local positions in the membrane. (2) An increase in salt concentration in

ro

the feed results in a higher salt content in the membrane, as well as a higher salt concentration

-p

gradient across the membrane. The high salt concentration gradient across the membrane means

re

an enhanced driving force for salt transport, which is unfavorable for the permeation of water molecules. This further explains the decreased water flux by increasing the feed salt

lP

concentration. (3) The accumulated salt uptake in the membrane follows the order of MgCl2 >

na

NaCl > Na2SO4. However, in our previous study [16], the water permeability followed the trend of NaCl solution > MgCl2 solution > Na2SO4 solution. These results indicate that the water

ur

permeability in the membrane may be influenced by other factors. Thus, the transport of salts in

below.

Jo

the membrane, including solubility, diffusivity and permeability, will be investigated in detail

The flux and salt rejection of multilayer membranes for feed solutions with different concentrations are shown in Table 1 The details about the pervaporation performance (e.g., the effects of feed salt concentration, operating temperature and membrane thickness on flux and salt rejection) can be obtained in our previous study [16].

11

Journal Pre-proof

Table 1 Flux and salt rejection of multilayer membranes (temperature: 25 °C, total thickness:100 μm) Concentration, % 2 10 20 2 10 20 2 10 20

NaCl

MgCl2

> 99.9

20 %

lP

NaCl MgCl2

0.020

re

-p

0.025

Na2SO4

na

0.015

ur

20 %

0.010

Jo

Salt uptake in membrane / 10-3 mol.g-1

Salt rejection, %

ro

Na2SO4

Water flux, [g/(m2.h)] 278.2 208.3 108.4 276.4 200.2 103.8 275.2 190.5 98.5

of

Salt solution

10 % 10 %

0.005

20 % 2% 10 % 2% 2%

0.000 0

0.25

0.5

0.75

1.0

-1

x.l / Fig. 2 Concentration profiles of NaCl, MgCl2 and Na2SO4 in the membrane. Temperature: 25 °C.

3.2 Solubility of salts in membrane 12

Journal Pre-proof Fig. 3 shows the salt and water uptake in the membrane as a function of salt concentration in the liquid solution. It should be mentioned that the salt uptake in membrane was calculated according to the volume of the membrane sample and its unit is “kmol.m-3” here in order to obtain the non-dimensional solubility coefficients. Within the range of feed concentrations investigated, salt sorption is proportional to the salt concentration in the feed, a relationship that is similar to Henry’s law, which has been observed for aroma sorption in membranes relevant to

of

aroma enrichment [17]. The salt uptake in the membrane follows the order of MgCl2 > NaCl >

ro

Na2SO4, which is in the same order as their accumulated uptake in the membrane during the

-p

pervaporation process in Sect 3.1. The solubility coefficients can be calculated from the slopes of

re

the straight lines, which are 1.05, 0.421 and 0.315, in units (mol/m3 membrane)/(mol/m3 solution), for MgCl2, NaCl and Na2SO4, respectively. By testing the surface zeta potential of the

lP

PEBA membrane under different pH values (shown in Fig. 4), the membrane appears

na

significantly negatively charged around pH=7. Thus, it is not surprising that the membrane

anion SO42-.

ur

shows the highest affinity to the divalent cation Mg2+ while the greatest repulsion to the divalent

Jo

The water uptake in the membranes decreases with increasing salt content in the solution due to the decreased water activity and osmotic deswelling [18]. The swelling degree of the membrane in different salt solutions is shown in Fig. 5. It was found that the water uptake in the membrane and the membrane swelling degree follow the same order of NaCl solution > MgCl2 solution > Na2SO4 solution, which is the same as the order of water permeability in the membrane during the pervaporative desalination process [16]. This further confirms that the osmotic pressure of the salt solution is an important factor influencing the transport of water molecules in the membrane. The osmotic pressure of the salt solution can be calculated as:

13

Journal Pre-proof Π

фΠ*

=

фibRT

=

[19]

(5) where Π*(=ibRT) is the osmotic pressure for an ideal solution, ф is the osmotic coefficient, i is the total number of ions given by one mole of salt, b is the solute molality, R is the gas constant, and T is the temperature. Table 2 shows the osmotic coefficient and osmotic pressure for 1 mol/m3 salt solutions at 298 K. The NaCl solution shows the smallest osmotic pressure and thus

of

has the least effect on membrane deswelling. The osmotic pressure of the MgCl2 solution is the

ro

highest, but the Na2SO4 solution shows the most significant effect on membrane deswelling as

-p

well as water uptake and water permeability in the membrane. Hence, in addition to the Donnan

2.5

na

1.5

NaC l

ur

2

MgCl2

Jo

Salt uptake in membrane / kmol.m-3

(a)

lP

probably influenced by another factor.

re

effects and osmotic pressure, the water transport of different salt solutions in the membrane is

1

0.5

Na2SO4

0

14

Journal Pre-proof 25

Water uptake in membrane / kmol.m -3

(b) 20

15

10

NaC l

Na2SO4 MgCl 2

0 1

2

3

4

-p

0

ro

of

5

re

Salt concentration / kmol.m-3

lP

Fig. 3 Sorption uptake of (a) salts and (b) water in the membrane under different salt concentrations. at 25 °C.

na

10

ur

-10

Jo

Zeta potential / MV

0

-20

-30

-40 1

2

3

4

5

6

7

8

9

10

11

12

pH / Fig. 4 Surface zeta potential of PEBA membrane (Tested with 0.001 M KCl at 25 °C). 15

Journal Pre-proof

40

NaCl MgCl2

35

Na2SO4

30 25 20

of

Swelling degree / %

45

15

ro

10

-p

5 0 0.5

1.0

1.5

2.0

2.5

re

0.0

3.0

4.0

lP

Salt concentration / kmol.m

3.5

-3

na

Fig. 5 Swelling degree of the membrane under different salt concentrations at 25 °C.

Table 2 Osmotic coefficient and osmotic pressure for 1 (mol/m3) salt solution at 298 K MgCl2

Na2SO4

2

3

3

ф

0.8945 [20]

1.1096 [21]

0.7063 [20]

Π [Pa]

4432.38

8247.34

5249.73

Jo

i

ur

NaCl

It is known that the presence of electrolytes in aqueous solutions disrupts the neighboring structure of water molecular [22]. Hofmeister ranked a series of ions according to the interactions between ions and water. The ions are known as structure makers or kosmotropes when the interactions between ion-water is stronger than water-water, whereas ions are known as structure breakers or chaotropes when the opposite effect exsits [23]. In the Hofmeister series

16

Journal Pre-proof [24], SO42- is a typical kosmotropic anion, and Na+ is also classified as a kosmotropic cation. Thus, Na2SO4 has the strongest interaction with water among the three electrolytes. It is understandable that the membrane in the Na2SO4 solution has the lowest swelling degree and water uptake because the water is likely to be “locked” by SO42- and Na+. This effect also explains the lowest water permeability of the Na2SO4 solution during pervaporative desalination

of

in our previous study [16].

ro

3.3 Permeability and diffusivity of salts in membrane

-p

Fig. 6 shows the change in the salt concentration in the receipting compartment as a

re

function of time through a membrane with the thickness of 56 μm at various initial salt concentrations. It was found that the time lag in diffusion was not significant. Thus, the salt

lP

diffusivity in the membrane cannot be evaluated from the time-lag method. Nonetheless, the

na

permeability coefficients can still be evaluated using the mass balance method in quasi-steady state permeation. The F(t)1 -t plots of the three salts are shown in Fig. 7, and no nonlinear part

ur

was found even when using t0 = 0, which further confirms that the time-lag method is not able to

Jo

determine the salt diffusivity in the membrane. This is probably because the transient permeation of salt in the membrane is very quick, the diffusion reaches the pseudo-steady state immediately after the salt leaves the liquid solution, and the time lag is too short to be detected accurately by the technique used in this study.

1

F(t) = -ln[(mT-VTCR)/(mT-VTa)], see the details in Supporting Information

17

Journal Pre-proof 100

(a) NaCl

Concentration of NaCl / mg.L-1

90 80

70

1%

60

5%

50

10%

40

15%

30

20%

20 10

of

0

ro

(b) MgCl2

90 80

-p

70 60

re

50 40 30

lP

Concentration of MgCl2 mg.L-1

100

20 10

na

0

3

2.5

Jo

Concentration of Na2SO4 / mg.L-1

ur

(c) Na2SO4

2

1.5 1 0.5 0

0

2

4

6

8

10 12 14 16 18 20 22

Time / min Fig. 6 Concentration of (a) NaCl, (b) MgCl2 and (c) Na2SO4 in the receipting compartment as a function of time. Membrane thickness: 56 μm.

18

Journal Pre-proof 0.01

(a) NaCl

0.008

1% 5% 10% 15% 20%

F(t)

0.006

0.004

0.002

of

0 0.01

ro

(b)

-p

0.006

re

F(t)

0.008

na

0.002

lP

0.004

Jo

ur

0

Fig. 7 F(t) vs t curves for (a) NaCl, (b) MgCl2 and (c) Na2SO4 diffusion. Membrane thickness: 56 μm.

19

Journal Pre-proof The permeability coefficients of the salts determined from the slope of the F(t)-t plots are shown in Fig. 8. It can be seen that: (1) For the same salt, the feed concentration has little influence on the permeability of the salt over the salt concentration range investigated here. (2) The salt permeability is related to the salt type and follows the order of NaCl > MgCl2 > Na2SO4. It is not surprising that NaCl has the highest permeability because it is the smallest salt (effective size of 0.15 nm [25]) among the three. MgCl2 and Na2SO4 have a similar effective molecular size

of

of 0.2 nm [25]; however, the repulsion between the negatively charged membrane and SO 42-

ro

resulted in the lowest permeability of Na2SO4 in the membrane. Please note that such

-p

permeability coefficients measure the ability of the salt to pass through the membrane under a concentration gradient across the membrane. These coefficients have dimensions of [(mol-

re

salt).(m-membrane thickness)]/[(m2-membrane area).(s-time)/[(mol-salt)/(m3-solution volume)]

lP

or [m2.s-1], which is commonly used in the literature.

na

NaC l

ur

1.5

MgCl2

Jo

Permeability coefficient / 10 -11 m2.s-1

2.0

1.0

0.5

Na2SO4 0.0 0

2

4

6

8

10

12

14

16

18

20

22

24

Salt concentration / wt% Fig. 8 Permeability coefficient of salt in the membrane as determined from the diffusion experiments. 20

Journal Pre-proof When the diffusion coefficient and solubility coefficient are independent of salt concentration, the permeability coefficient P will be equal to the product of the diffusion and solubility coefficients, that is, P=D∙S. The diffusivity coefficient can be estimated from D=P/S, and the results are shown in Fig. 9. Note that the solubility coefficient measures how much salt is sorbed in the membrane at a given salt concentration in the solution, and the diffusion coefficient measures how fast the salt diffuses through the membrane under a concentration gradient across

of

the membrane. The diffusivity of the three salts in the membrane also follows the order of NaCl >

ro

MgCl2 > Na2SO4. Therefore, it may be concluded that the permeability of the salts in the

-p

membrane is mainly determined by the diffusion coefficients.

re

5.0

lP ur

2.0

na

3.0

NaCl

Jo

Diffusivity / 10 -11 m2.s-1

4.0

MgCl2

1.0

Na2SO 0.0

4

0

2

4

6

8

10

12

14

16

18

20

22

24

Salt concentration / wt% Fig. 9 Salt diffusivity in the membrane estimated from the solubility and permeability coefficients.

21

Journal Pre-proof A comparison of salt transport properties of different membranes is illustrated in Table 3. The PEBA membrane studied in this work shows a medium-low salt permeability comparing with other polymeric membranes, which is favorable for desalination applications. Table 3 A comparison of salt transport properties Salt

S (dimensionless)

D (10-11 m2.s-1)

P (10-11 m2.s-1)

Ref

PEBA

NaCl

0.421±0.02

3.85±0.05

1.55±0.05

This study

PEBA

MgCl2

1.05±0.03

1.20±0.01

1.15±0.05

This study

PEBA

Na2SO4

0.315±0.02

0.35±0.03

0.15±0.01

This study

Disulfonated Poly (arylene ether sulfone)

NaCl

0.018±0.001

0.029±0.006

0.00058±0.00007

TRP-BP

NaCl

- 0.116±0.005

-p

ro

of

Membrane

- 4.78±0.21

- 0.554±0.0178

1.2±0.2

0.058±0.001

- 12±2

- 1.99±0.06

0.43 - 1.93

4.5- 49.6

1.9 - 95.4

0.067±0.002

2.4±0.2

0.16±0.01

- 0.791±0.036

- 44±4

- 27±3

re

0.050±0.008

NaCl

Poly(ethylene oxide) hydrogels

NaCl

[12] [26] [27]

ur

4. Conclusions

na

Hybrid PVA/MA/TEOS

lP

- 0.159±0.020

[11]

Jo

The salt transport in the PEBA membrane used in pervaporative desalination was studied. The concentration profile of salts in the membrane during pervaporation was investigated experimentally using a multilayer membrane. The solubility, diffusivity and permeability of salts in the membrane were determined. The following conclusions can be drawn: (1) The salt was found to be sorbed in the membrane but was not removed during the pervaporative desalination process, and the salt concentration in the membrane varied linearly with position. The accumulated salt uptake in the membrane follows the order of MgCl2 > NaCl >

22

Journal Pre-proof Na2SO4. High purity water was obtained as the permeate as long as the permeate side was kept dry under vacuum. (2) The solubility of salt in the membrane follows the order of MgCl2 > NaCl > Na2SO4. (3) Both the permeability and diffusivity of salts in the membrane follow the order of NaCl > MgCl2 > Na2SO4. The permeability of the salts in the membrane is not influenced by the feed salt

of

concentration. It is mainly determined by the diffusion coefficients.

ro

Acknowledgement

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Research support from the Natural Sciences and Engineering Research Council (NSERC) of

re

Canada is gratefully acknowledged. We also wish to acknowledge Arkema Inc. for generously

lP

supplying the polymer used in making the membranes.

Jo

ur

na

Conflict of interest statement: None

23

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Symbols used b

[mol.kg-1]

molality

D

[m2.s-1]

diffusion coefficient

F(t)

[-]

function of t

i

[-]

total number of ions given by one mole of salt

l

[μm]

total thickness of membrane -1

[kg.mol ]

molecular weight

m0

[kg]

weight of membrane sample before sorption

m1

[kg]

total weight of water and salt sorbed in the membrane

m2

[kg]

weight of membrane sample after sorption

m3

[kg]

weight of dry membrane sample after water desorption

ro

-p

re

P

2 -1

[m .s ]

permeability coefficient

3

-1

-1

[m ·Pa·mol ·K ] gas constant

S

[-]

T

[K]

t

[min]

na

solubility coefficients temperature

[kmol.m ] 3

[m ] 3

V2

[m ]

x

[μm]

ur

time

-3

Jo

V1

lP

R

U

of

M

uptake volume of membrane before sorption volume of membrane after sorption thickness of membrane at a certain point

Subscripts s

salt

w

water

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Journal Pre-proof Greek letters Π

[Pa]

osmotic pressure of the salt solution

Π*

[Pa]

osmotic pressure for an ideal solution

ф

[-]

osmotic coefficient

θ

[min]

time lag

Abbreviations maleic acid

MD

membrane distillation

PVA

poly(vinyl alcohol)

PEBAX

poly(ether-block-amide)

RO

reverse osmosis

TEOS

tetraethyl orthosilicate

TRP-BP

triptycene-containing sulfonated polysulfone

Jo

ur

na

lP

re

-p

ro

of

MA

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References [1] L. D. Tijing, Y. C. Woo, J-S. Choi, S. Lee, S-H. Kim, H. K. Shon, Fouling and its control in membrane distillation - A review, J. Membr. Sci., 2015, 475, 215-244. DOI: 10.1016/j.memsci.2014.09.042 [2] M. Laqbaqbi, M. C. García-Payo, M. Khayet, J.E. Kharraz, M.Chaouch, Application of direct contact membrane distillation for textile wastewater treatment and fouling study, Sep. Purif. Technol., 2019, 209, 815-825. DOI: 10.1016/j.seppur.2018.09.031

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Journal Pre-proof Figure legends Fig. 1 Amount of NaCl in each membrane sheet (a) and the accumulated amount of salt in the laminated membranes at different positions (b). Fig. 2 Concentration profiles of NaCl, MgCl2 and Na2SO4 in the membrane. Temperature: 25 °C. Fig. 3 Sorption uptake of (a) salts and (b) water in the membrane under different salt concentrations. at 25 °C.

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Fig. 4 Surface zeta potential of PEBA membrane (Tested with 0.001 M KCl at 25 °C).

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Fig. 5 Swelling degree of the membrane under different salt concentrations at 25 °C.

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Fig. 6 Concentration of (a) NaCl, (b) MgCl2 and (c) Na2SO4 in the receipting compartment as a function of time. Membrane thickness: 56 μm.

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Fig. 7 F(t) vs t curves for (a) NaCl, (b) MgCl2 and (c) Na2SO4 diffusion. Membrane thickness: 56 μm.

lP

Fig. 8 Permeability coefficient of salt in the membrane as determined from the diffusion experiments.

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Fig. 9 Salt diffusivity in the membrane estimated from the solubility and permeability coefficients.

29