chapter 6. membrane process (carrier mediated...

Chang-Han Yun / Ph.D.

National Chungbuk University

November 17, 2015 (Wed)

Chapter 6. Membrane Process

(Carrier Mediated Transport)

2 Chapter 6. Membrane Process(Concentration) Chungbuk University

Contents

Contents Contents

6.5 Other Driving Force

6.4 Concentration Driving Force

6.3 Pressure Driven Force

6.2 Osmosis

6.1 Introduction


6.4 Concentration Driving Force 6.4.4 Carrier

mediated transport

Membrane supply an interphase between two phases

Liquid as a membrane

Liquid membrane or Liquid film separates two phases from each other.

Differences in solubility and diffusivity in the liquid film ⇨ occur separation

Carrier

Contained at the inside of the membrane

Ability to complex with a specific solute to enhance the flux of solute

Characteristic of a facilitated or carrier mediated transport

Reversible chemical reaction(complexation) process + Diffusion process

① Diffusion = rate-limiting (fast reaction) ⇨ mainly occur in most of case

② Reaction = rate-limiting (slow reaction and relatively fast diffusion)



mediated transport

[Table 6-17] Diffusivities in carrier mediated

systems

System D(cm2/s)

Mobile carrier system

Solvent swollen or gel system

Fixed carrier

10–7 ∼ 10–5

10–8 ∼ 10–6

> 10–7

<Figure 6-29> Schematic drawing of a mobile carrier system (left) and a fixed carrier system (right).

Mobile or fixed type carrier(<Figure 6-29>)

Mobile type : Carrier dissolved in the liquid

• Carrier-solute complex diffuses across

the membrane.

• Higher diffusivity in the mobile system

Fixed type : Carrier bound chemically or

physically to a solid polymer

• Very restricted mobility

• Solute jumps or 'hops' from one site to

the other



mediated transport

6.4.4.1 Liquid membrane

Types of liquid membrane(see <Figure 6-30>)

1) Immobilized Liquid Membrane(ILM) or Supported Liquid Membrane(SLM)

• Liquid film : immobilized within the pores of a porous membrane

• Role of porous membrane : framework or supporting layer for the liquid film

• Preparation :

impregnating a hydrophobic porous membrane with a suitable organic solvent.

<Figure 6-30> Schematic drawing of two

types of liquid membrane

- left : supported liquid membrane(SLM)

- right: emulsion liquid membrane(ELM)



mediated transport

2) Preparation of ELM (<Figure 6-31>)

① Mix 2 immiscible phases vigorously with surfactant to stabilize the emulsion

⇨ form stable emulsion droplets (droplet size : 0.5 ∼ 10 μm)

② Add emulsion to aqueous phase ⇨ form W-O-W emulsion ⇨ Oil phase = Liquid membrane

※ Phase 1 and phase 2 : generally aqueous solutions

Liquid membrane phase : organic phase (immiscible with water)

※ Solubility of organic to water : very important factor to stabilize system

<Figure 6-31> Preparation of ELM.



mediated transport

Selectivity of LM : Low ⇨ only used in some specific applications

Solubility & Diffusivity ⇨ Selectivity

• Diffusivity : components size = similar ⇨ diffusivity = not much difference

• Solubility : difference in distribution coefficient of species i among W-O-W

Difference in distribution coefficient of species i among W-O-W ⇨ Selectivity

Without carrier, difference in diffusivity and solubility = low ⇨ low selectivity

Carrier-mediated transport or Facilitated transport (<Figure 6-32>)

Carrier : Accelerate the transport of specific component ⇨ Selectivity↑



mediated transport

U-tube experiment

Bottom of an U-tube : organic (higher density than water)

One arm of the U-tube : aqueous KCl solution

Organic phase : chloroform containing carrier(18-crown ether-6 : a high affinity to KCl salt)

Salt transport by ΔcKCl from high concentrated solution to pure water phase

• Without carrier : very low transport of salt (∵ KCl solubility to chloroform = very low)

• With carrier : form a reversible complex with the salt ⇨ transport of K

<Figure 6-33> 8-crown-6 complexed

with a potassium ion.

Other arm of the U-tube : pure water

[Figure 6-32] U-tube experiment to

demonstrate facilitated transport.



mediated transport

Carrier-mediated transport

Carrier molecule(C) : Enhance transport of component A (A+C → complex AC)

Coupled transport (<Figure 6-34>)

2 components are involved in carrier mediated-transport

Co-transport : 2 components are moving in the same direction

Counter-transport : 2 components are moving in opposite directions

Decomplexation in the opposing phases

Transport : low → high concentration

∵ Real driving force :

concentration gradient of complex(C)

<Figure 6-34> Transport mechanism in a liquid

membrane.

Left : Diffusive transport(without carrier)

Right : Facilitated transport(with carrier C)

Facilitated transport

uncoupled

Diffusive transport

(without carrier)

coupled



mediated transport

Transport mechanism

① Dissolving solute of aqueous phase 1(feed phase) into the membrane

② Complexation between the carrier and the solute at the phase 1 interface

③ Diffusion of carrier-solute complex to opposite interface through liquid membrane

④ Decomplexation at phase 2(stripping phase or receiving phase) interface

⑤ Releasing solute from the membrane to phase 2

⑥ Diffusion of free carrier back to phase 1 interface through membrane

<Figure 6-35> The mechanism of carrier-mediated transport

in liquid membranes with mobile carriers.



mediated transport

Basic feature of carrier-mediated transport

Complexation reaction = reversible

Affinity between the carrier and the solute = very high

• Strong complex ⇨ slow release

• Weak complex ⇨ only limited facilitation occurs ⇨ selectivity =low

• Bond energies of these reversible complexes = range of 10 ∼ 50 kJ/mol

※ Similar bond energy : H-bonding, acid-base interactions, chelation, π bond interactions

Effects contribute to the transport of component A

① Rate of complexation / decomplexation at the two interfaces

② Diffusion of the complex (and the free solutes) across the membrane

Another characteristics of facilitated transport

Flux = not proportional anymore to the driving force

At (very) low concentrations in feed phase, still appreciable fluxes can be obtained.



mediated transport

<Example> O2 and N2 transport through water film

Carrier(Co compound) : complexation with O2, but no complexation with N2

Without carrier (un-coupled transport)

• transport of O2 and N2 by free diffusion

• p↑ ⇨ solubility↑ ⇨ Flux of O2 and N2 ∝ partial pressure(concentration)

• Solubility : O2 > N2 ⇨ flux : O2 > N2

With carrier(coupled transport)

• N2 flux : no change (∵ no complexation with carrier)

• O2 flux : enhanced

<Figure 6-36> Oxygen and nitrogen

Flux through water with and

Without carrier (cobalthistidine)



mediated transport

<Example> Coupled transport nitrate ion (NO3–) : see <Figure 6-37>

Carrier : many ion-exchange components

Complexing agents for anions : Tertiary amines or quarternary ammonium salts

Charge density on the anion ⇨ affinity between anion ↔ anion-exchange component

※ Affinity sequence of various anions (anion ↔ quarternary ammonium salt)

I– > NO3– > NO2

– > Cl– > H2PO42 – > HSO4

– > SO42– > HCO3

– > PO43– > CO3

2–

Count-anion to exchange with nitrate : Cl– (Feed : NO3– ⇨ Cl– ; Strip : Cl– ⇨ NO3

– )

Transport of NO3– against its own driving force

∵ Actual driving force = Δc of Cl– in membrane

Affinity(NO3– ↔ carrier) ≫ Affinity(Cl– ↔ carrier)

Very high Cl– in strip phase ⇨ Easy decomplexation

Equilibrium reaction : RCl + NO3– ↔ R NO3 + Cl–

<Figure 6-37> Counter-current transport. Cl– concentration

in phase 2 (strip phase) is very high in comparison to the

low NO3– concentration in the feed (phase 1).



mediated transport

O2 and N2 transport through water film(<Figure 6-38>)

Mechanisms contribute to the total O2 flux through the

membrane

• Coupled transport : A + C ↔ AC

• Free diffusion ⇨ Follow normal Fick’s law

Total flux of component A : sum of the two contributions

(6-85)

Fick's law Carrier-mediated diffusion

6.4.4.2 Aspects of separation

<Figure 6-38> Schematic drawing of the

concentration profiles arising from free

O2 diffusion via Fick's law (curve b)

and by facilitated diffusion (curve a).



mediated transport

Equilibrium constant of the complexation reaction, (6-86)

Average carrier concentration in the membrane, c = cC + cAC,o (6-87)

where cC = concentration of free carrier

cAC,o = concentration of complexed carrier at a certain point in the membrane

Eq(6-86) and (6-87) → (6-85) and <assume> cA,ℓ ≈ cAC,ℓ ≈ 0

Total flux of component A, (6-88)

Define partition(distribution) coefficient k = cAo/cAf

where cAf = concentration of component A in the feed

Eq(6-88) → (6-89)

Two limiting cases from [Figure 6-38] and Eq(6-85) : Rate Determining Step

① 1st term(Fickean diffusion)

• Reaction rate = low

• cAC,o ≪ cA,o

② 2nd term(diffusion of the complex)

• Reaction rate = fast

• cAC,o ≫ cA,o



mediated transport

Damköhler number

Ratio between reaction rate and diffusion rate

Define the 2nd Damköhler number = ℓ2/(D∙t0.5)

where t0.5 = half life of the complexation reaction (reaction time constant)

D = diffusion coefficient of the free component

ℓ = membrane thickness

Reaction time constant(t0.5) ∝ D/ℓ2

2nd Damköhler number[ℓ2/(D∙t0.5)] ≫ 1

⇨ Reaction = rate determining

• Reaction rate = very fast

• Diffusion of free permeant = neglected

<Example> ℓ = 10 μm, t0.5 = 10–7 sec, D = 10–9 m2/sec ⇨ Damköhler number = range of 106

2nd Damköhler number[ℓ2/(D∙t0.5)] ≪ 1

⇨ Free diffusion = rate determining

• Reaction rate = slow

• Diffusion of complex = neglected



mediated transport

※ Flux ratio of 10 (total flux/Fickean flux) ⇨ facilitated transport = rate-determining step (region II)

<Figure 6-39> Schematic drawing of the ratio of the total flux

to the Fickean flux as a function of the Damköhler number.



mediated transport

For coupled process to transport NO3–

Chemical reaction : RCl + NO3– ↔ R NO3 + Cl–

Equilibrium constant(K) : (6-90)

where subscript o : refer to organic phase

subscript w : refer to aqueous phase

Total NO3– in organic = [NO3

–]o + [RNO3]o

Solubility of free ions in organic phase([NO3–]o) = very low

⇨ Total NO3– in liquid membrane ≈ [RNO3]o

Distribution coefficient on feed side

(6-91)

and distribution coefficient on strip(permeate) side

(6-92)

K = / = Ratio of distribution coefficient

K = / = high ⇨ carrier is very selective



mediated transport

Overall transport

Nitrate flow in the boundary layer (Jbl)

(6-93)

Ji, which is determined by the ease of complexation,

Ji = k1 [NO3–]w – k–1[NO3

–]m (6-94)

where k1 and k–1 = rate constants

[NO3–]w and [NO3

–]m = interfacial [NO3–] in aq.(w) and org. phase(m) respectively

Nitrate flux through the membrane phase(Jm)

(6-95)

Under steady-state, Jb1 = Ji = Jm = overall flux J

dc/dx = Δc/Δx and Eq(6-93), (6-94), (6-95) → (6-96)

where δ = thickness of the boundary layer and ℓ= membrane thickness.



mediated transport

[NO3–]w = f(t) ≠ constant

(6-97) where V = total feed volume and A = membrane area

<Assume> rate of complexation = very fast (6-96)

(6-98)

By dividing Eq(6-96) by k–1 and neglecting 1 in the denominator

Eq(6-98) & Eq(6-96) → (6-99)

① Diffusion process through liquid membrane = predominant

⇨ boundary layer phenomena = neglect ⇨ permeability coefficient, P = kNO3-∙Dm/ℓ

② Diffusion process through boundary layer = predominant

⇨ P = Dbl / δ

Eq(6-99) → Eq(6-97), and integration with the BCs

BC 1 : c = co at t = 0 & BC 2 : c = c at t = t

⇨ (6-100)



mediated transport

Main components of SLM

(Supported Liquid Membrane)

Free liquid film = very unstable ⇨ use porous membrane as a framework(SLM)

SLM : unstable with time

6.4.4.3 Liquid membrane development

Preparation technique Material

Stretching

Phase inversion

Polypropylene (Celgard)

Polytetrafluoroethylene (Gore-Tex)

Polypropylene (Accurel)

Polyethylene

[Table 6-18] Some porous membranes frequently used as supports

for supported liquid membranes (SLM).

Support membrane

Organic solvent

Carrier

For high stability, Hydrophobic(PE, PP, PVDF) as support

For high flux, Porosity of support = high

Membrane should be as thin as possible (∵ Flux ∝[thickness]－1 )



mediated transport

Requirements of organic solvent to apply to SLM systems

Solubility in the aqueous phase = extremely low

Volatility = low

Solvent for both the carrier and the carrier-solute complex

Viscosity = not much high

• Carrier or carrier-solute complex increases the viscosity of organic solvent

• Stokes-Einstein equation, : Viscosity↑ ⇨ Diffusivity↓ (6-101)

6.4.4.4 Choice of organic solvent

[Table 6-19] Viscosities at T = 298 K of some

solvents used in LM processes

Solvent Viscosity(g/(cm∙s))

o-dichlorobenzene

l-octanol

dibutylphthalate

o-nitrophenyl octyl ether

o-nitro diphenylether

0.013

0.076

0.154

0.128

0.161



mediated transport

By carrier concentration↑: two effects = counteracting

Eq(6-89) : ⇨ Flux↑

Viscosity↑ ⇨ Diffusity↓ ⇨ Flux↓

Very severe problem with SLM which causes the process to cease

Loss of the organic phase ⇨ unstability of the liquid film with time

• Essential for the solubility of the organic phase in the aqueous phase

• Shear forces generated by feed flow ⇨ emulsification of the organic phase

⇨ form small emulsion droplets ⇨ diffuse out of the organic phase

⇨ eventually the organic phase is completely removed. (<Figure 6-42>)

Carrier loss, and Osmotic effects

• Involving high ion strength ⇨ generate high osmotic pressure differences



mediated transport

Approach to solve these problems

Gelation of the liquid membrane phase

Change organic liquid to highly swollen crosslinked polymer(gel)

Negative effect on diffusion coefficient

Stability of the layer improved dramatically

Gelled liquid layer

Obtained by adding a small amount of a polymer to the organic phase

Polymers : PVC, PAN, PMMA ↑

<Figure 6-42> Schematic representation of the

emulsification of the organic phase

in supported liquid membranes.



mediated transport

Choice of the carrier = key factor in facilitated transport

Ratio of the distribution coefficients ⇨ determine selectivity

In fact, every specific solute ↔ its own specific carrier

Selection of the carrier : very important and very difficult

From liquid extraction ⇨ much information about carrier can be obtained.

Classification of carrier molecules

oximes

(tertiary) amines

crown ethers

cobalt complexes

calixarenes

6.4.4.5 Choice of carrier

[Table 6-20] Structures of various carriers



mediated transport

Classification of application : depend on species to be separated

Ion separation

Gas separation : completely different type of class of facilitated transport

Separation of O2 from N2

Removal of H2S from natural gas

NH3, NOx and SO2 from waste gases

Separation of organic mixtures

6.4.4.6 Application

Cations

Anions

Gases

Organic molecules

Wide range of carriers is available ⇨ Easily removed via facilitated transport

Cations to be recovered by LM : Cu2+, Hg2+, Ni2+, Cd2+, Zn2+, Pb2+

Anions to be recovered by LM : NO3–, Cr2O7

2–, uranyl [UO2(SO4)22–]

Separation of hydrocarbons

aliphatic/aromatic(benzene/hexane)

isomeric xylenes

Removal of phenol from waste water



mediated transport

6.4.4.7 Summary of carrier mediated transport

Items Characteristics

Membranes

Supported Liquid Membranes (SLM)

Emulsion Liquid Membranes (ELM)

Fixed carrier membranes

Solvent swollen membranes

Thickness 20 ∼ 150 μm (SLM), ≈ 0.1 ∼ l μm (ELM)

Pore sizes Non-porous (liquid !)

Driving force Concentration difference

Separation principle Affinity to carrier (carrier mediated transport)

Membrane material Hydrophobic porous membrane

Applications

Removal of specific ions

Cations (Cd, Cu, Ni, Pb)

Removal of gases

O2/N2 separation

Separation of organic liquids

Removal of phenol

Removal of H2S, CO2, SO2, CO, NH3

Anions (nitrate, chromate)

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