The rejection of salt ions by nanofiltration membranes is essentially the result of the synergistic effect between steric hindrance (size sieving) and the Donnan charge effect. Since most commercial nanofiltration membranes contain dissociable functional groups in the active layer (such as carboxyl and sulfonic groups), the membrane surface is usually negatively charged in neutral aqueous environments. This leads to a pronounced asymmetry in ion rejection behavior.
Rejection Order of Anions
General Rule
Multivalent anions > divalent anions > monovalent anions.
For ions with the same valence, the larger the hydrated radius (or the more negative the hydration free energy), the higher the rejection rate.
Highly Charged Anions (SO₄²⁻, PO₄³⁻, etc.)
Sulfate and phosphate ions carry multiple negative charges, resulting in very strong Donnan repulsion. At the same time, they possess relatively large hydrated ionic radii (for example, the hydrated radius of SO₄²⁻ is about 0.38 nm), making steric hindrance significant. Therefore, the rejection rate of these ions is often close to 100% (>98%), making them the easiest components to remove by nanofiltration.
Carbonate System Ions (CO₃²⁻, HCO₃⁻)
Carbonate ions are divalent anions and are therefore strongly repelled as well. Bicarbonate ions are monovalent, but they have relatively large hydrated radii and can partially dissociate. Under alkaline conditions, they are more likely to convert into CO₃²⁻. As a result, their overall rejection rate is higher than that of typical monovalent anions, although strongly influenced by pH.
Monovalent Anions (Halides, Nitrate, etc.)
For monovalent anions, Donnan repulsion is relatively weak. Steric hindrance and differences in hydration free energy become the dominant factors determining rejection performance.
The typical rejection order is:
F⁻ > Cl⁻ > NO₃⁻ > Br⁻ > I⁻
- F⁻: Although the bare ionic radius is very small, its hydration free energy is extremely negative (−465 kJ/mol). The hydration shell is very stable, giving fluoride the largest effective volume and the highest rejection among monovalent anions.
- Cl⁻: Hydration free energy is approximately −340 kJ/mol, with a hydrated radius around 0.33 nm, resulting in moderate rejection.
- NO₃⁻: Hydration free energy is only about −300 kJ/mol, meaning weaker hydration. In addition, its planar triangular structure allows easier orientation through membrane pores, leading to significantly lower rejection than chloride. Many loose nanofiltration membranes show nitrate rejection rates 10–20 percentage points lower than chloride rejection.
- Br⁻ and I⁻: These ions are even more weakly hydrated and have smaller effective hydrated radii, so rejection decreases further.
Rejection Order of Cations
Because the membrane surface is negatively charged, cations act as counter-ions and are electrostatically attracted toward the membrane surface or even into membrane pores. The higher the valence, the stronger the attraction and the easier the ion can permeate. Consequently, divalent cations may exhibit lower rejection than monovalent cations.
Monovalent Cations
Their transport mainly depends on dehydration and steric hindrance during entry into membrane pores. The larger the hydrated radius, the more difficult the passage.
Typical rejection order:
Li⁺ > Na⁺ > K⁺ > NH₄⁺ > Rb⁺ > Cs⁺
Li⁺ has extremely negative hydration free energy and the largest hydrated radius, giving it the highest rejection. K⁺ and NH₄⁺ are less strongly hydrated and therefore permeate more easily.
Divalent Cations (Ca²⁺, Mg²⁺, etc.)
Divalent cations experience strong electrostatic attraction to the membrane’s fixed negative charges and can be effectively “dragged” into the membrane phase. Therefore, conventional nanofiltration membranes often show lower rejection for divalent cations than for Na⁺.
Although Mg²⁺ has more negative hydration free energy than Ca²⁺ (−1830 vs −1505 kJ/mol) and a slightly larger hydrated radius, its higher charge density may make electrostatic attraction dominant. As a result, the apparent rejection of Mg²⁺ is often slightly lower than that of Ca²⁺.
In practice, the observed trend is often:
Monovalent cations > Ca²⁺ ≥ Mg²⁺
Apparent Rejection Order of Common Salts
When rejecting a salt, the membrane first repels ions having the same charge polarity as the membrane (typically anions for negatively charged nanofiltration membranes). To maintain electroneutrality, counter-ions (cations) are simultaneously retained. However, the “dragging effect” of divalent counter-ions weakens this coupled rejection.
For typical negatively charged nanofiltration membranes, the rejection order of common salts is generally:
Na₂SO₄ > MgSO₄ ≥ CaSO₄ > NaCl > NaNO₃ > CaCl₂ > MgCl₂
Na₂SO₄
SO₄²⁻ experiences strong electrostatic repulsion, forcing Na⁺ to be retained simultaneously. Total salt rejection can exceed 99%.
MgSO₄ and CaSO₄
Rejection is still dominated by sulfate repulsion. However, divalent cations partially enter the membrane phase and shield part of the membrane charge, slightly reducing rejection (still typically >90%).
NaCl and NaNO₃
These salts consist of monovalent anions and monovalent cations. Rejection generally ranges from 40–90%, depending on membrane tightness. Nitrate rejection is typically lower than chloride rejection.
CaCl₂ and MgCl₂
Strong Donnan attraction of divalent cations significantly promotes Cl⁻ permeation, resulting in substantially reduced apparent rejection, sometimes as low as 20–50%.
Key Influencing Factors
Membrane Charge and pH
Higher pH increases the negative charge density of the membrane surface, enhancing anion repulsion and cation attraction. This further amplifies rejection differences. Near the isoelectric point, membrane charge is minimized, so the rejection order still exists but the differences become smaller.
Feed Concentration
At higher feed concentrations, counter-ion shielding of membrane charges becomes stronger, suppressing the Donnan effect. Rejection rates of all ions decrease, although the relative order generally remains unchanged.
Membrane Structural Differences
Loose nanofiltration membranes rely more on steric sieving, leading to generally lower monovalent anion rejection. In some cases, strongly hydrated F⁻ ions may be rejected because of their large effective hydrated size, while certain weakly hydrated ions permeate more easily.
Dense nanofiltration membranes exhibit stronger Donnan exclusion, making their rejection behavior more consistent with the theoretical trends described above.