The Impact of Adsorption Property Modification by Crosslinkers on Graphene Oxide Membrane Separation Performance

Abstract

The health risks associated with the presence of heavy metals in drinking water can be severe. To address this issue, membrane separation technology is one of the consolidated alternatives. Inorganic, porous membranes were found in applications where low energy consumption is highly desirable. The selectivity of these membranes is attained by functionalisation. Graphene oxide functionalised membrane technology is promising for removing heavy metal ions. This work summarises, discusses and presents the relationship between adsorption and overall membrane separation process performance for heavy metal ions removal from wastewater when a graphene oxide-functionalised membrane is used. The separation performance depends on the hydrophobic interactions of the membrane and the solute. The electrostatic interaction between the negatively charged membrane surface and positively charged metal ions facilitates the adsorption, leading to the rejection of these metal ions. The influences of the chemical nature of the modifiers of graphene oxide layers are highlighted.

1. Introduction

The presence of heavy metals in drinking water can cause severe hazards to human health. Although they are naturally occurring elements, their multiple uses in industry, household, agriculture and medicine have contributed to their concentration in the environment close to industrial activity, thus increasing the recognition of their potentially harmful effects on human life and the environment [1]. For example, exposure to elevated levels of metallic, organic and inorganic mercury can damage the brain, kidneys and the developing foetus [2]. Various technologies, including precipitation−coagulation−flocculation, adsorption, ion exchange, flotation and membrane-based separation, have been developed to remove heavy metal ions (HMI) from wastewater [3,4,5]. The process of precipitation, coagulation-flocculation and ion exchange work efficiently when pollutant concentration is medium to high (over 100 ppm), thus requiring further remotion techniques to attain the restrictive level needed in the case of heavy metals pollution. Alternatives for this last removal step are adsorption- [6] and membrane-based [7] separation processes.

Nowadays, membrane process reverse osmosis (RO) is the dominant technique in large-scale water treatment and is also applied to heavy metal removal [8,9,10,11]. The results showed that RO could achieve up to 99% removal efficiency of Cu²⁺, Ni²⁺, Zn²⁺ and As⁵⁺. However, the main limitation of RO application is the high power consumption and operating cost [12,13] due to high pressures (15–75 bar). This drawback relies on the low water permeability of RO membranes, showing fluxes around 2–5 L m⁻² h⁻¹ bar⁻¹ [14]. On the other hand, the high permeability and selectivity of ceramic membranes could allow higher water flux (8–40 L m⁻² h⁻¹ bar⁻¹ [15]) and show high recovery and improved energy savings [16]. However, overcoming challenges such as reducing the capital cost [17], long-term stability [18] and scalability [19] would enable ceramic membranes to consolidate in the water treatment market. Graphene oxide (GO) stands out for its numerous properties among ceramic materials. For this reason, a wide range of applications have been explored, aiming at commercialisation [20] and offering significant environmental and economic benefits [21]. The main problem with GO membranes is the loss of stability over long periods of operation [22].

The long-term stability of GO membranes is mainly triggered by water molecules connecting with oxygenated groups located elsewhere in the GO structure, thus promoting the widening of nanochannels and allowing the transport of pollutant ions. This instability can be overcome by incorporating covalent or non-covalent binding additives within the GO matrix [23], commonly known as crosslinkers. Nevertheless, adding a new component to the GO alters the chemical nature of the matrix, and it could be responsible for a new behaviour towards rejecting specific contaminants.

Adsorption is the process taking place when a solute (adsorbate) accumulates on the surface of a solid (adsorbent) and forms a molecular or atomic film [6], while membrane-based separation is the process of using a barrier that inhibits the passage of certain constituents while allowing other constituents to pass through [24]. These techniques are commonly described as separate alternatives, but could they be related in their mechanisms of operation?

In the literature, several works refer to the adsorption or nanofiltration of heavy metal ions. However, none of the studies focus on the influence adsorption could have on the performance of membrane-based processes for wastewater treatment. For example, Burakov et al. [6] present a detailed review of the adsorption of noxious heavy metal ions from wastewater effluents using various adsorbents, such as conventional and nanostructured. Xiang et al. [25] review the latest developments, discoveries and prospective applications related to ultrafiltration, nanofiltration, reverse osmosis and electrodialysis, with an in-depth focus on heavy metal removal. Abadi et al. [26] have summarised and analysed processes in which nanofibers prepared by the electrospinning method were used as a photocatalyst or adsorbent in wastewater treatment.

The present work aims to describe the connection between adsorption and membrane-based processes, analysing experimental results for HMI removal from water when using functionalised graphene oxide inorganic membranes and the effect of the modification of the material with crosslinkers and covalent linkers between GO layers.

The review focuses on the relationship between adsorption and selectivity of GO membranes and considers only the data available referring to membrane performance, not including particular data for adsorption studies outside the context of membrane separation processes.

2. Adsorption of Heavy Metal Ions on Graphene Oxide

Graphene oxide (GO) is a compound derived from graphene, a single layer of carbon atoms arranged in a two-dimensional honeycomb lattice oxide. It usually contains hydroxyl, carboxyl, and epoxide functional groups on its surface. In combination with its high surface area, the material has a high adsorption capacity for the removal of HMI from aqueous solutions [27].

Table 1. Maximum adsorption capacities of heavy metal ions using different sorbents.

Adsorbed Heavy Metal Ions	Type of Sorbent	qmax (mg g−1)	Operating Conditions	Adsorption Isotherm Models	Reference
As(III)	GO	1432.80	pH N.A., T N.A.	Langmuir	[34]
		0.02	pH 7, T 298 K	Langmuir	[35]
Au(III)	GO	149.20	pH N.A., T 298 K	Langmuir	[36]
Cd(II)	GO	83.80	pH 5.7, T 305 K	Langmuir	[37]
		530.00	pH 5.0, T 298 K	Langmuir	[30]
	Ze-nWRT	270.00	pH 4.0, T 307 K	Langmuir	[38]
	ZIF-8-EDA	294.11	pH 6.0, T N.A.	Langmuir	[31]
Co(II)	GO	21.28	pH 5.5, T 298 K	Freundlich	[39]
	LL-NaOH	25.40	pH 6.0, T 301 K	Langmuir	[40]
Cr(VI)	GO	1.22	pH 4.0, T N.A.	Langmuir	[41]
Cu(II)	GO	46.60	pH 5.0, T N.A.	Langmuir	[42]
		72.60	pH 5.7, T 303 K	Langmuir	[37]
		294.00	pH 5.0, T 298 K	Langmuir	[30]
		117.50	pH 5.3, T N.A.	Freundlich	[43]
	LC-Al2O3	15.69	pH 5.0, T 298 K	Langmuir	[44]
	LVB	23.18	pH 5.0, T 298 K	Langmuir	[45]
Eu(III)	GO	175.44	pH 6.0, T 298 K	Langmuir	[46]
	TNRs	115.30	pH 5.0, T N.A.	Langmuir	[47]
Hg(II)	GO	8.65	pH N.A., T 298 K	Intraparticle diffusion	[48]
Mn(II)	GO	32.00	pH 5.0, T 298 K	Langmuir	[49]
Ni(II)	GO	62.30	pH 5.7, T 304 K	Langmuir	[37]
		38.61	pH 6.0, T 298 K	Langmuir	[50]
Pb(II)	GO	250.00	pH 6.0, T 298 K	N.A.	[51]
		842.00	pH 6.0, T 293 K	Langmuir	[52]
		1119.00	pH 5.0, T 298 K	Langmuir	[30]
Sb(III)	GO	8.06	pH 11.0, T 303 K	Freundlich	[53]
Sr(II)	GO	5.93	pH 3.0, T 293 K	Langmuir	[54]
Th(IV)	GO	58.59	pH 1.4, T 293 K	Langmuir	[55]
U(VI)	GO	299.00	pH 4.0, T 298 K	Langmuir	[56]
		5.12	pH 3.0, T 293 K	Langmuir	[54]
	TNRs	282.50	pH 5.0, T N.A.	Langmuir	[47]
Zn(II)	GO	246.00	pH 7.0, T 293 K	Langmuir	[57]
		345.00	pH 5.0, T 298 K	Langmuir	[30]

q_max: maximum adsorption capacity; T: temperature of adsorption; N.A.: not available.

shows the maximum adsorption capacity (q_max), which represents an adsorbent’s overall adsorption capability [28]. GO has a strong adsorption affinity to various heavy metal ions, and the maximum adsorption capacities are generally more significant than those of other adsorbents [5,6]. For example, Šljivić et al. [29] demonstrated that Cu(II) adsorption in zeolite was 8.13 mg g⁻¹ (pH 5.0, T 298 K), while in GO, it is 294.00 mg g⁻¹ [30] at the same conditions. Khosravi et al. [31] determined that amino-functionalized zeolite imidazolate framework-8 (ZIF-8-EDA) possesses a maximum adsorption capacity of Cd(II), equivalent to half the maximum adsorption capacity of GO. This can be explained by the negative charge on the surface of GO nanosheets in aqueous solutions due to the ionisation of the carboxylic groups and the lone-pair oxygen atoms in GO. Consequently, GO is an ideal sorbent to bind metal ions through ionic and coordinative interaction [32]. Also, the complexation of heavy metal species with surface oxygenous functional groups (e.g., –OH and –COOH) is also one possible adsorption mode [33].

The adsorption capacity of a material is influenced by both pH and temperature. Table 1 presents the operating conditions for achieving maximum adsorption capacity. To increase the attraction between GO and HMI, the solution is brought to a pH above pH_pzc (point of zero charge), where the surface charge of GO is negative, and the electrostatic interactions become stronger [30]. Furthermore, Table 1 presents the adsorption isotherm models where the Langmuir model indicates that the adsorbent surface contains only a certain number of active sites for a single molecule to be adsorbed, while the Freundlich model indicates that there are several different adsorption sites on a heterogeneous adsorbent material. According to the data, metal ions fit the Langmuir model best, describing the chemisorption process when ionic or covalent chemical bonds are formed between the adsorbent (GO) and the adsorbate (HMI) [58].

3. Adsorption of Heavy Metal Ions on Modified Graphene Oxide

Different materials have been used to modify graphene oxide and improve its stability and capacity. These compounds, called crosslinkers, have different characteristic functional groups, which allow the structure and properties of the GO to be modified. The modification of GO with carboxylic acids [59], diamines [59,60,61], dialdehydes [62], metal groups [63,64], and amino acids [65] has been widely reported, where the functional group is the main responsible for the cross-linking to the GO layer through chemical bonds or physical interactions. Chemical functionalisation of GO nanosheets is usually carried out in temperature-assisted solution [66], layer-by-layer deposition [67,68], use of the sol-gel method [69] or immersion in solution with the crosslinker [70]. In addition to crosslinkers, GO can also be improved by adding a second compound, called a covalent linker, which increases the number of covalent bonds between the functionalised GO sheets and the contaminants. The incorporation of a covalent linker within the functionalised GO membrane structure can be performed directly into the synthesis GO-crosslinker solution or by immersing the already functionalised GO-crosslinker membrane in a solution containing the second functional material [70].

Table 2 shows the maximum adsorption capacities of most heavy metal ions on modified GO. It can be observed that the adsorption capacity is higher than those on unmodified GO (Table 1). This suggests that the materials used to modify GO enhance the adsorption capacity of the modified GO composites. Figure 1a depicts the box plots for the data presented in Table 1 and Table 2, showing a clear difference between GO material with or without additives. The addition of a crosslinker into the GO matrix increases the adsorption of heavy metal ions, showing a median twofold superiority to unmodified GO. Crosslinkers may incorporate more connection sites between the material and the heavy metal ion; for example, nitrogen-based crosslinkers have one connection point per nitrogen atom, and oxygen-based crosslinkers have two connection points per oxygen atom. Metal crosslinkers have electrostatic interactions with metal ions. However, adding a second material seems to decrease the adsorption, likely due to the bonding between the covalent linker and the GO functionalised nanosheets (decreasing the connection sites for the metal ions). In the case of GO, the maximum adsorption capacity is 253.58 ± 75.39 mg g⁻¹, while for GO-crosslinker and GO-crosslinker-covalent linker, the maximum capacity is 362.89 ± 48.86 mg g⁻¹ and 128.41 ± 26.15 mg g⁻¹.

Figure 1b depicts the box plot of the maximum adsorption of capacities for Cu(II) and Pb(II) using GO-based materials. It is noticeable that, despite having the same ionic charges, the adsorption has different values. This is because the q_max is related to the characteristics of the metal ion, in addition to the properties of the GO-based sorbent [71].

In Table 2, both the crosslinker and covalent linker are classified in terms of the dominant functional groups and are denoted according to the connecting element between the compound and the GO nanosheet: nitrogen (N), oxygen (O) and metallic element (M).

Table 2. Maximum adsorption capacities of crosslinker and crosslinker-covalent linker-functionalised GO for removing heavy metal ions.

Heavy Metal Ion	Crosslinker (Classification)	Chemical Formula Crosslinker *	Covalent Linker (Classification)	Chemical Formula Covalent Linker *	qmax (mg g−1)	Operating Condition	Reference
As(V)	Fe-NPs (M)	Fe3O4	-	-	73.42	pH 7.0, T 298 K	[72]
Au(ΙΙΙ)	CS (N, O)	C6H11NO4	-	-	1076.65	pH 4.0, Τ 323 Κ	[36]
	PAM (N, O)	C3H5NO	-	-	253.81	pH 5.0, T 298 K	[73]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	106.00	pH 5.2–6.8	[74]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	27.83	pH 6.0–7.0, T 293 K	[75]
	PDA (N)	C7H9NO2	-	-	210.00	T 298 K	[76]
	PDA (N)	C7H9NO2	-	-		pH 6.0	[77]
Co(II)	PPhDA (N)	C6H8N2	-	-	116.35	pH 6.0, Τ 298 Κ	[78]
Cr(VI)	MgAl-LDH (M)	-	-	-	172.55	pH 2.0, 293 K	[79]
	Fe-NPs (M)	Fe3O4	CS (N, O)	C6H11NO4	162.00	pH 4.25, T 293 K	[80]
	TETA (N)	C6H18N4	-	-	219.50	pH 2.0, Τ 303 Κ	[81]
	PAAm (N)	C3H7N	-	-	485.00	pH 4.0, T 298 K	[82]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	17.29	pH 1.0–3.0, T 293 K	[75]
	CDx (O)	C42H70O35	CS (N)	C6H11NO4	67.66	T 298 K	[83]
	Fe-NPs (M)	Fe3O4	CS (N)	C6H11NO4	107.99	pH 2.0, T 303 K	[84]
	Fe-NPs (M)	Fe3O4	DACHTA (N)	C14H22N2O8	83.66	pH 3.0, T 303 K	[85]
Cu(II)	Fe-NPs (M)	Fe3O4	SAc (O)	C6H6NO3S	62.73	pH 5.0, T 298 K	[86]
	EDTA (N, O)	C10H14N2O8	-	-	301.20	T 318 Κ	[87]
	Ca2+ (M)	-	SA (O)	C6H9NaO7	60.20		[88]
	TETA (N)	C6H18N4	-	-	209.10	pH 6.0, T 293 K	[89]
	SA (O)	C6H9NaO7	-	-	98.00	pH 5.0, Τ 303 Κ	[90]
	PAM (N, O)	C3H5NO	-	-	68.68	pH 4.5, T 298 K	[73]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	87.00	pH 5.2–6.8	[74]
	PAAm (N)	C3H7N	-	-	349.04	pH 6.0, T 293 K	[91]
	L-Trp (N, O)	C10H12N2O2	-	-	588.00	pH 5.0, T 293 K	[92]
	ATP (N, O)	C6H7NS	-	-	99.17	pH 6.0, T 298 K	[93]
	APTES (N, M)	C9H23NSiO3	-	-	103.28	pH 6.0, T 298 K	[93]
	EDTA (N, O)	C10H14N2O8	-	-	108.70	pH 5.0	[94]
Hg(II)	EDTA (N, O)	C10H14N2O8	-	-	268.40	T 318 Κ	[87]
	PPy (N)	C8H6N2	-	-	980.00	pH 3.0, Τ 293 Κ	[95]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	110.00	pH 3.5–4.0	[74]
	Co-NPs (M)	Co3O4	CS (N, O)	C6H11NO4	361.00	pH 7.0, T 323 K	[96]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	23.03	pH 6.0–7.0, T 293 K	[94]
Mn(II)	PAM (N, O)	C3H5NO	-	-	18.29	pH 4.0, T 298 K	[73]
Ni(II)	Gly (N, O)	C2H5NO2	-	-	36.63	pH 6.0, Τ 293 Κ	[50]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	22.07	pH 6.0–7.0, T 293 K	[94]
Pb(II)	EDTA (N, O)	C10H14N2O8	-	-	508.40	T 318 Κ	[87]
	EDTA (N, O)	C10H14N2O8	-	-	479.00	pH 6.8, Τ 298 Κ	[97]
	CS (N, O)	C6H11NO4	-	-	120.00	pH 6.0, T 298 K	[98]
	PAM (N, O)	C3H5NO	-	-	1000.00	pH 6.0, T 298 Κ	[99]
	CS (N, O)	C6H11NO4	-	-	99.00	Τ Room	[100]
	PVK (N)	C14H11N	-	-	887.98	pH 7.0, T 298 K	[101]
	APTES (N, O, M)	C9H23NSiO3	-	-	312.50	pH 4–5, T 303 K	[102]
	PAM (N, O)	C3H5NO	-	-	819.67	pH 6.0, T 293 K	[103]
	SA (O)	C6H9NaO7	-	-	267.40	pH 5.5, T 303 K	[90]
	CS (N, O)	C6H11NO4	-	-	216.92	pH 3.0, T 323 K	[36]
	PAAM (N, O)	C3H5NO	-	-	568.18	pH 4.5, T 298 K	[73]
	LS (O)	C20H24Na2O10S2	PANI (N)	C6H5N	216.40	pH 5.0, T 303 K	[104]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	197.00	pH 4.0–5.4	[74]
	OPhDA (N)	C6H8N2	PDA (N)	C7H9NO2	228.0		[105]
	PAM (N, O)	C3H5NO	-	-	819.67	pH 6.0, T 293 K	[103]
	L-Trp (N, O)	C10H12N2O2	-	-	222.00	pH 4.0, T 293 K	[92]
	Fe-NPs (M)	Fe3O4	L-Cys	C3H7NO2S	459.33	pH 6.0	[106]
	HPEI (N)	C2H5N	-	-	438.6	pH 5.5, T 298 K	[107]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	27.95	pH 6.0–7.0, T 293 K	[94]
	PDA (N)	C7H9NO2	-	-	365.00	T 298 K	[76]
	HPA (N)	C5H15N3	-	-	740.7	pH 5.9, T 298 K	[108]
	PDA (N)	C7H9NO2	-	-		pH 6.0	[77]
	EDTA (N, O)	C10H14N2O8	-	-	454.60	pH 3.0	[94]
Sr(II)	PAM (N, O)	C3H5NO	-	-	184.88	pH 8.5, T 303 K	[109]
U(VI)	Sep (M)	-	-	-	161.29	pH 5.0, T 298 K	[110]
	Fe-NPs (M)	Fe3O4	DETA (N)	C4H13N3	141.12	pH 6.0, T 298 K	[111]

q_max: Maximum adsorption capacity; (N): nitrogen-based compounds; (O): oxygen-based compounds; (M): metal-based compounds; T: temperature of adsorption test; *: for crosslinkers/covalent linkers that are polymeric, the chemical formula corresponds to the formula of the corresponding monomer.

Table 2. Maximum adsorption capacities of crosslinker and crosslinker-covalent linker-functionalised GO for removing heavy metal ions.

Heavy Metal Ion	Crosslinker (Classification)	Chemical Formula Crosslinker *	Covalent Linker (Classification)	Chemical Formula Covalent Linker *	qmax (mg g−1)	Operating Condition	Reference
As(V)	Fe-NPs (M)	Fe3O4	-	-	73.42	pH 7.0, T 298 K	[72]
Au(ΙΙΙ)	CS (N, O)	C6H11NO4	-	-	1076.65	pH 4.0, Τ 323 Κ	[36]
	PAM (N, O)	C3H5NO	-	-	253.81	pH 5.0, T 298 K	[73]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	106.00	pH 5.2–6.8	[74]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	27.83	pH 6.0–7.0, T 293 K	[75]
	PDA (N)	C7H9NO2	-	-	210.00	T 298 K	[76]
	PDA (N)	C7H9NO2	-	-		pH 6.0	[77]
Co(II)	PPhDA (N)	C6H8N2	-	-	116.35	pH 6.0, Τ 298 Κ	[78]
Cr(VI)	MgAl-LDH (M)	-	-	-	172.55	pH 2.0, 293 K	[79]
	Fe-NPs (M)	Fe3O4	CS (N, O)	C6H11NO4	162.00	pH 4.25, T 293 K	[80]
	TETA (N)	C6H18N4	-	-	219.50	pH 2.0, Τ 303 Κ	[81]
	PAAm (N)	C3H7N	-	-	485.00	pH 4.0, T 298 K	[82]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	17.29	pH 1.0–3.0, T 293 K	[75]
	CDx (O)	C42H70O35	CS (N)	C6H11NO4	67.66	T 298 K	[83]
	Fe-NPs (M)	Fe3O4	CS (N)	C6H11NO4	107.99	pH 2.0, T 303 K	[84]
	Fe-NPs (M)	Fe3O4	DACHTA (N)	C14H22N2O8	83.66	pH 3.0, T 303 K	[85]
Cu(II)	Fe-NPs (M)	Fe3O4	SAc (O)	C6H6NO3S	62.73	pH 5.0, T 298 K	[86]
	EDTA (N, O)	C10H14N2O8	-	-	301.20	T 318 Κ	[87]
	Ca2+ (M)	-	SA (O)	C6H9NaO7	60.20		[88]
	TETA (N)	C6H18N4	-	-	209.10	pH 6.0, T 293 K	[89]
	SA (O)	C6H9NaO7	-	-	98.00	pH 5.0, Τ 303 Κ	[90]
	PAM (N, O)	C3H5NO	-	-	68.68	pH 4.5, T 298 K	[73]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	87.00	pH 5.2–6.8	[74]
	PAAm (N)	C3H7N	-	-	349.04	pH 6.0, T 293 K	[91]
	L-Trp (N, O)	C10H12N2O2	-	-	588.00	pH 5.0, T 293 K	[92]
	ATP (N, O)	C6H7NS	-	-	99.17	pH 6.0, T 298 K	[93]
	APTES (N, M)	C9H23NSiO3	-	-	103.28	pH 6.0, T 298 K	[93]
	EDTA (N, O)	C10H14N2O8	-	-	108.70	pH 5.0	[94]
Hg(II)	EDTA (N, O)	C10H14N2O8	-	-	268.40	T 318 Κ	[87]
	PPy (N)	C8H6N2	-	-	980.00	pH 3.0, Τ 293 Κ	[95]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	110.00	pH 3.5–4.0	[74]
	Co-NPs (M)	Co3O4	CS (N, O)	C6H11NO4	361.00	pH 7.0, T 323 K	[96]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	23.03	pH 6.0–7.0, T 293 K	[94]
Mn(II)	PAM (N, O)	C3H5NO	-	-	18.29	pH 4.0, T 298 K	[73]
Ni(II)	Gly (N, O)	C2H5NO2	-	-	36.63	pH 6.0, Τ 293 Κ	[50]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	22.07	pH 6.0–7.0, T 293 K	[94]
Pb(II)	EDTA (N, O)	C10H14N2O8	-	-	508.40	T 318 Κ	[87]
	EDTA (N, O)	C10H14N2O8	-	-	479.00	pH 6.8, Τ 298 Κ	[97]
	CS (N, O)	C6H11NO4	-	-	120.00	pH 6.0, T 298 K	[98]
	PAM (N, O)	C3H5NO	-	-	1000.00	pH 6.0, T 298 Κ	[99]
	CS (N, O)	C6H11NO4	-	-	99.00	Τ Room	[100]
	PVK (N)	C14H11N	-	-	887.98	pH 7.0, T 298 K	[101]
	APTES (N, O, M)	C9H23NSiO3	-	-	312.50	pH 4–5, T 303 K	[102]
	PAM (N, O)	C3H5NO	-	-	819.67	pH 6.0, T 293 K	[103]
	SA (O)	C6H9NaO7	-	-	267.40	pH 5.5, T 303 K	[90]
	CS (N, O)	C6H11NO4	-	-	216.92	pH 3.0, T 323 K	[36]
	PAAM (N, O)	C3H5NO	-	-	568.18	pH 4.5, T 298 K	[73]
	LS (O)	C20H24Na2O10S2	PANI (N)	C6H5N	216.40	pH 5.0, T 303 K	[104]
	PEI (N)	C2H5N	PDA (N)	C7H9NO2	197.00	pH 4.0–5.4	[74]
	OPhDA (N)	C6H8N2	PDA (N)	C7H9NO2	228.0		[105]
	PAM (N, O)	C3H5NO	-	-	819.67	pH 6.0, T 293 K	[103]
	L-Trp (N, O)	C10H12N2O2	-	-	222.00	pH 4.0, T 293 K	[92]
	Fe-NPs (M)	Fe3O4	L-Cys	C3H7NO2S	459.33	pH 6.0	[106]
	HPEI (N)	C2H5N	-	-	438.6	pH 5.5, T 298 K	[107]
	Fe-NPs (M)	Fe3O4	EDA (N)	C2H8N2	27.95	pH 6.0–7.0, T 293 K	[94]
	PDA (N)	C7H9NO2	-	-	365.00	T 298 K	[76]
	HPA (N)	C5H15N3	-	-	740.7	pH 5.9, T 298 K	[108]
	PDA (N)	C7H9NO2	-	-		pH 6.0	[77]
	EDTA (N, O)	C10H14N2O8	-	-	454.60	pH 3.0	[94]
Sr(II)	PAM (N, O)	C3H5NO	-	-	184.88	pH 8.5, T 303 K	[109]
U(VI)	Sep (M)	-	-	-	161.29	pH 5.0, T 298 K	[110]
	Fe-NPs (M)	Fe3O4	DETA (N)	C4H13N3	141.12	pH 6.0, T 298 K	[111]

q_max: Maximum adsorption capacity; (N): nitrogen-based compounds; (O): oxygen-based compounds; (M): metal-based compounds; T: temperature of adsorption test; *: for crosslinkers/covalent linkers that are polymeric, the chemical formula corresponds to the formula of the corresponding monomer.

The results presented in Table 2 can be analysed in terms of the influence of electrostatic forces (also known as Coulombic forces) on the adsorption process of oppositely charged pollutants onto the binding sites [112]. The adsorbent surface enriched with active functional groups contains electron donor elements, acting as adsorptive sites for metal binding [27,113] through chemical interaction (ion exchange, surface complexation and Lewis’s acid-base interactions) [112]. Indeed, the use of adsorbents possessing nitrogenous and oxygenated groups (e.g., –NH₂, –OH, –COOH, –CONH₂) allows coordination or chemical bonding with heavy metal cations due to the vacant 3d orbital [114,115]. For example, the incorporation of polyethyleneimine (PEI) as a crosslinker into the GO matrix increased the sorption capacity by interacting with As(III) and As(V) through complexation and electrostatic interactions [116], where PEI showed that up to 70% of the polymer links take part in complex formation [117]. However, pH values under 7.8 promote the protonation of –NH₂ (–NH₃⁺) and –OH (–OH₂⁺) functional groups, then attract anions and repel cations [118]. Moreover, the high concentrations of H⁺ and H₃O⁺ in solution would compete with HMI to attach to the available binding sites of GO-based nanomaterials, finally reducing the adsorption of metal ions at low pH [119]. The cationic-π binding mechanism involves the non-covalent interaction between a positively charged pollutant and the negatively charged electron cloud of the π system in GO-based sorbents [120].

In the case of GO modified by a metal-based crosslinker, HMI can be adsorbed by forming surface complexes with one, two or multiple binding points [121]. For example, the adsorption of As(V) for GO modified with gadolinium oxide (Gd₂O₃) is mainly due to the electrostatic attraction of carbonyl groups with gadolinium oxide and the electrons of the π–π bounds [122,123]. It has been reported that the adsorption capacity is increased by having oxygenated groups along the surface, and this benefits the porous structure and superparamagnetic properties [124]. Figure 2 summarises the HMI adsorption mechanisms with GO materials functionalised with nitrogen, oxygen and metal compounds, where M^x+ represents a heavy metal cation and MO_x^y− represents a heavy metal anion.

Concerning the chemical structure of crosslinker/covalent linker, the number of binding sites could be considered. For instance, the nitrogen groups have one bonding point (one non-bonding electron pair), the oxygen groups have two bonding points (two non-bonding electron pairs), and the benzene rings of the GO/crosslinker/covalent linker have one bonding point (cation–π interaction). Then, the structure of the functionalised GO can be related to the maximum adsorption capacity of this material. Figure 3 presents the relationship between GO-crosslinker/covalent linker bonding points and the maximum adsorption capacity from the data in Table 2.

At first glance, adding the covalent linker decreases the adsorption of HMI despite the higher number of bonding points. Excessive cross-linking not only disrupts and blocks water transport within the GO nanochannels [23], but it can also decrease the adsorption capacity of HMI due to the disruption of binding sites caused by the covalent linker in the GO-cross-linking structure [125]. In addition, the molecular structure of GO-crosslinker-covalent linker adsorbent is generally large and unstable, which leads to structural damage in the adsorption process [126].

4. Separation of Heavy Metal Ion Performance by Modified Graphene Oxide Functionalised Membranes

In membrane separation processes, rejection refers to the ability of a membrane to block specific solutes from passing through, allowing only solvent permeation. Essentially, the percentage of the solute prevented passage through the membrane. Conversely, flux is the permeate flow rate through the membrane per unit area. These two parameters are essential in understanding the efficiency and effectiveness of the membrane separation processes.

Table 3. Performance and operating conditions of crosslinker and crosslinker-covalent linker-functionalised GO membranes for removing heavy metal ions.

Heavy Metal Ion	Crosslinker (Classification)	Covalent Linker (Classification)	Rejection (%)	Operating Condition	Reference
As(III)	TETA (N)	CuFe2O4 (M)	81.2%	4.0 bar	[127]
	QT (O)	-	67.0%	1.0 bar	[128]
As(V)	TETA (N)	CuFe2O4 (M)	87.9%	4.0 bar	[127]
	H2SO4 (O)	-	79.0%	2.0 bar	[129]
Cd(II)	QT (O)	-	75.0%	1.0 bar	[128]
	IPDI (N)	-	52.8%	1.0 bar	[130]
	PMMA (O)	-	68.0%	5.0 bar	[131]
	EDA (N)	PEI (N)	90.5%	1.0 bar	[132]
	CR (N, O)	Ca2+ (M)	99.5%	5.0 bar	[133]
Cr(II)	POSS (M)	PERI (N)	80.0%	4.5 bar	[134]
	IPDI (N)	-	71.1%	1.0 bar	[130]
Cr(VI)	QT (O)	-	70.0%	1.0 bar	[128]
	H2SO4 (O)	-	37.5%	2.0 bar	[129]
	EDA (N)	-	100.0%	21.0 bar	[135]
Cu(II)	MeF (N)	Fe3O4 (M)	92.0%	4.0 bar	[136]
	POSS (M)	PERI (N)	55.0%	4.5 bar	[134]
	IPDI (N)	-	46.2%	1.0 bar	[130]
	UR (N, O)	-	81.0%	1.0 bar	[137]
	EDA (N)	-	59.0%	1.0 bar	[137]
	PMMA (O)	-	58.0%	5.0 bar	[131]
	K+ (M)	-	97.5%	1.0 bar	[138]
	Ba2+ (M)	-	96.4%	1.0 bar
	Ca2+ (M)	-	96.2%	1.0 bar
	Mg2+ (M)	-	95.7%	1.0 bar
	CR (N, O)	Ca2+ (M)	99.0%	5.0 bar	[133]
Ni(II)	PMMA (O)	-	73.0%	5.0 bar	[131]
	EDA (N)	PEI (N)	96.0%	1.0 bar	[132]
	K+ (M)	-	94.3%	1.0 bar	[138]
	Ba2+ (M)	-	93.4%	1.0 bar
	Ca2+ (M)	-	93.3%	1.0 bar
	Mg2+ (M)	-	92.4%	1.0 bar
	CR (N, O)	Ca2+ (M)	98.0%	5.0 bar	[133]
Pb(II)	QT (O)	-	74.0%	1.0 bar	[128]
	POSS (M)	PERI (N)	78.0%	4.5 bar	[134]
	IPDI (N)	-	66.4%	1.0 bar	[130]
	EDA (N)	PEI (N)	95.7%	1.0 bar	[132]
	K+ (M)	-	92.2%	1.0 bar	[138]
	Ba2+ (M)	-	91.9%	1.0 bar
	Ca2+ (M)	-	92.5%	1.0 bar
	Mg2+ (M)	-	91.2%	1.0 bar
	CR (N, O)	Ca2+ (M)	98.0%	5.0 bar	[133]
Zn(II)	PMMA (O)	-	79.0%	5.0 bar	[131]
	EDA (N)	PEI (N)	97.4%	1.0 bar	[132]

(N): nitrogen-based compounds; (O): oxygen-based compounds; (M): metal-based compounds.

presents the HMI rejection of GO membranes modified by different crosslinkers/covalent linkers.

In general, nitrogenous and oxygenated crosslinkers have been the most widely used for HMI nanofiltration processes because covalent crosslinking between nitrogen-containing (–NH₂) or oxygen-containing functional groups (–OH, –COOH, –COC–) with GO [139], is stronger than the non-covalent crosslinking (Van der Waals forces, hydrophobic interaction, π–π interactions, electrostatic and hydrogen bonding) of the metal-based crosslinker and GO [23].

Enhancing the hydrophilicity of hydrophobic surfaces has been widely regarded as an effective strategy for improving water permeability [140]. The non-oxidized GO surface and the hydrophilic functional groups of GO induce water molecules to cross the membrane to increase their transfer rate [141,142], such as a “sliding effect”, which is detrimental when treating hydrated ions. Water molecules are generally viewed as vehicles for ion transport in an aqueous environment, which can form a shell around ions with the help of hydrogen bonds [143]. This may result in an increase in ionic flow, which would be controlled by pore size and the transmembrane pressure [144]. On the other hand, Donnan exclusion involves a local equilibrium in the membrane, which results in the exclusion of almost all co-ions at the membrane entrance while counter-ions are absorbed and transported [145]. In the case of HMI, electrostatic attraction between the nanocomposites and cations will occur, while electrostatic repulsion will occur with anions [118]. For example, the introduction of –NH₃⁺ groups makes the GO membrane impermeable to Fe²⁺ successfully [143]. This phenomenon can be explained due to the protonation of amine and carboxylic groups of GO functionalised by an N-based crosslinker, which confers to the membrane a positive charge [146].

Figure 4a depicts the box plots for the data presented in Table 3. In the case of HMI rejection, incorporating the covalent linker leads to increased metal ion removal compared to GO-crosslinker-only membranes due to the precise control of interlayer spacing [147,148]. For this reason, the rejection of GO-crosslinker-covalent linker membranes is higher than that of GO-crosslinker membranes.

The following question arises from the previous section: can the performance of functionalised GO membranes be related to the adsorption of metal contaminants? Figure 4b presents the relationship between the maximum adsorption capacity of GO-crosslinker/covalent linker and the rejection of HMI with these membranes. Membranes with GO-crosslinker-covalent linkers show a lower adsorption capacity, but higher HMI rejection than functionalised GO with a crosslinker. However, there is a need to study what happens in pollutant removal processes with functionalised GO membranes.

5. Phenomenological Aspects of the Membrane Separation Process

Several principal equations are commonly used to describe and analyse the phenomena involved in membrane separation processes. Equation (1) describes the three transport mechanisms involved simultaneously in the nanofiltration process for ionic solutes: diffusion, convection, and electro-migration [149]. All equations use S.I. units.

$$J_i=-D_{i,p}\cdot \nabla c_i+K_{i,c}\cdot c_i\cdot J_p-{\displaystyle \frac{z_i\cdot F}{R\cdot T}}\cdot D_{i,p}\cdot c_i\cdot \nabla \psi$$

(1)

where $J_i$ is the flux per unit area of ion $i$, $D_{i,p}$ is the diffusivity of species $i$ within the membrane pore, $c_i$ is the concentration of species $i$ in the pore, $z_i$ is the valence of species $i$, $R$ is the universal gas constant, $T$ is the absolute temperature, $F$ is Faraday’s constant, $\mathsf{\psi }$ is the Donnan potential of the membrane, $K_{i,c}$ is the hindrance factor for the convective term and $J_p$ is the permeate flow rate. To determinate $D_{i,p}$, this can be calculated by Equation (2).

$$D_{i,p}=K_{i,d}\cdot D_{i,\mathrm{\infty }}$$

(2)

where $D_{i,\mathrm{\infty }}$ is the diffusivity of species $i$ in the bulk solvent, $K_{i,d}$ is the hindrance factor for the diffusive term. The hindrance factors $K_{i,d}$ and $K_{i,c}$ are functions of the ratio between the solute radius ($r_i$) and the membrane pore radius ($r_p$) (Equation (3)).

$$\lambda ={\displaystyle \frac{r_i}{r_p}}$$

(3)

Equations (4) and (5) allow for the determining of hindrance factors for $0<\mathsf{\lambda }<0.8$.

$$K_{i,d}=1.0-2.30\cdot \lambda +1.154\cdot {\lambda }^2+0.224\cdot {\lambda }^3$$

(4)

$$K_{i,c}=\left(2-\Phi \right)\cdot \left(1.0+0.054\cdot \lambda -0.998\cdot {\lambda }^2+0.441{\lambda }^3\right)$$

(5)

where $\Phi$ is the steric partition coefficient, representing the likelihood of a solute, smaller than the pore, successfully entering the pore (Equation (6)).

$$\Phi =\left\{\begin{array}{cc}{\left(1-\lambda \right)}^2,& r_i<r_p\\ 0,& r_i\ge r_p\end{array}\right.$$

(6)

Regarding the electroneutrality principle and electrostatic interaction between solutes and membrane pores, the Poisson–Nernst–Planck (PNP) equation determines the change in ion concentration over time (Equation (7)) [150]. This equation could be used to predict the content of metal ions in both the membrane structure and the permeate by a mass balance.

$${\displaystyle \frac{\partial c_i}{\partial t}}+\nabla \cdot J_i=0$$

(7)

Replacing Equation (1) in Equation (7), we obtain Equation (8).

$${\displaystyle \frac{\partial c_i}{\partial t}}=D_{i,p}\cdot {\nabla }^2{c}_i+K_{i,c}\cdot \left(c_i\cdot \nabla J_p+\nabla c_i\cdot J_p\right)-{\displaystyle \frac{z_i\cdot F}{R\cdot T}}\cdot D_{i,p}\cdot \left(\nabla c_i\cdot \nabla \psi +c_i\cdot {\nabla }^2\psi \right)$$

(8)

Regarding Donnan potential, if the electric potential gradient is uniform for all ions within the membrane, this gradient results in Equation (9) [149]:

$$\nabla \psi ={\displaystyle \frac{{\sum }_{i=1}^n\left(\frac{z_i\cdot J_v}{D_{i,p}}\cdot \left(K_{i,c}\cdot c_i-C_{i,p}\right)\right)}{\frac{F}{RT}\cdot {\sum }_{i=1}n\left(z_i^2\cdot c_i\right)}}$$

(9)

where $C_{i,p}$ is the concentration of the species $i$ in the permeate. Considering that Donnan potential is usually very low ($\nabla \psi \approx 0$), the system is an incompressible fluid ($\nabla J_p=0$), and ${\nabla }^2\psi$ can be calculated by Equation (10), and Equation (8) is reduced to Equation (11).

$${\nabla }^2\psi =-{\displaystyle \frac{{\rho }_e}{\epsilon }}$$

(10)

$${\displaystyle \frac{\partial c_i}{\partial t}}=D_{i,p}\cdot {\nabla }^2{c}_i-K_{i,c}\cdot J_p\cdot \nabla c_i+{\displaystyle \frac{z_i\cdot F}{R\cdot T}}\cdot D_{i,p}\cdot {\displaystyle \frac{{\rho }_e}{\epsilon }}\cdot c_i$$

(11)

where ${\rho }_e$ is the charge density, and $\epsilon$ is the permittivity of the membrane. The change in concentration in the permeate would be related to adsorption by means of the charge density. Zhang et al. [151] investigate the effect of layer charge density and cation concentration on the structures and dynamics of Pb²⁺, Ba²⁺ and Cs⁺ adsorbed in the interlayer and nanopore of montmorillonite. The results show that the higher the charge density, the higher the adsorption amount. Therefore, there is a direct relationship between metal adsorption and charge density [152], e.g., Kalaitzidou et al. [153] determined that the adsorption capacity of iron oxy-hydroxides (FeOOH) for Se(IV) is strongly related to positive surface charge density when the metal is as SeO₃²⁻ and increases when synthesis pH is lowered (more positive surface charge density).

On the other hand, Osorio et al. [154] proposed a model to determinate the relationship between membrane charge density and cation concentration, where the membrane charge density is defined as a function of the local concentration of divalent cations (Equation (12)).

$${\rho }_e={\rho }_{e,0}\cdot {\displaystyle \frac{1-K_b\cdot c_i}{1+K_b\cdot c_i}}$$

(12)

where $c_i—$concentration of divalent cation, $K_b$—the membrane-cation binding constant and ${\rho }_{e,0}$—the bare membrane charge density (the charge in the absence of cations in solution). Additionally, Li et al. [155] demonstrated by means of molecular dynamics simulations that the higher the surface charge density, the greater the passage of metal ions in graphene membranes. This provides a direct relationship between the surface charge density and the permeate of metal ions, which is described by Equation (11).

Another model for determining the surface charge density is by correlating the bulk ion concentration with the membrane surface charge density through the Freundlich-type isotherm. This model is acceptable at low electrolyte concentrations, but for real-life brackish or saline water, the bulk concentration is quite high [156]. Finally, the zeta potential can be used to measure the membrane charge density. Then, the charge density can then be incorporated into a model based on the Teorell–Meyer–Sievers theory to calculate the rejection of nanofiltration membranes under the assumption of constant membrane potential [157].

In summary, the phenomenological analysis shows that an increase in surface charge density leads to increased adsorption and flux of metal ions in functionalised GO membrane systems, thus reducing the membrane selectivity. This concurs with the experimental data collected and displayed in Figure 3. However, there are no studies in the literature that relate the characteristics of the functionalising compound (crosslinker and covalent linker) to the surface charge density and, consequently, to the adsorption and permeation of heavy metal ions. Under this logic, it is recommended to study the effects that crosslinkers or covalent linkers would have considering Equations (1)–(12). In addition, it is known that membrane desorption and regeneration cause secondary pollution [158] and the decrease in adsorption performance due to the loss of adsorbent material during multiple cycles [159], the dissolution of adsorbent in the treated flow [160] or the loss of functional groups [161]. So, it is necessary to study the enhanced reuse of functionalized GO membranes and the final disposal of the waste generated.

6. Conclusions

Membrane separation includes the linked phenomenon of adsorption and filtration; this fact is confirmed after an analysis of published results with modified graphene oxide-functionalised inorganic membrane. In this material separation, performance depends on the hydrophobic interactions of the membrane and the solute [162].

The underlying mechanism that governs the interaction between graphene oxide membrane and heavy metal ions is directly linked with the adsorption phenomena through different mechanisms, including both ionic and coordinative interaction and metal complexation with oxygenate functional groups. These interactions are affected by the chemical modification arising from the functionalization procedures.

The nature of the crosslinker directly affects the performance of functionalised GO membranes, where the adsorption of heavy metal ions is determined by the attachment points of the crosslinker.

Adsorption of heavy metal ions changes the charge density of the membrane, leading to an increase in ions in the permeate. Depending on the material, the change in charge density will be different.

Further research effort is still necessary to obtain a complete description of the relationship between nanofiltration and HMI adsorption performance when using inorganic GO-functionalised membranes that have been modified with different crosslinkers to offer a predictive tool for designing new materials.

This predictive tool must support the development of many relevant areas which need more research for massive industrial applications of the inorganic functionalised membrane technology, such as improved life cycle and recyclability, scalable commercial manufacturing and the real-scale demonstration of the energetic benefits in comparison of dense polymeric membranes.