Appendix S1. Effect of operating parameters on chromium (VI) removal
S1.1 pH
The effect of pH on the removal of chromium (VI) from wastewater using cross flow nanofiltration was studied in the pH range of 5 – 12 at cross flow rate 700 L/h, transmembrane pressure 10 bars and temperature 30 o C. The NF1 membrane selected for carrying out the present investigation is stable up to pH 2, in accordance with the specifications provided by the manufacturer. However, in the present case, the NF membrane exhibited poor Cr (VI) rejection efficiency, mainly owing to the fact that the point of zero surface charge for NF1 membrane (isoelectric point) was found to be less than 3. As such, an increase in the electrostatic charge repulsion between the target anions and the negatively charged membrane surface was observed in response to the increase in solution pH. This behaviour can be attributed to the progressive increase in the negative surface charge of the membranes and the dominance of chromate anions bearing higher charge valency in the alkaline media, which had resulted in increased charged solute rejection due to Donnan exclusion [33]. The objective of the present study was to determine the optimal process conditions corresponding to maximum hexavalent chromium rejection. Hence, pH range of 5-
12 was selected for examination owing to the fact that the region was considered as the ideal or more concentrated region within the entire independent variable space, which enabled easier evaluation of the near-optimal process factor levels by RSM, by eliminating experimental trials under conditions which are considerably far from the corresponding near optimal levels, and at the same time indicated the variation in response following the transition from acidic to alkaline media.

The relation between the pH of the solution and the percentage removal of chromium (VI) is shown in Fig. S1(b) .
The effect on rejection with respect to pH alteration exhibited a consistent augmentation with increasing pH values.
Fig. S1
The rejection of chromium (VI) increased from 0.75 to 0.884 using NF1 membrane by increasing the pH from 5 to 12. Similar inclination towards removal of chromium (VI) using nanofiltration due to solution pH has been reported in the literature [38] . This behaviour may be explained on the basis of change in chromium (VI) species with the pH of the medium and change in membrane surface charge density [34]. Chromium (VI) exists in the aqueous solution in different ionic forms (HCrO
4
-
, CrO
4
2-
, Cr
2
O
7
2-
) depending on the chromium (VI) concentration and solution pH. Monovalent species HCrO
4
- is dominant at pH below 6.5 and as the pH is increased beyond 7 it gets converted into divalent species CrO
4
2 – and Cr
2
O
7
2-
.
Further, with high pH membrane surface potential changes which cause charge repulsion due to electrostatic interaction and hence the separation of ionic species based on Donnan effect becomes dominant in nanofiltration. The charged NF membrane normally allows the monovalent ions to pass through and reject more di and multivalent ions and thus enhances retention of chromium ion. This amplifying rejection of chromium (VI) from wastewater with regard to pH may also be attributed to the contraction or expansion of polyamide NF1 membrane pores due to existent or nonexistent repulsion between the dissociated functional groups of membrane polymer at different pH values of the feed [32].
S1.2 Cross flow rate

Cross flow rate is an important parameter in removal of heavy metals from wastewater since it has a significant contribution towards reduction of concentration polarization through sweeping action on the membrane surface and thus tumbles the fouling [33]. However, there is no study available showing the effect of cross flow rate on the removal of chromium (VI) from wastewater using cross flow nanofiltration. This effect has been illustrated in the present work by varying the cross flow rate in the range of 300 – 700 L/h at pH 7.5, transmembrane pressure 10 bar and temperature 30 o C. The relation between the cross flow rate of the solution and the percentage removal of chromium (VI) is shown in Fig. S1(c).
The effect on chromium (VI) retention with respect to cross flow rate variation demonstrated a regular escalation with increasing cross flow rate. The chromium (VI) rejection from wastewater feed using NF1 membrane increased by about 0.936 – 0.974 as the cross flow rate increased from
300 – 700 L/h. This tendency may be accredited to the decrease in concentration polarization with the increase of the cross flow rate. In cross flow membrane module, the feed solution flows parallel to/and over the membrane surface, and permeate is collected in a direction perpendicular to the membrane surface. The problem of fouling is overcome to a great extent because the retentate accumulated over the membrane is carried away by the continuously flowing feed solution. This problem can further be minimized by increasing the cross flow.
Increase in cross flow rate leads to greater convective force which in turn enhances solvent flux and the uncoupling effect between solute and solvent flux results in a corresponding increase in retention of solute [33].
S1.3 Transmembrane pressure
The effect of transmembrane pressure for the removal of chromium (VI) from wastewater using cross flow nanofiltration was studied in the range of 2 – 13 bar at a cross flow rate 700

L/h, pH 7.5 and temperature 30 o
C. The pH range originally selected for study was 5-12. An intermediate pH 7.5 was maintained in the present case, owing to the fact that the pH 7.5 was the unbuffered pH of the prepared aqueous samples. The objective was to study the effects of cross flow rate and transmembrane pressure on Cr (VI) separation without varying or modifying the pH. The relation between the transmembrane pressure of the solution and the percentage removal of chromium (VI) is shown in Fig. S1(d) .
The effect on rejection with respect to transmembrane pressure adjustment revealed a steady intensification with increasing applied pressure values. The rejection of chromium (VI) increased from 0.905 to
0.954 using NF1 membrane with decreasing the transmembrane pressure from 12.5 to 2.5.
Same nature of chromium (VI) rejection with transmembrane pressure was observed by
Babaee et al [18].
This behavior may be explicated on the basis of solution diffusion mechanism prevalent in nanofiltration where solute and solvent fluxes are uncoupled due to which increase of solvent flux with an increase of transmembrane pressure does not result in a proportionate increase of solute flux and a relative increase of solvent flux impedes the transport of solute though the membrane leading to greater solute retention [32-33]. The presence of chromium (VI) as several monovalent or divalent anionic forms in water results in an electrostatic repulsion when it interacts with negatively charged nanofiltration membrane surface and this results in retention or removal of chromium from wastewater feed. However, this trend was somewhat different from that for removal of chromium (VI) using nanofiltration [20]. They observed that the retention of chromium (VI) ions first increased with increase in pressure and then decreases as the pressure goes beyond 10 bar.
This difference in observation may be ascribed to the salt addition effect studied by them where they added varying amount of different salts to the K
2
Cr
2
O
7
solution. The plots in Fig.
S1, thus, mostly exhibit the main or linear effects of the process factors on the response, wherein the linear and quadratic effects of the process variables are excluded. The plots by no

means attempt to establish the fact that the quadratic and the interaction terms of the model are not significant, but rather graphically highlight the singular effects of the factors on response, thereby providing an overview of the correlation between the response and the process variables and that of the degree of variation witnessed in the response profile following a variation in a process factor level, while keeping the other parameters constant.
Figure
Figure S1 . (a) Pure water flux as a function of transmembrane pressure for NF1 membrane at temperature 30
o
C; (b) Influence of wastewater pH on chromium (VI) rejection; (c) Influence of cross flow rate on chromium (VI) rejection; (d) Influence of transmembrane pressure on chromium (VI) rejection.

Table
Table S1.
Experimental design and response matrix.
1
2
3
4
5
Run
6
7
8
9
10
1
1
11 -1
12 -1.682
13
14
0
0
X
1
-1
0
0
-1
0
0
0
-1
Coded values
X
2
-1
0
1.682
1
0
0
-1.682
1
1
1
-1
0
0
0
1
-1
1
0
1.682
0
X
3
-1
0
0
-1
0
0
0
1
15
16
1
0
17
18
19
1
0
0
20 1.682
-1
0
-1
0
0
0
1
0
-1
0
-1.682
0
X
1
Un-coded values
X
2
X
3
5
5
8
8
11
11
8
8
11
8
400
700
550
550
700
700
5 400
2.95 550
400
550
11
8
8
400
550
550
13.05 550
5
8 550 10
8 802.27 10
5
10
10
8 297.73 10
5 700 15
15
5
15
10
550 18.41
550 10
15
10
5
10
1.59
10
Response
(Rejection)
0.9278
0.9722
0.9795
0.9567
0.9729
0.9700
0.9489
0.9623
0.9957
0.9778
0.9487
0.9429
0.9803
0.9752
0.9921
0.9789
0.9513
0.9762
0.9556
0.9889