2.2.3. Pretreatment of PEIs

Polydisperse substances such as (modified) PEIs show a broad molar mass distribution. Low molecular weight fractions have to be removed to ensure that the polymers are retained by the membrane in the subsequent PAUF experiments. Thus, the polymers were pretreated in an ultrafiltration step, to remove small polymer molecules that can pass the membrane. For this purpose, ultrafiltration membranes (MWCO = 10 kDa) were used and the permeate was led into a separate vessel. During precleaning, polymer concentration in permeate and feed was continuously determined by TOC measurement and the polymer retention was calculated according to Equation (1). The precleaning of the polymer was terminated after reaching a polymer retention of more than 98%.

### 2.2.4. Determination of Metal Retention Behavior of PEIs

Prior to their use in ultrafiltration experiments, the fly ash extracts were filtered using syringe filter holders. The feed solutions of the PAUF experiments consisted of diluted fly ash extract (1:2 in ultrapure water) from MVA Ingolstadt and KEBAG Zuchwil and a final concentration (7.9–10.0 g L<sup>−</sup>1) of HB-PEI, PE-PEI, or MOD-PEI. Control experiments without the addition of polymer were also carried out. The ultrafiltration experiments using membranes with a MWCO of 10 kDa were carried out in total recirculation mode, which means permeate and retentate flows were returned to the feed. At first, the pH value of the feed solutions was decreased to pH 0.7–1.0 by the addition of nitric acid (65%). Afterwards, the pH was successively increased up to 5.0–5.8 by the addition of sodium hydroxide solution (6*M*). Finally, to investigate the metal release from the PEIs, the pH was decreased to 1.0. The permeate and feed samples that were taken after each pH adjustment were analyzed by ICP-OES. Additionally, TOC measurements were carried out to control the polymer retention.

In addition, all feed samples were centrifuged for 10 min at 4427 *g* (Z 206A, Hermle, Wehingen, Germany) and the resulting supernatants were analyzed by ICP-OES.

### 2.2.5. Determination of Cu(II) Loading Capacity of PEIs

To investigate the maximum Cu(II) loading capacity of each PEI, further ultrafiltration experiments were carried out. The feed solutions consisted of fly ash extract from KEBAG Zuchwil and HB-PEI at a final concentration of 4.6 g L−1, PE-PEI at 4.7 g L−1, and MOD-PEI at 3.7 g L−1. Membranes with a MWCO of 5 kDa were used. During the whole experiment, the pH was kept constant at 4.0 (HB-PEI, MOD-PEI) or 4.3 (PE-PEI) and the ultrafiltration system was operated in total recirculation mode (see Section 2.2.4). After the pH was adjusted to 4.0 or 4.3, the Cu(II) concentration of the feed solutions was stepwise increased by adding a Cu(II) nitrate trihydrate solution (for analysis; Merck) diluted with ultrapure water. Finally, pH was adjusted to 1.0 by adding nitric acid (65%) to examine the Cu(II) release from the PEIs. Fifteen minutes after each Cu(II) addition and after adjusting the final pH to 1.0, samples of permeate and feed were taken and analyzed by ICP-OES and TOC.

### *2.3. Viscosity Determination of Aqueous Polymer Solutions*

The viscosity of aqueous solutions containing HB-PEI, PE-PEI, and MOD-PEI was determined using a DV-III+ rheometer (Brookfield, Middleboro, MA, USA) with cone/plate setup (CPE40). Temperature was controlled at 30 ◦C by a circulation thermostat (LAUDA RE204, Koenigshofen, Germany). In order to remove membrane-permeable size fractions of the polymers, pretreatment was performed according to Section 2.2.3.
