Molecular Structure and Conformation of Biodegradable Water-Soluble Polymers Control Adsorption and Transport in Model Soil Mineral Systems

Water-soluble polymers (WSPs) are used in diverse applications, including agricultural formulations, that can result in the release of WSPs to soils. WSP biodegradability in soils is desirable to prevent long-term accumulation and potential associated adverse effects. In this work, we assessed adsorption of five candidate biodegradable WSPs with varying chemistry, charge, and polarity characteristics (i.e., dextran, diethylaminoethyl dextran, carboxymethyl dextran, polyethylene glycol monomethyl ether, and poly-l-lysine) and of one nonbiodegradable WSP (poly(acrylic acid)) to sand and iron oxide-coated sand particles that represent important soil minerals. Combined adsorption studies using solution-depletion measurements, direct surface adsorption techniques, and column transport experiments over varying solution pH and ionic strengths revealed electrostatics dominating interactions of charged WSPs with the sorbents as well as WSP conformations and packing densities in the adsorbed states. Hydrogen bonding controls adsorption of noncharged WSPs. Under transport in columns, WSP adsorption exhibited fast and slow kinetic adsorption regimes with time scales of minutes to hours. Slow adsorption kinetics in soil may lead to enhanced transport but also shorter lifetimes of biodegradable WSPs, assuming more rapid biodegradation when dissolved than adsorbed. This work establishes a basis for understanding the coupled adsorption and biodegradation dynamics of biodegradable WSPs in agricultural soils.


Section S1. Chemicals
Information on the purities and the suppliers of chemicals used are provided in Table S1.Table S1.Overview of chemicals used, their purities and suppliers.

Section S2. Polymers
The properties of polymers used are listed in Table S2.
Table S2.Overview of polymers used in this study and their physicochemical properties.

Section S3. Sorbents
Iron oxide-coated sand (IOCS).The sand (Sigma Aldrich, Switzerland, acid-washed and calcined, ≥ 99.7%) was coated with iron oxide using a method established by Mills et al. 4 .The first step involved cleaning the sand.In brief, we reacted 100 g of sand with 90 mL of a 10% nitric acid solution for 2 hours in an Erlenmeyer flask placed on an orbital rotary shaker (250 rpm).We subsequently decanted the supernatant and rinsed the sand with MQ water until the liquid was transparent.Next, the MilliQ water was decanted from the flask, and 90 mL of a 0.5 M NaOH solution was added to the sand, followed by shaking the sand on an orbital rotary shaker (250 rpm) for another 2 hours.We thoroughly rinsed the sand with MilliQ water and air-dried the sand overnight at 90°C.
We transferred 150 g of the cleaned sand (as described above) to a Nalgene bottle containing 300 mL of a 1 M FeCl3 * 6 H2O solution.The Nalgene bottle was then placed in a heating block and maintained at a constant temperature of 30°C.The suspension was stirred continuously using an overhead stirrer (uniSTIRRER OH2, LLG Labware, Germany).We adjusted the pH of the suspension from pH 1.2 to pH 5.5 by using a 2. MilliQ water until the filtrate was clear.We dried the IOCS in an oven at 60°C for at least 24 hours before mixing and homogenizing the IOCS from various coating batches to be used in column transport experiments.Using 1,10-phenanthroline hydrochloride monohydrate as a complexing agent, we colorimetrically measured the total iron concentrations on the surfaces of IOCS. 5 Absorbance was measured at a wavelength of 510 nm using a microplate absorbance reader (Infinite M Nano, Tecan, Switzerland).
The pH-dependent surface charge and the point of zero charge of the sand and IOCS were determined using a computer-controlled potentiometric acid-base titration system 6 from pH 4 to pH 10 and at two ionic strengths of IS = 0.01 M and 0.1 M NaCl, as shown in Figure S2.monitoring the resulting mass-dependent changes in the resonance frequencies of piezoelectric quartz oscillators that are integrated into these sensors.We used a peristaltic pump to deliver polymer solutions (5 μg mL -1 ) and buffer solutions at a constant volumetric flow rate of 20 μL min -1 at room temperature to the sensor cells.To obtain stable baseline readings, the sensors were equilibrated to polymer-free buffer solution for four to six hours under continuous flow.) We subsequently delivered polymer-containing solutions to the cells for 60 minutes, followed  polymer solution to the cell for at least five minutes to ensure that stable final readings were obtained also when re-delivering polymer to the cell.Afterwards, the flow cells were rinsed continuously with polymer-free buffer solution for 5 minutes to assess adsorption reversibility.
The results the OWLS experiments for DEX-DEAE and PLL are shown in Figure S4.

Section S6. Column breakthrough experiments
A detailed scheme of the column setup is depicted in Figure S5.Borosilicate glass columns (Omnifit GmbH, Germany, inner diameter and length of 0.66 cm and 7.0 cm, respectively) were wet-packed with sorbents (i.e., sand or IOCS) in buffer solution (N,N-diethyl piperazine (3 mM for pH 5 and 9 and 3-(N-morpholino)propane sulfonic acid (3 mM) for pH 7) calculating a pore volume (PV) of 1.2 ± 0.05 mL (corresponding to a porosity of approx.0.5 ± 0.02).We equipped the column end pieces with regenerated cellulose filter papers to retain potentially

Section S7. Adsorption and Transport Model
We modeled all breakthrough curves using Aquasim (2.1g software package) 8 .We divided the one-dimensional compartment into 190 nodes with uniform node spacing, using the 'advectivediffusive reactor compartment' option.We linked the outflow to a small-volume (0.001 mL) "mixed-reactor compartment" in order to generate flux-averaged 5 concentrations in the column outflow.Aquasim estimates the model parameters of equation 5 and equation 6 in the manuscript by minimizing the sum of squares of the weighted deviations  " ( # ) between calculated model and measured breakthrough curve: with pi = (kads,1, kads,2, S1,max, S2,max) and where yBTC,k is the value of the l th datapoint of the breakthrough curve,  !"#$,& is the standard deviation estimated by the program and yk(pi) is the calculated value of the model parameter pi for the l th data point of the measurement, and n is the number of data points.We modeled the nitrate breakthrough setting   We used two models to estimate the maximum polymer adsorption capacities on the sorbent surface.Both models assume that adsorption stopped when a monolayer of polymers had covered the surface (i.e., assuming no adsorption of additional polymers on those adsorbed onto the sorbent).In both models, we assume that the polymers behave like hard spheres with a fixed radius Rh.

Hexagonal close packing (HCP).
Assuming 2D hexagonal close packing of polymer 'spheres', a total area of a hexagon of 6√3  , -corresponding to the total footprint of three

Random sequential adsorption (RSA).
Within the RSA model, we assume random and irreversible adsorption of the polymer 'spheres' onto the surface.the model that does not permit direct contact between polymers or allow for surface diffusion.Computer simulations of RSA predict a maximum occupied area of 54.6 % (jamming limit  4(5 , Figure S12b). 10e results of the calculations using equation 7 for the monolayer adsorbed surface concentrations of the HCP model  132,!#7 (ng cm -2 ) and the RSA model  89:,!#7 (ng cm -2 ), respectively, the used hydrodynamic radii of the polymers Rh (nm), and the molecular weights of the polymers Mw (g mol -1 ) are summarized in Table S3.

3 a
Figure S1.(a) Acid-base titration data for diethyl aminoethyldextran-FITC (DEX-DEAE) and (b) schematic chemical structure of two types of ionizable DEAE groups.

5 M
NaOH solution, pK a = 5.5 pK a = 9.2 Volume of NaOH (mL) leading to the precipitation of Fe(III) oxyhydroxide on the sand surface.The suspension was aged under vigorous stirring at this pH and temperature for over 55 hours.The iron oxidecoated sand (IOCS) was then washed thoroughly with MilliQ water until the supernatant was clear, and then transferred to a filter paper (Macherey-Nagel MN615) and washed again with

Figure S2 .
Figure S2.Acid-base titration of (a) sand and (b) the iron oxide-coated sand (IOCS) in ionic strengths of IS= 0.01 M and 0.1 M, set by NaCl as background electrolyte.
by rinsing the sensors by delivering polymer-free solutions for 30 min.The results of the QCM-D experiments for PLL are shown in Figure S3, while the results for DEX-DEAE are shown in Figure 1 in the manuscript.

Figure S3 . 2 ,
Figure S3.Changes in adsorbed surface concentration of poly-L-lysine (PLL) on SiO2 sensors in the Quartz Crystal Microbalance with Dissipitation monitoring (QCM-D) over time at (a) different solution pH (ionic strength IS = 10 mM) and (b) ionic strengths (all at pH 7).

Figure S4 .
Figure S4.Changes in adsorbed surface concentrations of polymers on silica (SiO2) sensors over time determined by Optical Waveguide Lightmode Spectroscopy (OWLS) for (a, b) diethyl aminoethyl dextran (DEX-DEAE) at different pH values (ionic strength IS = 10 mM; panel a) and ionic strengths (pH 7; panel b) and for (c, d) poly-L-lysine (PLL) at different pH values (ionic strength IS = 10 mM; panel c) and ionic strengths (IS) (pH 7; panel d).

- 2 )
SiO 2 , PLL (c = 5 µg mL -1 ), IS = SiO 2 , PLL (c = 5 µg mL -1 ), SiO 2 , DEX-DEAE (c = 5 µg mL -1 ), pH 7 (b) Rinse Time t (min) Time t (min) Time t (min) Time t (min) S7 mobilized colloids in the columns.Solutions were delivered to the columns from 25 mL and 50 mL syringes at a constant volumetric flow rate of 0.2 mL min -1 using a syringe pump system (Cetoni GmbH, Germany).To calculate the flushed PVs during one breakthrough experiment, we multiplied the flow time by the flowrate and then divided the result by the volume of one PV.The concentrations of the inert tracer nitrate in the column effluent were continuously monitored by using UV absorption measurements (lads = 220 nm) in a spectrophotometric flow-through cell (UV Flow cell, 1/16"; Knauer, Germany) connected to a UV light source and a spectrophotometer (HL2000, Ocean Optics, USA) and by converting measured absorbance values to concentrations using nitrate calibration standards separately run through the flow cell.We determined (B)WSP concentrations in the column effluent by continuous fluorescence measurement using a fluorescence flow-through cell (SMA-FL, FIA Lab) that was fiber optically coupled to a LED light source (lex = 470 nm ± 30 nm, 17.2 mW, 1000 mA, ThorLabs, Germany) and a spectrophotometer (Maya 2000 Pro, Ocean Optics, USA).We transformed the fluorescence signal into polymer concentrations by calibrating with standards of known concentration, separately run through the flow cell, and observing a linear relationship between fluorescence signal and concentration.

Figure S8 .Figure S9 .
Figure S8.Breakthrough curves of (a) diethyl aminoethyl dextran (DEX-DEAE), (b) poly-Llysine (PLL), (c) carboxymethyl dextran (DEX-CM), (d) polyacrylic acid (PAA) and (e) dextran (DEX) in iron oxide-coated sand IOCS columns different pH values (ionic strength IS = 10 mM).We note that occasional sharp peaks in the fluorescence readings resulted from degassing of water and formation of small bubbles in the fluorescence flow cell which, however, were then transported out of the cells.
'((*)'* to zero in equation 5 in the manuscript, and thereby assumed nitrate.Thus, for nitrate, we minimized the sum of squares of the weighted deviations  " () only through variation of the hydrodynamic dispersion coefficient D. FiguresS10 and S11show the dependencies of modeled maximum adsorption capacities, Si,max and adsorption rate constants, kads,i, respectively, of the first (i=1) and second (i=2) kinetic adsorption regimes for polymers DEX-DEAE and PLL on sand.

Figure S10 .
Figure S10.Dependencies of modeled maximum adsorption capacities of (a) the first and (b) the second kinetic adsorption regimes and of adsorption rate constants for the (c) the first and (d) the second kinetic adsorption regime for diethyl aminoethyl dextran (DEX-DEAE) and poly-L-lysine (PLL) adsorption to sand at different pH values (ionic strength = 10 mM).Data points represent the mean values of duplicate experiments, and error bars are the absolute deviation of single measurements from the mean propagated with modeled standard deviations via Gaussian error propagation.

Figure S11 .
Figure S11.Dependencies of modeled maximum adsorption capacities of (a) the first and (b) the second kinetic adsorption regimes and of adsorption rate constants for the (c) the first and (d) the second kinetic adsorption regime for diethyl aminoethyl dextran (DEX-DEAE) and poly-L-lysine (PLL) adsorption to sand at ionic strengths (pH 7).Data points represent the mean values of duplicate experiments, and error bars are the absolute deviation of single measurements from the mean propagated with modeled standard deviations via Gaussian error propagation.

Figure S12 .
Figure S12.Schematic illustration of surface coverages for (a) hexagonal close packing and (b) random sequential adsorption of polymers as hard spheres (white circles) on a model surface area (blue areas).

Table S3 .
Summary of modeled monolayer adsorbed surface concentrations  !;<"=,!#7 , used molecular weights of the polymers Mw, and used hydrodynamic radii of the polymers Rh.The