Characterization of the physical properties of the thermoresponsive block-copolymer PAGB2000 and numerical assessment of its potentialities in Forward Osmosis desalination

Forward Osmosis is a promising strategy for desalination processes, however some aspects have to be better characterized to make it competitive with other affirmed technologies. One of these aspects is the selection of the draw agent, i.e., a polymeric solution that has to fulfill different requirements to guarantee both high membrane performances and good regeneration process. Previous studies have identified a thermoresponsive copolymer known as PAGB2000 as potential draw agent. However, in the open literature there is no information on the thermo-physical properties required for a fully characterization of the polymer itself, hence, different experimental campaigns have been conducted to quantify: phase behavior, osmotic pressure, density, dynamic viscosity, thermal conductivity, thermal diffusivity and isobaric specific heat capacity. These properties were then used in a computational model to simulate the whole desalination process. Recovery ratio, specific electric consumption and specific thermal consumption were compared with the ones obtained in a previous work, showing that a detailed characterization of the thermo-physical properties is required to get accurate and realistic predictions of the system performance.


Introduction
Water is fundamental for humankind, however, at present, one-fifth of the global population is dealing with water scarcity [1].Additionally, one-fourth of the population lacks suitable means for water purification in spite of having access to water sources [1].This crisis is expected to worsen.According to the United Nations World Assessment Program (UNESCO, Paris 2015) about 40% of the population will experience water scarcity by 2030 [1].This is mainly linked to the fact that only the 3% of the overall water reserves is available as freshwater (i.e., glaciers, ice caps), with seawater representing the remaining percentage [2].Climate change and population growth are additional factors that threaten the future availability of freshwater [2].Even if the improvement and conservation of the existing water facilities are crucial, additional freshwater accessibility must be guaranteed to tackle the compelling water crisis [2].
In this prospective it is clear that desalination might play a primary role considering the large quantity of saline water on the Earth.In general terms, desalination is the purification process used to obtain The driving force of FO processes is the difference in the osmotic pressure that establishes between the feed solution to treat (i.e., seawater), showing the lower osmotic pressure, and the more concentrated draw solution (DS).In reason of this pressure difference, water diffuses across the membrane, from the less concentrated side, diluting the draw solute and balancing the concentration levels; whereas the solute or salt molecules in the feed solution are rejected [6].The obtained diluted DS has to be further treated to separate the water (now freshwater) from the DS (now re-concentrated), making the latter reusable for a new dilution.The aspect of not relying on the application of external hydraulic pressure along with the fact that both low membrane fouling and a greater water recovery are expected [7], justify the increasing interest for this new desalination technology.Up to now, researchers are mainly focused on studying two crucial aspects: membranes and draw solutes.

Nomenclature
Focusing on the draw solutions available, as reported by Long et al. in [8], they can be classified on the type of energy required to perform the regeneration and six categories are identified: (1) direct use, (2) chemical energy, (3) waste heat/thermal energy, (4) electric energy, (5) solar energy/irradiating, and (6) magnetic field energy.Among these types, the most interesting for this work, and for lowgrade heat applications in general, is represented by the thermally regenerative DSs, being a more cost-effective solution compared to the others [8].Currently, different kinds of DS, that are regenerated providing heat power, are reported in the open literature, to cite few: (1) gas and volatile compounds [9], (2) phase transition materials (such as lower/upper critical solution temperature (LCST [10]/UCST [11]) compounds and thermo-sensitive gels [12]), and (3) membrane distillations [13].In particular, phase transition materials exhibit unique phase behavior, characterized by a temperature-dependent miscibility with water.In Lower Critical Solution Temperature (LCST) mixtures the two liquid components are miscible below a certain temperature level, vice versa in upper critical solution temperature (UCST) mixtures the miscibility is achieved above a certain temperature level.
In a previous work by Colciaghi et al. [14], which stands on the works of Inada et al. [15,16], both an Ammonium Based (AB) and three different poly (propylene glycol-ran-ethylene glycol) monobutyl ethers (PAGBs), namely PAGB1000, PAGB2000 and PAGB4000, have been considered as draw agents.From the analysis conducted resulted that PAGB1000 and PAGB2000 have very similar consumption trends.PAGB1000 has lower electrical consumptions and higher water flux, but it is penalized in the regeneration step, as it has the higher regeneration temperature (  ) among the selected polymers (i.e., 77.2 • C for PAGB2000, 83.6 • C for PAGB1000 and 80.1 • C for PAGB4000,).Hence, PAGB2000 shows overall better performances compared with the other two polymers, and it was selected as draw agent.
However, from the literature analysis conducted, very few and sparse information can be found on PAGB2000 thermo-physical properties, which on the other hand are fundamental to understand both the feasibility and the function of a desalination power plant with FO technology.Hence, an extensive experimental campaign is conducted to fully characterize this polymer, to be efficiently used as draw agent in FO desalination power plant.

Materials and sample preparation
The selected thermoresponsive draw agent is a poly (propylene glycol-ran-ethylene glycol) monobutyl ether with molar mass of   ≃ 1810 Da (PAGB2000).This block copolymer has a chemical structure C 4 H 9 -[(C 2 H 4 0) 17 -(C 3 H 6 0) 17 ] ran -OH (see Fig. 1 for the structural formula), with a butyl ether group bonded to the amphiphilic part composed by an equal number of random copolymerized propylenoxyde and ethylenoxyde groups.It appears as a highly viscous and colorless liquid that is miscible with water at any ratio.
In our study, PAGB2000, known with the commercial name of UNILUBE 50MB-26, is purchased from NOF Corporation ® (Tokyo, Japan) and used without further purification.The aqueous samples employed for the characterization are prepared on an analytic scale (sensitivity 10 −4 g) by slowly dissolving the polymer in distilled water.After the dissolution, the samples are gently mixed by hand in order to ensure a perfect homogenization and kept in a refrigerator waiting for the complete removal of air bubbles that unavoidably show up while shaking the polymer solution.

Methods
In this section, we provide a description of the methods used to measure the physical properties of the PAGB2000 aqueous solutions.Unless otherwise stated, all quantities are determined in the temperature range 20-40 • C and in the whole concentration interval, ranging from distilled water to pure polymer.

Refractive index
The refractive index  of the polymer solutions is evaluated in order to determine the polymer content in the phase-separated samples and as auxiliary data for the optical methods.The refractive index is measured with a temperature-controlled Abbemat RXA digital refractometer (Anton Paar, Graz, Austria), with a sensitivity  ≃ 10 −5 .

Phase diagram
The phase separation points of the PAGB2000 solution are determined inserting the polymer solutions in a water thermostat (Haake F3, Thermo Fisher Scientific, Waltham (MA), United States, 0.1 • C sensitivity) with a window allowing for optical inspection.As a preliminary analysis, ten samples at different concentrations ranging from 0.01 to 0.8, are sealed in glass ampules and submerged in the thermal bath; the temperature is gradually raised from  = 20 • C until we observed the sample at  = 0.2 becoming turbid at  ≃ 40 • C, marking therefore the incipient phase separation, as shown in Fig. 2.Then, nine different samples at  = 0.2 are immersed in the water thermostat at  = 20 • C and the phase separation is studied for each sample at a different temperature level from 43 • C to 80 • C. Once each temperature level is reached, the system thermalizes for at least half an hour in order to complete the separation in the polymer-rich and polymer-poor phases.When the transition is over, the diluted and concentrated phases are collected and stored separately at room temperature.The refractive indexes of the two phase-separated samples are then measured at  = 20 • C and their concentration is retrieved from the calibration curve obtained at the same temperature (see Fig. 3(b)).

Osmotic pressure
The osmotic pressure of the polymer solution is evaluated with Static Light Scattering (SLS), an optical technique in which the laser light scattered by a fluid sample is collected at a given angle by a quadratic detector, allowing us to assess microscopic structural information of the sample at a lenghtscale comparable to the probing wavelength.
In general, a macro-molecular fluid can be described as a continuum in which the presence of molecules causes refractive index fluctuations which, in turns, are responsible for the elastic spreading of the incident radiation.These variations are related to concentration fluctuations, from which the osmotic compressibility and then the osmotic pressure can be retrieved.Consider an incident laser beam with wavelength  and a detector placed at an angle  which reveals the scattered intensity from a sample with refractive index .Assuming an isotropic medium with point-like scatterers (the molecules in solution), thus working in the so-called Rayleigh regime, it can be shown [17] that the scattered intensity   () at a given wave vector  = 4(sin ∕2)∕ is proportional to the averaged-squared refractive index fluctuations ) . Fluctuations can be associated to local variations of polymer concentration (), therefore we can write: where c is the macroscopic concentration and ( c) = .Thus, we obtain: As, in our case, the wavelength is always much larger than the average distance between the scatterers, we always look at the laser intensity   scattered at  = 0, whatever is the detection angle.The concentration fluctuations at  = 0 (thus associated to the whole sample) are related to osmotic compressibility   = (1∕)(∕) −1 by the fluctuation-dissipation theorem, a general result relating spontaneous fluctuations of a given quantity to the response functions of a system [18].Quantitatively, we can write: ⟨|(0)| 2 ⟩ = (    2 ∕ )  , where   is the Boltzmann constant,  is the absolute temperature and  is the sample volume.As a whole, the scattered intensity is then proportional to the osmotic compressibility as: where  is an instrumental constant.The refractive index increment ∕ of the solution with respect to the solvent can be evaluated independently from  measurements of the solution at different polymer concentration.Thus, from the measured scattered intensity   , the osmotic compressibility is retrieved exploiting Eq. ( 3).Eventually, since the measurements of   are performed as a function of the polymer concentration , from the numerical integration of   (), we get the osmotic pressure.
The measurements are performed with a custom-made light scattering setup, equipped with a 70 mW doubled Nd-YAG laser (wavelength  = 532 nm), a photomultiplier mounted on a rotating arm and a temperature-controlled sample holder, which allows for careful filtration of the samples with 0.2 μm nylon membrane syringe filters (Pall ® , Port Washington (NY), United States), without opening the cuvette lid.All measurements are made at a scattering angle of  = 90 • , corresponding to  ≃ 22 μm −1 and the relative uncertainty on the intensity is at most ∕ ≃ 5%.In this case, the maximum analyzed concentration is  = 0.8.Absolute calibration of the scattering signal to get the instrumental constant  is made with a reference aqueous micellar solution of Triton X-100, a non-ionic surfactant, which forms micelles in water of molar mass   ≃ 90 kDa [19]; in particular, the reference signal is taken from a  = 0.01 Triton solution at  = 20 • C.

Density
Density measurements are made in the thermal bath with a Poulten Selfe & Lee ® 541/09 hydrometer (Burnham-on-Crouch, United Kingdom), which is calibrated at T = 20 • C in the density range 1000-1050 kg/m 3 .For measures at temperatures higher than T , we recalibrated the hydrometer by measuring the density of a test waterglycerol solution, which is well characterized in terms of its density temperature dependence [20].

Dynamic viscosity
Viscosity measurements are performed with two calibrated Ubbelohde microviscometers (Xylem Analytics GmbH ® , Weilheim, Germany, filling volume 3 ml, measurement ranges 0.4-6 and 1.2-18 mm 2 /s, respectively), immersed in the Haake F3 thermostat.The dynamic viscosity at a given temperature  =  is then obtained from the measured kinematic viscosity  and density .For each temperature and polymer concentration, the measurement has been repeated three times.
For samples with a kinematic viscosity higher than 18 mm 2 /s, we resorted on a different method, already tested for polymer solutions [21].We measured the settling speed of a steel ball G100 (radius  = 250 m, density   ≃ 8 g/cm 3 ), which is related to the fluid dynamic viscosity by the Stokes' velocity   = 2(  − ) 2 ∕(9).A glass cuvette (square cross section 1 × 1 cm 2 , height 4 cm) was partially filled with the solution and put in the water thermostat, and for each temperature the probe ball was gently inserted in the solution with the help of an Eppendorf micropipette tip partially immersed in the fluid, such that the fall is ℎ = 3 cm.The settling speed   = ℎ∕ was evaluated by filming the settling bead from ℎ in a time  with an accuracy of the order of 10 ms.

Thermal properties
The thermophysical quantities of the PAGB2000 aqueous solutions, namely thermal conductivity (), thermal diffusivity () and isobaric specific heat capacity (  ), are evaluated with the Thermal Lens (TL) technique, an all-optical, fast and non-invasive method, which enables assessing the opto-thermal properties of simple and complex fluids from the temporal variation of a probing laser beam intensity that is weakly absorbed by the analyzed sample [22,23].
The TL effect is based on the partial absorption of the laser beam light: by heating up the sample locally, the consequent thermal expansion turns into a local refractive index inhomogeneity, which makes the heated region act as a lens element.In particular, neglecting the heat flow along the optical axis, the heat equation leads to a parabolic temperature profile and therefore to a negative radial refractive index distribution acting as a thin diverging lens for the propagating laser beam [24][25][26].Let us consider a sample with refractive index , absorption coefficient  and thickness  in which it is focused a Gaussian laser beam of optical power  , wavelength , beam waist (minimal beam size)  0 and Rayleigh length (distance from the waist where  = √ 2 0 )   =  0 2 ∕.Taking into account also aberrations and assuming that the sample is positioned at a distance  = √ 3  from the beam waist, the time-dependent central beam intensity variation, i.e. the TL signal, can be written as () = (0)∕(1 +  () + 1  2  () 2 ), where with the dimensionless thermal lens number  ℎ and the characteristic heat diffusion time  ℎ over the beam spot size  defined as follows Therefore, the sample thermal conductivity and diffusivity can be simultaneously extracted by fitting the measured TL signal, to get  ℎ and  ℎ [27].Once  and  are known, the isobaric specific heat capacity is immediately retrieved since   = ∕().It is worth noting that in binary mixtures and colloidal suspensions, thermo-diffusive phenomena arising from the optically-generated thermal gradient cause an additional lens effect [28,29].However, it can be unambiguously traced out since it sets up on time-scales that are related to the Brownian mass diffusivity  and therefore are much larger than  ℎ .The TL technique has been recently used also to measure the thermal expansivity in thermosensitive polymer solutions [30].
Our custom-made experimental setup is equipped with a nearinfrared laser source at  = 976 nm, which exploits a weak vibrational band of water with absorption coefficient   ≃ 0.55 cm −1 at  = 20 • C. The laser is focused by a lens of focal length  = 50 mm to a beam spot size  0 ≃ 30 μm in a cylindrical quartz sample cell (Hellma 165QS, Müllheim, Germany), of thickness  = 1 mm and internal diameter 9 mm, which has an external jacket for water circulation coming from an external water bath (Lauda Loop L100, Lauda-Königshofen, Germany, sensitivity 0.1 • C) in order to carefully control the sample temperature.The cell is mounted on a micrometric translator, allowing for the optimal positioning along the optical axis for the maximization of the TL effect (at  = √ 3  ) and is filled through capillary PTFE tubing connected to the cell stoppers.The signal is eventually detected by a fast pinhole photodiode, acquired and elaborated by a custommade software.Further details on the TL apparatus can be found in [31].The samples thermal properties have been measured up to a concentration of  = 0.8 and the measurements are repeated four times for each temperature, showing relative uncertainties on the fitting parameters not exceeding 3%.
For the evaluation of  from the thermal lens number  ℎ , the refractive index temperature derivatives are extracted from the  -dependent measurements of  performed with the refractometer.Moreover, we considered also the small absorption of the PAGB2000 detected at the probing wavelength and the full-temperature dependence of the water absorption coefficient   ( ) [32].In particular, for the pure polymer we measured with a UV-Vis-NIR spectrophotometer (JASCO Corp. V-570, Tokyo, Japan), an absorption coefficient   ≃ 0.05 cm −1 at  = 976 nm and  ≃ 25 • C. Thus, for a given temperature and concentration, the sample absorption coefficient is evaluated as (,  ) =    +   ( )(1 − ), where  = ∕  is assumed to be the polymer volume fraction at a given mass concentration , solution density  and polymer density   .

Desalination plant
The measured properties are used in a computational model [14] to simulate a desalination process via Forward Osmosis.The scheme of the plant is reported in Fig. 4 to help the reader.
The seawater enters the plant (pt.1), and after a pre-treatment goes in the FO membrane (pt.2).Within the membrane the seawater stream is split in two: a highly salt-concentrated stream, that leaves the membrane (pt.3), and a fresh water stream.The latter dilutes the concentrated polymeric draw solution, which enters the membrane (pt.19).Eventually, the diluted draw solution leaves the membrane (pt.4) and undergoes a regeneration process in which fresh water and polymeric solutions are separated.
The membrane module configuration is counter-current to maximize the permeation driving force.The membrane is oriented in the so called ''FO mode'', in which the dense active layer is faced against the feed solution [33].A regeneration temperature of 76 • C was selected, which is significantly higher than the LCST, as the higher velocity of the phase separation significantly overcomes the thermodynamic drawbacks of using higher temperature heat source.The thermodynamic conditions of the most relevant points in the FO process are reported in Appendix.
To evaluate the performances of the plant three parameters are used: • Recovery Ratio () [-]: the ratio between the freshwater flowrate extracted from the seawater (  ) and the seawater flowrate that enters the membrane (  ): • Specific Electric Consumption (  ) [kWh/m 3 ]: the ratio between the electricity consumed and the freshwater produced: • Specific Heat Consumption ( ℎ ) [kWh/m 3 ]: the ratio between the requested heat and the freshwater produced:

Experimental results
The results of the physical-chemical properties characterization are here reported in term of: • refractive index, phase behavior diagram, osmotic pressure; • density, dynamic viscosity; • thermal conductivity, thermal diffusivity, isobaric specific heat capacity.
The modeling performance is checked, with respect to the experimental values, in term of  and  defined as follows (where   is a generic quantity):

Refractive index
The characterization of this property is fundamental, as reported in Section 2, to compute all the related properties.Refractive Index is reported as a function of temperature (Fig. 3(a)) and concentration (Fig. 3(b)).
The results show that  strongly depends on the concentration, showing a monotonic increase.On the other hand the dependence on temperature is mild, reporting a slightly-monotonic decrease.

Phase diagram
As stated in Section 2.2.2 the phase behavior diagram is obtained comparing the refractive indexes of the diluted and concentrated phases with the solution one, reported in Fig. 3 The phase diagram is reported in Fig. 5 and it is compared with the one measured by Inada et al. [16].Despite the overall similarity, our result shows a minimum of the phase-separation curve around  = 0.2 that was not individuated in the previous investigation likely due to the different starting concentration of  = 0.5 from which the phase behavior was extracted, making the detection of separation at lower dilutions unfeasible.It is worth noticing that the peculiar shape of the curve may be related to the polydispersity of the polymer chains that can affect the position of the minimum of the coexistence curve, which does not necessarily coincide with the LCST [34].(10)

Osmotic pressure
The experimental campaign has been conducted to evaluate the osmotic pressure at four different temperatures and the results are reported in Fig. 6.Each experimental data series is fitted with a power-law function: where   and   depend on the temperature.Both parameters show a linear dependence on the temperature (Fig. 7(a) and (b)).Therefore: (,  ) = (118.37− 1.48 ) (0.02 +1. 32). ( The model predicts well the experimental results with a  = 0.57% and  = 9.67%.Moreover, the obtained data agree with the ones reported in [16], in which the osmotic pressure value was measured only at 25 • C. Worth of mentioning is that at the high concentrations tested ( > 0.5) the Van't Hoff equation, used for diluted solutions and commonly adopted to describe the osmotic pressure behavior, cannot be used as it tends to overestimate the osmotic pressure values (cf.black dashed lines in Fig. 6(a) and (b)).
Moreover, a lower osmotic pressure than that of the ideal mixture is expected when attraction between polymer chains occurs, which will then lead to phase separation at higher temperatures.

Density
From the experimental campaign the solution density, for each concentration, shows a linear decrease with temperature (Fig. 8(a)).As the dependence of the density on the concentration cannot be easily determined using the same plot, the experimental data are elaborated and plotted against concentration at fixed temperatures (Fig. 8(b)).The analysis shows a quadratic dependence of the density with respect to concentration: A linear dependence on the temperature is obtained (Fig. 9) for all the three parameters (i.e.,  1 ,  2 and  3 ). Therefore: The model predicts very well the experimental results with a  = −0.02%and  = 0.04%.13)).

Dynamic viscosity
The viscosity of the solution, for each concentration, is plotted against ( −1 −  −1 0 ) [K] (Fig. 10) in accordance with the Arrhenius law: where  0 is the reference temperature set as 298.15K,  0, is the viscosity value at the reference temperature,   is the activation energy in Jmol −1 ,  is the universal gas constant set as 8.314 Jmol −1 K , and the subscript  refers to each of the concentrations tested.Hence, the results are fitted with an exponential function, i.e.,  =  exp(), where  represents  0, and  represents (∕)  , respectively.The obtained coefficients plotted as a function of concentration (Fig. 11(a) and (b)).
(∕)  depends linearly on concentration, whereas  0, shows a power law function with respect to concentration: for  ≥ 0.2,  0 is the viscosity at the reference concentration, i.e.,  0 = 0.05 and  is the law exponent, equal to 2.912.
Therefore, the dependence of viscosity on both temperature and concentration (Eq.( 15)) can be made explicit: In Fig. 12 both the experimental results and the model are reported.( = −17% and  = 20%).

Thermal properties
Eventually, the thermal properties are characterized, as reported in Section 2.2.6, through Eqs. ( 4) and ( 5) to determine the thermal conductivity and diffusivity, respectively.Hence, the isobaric specific heat capacity is retrieved from: In the open literature, to the authors knowledge, very few information can be found regarding thermal properties and concentration for polymeric solutions, hence this work represents a first step towards a more complete characterization of highly concentrated polymeric solutions.

Thermal conductivity
The obtained results show a negligible dependence of the thermal conductivity on temperature within the investigated temperature range (i.e., 24 -40 • C), being the difference in thermal conductivity always lower than the measurement uncertainty.On the other hand, the thermal conductivity strongly depends on the concentration, specifically, it decreases as the polymer concentration increases, indicating the insulating nature of the chosen polymer [35] (see Fig. 13).

diffusivity
Regarding the thermal diffusivity, a behavior as the thermal conductivity found (see Fig. 14).15)).

Table 1
Comparison of performance results with other technologies [36] and [37].A quadratic dependence on concentration is found:

Isobaric specific heat capacity
Once defined ,  and , using Eq. ( 19), it is found how the specific heat capacity varies with respect to the concentration (see Fig. 15).
Specifically, a linear dependence on concentration is found:

Discussion
The properties, once experimentally determined, are inserted in the model and the same analysis reported in [14] has been performed.The results are here compared in terms of: recovery ratio, specific electric consumption and specific heat consumption.
The  (Eq.( 6)) is a key parameter to understand the quality of the desalination process through FO membranes.Being the parameter that represents the quantity of pure water that is extracted from the seawater, it is affected by the draw agent osmotic pressure, which decreases as the temperature increases (cf.Fig. 6).Hence, considering the osmotic pressure dependence on both temperature and concentration, there is a reduction of about 30% (Fig. 16).
Along with a reduction in the , we envisage an increase in the specific electric consumption (Eq.( 7)) of about 40% (Fig. 17(a)).This result is consistent with the definition reported in Eq. ( 7) being the numerator equal for the two modeled cases, whereas the denominator decreases as previously noticed.
On the other hand, a reduction of about 20% in the thermal energy (Eq.( 8)) required to warm the solution from  9 (  ) to  10 (  ) (Fig. 4) is envisaged (Fig. 17(b)).This is mainly caused by the reduction in the draw solution (  ), which decreases the water flowrate that crosses the membrane is less.
In Table 1, the key performance parameters of both models (i.e., old and new) and of other desalination technologies, already studied and analyzed in the open literature [36,37], are reported.The differences between the outputs of the two FO models show that the performances obtained with the updated properties are slightly worse, in particular with respect to the drinkable water production ().
On the other hand, comparing the FO performances with the ones of other technologies, we can state that FO is still very competitive thanks to the very limited electric consumption.
However, being the  considerably lower with respect to more affirmed technologies (i.e., RO and ED) [36,37], efforts have to be made to fill this gap, perhaps acting on the membrane surface area available to perform the process.

Conclusions
In this study, we focused on characterizing the draw agent polymeric solution, particularly examining PAGB2000 as a potential draw agent for forward osmosis (FO) in water desalination.Our analysis of the experimental results yielded the following conclusions: • The osmotic pressure exhibited a linear dependence on temperature and a power-law dependence on concentration.• The density of the polymeric mixture displayed a linear relationship with temperature and a quadratic relationship with concentration, reaching a maximum at approximately  ≈ 0.6.• The viscosity of the polymeric mixture could be accurately described by the Arrhenius law, providing reliable estimations for concentrations exceeding 0.2.• Thermal conductivity and thermal diffusivity both exhibited quadratic dependencies on concentration, with no discernible temperature dependence within the range of temperatures investigated.
These findings played a crucial role in developing a comprehensive model for simulating the entire desalination process.Our characterization of the polymer suggests that PAGB2000 holds promise as a draw agent for FO technology.Moreover, when compared to other desalination methods, FO technology employing PAGB2000 demonstrated significant advantages in terms of energy consumption, particularly with regard to electrical consumption.However, it is important to note that FO technology does suffer from a lower recovery ratio, approximately 3 to 4 times lower than well-established technologies like reverse osmosis and electrodialysis.This aspect warrants further attention and consideration in the context of FO applications.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .
Fig. 2. Picture of the preliminary phase separation experiment taken at  ≃ 40 • C. Each sample is labeled with its nominal weight percent concentration.The white arrow points to the most turbid sample that is phase-separating at  = 0.2.

Fig. 4 .
Fig. 4. Scheme of the forward osmosis plant modeled with the tested thermoresponsive copolymer as draw solute.
According to the phase diagram, suitable separation temperatures to obtain a water-rich solution with a very small amount of polymer are in the range of 70-90 • C. The experimental data are fitted as:  () = 1909.1 4− 3245.3 3 + 1902.1 2 − 428.6 + 75.1.

Fig. 16 .
Fig. 16.Parity plot representing the the variation of the Recovery Ratio between the old and new model (boundaries ±30%).

Fig. 17 .
Fig. 17.Parity plots representing the variation between the old and new model.
Thermal conductivity vs. Concentration at different temperatures.

Table A . 2
Solute mass concentration, temperature and mass flow rates using PAGB2000 assuming an initial concentration of 0.75, and seawater and draw solution flowrates of 0.20 and 0.27 kg/s (12 and 16 kg/min), respectively.Numbers refer to Fig.4.