From batch to continuous free-radical solution polymerization of acrylic acid using a stirred tank reactor

Juri Ilare , Mattia Sponchioni *, Giuseppe Storti and Davide Moscatelli
Department of Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Via Mancinelli 7, 20131 Milano, Italy. E-mail: mattia.sponchioni@polimi.it

Received 15th June 2020 , Accepted 14th August 2020

First published on 14th August 2020


Nowadays, the majority of the world polymer production is obtained through discontinuous or semi-continuous processes. In the specific case of free-radical polymerization (FRP), discontinuous processes suffer from many limitations with respect to safety, productivity, product quality and cost. In this work, we report a model-assisted strategy for transition of the solution FRP of non-ionized acrylic acid (AA) from batch to continuous with the aim of preserving the product quality in terms of weight-average molecular weight. A basic kinetic model is developed and validated by comparison with experimental results for three reactor configurations, batch, semibatch and continuous stirred tank reactor (CSTR). Then, examples of transitioning from a semibatch to a continuous process, using a stirred tank reactor, are analysed. Taking advantage of the validated model, a successful transition is designed through an optimization procedure. Based on a minimum acceptable monomer conversion of 98%, an increase in the polymer productivity up to 88% is achieved.


1. Introduction

According to PlasticsEurope (a leading pan-European association of plastic manufacturers),1 360 million tons of polymers were produced in 2018. The possibility of finely controlling the product microstructure (i.e. molecular weight distribution (MWD), chain composition distribution (CCD), and chain architecture, as well as particle size distribution (PSD) and particle surface charge in the case of heterogeneous processes) by properly tuning the process conditions makes these materials the most appealing on the market.2–6 In fact, the polymer microstructure determines the final properties of the material, such as tensile strength, crystallinity, flexibility and conductivity. These properties are crucial for successful use of polymer materials in everyday applications like coatings,7–9 paintings,10 adhesives,11 cosmetic products,12,13,40 wastewater treatments14 and biomedical devices.15,16

Typically, industrial scale polymerization processes rely on discontinuous or semi-continuous operations.17,18 However, to face the ever-increasing polymer demand, the transition towards continuous processes is desirable and indeed considered with more and more interest by the manufacturers. In addition to higher production rate, continuous processes would also bring improvements in terms of safety, sustainability and product quality.2,19–22 Regarding safety, for example, runaway is a persistent phenomenon involved in free-radical polymerization (FRP). It is particularly dangerous in the case of discontinuous processes, because of the large monomer hold-up and the limited heat removal efficiency typical of batch reactors. On the other hand, heat management is generally easier in tubular flow reactors, mainly due to higher specific surfaces (i.e. larger surface to volume ratio).19 This is also true for continuous stirred tank reactors (CSTRs) if we consider the same daily production of an analogous discontinuous tank reactor. In fact, the well-known higher productivity of these configurations permits operation with smaller reactors, thus increasing the specific surface area for improved heat exchange and reducing their potential risk. From all these considerations, it should be clear that process intensification, achieved through the transition from discontinuous to continuous polymer manufacturing, would improve not only the process productivity but also its sustainability. This is the inspiration of the EU funded project F3 Factory, one of the most vivid examples of the urgency of the topic.23–25

FRP of acrylic acid is a very popular process, mainly because poly(acrylic acid) (PAA) finds manifold applications (wastewater treatments, thickeners, dispersants, textiles, paper industries) due to its tuneable features as MWD and degree of ionization. The relevance of the transition from discontinuous to continuous PAA production is confirmed by the extensive research effort of many authors and polymer companies.23,26–29,41 Chevrel et al.23,26,27 for example studied the continuous solution polymerization of non-ionized acrylic acid in a pilot-scale continuous tubular reactor equipped with CSE-X static mixers. First, they developed a kinetic model and used rheo-Raman technology to acquire data (i.e. kinetic parameters, molar mass distributions, viscosity variations) to validate the model. Then, given the good agreement between model predictions and experimental data, they successfully scaled-up the process from the lab- to pilot-scale. On the basis of this study, Kohlmann and collaborators28 proposed a strategy to switch from batch to continuous the production of both AA homopolymers in the presence of a chain transfer agent (CTA) and AA-based copolymers. All of the syntheses were performed in the same modular pilot plant, thus proving high process flexibility. The unique feature of this study was the “plug-and-produce” concept and, in fact, the plant was successfully moved and operated in an external site (INVITE Center, Leverkusen, Germany).

Notably, predictive and reliable models were essential to guide the transition to continuous processes in all studies mentioned above.

However, some recurrent hurdles make this transition challenging. Among them, clogging in solution FRP is the most frequent due to: i) difficult solubilisation of the polymer at high concentrations and ii) increasing solution viscosity with the reaction progress. In addition, the sticky nature of poly(acrylic acid) also favours its accumulation inside the reactor, with the formation of flow restrictions. This in turn has an impact on the average residence time as well as on the heat removal capacity of the reactor: both aspects affect the process reproducibility, thus representing an additional difficulty to the transition of the process mode in the polymer industry. Furthermore, the transition towards continuous reactors, characterized by different residence times and different fluid dynamics conditions, typically leads to polymer properties remarkably different from those obtained from traditional discontinuous processes. Therefore, polymer companies interested in such transition should put a lot of effort into modulating their processes for preserving their product portfolio. On the other hand, a model-based approach for converting a discontinuous process to a continuous one preserving key product features like the weight-average molecular weight (Mw) and the solid content would allow saving experimental effort and money and is therefore highly desirable.

In this work, the transition from discontinuous to continuous solution FRP of non-ionized acrylic acid is examined with this aim clear in mind. First, a kinetic model applicable to different reactor types, namely batch, semibatch and CSTR, and suitable to predict conversion and Mw is developed. After the experimental validation of the model, based on our own and literature experimental data,18,30 we developed an optimization procedure using rigorous model equations for transferring, using the same reactor, a semibatch process to a continuous process in the case of a CSTR. In this way, a polymer with the same quality, in terms of Mw and with the same final polymer mass concentration is obtained. Finally, the selection of the best process parameters based on a minimum acceptable monomer conversion enabled us to demonstrate the superior performance of continuous FRP compared to its semi-continuous counterpart with respect to productivity and heat management.

2. Experimental section

2.1. Materials

Acrylic acid (AA, 99%, Sigma Aldrich), ammonium persulfate (APS, 98%, Sigma Aldrich) and hydroquinone (≥99%, Sigma Aldrich) were used as received. All solvents, i.e. water and acetonitrile, were of analytical grade purity and used without further treatment.

2.2. Non-ionized acrylic acid solution polymerization

2.2.1. Batch FRP. The batch acrylic acid polymerization was run in a 100 mL septa-sealed round bottom flask equipped with a magnetic stirrer operated at a constant rate of 300 rpm. The scheme of the experimental setup is shown in Fig. S1a (see the ESI). The reaction temperature was kept constant by dipping the flask in an oil bath at 60 °C. 2.50 g (34.69 mmol) of acrylic acid were dissolved in 45 g of distilled water (i.e. 5% w/w monomer concentration), the mixture being purged for 20 minutes by bubbling nitrogen and placed in the pre-heated flask at 60 °C under magnetic stirring. When the reaction mixture reached the target temperature, 0.025 g (0.11 mmol) of APS (1% w/w based on monomer, wbm) in 2.475 g of water were fed in one shot into the flask using a syringe. The polymerization was carried out for 4 hours and samples were taken at regular time intervals. Each sample was inhibited by adding hydroquinone, then frozen in order to prevent monomer evaporation and finally analysed via thermogravimetric analysis to evaluate the monomer conversion. An aliquot was freeze-dried overnight using a Telstar Lyoquest freeze-drier and the molecular weight distribution was determined via gel permeation chromatography (GPC). The full description of the characterization techniques is reported in section 2.3.
2.2.2. Semibatch FRP. The scheme of the experimental setup is schematically shown in Fig. S1b (see the ESI). Like in batch experiments, magnetic stirring and external thermostatic bath were employed. Initially, 0.23 g (1.01 mmol) of APS and 49.77 g of distilled water were charged into a 100 mL septa-sealed round bottom flask equipped with a magnetic stirrer. The mixture was purged for 20 minutes by bubbling nitrogen and then placed in a pre-heated oil bath at 60 °C under magnetic stirring. In order to reproduce the semibatch configuration, a syringe pump (New Era Pump Systems, NE-300) was employed, filled with 10 g (138.80 mmol) of acrylic acid. The feeding time was 2 hours and the samples, after inhibition and freezing, were analysed via thermogravimetric analysis at regular times (i.e. 0, 30, 60, 90, 120, 150 minutes). The polymerization was quenched by cooling to room temperature after 2 hours and 30 minutes. Each sample was freeze-dried overnight and analysed via GPC to evaluate the molecular weight distribution. Again, the full description of the characterization techniques is reported in section 2.3.
2.2.3. CSTR. One 100 mL round bottom flask fed and discharged by peristaltic pumps (New Era Pump systems, NE-9000B) was used. This experimental set up is illustrated in Fig. S1c (see ESI). At first, the flask was filled with 50 g of water, purged with nitrogen and pre-heated to 60 °C. Sequentially, a 0.694 M monomer aqueous solution and a 0.020 M initiator aqueous solution were fed to the reactor at constant volumetric flow rate of 2.10 mL min−1. The outlet stream of the CSTR was implemented as predicted by the mathematical model to ensure a constant reaction volume. Namely, the calculated flowrate was discretized into four steps at constant value. The samples were taken from the reactor at regular time intervals and analysed via thermogravimetric analysis to evaluate the monomer conversion and via GPC to evaluate the molecular weight distribution. The reaction time was set long enough (i.e. 24 h) to establish steady state conditions.

2.3. Characterization techniques

2.3.1. Thermogravimetric analysis. Thermogravimetric analysis was applied to determine the monomer conversion. An Ohaus MB35 moisture analyser was employed as a thermobalance. 1 mL of the reaction mixture comprising acrylic acid, water, initiator and inhibitor (both negligible) and poly(acrylic acid) was weighed on an aluminium disk and heated to 145 °C to ensure the evaporation of the unreacted monomer and water. The final mass, which corresponds to the dry polymer, was then employed to evaluate the monomer conversion for the three different reactor configurations (Table 1).
Table 1 Equations used to evaluate the conversion profiles in different reactor configurations. The expressions reported are for: (1) batch, (2) semibatch, and (3) CSTR
image file: d0re00252f-t1.tif (1)
image file: d0re00252f-t2.tif (2)
image file: d0re00252f-t3.tif (3)


Here, X is the conversion, %vap(t) is the mass percentage of the sample taken at time t that vaporized during the thermogravimetric analysis, %M0 is the mass percentage of the monomer in the mixture initially charged to the batch reactor, %Mtot is the mass percentage of the fed monomer evaluated over the entire semibatch time, Qout and Qin are the overall volumetric flow rates leaving and entering the CSTR, respectively, and %Min is the percentage mass concentration of the monomer in the stream entering the tank.

2.3.2. Size exclusion chromatography (SEC). Aqueous gel permeation chromatography was carried out on a Jasco 2000 system. Polymer samples were freeze-dried and dissolved at 5 mg mL−1 in 0.05 M Na2SO4/acetonitrile 80/20 v/v solution and filtered through a 0.45 μm pore-size nylon membrane. The analyses were performed at a flow rate of 0.5 mL min−1 at 35 °C, with a guard column and three Suprema columns (Polymer Standards Service; particle size 10 μm, pore sizes of 100, 1000, and 3000 Å), poly(acrylic acid) standards (16–1100 kDa) being employed for the calibration curve.

3. Model development and parameter values

FRP of non-ionized acrylic acid in aqueous solution was simulated according to the kinetic scheme reported in Table 2. Even though the formation of mid-chain radicals has been reported for acrylic acid polymerization,17 the kinetic constant of the backbiting reaction in an aqueous environment in the considered temperature range 60–70 °C is much lower (<1%) than the propagation rate constant.17,31 Therefore, this reaction is not considered in the present work. Primary radicals R˙1, the growing species of chain length one, are produced by thermal decomposition of the initiator (I2) and very fast react with the monomer. After such initiation, active radicals (R˙n) undergo further propagation, termination and chain transfer reactions. The corresponding rate constants and reaction rates are summarized in the table. Dead polymer chains (Pn) are produced by chain transfer to monomer, termination by disproportionation and termination by combination.
Table 2 Kinetic scheme applied for the solution polymerization of non-ionized acrylic acid. Reaction steps: (4) initiation, (5) propagation, (6) termination, (7) chain transfer to monomer. Capital letters indicate molar concentrations
Chain initiation image file: d0re00252f-t4.tif r i = 2·f·kd·I (4)
Propagation image file: d0re00252f-t5.tif r p = kp·M·R (5)
Termination by disproportionation image file: d0re00252f-t6.tif r t = (ktc + ktd) R2 (6)
Termination by combination image file: d0re00252f-t7.tif
Chain transfer to monomer image file: d0re00252f-t8.tif r tr,M = ktr,M·M·R (7)


The values of the reaction rate constants mentioned in Table 2 have been obtained from the literature and are reported with the corresponding reference in Table 3. Most of these values have been measured by Buback et al. by pulsed-laser polymerization.17 Note that the dependencies of the rate constants on reaction temperature, instantaneous monomer concentration, and average chain length are accounted for. In the same table, the density of each component is also reported as a function of temperature.36

Table 3 Numerical values of model parameters and corresponding references
image file: d0re00252f-t9.tif 32
f = 0.5
image file: d0re00252f-t10.tif 17, 33
image file: d0re00252f-t11.tif 17, 34, 35
image file: d0re00252f-t12.tif
if in ≤ 30:
k t/(L mol−1 s−1) = k1,1t·in−0.6
if in > 30:
k t/(L mol−1 s−1) = k1,1t·30−0.44·in−0.16
k tc/(L mol−1 s−1) = 0.95·kt
k td/(L mol−1 s−1) = 0.05·kt
image file: d0re00252f-t13.tif 17
ρ M/(g mL−1) = 1.0731 − 1.0826 × 10−3 (T/°C) − 7.2379 × 10−7 (T/°C)2 36
ρ p/(g mL−1) = 1.7 − 6 × 10−4 (T/°C)
ρ H2O/(g mL−1) = 0.9999 + 2.3109 × 10−5 (T/ °C) − 5.44807 × 10−6 (T/ °C)2


In the table, T is the temperature, f the initiation efficiency, image file: d0re00252f-t14.tif the mass fraction of AA in solution on a polymer-free basis, k1,1t the overall rate coefficient of bimolecular termination of two radicals of chain length 1, in is the number-average chain length of the radicals, and ρM, ρp, ρH2O are the monomer, polymer and water density, respectively.

Note that the dissociation degree of the monomer and polymer should be considered for acrylic acid polymerization in aqueous solution in order to account for the impact of the solution pH on the rate constants of the different reactions, mainly propagation and termination. However, very minor variations of pH (i.e. in the range 2–3) were measured or estimated under all examined reaction conditions, corresponding to a maximum extent of monomer dissociation below 11% in the worst case (see Fig. S2). Therefore, we can safely assume rate constant values corresponding to non-ionized conditions, namely those reported in the literature mentioned in Table 3.

The simulation of the solution polymerization under examination carried out in the different reactor configurations (i.e. batch, semibatch, and CSTR) was performed by solving numerically the mass balance equations of all the involved species detailed in Table 4, eqn (8)–(13). The molecular weight distribution was calculated by solving the corresponding population balance equations for selected values of the chain length (every 10 repeating units) as well as using the method of moments to evaluate the average properties (Table 4, eqn (15) and (16)). Namely, the moments of the first three orders were considered to evaluate the number- and weight-average molecular weights as well as the dispersity.

Table 4 Mathematical model of the AA solution polymerization process. Material balances of: (8) monomer, (9) initiator, (10) radical, (11) solvent, and (12) polymer. Eqn (13) provides the overall reaction volume, (14) the first order moment of the active chain distribution, (15) is the population balance for n-long dead polymer chains, (16) are the jth-order moment equations (j = 0, 1, 2), (17) are the instantaneous chain length distributions of n-length, and (18) are the instantaneous jth-order moment equations
image file: d0re00252f-t15.tif (8)
image file: d0re00252f-t16.tif (9)
image file: d0re00252f-t17.tif (10)
image file: d0re00252f-t18.tif (11)
image file: d0re00252f-t19.tif (12)
image file: d0re00252f-t20.tif (13)
image file: d0re00252f-t21.tif (14)
image file: d0re00252f-t22.tif (15)
image file: d0re00252f-t23.tif (16)
image file: d0re00252f-t24.tif (17)
image file: d0re00252f-t25.tif (18)


In this table, V is the overall reaction volume, Qin and Q the inlet and outlet volumetric flow rates, Xin and X the inlet and outlet concentrations, and M, I, W, R, and P indicate the monomer, initiator, water, radical and dead polymer concentration, respectively. Note that the last two quantities correspond to the overall concentrations of polymer chains, regardless of their chain length. MWM is the monomer molecular weight, ρp the polymer density, ρM the monomer density. τ and β are the monomolecular and bimolecular termination parameters, defined in terms of characteristic times of the reactions as image file: d0re00252f-t26.tif and image file: d0re00252f-t27.tif, respectively. Finally, Finstn is the instantaneous chain length distribution and μinstj are the jth-order instantaneous moments.

4. Results and discussion

4.1. Model validation

Model validation was carried out first using the batch data of conversion and final Mw. The following range of experimental conditions was examined: monomer 5–21% w/w, initiator 0.2–1.2% wbm, and temperature 60–80 °C. The four batch reactions whose conditions are shown in Table 5 have been simulated: reactions 1–3 are our own experiments, while reaction 4 is from the literature.30
Table 5 Reaction conditions of the batch experiments used for preliminary model validation
Reaction Monomer [%] Initiator [% wbm] T [°C]
1 5 0.2 60
2 5 1.0 60
3 5 1.0 80
4 21 1.2 67


The predicted evolutions of monomer conversion as a function of time are compared to the experimental data in Fig. 1. Despite a small deviation in the initial reaction rates (higher monomer conversions are predicted, most likely reflecting the retardation caused by the inhibitor in the commercial monomer), the model predictions of monomer conversion are satisfactory both at low (Fig. 1a–c, reactions 1–3 in Table 5) and at high initial monomer concentrations (Fig. 1d, reaction 4 in Table 5). The polymerization rate was properly predicted also at high temperature (Fig. 1c, reaction 3 in Table 5) and different initiator concentrations (Fig. 1a, b and d, reaction 1, 2 and 4 in Table 5), thus confirming the general reliability of the model and of the selected values of the rate constants.


image file: d0re00252f-f1.tif
Fig. 1 Conversion vs. time for the FRP of non-ionized acrylic acid in a batch reactor. Curves: model predictions; symbols: experimental values. Reaction entries as in Table 5: 1 (a), 2 (b), 3 (c), and 4 (d).

The final molecular weight values are available only for our own experiments, the first three reactions in Table 5. Pure model predictions (i.e. using the parameters reported in Table 3 without any adjustment) exhibited a systematic overestimation of the experimental values of the weight-average molecular weight as measured by GPC. Given the linear behaviour of such discrepancy, the fitting was improved by adjusting the rate coefficient of a monomolecular termination mechanism, specifically the chain transfer to monomer. The final predictions, corresponding to an increase in the value of ktr,M of 3.5 times, are compared with the experimental values in Table 6.

Table 6 Experimental (Mw,exp) and predicted weight-average molecular weights (Mw,model)
Reaction M w,exp M w,model
[g mol−1]
1 6.7 × 105 5.3 × 105
2 6.4 × 105 5.1 × 105
3 3.1 × 105 4.2 × 105


The model was then further assessed by comparison with the experimental data of semibatch reactions. Namely, the literature experiments reported in Table 7 were considered, again focusing on monomer conversion and weight-average molecular weight.18 Different feeding times were inspected, namely 60, 120, and 180 minutes, while a final batch stage of 30 min (post-feeding time) was applied to maximize monomer conversion.

Table 7 Reaction conditions of the examined semibatch experiments (from Minari et al.18)
Reaction Monomer [%] Initiator [% wbm] Temperature [°C] Feeding time [min] Post-feeding time [min]
5 20 0.75 60 120 30
6 20 2.30 60 120 30
7 20 6.00 60 120 30
8 20 0.75 60 60 30
9 20 0.75 60 180 30


The results of the predictive simulations of such reactions, carried out without any further parameter adjustment, are compared with the experimental data in Fig. 2 in terms of monomer conversion. A good agreement is found in all cases.


image file: d0re00252f-f2.tif
Fig. 2 Cumulative (a) and instantaneous (b) conversion vs. time for the non-ionized acrylic acid polymerization in a semibatch reactor. The instantaneous conversion was defined as the ratio between the produced polymer at time t and the monomer cumulatively fed to the reactor up to the same time t. Experimental data by Minari et al.,18 reaction conditions in Table 7. Reaction 5: experimental (■) and model (-); reaction 6: experimental (♦) and model (-.-); reaction 7: experimental (▲) and model (…); reaction 8: experimental (●) and model (-..); reaction 9: experimental (▶) and model (--).

The cumulative monomer conversion (Fig. 2a) revealed close-to-starved conditions in all circumstances (the experimental values are always very close to those of fed amount). This situation occurs when the feed flow rate is slow enough to guarantee instantaneous monomer depletion right after entering the reactor. In this way, the accumulation of unreacted monomer becomes negligible and safe conditions with respect to thermal runaway are established.6,37,38 On the other hand, long feeding times decrease significantly the process productivity. Therefore, a trade-off between productivity and safety is operative in this reaction mode.

Focusing on molecular weight data, the experimental values reported by Minari et al.18 were estimated by GPC based on pullulan standards. Therefore, to evaluate the potential deviations of the polymer molecular weights estimated using non-PAA standards, we replicated the semibatch experiment in Table 7, reaction 6, and measured the molecular weight of the collected samples by GPC using PAA-based calibration. Negligible differences were found using the two standards (Fig. S3 in the ESI) and, therefore, we can consider the literature data as close enough to absolute molecular weights to be fairly compared to the model predictions. Using the same correction factor for ktr,M as previously applied in the batch case, the comparison between model predictions and experimental data of weight-average molecular weight is shown in Fig. 3. Given the predictive use of the model, the agreement is acceptable, with an average overestimation of about 17%.


image file: d0re00252f-f3.tif
Fig. 3 Weight-average molecular weight vs. time for the non-ionized acrylic acid polymerization in a semibatch reactor. Experimental data by Minari et al.,18 reaction conditions in Table 7. Reaction 5: experimental (■) and model (-); reaction 6: experimental (♦) and model (-.-); reaction 7: experimental (▲) and model (…); reaction 8: experimental (●) and model (-..); reaction 9: experimental (▶) and model (--).

In conclusion, at the expense of very limited parameter tuning, the developed model can reliably simulate the homogeneous polymerization of AA carried out in batch and semibatch reactors within the following range of experimental operating conditions: monomer content up to 21%, initiator 0.75–6% wbm, and temperature 60–80 °C.

4.2. Shift from a discontinuous to a continuous process

The predictive model developed and validated for batch and semibatch processes was finally adapted to the case of a single CSTR and applied to guide the transition from semibatch to continuous PAA production while ensuring the same polymer content (PC) and quality (i.e. same value of final weight-average molecular weight) of the semibatch process.

First, the model was validated in the case of the CSTR by comparison with the results of an ad hoc experiment. A reactor volume of 50 mL was considered, with an inlet monomer concentration of 5% w/w (0.694 M), and QCSTRin and ICSTRin equal to 2.10 mL min−1 and 0.02 M, respectively. Since the system was operated at a constant reaction volume, the model was first applied to predict the profile of the flow rate leaving the reactor as a function of time through the steady-state version of eqn (13). Such variable flow rate was experimentally implemented by discretization in different steps, each one at a constant flow rate, as shown in Fig. S4. The collected experimental data of monomer conversion vs. time until reaching the steady state are compared with the model predictions in Fig. 4.


image file: d0re00252f-f4.tif
Fig. 4 Conversion vs. time for the FRP of non-ionized acrylic acid in a CSTR. Model results (continuous line) are compared with experimental values (■).

The predicted conversion at steady state (84.3%) is in good agreement with the experimental data (86.7% ± 2.5% after 24 h). On the other hand, the predicted and experimental values of weight-average molecular weight again at steady state are 4.1 × 105 and 5.0 × 105 g mol−1, respectively: these values correspond to a discrepancy of about 18%, quite close to the experimental reproducibility of the GPC results, estimated as ±15%.

The good prediction of the experimental data enables the reliable use of the model to design the transition from a semibatch process to a continuous one using a single CSTR, preserving the PC and weight-average molecular weight. The procedure comprises two consecutive steps: (i) preliminary estimation of the optimal operating conditions through the model and (ii) selection of the most convenient set of operating parameters of the continuous process.

This strategy was applied to the semibatch process reported in Table 7, reaction 6, leading to a product (PC = 0.20) characterized by a weight-average molecular weight of 4.0 × 105 g mol−1 and almost 100% monomer conversion, with a productivity (mass of polymer produced per unit time and reactor volume) of 1.17 × 10−3 g mL−1 min−1. For the CSTR, we considered a reactor volume of 50 mL (the same used in the semibatch process) while evaluating the values of the inlet initiator concentration and inlet volumetric flow rate through optimization using Matlab® (lsqnonlin function). More in detail, the steady-state versions of eqn (8)–(14) and (16) in Table 4 have been applied. Considering the evaluation of the molecular weight distribution moments of the first three orders, the resulting nonlinear system is made of 10 equations with 21 unknowns. Given the absence of active species (Rin and λin1) and pre-formed polymer (Pin, μj,in) in the stream entering the reactor, the number of unknowns reduces to 15, corresponding to 5 degrees of freedom. By imposing the reactor volume to 50 mL, the PC to 0.20 (same as for the semibatch reaction) and considering different values of monomer conversion reached at steady-state (see Table S1, from which the monomer and water inlet concentrations, Min and Win, are readily evaluated), two degrees of freedom remains as optimization variables, the inlet volumetric flow rate and initiator concentration, Qin and Iin. The objective function (Φ) to be minimized was defined in order to achieve the same PC and weight-average degree of polymerization DPw of the corresponding semibatch process, that is:

 
image file: d0re00252f-t28.tif(19)
where the sub/superscript SB and CSTR indicate the semibatch and the continuous reactors. In particular, the polymer content is expressed as:
 
image file: d0re00252f-t29.tif(20)
while the DPw is evaluated according to eqn (21).
 
image file: d0re00252f-t30.tif(21)
The results of this optimization are shown in Fig. 5 in terms of conversion and inlet initiator concentration as a function of the average residence time (the specific values of Iin and Qin as well as the corresponding Min and Win are summarized in Table S1).


image file: d0re00252f-f5.tif
Fig. 5 Conversion (●) and inlet initiator concentration (★) vs. average residence time in a single CSTR. Reactor volume = 50 mL, PC = 0.20.

Reducing the inlet flow rate of the monomer, i.e. increasing the residence time, increases the conversion, as expected, while the required amount of the initiator to preserve the target weight-average molecular weight decreases. At the same time, incomplete conversion is invariably achieved, even at very large residence times: this is an intrinsic limitation of the continuous system, where huge residence time values are required when very high conversion is required. Thus, the best conditions of the CSTR have been selected by setting the minimum acceptable value of conversion. Assuming 97% of minimum monomer conversion, a residence time of about 160 minutes was found, leading to a productivity of 1.35 × 10−3 g mL−1 min−1, corresponding to an increase of more than 15% with respect to the original semibatch process when neglecting dead times (e.g., reactor charging/discharging, cleaning after every campaign). This intensification is indeed a major beneficial effect associated with the transition to the continuous process. Furthermore, the maximum rate of polymerization of the CSTR (Rmaxp = 2.01 × 10−2 mol L−1 min−1) is smaller than the one in the semibatch reactor (Rmaxp = 2.20 × 10−2 mol L−1 min−1). Therefore, a lower generation of heat is expected for the CSTR and no additional devices are required for heat removal. Accordingly, the same reactor previously applied in semibatch mode can be safely operated in continuous mode with clear savings in terms of fixed costs together with an improved productivity.

In order to propose an industrially appealing process, the same optimization procedure has been applied considering a higher solid content (PC = 0.35) and the same Mw of 4.0 × 105 g mol−1 (optimal conditions reported in Table S2). Fig. S5 shows that the molecular weight distribution of the polymer produced using the optimal CSTR process (see Table S2) is practically superimposed on that of the selected semibatch reactor (see Table 7, reaction 6). The difference with respect to the previous case in terms of conversion as a function of the residence time can be seen in Fig. 6. It is evident that a higher monomer inlet concentration is necessary to achieve the desired polymer content, thus resulting in higher polymerization rates and steady-state conversions.


image file: d0re00252f-f6.tif
Fig. 6 Conversion vs. residence time in a CSTR (reactor volume = 50 mL). Every symbol corresponds to specific values of inlet monomer, water, and initiator concentrations, and inlet volumetric flow rate which guarantee the desired polymer content (PC = 0.20: black dots, PC = 0.35: red dots) and weight-average molecular weight of 4.0 × 105 g mol−1.

In particular, it is easily verified that a final conversion of 98% is achieved in about 184 minutes. This value is still quite close to the process time of the semibatch reactor. However, with this continuous process, a larger productivity (2.20 × 10−3 g mL−1 min−1) is obtained (Fig. 7), with an increase of more than 88% with respect to the semibatch case.


image file: d0re00252f-f7.tif
Fig. 7 Productivity vs. conversion in a CSTR (reactor volume = 50 mL). Each symbol corresponds to specific values of inlet monomer, water, and initiator concentrations, and inlet volumetric flow rate which guarantee the desired polymer content (PC = 0.20: black dots, PC = 0.35: red dots) and weight-average molecular weight of 4.0 × 105 g mol−1.

Such a major increase in productivity indicates a maximum rate of polymerization larger than that in semibatch (Rmaxp = 3.30 × 10−2 mol L−1 min−1 instead of Rmaxp = 2.20 × 10−2 mol L−1 min−1 in semibatch), thus requiring additional capacity of heat removal. Depending upon the maximum capacity of heat removal of the reactor, the minimum tolerable conversion is limited accordingly. In particular, the thermal power QG associated with the different values of final conversion is easily calculated from eqn (22).

 
QG = RpVΔHp(22)
where ΔHp is the specific heat of reaction equal to 77.5 kJ mol−1.39 The evolution of QG as a function of the conversion is shown in Fig. 8 for the same conditions of PC = 0.35 shown in Fig. 7.


image file: d0re00252f-f8.tif
Fig. 8 Thermal power of the reaction vs. conversion. Same conditions as Fig. 7 at PC = 0.35.

Since the productivity increases when the monomer conversion decreases, the maximum productivity achievable in the CSTR, with the corresponding process required to obtain Mw = 4.0 × 105 g mol−1 and PC = 0.35, is selected based on the conversion corresponding to QG equal to the maximum thermal power removable by the available cooling system.

5. Conclusions

In this work, the transition from discontinuous to continuous polymer production is studied in the specific case of the solution FRP of non-ionized acrylic acid. In particular, we apply a model-assisted approach to make the production of a polymer originally produced in a starved semibatch reactor continuous using a single CSTR while preserving the weight-average molecular weight and the final polymer content.

A kinetic model was developed and validated by comparison with batch and semibatch experimental data. Literature values of all model parameters were used, with the exception of a scaling factor of 3.5 applied to the rate constant of chain transfer to monomer, ktr,M. The model reliability was finally confirmed by comparison with experimental data in a CSTR.

Then, the transition of a selected semibatch process to a CSTR process was explored. Imposing the same values of the weight-average molecular weight and final polymer content between the two processes, it was first possible to evaluate, through an optimization procedure, the required inlet flow rate and initiator concentration at a given inlet monomer concentration and reactor volume. By means of such evaluation, it was possible to design a reaction process suitable to provide the same polymer quality in a CSTR. Finally, to increase the polymer productivity the same methodology was also applied for higher polymer content. The approach was proved successful in designing new reaction conditions and, whenever possible, optimizing the conditions to intensify the production process. This transition is especially welcome in industry due to better reproducibility typically associated with continuous processes with respect to the corresponding discontinuous case.

Conflicts of interest

The authors declare no conflict of interests for this work.

Acknowledgements

Financial support from Icap Leather Chem, Lainate, is gratefully acknowledged. The authors acknowledge Matteo Gomba and Raffaele Ligrone for their assistance with the experiments.

Notes and references

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Footnote

Electronic supplementary information (ESI) available: Schematic representations of reactor configurations, monomer dissociation degree as a function of conversion, comparison between AA and pullulan based Mw taken during the reproduction of an industrially appealing semibatch experiment, discretization of the outlet flow rate for a CSTR and the optimal CSTR processes for both 20% and 35% polymer content situations, molecular weight distributions for the optimal CSTR process and the reproduced semibatch product. See DOI: 10.1039/d0re00252f

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