Continuous and direct ‘in situ’ reaction monitoring of chemical reactions via dielectric property measurement: controlled polymerisation

Abstract

This paper demonstrates that direct, “in situ” measurement of a reaction mixture using a coaxial probe technique can be used to accurately follow the progress of a chemical reaction. Such a system was shown to clearly indicate the presence/onset of and define the magnitude of key reaction parameters such as induction periods and end-points over a broad range of temperatures and viscosities. Thus it allowed the reaction to be conducted for the ideal time period, so maximising reactor through-put, energy efficiency and end product quality. Furthermore, by relating these ‘in situ’ measurements to a pre-prepared calibration curve, key experimentally achieved reaction rates could be determined. Finally, these continuously acquired, non-intrusive ‘in situ’ measurements were validated by comparison to conventional and industry accepted off-line measurement techniques.

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Introduction

In many regards the synthesis of polymers can be viewed as a mature technology, where many processes have been successfully developed to industrial scale/are currently commercially exploited.¹ However, the last 20 years have witnessed the development of novel synthetic techniques that deliver previously unprecedented levels of mechanistic control over the polymerisation chemistry and the ability to influence the molecular structures produced. Examples of such controlled polymerisation (CP) techniques are nitroxide (NMP),² copper (ATRP),³ sulfur (RAFT),^3a–c,4 cobalt (CCTP, OCRP)⁵ based systems for free radical polymerisation (FRP) and well-defined single site metal complexes,⁶ or selective enzymes for ring opening polymerisation (ROP).⁷ These strategies have allowed fine control to be exercised over the molecular architecture and/or polydispersity (Ð) of the polymers synthesized. As a result, the synthesis of linear block copolymers with very narrow Ð's,^3b,d or three dimensional polymer structures such as graft,⁸ star,⁹ hyperbranch^10,11 polymers has been reported in many academic publications and patents.^2–5,12 However, whilst CP methods have become widely practiced laboratory procedures, very few have successfully up-scaled to become a commercial reality.¹³ Key issues responsible for this are the requirement for stringent process conditions, lack of availability of the control agents and the need for accurate process monitoring to follow the reaction's progress.^13,14 Typically, failure to address these processing difficulties has resulted in a reduction in application performance sufficient to undermine the business case behind the commercialisation.

These difficulties in following the true reaction progress are evident in both laboratory and industrially applied ROP of cyclic monomers. Many of these are obtained from natural or agricultural sources, so represent a real opportunity to replace petrochemically derived polymers with more environmentally acceptable alternatives. ROP is a chain growth polymerisation, and many of the synthetic methods used to successfully achieve this exhibit pseudo living/controlled characteristics (i.e. linear growth of molecular weight with both time and conversion).¹⁵ A variety of cyclic monomers have been evaluated for ROP such as cyclic ethers,^15b,16 amides,^16b,17 lactams,^16a and esters, which include lactones,¹⁸ lactides,¹⁹ glycoglides.^15,20 Typically, these are CP systems because their mechanisms contain fast, reversible or temporary deactivation reactions as detailed by Duda et al.^15a These influence the kinetics by limiting/removing the overall potential for side reactions or termination processes in the similar way to RAFT or ATRP control in FRP.^15b,21

The dielectric properties of a particular molecular entity can be expressed in a number of ways to best rationalise/predict how it will respond to an incident electromagnetic (EM) field.²² The real part of its complex permittivity (dielectric constant, ε′) defines the extent to which it will store energy through polarisation.²³ Meanwhile, the imaginary part of complex permittivity (dielectric loss factor, ε′′) expresses its ability to dissipate this stored energy into heat.²³ A third parameter loss tangent (tan δ = ε′′/ε′) can then be defined, which indicates the potential for the material to heat under the influence of an applied electric field. Clearly, if an alternating electric field of high frequency is applied to a chemical reaction mixture, then the overall measured dielectric response will be a function of the respective dielectric properties of all the molecular species present and the interactions that occur between them.²⁴ Thus, by definition it should be possible to follow the progress of a specific chemical reaction by monitoring the dielectric changes in the medium if they are altered as a result of the target chemical reaction. There have been only been a small number of papers in which the progress of polymerisation reactions have been followed using dielectric properties across a significantly broad conversion range. Most of these studies have all involved the use of either (a) an exclusive off-line measurement of dielectric properties²⁵ and/or (b) specialised detectors which are inappropriate for use with polymerisations because they have μm gaps which can easily be blocked as the viscosity of the reaction mixture increases.²⁶ In general, direct measurement techniques have found limited application in industrial polymerisation processes due to the inherent difficulty in making measurements in systems that are typically either heterogeneous or exhibit large changes in viscosity. Some use of near infra-red techniques has been made, but many processes still rely on a strategy of sampling followed by an off-line assessment such as acid/hydroxyl value, refractive index measurement, GPC/HPLC data, etc. Furthermore, as these reported dielectric monitoring strategies typically have a requirement to introduce a sampling system and/or specific analysis loop or mesh detector, they are not suited to the constant, direct monitoring regimes required to follow a controlled polymerisation in real time. This can also be said to be true of AC impedance measurements, which would need to be made at much lower frequency to prevent radiation of EM energy. However, even at these lower frequencies, this measurement would involve a capacitor containing a small inter-plate gap being placed into the polymerisation mixture, which would result in a high potential for blockage. Typically, the small number of dielectric property studies that have involved ROP of lactones: have only focused on the monomer without considering the other precursors; have not dealt with the concentration effects of the actual reactant mixture,^26b,c and have been collected over a limited temperature range that often did not include the actual reaction temperature used. Thus, because the dielectric property data has been shown to exhibit significant, non-linear changes with temperature, this data is of little real use for trying to monitor the reaction.²² A recent study by Nakamura et al.²⁷ did investigate the change in dielectric properties during the polycondensation of lactic acid by following the dielectric properties of the individual components as a function of temperature. However, this study was limited to the individual components and it did not consider how the dielectric properties of the reaction mixture behaved with reaction time or conversion.

The aim of this study is to rigorously quantify the dielectric properties of all precursors, reactant mixtures and product polymers involved in the tin catalysed ROP of ε-caprolactone (CL) across a broad temperature range (ambient to 180 °C) at a frequency of 2.45 GHz.^18h,28 This data is used to follow the progress of this ROP using a coaxial probe.

Experimental

Materials

All materials were used as received without any further purification. The ε-caprolactone (99%) was purchased from Acros and had its water content assessed by Karl-Fisher titration (67 ppm). Tin 2-ethylhexanoate (96%) (Sn(Oct)₂) was purchased from Advocado. Anhydrous benzyl alcohol (99%) (BzOH) was purchased from Sigma-Aldrich.

Ring opening polymerisation (ROP) procedure

In the standard bulk ROP procedure, 200 g (1.75 mol) of CL was introduced into a 300 mL flask which contained an inert N₂ atmosphere. The required amounts of Sn(Oct)₂ catalyst and BzOH to achieve the target degree of polymerisation (DP) then were added via syringe to the stirring CL. For all experiments the [BzOH] : [Sn(Oct)₂] ratio was kept constant at 1 : 0.012. For example to achieve a DP of 20, Sn(Oct)₂ (17.50 mL of a 0.06 M Sn(Oct)₂/toluene solution, 1.05 mmol) and BzOH (9.07 mL, 87.57 mmol) were added via syringe and this solution was mechanically stirred until the mixture was homogeneous, and then heated to the target reaction temperature (150 °C) by being immersed in a pre-heated oil bath. The mixture was rigorously stirred throughout the reaction and small samples were removed via syringe at set times and immediately quenched by immersing the sample vial in liquid nitrogen to halt the reaction so that it remained representative of the reaction system at the time it was taken. Additionally, at this point a direct, ‘in situ’ coaxial probe measurement of the systems dielectric properties was collected. These measurements were compared to off-line analysis of the sampled material which included cavity perturbation (below), gel permeation chromatography (GPC) and nuclear magnetic resonance (NMR).

Dielectric characterization methods

(a) Off-line cavity perturbation method. The cavity perturbation method was used to both define the dielectric properties of the individual molecular species and their mixtures prior to the ‘in situ’ study and validate the ‘in situ’ data via a second independent assessment of the removed samples' dielectric properties. The system consists of a cylindrical copper cavity (diameter 570 mm height 50 mm) connected to an HP 8753B vector network analyser (VNA). A linear stage driven by a step motor and a furnace are also incorporated into the apparatus. The cavity resonates at spot frequencies, including 910 MHz and 2450 MHz, which are similar to the frequencies allocated for microwave industrial heating. Quartz tubes were used to hold the samples. A diagram of the apparatus is shown in Fig. 1.

Fig. 1 Schematic of cavity perturbation apparatus.

At the outset of each measurement the properties of the empty quartz sample holders were measured. The samples then were placed into the holders and introduced into the cavity with the use of the linear stage and during the measurements they were repeatedly moved from the furnace to the cavity and vice versa to enable measurements at high temperatures. The different values of frequency shift and quality factor between the empty and the loaded quartz sample holders were recorded, and the complex permittivity of the samples was calculated with the use of the simple perturbation equations. Further details of the experimental technique can be found in the literature.²⁹ The test compound or mixture was then introduced into the tube using a scaled syringe (10–500 mL). Typically, the sample was prepared such that the ratio between its diameter and height is ∼0.1. It was then positioned in the furnace at ambient temperature at the outset of the experiment. The dielectric properties of the sample material introduced into the tube were studied in two ways. (i) Single set temperature measurement: The prepared sample was heated directly to the reaction temperature chosen for the subsequent ROP (150 °C). Once the sample reached the target temperature, a period of 10 minutes was allowed for the material of equilibrate. It was then introduced into the resonant cavity and measurements of the frequency shift and alteration in the quality factor in the cavity upon the introduction of the sample were conducted at 2470 and 912 MHz respectively. (ii) Temperature range measurement: the temperature of the furnace was increased at a rate of 1 °C per minute. When a pre-set measurement temperature was reached, the furnace temperature was kept constant for 10 minutes to stabilise sample temperature before the dielectric measurements were taken. The dielectric properties of the samples were assessed across a range from ambient −180 °C at 10 °C intervals. In both cases, each data point represents the average of 5 measurements, and the standard deviation of these was used to estimate error. Any volume change in the sample during the temperature sweep was quantified and the data corrected. The method and equations used to calculate the permittivity, dielectric loss and dissipation factor (tan δ) are those detailed in previous publications.²²

(b) ‘In situ’ coaxial probe method. This procedure involved the use of an Agilent 8753 ES VNA (100–5000 MHz) network analyser, a flexible coaxial cable and a 7 mm coaxial probe. The probe was made of Inconel steel and was capable of operating over the temperature range of −40 to +250 °C. The probe construction took the form of a 7 mm coaxial line with an inner conductor of 3 mm diameter which terminated to a radiating annular aperture with a metallic flange. The scattering parameters of the system under test were collected via the network analyser and stored on a dedicated PC. In this technique, the coaxial probe flange was immersed into the test compound or reactant mixture and a swept frequency signal (0.1–5.0 GHz) was transmitted from the VNA into the sample via the coaxial line. As this was done, the reflection coefficient (Γ) was monitored because the amplitude and the phase of Γ are linked to the dielectric properties of the sample material. Thus the complex permittivity of the sample can be calculated by the use of a modal analysis.³⁰ A detailed description of the equipment used to conduct these dielectric measurements is discussed in previous publications.^30a Again, each data point represents the average of 5 measurements and the standard deviation was used to estimate error.

Off line molecular analysis

The samples removed from the reaction were also subjected to molecular analysis to define the molecular weight, polydispersity index value and end-group character of the product polymers.

(a) Gel permeation chromatography (GPC). PC was performed utilising a refractive index (RI) detector with HPLC THF as the eluent. Analysis was performed at 40 °C with a flow rate of 1 mL min⁻¹ through two PLgel Mixed-C columns with a calibration range of 580–377 400 Da calibrated with poly(styrene) narrow standards. All equipment and standards were supplied by Polymer Laboratories (Varian Inc). GPC data was analysed using the Cirrus GPC Off-line software package.

(b) Nuclear magnetic resonance (NMR). ¹H NMR spectra were obtained in CDCl₃ on a Bruker DPX-400 (400 MHz) spectrometer. Analysis of the data was performed using the MestRe-C software package from Mestrelab Research.

(c) Karl-Fisher titration (KFT). Water content was determined via Karl-Fisher titration (KFT).³¹ A Mitsubishi CA-100 moisture meter equipped with Aquamicron AKX solution designed for use with ketones and Aquamicron CXU catholyte was used for columbic titration of the samples to provide accurate water content analysis. Calibration was achieved using NIST traceable water standards.

Results and discussion

There have been contradictory reports in the literature on the true role of Sn(Oct)₂ in the ROP of lactones. Two mechanisms have been proposed: a direct catalytic type mechanism^19b,32 and a coordinative-insertion mechanism,^28a,d,33 with the latter mechanism favoured by most recent reports. This requires the “true catalytic” species to be formed from the coordination of the hydroxyl functional initiator and the metal centre of the pre-catalyst to form the tin dialkoxide as part of an equilibrium exchange process. As a result, the presence of an experimentally observed induction period (i.e. a period at the start of the reaction where no polymerisation is observed) has been attributed to this need to complete this process prior to polymerisation commencing.^26b,34 However, it has also been suggested that this may be due to inefficient heat transfer in conventional heating,³⁵ or the consumption of initiator molecules by free radicals.^26c,36 Post this induction period, the initiation and propagation are observed to follow a pseudo living/controlled manner because the poly(caprolactone) (PCL) chains are constantly involved in a dynamic equilibrium exchange between being activated (Sn coordinated) and deactivated (dormant hydroxyl end groups) and so irreversible termination is disfavoured.^16b However, in practice this control is achieved only until approximately 60–70% of the monomer has been consumed. This is because the tin reactive centre has also been shown to be a facile active centre for promoting trans-esterification and by-product reactions. Thus as the monomer is consumed, side reactions that result from interactions between two chains rather than between a growing chain and a monomer, become more dominant and lead to a reduction in the control over the polymerisation. This results in a broadening of the polydispersity index (Ð) and a drift away from the theoretical molecular weight (Mw).³⁷ Consequently, this proposed mechanism introduces two key challenges for larger scale manufacture of high performance PCL containing materials; (a) to define when polymerisation has commenced after the variable induction period and (b) to terminate the polymerisation before a set conversion level to retain good control over M_n/Ð or manufacture block, graft, star polymers, etc. via the accurate addition of a second monomer species. A key focus of this study was to define if direct dielectric property measurements could be used to identify these zones and the transition between them in a single step, bulk PCL ROP process.

Pre-polymerisation dielectric property assessment of individual precursors and reaction mixtures

The measured standard deviation in the repeat measurements made with the coaxial probe data was defined to be less than 4%, which confirms good measurement repeatability. Meanwhile that of the cavity perturbation method was approximately 12% for the higher loss CL reagent and is consistent with values in the literature.³⁸ In almost all cases, the error bars were found to be indistinguishable from the data points and so were not plotted. Several factors contribute to the difference in error between the two techniques. In cavity perturbation, the sample volume must be taken into account, thereby introducing errors in the measurement. The accuracy of the coaxial measurement is independent of sample volume, provided that it possesses sufficiently high dielectric loss.³⁸ Comparing the coaxial probe and cavity perturbation data showed good agreement between the results (see ESI Fig. 1†). The data for both CL and PCL over the same temperature range are shown in Fig. 2 and 3.

Fig. 2 Variation in ε′ and ε′′ of CL at 2.45 GHz over temperature range 20–180 °C via coaxial probe technique.

Fig. 3 Variation of ε′ and ε′′ of PCL DP56 at 2.45 GHz over temperature range 20–180 °C via cavity perturbation technique.

The dielectric properties of both materials were found to depend strongly upon and non-linearly with temperature. The monomer is a liquid at ambient temperature and, as expected from previous work, its dielectric loss (ε′′) was found to decrease across the temperature range measured.^6,7 With the polymer, ε′′ was observed to be very low up to 35 °C. However, at approximately 40–60 °C, it underwent a sharp increase to reach a maximum value at about 55 °C, from which it too gradually decreased until 180 °C. Meanwhile, the behaviour of ε′ for the monomer and polymer were both observed to increase steadily from ambient to 60 °C. From 60 °C to 180 °C, the ε′ value of the polymer remained relatively constant, whereas that of the monomer decreased very slightly. These trends have been attributed to the influence of a number of competing physical and chemical effects.^6,7 Below 35 °C, the polymer has a definite solid physical form and thus its dielectric relaxation characteristics are influenced by the presence of intermolecular/inter-chain interactions. Between 45 and 60 °C the material is progressing through its melting point transition (PCL m.p. = ∼55 °C and T_g = ∼−60 °C).^6,7 This results in a change in the amount/strength of the intermolecular interactions, a process that reflects a change (increase) in the interaction of the material's electronic structure with the applied electric field. Finally, between 60 °C and 180 °C, the behaviour of ε′′ has been related to the rise in sample temperature resulting in a reduction in sample viscosity/density and thus intermolecular interaction within the sample. Meanwhile, the differing trends in ε′ exhibited by the liquid and solid phases are proposed to be related to the different relaxation characteristics of the materials, where the respective relaxation times are temperature dependent, and a study of this effect will be the subject of a subsequent publication. The key observation that is central to this study is that the measured dielectric responses for the monomer and its related polymer are an order of magnitude different (i.e. a ε′ value of 25 versus 2 respectively). This difference is thought to be partially due to the reduction in the degrees of freedom that each bond/functional group within the polymer has to rotate as the chain is built, which in turn affects the overall dipolar moment of the molecule. A more detailed discussion of the molecular effects is not relevant to this publication, which is concerned with exploiting this difference, but will be included in the future publication mentioned above.

The dielectric responses of the other precursors (ESI Fig. 2†) and two polymerisation mixtures containing different Mw polymer (Fig. 4 and 5) were then evaluated via the cavity perturbation technique. This shows that (a) the dielectric properties did indeed predominantly follow the properties of the monomer and (b) the data was essentially independent of the Mw of the polymer, as the data following a PCL DP 20–monomer mixture exhibits the same trend to that of a PCL DP 200–monomer combination.

Fig. 4 Variation in ε′ of monomer and ROP polymerisation mixture at 2.47 GHz vs. temperature via coaxial probe technique.

Fig. 5 Variation in ε′′ of monomer and ROP polymerisation mixture at 2.47 GHz vs. temperature via coaxial probe technique.

As shown in a previous paper by the authors,³⁹ the major conclusion drawn from this data is that the key component that will dominate the measured dielectric properties of this specific ROP polymerisation mixture at the chosen reaction temperature will be the monomer.

Relationship between dielectric properties, monomer conversion and polymerisation control

To investigate the link between the dielectric property behaviour of a PCL reaction mixture and the progress of the polymerisation process, a series of ring opening polymerisations were conducted using the procedure detailed in the Experimental section. These reactions were designed to produce different target DPs and Table 1 contains the experimental conditions, the conversion adjusted theoretical & observed M_ns for the resultant polymers. The consistency between the calculated and observed M_n values coupled with the relatively low Ð′ of these isolated final products indicated that the quality of the reagents and rigorousness of the experimental techniques used were sufficient to ensure that the polymerisations demonstrated controlled characteristics.

Table 1 Experimental conditions of the PCL ring opening polymerisation run

PCL (DP)	Molar ratios CL : BzOH : Sn(Oct)2	Theoretical Mn at >90% conv. (g mol^−1)	Observed Mn at >90% conv. (g mol^−1)	Ð	Time to detect polymer (min)	No. of samples >90% conv.
20	20 : 1 : 0.012	2054	2071	1.48	<30	3
87	87 : 1 : 0.012	8937	8077	1.43	60	2
200	200 : 1 : 0.012	20545	18751	1.62	120	1

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Fig. 6 plots a comparison of both ε′ change and M_n build of the polymer (measure off-line by GPC) against reaction time. This clearly shows that the dielectric measurement trends are consistent with loss of monomer as it is converted into polymer.

Fig. 6 Comparison plot of ε′ and measured M_n versus time for the same ROP via coaxial probe technique.

Relationship between polymer molecular weight and dielectric response

As previously reported,³⁹ it was observed that the ε′ values decrease during the polymerisation process in all cases. The experimentally achieved M_ns for these polymers are included in Table 1 and show good agreement with the target DPs. However, whilst the monomer depletion is approximately constant at each of the sample points in Fig. 5, the actual M_n of the polymer in each of these 3 experiments at each of these conversion points is very different. Thus the dielectric measurements can be concluded to be polymer M_n independent, further supporting the proposal that the dielectric response is dominated by the monomer concentration.

Construction of a calibration curve

In order to further prove that properties of the PCL polymerisation mixture are dependent on the [PCL] : [CL] ratio and to show that this measurement can be successfully used to follow the course of such a controlled ROP reaction, a calibration curve was constructed using the method detailed in the literature.³⁹ To further evaluate the influence of the measurement temperature on the ε′ value, another identical series of pre-prepared molar mixtures of precipitated PCL (DP = 20) and Cl were prepared via the procedure described above and the dielectric properties of the mixtures were measured using the coaxial probe technique at 80, 100, 120 and 150 °C. Fig. 7 and 8 show the plots of the ε′ and ε′′ values versus molar ratio for these mixtures at different temperatures.

Fig. 7 Plot of ε′ vs. molar ratio for pre-prepared PCL/CL mixtures at different temperatures via coaxial probe technique.

Fig. 8 Plot of ε′′ vs. molar ratio for pre-prepared PCL/CL mixtures at different temperatures via coaxial probe technique.

Fig. 7 and 8 show that both the recorded ε′ and ε′′ data decrease linearly with increasing molar ratio at a given temperature. Thus, this experiment demonstrates that these plots can be used directly as calibration curves for any PCL ROP polymerisation at a single specific reaction temperature as the data has been shown to be M_n independent. As expected from the survey of the monomer's dielectric properties (Fig. 2), the ε′′ data was observed to be more temperature dependant than ε′. In fact Fig. 8 shows that ε′′ is so dependent on temperature that a new calibration curve would have to be drawn for every change in reaction temperature. However, at a specific temperature the ε′′ relationship is clearly noted to be linear across the whole temperature range, suggesting that it may in fact be possible to use this relationship to indicate the actual reaction temperature achieved for a specific reaction using a specific reactor geometry/conditions. Meanwhile, the data in Fig. 7 shows that the ε′ data is far less dependent on temperature. Furthermore, it demonstrates that above a molar ratio of 47 : 53,which is equivalent to ∼50% conversion, the ε′ values can be regarded as temperature independent across all the temperatures investigated in this study (provided that the polymer is above its melting point). This is because the variance in the gradient of the calibration curves is less that the measurement errors of the technique. The data in Fig. 2 and 3 show that whilst the ε′ value for the polymer is essentially constant from ∼75 to 180 °C, that of the monomer exhibits a significant decrease as the temperature increases from 20 °C to 180 °C. Therefore, this difference in the monomer response to the applied field results in the calibration curves for the lower temperature mixtures presenting a slightly different gradient, which in turn produces a spreading of the curves at low conversion, i.e. high monomer concentration. Closer inspection of the data reveals that at temperatures above 100 °C the gradient difference in the calibration curves had reduced and this meant that the temperature independent window of the ε′ data had been extended from the 50% conversion and above for the 80–100 °C range to approximately 25% conversion and above. This is because the monomer's ε′ reduction is at its most non-linear between 80 and 100 °C, as it is in the transition from cresting the maximum to beginning its linear decrease.

Thus, it was concluded for mixtures that are above the polymer's melting point that; (a) it has been confirmed that ε′ rather than ε′′ is the better property to use for ‘in situ’ monitoring of a broad range of temperatures on the grounds of temperature independence, (b) the size of the operational ε′ window can be related back to the original dielectric survey of the pre-cursors and (c) ε′′ also defines a linear relationship over the whole conversion range of an individual set temperature thus is as conversion sensitive as ε′, but that its greater sensitivity may make it possible to relate the ε′′ data to the actual reaction temperature achieved in a particular reaction vessel/chemical process. However, it should be noted that the measurement errors are greater in the determination of ε′′ because of the lower magnitude of the overall response. Furthermore, in this specific case where the typical reaction temperature used for a ROP reaction of CL is between 120 and 180 °C, the ‘in situ’ data from the polymerisation experiments can be regarded as being temperature independent from 25 to 100% conversion. Therefore, for reaction systems that were operating within this conversion range, it would be necessary to only develop a single correlation between the monomer conversion and ε′ value. Consequently, work is now underway to ascertain if these calibration curves and temperature window estimations can be predicted directly by predictive mathematical calculation from the original dielectric property survey of the reaction precursors, preventing the need to experimentally generate the calibration curve.

Use of ‘in situ’ dielectric measurement to define reaction rate, polymerisation induction period and polymerisation end-point

Fig. 9 plots the relationship between ε′ and polymerisation time for different target DP PCLs. It demonstrates that the ε′ values of the particular reaction mixtures are observed to decrease linearly at all tin pre-catalyst concentrations.

Fig. 9 Plot of ε′ vs. reaction time for ROP to synthesize PCL of three different DPs at 150 °C via coaxial probe technique.

However, the gradient of this linear relationship increases with the pre-catalyst concentration and could, therefore, be used to rank the polymerisation rates of these comparative reactions, defining the empirically achieved rate of reaction in the polymerisation.

In addition, information on three other features can be extracted from this data.

(a) Estimation of induction time. It is known that there is an induction time associated with this polymerisation system, believed to be related to the production of the active intermediate, tin dialkoxide. Furthermore, this lag is noted to vary depending on the target degree of polymerisation sought and this inter-relationship is thought to be the result of a concentration effect. The lower the molar levels of BzOH and Sn(Oct)₂ relative to CL required to achieve higher M_n polymer, the longer the induction period. This is because the greater dilution of the pre-cursors results in a reduced rate of catalyst formation. The time taken to detect any polymer formation in the GPC analysis of the kinetic experiments for these experiments has been included in Table 1. Fig. 9 shows that it is possible to accurately define the length of the induction period from the dielectric data collected from the ‘in situ’ coaxial probe, as the dielectric properties are essentially constant during the induction period. The point at which the dielectric response is observed to begin to decrease directly correlates with the observation of polymer generation in the GPC data of the time sampled experiments.

(b) Evaluation of apparent reaction rate (k^app) and propagation rate (k_p) for the polymerisation. The apparent rate constant for the polymerisation (k^app) can also be obtained from plotting monomer conversion variation with time. In this case a logarithmic plot of ln(1/1 − c) (where c is the decimal monomer conversion) vs time will result in a linear relationship, where the gradient will be k^app.⁴⁰ Since the ε′ value of a kinetic sample taken during the polymerisation can be taken to be a direct measurement of monomer conversion using the calibration curve, it can be used to generate ln(1/1 − c) terms to define k^app. Thus the data in Fig. 9 was cross-referenced with the calibration curve (Fig. 7) collected at the same bulk temperature (150 °C) to produce c values for each point sample, which in turn were used to generate the logarithmic plots in Fig. 10. This was done for the DP 87 and 200 samples but there was insufficient data for DP 20 due to the rapid nature of the reaction to build a meaningful data set.

Fig. 10 Plot of ln(1/1 − c) against time for the DP200 and DP87 ROP polymerisations using different Sn catalyst levels.

Fig. 10 defined that the k^app predicted from the coaxial dielectric monitoring of the polymerisation to synthesise the DP 87 polymer is 0.0089 min⁻¹, which is over twice that of the DP 200 reaction (0.0042 min⁻¹). The predicted propagation constant (k_p) can then be calculated by using the relationship k_p = k^app/[I]_o, where [I]_o is the initial concentration of initiator (DP 87 [BzOH]_o = 0.103 mol L⁻¹ and DP 200 [BzOH]_o = 0.043 mol L⁻¹). This gives a propagation rate for DP 87 of 0.086 mol⁻¹ L min⁻¹ and for DP 200 of 0.098 mol⁻¹ L min⁻¹. This data was compared and contrasted with results from an identical DP 87 polymerisation which had its conversion assessed in the conventional manner, i.e. by precipitating the polymer and taking the gravimetric yield. By this method, the predicted k^app and k_p were 0.009 mol⁻¹ and 0.092 mol⁻¹ L min⁻¹ respectively. The fact that the actual initiator corrected propagation rates of the dielectric monitoring (both DP 87 and DP 200) and the gravimetric monitoring are essentially the same supports the conclusion that this dielectric monitoring is an accurate method to determine the rate of propagation for a polymerisation.

It had been hoped to use this method of k^app assessment to determine the activation energy (E_a) of the process by plotting a graph of k^app versus 1/Temperature for a series of experiments run at different reaction temperatures. In this case the gradient of the resultant linear relationship is equivalent to E_a/R (where R is the gas constant). However, due to the fact that the ε′ and ε′′ values exhibited some degree of temperature dependence which may influence this calculation, it was concluded that fundamental reasons behind this temperature dependence would need to be further investigated before this analysis was conducted.

(c) Estimation of reaction rate and end-point.. It has been possible to use the dielectric measurement values to target a specific end-point for this reaction, which has resulted in the isolation of a better quality product. From the synthetic procedures involved in this experimental program, it was identified that control over the polymerisation was reduced above 90% conversion. This was defined by both a rise in the Ð and deviation from target M_n because trans-esterification/by-product reactions become dominant at low monomer concentrations.³⁶ This is exemplified in Table 2, which contains the GPC data for all the DP 20 experimental samples.

Table 2 Results of experiments to terminate the reaction at a given end point (target DP20)

	Time of sample (min)	ε′^a	Conv.^b (%)	Mn^c (g mol^−1)	Ð	Corrected theoretical Mn (g mol^−1)	Conversion observed Mn (g mol^−1)
a Measured using online coaxial probe at 2.45 GHz.b Determined using ^1H NMR (300 MHz, CDCl3).c Determined using GPC calibrated with polystyrene standards (580–370 000 g mol^−1).
1	0	18.59	0	200	1.1	180	200
2	30	6.74	82	1720	1.27	1880	1960
3	45	4.12	97	1880	1.47	2200	2210
4	60	3.66	98	1900	1.58	2240	2250
5	75	3.29	100	1940	1.61	2280	2260

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The end point of these reactions (i.e. targeted as 90% conversion in this case) was defined as an ε′ value of ∼7 by experimentally measuring the ε′ value of a pre-prepared solution of 10% monomer–90% polymer. A series of polymerisations targeting a product of DP 20 were then conducted, which were terminated as the dielectric response reached a value of 7 to 8, which should approximate to just under 90% conversion. For comparison, the data from a typical DP 20 polymerisation which has its end-point above 90% has been included in Table 1 as entry 1. This data was found to map well on to the experimental data from following the polymerisation in real time (Fig. 9), where the number of samples that were: (a) below a ε′ value of 7, (b) defined by NMR to have greater than 90% conversion (Table 1) and (c) noted to exhibit a deviation away from the linear propagation relationship via GPC (Fig. 9) were found to be identical. This confirms that that the dielectric data can be accurately used to achieve a particular desired molecular structure of product.

Conclusions

This study has shown that direct, non-intrusive, ‘in situ’ measurement of the dielectric properties of a reaction mixture using a coaxial probe can be accurately used follow the progress of the reaction in real time. Consequently, this data can be used to optimise the process cycle time, product quality and batch-to-batch repeatability, by identifying specific reaction features such as induction periods and end points via comparison to a calibration curve. As a direct result, energy use can be minimised, waste and purification reduced and product performance maximised by increasing the yield of target material. In the specific case of the controlled polymerisations discussed here, this equates to isolation of polymer with target Mw and low PDI.

The most appropriate dielectric property to use for this ‘in situ’ monitoring process was concluded to be the dielectric constant, ε′, because it exhibits; (a) the largest scale measurement change thus minimising error and (b) is applicable across the broadest temperature range. For these polymerisations, which are conducted above 100 °C due to the physical characteristics of the reagents, the measurements were shown to be temperature independent above 25% conversion to polymer. Thus the generation of a single calibration curve will be sufficient for all reaction conditions applied.

Additionally, by using this monitoring process it has been found possible to calculate the true experimentally achieved reaction rates, i.e. k^app and k_p, hence, application of this technique significantly reduces the barriers to the industrial operation of these controlled catalytic polymerisations mechanisms at scale.

Furthermore, this combination of capabilities also has the potential to allow successful product range extension/development of novel differentiated materials, without the need to generate novel chemistry. For example, by indicating the exact point that a second monomer should be added, block copolymers can be accurately manufactured at scale. Hence, the coaxial probe technique exhibits significant potential importance in the field of improving the efficiency of not only polymer but general chemical manufacture. It should have broad applicability to any chemical synthesis/manufacturing processes where detectable changes in dielectric properties result from conducting the desired molecular transformation.

Acknowledgements

The authors acknowledge the Ministry of Higher Education, Malaysia/Universiti Teknologi Malaysia (MJK) for their funding support.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c3ra46941g

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