Kinetic study of the solution polymerization of methacrylamide initiated with potassium persulfate...

Kinetic Study of the Solution Polymerization ofMethacrylamide Initiated with Potassium PersulfateUsing In Situ Raman Spectroscopy and Band-TargetEntropy Minimization

YING JIANG, MARC GARLAND, KEITH J. CARPENTER, PARAPPUVEETIL S. SURESH, EFFENDI WIDJAJA

Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833, Singapore

Received 19 December 2006; accepted 16 July 2007DOI: 10.1002/pola.22319Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: In this paper, the use of in situ Raman spectroscopy together with a novelmultivariate data analysis method, band-target entropy minimization (BTEM), is dis-cussed to monitor the solution polymerization of methacrylamide in aqueous medium.Although FTIR spectroscopy is a more popular spectroscopic technique for polymercharacterization and in situ polymerization monitoring, Raman spectroscopy isselected over FTIR in the current study. This is because water has very strong andbroad infrared absorption bands and thus masks most of the other infrared signalscontributed from monomer and polymer. On the contrary, water has very weakRaman scattering and thus it does not interfere the other Raman signals. The poly-merization was initiated with potassium persulfate (KPS). A series of experimentswere carried out varying initial monomer concentration, initial KPS concentration,and polymerization temperature. In situ Raman spectroscopy was used to monitorthe polymerizing mixture and measure the compositions. The collected reaction spec-tra were subjected to BTEM to elucidate the pure component spectra, and then deter-mine the conversion of monomer. The conversion data was then used to obtain kineticparameters for the polymerization. The rate of consumption of monomers was found tofollow the expression R ¼ keff [I]

0.55[M]1.41. The activation energy of the system was esti-mated at 121 kJ/mol. VVC 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5697–

5704, 2007

Keywords: activation energy; band-target entropy minimization (BTEM); kinetics(polym.); multivariate data analysis; Raman spectroscopy

INTRODUCTION

Raman spectroscopy has been applied as anin situ monitoring tool to a wide variety of poly-merizing systems of vinyl monomers. Most nota-bly, the kinetics of styrene polymerization has

been extensively investigated.1–4 Other systemsinvestigated include derivatives of acrylic acid,divinyl ether, and other vinyl ester monomers.3,5–7

Curing processes have also been monitored within situ Raman.8–11 Kinetic studies for persulfate-initiated solution polymerization of methacryl-amide (MA), and, more commonly, acrylamide havebeen carried out previously using dilatometricmethods,12 high performance liquid chromatogra-phy,13 and IR spectroscopy.14 While the absence ofsampling procedures renders spectroscopic tech-

Correspondence to: E. Widjaja (E-mail: [email protected])

Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 45, 5697–5704 (2007)VVC 2007 Wiley Periodicals, Inc.

5697

niques favorable for real-time analysis, the advan-tages of Raman spectroscopy over infrared (IR)spectroscopy are well known in aqueous phase ki-netic studies.1 While quantitative IR spectroscopymeasures absorbance and requires preparation ofvery thin aqueous sample layers, Raman spectros-copy, which works by a scattering process, is moreeasily amenable to the examination of bulk aque-ous samples. The aqueous medium of the polymer-ization process gives rise to little problem inRaman compared to IR spectroscopy since watergives rise to very weak Raman scattering. Theaddition of initiator, which is usually used only insmall amounts, also does not interfere with thesystem’s Raman spectra due to the low concentra-tions used. Summarized, Raman spectroscopy as anoninvasive and nondestructive tool (particularlywhen using a near-infrared source) is ideal forexamining the kinetics of a polymerizing systemin aqueous solution.

This paper extends the application of in situRaman spectroscopy to the monomer MA. It alsodevelops the method of investigating a liquidsystem in flow-through mode via spectroscopicRaman microscopy, thereby demonstrating thatit is possible to obtain reproducible data whileeliminating any contact between the analyticaltool and the polymerizing system. Furthermore,in the current study, we take advantage ofband-target entropy minimization (BTEM),15–26

one of the self-modeling curve resolution(SMCR) techniques, to de-convolute the mea-sured multi-component Raman spectra. BTEMis a novel spectral reconstruction techniquebased on information entropy27 and does notrequire any a priori chemical or spectral infor-mation what-so-ever. The main advantages ofthe BTEM technique, which make it unique anddifferent from other SMCR methods, are as fol-lows: (1) its ability to recover pure componentspectra of species at subppm levels,19 (2) its abil-ity to considerably enhance the signal to noiseratio of recovered minor compounds, (3) norequirement for any a priori estimate of thenumber of species present in a system, and (4)its goal-oriented approach, whereby the usertargets a single spectral feature of interest, andthe algorithm yields the full-range reconstructedpure spectrum associated with the targetedfeature.

So far, BTEM has been extensively applied toresolve the pure component spectra of reagents,products and transient intermediates fromin situ FTIR reaction spectra of organometallic

and homogeneous catalytic reactions17–23 and toresolve pure component spectra from solid statemixtures measured by Raman24,25 and XRD.26

Application of BTEM to in situ and/or on-lineRaman spectroscopic monitoring of reactive sys-tems are only reported for reaction of[Rh4(CO)9(l-CO)3] with 3-hexyne to form thebutterfly cluster [(l4-g

2-3-hexyne)Rh4(CO)8(l-CO)2]

28 and hydrolysis of acetic anhydride.29

Thus, the current study is the first applicationof BTEM to the kinetic investigation of solutionpolymerization. Since BTEM is able to resolvepure component spectra having a high degree ofspectral overlap (i.e., monomer and polymer), itis expected a BTEM-based multivariate analysisis considerably more accurate compared to com-monly used univariate analyses (i.e., those basedon peak height, band-integration, spectralcurve-fitting)30–33 for this type of polymerizationkinetic study.

EXPERIMENTAL

Chemicals

Methacrylamide (MA; 98%) and potassium per-sulfate (KPS; �99.0%) were purchased fromAldrich Chemicals. MA was recrystallized fromethyl acetate and dried under vacuum at roomtemperature. KPS was used without furtherpurification. Water was filtered and deionized inan AquaMAX Basic 321 water purification unit.

Polymerization

The polymerization processes were carried outin a 100-mL three-neck jacketed reactor. A peri-staltic pump (MasterFlex CL Model 77,120-70)circulated the contents of the reactor through a2 mm path-length quartz flow-through cell(Starna) fixed under the Raman microscope.Prior to the addition of monomer, 80 mL ofwater was circulated and monitored over half anhour to ensure a stable solvent background sig-nal. MA was introduced into the three-neck jack-eted reactor under stirring. The MA slowly dis-solved into the water and was warmed to thedesired reaction temperature (PolyScience pro-grammable temperature controller was used forthe jacket). The monomer solution was continu-ously purged under nitrogen for 45 min. The so-lution was further monitored for 1–2 h, to obtaina stable profile of the circulating solution,whereupon the initiator solution was injected.

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Journal of Polymer Science: Part A: Polymer ChemistryDOI 10.1002/pola

The polymerizing mixture was stirred at a con-stant rate of 600 rpm with a Micro 20 magneticstirrer and its temperature was monitored witha Fluke thermocouple. Three series of polymer-ization reactions were carried out, each seriesvarying (1) initial monomer concentration, (2)initial KPS concentration, and (3) polymeriza-tion temperature respectively.

In Situ Raman

In situ reaction monitoring was carried out witha Renishaw InVia Reflex dispersive Ramanmicroscope. Scattering was achieved with a 785nm near-IR diode laser. A 53 objective lens wasused to examine the system under study. Eachspectrum was collected over the range 540–1800cm�1, taken at the full laser power (� 100 mW),integrated for 20 s, and accumulated once. Inthe series of experiments varying initial mono-mer concentration, spectra were taken continu-ously at � 75 s intervals over 1–3 h. In the se-ries of experiments varying initial KPS concen-tration and temperature, spectra were taken at5 min intervals over 1.6 h.

Band-Target Entropy Minimization

As previously mentioned, the primary use ofBTEM is to extract the pure component spectrafrom a set of mixture spectra. Let Ik3m representthe Raman intensity in the consolidated spectro-scopic data matrix where k denotes the numberof spectra taken, and m denotes the number ofdata channels associated with the spectroscopicrange. The experimental intensities Ik3m has abilinear data structure and can be described asa product of two submatrices, namely, the con-centration matrix Ck3s and the Raman purecomponent scattering coefficient matrix Js3m

(where s denotes number of observable speciesin the chemical mixture). Accordingly, the asso-ciated error matrix ek3m contains both experi-mental error and model error (nonlinearities).34

Ik3m ¼ Ck3sJs3m þ ek3m ð1Þ

The BTEM algorithm proceeds by first decom-posing Ik3m into its singular vectors VT usingsingular value decomposition (SVD).35

Ik3m ¼ Uk3kRk3mVTm3m ð2Þ

Different from other self-modeling curve reso-lution (SMCR) methods, BTEM is uniquely

developed to resolve one pure spectrum J_

13m ata time.

J_

13m ¼ T13zVTz3m ð3Þ

The number of eigenvectors, z, taken for inclu-sion in the transformation is usually muchlarger than s due to the nonlinearities present(nonstationary spectral characteristics). Thenumber z is usually determined by identifyingthe vectors which possess localized signals ofclear physical significance and retaining these,while discarding the vectors that are more-or-less randomly distributed noise. This is then fol-lowed by the appropriate transformation of rightsingular vectors, VT

z3m , into physically meaning-ful pure component spectra.

To extract a pure J_13m, a selected band in thefirst few VT vectors is targeted. The BTEM algo-rithm then retains this feature, and at the sametime, returns an entire spectrum that has mini-mum entropy. This routine is repeated for allimportant observable physical features in theselected VT vectors. A superset of reconstructedspectra are obtained and this set is reduced toeliminate redundancies. This results in anenumeration of all observable pure componentspectra.

As mentioned, the targeted bands are re-tained during the reconstruction. As part ofthe process, the resulting pure spectral patternsare returned in a normalized form. When allnormed observable pure component spectra havebeen reconstructed, the individual relative con-centration profiles are recovered by projectingthe normed pure component spectra onto theoriginal data set. For detailed descriptionsof the BTEM algorithm, readers can refer torefs. 15–18.

RESULTS AND DISCUSSION

Data Processing

The spectra collected from the each of the threeseries of experiments were combined into onedata matrix and preprocessed with adjacentfive-point smoothing to reduce noise, and thenwith background fluorescence subtraction usinga third-order modified polynomial fitting.36 Fig-ure 1 shows a set of preprocessed spectraacquired at 25 min intervals over 150 min.

SOLUTION POLYMERIZATION OF METHACRYLAMIDE 5699


A rough estimate of the progress of polymer-ization can be obtained by monitoring thegrowth of the Raman band at 736 cm�1, whichrepresents the C��C bending mode. Ramanshifts that elucidate information on structuralchanges during polymerization are summarizedin Table 1.

Next, BTEM was used to extract Raman spec-tra for the pure components in the system—namely aqueous MA, aqueous polymethacryl-amide, and the quartz flow cell background, fromthe multi-component mixture spectra acquiredfrom in situ monitoring, such as the set inFigure 1. The band-targets used for resolvingMA, polymethacrylamide, and the quartz flowcell background in BTEM analysis were 766–770,735–739, and 790–805 cm�1 respectively. Typicalvalues of the number of right singular vectors

used were z ¼ 15. The resolved pure componentspectra are shown in Figure 2.

As seen in Figure 2, the pure Raman spec-trum of polymer has a high degrere of overlapwith the pure Raman spectrum of monomer. Assuch, univariate analysis based on the use ofthe primary bands or peaks to monitor thedynamical changes of spectral intensities wouldcertainly not be accurate. As an example, a con-centration profile of the monomer based on theRaman peak at 768 cm�1 would not be accuratesince the signal would include the contributionsfrom polymer and background signals as well.

The use of multivariate reaction spectrum fit-ting, after BTEM pure component spectral recon-struction, increases the accuracy of data analysis,since information from the whole spectral rangeis used. First, the pure component spectra ofobservable components in the reaction mixturespectra are resolved, and secondly, signal contri-butions of these observed components areobtained by solving the associated inverse prob-lem using the pure component spectral informa-tion. The quality of spectral reconstructions canbe checked by comparing the original reactionspectrum with the reconstructed spectrum (calcu-lated based on BTEM estimates). If the averagespectral difference over the entire Raman spectrais less than a few percent, it indicates thatalmost all spectra information contained in thereaction mixture spectra has been recovered.

In the current study, the contributions ofeach individual component to the total measuredspectra were back-calculated using resolvedBTEM pure component spectra of monomer, poly-mer, and background. This generated relativeconcentration profiles of each pure component,(the quartz cell background was used as the in-

Figure 1. Preprocessed Raman spectra measuredfor the polymerization of MA. [MA] ¼ 0.94 mol/L;[KPS] ¼ 2.22 mmol/L; temperature ¼ 67.5 8C.

Table 1. Raman Spectrum of Polymerization Mixture of Methacrylamide Excited at785 nm: Raman Shifts (cm�1) and Approximate Descriptions of Vibrational Modes

Wavenumber (cm�1) Band Assignment Species

736 C��C stretch Polymethacrylamide768 ¼¼CH2 wag Methacrylamide945 C��C skeletal stretch Polymethacrylamide1100 C��N stretch Both1205 ��CH2 twist and rock Polymethacrylamide1420 C¼¼C scissors deformation Methacrylamide1445 CH2��CH3 bending vibration Polymethacrylamide1606 C¼¼N stretch Both1644 C¼¼C stretch Methacrylamide1657 C¼¼O stretch (Amide I) Both

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ternal standard or reference signal). As an exam-ple, Figure 3 shows the background-normalizedconcentration profiles of MA and polymethacryla-mide taken from the set of six experiments vary-ing initial initiator concentration. The first 20Raman spectra for each experiment contain onlysignal contributions from monomer and back-

ground, since no polymerization occurred beforethe initiator solution was injected at the 21stRaman spectra. Slight fluctuations of monomerconcentration profiles over the first 20 spectramight be due to small variability in the focus ofthe Raman microscope. Figure 3 also shows thatthe consumption rate of monomer increases withincreased initiator KPS concentrations, as theslopes of monomer concentration profiles becomesteeper and higher polymer yield is achieved inthe same length of reaction time.

The fractional conversion profiles of themonomer were calculated from the background-normalized monomer concentration profiles. Fig-ures 4–6 show the conversion profiles of thethree series of experiments performed.

Rate Dependence on Monomer and InitiatorConcentration

Figures 4 and 5 shows the effect of monomerconcentration (0.41–1.76 mol/L) and initiator con-centration (0.37–3.7 mmol/L) on fractional con-versions. The results clearly indicate that therate of polymerization increases with increasingconcentration of monomer and initiator.

Effect of Temperature

Figure 6 shows the effect of temperature on therate of polymerization. The investigation wasperformed over the range of 53.5–67.5 8C at con-stant initial monomer and initiator concentra-

Figure 2. Pure component spectral estimates of thepolymerization system obtained from BTEM analysis.

Figure 3. Relative concentration profiles of monomerand polymer for six experiments with respective initialKPS concentrations of 0.37 mmol/L (Exp 1), 0.74 mmol/L (Exp 2), 1.48 mmol/L (Exp 3), 2.22 mmol/L (Exp 4),2.96 mmol/L (Exp 5), 3.76 mmol/L; initial monomer con-centration of 0.94 mol/L (Exp 6); temperature ¼ 67.5 8C.

Figure 4. Conversion profiles for various initialmonomer concentrations at circa 2.22 mmol/L KPSand 67.5 8C.



tions. Figure 6 clearly indicates that the rate ofpolymerization increases with increasing reac-tion temperature. Free radicals were producedat a faster rate due to the faster decompositionof S2O8

2� ion at higher temperatures.

Kinetic Model Fitting

In radical polymerization reactions, the empiri-cal expression for monomer consumption rate is:

R ¼ �d½M�dt

¼ keff ½I�a½M�b ð4Þ

Using the definition for the conversion of themonomer, XM ¼ ð½M�0 � ½M�Þ=½M�0, and assumingthat the initiator concentration is constant, therate in (4) could be re-expressed in terms of frac-tional conversion as the following:

R ¼ �d½XM�dt

¼ keff ½I0�a½M�b�10 ð1� ½M�Þb ð5Þ

The value of a, b, and keff were assumed to beinvariant at the same temperature over variousinitial monomer and initiator concentrations.Optimization tools such as the ODE45 functionin MATLAB 6.5 (The Mathworks, Natick, MA)and the global optimizer Corana’s simulatedannealing technique37 were used to obtain theoptimal kinetic parameters for the system. Fit-ting the rate expression in (5) to the data at67.5 8C provided optimal values a ¼ 0.554 and b¼ 1.408 with an average fitting error of 7.6% formonomer conversions up to circa 65%. Thesevalues were found to be in good agreement withtypical literature values, where a is circa 0.5and b is between 1.0 and 1.5.12–14

Next, fitting the rate expression to the thirdseries of experiments (temperature variation)yielded the values of keff at their correspondingtemperatures of polymerization. The resultingArrhenius plot (Fig. 7) displays good linearity andindicated that the activation energy of the poly-merization of MA initiated with KPS in aqueoussolution was about 121 kJ/mol. This value can becompared to the study conducted by Burfield andNg12 (77 kJ/mol), which used the dilatometricmethod to monitor the reaction rate. The reasonfor the differences in the observed activationenergies is unclear. But it can be noted that thelimiting conversion in this study (up to 65%), was

Figure 5. Conversion profiles for various initialKPS concentrations at circa 0.94 mol/L MA and67.5 8C.

Figure 6. Conversion profiles for various reactiontemperatures at circa 0.94 mol/L MA and 2.22 mmol/LKPS.

Figure 7. Arrhenius plot of ln keff versus 1/T with[MA] ¼ 0.94 mol/L, [KPS] ¼ 2.22 mmol/L.

5702 JIANG ET AL.


considerably less than the studies conducted byBurfield et al. (at least 80% conversion). Higherconversions could not be measured with the pres-ent experimental setup especially at high mono-mer concentrations due to viscosity increases,leading to increased pressure drops in the experi-mental system and leakages.

Advantages of the Proposed Method Comparedto Other Methods

The integration of in situ Raman spectroscopyand BTEM analysis is well suited for in situ mon-itoring of solution polymerization, especiallywhen water is the solvent. While Raman directlyprobes the disappearance of C¼¼C bonds and theformation of C��C bonds, it shows very weakresponse to water, which has very strong andbroad infrared signals particularly at 400–900cm�1 and 1600–1700 cm�1. Similarly, strongwater peaks are also expected from 1H NMRspectroscopy. These limitations in infrared andNMR will obscure the signals from monomer andpolymer and hinder the kinetic data analysis.Therefore, the use of in situ Raman spectroscopyfor monitoring aqueous-phase polymerization hasdistinct advantages compared to in situ FTIR orNMR spectroscopy. In addition, BTEM analysis,which is one of the most powerful multivariatedata analysis techniques, yields high quality purecomponent spectral estimates for monomer andpolymer. These spectral estimates allow accurateevaluation of the individual signal contributions,and subsequently enhanced kinetic modeling. Aspure component Raman spectra of monomer andpolymer are highly overlapping as seen in Figure2, conventional data analysis based on univariateapproaches (peak height and band-integration)will fail to obtain accurate results. Currentresults appear to suggest that the combined useof in situ Raman spectroscopy and BTEM can bean excellent future tool for aqueous-phase poly-merization reaction monitoring and kinetic inves-tigations.

The use of other types of multivariate-basedSMCR techniques to process in situ near-infra-red (NIR) spectroscopic data of curing reactionswas also recently reported.38,39 Multivariatecurve resolution/alternating least squares(MCR-ALS) was used to extract the pure compo-nent spectra and the associated concentrationprofiles for all observable species. However,although MCR-ALS has a similar purpose likeBTEM, it should be noted that this method

requires an a priori or statistical estimate of thenumber of observable species (chemical rank ofspectroscopic observations), while BTEM doesnot. In addition, BTEM has also repeatedlyshown that it could resolve the pure componentspectra of minor components having lower spec-troscopic signals. Such characteristics are alsonovel and cannot be found in other SMCR meth-ods. With this ability, it is expected that thededuction of polymerization reaction mecha-nisms based on the identification of minor tran-sient and/or intermediate components in acomplex polymerization reaction can be betterachieved if BTEM is used to process the in situspectroscopic data. The application of BTEM toinvestigate such complex polymerization reac-tion is currently underway.

CONCLUSIONS

In situ Raman spectroscopy was used to monitorthe solution polymerization of MA initiated withKPS to investigate the effects of initial mono-mer, initial KPS concentrations and polymeriza-tion temperature on the kinetics. Raman spec-troscopy appears to be an excellent analyticaltool for in situ monitoring of this polymerizationreaction. It is noninvasive and nondestructive tothe system and is able to generate reproducibleexperimental data. BTEM is a valuable model-ing tool for spectral processing. It is able to gen-erate accurate pure component spectra and con-version profiles that fit well with known kineticmodels. The reaction order with respect tomonomer concentration was 1.41 for an initialmonomer concentration between 0.71 and 1.65mol/L. The order of reaction with respect to ini-tiator concentration was 0.55 for an initial KPSconcentration between 0.37 and 3.70 mmol/L.With the optimized kinetic parameters, the rateof monomer consumption is estimated as:

R ¼ keff ½I�0:55½M�1:41

The activation energy for the polymerizationwas 121 kJ/mol.

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Kinetic study of the solution polymerization of methacrylamide initiated with potassium persulfate...

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