A new high-throughput approach to measure copolymerization reactivity ratios using real-time FTIR...

A New High-Throughput Approach to MeasureCopolymerization Reactivity Ratios UsingReal-Time FTIR Monitoring

SOHEL SHAIKH,1 JUDIT E. PUSKAS,1 GABOR KASZAS2

1Department of Chemical and Biochemical Engineering, University of Western Ontario, London,Ontario, Canada N6A 5B9

2Rubber Division, Bayer Incorporated, 1265 Vidal St. South, Sarnia, Ontario, Canada, N7T 7M2

Received 20 October 2003; accepted 2 April 2004DOI: 10.1002/pola.20244Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: This paper presents a novel high-throughput approach to measure copoly-merization reactivity ratios from a single experiment using high-speed real-time Fou-rier transform infrared (FTIR) monitoring of the isobutylene/isoprene (IB/IP) systeminitiated by 2-chloro-2,4,4-trimethyl-pentane (TMPCl)/TiCl4 in hexane/methyl chloride(Hx/MeCl) 60:40 v/v solvent at �80 °C. Traditional polymer analysis is severely limitedin this system, which is riddled by side reactions. The reactivity ratios calculated bylinear (Mayo-Lewis and Kelen-Tudos) methods and by a nonlinear least square (NLLS)method (van Herk algorithm) showed good agreement with r1 �1.32 and r2 � 0.74calculated using Mayr’s nucleophilicity scale. Combination of the Kelen-Tudos andNLLS methods yielded r1 � 1.17 � 0.01 and r2 � 0.99 � 0.02. These values agree wellwith those reported by Thaler et al. but disagree with most reported data. © 2004 WileyPeriodicals, Inc. J Polym Sci Part A: Polym Chem 42: 4084–4100, 2004Keywords: high-throughput analysis; combinatorial approach; copolymerization re-activity ratios; real-time fiberoptic FTIR monitoring; isobutylene; isoprene; carboca-tionic polymerization

INTRODUCTION

Real-time infrared (IR) spectroscopy is becomingincreasingly popular with researchers to monitorpolymerization and associated reactions.1–11 Simi-larly to traditional polymer science, most of theresearch focuses on homopolymerization, althoughreports on in situ Fourier transform infrared (FTIR)monitoring of copolymerization reactions have alsoappeared.8–13 Copolymers are immensely impor-

tant; for instance only one-third of the estimated 10million metric tons of polystyrene produced com-mercially is used as a homopolymer; the balance isused in copolymers or blends.14 The composition ofa copolymer is defined by the ratio of reactivitybetween the comonomers. If the terminal model isassumed to be valid, the copolymerization reactivityratios in a simple binary system (monomers 1 and2) are defined as r1 � k11/k12 and r2 � k22/k21, wherek refers to rate constants of homo- and cross-prop-agation:

�� M*1 � M1O¡k11

�� M*1

This paper is dedicated to Tibor Kelen, Ferenc Tudos, andBela Turcsanyi.

Correspondence to: J. Puskas (Email: [email protected])Journal of Polymer Science: Part A: Polymer Chemistry, Vol. 42, 4084–4100 (2004)© 2004 Wiley Periodicals, Inc.

4084

�� M*1 � M2O¡k12

�� M*2

�� M*2 � M1O¡k21

�� M*1

�� M*2 � M2O¡k22

�� M*2

The availability of accurate copolymerization re-activity ratios is extremely important commer-cially. The vast majority of published reactivityratio data15 was obtained by carrying out copoly-merization experiments to low conversion withvarious feed compositions, analyzing the chemicalcomposition of the copolymers, and evaluating thedata using linear methods such as the Mayo-Lewis, Finemann-Ross, and Kelen-Tudos meth-ods.16–18 The extended Kelen-Tudos method19

was developed for high conversion data. Later,with the advent of computer technology, nonlin-ear methods of analysis were also developed; exam-ples include methods by Tidwell and Mortimer20

and Reilly and Patino-Neal.21 Simple user-friendlycomputer programs based on these methods havebeen proposed in recent years.22,23

Admittedly, there is much discrepancy andlarge errors in the reactivity ratio data reportedin the literature. In situ monitoring of copolymer-ization is expected to provide more accurate in-stantaneous monomer composition data, whichwould allow calculation of more accurate reactiv-ity ratios. The Long Laboratory has been pursu-ing this approach; Wiles et al.12 have reported onreal-time FTIR monitoring of the free-radical co-polymerization of acrylonitrile with methacrylateand calculated the reactivity ratios from low con-version data using a nonlinear method. Theyclaimed more accurate reactivity ratio valuesthan those obtained using a traditional approach.Pasquale et al.13 from the same lab outlined alinear graphical procedure to calculate reactivityratios using low conversion data obtained fromreal-time FTIR monitoring of the free-radical co-polymerization of maleic anhydride with nor-bornene. Catalgil-Giz et al.24 described an on-linetechnique for measuring the reactivity ratios infree-radical methyl methacrylate-styrene copoly-merization. The instantaneous monomer concen-trations were measured by monitoring a side

stream removed continuously from the reactor,using both refractive index (RI) and UV measure-ments.24 The reactivity ratios were calculated us-ing a nonlinear errors-in-variables method. Reac-tivity ratio calculations utilizing in situ 1H NMRhave also been reported25 for the peroxide-initi-ated copolymerization of 2-hydroxy-ethylmethac-rylate and N,N-dimethyl acrylamide with 2-acryl-amido-2-methylpropenesulfonic acid. The reactiv-ity ratios were determined by fitting a nonlinearform of the integrated copolymer equation to ex-perimental low conversion data. These reportsused real-time monitoring techniques but em-ployed well-established methods to analyze in-stantaneous composition data.

This paper reports on the development of a newconcept to measure reactivity ratios using a high-throughput approach. This new approach has el-ements of a combinatorial approach. Combinato-rial chemistry was developed for high-throughputtesting of pharmaceutical compounds.26 This verypowerful method has also been applied in thesearch for new solid-state materials having novelphysical or chemical properties27 and extended topolymer science.28 A recent patent describes afiber optic FTIR apparatus capable of rapid char-acterization of liquid samples to determine prop-erties such as particle size, particle size distribu-tion, molar mass, and molar mass distribution.29

The combinatorial concept can successfully be ap-plied to problems that require rapid scanning ofmultidimensional space to gain a better under-standing of the underlying physical and chemicalphenomena. Meredith et al.30 at NIST applied acomposition and a temperature gradient simulta-neously to a polystyrene/poly(methyl vinyl ether)(PS/PVME) blend film library deposited on a sil-icon substrate. The cloud point-lower critical so-lution temperature (LCST) curve was obtainedfrom a single experiment and agreed well withconventional light scattering measurements.

In this work, we demonstrate that reactivityratios can be obtained reliably from a singlecopolymerization experiment monitored in situby FTIR or other methods capable of generatinghigh-speed data and a large number of datapoints. Our approach is combinatorial in thesense that the disappearance of monomers (twoor more) is monitored simultaneously in time,so a single experiment is composed of a largenumber of low conversion experiments withvarying feed composition. In addition, it isshown that real-time FTIR monitoring of copo-lymerizations riddled with side reactions, in

COMBINATORIAL APPROACH TO COPOLYMERIZATION 4085

which chemical analysis of the product wouldlead to erroneous conclusions, can provide reli-able reactivity ratio data.

CONCEPT DEVELOPMENT

Background

We selected the isobutylene/isoprene (IB/IP) copoly-merization system to demonstrate the concept. Co-polymers of IB with up to 2.5 mol % IP are producedcommercially as “butyl rubber.” These are of im-mense commercial importance, primarily because oftheir superior properties such as their exceptionallylow permeability to gases and moisture and theirexcellent damping characteristics. They have beentargeted for end-use applications as diverse as innertubes, inner liners, dampeners in vibrating equip-ment, and chewing gum.31 The measurement ofreactivity ratios in systems with high IP content isdifficult because of the tendency of IP to cyclize,branch, and crosslink, leading to insoluble prod-ucts.32–40 Generally, in carbocationic polymeriza-tions the carbenium ion is prone to side reactionsbecause of its inherently reactive nature.41 Hencethe growing copolymer chain may form energeti-cally favored, more stable structures as part of the

propagation step or may undergo termination orchain transfer. For example, the tertiary alkyl �IP-IB-IB� cation can undergo an intramolecular rear-rangement via hydride transfer to produce a morestable secondary allylic cation, as illustrated in Fig-ure 1. Subsequent addition of isobutylene leads to abranched structure in which the short branch con-sists of two isobutylene units.36 In IB/IP copolymer-izations, IP reportedly dominates the chain break-ing process.32–35 IP is known to act as a strong chaintransfer agent by �-proton elimination.

Chain transfer can also occur via the formationof cyclic structures, such as the C13 and C21 oli-gomers identified in butyl polymer.37 Figure 2(a)shows the mechanism of C13 oligomer formationas proposed by Kuntz et al.37 Initiation occurs bythe protonation of an IP unit, and the addition oftwo IB units creates favorable conditions for ringformation. This sequence of events can also occurvia the participation of a �IP-IB-IBQ triad at thegrowing chain end, leading to the formation of acycle at the chain end. We believe that the mech-anism proposed for the formation of C21 is veryconvoluted,37 and here we suggest a new mecha-nism, shown in Figure 2(b). This new mechanismis a combination of two steps. The first step is thehydride transfer reaction of an IP-IB-IBQ triad,

Figure 1. Short chain branching via hydride shift in IB/IP copolymerization.

4086 SHAIKH, PUSKAS, AND KASZAS

similar to that shown in Figure 1. It is followed bythe incorporation of two isobutylene units and acyclization step, as outlined in Figure 2(a). Figure2(b) summarizes the sequence of reactions, start-

ing at the secondary allylic carbocation formedfrom the IP-IB-IBQ triad. This sequence can alsooccur with an �IB-IB-IPQ chain end, leading to acycle at the chain end and chain transfer.

Figure 2. (a, b) Chain transfer via intramolecular alkylation in IB/IP copolymeriza-tion; formation of C13 and C21 and cyclic chain ends.


At high IP concentration, intermolecular alky-lation reactions are known to take place (Fig. 3),resulting in long-chain branching and eventuallygel formation.32 Cyclization of longer polyiso-prene sequences leading to loss of unsaturation(Fig. 4) has also been reported.38,39 Thaler et al.32

have found that the amount of gelation due toalkylation was directly related to the orientationof the growing polymer chain in the solvent sys-tem used. It was suggested that a fully solvatedpolymer chain is less likely to undergo alkylation.In contrast, when the polymer chain is in a �solvent and occupies a much smaller hydrody-namic volume, chances of alkylation are greatly

increased. Keeping the polymer chain dissolvedvia the introduction of a nonpolar cosolvent (hex-ane) resulted in reduced intermolecular alkyla-tion; thus gelation was reduced or avoided. Low-conversion copolymerizations yielded gel-freehigh molecular weight IB/IP copolymers.32,35 Gel-free high-molecular-weight IB/IP copolymerswere also produced using a mixture of alkyl alu-minum chlorides as co-initiators in hexane in the�60 °C to �75 °C temperature range.49

Due to the side reactions discussed above, thecomposition range was severely constrained tolow IP content in IB/IP copolymerization studies.Table 1 lists copolymerization reactivity ratio

Figure 3. Long chain branching via intermolecular alkylation in IB/IP copolymeriza-tion.

Figure 4. Cyclization of longer PIP sequences in IB/IP copolymerization.


data published for this system (monomer 1 � IB,monomer 2 � IP). In these studies, the composi-tion of the copolymer was usually determined bynuclear magnetic resonance (NMR) spectroscopicanalysis of the product. In some studies, GC anal-ysis of the unreacted monomers was used.32,43

These data were then processed by a linearmethod. Jaack’s simplified equation,44 an inte-grated form of the Mayo-Lewis equation, was alsoused for determining the reactivity ratio for IB.43

The r1 � 1.6 value calculated by this procedurewas found to agree well with that determined by500-MHz NMR analysis and epoxy titration of theproduct. According to these data and those re-ported by other research groups, IB is more reac-tive than IP (Table 1). However, Thaler et al.’sdata suggest that with increasing solubility (de-creasing polarity), r1 decreases while r2 remainsthe same. In pure hexane they reported r1 � 0.8and r2 � 1.28. These values and those in Faust etal.38 suggest that IB is less reactive than IP. Thusliterature data for the relative reactivity of IB andIP in carbocationic polymerization are somewhatcontradictory.

Recently Mayr developed a new concept to cal-culate rate constants, using eq 1:

lg k � s�N � E� (1)

where E is the electrophilicity of the propagat-ing cation, and N and s are nucleophilicity pa-rameters for the monomers obtained experi-

mentally by measuring the rate of reaction be-tween diarylcarbenium ions and variousmonomers using UV-visible spectroscopy.50,51

The E, N, and s values for the IB/IP system areshown in Table 2. Although these values werereported for ambient temperature, their use tocalculate rate constants at low temperatures(�80 °C to �100 °C2,3) normally used for theIB/IP system is justified, as the reaction of car-bocations with alkenes was shown to have neg-ligible activation enthalpy.52 Based on the Nvalues, IB and IP occupy an intermediate posi-tion among monomers active in carbocationicpolymerization (Fig. 5). It would be expectedthat a monomer of higher nuleophilicity (i.e.,resulting in a more stable cation) would domi-nate carbocationic copolymerization.

Table 2 summarizes rate constants calculatedusing Mayr’s approach. Roth and Mayr reportedk11 � 6 � 2 �108 L mol�1 s�1, measured experi-mentally in living IB polymerization,53 whichagrees well with the calculated value. It must benoted here that this value is highly debated in theliterature.54 As seen from the data in Table 2, thereactivity ratio values of r1 �1.32 and r2 � 0.74calculated using Mayr’s approach indeed indicatethat IB will dominate in the IB/IP copolymeriza-tion system.

Against this theoretical background, an exper-imental design was developed to investigate thehighly complex IB/IP system.

Table 1. Reactivity Ratios Reported for the IB/IP Copolymerization System

Initiating System Solvent T (°C) r1 r2 Ref.

AlCl3 CH3Cl �103 2.5 � 0.5 0.4 � 0.1 [45]EtAlCl2 CH3Cl �100 2.17 0.5 [46]AlCl3 CH3Cl �90 2.3 [47]EtAlCl2 � Cl2 CH3Cl �35 2.5 [48]AlCl3 EtCl �95 2.26 0.38 [15]EtAlCl2 EtCl �90 2.27 0.44 [15]EtAlCl2 CH3Cl 88%/hexane 12% �80 2.15 1.03 [32]EtAlCl2 CH3Cl 50%/hexane 50% �80 1.9 1.05 [32]EtAlCl2 CH3Cl 12%/hexane 88% �80 1.17 1.08 [32]EtAlCl2 Hexane �80 0.8 1.28 [32]Et2AlCl � EtAlCl2/H2O Hexane �75 1.1 [49]Et2AlCl � EtAlCl2/MAO Hexane �75 1.0 [49]Et2AlCl � EtAlCl2 Hexane �75 1.54 [49]AlCl3 C5 50%/CH2Cl2 50% �70 1.56 � 0.19 0.95 � 0.17 [40, 42]AlCl3 CH3Cl �80 1.6 [43]BCl3 CH3Cl �30 2.4 � 0.35 4.5 � 3.0 [38](CH3)3Si[B(C6F5)4] Isobutylene/isoprene �20 1.8 1.5 [35]


Experimental Design

The object of this work was to develop a high-speed method to obtain reliable reactivity ratiosfrom a single experiment. We selected polymer-ization conditions under which IB exhibits aliving character, a system well investigated inthe literature.2– 4,7 Thus 2-chloro-2,4,4-trimeth-ylpentane (TMPCl), essentially a PIB-dimer,was used as the initiator, with TiCl4 as thecoinitiator in a hexane/methyl chloride (Hx/MeCl) 60:40 v/v mixed solvent in the presence of2,6-di-tertiary-butylpyridine (DtBP) as the pro-ton trap. Four different starting feed composi-tions were selected, and [TMPCl]0 and [TiCl4]0were adjusted to achieve reasonable rates. Ta-ble 3 presents the design. If we accept the mostfrequently reported r1 � 2.5 and r2 � 0.4 for theIB/IP system (see Table 1), the composition ofthe feed would change during a single copoly-merization experiment. For instance, startingan experiment with 10 mol % IP would yield afeed composition of 35 mol % IP at 90% conver-sion. Figure 6 shows the feed composition driftwith conversion, calculated by an integratedform (Skiest solution) of the copolymer equa-tion.55 Thus a single experiment would scan a

wide feed composition range. However, in orderto check the validity of the new concept, theinitial feed composition was varied between 10and 50 mol % IP. FTIR monitoring was carriedout using an attenuated total reflectance (ATR)and a transmission (TR) probe; details will begiven in the Experimental part.

EXPERIMENTAL

Materials

Methyl chloride (MeCl; 99.9%, Matheson) andisobutylene (IB; 99%, Matheson) were dried bypassing through a packed bed consisting of CaCl2/BaO. Isoprene (IP; 99%, Aldrich) was freshly dis-tilled under vacuum before use. Hexane (Hx; 99%,Caledon) was freshly distilled from CaH2 prior tobeing used. TMPCl was synthesized as reported56

and purified by vacuum distillation; 1H NMR wasused to check its purity. Titanium tetrachloride(TiCl4; 99.9%, Aldrich) and 2,6-di-tertiary-bu-tylpyridine (DtBP; 97%, Aldrich) were used asreceived.

Figure 5. Monomers ranked by Mayr’s nucleophilicity scale.

Table 2. Rate Constants and Reactivity Ratios Calculated According to Mayr’sLinear Free Energy Relationship

E

Isobutyl Cation (IB�) Isoprenyl Cation (IP�)

7.5 8.1

IB (Monomer 1) IP (Monomer 2)N 1.07 1.12s 1.02 1.00

Rate Constants, L mol�1 s�1 (calculated using Eq. 1)k11 5.51 � 108

k12 4.17 � 108

k22 1.66 � 109

k21 2.26 � 109

Reactivity Ratiosr1 (� k11/k12) 1.32r2 (� k22/k21) 0.74


Polymerization Procedure and Real-Time DataCollection

All polymerizations were conducted in an MbraunGlove box under nitrogen. The O2 (�5 ppm) andthe moisture level (5 ppm) were monitored dur-ing the reaction. The temperature of the bath wasmaintained at �80 °C. A typical experiment wasconducted as follows: a three-necked round-bot-tomed flask was charged with a solvent mixture ofHx and MeCl (Hx/MeCl � 60/40, v/v), followed bymonomers (IB and IP), initiator (TMPCl), andproton trap (DtBP). The reaction mixture wascooled to �80 °C, and a chilled stock of TiCl4 inHx (50:50 v/v) was then added to initiate thereaction. The progress of the polymerization wasmonitored by an ATR or TR probe. The probe wasimmersed in the polymerization medium and in-terfaced to a Bio-Rad FTS 175C FTIR unit byfiberoptic cables through a port in the dry box.

A schematic representation of the experimen-tal setup is shown in Figure 7. A background

spectrum (64 transients) was taken after the ini-tiator, and the solvents were added, to establish anet zero baseline. After initiation with TiCl4, aspectrum (each consisting of 32 transients) wascollected every 14 s. The spectra were then col-lated into one multifile (50–250 spectra). Datacollection was accomplished on-line by the BIO-Rad Win-IR software. In addition, in two experi-ments samples were taken at specified times forgravimetric conversion measurements, and NMRand size exclusion chromatography (SEC) analy-sis; details will be given in the text and figurecaptions. The reactions were terminated by theaddition of prechilled methanol to the reactionmixture. Final conversion was determined bygravimetry. The FTIR data were evaluated withthe GRAMS® software. A Lorentzian curve fit wasused for the spectral fit, and calibration was usedto establish proportionality between IR peak ar-eas and concentrations.

Polymer Analysis

NMR analysis was carried out in deuterated chlo-roform. Tetramethylsilane (TMS) was used as theinternal reference. Spectra were recorded on aBruker Avance 500 spectrometer. Polymer molec-ular weights were determined by SEC using aViscotek Triple Detector Model 300 systemequipped with a mixed bed column (Viscogel GMH-HRH) thermostated at 35 °C. The detectors usedwere a four-capillary differential viscometer, a rightangle laser light scattering detector, and an RI de-tector. THF, freshly distilled from CaH2, was usedas the mobile phase with a flow rate of 0.5 mL/min.

RESULTS AND DISCUSSION

Conventional Analysis of IB/IP Copolymerization

Table 4 summarizes conversion and molecularweight data for the four copolymerization experi-ments. High conversion (89–96%) was achievedin all cases, producing low-molecular-weight co-

Figure 6. Shift of monomer composition with conver-sion: mole fraction of IP (f2) versus conversion. [f2]0 �0.1, r1 � 2.5, r2 � 0.45.

Table 3. Experimental Design for IB/IP Copolymerizations

Run Probe Used [IB]0 (mol/L) [IP]0 (mol/L) IP mol % in Feed [TiCl4]0 (mol/L) [TMPCl]0 (mol/L)

1 TR 1.80 0.20 10.00 0.35 0.0352 ATR 1.78 0.45 20.25 0.69 0.0363 TR 1.45 0.55 27.50 0.35 0.0354 ATR 0.97 0.96 49.80 0.38 0.037


Figure 7. Real-time FTIR polymerization monitoring using a fiberoptic probe.

Table 4. Molecular Weight and Conversion Data with Time for Runs 1–4

Run IP mol% in Feed Time (s) Mn (g/mol) Mw (g/mol) Conversion N2 (%) Commentsa

1 10.00 90 1120 2330 11.5240 1410 3100 28.1590 1510 3790 55.6860 1680 4340 69.3 PS

1090 1750 4640 77.51410 2350 5010 85.6 PS

2 20.25 2492 5600 19,300 96.3b (95.8)c PS, bimodal3 27.50 396 1030 2700 42.0 PS

525 1280 3380 49.5 PS1230 1750 6930 79.8 PS, bimodal1880 1580 12,460 92.2 PS, bimodal

4 49.80 790 — — 89.2b (97.1)c Gel

a PS, partially soluble.b FTIR.c Gravimetry.


polymers with gel content; the experiment with49.8 mol % IP in the feed gelled up completely, somolecular weight data could not be obtained.Gravimetric conversion data compared well withFTIR measurements. Inspection of the Mn conver-sion data for runs 1 and 3 reveals nonlinearity,indicating chain transfer and nonliving condi-tions. Previous reports35,38 showed similar phe-nomena for low as well as high IP content. SEC

analysis of the soluble fractions indicated mono-modal molecular weight distribution (MWD) atlow conversion, which turned into bimodal/multi-modal with increasing conversion. Figure 8 dis-plays the MWD conversion plots. At 10 mol %initial IP content, the MWD starts from the mostprobable distribution of around 2 and increasesslightly with conversion. With 27.5 mol % initialIP concentration the MWD increase with conver-sion is nearly exponential, indicating branching.MWD increase at higher IP concentration wasobserved by other researchers as well.35,38

The 1H NMR spectrum of the IB/IP copolymerobtained with 20.25 mol % IP in the feed is shownin Figure 9. The spectrum is overly complex, andfull peak assignment proved to be impossible. Theunsaturation calculated from the area of all peaksin the olefinic region (4.5–5.5 ppm) in relation tothe aliphatic region (1–2 ppm) was found to be 7.2mol %, which is considerably lower than the 20.25mol % of IP in the feed. From the spectrum thereis ample evidence of the side reactions discussedin the introduction. At 49.5 mol % IP in the feed,the system gelled completely. Even if the finalproduct were soluble and could be analyzed usingtraditional chemical methods, potential cycliza-tion of longer polyisoprene sequences would re-sult in artificially lower IP content in the copoly-mer. It is evident from the data that the use of

Figure 8. Mw/Mn versus conversion plots for IB andIP copolymerization for runs 1 and 3.

Figure 9. 1H spectrum of the IB/IP copolymer produced in run 2 (see Table 1).


real-time FTIR monitoring for the determinationof reactivity ratios should therefore be a very aptalternative for the IB/IP system plagued by sidereactions.

FTIR Monitoring and Data Analysis

Monitoring

The waterfall plots of the copolymerizations mon-itored by ATR and TR probes are shown in Fig-

ures 10 and 11, respectively. The peak areas mon-itored with the ATR probe were the CAC stretch-ing at 1655 cm�1 for IB and the CAC stretchingat 1600 cm�1 for IP. The area under the1655cm�1 peak was shown to be proportional to IBconcentration up to 6 mol/L.2 However, the ATRprobe was found to have limited sensitivity at lowmonomer concentrations. Figure 12 shows thatbelow a critical concentration of 0.24 mol/L of IB,the scatter of the data points is too large. The

Figure 10. Real-time FTIR spectra of an IB/IP copolymerization (run 4) monitoredwith the ATR probe: [IB]0 � 0.97 mol/L, [IP]0 � 0.96 mol/L, [TMPCl]0 � 0.037 mol/L,[TiCl4]0 � 0.38 mol/L, [DtBP]0 � 0.007 mol/L, MeCl/Hx 40:60 v/v, T � �80 °C.

Figure 11. Real-time FTIR monitoring of an IB/IP copolymerization (run 3) with theTR probe: [IB]0 � 1.45 mol/L, [IP]0 � 0.55 mol/L, [TMPCl]0 0.035 mol/L, [TiCl4]0 � 0.35mol/L, [DtBP] � 0.007 mol/L, MeCl/Hx 40:60 v/v, T � �80 °C.


critical limit for IP was 0.30 mol/L. Thus datapoints obtained by ATR below these critical con-centrations were excluded from the evaluation.The TR probe is more sensitive, and in general itshowed less scatter. However, it was found inearlier studies that the CAC stretching peak ofIB was saturated beyond 0.5 mol/L when moni-tored with the TR probe. Therefore, the ACH2wagging overtone of IB (1780 cm�1) was moni-tored at the beginning of the reaction, until thisovertone disappeared, when monitoring was con-tinued following the CAC stretch. Both peaksgave identical results, as reported earlier.2,10

These results demonstrate that it is very im-portant to establish concentration ranges inwhich the FTIR signals are proportional to theconcentration of the monomer being monitored.Figure 13 shows these ranges for IP measuredwith the TR probe. In the beginning of the reac-tion theAC-H out-of-plane vibration (1815 cm�1)was monitored, followed by monitoring of theCAC stretch at 1600 cm�1. As observed in thewaterfall plots, the IB and IP peaks at 1780 cm�1

and 1815 cm�1 overlap, so these were deconvo-luted utilizing the GRAMS® software. Figure 13demonstrates that monitoring the 1815 cm�1

overtone or the 1600 cm�1CAC stretch with theTR probe in the appropriate concentration rangesgives identical results. For convenience’s sake, inthis work the overtones were used for monitoringwith the TR probe, whereas the CAC stretchsignals were monitored with the ATR probe forboth IB and IP.

Equations 2 and 3 were used to establish pro-portionality factors for the individual monomers:

C1 �A1�0

M1�0(2)

C2 �A2�0

M2�0(3)

where C1 and C2 are proportionality factors. Withthis, the instantaneous monomer concentrationat any time can be calculated from the FTIR databy eqs 4 and 5:

M1�t �A1�t

C1(4)

M2�t �A2�t

C2(5)

Figures 14 and 15 show ln([M]0/[M]t) versus timeplots for runs 3 and 4; similar plots were obtainedfor runs 1 and 2. The plots are linear; thus therate equations can be written as follows:

ln��M1�0

�M1�t� � k1appt (6)

ln��M2�0

�M2�t� � k2appt (7)

Figure 12. ln ([M]0/[M]) versus time plot for the CACstretch of IB at 1655 cm�1 monitored with the ATRprobe (run 4); the critical IB concentration is marked.

Figure 13. ln ([M]0/[M]) versus time plots for theCAC stretch (1600 cm�1) and the COH overtone (1815cm�1) of IP monitored with the TR probe (run 1).


k1app and k2app are apparent rate constants for theconsumption of IB and IP, respectively. Interest-ingly, the rate of IP consumption was not verydifferent from IB, indicating reactivity ratiosclose to 1. This is in contradiction with most of ther1 values listed in Table 1 reported for polymer-ization in polar solvents but is in good agreementwith Thaler et al.’s32 and Gronowski’s49 predic-tions for nonpolar systems. The next section willdiscuss data evaluation strategies.

Data Evaluation

Method 1: the Mayo-Lewis (M-L) Method. The dif-ferential form of the M-L equation16 was used forreactivity ratio calculations:

�dM1�t

dM2�t� �

M1�t�r1M1�t � M2�t�

M2�t�M1�t � r2M2�t�(8)

This equation is based on the simple terminalmodel, which was shown to be sufficient to de-scribe most cationic polymerization systems.57

According to the new concept, sets of data pointpairs were considered as individual low conver-sion experiments. Instantaneous differentialmonomer consumption was assumed to be equalto the instantaneous copolymer composition andwas calculated based on the linear fit of ln([M]0/[M]t) (see eqs 6 and 7). d[M1]t and d[M2]t werecalculated from FTIR data as shown by eqs 9 and10:

dM1�t � M1�t��t � M1�t (9)

dM2�t � M2�t��t � M2�t (10)

The time interval between two consecutive datapoints was 14 s in our study.

Figure 14. ln ([M]0/[M]) versus time plots for anIB/IP copolymerization monitored by the ATR probe(run 4). IB, 1655 cm�1; IP, 1600 cm�1.

Figure 15. ln ([M]0/[M] versus time plots for an IB/IPcopolymerization monitored by the TR probe (run 3).IB, 1780 cm�1 overtone; IP, 1815 cm�1 overtone.

Table 5. r1 and r2 Calculated by the M-L Copolymer Equation

Run No. IP mol% in Feed Probe r1 (SD) r2 (SD) No. of Data Points

1 10.00 TR 1.16 0.86 200(0.0004) (0.0007)

2 20.25 ATR 1.03 0.97 30(0.0008) (0.0028)

3 27.50 TR 1.17 0.85 200(0.0012) (0.0007)

4 49.80 ATR 1.08 0.93 70(0.0017) (0.0013)


The M-L equation (eq 8) was solved simulta-neously for the two unknowns r1 and r2. Table 4lists the average r1 and r2 values calculated forthe four experimental runs. Very good agreementwas found between r1 and r2 values calculatedwith various IP contents, but the TR probeyielded consistently slightly higher r1 and lowerr2. The standard deviation (SD) data reported inTable 5 show that r values are consistent over theentire conversion range. It should be noted herethat as monomer is converted into polymer, theviscosity of the reaction medium increases, andother parameters such as polarity might change.This could have an effect on the calculated r1 andr2 values. In our system such an effect was notfound. However, this method would be able toshow whether r1 and r2 changed with conversion.In the commercial production of copolymers thisinformation would be more important than lowconversion r1 and r2 data published in the litera-ture.

Method 2: the Kelen-Tudos (K-T) Method. The K-T method is also a linear method, based on theterminal model.18,19 It is insensitive to index-ation, and a symmetric distribution of data pointsmay be achieved. The K-T equation is given asfollows:

� � �r1 �r2

� � �r2

�(11)

where

� �G

� � F ; �F

� � F ; X �M1�t

M2�t;

Y �dM1�t

dM2�t; G �

X�Y � 1�

Y ; F �X2

Y (12)

and � � �(Fmin � Fmax) the minimum and maxi-mum values of F for that particular data set).Instantaneous values of � and were calculatedfrom eq 12. From the slope of the � versus plot,the reactivity ratios r1 and 2 were calculated. Theanalysis was also conducted considering all fourruns simultaneously. It can be seen from Figure16 that the � versus plot is linear, so there is nopenultimate effect and the terminal model is suf-ficient to describe the system. Table 6 summa-rizes the data. The reactivity ratios obtained fromthe slope and intercept of the combined plot (Fig.16) yielded r1 � 1.17 and r2 � 0.98, in excellentagreement with the TR data evaluated by theM-L method.

Method 3: the Nonlinear Least Square (NLLS)Method. Even though the linear methods for de-termining reactivity ratios are popular and easyto use, they have statistical limitations. If thecopolymer equation is linearized as in Methods 1and 2, the error distributions associated with thedata are misrepresented. Hence we utilized a sim-ple nonlinear least square algorithm (CON-TOUR) developed by van Herck22 Based on amethod first described by Tidwell and Mor-timer,20 it minimizes the sum of squares of thedifferences between the observed and theoretical(computed) copolymer compositions. In eq 13,[F1

th]t is the theoretical mole fraction of monomer1 in the copolymer and was calculated by thedifferential copolymer equation:

F1th�t �

r*1f1�t2 � f1�tf2�t

r*1f1�t2 � 2f1�tf2�t � r*2f2�t

2 (13)

Figure 16. Kelen-Tudos plot for runs 1, 2, 3, and 4.Fmin � 0.69, Fmax � 3.82; � � 1.63; r1 � 1.17 (IB), r2 �0.98 (IP).

Table 6. Reactivity Ratios r1 and r2 Calculated bythe K-T Method

Run Probe Used r1 r2 No. of Data Points

1 TR 1.15 0.87 2002 ATR 1.05 0.92 303 TR 1.13 0.89 2004 ATR 1.23 0.81 70

1–4 ATR/TR 1.17 0.98 500


[f1]t and [f2]t are the mole fractions of monomersM1 and M2 in the feed, and these were calculatedby eq 14 using raw FTIR data:

f1�t �M1�t

M1�t � M2�t; f2�t �

M2�t

M1�t � M2�t(14)

[F1th]t was calculated by assuming an initial guess

for r*1 and r*2. In our case r*1 � 1.17 and r*2 � 0.98obtained by the KT method were used as theinitial guess values. The experimental copolymercomposition [F1

exp]t was determined by eq 15based on instantaneous real-time FTIR data:

F1exp�t �

dM1�t

dM1�t � dM2�t(15)

The difference between the theoretical and exper-imental copolymer compositions, defined as [dF1]twas calculated by:

dF1�t � F1th�t � F1

exp�t (16)

The CONTOUR NLLS algorithm requires [f1]t,[F1

exp]t, and [dF1]t as input values. These valueswere calculated for each time interval for all 4experiments from the raw FTIR data without lin-earization and were provided as an input data fileto the program. Calculations were then carriedout to determine reactivity ratios. The algorithmutilizes a Gauss-Newton procedure for the mini-mization routine in such a way that the last iter-ation converges to the least squares estimate of r1

and r2. The output of the program is a reactivityratio plot, which also shows the 95% joint confi-dence interval. A summary of the results is shownin Table 7. The reactivity ratio plots are alsoshown for run 3 [TR probe (200 data points, Fig.17)] and for all runs combined (500 data points,Fig. 18). The reactivity ratio values obtainedwhen data from all runs were processed togetherwere r1 � 1.17 � 0.01 and r2 � 0.99 � 0.02.

These are in excellent agreement with valuesobtained from the K-T method and also from sin-gle TR measurements with 200 data points, al-though the latter had a larger 95 % joint confi-dence interval (JCI); it is evident that increasingthe number of data points drastically reduces the95% JCI. The nonlinear procedure was also re-peated with an initial guess of r*1 � 2.5 and r*2 �0.5, and it did not converge. This therefore indi-cates the importance of generating a good initialguess for the NLLS procedure. This might beconstrued as a limitation of this method. There-fore the best method seems to be data analysisbased on the combination of a linear method withthe NLLS procedure. Although the application ofthe linear method requires fitting the raw datawith a smooth curve to filter out the scatter of theFTIR data, it can provide a good initial estimate.In the NLLS method we used the raw FTIR data,

Figure 17. Reactivity ratios and JCI for the TR probewith 200 data points (run 3).

Table 7. Reactivity Ratios r1 and r2 Calculated by the NLLS Method

Run Probe Used IP mol% in Feed r1 r2 Data Points in Analysis

1 TR 10.00 1.18 � 0.05 0.97 � 0.06 2003 TR 27.50 1.16 � 0.06 0.86 � 0.36 200

1 � 3 TR 1.18 � 0.02 1.00 � 0.30 4002 ATR 20.25 1.23 � 2.96 1.29 � 10.3 304 ATR 49.80 No convergence 70

2 � 4 ATR 1.13 � 0.03 0.97 � 0.03 1001–4 ATR/TR 1.17 � 0.01 0.99 � 0.02 500


but convergence was shown to require a goodinitial estimate.

In summary, our analysis of in situ FTIR mon-itoring of IB/IP copolymerizations demonstratedthat reactivity ratios could be obtained from asingle run, provided it has a sufficiently largenumber of data points ( 200). The IB/IP systemwas found to be very close to an ideal copolymer-ization system with r1 � 1.17 � 0.01 and r2 � 0.99� 0.02 under the conditions investigated. Thiscase represented a “worst case” scenario for theproposed new method of analysis, since the feedcomposition drift was very small. Nevertheless,the method yielded consistent numbers in thewhole range. The r1 and r2 values are close tovalues reported by Thaler et al. and Gronowskifor nonpolar media, and to Mayr’s theoretical pre-diction.

CONCLUSIONS

A new concept utilizing real-time FTIR data tocalculate copolymerization reactivity ratiosfrom a single experiment has been developedand is presented in this paper. This method haselements of a combinatorial approach and al-lows a high-throughput analysis of copolymer-ization systems. It is especially applicable tocopolymerization systems plagued with side re-actions. Caution should, however, be exercisedin the proper selection of appropriate probes,characteristic FTIR peaks and concentration

ranges, and data analysis. The results pre-sented for the IB/IP copolymerization systeminitiated by TMPCl/TiCl4 indicate that this sys-tem in Hx/MeCl 60:40 v/v solvent at �80 °Cexhibits close to ideal behavior.

Financial support by the Rubber Division of Bayer, Inc.and the Natural Science and Engineering ResearchCouncil of Canada (NSERC) is greatly appreciated.Prof. A. V. van Herk’s help in providing the CONTOURalgorithm for the nonlinear least square analysis is alsogratefully acknowledged.

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